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Carabus albrechti awashimae
Carabus albrechti awashimae is a subspecies of ground beetle in the subfamily Carabinae that is endemic to Japan.
References
albrechti awashimae
Category:Beetles described in 1996
Category:Endemic fauna of Japan |
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abstract: |
The aim of this paper is to numerically solve a diffusion differential problem having time derivative of fractional order. To this end we propose a collocation-Galerkin method that uses the fractional splines as approximating functions. The main advantage is in that the derivatives of integer and fractional order of the fractional splines can be expressed in a closed form that involves just the generalized finite difference operator. This allows us to construct an accurate and efficient numerical method. Several numerical tests showing the effectiveness of the proposed method are presented.\
[**Keywords**]{}: Fractional diffusion problem, Collocation method, Galerkin method, Fractional spline
author:
- 'Laura Pezza[^1], Francesca Pitolli[^2]'
title: 'A fractional spline collocation-Galerkin method for the time-fractional diffusion equation'
---
Introduction. {#sec:intro}
=============
The use of fractional calculus to describe real-world phenomena is becoming increasingly widespread. Integro-differential equations of [*fractional*]{}, [*i.e.*]{} positive real, order are used, for instance, to model wave propagation in porous materials, diffusive phenomena in biological tissue, viscoelastic properties of continuous media [@Hi00; @Ma10; @KST06; @Ta10]. Among the various fields in which fractional models are successfully used, viscoelasticity is one of the more interesting since the memory effect introduced by the time-fractional derivative allows to model anomalous diffusion phenomena in materials that have mechanical properties in between pure elasticity and pure viscosity [@Ma10]. Even if these models are empirical, nevertheless they are shown to be consistent with experimental data.\
The increased interest in fractional models has led to the development of several numerical methods to solve fractional integro-differential equations. Many of the proposed methods generalize to the fractional case numerical methods commonly used for the classical integer case (see, for instance, [@Ba12; @PD14; @ZK14] and references therein). But the nonlocality of the fractional derivative raises the challenge of obtaining numerical solution with high accuracy at a low computational cost. In [@PP16] we proposed a collocation method especially designed for solving differential equations of fractional order in time. The key ingredient of the method is the use of the fractional splines introduced in [@UB00] as approximating functions. Thus, the method takes advantage of the explicit differentiation rule for fractional B-splines that allows us to evaluate accurately the derivatives of both integer and fractional order.\
In the present paper we used the method to solve a diffusion problem having time derivative of fractional order and show that the method is efficient and accurate. More precisely, the [*fractional spline collocation-Galerkin method*]{} here proposed combines the fractional spline collocation method introduced in [@PP16] for the time discretization and a classical spline Galerkin method in space.\
The paper is organized as follows. In Section \[sec:diffeq\], a time-fractional diffusion problem is presented and the definition of fractional derivative is given. Section \[sec:fractBspline\] is devoted to the fractional B-splines and the explicit expression of their fractional derivative is given. The fractional spline approximating space is described in Section \[sec:app\_spaces\], while the fractional spline collocation-Galerkin method is introduced in Section \[sec:Galerkin\]. Finally, in Section \[sec:numtest\] some numerical tests showing the performance of the method are displayed. Some conclusions are drawn in Section \[sec:concl\].
A time-fractional diffusion problem. {#sec:diffeq}
====================================
We consider the [*time-fractional differential diffusion problem*]{} [@Ma10] $$\label{eq:fracdiffeq}
\left \{ \begin{array}{lcc}
\displaystyle D_t^\gamma \, u(t, x) - \frac{\partial^2}{\partial x^2} \, u(t, x) = f(t, x)\,, & \quad t \in [0, T]\,, & \quad x \in [0,1] \,,\\ \\
u(0, x) = 0\,, & & \quad x \in [0,1]\,, \\ \\
u(t, 0) = u(t, 1) = 0\,, & \quad t \in [0, T]\,,
\end{array} \right.$$ where $ D_t^\gamma u$, $0 < \gamma < 1$, denotes the [*partial fractional derivative*]{} with respect to the time $t$. Usually, in viscoelasticity the fractional derivative is to be understood in the Caputo sense, [*i.e.*]{} $$\label{eq:Capfrac}
D_t^\gamma \, u(t, x) = \frac1{\Gamma(1-\gamma)} \, \int_0^t \, \frac{u_t(\tau,x)}{(t - \tau)^\gamma} \, d\tau\,, \qquad t\ge 0\,,$$ where $\Gamma$ is the Euler’s gamma function $$\Gamma(\gamma+1)= \int_0^\infty \, s^\gamma \, {\rm e}^{-s} \, ds\,.$$ We notice that due to the homogeneous initial condition for the function $u(t,x)$, solution of the differential problem (\[eq:fracdiffeq\]), the Caputo definition (\[eq:Capfrac\]) coincides with the Riemann-Liouville definition (see [@Po99] for details). One of the advantage of the Riemann-Liouville definition is in that the usual differentiation operator in the Fourier domain can be easily extended to the fractional case, [*i.e.*]{} $${\cal F} \bigl(D_t^\gamma \, f(t) \bigr) = (i\omega)^\gamma {\cal F} (f(t))\,,$$ where ${\cal F}(f)$ denotes the Fourier transform of the function $f(t)$. Thus, analytical Fourier methods usually used in the classical integer case can be extended to the fractional case [@Ma10].
The fractional B-splines and their fractional derivatives. {#sec:fractBspline}
==========================================================
The [*fractional B-splines*]{}, [*i.e.*]{} the B-splines of fractional degree, were introduced in [@UB00] generalizing to the fractional power the classical definition for the polynomial B-splines of integer degree. Thus, the fractional B-spline $B_{\alpha}$ of degree $\alpha$ is defined as $$\label{eq:Balpha}
B_{\alpha}(t) := \frac{{ \Delta}^{\alpha+1} \, t_+^\alpha} {\Gamma(\alpha+1)}\,, \qquad \alpha > -\frac 12\,,$$ where $$\label{eq:fracttruncpow}
t_+^\alpha: = \left \{ \begin{array}{ll}
t^\alpha\,, & \qquad t \ge 0\,, \\ \\
0\,, & \qquad \hbox{otherwise}\,,
\end{array} \right. \qquad \alpha > -1/2\,,$$ is the [*fractional truncated power function*]{}. $\Delta^{\alpha}$ is the [*generalized finite difference operator*]{} $$\label{eq:fracfinitediff}
\Delta^{\alpha} \, f(t) := \sum_{k\in \NN} \, (-1)^k \, {\alpha \choose k} \, f(t-\,k)\,,
\qquad \alpha \in \RR^+\,,$$ where $$\label{eq:binomfrac}
{\alpha \choose k} := \frac{\Gamma(\alpha+1)}{k!\, \Gamma(\alpha-k+1)}\,, \qquad k\in \NN\,, \quad \alpha \in \RR^+\,,$$ are the [*generalized binomial coefficients*]{}. We notice that ’fractional’ actually means ’noninteger’, [*i.e.*]{} $\alpha$ can assume any real value greater than $-1/2$. For real values of $\alpha$, $B_\alpha$ does not have compact support even if it belongs to $L_2(\RR)$. When $\alpha=n$ is a nonnegative integer, Equations (\[eq:Balpha\])-(\[eq:binomfrac\]) are still valid; $\Delta^{n}$ is the usual finite difference operator so that $B_n$ is the classical polynomial B-spline of degree $n$ and compact support $[0,n+1]$ (for details on polynomial B-splines see, for instance, the monograph [@Sc07]).
The fractional B-splines for different values of the parameter $\alpha$ are displayed in Figure \[fig:fractBsplines\] (top left panel). The classical polynomial B-splines are also displayed (dashed lines). The picture shows that the fractional B-splines decay very fast toward infinity so that they can be assumed compactly supported for computational purposes. Moreover, in contrast to the polynomial B-splines, fractional splines are not always positive even if the nonnegative part becomes more and more smaller as $\alpha$ increases.
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![Top left panel: The fractional B-splines (solid lines) and the polynomial B-splines (dashed lines) for $\alpha$ ranging from 0 to 4. Top right panel: The fractional derivatives of the linear B-spline $B_1$ for $\gamma = 0.25, 0.5, 0.75$. Bottom left panel: The fractional derivatives of the cubic B-spline $B_3$ for $\gamma$ ranging from 0.25 to 2. Bottom right panel: The fractional derivatives of the fractional B-spline $B_{3.5}$ for the $\gamma$ ranging from 0.25 to 2. Ordinary derivatives are displayed as dashed lines. []{data-label="fig:fractBsplines"}](Fig_fract_Bspline.png "fig:"){width="6cm"} ![Top left panel: The fractional B-splines (solid lines) and the polynomial B-splines (dashed lines) for $\alpha$ ranging from 0 to 4. Top right panel: The fractional derivatives of the linear B-spline $B_1$ for $\gamma = 0.25, 0.5, 0.75$. Bottom left panel: The fractional derivatives of the cubic B-spline $B_3$ for $\gamma$ ranging from 0.25 to 2. Bottom right panel: The fractional derivatives of the fractional B-spline $B_{3.5}$ for the $\gamma$ ranging from 0.25 to 2. Ordinary derivatives are displayed as dashed lines. []{data-label="fig:fractBsplines"}](Fig_fractder_Bspline_linear.png "fig:"){width="6cm"}
![Top left panel: The fractional B-splines (solid lines) and the polynomial B-splines (dashed lines) for $\alpha$ ranging from 0 to 4. Top right panel: The fractional derivatives of the linear B-spline $B_1$ for $\gamma = 0.25, 0.5, 0.75$. Bottom left panel: The fractional derivatives of the cubic B-spline $B_3$ for $\gamma$ ranging from 0.25 to 2. Bottom right panel: The fractional derivatives of the fractional B-spline $B_{3.5}$ for the $\gamma$ ranging from 0.25 to 2. Ordinary derivatives are displayed as dashed lines. []{data-label="fig:fractBsplines"}](Fig_fractder_Bspline_cubica.png "fig:"){width="6cm"} ![Top left panel: The fractional B-splines (solid lines) and the polynomial B-splines (dashed lines) for $\alpha$ ranging from 0 to 4. Top right panel: The fractional derivatives of the linear B-spline $B_1$ for $\gamma = 0.25, 0.5, 0.75$. Bottom left panel: The fractional derivatives of the cubic B-spline $B_3$ for $\gamma$ ranging from 0.25 to 2. Bottom right panel: The fractional derivatives of the fractional B-spline $B_{3.5}$ for the $\gamma$ ranging from 0.25 to 2. Ordinary derivatives are displayed as dashed lines. []{data-label="fig:fractBsplines"}](Fig_fractder_Bspline_alpha3p5.png "fig:"){width="6cm"}
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The fractional derivatives of the fractional B-splines can be evaluated explicitly by differentiating (\[eq:Balpha\]) and (\[eq:fracttruncpow\]) in the Caputo sense. This gives the following differentiation rule $$\label{eq:diffrule_tronc}
D^{\gamma}_t \, B_{\alpha} (t)= \frac{\Delta^{\alpha+1} \, t_+^{\alpha-\gamma}} {\Gamma(\alpha-\gamma+1)}\,, \qquad 0 < \gamma < \alpha + \frac12\,,$$ which holds both for fractional and integer order $\gamma$. In particular, when $\gamma, \alpha$ are nonnegative integers, (\[eq:diffrule\_tronc\]) is the usual differentiation rule for the classical polynomial B-splines [@Sc07]. We observe that since $B_\alpha$ is a causal function with $B_\alpha^{(n)}(0)=0$ for $n\in \NN\backslash\{0\}$, the Caputo fractional derivative coincides with the Riemann-Liouville fractional derivative.\
From (\[eq:diffrule\_tronc\]) and the composition property $\Delta^{\alpha_1} \, \Delta^{\alpha_2} = \Delta^{\alpha_1+\alpha_2}$ it follows [@UB00] $$\label{eq:diffrule_2}
D^{\gamma}_t \, B_{\alpha} = \Delta ^{\gamma} \, B_{\alpha-\gamma}\,,$$ [*i.e.*]{} the fractional derivative of a fractional B-spline of degree $\alpha$ is a fractional spline of degree $\alpha-\gamma$. The fractional derivatives of the classical polynomial B-splines $B_n$ are fractional splines, too. This means that $D^{\gamma}_t \, B_{n}$ is not compactly supported when $\gamma$ is noninteger reflecting the nonlocal behavior of the derivative operator of fractional order.\
In Figure \[fig:fractBsplines\] the fractional derivatives of $B_1$ (top right panel), $B_3$ (bottom left panel) and $B_{3.5}$ (bottom right panel) are displayed for different values of $\gamma$.
The fractional spline approximating spaces. {#sec:app_spaces}
===========================================
A property of the fractional B-splines that is useful for the construction of numerical methods for the solution of differential problems is the [*refinability*]{}. In fact, the fractional B-splines are [*refinable functions*]{}, [*i.e.*]{} they satisfy the [*refinement equation*]{} $$B_\alpha(t) = \sum_{k\in \NN} \, a^{(\alpha)}_{k} \, B_\alpha(2\,t-k)\,, \qquad t \ge 0\,,$$ where the coefficients $$a^{(\alpha)}_{k} := \frac{1}{2^{\alpha}} {\alpha+1 \choose k}\,,\qquad k\in \NN\,,$$ are the [*mask coefficients*]{}. This means that the sequence of nested approximating spaces $$V^{(\alpha)}_j(\RR) = {\rm span} \,\{B_\alpha(2^j\, t -k), k \in \ZZ\}\,, \qquad j \in \ZZ\,,$$ forms a [*multiresolution analysis*]{} of $L_2(\RR)$.
As a consequence, any function $f_j(t)$ belonging to $V^{(\alpha)}_j(\RR)$ can be expressed as $$f_j(t) = \sum_{k\in \ZZ}\, \lambda_{jk} \, B_\alpha(2^j\, t -k)\,,$$ where the coefficient sequence $\{\lambda_{j,k}\} \in \ell_2(\ZZ)$. Moreover, any space $V^{(\alpha)}_j(\RR)$ reproduces polynomials up to degree $\lceil \alpha\rceil$, [*i.e.*]{} $x^d \in V^{(\alpha)}_j(\RR)$, $ 0 \le d \le \lceil \alpha\rceil$, while its approximation order is $\alpha +1$. We recall that the polynomial B-spline $B_n$ reproduces polynomial up to degree $n$ whit approximation order $n+1$ [@UB00].
To solve boundary differential problems we need to construct a multiresolution analysis on a finite interval. For the sake of simplicity in the following we will consider the interval $I=[0,1]$. A simple approach is to restrict the basis $\{B_\alpha(2^j\, t -k)\}$ to the interval $I$, [*i.e.*]{} $$\label{eq:Vj_int}
V^{(\alpha)}_j(I) = {\rm span} \,\{B_\alpha(2^j\, t -k), t\in I, -N \le k \le 2^j-1\}\,, \qquad j_0 \le j\,,$$ where $N$ is a suitable index, chosen in order the significant part of $B_\alpha$ is contained in $[0,N+1]$, and $j_0$ is the starting refinement level. The drawback of this approach is its numerical instability and the difficulty in fulfilling the boundary conditions since there are $2N$ boundary functions, [*i.e.*]{} the translates of $B_\alpha$ having indexes $ -N\le k \le -1$ and $2^j-N\le k \le 2^j-1$, that are non zero at the boundaries. More suitable refinable bases can be obtained by the procedure given in [@GPP04; @GP04]. In particular, for the polynomial B-spline $B_n$ a B-basis $\{\phi_{\alpha,j,k}(t)\}$ with optimal approximation properties can be constructed. The internal functions $\phi_{\alpha,j,k}(t)=B_\alpha(2^j\, t -k)$, $0 \le k \le 2^j-1-n$, remain unchanged while the $2n$ boundary functions fulfill the boundary conditions $$\begin{array}{llcc}
\phi_{\alpha,j,-1}^{(\nu)}(0) = 1\,, & \phi_{\alpha,j,k}^{(\nu)}(0) = 0\,, &\hbox{for} & 0\le \nu \le -k-2\,, -n \le k \le -2\,,\\ \\
\phi_{\alpha,j,2^j-1}^{(\nu)}(1) = 1\,, & \phi_{\alpha,j,2^j+k}^{(\nu)}(1) = 0\,, & \hbox{for} & 0\le \nu \le -k-2\,, -n \le k \le -2\,,\\ \\
\end{array}$$ Thus, the B-basis naturally fulfills Dirichlet boundary conditions.\
As we will show in the next section, the refinability of the fractional spline bases plays a crucial role in the construction of the collocation-Galerkin method.
The fractional spline collocation-Galerkin method. {#sec:Galerkin}
==================================================
In the collocation-Galerkin method here proposed, we look for an approximating function $u_{s,j}(t,x) \in V^{(\beta)}_s([0,T]) \otimes V^{(\alpha)}_j([0,1])$. Since just the ordinary first spatial derivative of $u_{s,j}$ is involved in the Galerkin method, we can assume $\alpha$ integer and use as basis function for the space $V^{(\alpha)}_j([0,1])$ the refinable B-basis $\{\phi_{\alpha,j,k}\}$, [*i.e.*]{} $$\label{uj}
u_{s,j}(t,x) = \sum_{k \in {\cal Z}_j} \, c_{s,j,k}(t) \, \phi_{\alpha,j,k}(x)\,,$$ where the unknown coefficients $c_{s,j,k}(t)$ belong to $V^{(\beta)}_s([0,T])$. Here, ${\cal Z}_j$ denotes the set of indexes $-n\le k \le 2^j-1$.\
The approximating function $u_{s,j}(t,x)$ solves the variational problem $$\label{varform}
\left \{
\begin{array}{ll}
\displaystyle \left ( D_t^\gamma u_{s,j},\phi_{\alpha,j,k} \right ) -\left ( \frac {\partial^2} {\partial x^2}\,u_{s,j},\phi_{\alpha,j,k} \right ) = \left ( f,\phi_{\alpha,j,k} \right )\,, & \quad k \in {\cal Z}_j\,, \\ \\
u_{s,j}(0, x) = 0\,, & x \in [0,1]\,, \\ \\
u_{s,j}(t, 0) = 0\,, \quad u_{s,j}(t,1) = 0\,, & t \in [0,T]\,,
\end{array} \right.$$ where $(f,g)= \int_0^1 \, f\,g$.\
Now, writing (\[varform\]) in a weak form and using (\[uj\]) we get the system of fractional ordinary differential equations $$\label{fracODE}
\left \{ \begin{array}{ll}
M_j \, D_t^\gamma\,C_{s,j}(t) + L_j\, C_{s,j}(t) = F_j(t)\,, & \qquad t \in [0,T]\,, \\ \\
C_{s,j}(0) = 0\,,
\end{array} \right.$$ where $C_{s,j}(t)=(c_{s,j,k}(t))_{k\in {\cal Z}_j}$ is the unknown vector. The connecting coefficients, i.e. the entries of the mass matrix $M_j = (m_{j,k,i})_{k,i\in{\cal Z}_j}$, of the stiffness matrix $L_j = (\ell_{j,k,i})_{k,i\in{\cal Z}_j}$, and of the load vector $F_j(t)=(f_{j,k}(t))_{k\in {\cal Z}_j}$, are given by $$m_{j,k,i} = \int_0^1\, \phi_{\alpha,j,k}\, \phi_{\alpha,j,i}\,, \qquad \ell_{j,k,i} = \int_0^1 \, \phi'_{\alpha,j,k} \, \phi'_{\alpha,j,i}\,,$$ $$f_{j,k}(t) = \int_0^1\, f(t,\cdot)\, \phi_{\alpha,j,k}\,.$$ The entries of $M_j$ and $L_j$ can be evaluated explicitly using (\[eq:Balpha\]) and (\[eq:diffrule\_tronc\]), respectively, while the entries of $F_j(t)$ can be evaluated by quadrature formulas especially designed for wavelet methods [@CMP15; @GGP00].
To solve the fractional differential system (\[fracODE\]) we use the collocation method introduced in [@PP16]. For an integer value of $T$, let $t_p = p/2^q$, $0\le p \le 2^q\,T$, where $q$ is a given nonnegative integer, be a set of dyadic nodes in the interval $[0,T]$. Now, assuming $$\label{ck}
c_{s,j,k}(t) = \sum_{r\in {\cal R}_s} \, \lambda_{k,r}\,\chi_{\beta,s,r}(t) \,, \qquad k \in {\cal Z}_j\,,$$ where $\chi_{\beta,s,r}(t)=B_\beta(2^s\,t-r)$ with $B_\beta$ a fractional B-spline of fractional degree $\beta$, and collocating (\[fracODE\]) on the nodes $t_p$, we get the linear system $$\label{colllinearsys}
(M_j\otimes A_s + L_j\otimes G_s) \,\Lambda_{s,j} =F_j\,,$$ where $\Lambda_{s,j}=(\lambda_{k,r})_{r\in {\cal R}_s,k\in {\cal Z}_j}$ is the unknown vector, $$\begin{array}{ll}
A_s= \bigl( a_{p,r} \bigr)_{p\in {\cal P}_q,r\in {\cal R}_s}\,, & \qquad a_{p,r} = D_t^\gamma \, \chi_{\beta,s,r}(t_p)\,, \\ \\
G_s=\bigl(g_{p,r}\bigr)_{p \in {\cal P}_q,r\in {\cal R}_s}\,, & \qquad g_{p,r} = \chi_{\beta,s,r}(t_p)\,,
\end{array}$$ are the collocation matrices and $$F_j=(f_{j,k}(t_p))_{k\in{\cal Z}_j,p \in {\cal P}_q}\,,$$ is the constant term. Here, ${\cal R}_s$ denotes the set of indexes $-\infty < r \le 2^s-1$ and ${\cal P}_q$ denotes the set of indexes $0<p\le 2^qT$. Since the fractional B-splines have fast decay, the series (\[ck\]) is well approximated by only few terms and the linear system (\[colllinearsys\]) has in practice finite dimension so that the unknown vector $\Lambda_{s,j}$ can be recovered by solving (\[colllinearsys\]) in the least squares sense.\
We notice that the entries of $G_s$, which involve just the values of $\chi_{\beta,s,r}$ on the dyadic nodes $t_p$, can be evaluated explicitly by (\[eq:Balpha\]). On the other hand, we must pay a special attention to the evaluation of the entries of $A_s$ since they involve the values of the fractional derivative $D_t^\gamma\chi_{\beta,s,r}(t_p)$. As shown in Section \[sec:fractBspline\], they can be evaluated efficiently by the differentiation rule (\[eq:diffrule\_2\]).
In the following theorem we prove that the fractional spline collocation-Galerkin method is convergent. First of all, let us introduce the Sobolev space on bounded interval $$H^\mu(I):= \{v \in L^2(I): \exists \, \tilde v \in H^\mu (\RR) \ \hbox{\rm such that} \ \tilde v|_I=v\}, \quad \mu\geq 0\,,$$ equipped with the norm $$\|v\|_{\mu,I} = \inf_{\tilde v \in H^\mu(\RR), \tilde v|_I=v} \|\tilde v\|_{\mu,\RR}\,,$$ where $$H^\mu(\RR):= \{v: v\in L^2(\RR) \mbox{ and } (1+|\omega|^2)^{\mu/2} {\cal F}(v)(\omega) \in L^2(\RR)\}, \quad \mu\geq 0\,,$$ is the usual Sobolev space with the norm $$\| v \| _{\mu,\RR} =\bigl \| (1+|\omega|^2)^{\mu/2} {\cal F}(v)(\omega) \bigr \| _{0,\RR}\,.$$
\[Convergence\] Let $$H^\mu(I;H^{\tilde \mu}(\Omega)):= \{v(t,x): \| v(t,\cdot)\|_{H^{\tilde \mu}(\Omega)} \in H^\mu(I)\}, \quad \mu, {\tilde \mu} \geq 0\,,$$ equipped with the norm $$\|v\|_{H^\mu(I;H^{\tilde \mu}(\Omega))} := \bigl \| \|v(t,\cdot)\|_{H^{\tilde \mu}(\Omega)} \bigr\|_{\mu,I}\,.$$ Assume $u$ and $f$ in (\[eq:fracdiffeq\]) belong to $H^{\mu}([0,T];H^{\tilde \mu}([0,1]))$, $0\le \mu$, $0\le \tilde \mu$, and $H^{\mu-\gamma}([0,T];$ $H^{{\tilde \mu}-2}([0,1]))$, $0\le \mu-\gamma$, $0\le \tilde \mu-2$, respectively. Then, the fractional spline collocation-Galerkin method is convergent, [*i.e.*]{}, $$\|u-u_{s,j}\|_{H^0([0,T];H^0([0,1]))} \, \to 0 \quad \hbox{as} \quad s,j \to \infty\,.$$ Moreover, for $\gamma \le \mu \le \beta+1$ and $1 \le \tilde \mu \le \alpha +1$ the following error estimate holds: $$\begin{array}{lcl}
\| u-u_{s,j}\|_{H^0([0,T];H^0([0,1]))} &\leq & \left (\eta_1 \, 2^{-j\tilde \mu} + \eta_2 \, 2^{-s\mu} \right ) \| u\|_{H^\mu([0,T];H^{\tilde \mu}([0,1]))}\,,
\end{array}$$ where $\eta_1$ and $\eta_2$ are two constants independent of $s$ and $j$.
Let $u_j$ be the exact solution of the variational problem (\[varform\]). Following a classical line of reasoning (cf. [@Th06; @FXY11; @DPS94]) we get $$\begin{array}{l}
\| u-u_{j,s}\|_{H^0([0,T];H^0([0,1]))} \leq \\ \\
\rule{2cm}{0cm} \leq \|u-u_{j}\|_{H^0([0,T];H^0([0,1]))} + \| u_j-u_{j,s}\|_{H^0([0,T];H^0([0,1]))}\, \leq
\\ \\ \rule{2cm}{0cm} \leq \eta_1 \, 2^{-j\tilde \mu}\, \| u\|_{H^0([0,T];H^{\tilde \mu}([0,1]))} + \eta_2 \, 2^{-s\mu} \, \| u\|_{H^\mu([0,T];H^0([0,1]))} \leq
\\ \\ \rule{2cm}{0cm} \leq \left ( \eta_1 \, 2^{-j\tilde \mu} + \eta_2 \, 2^{-s\mu} \right ) \, \|u\|_{H^\mu([0,T];H^{\tilde \mu}([0,1]))}\,.
\end{array}$$
Numerical tests. {#sec:numtest}
================
To shown the effectiveness of the fractional spline collocation-Galerkin method we solved the fractional diffusion problem (\[eq:fracdiffeq\]) for two different known terms $f(t,x)$ taken from [@FXY11]. In all the numerical tests we used as approximating space for the Galerkin method the (polynomial) cubic spline space. The B-splines $B_3$, its first derivatives $B_3'$ and the B-basis $\{\phi_{3,3,k}\}$ are displayed in Figure \[fig:Bcubic\]. We notice that since the cubic B-spline is centrally symmetric in the interval $[0,4]$, the B-basis is centrally symmetric, too. All the numerical tests were performed on a laptop using a Python environment. Each test takes a few minutes.
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![Left panel: The cubic B-spline (red line) and its first derivative (blue line). Right panel: The B-basis $\{\phi_{3,3,k}(x)\}$.[]{data-label="fig:Bcubic"}](Fig_Bspline_n3.png "fig:"){width="45.00000%"} ![Left panel: The cubic B-spline (red line) and its first derivative (blue line). Right panel: The B-basis $\{\phi_{3,3,k}(x)\}$.[]{data-label="fig:Bcubic"}](OptBasis_alpha3.png "fig:"){width="45.00000%"}
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Example 1
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In the first test we solved the time-fractional diffusion equation (\[eq:fracdiffeq\]) in the case when $$f(t,x)=\frac{2}{\Gamma(3-\gamma)}\,t^{2-\gamma}\, \sin(2\pi x)+4\pi^2\,t^2\, \sin(2\pi x)\,.$$ The exact solution is $$u(t,x)=t^2\,\sin(2\pi x).$$ We used the fractional B-spline $B_{3.5}$ as approximating function for the collocation method and solved the problem for $\gamma = 1, 0.75, 0.5, 0.25$. The fractional B-spline $B_{3.5}$, its first derivative and its fractional derivatives are shown in Figure \[fig:fract\_Basis\] along with the fractional basis $\{\chi_{3.5,3,r}\}$. The numerical solution $u_{s,j}(t,x)$ and the error $e_{s,j}(t,x) = u(t,x)-u_{s,j}(t,x)$ for $s=6$ and $j=6$ are displayed in Figure \[fig:numsol\_1\] for $\gamma = 0.5$. In all the numerical tests we set $q = s+1$.
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![Left panel: The fractional B-spline $B_{3.5}$ (green line), its first derivative (red line) and its fractional derivatives of order $\gamma =0.75$ (blue line), 0.5 (cyan line), 0.25 (black line). Right panel: The fractional basis $\{\chi_{3.5,3,r}\}$(right).[]{data-label="fig:fract_Basis"}](Fig_Bspline_n3p5.png "fig:"){width="45.00000%"} ![Left panel: The fractional B-spline $B_{3.5}$ (green line), its first derivative (red line) and its fractional derivatives of order $\gamma =0.75$ (blue line), 0.5 (cyan line), 0.25 (black line). Right panel: The fractional basis $\{\chi_{3.5,3,r}\}$(right).[]{data-label="fig:fract_Basis"}](FractBasis_alpha3p5.png "fig:"){width="45.00000%"}
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![Example 1. The numerical solution (left panel) and the error (right panel) for $j=6$ and $s=6$ when $\gamma = 0.5$.[]{data-label="fig:numsol_1"}](Fig_NumSol_jGK6_sref7_beta3p5_gamma0p5_ex1.png "fig:"){width="45.00000%"} ![Example 1. The numerical solution (left panel) and the error (right panel) for $j=6$ and $s=6$ when $\gamma = 0.5$.[]{data-label="fig:numsol_1"}](Fig_Error_jGK6_sref7_beta3p5_gamma0p5_ex1.png "fig:"){width="45.00000%"}
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We analyze the behavior of the error as the degree of the fractional B-spline $B_\beta$ increases. Figure \[fig:L2\_error\_1\] shows the $L_2$-norm of the error as a function of $s$ for $\beta$ ranging from 2 to 4; the four panels in the figure refer to different values of the order of the fractional derivative. For these tests we set $j=5$. The figure shows that for $s \le 4$ the error provided by the polynomial spline approximations is lower than the error provided by the fractional spline approximations. Nevertheless, in this latter case the error decreases reaching the same value, or even a lower one, of the polynomial spline error when $s=5$. We notice that for $\gamma=1$ the errors provided by the polynomial spline approximations of different degrees have approximatively the same values while the error provided by the polynomial spline of degree 2 is lower in case of fractional derivatives. In fact, it is well-known that fractional derivatives are better approximated by less smooth functions [@Po99].
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
![Example 1: The $L_2$-norm of the error as a function of $q$ for different values of $\gamma$. Each line corresponds to a spline of different degree: solid lines correspond to the polynomial splines; non solid lines correspond to fractional splines.[]{data-label="fig:L2_error_1"}](Fig_L2Error_gam1_ex1.png "fig:"){width="45.00000%"} ![Example 1: The $L_2$-norm of the error as a function of $q$ for different values of $\gamma$. Each line corresponds to a spline of different degree: solid lines correspond to the polynomial splines; non solid lines correspond to fractional splines.[]{data-label="fig:L2_error_1"}](Fig_L2Error_gam0p75_ex1.png "fig:"){width="45.00000%"}
![Example 1: The $L_2$-norm of the error as a function of $q$ for different values of $\gamma$. Each line corresponds to a spline of different degree: solid lines correspond to the polynomial splines; non solid lines correspond to fractional splines.[]{data-label="fig:L2_error_1"}](Fig_L2Error_gam0p5_ex1.png "fig:"){width="45.00000%"} ![Example 1: The $L_2$-norm of the error as a function of $q$ for different values of $\gamma$. Each line corresponds to a spline of different degree: solid lines correspond to the polynomial splines; non solid lines correspond to fractional splines.[]{data-label="fig:L2_error_1"}](Fig_L2Error_gam0p25_ex1.png "fig:"){width="45.00000%"}
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Then, we analyze the convergence of the method for increasing values of $j$ and $s$. Table \[tab:conv\_js\_fract\_1\] reports the $L_2$-norm of the error for different values of $j$ and $s$ when using the fractional B-spline $B_{3.5}$ and $\gamma = 0.5$. The number of degrees-of-freedom is also reported. The table shows that the error decreases when $j$ increases and $s$ is held fix. We notice that the error decreases very slightly when $j$ is held fix and $s$ increases since for these values of $s$ we reached the accuracy level we can expect for that value of $j$ (cf. Figures \[fig:L2\_error\_1\]). The higher values of the error for $s=7$ and $j=5,6$ are due to the numerical instabilities of the basis $\{\chi_{3.5,s,r}\}$ which result in a high condition number of the discretization matrix. The error has a similar behavior even in the case when we used the cubic B-spline space as approximating space for the collocation method (cf. Table \[tab:conv\_js\_cubic\_1\]).
3 4 5 6
-------------------------------- ---------------- ---------------- ---------------- ----------------
$\sharp V_j^{(\alpha)}([0,1])$ 9 17 33 65
5 0.02037 (369) 0.00449 (697) 0.00101 (1353) 0.00025 (2665)
6 0.02067 (657) 0.00417 (1241) 0.00093 (2409) 0.00024 (4745)
7 0.01946 (1233) 0.00381 (2329) 0.00115 (4521) 0.00117 (8905)
: Example 1: The $L_2$-norm of the error for increasing values of $s$ and $j$ when using the fractional B-spline of degree $\beta=3.5$. The numbers in parenthesis are the degrees-of-freedom. Here, $\gamma =0.5$.
\[tab:conv\_js\_fract\_1\]
3 4 5 6
-------------------------------- ---------------- ---------------- ---------------- ----------------
$\sharp V_j^{(\alpha)}([0,1])$ 9 17 33 65
5 0.02121 (315) 0.00452 (595) 0.00104 (1155) 0.00025 (2275)
6 0.02109 (603) 0.00443 (1139) 0.00097 (2211) 0.00023 (4355)
7 0.02037 (1179) 0.00399 (2227) 0.00115 (4323) 0.00115 (8515)
: Example 1: The $L_2$-norm of the error for increasing values of $s$ and $j$ when using the cubic B-spline. The numbers in parenthesis are the degrees-of-freedom. Here, $\gamma =0.5$.
\[tab:conv\_js\_cubic\_1\]
Example 2
---------
In the second test we solved the time-fractional diffusion equation (\[eq:fracdiffeq\]) in the case when $$\begin{array}{lcl}
f(t,x) & = & \displaystyle \frac{\pi t^{1-\gamma}}{2\Gamma(2-\gamma)} \left( \, {_1F_1}(1,2-\gamma,i\pi\,t) + \,{_1F_1}(1,2-\gamma,-i\pi\,t) \right) \, \sin(\pi\,x) \\ \\
& + & \pi^2 \, \sin(\pi\,t) \, \sin(\pi\,x)\,,
\end{array}$$ where $_1F_1(\alpha,\beta,z)$ is the Kummer’s confluent hypergeometric function defined as $$_1F_1(\alpha,\beta, z) =
\frac {\Gamma(\beta)}{\Gamma(\alpha)} \, \sum_{k\in \NN} \, \frac {\Gamma(\alpha+k)}{\Gamma(\beta+k)\, k!} \, z^k\,, \qquad \alpha \in \RR\,, \quad -\beta \notin \NN_0\,,$$ where $\NN_0 = \NN \backslash \{0\}$ (cf. [@AS65 Chapter 13]). In this case the exact solution is $$u(t,x)=\sin(\pi t)\,\sin(\pi x).$$ We performed the same set of numerical tests as in Example 1. The numerical solution $u_{s,j}(t,x)$ and the error $e_{s,j}(t,x)$ for $s=5$ and $j=6$ are displayed in Figure \[fig:numsol\_2\] in the case when $\gamma = 0.5$. Figure \[fig:L2\_error\_2\] shows the $L_2$-norm of the error as a function of $s$ for $\beta$ ranging from 2 to 4 and $j=5$; the four panels in the figure refer to different values of the order of the fractional derivative. Tables \[tab:conv\_js\_fract\_2\]-\[tab:conv\_js\_cubic\_2\] report the $L_2$-norm of the error for different values of $j$ and $s$ and $\beta = 3.5, 3$, respectively. The number of degrees-of-freedom is also reported.\
Figure \[fig:L2\_error\_2\] shows that value of the error is higher than in the previous example but it decreases as $s$ increases showing a very similar behavior as that one in Example 1. The values of the error in Tables \[tab:conv\_js\_fract\_2\]-\[tab:conv\_js\_cubic\_2\] are approximatively the same as in Tables \[tab:conv\_js\_fract\_1\]-\[tab:conv\_js\_cubic\_1\].
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
![Example 2: The numerical solution (left panel) and the error (right panel) when $j=6$ and $s=5$. []{data-label="fig:numsol_2"}](Fig_NumSol_jGK6_sref6_beta3p5_gamma0p5_ex2.png "fig:"){width="45.00000%"} ![Example 2: The numerical solution (left panel) and the error (right panel) when $j=6$ and $s=5$. []{data-label="fig:numsol_2"}](Fig_Error_jGK6_sref6_beta3p5_gamma0p5_ex2.png "fig:"){width="45.00000%"}
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
![Example 2: The $L_2$-norm of the error as a function of $s$ for different values of $\gamma$. Each line corresponds to a spline of different degree: solid lines correspond to the polynomial splines; non solid lines correspond to fractional splines.[]{data-label="fig:L2_error_2"}](Fig_L2Error_gam1_ex2.png "fig:"){width="45.00000%"} ![Example 2: The $L_2$-norm of the error as a function of $s$ for different values of $\gamma$. Each line corresponds to a spline of different degree: solid lines correspond to the polynomial splines; non solid lines correspond to fractional splines.[]{data-label="fig:L2_error_2"}](Fig_L2Error_gam0p75_ex2.png "fig:"){width="45.00000%"}
![Example 2: The $L_2$-norm of the error as a function of $s$ for different values of $\gamma$. Each line corresponds to a spline of different degree: solid lines correspond to the polynomial splines; non solid lines correspond to fractional splines.[]{data-label="fig:L2_error_2"}](Fig_L2Error_gam0p5_ex2.png "fig:"){width="45.00000%"} ![Example 2: The $L_2$-norm of the error as a function of $s$ for different values of $\gamma$. Each line corresponds to a spline of different degree: solid lines correspond to the polynomial splines; non solid lines correspond to fractional splines.[]{data-label="fig:L2_error_2"}](Fig_L2Error_gam0p25_ex2.png "fig:"){width="45.00000%"}
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3 4 5 6
-------------------------------- ---------------- ---------------- ---------------- ----------------
$\sharp V_j^{(\alpha)}([0,1])$ 9 17 33 65
5 0.01938 (369) 0.00429 (697) 0.00111 (1353) 0.00042 (2665)
6 0.01809 (657) 0.00555 (1241) 0.00507 (2409) 0.00523 (4745)
7 0.01811 (1233) 0.01691 (2329) 0.01822 (4521) 0.01858 (8905)
: Example 2: The $L_2$-norm of the error for increasing values of $s$ and $j$ for the fractional B-spline of degree $\beta=3.5$. The numbers in parenthesis are the degrees-of-freedom. Here, $\gamma=0.5$.
\[tab:conv\_js\_fract\_2\]
3 4 5 6
-------------------------------- ---------------- ---------------- ---------------- ----------------
$\sharp V_j^{(\alpha)}([0,1])$ 9 17 33 65
5 0.01909 (315) 0.00404 (595) 0.00102 (1155) 0.00063 (2275)
6 0.01810 (603) 0.00546 (1139) 0.00495 (2211) 0.00511 (4355)
7 0.01805 (1179) 0.01671 (2227) 0.01801 (4323) 0.01838 (8515)
: Example 2: The $L_2$-norm of the error for increasing values of $s$ and $j$ for the cubic B-spline. The numbers in parenthesis are the degrees-of-freedom. Here, $\gamma=0.5$.
\[tab:conv\_js\_cubic\_2\]
Conclusion {#sec:concl}
==========
We proposed a fractional spline collocation-Galerkin method to solve the time-fractional diffusion equation. The novelty of the method is in the use of fractional spline spaces as approximating spaces so that the fractional derivative of the approximating function can be evaluated easily by an explicit differentiation rule that involves the generalized finite difference operator. The numerical tests show that the method has a good accuracy so that it can be effectively used to solve fractional differential problems. The numerical instabilities arising in the fractional basis when $s$ increases can be reduced following the approach in [@GPP04] that allows us to construct stable basis on the interval. Moreover, the ill-conditioning of the linear system (\[colllinearsys\]) can be reduced using iterative methods in Krylov spaces, such as the method proposed in [@CPSV17]. Finally, we notice that following the procedure given in [@GPP04], fractional wavelet bases on finite interval can be constructed so that the proposed method can be generalized to fractional wavelet approximating spaces.
[10]{}
Milton Abramowitz and Irene A. Stegun. , volume 55. Dover Publications, 1965.
Dumitru Baleanu, Kai Diethelm, Enrico Scalas, and Juan J. Trujillo. Fractional calculus. models and numerical methods. , 3:10–16, 2012.
Francesco Calabr[ò]{}, Carla Manni, and Francesca Pitolli. Computation of quadrature rules for integration with respect to refinable functions on assigned nodes. , 90:168–189, 2015.
Daniela Calvetti, Francesca Pitolli, Erkki Somersalo, and Barbara Vantaggi. Bayes meets [K]{}rylov: preconditioning [CGLS]{} for underdetermined systems. , in press.
Wolfgang Dahmen, Siegfried Pr[ö]{}ssdorf, and Reinhold Schneider. Wavelet approximation methods for pseudodifferential equations: I stability and convergence. , 215(1):583–620, 1994.
Neville Ford, Jingyu Xiao, and Yubin Yan. A finite element method for time fractional partial differential equations. , 14(3):454–474, 2011.
Walter Gautschi, Laura Gori, and Francesca Pitolli. Gauss quadrature for refinable weight functions. , 8(3):249–257, 2000.
Laura Gori, Laura Pezza, and Francesca Pitolli. Recent results on wavelet bases on the interval generated by [GP]{} refinable functions. , 51(4):549–563, 2004.
Laura Gori and Francesca Pitolli. Refinable functions and positive operators. , 49(3):381–393, 2004.
Rudolf Hilfer. . World Scientific, 2000.
Francesco Mainardi. . World Scientific, 2010.
Arvet Pedas and Enn Tamme. Numerical solution of nonlinear fractional differential equations by spline collocation methods. , 255:216–230, 2014.
Laura Pezza and Francesca Pitolli. A multiscale collocation method for fractional differential problems. , 147:210–219, 2018.
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[^1]: [*Dept. SBAI, University of Roma ”La Sapienza”*]{}, Via A. Scarpa 16, 00161 Roma, Italy. e-mail: [[email protected]]{}
[^2]: [*Dept. SBAI, University of Roma ”La Sapienza”*]{}, Via A. Scarpa 16, 00161 Roma, Italy. e-mail:
|
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Press
New Wellesley Business Wants To Teach The World To Sew!
Lauren Johnston is doing her part to ensure sewing doesn’t become a lost art.
Sew Easy, a business she started 15 years ago in Needham to teach kids and teens how to sew, expanded this summer into a second floor space in Wellesley at 159 Linden St. 3C.
Sew easy, which begins its next 8-week session in Wellesley on Sept. 17, has taught more than 9,000 girls and boys to sew over the years. Students range in age from 5.5 to about 16, and classes are held after school and on Saturdays. Sew Easy charges about $325 per session, which includes materials. The Wellesley location has 12 sewing machines.
“I want to teach the world to sew,” says Johnston, whose programs mainly involve using sewing machines, though also include hand sewing. She says that she thinks sewing is coming back, even though most kids’ parents don’t sew and even though sewing classes are rare in school these days. “They’ve seen grandparents sewing,” she says.
At Sew Easy, kids learn how to sew buttonholes, zippers, pockets and hems as well as how to thread the sewing machines. They get to use a variety of fabrics, including cotton and fleece. Students complete between 5 and 10 projects per session, creating clothes, bags and even American Doll outfits.
While Sew Easy’s two locations are just a few miles far apart, Johnston says she appreciates that the closer the better for parents shuttling their children from activity to activity after school. She said parents of kids who have taken classes at the Needham spot have been begging her to open a place in Wellesley.
It would be a stretch to call Wellesley the sewing capital of the world, but there is maybe more needle-and-thread action around here than you might think. For example, there’s the Button Box shop on Rte. 9 that caters to quilters, the Wellesley Needlepoint Collection on Grove Street, and local artist Abby Glassenberg has made a name for herself via the soft sculptures she sews.
Classes start at 3:15 p.m., but children’s noses press up against the glass of the Needham storefront long before the door is unlocked. Here, six days a week, the nearly lost art of sewing is revered and creativity is unleashed.
By Bob Brown | THE SWELLESLEY REPORT
Enriching Fabric of Their Lives
Lauren Johnston says she has taught over 8,000 students since launching Sew Easy 13 years ago. Last week she opened a second branch in West Roxbury, where she hopes to further disseminate an old-fashioned skill that is still indispensable in this high-tech age.
“In an instant, children feel empowered,” said Johnston, whose students, male and female, range in age from elementary through high school. “They choose the project that they want to work on and the fabrics that they want to use, and are excited and proud about expressing their creativity.”
Johnston has over 300 projects for her students to choose from – book bags, fleece vests, ponchos, mittens, quilts, American Girl Doll accessories, pajama pants. Some use their time to alter clothing, and during the holiday season they tend to make gifts.
Each time someone finishes a project, they ring a large bell and the class goes silent in order to see what has been completed and give the student a round of applause. Johnston then encourages them to place their project in the storefront window “to show the world what they’ve made.”
Some projects are basic, like small decorative pillows, and others are more elaborate. One girl, she said, walked in with a sketch of a lobster costume and made it for Halloween.
An eight-week session of one class a week costs $299, which includes all materials. On average, classes are capped at 18 students. With 15 sewing machines, no one has to wait to use one, since not every student needs a machine all the time. “They help each other out and really feel like they’re a part of this place,” she said.
Johnston said parents often tell her that their child is creating things using tape and staples to hold the fabric together. Those kids, she said, are really ready to learn. But it’s not just the creative and technical aspects of teaching that bring Johnston satisfaction, it’s also observing the emotional growth of her students.
“There is no gossip allowed in here,” said Johnston. “I tell the kids ‘I’d rather hear about you.’ ” Sometimes during a snack break, she will throw out questions for discussion, such as “What is something positive that we would never guess about you?” or “What are some experiences that you would like to have but aren’t yet old enough?”
And on occasion she will read aloud an inspirational thought for the day.
“They laugh, but then they quiet down and listen,” said Johnston, who hopes that insightful, introspective words will encourage self-awareness and confidence.
By Susan Chaityn Lebovits | THE BOSTON GLOBE
Sew Easy opens new location in Wellesley
Lauren Johnston, owner and founder of Sew Easy, has been teaching children how to sew since 1995. She said she’s taught the “dying art” to more than 9,000 kids and teens in the past 15 years.
Johnston recently expanded her operation to Wellesley. The Townsman caught up with Johnston at the new location, 159 Linden St., to ask her about her business and why so many children still want to learn to sew.
“I always loved sewing,” Johnston said. “So my children always wanted to get at the machine. I saw that it was easy to teach them and then their friends started joining and the masses came.”
What prompted your expansion to Wellesley?
“Wellesley wanted us to come and so I said, ‘Why not?’” Johnston said. “Wellesley asked us over and over to come here.”
Why do you think kids and teens want to sew when they could just buy everything they needed?
“It’s not about being able to buy it,” Johnston said. “When you create something you feel empowered. Most of the last generation doesn’t know how to sew so kids feel empowered because their parents don’t know how to sew.”
What kind of items do the students sew?
“We have over 300 projects,” Johnston said. She said that students make everything from clothing to American Girl Doll accessories and even, sometimes, dog clothing.
Do any boys come to these classes?
“I usually have one or two in a class,” she said. Classes range in size from 12 to 20.
Where did you learn to sew?
“[I learned from] my grandma and Home Ec in junior high.”
Is that where the passion began?
“Yes, it felt so good to complete a project from scratch and I couldn’t believe I made it myself. The stuff I made when I was young was so elaborate,” Johnston said. “I really loved it.”
What would you say to a kid who said sewing is boring?
“I’ve never heard that once from the 9,000 kids I’ve taught,” Johnston said. “So I don’t think I have to answer that.”
“It’s word of mouth,” she added. “It’s the kids that do all the advertising. I’m always full despite the bad economy.”
How do you stay current?
“We know what kids like,” Johnston said. “After 15 years and 9,000 kids, we know. I have to buy fabric with peace signs, turtles, polka dots and monkeys.”
What do you love about teaching?
‘I love to teach,” Johnston said, “and the some of the kids come in nervous, but within an hour and a half they don’t want to leave.
“I love to see the shift in kids to when they start feeling empowered. I get to witness the shift from knowing nothing to feeling like they know a lot in a short amount of time – it’s instant.
“I ask them, ‘do you feel like a good sewer?’ and they say ‘yes.’”
“Our mission is to instill confidence and creativity. And we feel every child needs to feel success. We want them to walk away with that feeling and completing a project makes them feel that way.”
Johnston said it’s her particular system that helps her students find this success.
“The system is the reason why we are successful,” Johnston said. “It allows kids to create quicker. The way we design our things more streamlined. The detail is not like yesteryears.”
“The kids that come in with learning disabilities,” Johnston said, “in 99 percent of them I don’t find what they’ve been diagnosed with here. And I’m looking for it, but I never find it. They just take it in and grasp it.” |
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<param name="store_buffer_size" value="32"/>
<!-- By default, in-order cores do not have load buffers -->
<param name="load_buffer_size" value="32"/>
<!-- number of ports refer to sustainable concurrent memory accesses -->
<param name="memory_ports" value="1"/>
<!-- max_allowed_in_flight_memo_instructions determins the # of ports of load and store buffer
as well as the ports of Dcache which is connected to LSU -->
<!-- dual-pumped Dcache can be used to save the extra read/write ports -->
<param name="RAS_size" value="32"/>
<!-- general stats, defines simulation periods;require total, idle, and busy cycles for senity check -->
<!-- please note: if target architecture is X86, then all the instrucions refer to (fused) micro-ops -->
<stat name="total_instructions" value="800000"/>
<stat name="int_instructions" value="600000"/>
<stat name="fp_instructions" value="20000"/>
<stat name="branch_instructions" value="0"/>
<stat name="branch_mispredictions" value="0"/>
<stat name="load_instructions" value="100000"/>
<stat name="store_instructions" value="100000"/>
<stat name="committed_instructions" value="800000"/>
<stat name="committed_int_instructions" value="600000"/>
<stat name="committed_fp_instructions" value="20000"/>
<stat name="pipeline_duty_cycle" value="0.6"/><!--<=1, runtime_ipc/peak_ipc; averaged for all cores if homogenous -->
<!-- the following cycle stats are used for heterogeneouse cores only,
please ignore them if homogeneouse cores -->
<stat name="total_cycles" value="100000"/>
<stat name="idle_cycles" value="0"/>
<stat name="busy_cycles" value="100000"/>
<!-- instruction buffer stats -->
<!-- ROB stats, both RS and Phy based OoOs have ROB
performance simulator should capture the difference on accesses,
otherwise, McPAT has to guess based on number of commited instructions. -->
<stat name="ROB_reads" value="263886"/>
<stat name="ROB_writes" value="263886"/>
<!-- RAT accesses -->
<stat name="rename_accesses" value="263886"/>
<stat name="fp_rename_accesses" value="263886"/>
<!-- decode and rename stage use this, should be total ic - nop -->
<!-- Inst window stats -->
<stat name="inst_window_reads" value="263886"/>
<stat name="inst_window_writes" value="263886"/>
<stat name="inst_window_wakeup_accesses" value="263886"/>
<stat name="fp_inst_window_reads" value="263886"/>
<stat name="fp_inst_window_writes" value="263886"/>
<stat name="fp_inst_window_wakeup_accesses" value="263886"/>
<!-- RF accesses -->
<stat name="int_regfile_reads" value="1600000"/>
<stat name="float_regfile_reads" value="40000"/>
<stat name="int_regfile_writes" value="800000"/>
<stat name="float_regfile_writes" value="20000"/>
<!-- accesses to the working reg -->
<stat name="function_calls" value="5"/>
<stat name="context_switches" value="260343"/>
<!-- Number of Windowes switches (number of function calls and returns)-->
<!-- Alu stats by default, the processor has one FPU that includes the divider and
multiplier. The fpu accesses should include accesses to multiplier and divider -->
<stat name="ialu_accesses" value="800000"/>
<stat name="fpu_accesses" value="10000"/>
<stat name="mul_accesses" value="100000"/>
<stat name="cdb_alu_accesses" value="1000000"/>
<stat name="cdb_mul_accesses" value="0"/>
<stat name="cdb_fpu_accesses" value="0"/>
<!-- multiple cycle accesses should be counted multiple times,
otherwise, McPAT can use internal counter for different floating point instructions
to get final accesses. But that needs detailed info for floating point inst mix -->
<!-- currently the performance simulator should
make sure all the numbers are final numbers,
including the explicit read/write accesses,
and the implicite accesses such as replacements and etc.
Future versions of McPAT may be able to reason the implicite access
based on param and stats of last level cache
The same rule applies to all cache access stats too! -->
<!-- following is AF for max power computation.
Do not change them, unless you understand them-->
<stat name="IFU_duty_cycle" value="0.25"/>
<stat name="LSU_duty_cycle" value="0.25"/>
<stat name="MemManU_I_duty_cycle" value="1"/>
<stat name="MemManU_D_duty_cycle" value="0.25"/>
<stat name="ALU_duty_cycle" value="0.9"/>
<stat name="MUL_duty_cycle" value="0.5"/>
<stat name="FPU_duty_cycle" value="0.4"/>
<stat name="ALU_cdb_duty_cycle" value="0.9"/>
<stat name="MUL_cdb_duty_cycle" value="0.5"/>
<stat name="FPU_cdb_duty_cycle" value="0.4"/>
<component id="system.core0.predictor" name="PBT">
<!-- branch predictor; tournament predictor see Alpha implementation -->
<param name="local_predictor_size" value="10,3"/>
<param name="local_predictor_entries" value="1024"/>
<param name="global_predictor_entries" value="4096"/>
<param name="global_predictor_bits" value="2"/>
<param name="chooser_predictor_entries" value="4096"/>
<param name="chooser_predictor_bits" value="2"/>
<!-- These parameters can be combined like below in next version
<param name="load_predictor" value="10,3,1024"/>
<param name="global_predictor" value="4096,2"/>
<param name="predictor_chooser" value="4096,2"/>
-->
</component>
<component id="system.core0.itlb" name="itlb">
<param name="number_entries" value="64"/>
<stat name="total_accesses" value="800000"/>
<stat name="total_misses" value="4"/>
<stat name="conflicts" value="0"/>
<!-- there is no write requests to itlb although writes happen to itlb after miss,
which is actually a replacement -->
</component>
<component id="system.core0.icache" name="icache">
<!-- there is no write requests to itlb although writes happen to it after miss,
which is actually a replacement -->
<param name="icache_config" value="16384,32,4,1,1,3,8,0"/>
<!-- the parameters are capacity,block_width, associativity, bank, throughput w.r.t. core clock, latency w.r.t. core clock,output_width, cache policy -->
<!-- cache_policy;//0 no write or write-though with non-write allocate;1 write-back with write-allocate -->
<param name="buffer_sizes" value="16, 16, 16,0"/>
<!-- cache controller buffer sizes: miss_buffer_size(MSHR),fill_buffer_size,prefetch_buffer_size,wb_buffer_size-->
<stat name="read_accesses" value="200000"/>
<stat name="read_misses" value="0"/>
<stat name="conflicts" value="0"/>
</component>
<component id="system.core0.dtlb" name="dtlb">
<param name="number_entries" value="64"/>
<stat name="total_accesses" value="200000"/>
<stat name="total_misses" value="4"/>
<stat name="conflicts" value="0"/>
</component>
<component id="system.core0.dcache" name="dcache">
<!-- all the buffer related are optional -->
<param name="dcache_config" value="8192,16,4,1,1,3,16,0"/>
<param name="buffer_sizes" value="16, 16, 16, 16"/>
<!-- cache controller buffer sizes: miss_buffer_size(MSHR),fill_buffer_size,prefetch_buffer_size,wb_buffer_size-->
<stat name="read_accesses" value="200000"/>
<stat name="write_accesses" value="27276"/>
<stat name="read_misses" value="1632"/>
<stat name="write_misses" value="183"/>
<stat name="conflicts" value="0"/>
</component>
<component id="system.core0.BTB" name="BTB">
<!-- all the buffer related are optional -->
<param name="BTB_config" value="8192,4,2,1, 1,3"/>
<!-- the parameters are capacity,block_width,associativity,bank, throughput w.r.t. core clock, latency w.r.t. core clock,-->
</component>
</component>
<component id="system.L1Directory0" name="L1Directory0">
<param name="Directory_type" value="0"/>
<!--0 cam based shadowed tag. 1 directory cache -->
<param name="Dir_config" value="2048,1,0,1, 4, 4,8"/>
<!-- the parameters are capacity,block_width, associativity,bank, throughput w.r.t. core clock, latency w.r.t. core clock,-->
<param name="buffer_sizes" value="8, 8, 8, 8"/>
<!-- all the buffer related are optional -->
<param name="clockrate" value="3500"/>
<param name="ports" value="1,1,1"/>
<!-- number of r, w, and rw search ports -->
<param name="device_type" value="0"/>
<!-- altough there are multiple access types,
Performance simulator needs to cast them into reads or writes
e.g. the invalidates can be considered as writes -->
<stat name="read_accesses" value="800000"/>
<stat name="write_accesses" value="27276"/>
<stat name="read_misses" value="1632"/>
<stat name="write_misses" value="183"/>
<stat name="conflicts" value="20"/>
<stat name="duty_cycle" value="0.45"/>
</component>
<component id="system.L2Directory0" name="L2Directory0">
<param name="Directory_type" value="1"/>
<!--0 cam based shadowed tag. 1 directory cache -->
<param name="Dir_config" value="1048576,16,16,1,2, 100"/>
<!-- the parameters are capacity,block_width, associativity,bank, throughput w.r.t. core clock, latency w.r.t. core clock,-->
<param name="buffer_sizes" value="8, 8, 8, 8"/>
<!-- all the buffer related are optional -->
<param name="clockrate" value="3500"/>
<param name="ports" value="1,1,1"/>
<!-- number of r, w, and rw search ports -->
<param name="device_type" value="0"/>
<!-- altough there are multiple access types,
Performance simulator needs to cast them into reads or writes
e.g. the invalidates can be considered as writes -->
<stat name="read_accesses" value="58824"/>
<stat name="write_accesses" value="27276"/>
<stat name="read_misses" value="1632"/>
<stat name="write_misses" value="183"/>
<stat name="conflicts" value="100"/>
<stat name="duty_cycle" value="0.45"/>
</component>
<component id="system.L20" name="L20">
<!-- all the buffer related are optional -->
<param name="L2_config" value="1048576,64,16,1, 4,23, 64, 1"/>
<!-- consider 4-way bank interleaving for Niagara 1 -->
<!-- the parameters are capacity,block_width, associativity, bank, throughput w.r.t. core clock, latency w.r.t. core clock,output_width, cache policy -->
<param name="buffer_sizes" value="16, 16, 16, 16"/>
<!-- cache controller buffer sizes: miss_buffer_size(MSHR),fill_buffer_size,prefetch_buffer_size,wb_buffer_size-->
<param name="clockrate" value="3500"/>
<param name="ports" value="1,1,1"/>
<!-- number of r, w, and rw ports -->
<param name="device_type" value="0"/>
<stat name="read_accesses" value="200000"/>
<stat name="write_accesses" value="0"/>
<stat name="read_misses" value="0"/>
<stat name="write_misses" value="0"/>
<stat name="conflicts" value="0"/>
<stat name="duty_cycle" value="0.5"/>
</component>
<!--**********************************************************************-->
<component id="system.L30" name="L30">
<param name="L3_config" value="1048576,64,16,1, 2,100, 64,1"/>
<!-- the parameters are capacity,block_width, associativity, bank, throughput w.r.t. core clock, latency w.r.t. core clock,output_width, cache policy -->
<param name="clockrate" value="3500"/>
<param name="ports" value="1,1,1"/>
<!-- number of r, w, and rw ports -->
<param name="device_type" value="0"/>
<param name="buffer_sizes" value="16, 16, 16, 16"/>
<!-- cache controller buffer sizes: miss_buffer_size(MSHR),fill_buffer_size,prefetch_buffer_size,wb_buffer_size-->
<stat name="read_accesses" value="58824"/>
<stat name="write_accesses" value="27276"/>
<stat name="read_misses" value="1632"/>
<stat name="write_misses" value="183"/>
<stat name="conflicts" value="0"/>
<stat name="duty_cycle" value="0.35"/>
</component>
<!--**********************************************************************-->
<component id="system.NoC0" name="noc0">
<param name="clockrate" value="3500"/>
<param name="type" value="1"/>
<!-- 1 NoC, O bus -->
<param name="horizontal_nodes" value="8"/>
<param name="vertical_nodes" value="8"/>
<param name="has_global_link" value="1"/>
<!-- 1 has global link, 0 does not have global link -->
<param name="link_throughput" value="1"/><!--w.r.t clock -->
<param name="link_latency" value="1"/><!--w.r.t clock -->
<!-- througput >= latency -->
<!-- Router architecture -->
<param name="input_ports" value="5"/>
<param name="output_ports" value="5"/>
<param name="virtual_channel_per_port" value="1"/>
<!-- input buffer; in classic routers only input ports need buffers -->
<param name="flit_bits" value="256"/>
<param name="input_buffer_entries_per_vc" value="4"/><!--VCs within the same ports share input buffers whose size is propotional to the number of VCs-->
<param name="chip_coverage" value="1"/>
<!-- When multiple NOC present, one NOC will cover part of the whole chip. chip_coverage <=1 -->
<stat name="total_accesses" value="360000"/>
<!-- This is the number of total accesses within the whole network not for each router -->
<stat name="duty_cycle" value="0.1"/>
</component>
<!--**********************************************************************-->
<component id="system.mem" name="mem">
<!-- Main memory property -->
<param name="mem_tech_node" value="32"/>
<param name="device_clock" value="200"/><!--MHz, this is clock rate of the actual memory device, not the FSB -->
<param name="peak_transfer_rate" value="3200"/><!--MB/S-->
<param name="internal_prefetch_of_DRAM_chip" value="4"/>
<!-- 2 for DDR, 4 for DDR2, 8 for DDR3...-->
<!-- the device clock, peak_transfer_rate, and the internal prefetch decide the DIMM property -->
<!-- above numbers can be easily found from Wikipedia -->
<param name="capacity_per_channel" value="4096"/> <!-- MB -->
<!-- capacity_per_Dram_chip=capacity_per_channel/number_of_dimms/number_ranks/Dram_chips_per_rank
Current McPAT assumes single DIMMs are used.-->
<param name="number_ranks" value="2"/>
<param name="num_banks_of_DRAM_chip" value="8"/>
<param name="Block_width_of_DRAM_chip" value="64"/> <!-- B -->
<param name="output_width_of_DRAM_chip" value="8"/>
<!--number of Dram_chips_per_rank=" 72/output_width_of_DRAM_chip-->
<!--number of Dram_chips_per_rank=" 72/output_width_of_DRAM_chip-->
<param name="page_size_of_DRAM_chip" value="8"/> <!-- 8 or 16 -->
<param name="burstlength_of_DRAM_chip" value="8"/>
<stat name="memory_accesses" value="1052"/>
<stat name="memory_reads" value="1052"/>
<stat name="memory_writes" value="1052"/>
</component>
<component id="system.mc" name="mc">
<!-- Memeory controllers are for DDR(2,3...) DIMMs -->
<!-- current version of McPAT uses published values for base parameters of memory controller
improvments on MC will be added in later versions. -->
<param name="mc_clock" value="200"/><!--DIMM IO bus clock rate MHz DDR2-400 for Niagara 1-->
<param name="peak_transfer_rate" value="3200"/><!--MB/S-->
<param name="llc_line_length" value="64"/><!--B-->
<param name="number_mcs" value="4"/>
<!-- current McPAT only supports homogeneous memory controllers -->
<param name="memory_channels_per_mc" value="1"/>
<param name="number_ranks" value="2"/>
<!-- # of ranks of each channel-->
<param name="req_window_size_per_channel" value="32"/>
<param name="IO_buffer_size_per_channel" value="32"/>
<param name="databus_width" value="128"/>
<param name="addressbus_width" value="51"/>
<!-- McPAT will add the control bus width to the addressbus width automatically -->
<stat name="memory_accesses" value="33333"/>
<stat name="memory_reads" value="16667"/>
<stat name="memory_writes" value="16667"/>
<!-- McPAT does not track individual mc, instead, it takes the total accesses and calculate
the average power per MC or per channel. This is sufficent for most application.
Further trackdown can be easily added in later versions. -->
</component>
<!--**********************************************************************-->
</component>
</component>
|
About This Video
Episode 8
699 votes
“Trick Play”
Targeted by a “hacker hunter,” Enokida is forced to run from place to place in Hakata. Assassins after the bounty on his
head are steadily closing in, and Enokida has been cut off from using computers, his only weapon. He’s fallen into a desperate situation. Meanwhile, Banba receives a message from Enokida. It’s a desperate counter to the cyberterrorist cell which came to Banba and Lin. ...more |
Conservation and reiteration of a kinase cascade.
A cascade of three protein kinases has emerged as a conserved functional module in a wide variety of signal transduction pathways in diverse organisms. In addition to this evolutionary conservation, studies in yeast demonstrate that versions of this module are used in different signalling pathways. Thus, homologous kinase cascades function in response to different stimuli in the same cell. |
Q:
Passing custom flags to "open" in a device driver
I need to pass some custom flags to the open() call of my device driver.
I found this example in LDD3:
int dev_open(struct inode *inode, struct file *filp)
{
if ((filp->f_flags & O_ACCMODE) == O_WRONLY) {
...
}
}
My question is: is it possibile to define other flags (like O_ACCMODE and O_WRONLY) without conflicts with any others?
A:
Yes, it's possible. Take a look at include/uapi/asm-generic/fcntl.h. Pay attention to next comment:
/*
* When introducing new O_* bits, please check its uniqueness in fcntl_init().
*/
Now look into fcntl_init() function (defined at fs/fcntl.c):
/*
* Please add new bits here to ensure allocation uniqueness.
* Exceptions: O_NONBLOCK is a two bit define on parisc; O_NDELAY
* is defined as O_NONBLOCK on some platforms and not on others.
*/
BUILD_BUG_ON(20 - 1 /* for O_RDONLY being 0 */ != HWEIGHT32(
O_RDONLY | O_WRONLY | O_RDWR |
O_CREAT | O_EXCL | O_NOCTTY |
O_TRUNC | O_APPEND | /* O_NONBLOCK | */
__O_SYNC | O_DSYNC | FASYNC |
O_DIRECT | O_LARGEFILE | O_DIRECTORY |
O_NOFOLLOW | O_NOATIME | O_CLOEXEC |
__FMODE_EXEC | O_PATH | __O_TMPFILE
));
So first you need to find unique value for your new definition, so it can be bitwise-or'd with flags listed in fcntl_init(). Next you need to add your new definition to include/uapi/asm-generic/fcntl.h. And finally add your new define to fcntl_init(), so it will be checked at compile time.
In the end it boils down to finding the value that doesn't conflict with existing definitions. E.g. as I can see all 10, 100, 1000, 10000, 100000, 1000000 and 10000000 are used. So for your new flags you can use 100000000, 200000000, 400000000 and 800000000 values.
UPDATE: As SailorCaire correctly mentioned, you also need to increment first number in BUILD_BUG_ON() macro. For example, if it originally was BUILD_BUG_ON(20 - 1, and you are to add one element to this list, you should make it BUILD_BUG_ON(21 - 1.
UPDATE 2: Another valuable addition from SailorCaire:
By the way, you'll need to do make install_headers, copy the new headers, and it looks like you'll need to recompile glibc so it becomes aware of the API change.
|
log.level=${log.level}
log.path=${log.path}
dubbo.registry.address=${dubbo.registry.address}
dubbo.protocal.port=${dubbo.protocal.port}
dubbo.service.version=${dubbo.service.version}
ws.connect.path=${ws.connect.path}
ws.connect.port=${ws.connect.port}
ws.connect.bus.port=${ws.connect.bus.port}
service.name=ws_server
service.version=1.0
service.bus.name=bus_ws_server
service.bus.version=1.0
consul.host=${consul.host}
consul.port=${consul.port} |
Significance of early tubular extraction in the first minute of Tc-99m MAG3 renal transplant scintigraphy.
Renal transplant perfusion curves obtained using Tc-99m MAG3 differ from those with Tc-99m DTPA. The perfusion curve can be divided into a first phase (up to the first-pass peak) and a second phase (the curve after the initial peak). The second phase of the MAG3 perfusion curve is usually ascending in contrast to the descending Tc-99m DTPA curve. This ascending MAG3 curve reflects early tubular extraction of MAG3. However, the second phase of the MAG3 curve is sometimes flat or descending. We hypothesized that a flat or descending curve reflects poor early tubular extraction and therefore graft dysfunction. Ninety-two studies of 59' renal transplant patients were retrospectively reviewed. The second phase of the perfusion curve was visually classified as ascending, flat, or descending. 77.2% of studies had ascending curves, 16.3% flat curves, and 6.5% descending curves. A descending curve had a positive predictive value (PPV) of 100% for medical graft dysfunction, while a flat curve had a PPV of 93.3%. A nonascending second phase curve was specific (96.4%) but not sensitive (33.9%) for graft dysfunction. Patients with acute tubular necrosis were not significantly more likely to have a nonascending curve than those with acute rejection. There was no significant difference in creatinine level between patients with medical graft dysfunction and ascending vs. nonascending curves. A nonascending second phase Tc-99m MAG3 perfusion curve is predictive for graft dysfunction. An ascending curve is nonspecific and can be seen in both normally and poorly functioning grafts. |
/*
* Copyright (c) 2017, 2019, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*
*/
#include "precompiled.hpp"
#include "jfr/recorder/checkpoint/types/jfrTypeSetUtils.hpp"
#include "oops/instanceKlass.hpp"
#include "oops/oop.inline.hpp"
#include "oops/symbol.hpp"
static JfrSymbolId::CStringEntry* bootstrap = NULL;
JfrSymbolId::JfrSymbolId() :
_sym_table(new SymbolTable(this)),
_cstring_table(new CStringTable(this)),
_sym_list(NULL),
_cstring_list(NULL),
_sym_query(NULL),
_cstring_query(NULL),
_symbol_id_counter(1),
_class_unload(false) {
assert(_sym_table != NULL, "invariant");
assert(_cstring_table != NULL, "invariant");
bootstrap = new CStringEntry(0, (const char*)&BOOTSTRAP_LOADER_NAME);
assert(bootstrap != NULL, "invariant");
bootstrap->set_id(1);
_cstring_list = bootstrap;
}
JfrSymbolId::~JfrSymbolId() {
clear();
delete _sym_table;
delete _cstring_table;
delete bootstrap;
}
void JfrSymbolId::clear() {
assert(_sym_table != NULL, "invariant");
if (_sym_table->has_entries()) {
_sym_table->clear_entries();
}
assert(!_sym_table->has_entries(), "invariant");
assert(_cstring_table != NULL, "invariant");
if (_cstring_table->has_entries()) {
_cstring_table->clear_entries();
}
assert(!_cstring_table->has_entries(), "invariant");
_sym_list = NULL;
_symbol_id_counter = 1;
_sym_query = NULL;
_cstring_query = NULL;
assert(bootstrap != NULL, "invariant");
bootstrap->reset();
_cstring_list = bootstrap;
}
void JfrSymbolId::set_class_unload(bool class_unload) {
_class_unload = class_unload;
}
void JfrSymbolId::on_link(const SymbolEntry* entry) {
assert(entry != NULL, "invariant");
const_cast<Symbol*>(entry->literal())->increment_refcount();
assert(entry->id() == 0, "invariant");
entry->set_id(++_symbol_id_counter);
entry->set_list_next(_sym_list);
_sym_list = entry;
}
bool JfrSymbolId::on_equals(uintptr_t hash, const SymbolEntry* entry) {
assert(entry != NULL, "invariant");
assert(entry->hash() == hash, "invariant");
assert(_sym_query != NULL, "invariant");
return _sym_query == entry->literal();
}
void JfrSymbolId::on_unlink(const SymbolEntry* entry) {
assert(entry != NULL, "invariant");
const_cast<Symbol*>(entry->literal())->decrement_refcount();
}
static const char* resource_to_cstring(const char* resource_str) {
assert(resource_str != NULL, "invariant");
const size_t length = strlen(resource_str);
char* const c_string = JfrCHeapObj::new_array<char>(length + 1);
assert(c_string != NULL, "invariant");
strncpy(c_string, resource_str, length + 1);
return c_string;
}
void JfrSymbolId::on_link(const CStringEntry* entry) {
assert(entry != NULL, "invariant");
assert(entry->id() == 0, "invariant");
entry->set_id(++_symbol_id_counter);
const_cast<CStringEntry*>(entry)->set_literal(resource_to_cstring(entry->literal()));
entry->set_list_next(_cstring_list);
_cstring_list = entry;
}
static bool string_compare(const char* query, const char* candidate) {
assert(query != NULL, "invariant");
assert(candidate != NULL, "invariant");
const size_t length = strlen(query);
return strncmp(query, candidate, length) == 0;
}
bool JfrSymbolId::on_equals(uintptr_t hash, const CStringEntry* entry) {
assert(entry != NULL, "invariant");
assert(entry->hash() == hash, "invariant");
assert(_cstring_query != NULL, "invariant");
return string_compare(_cstring_query, entry->literal());
}
void JfrSymbolId::on_unlink(const CStringEntry* entry) {
assert(entry != NULL, "invariant");
JfrCHeapObj::free(const_cast<char*>(entry->literal()), strlen(entry->literal() + 1));
}
traceid JfrSymbolId::bootstrap_name(bool leakp) {
assert(bootstrap != NULL, "invariant");
if (leakp) {
bootstrap->set_leakp();
}
return 1;
}
traceid JfrSymbolId::mark(const Symbol* symbol, bool leakp) {
assert(symbol != NULL, "invariant");
return mark((uintptr_t)symbol->identity_hash(), symbol, leakp);
}
traceid JfrSymbolId::mark(uintptr_t hash, const Symbol* data, bool leakp) {
assert(data != NULL, "invariant");
assert(_sym_table != NULL, "invariant");
_sym_query = data;
const SymbolEntry& entry = _sym_table->lookup_put(hash, data);
if (_class_unload) {
entry.set_unloading();
}
if (leakp) {
entry.set_leakp();
}
return entry.id();
}
traceid JfrSymbolId::mark(uintptr_t hash, const char* str, bool leakp) {
assert(str != NULL, "invariant");
assert(_cstring_table != NULL, "invariant");
_cstring_query = str;
const CStringEntry& entry = _cstring_table->lookup_put(hash, str);
if (_class_unload) {
entry.set_unloading();
}
if (leakp) {
entry.set_leakp();
}
return entry.id();
}
/*
* jsr292 anonymous classes symbol is the external name +
* the identity_hashcode slash appended:
* java.lang.invoke.LambdaForm$BMH/22626602
*
* caller needs ResourceMark
*/
uintptr_t JfrSymbolId::unsafe_anonymous_klass_name_hash(const InstanceKlass* ik) {
assert(ik != NULL, "invariant");
assert(ik->is_anonymous(), "invariant");
const oop mirror = ik->java_mirror_no_keepalive();
assert(mirror != NULL, "invariant");
return (uintptr_t)mirror->identity_hash();
}
static const char* create_unsafe_anonymous_klass_symbol(const InstanceKlass* ik, uintptr_t hash) {
assert(ik != NULL, "invariant");
assert(ik->is_anonymous(), "invariant");
assert(hash != 0, "invariant");
char* anonymous_symbol = NULL;
const oop mirror = ik->java_mirror_no_keepalive();
assert(mirror != NULL, "invariant");
char hash_buf[40];
sprintf(hash_buf, "/" UINTX_FORMAT, hash);
const size_t hash_len = strlen(hash_buf);
const size_t result_len = ik->name()->utf8_length();
anonymous_symbol = NEW_RESOURCE_ARRAY(char, result_len + hash_len + 1);
ik->name()->as_klass_external_name(anonymous_symbol, (int)result_len + 1);
assert(strlen(anonymous_symbol) == result_len, "invariant");
strcpy(anonymous_symbol + result_len, hash_buf);
assert(strlen(anonymous_symbol) == result_len + hash_len, "invariant");
return anonymous_symbol;
}
bool JfrSymbolId::is_unsafe_anonymous_klass(const Klass* k) {
assert(k != NULL, "invariant");
return k->is_instance_klass() && ((const InstanceKlass*)k)->is_anonymous();
}
traceid JfrSymbolId::mark_unsafe_anonymous_klass_name(const InstanceKlass* ik, bool leakp) {
assert(ik != NULL, "invariant");
assert(ik->is_anonymous(), "invariant");
const uintptr_t hash = unsafe_anonymous_klass_name_hash(ik);
const char* const anonymous_klass_symbol = create_unsafe_anonymous_klass_symbol(ik, hash);
return mark(hash, anonymous_klass_symbol, leakp);
}
traceid JfrSymbolId::mark(const Klass* k, bool leakp) {
assert(k != NULL, "invariant");
traceid symbol_id = 0;
if (is_unsafe_anonymous_klass(k)) {
assert(k->is_instance_klass(), "invariant");
symbol_id = mark_unsafe_anonymous_klass_name((const InstanceKlass*)k, leakp);
}
if (0 == symbol_id) {
Symbol* const sym = k->name();
if (sym != NULL) {
symbol_id = mark(sym, leakp);
}
}
assert(symbol_id > 0, "a symbol handler must mark the symbol for writing");
return symbol_id;
}
JfrArtifactSet::JfrArtifactSet(bool class_unload) : _symbol_id(new JfrSymbolId()),
_klass_list(NULL),
_total_count(0) {
initialize(class_unload);
assert(_klass_list != NULL, "invariant");
}
static const size_t initial_class_list_size = 200;
void JfrArtifactSet::initialize(bool class_unload, bool clear /* false */) {
assert(_symbol_id != NULL, "invariant");
if (clear) {
_symbol_id->clear();
}
_symbol_id->set_class_unload(class_unload);
_total_count = 0;
// resource allocation
_klass_list = new GrowableArray<const Klass*>(initial_class_list_size, false, mtTracing);
}
JfrArtifactSet::~JfrArtifactSet() {
_symbol_id->clear();
delete _symbol_id;
// _klass_list will be cleared by a ResourceMark
}
traceid JfrArtifactSet::bootstrap_name(bool leakp) {
return _symbol_id->bootstrap_name(leakp);
}
traceid JfrArtifactSet::mark_unsafe_anonymous_klass_name(const Klass* klass, bool leakp) {
assert(klass->is_instance_klass(), "invariant");
return _symbol_id->mark_unsafe_anonymous_klass_name((const InstanceKlass*)klass, leakp);
}
traceid JfrArtifactSet::mark(uintptr_t hash, const Symbol* sym, bool leakp) {
return _symbol_id->mark(hash, sym, leakp);
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traceid JfrArtifactSet::mark(const Klass* klass, bool leakp) {
return _symbol_id->mark(klass, leakp);
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traceid JfrArtifactSet::mark(const Symbol* symbol, bool leakp) {
return _symbol_id->mark(symbol, leakp);
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traceid JfrArtifactSet::mark(uintptr_t hash, const char* const str, bool leakp) {
return _symbol_id->mark(hash, str, leakp);
}
bool JfrArtifactSet::has_klass_entries() const {
return _klass_list->is_nonempty();
}
int JfrArtifactSet::entries() const {
return _klass_list->length();
}
void JfrArtifactSet::register_klass(const Klass* k) {
assert(k != NULL, "invariant");
assert(_klass_list != NULL, "invariant");
assert(_klass_list->find(k) == -1, "invariant");
_klass_list->append(k);
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size_t JfrArtifactSet::total_count() const {
return _total_count;
}
|
goog.module('nested.exported.enums');
/** @const */
exports = {
/** @const @enum {string} */
A: {
A1: 'a1',
},
// The structure of the AST changes if this extra property is present.
B: 0,
}; |
---
abstract: 'Unprecedentedly precise cosmic microwave background (CMB) data are expected from ongoing and near-future CMB Stage-III and IV surveys, which will yield reconstructed CMB lensing maps with effective resolution approaching several arcminutes. The small-scale CMB lensing fluctuations receive non-negligible contributions from nonlinear structure in the late-time density field. These fluctuations are not fully characterized by traditional two-point statistics, such as the power spectrum. Here, we use $N$-body ray-tracing simulations of CMB lensing maps to examine two higher-order statistics: the lensing convergence one-point probability distribution function (PDF) and peak counts. We show that these statistics contain significant information not captured by the two-point function, and provide specific forecasts for the ongoing Stage-III Advanced Atacama Cosmology Telescope (AdvACT) experiment. Considering only the temperature-based reconstruction estimator, we forecast 9$\sigma$ (PDF) and 6$\sigma$ (peaks) detections of these statistics with AdvACT. Our simulation pipeline fully accounts for the non-Gaussianity of the lensing reconstruction noise, which is significant and cannot be neglected. Combining the power spectrum, PDF, and peak counts for AdvACT will tighten cosmological constraints in the $\Omega_m$-$\sigma_8$ plane by $\approx 30\%$, compared to using the power spectrum alone.'
author:
- 'Jia Liu$^{1,2}$'
- 'J. Colin Hill$^{2}$'
- 'Blake D. Sherwin$^{3}$'
- 'Andrea Petri$^{4}$'
- 'Vanessa Böhm$^{5}$'
- 'Zoltán Haiman$^{2,6}$'
bibliography:
- 'paper.bib'
title: 'CMB Lensing Beyond the Power Spectrum: Cosmological Constraints from the One-Point PDF and Peak Counts'
---
Introduction {#sec:intro}
============
After its first detection in cross-correlation nearly a decade ago [@Smith2007; @Hirata2008] and subsequent detection in auto-correlation five years ago [@das2011; @sherwin2011], weak gravitational lensing of the cosmic microwave background (CMB) is now reaching maturity as a cosmological probe [@Hanson2013; @Das2013; @PolarBear2014a; @PolarBear2014b; @BICEPKeck2016; @Story2014; @Ade2014; @vanEngelen2014; @vanEngelen2015; @planck2015xv]. On their way to the Earth, CMB photons emitted at redshift $z=1100$ are deflected by the intervening matter, producing new correlations in maps of CMB temperature and polarization anisotropies. Estimators based on these correlations can be applied to the observed anisotropy maps to reconstruct a noisy estimate of the CMB lensing potential [@Zaldarriaga1998; @Zaldarriaga1999; @HuOkamoto2002; @Okamoto2003]. CMB lensing can probe fundamental physical quantities, such as the dark energy equation of state and neutrino masses, through its sensitivity to the geometry of the universe and the growth of structure (see Refs. [@Lewis2006; @Hanson2010] for a review).
In this paper, we study the non-Gaussian information stored in CMB lensing observations. The Gaussian approximation to the density field breaks down due to nonlinear evolution on small scales at late times. Thus, non-Gaussian statistics (i.e., statistics beyond the power spectrum) are necessary to capture the full information in the density field. Such work has been previously performed (theoretically and observationally) on weak gravitational lensing of galaxies, where galaxy shapes, instead of CMB temperature/polarization patterns, are distorted (hereafter “galaxy lensing”). Several research groups have found independently that non-Gaussian statistics can tighten cosmological constraints when they are combined with the two-point correlation function or angular power spectrum.[^1] Such non-Gaussian statistics have also been applied in the CMB context to the Sunyaev-Zel’dovich signal, including higher-order moments [@Wilson2012; @Hill2013; @Planck2013tSZ; @Planck2015tSZ], the bispectrum [@Bhattacharya2012; @Crawford2014; @Planck2013tSZ; @Planck2015tSZ], and the one-point probability distribution function (PDF) [@Hill2014b; @Planck2013tSZ; @Planck2015tSZ]. In all cases, substantial non-Gaussian information was found, yielding improved cosmological constraints.
The motivation to study non-Gaussian statistics of CMB lensing maps is three-fold. First, the CMB lensing kernel is sensitive to structures at high redshift ($z\approx2.0$, compared to $z\approx0.4$ for typical galaxy lensing samples); hence CMB lensing non-Gaussian statistics probe early nonlinearity that is beyond the reach of galaxy surveys. Second, CMB lensing does not suffer from some challenging systematics that are relevant to galaxy lensing, including intrinsic alignments of galaxies, photometric redshift uncertainties, and shape measurement biases. Therefore, a combined analysis of galaxy lensing and CMB lensing will be useful to build a tomographic outlook on nonlinear structure evolution, as well as to calibrate systematics in both galaxy and CMB lensing surveys [@Liu2016; @Baxter2016; @Schaan2016; @Singh2016; @Nicola2016]. Finally, CMB lensing measurements have recently entered a regime of sufficient sensitivity and resolution to detect the (stacked) lensing signals of halos [@Madhavacheril2014; @Baxter2016; @Planck2015cluster]. This suggests that statistics sensitive to the nonlinear growth of structure, i.e., non-Gaussian statistics, will also soon be detectable. We demonstrate below that this is indeed the case, taking as a reference experiment the ongoing Advanced Atacama Cosmology Telescope (AdvACT) survey [@Henderson2016].
Non-Gaussian aspects of the CMB lensing field have recently attracted attention, both as a potential signal and a source of bias in CMB lensing power spectrum estimates. Considering the lensing non-Gaussianity as a signal, a recent analytical study of the CMB lensing bispectrum by Ref. [@Namikawa2016] forecasted its detectability to be 40$\sigma$ with a CMB Stage-IV experiment. Ref. [@Bohm2016] performed the first calculation of the bias induced in CMB lensing power spectrum estimates by the lensing bispectrum, finding non-negligible biases for Stage-III and IV CMB experiments. Refs. [@Pratten2016] and [@Marozzi2016] considered CMB lensing effects arising from the breakdown of the Born approximation, with the former study finding that post-Born terms substantially alter the predicted CMB lensing bispectrum, compared to the contributions from nonlinear structure formation alone. We emphasize that the $N$-body ray-tracing simulations used in this work naturally capture such effects — we do not use the Born approximation. However, we consider only the lensing potential $\phi$ or convergence $\kappa$ here (related by $\kappa = -\nabla^2 \phi/2$), leaving a treatment of the curl potential or image rotation for future work (Ref. [@Pratten2016] has demonstrated that the curl potential possesses non-trivial higher-order statistics). In a follow-up paper, the simulations described here are used to more precisely characterize CMB lensing power spectrum biases arising from the bispectrum and higher-order correlations [@Sherwin2016].
We consider the non-Gaussianity in the CMB lensing field as a potential signal. We use a suite of 46 $N$-body ray-tracing simulations to investigate two non-Gaussian statistics applied to CMB lensing convergence maps — the one-point PDF and peak counts. We examine the deviation of the convergence PDF and peak counts from those of Gaussian random fields. We then quantify the power of these statistics to constrain cosmological models, compared with using the power spectrum alone.
The paper is structured as follows. We first introduce CMB lensing in Sec. \[sec:formalism\]. We then describe our simulation pipeline in Sec. \[sec:sim\] and analysis procedures in Sec. \[sec:analysis\]. We show our results for the power spectrum, PDF, peak counts, and the derived cosmological constraints in Sec. \[sec:results\]. We conclude in Sec. \[sec:conclude\].
CMB lensing formalism {#sec:formalism}
=====================
To lowest order, the lensing convergence ($\kappa$) is a weighted projection of the three-dimensional matter overdensity $\delta=\delta\rho/\bar{\rho}$ along the line of sight,
$$\label{eq.kappadef}
\kappa(\thetaB) = \int_0^{\infty} dz W(z) \delta(\chi(z)\thetaB, z),$$
where $\chi(z)$ is the comoving distance and the kernel $W(z)$ indicates the lensing strength at redshift $z$ for sources with a redshift distribution $p(z_s)=dn(z_s)/dz$. For CMB lensing, there is only one source plane at the last scattering surface $z_\star=1100$; therefore, $p(z_s)=\delta_D(z_s-z_\star)$, where $\delta_D$ is the Dirac delta function. For a flat universe, the CMB lensing kernel is
$$\begin{aligned}
W^{{\kappa_{\rm cmb}}}(z) &=& \frac{3}{2}\Omega_{m}H_0^2 \frac{(1+z)}{H(z)} \frac{\chi(z)}{c} \nonumber\\
&\times& \frac{\chi(z_\star)-\chi(z)}{\chi(z_\star)}.\end{aligned}$$
where $\Omega_{m}$ is the matter density as a fraction of the critical density at $z=0$, $H(z)$ is the Hubble parameter at redshift $z$, with a present-day value $H_0$, and $c$ is the speed of light. $W^{{\kappa_{\rm cmb}}}(z)$ peaks at $z\approx2$ for canonical cosmological parameters ($\Omega_{m}\approx0.3$ and $H_0\approx70$ km/s/Mpc, [@planck2015xiii]). Note that Eq. (\[eq.kappadef\]) assumes the Born approximation, but our simulation approach described below does not — we implement full ray-tracing to calculate $\kappa$.
Simulations {#sec:sim}
===========
Our simulation procedure includes five main steps: (1) the design (parameter sampling) of cosmological models, (2) $N$-body simulations with Gadget-2,[^2] (3) ray-tracing from $z=0$ to $z=1100$ to obtain (noiseless) convergence maps using the Python code LensTools [@Petri2016],[^3] (4) lensing simulated CMB temperature maps by the ray-traced convergence field, and (5) reconstructing (noisy) convergence maps from the CMB temperature maps after including noise and beam effects.
Simulation design
-----------------
We use an irregular grid to sample parameters in the $\Omega_m$-$\sigma_8$ plane, within the range of $\Omega_m \in [0.15, 0.7]$ and $\sigma_8 \in [0.5, 1.0]$, where $\sigma_8$ is the rms amplitude of linear density fluctuations on a scale of 8 Mpc/$h$ at $z=0$. An optimized irregular grid has a smaller average distance between neighboring points than a regular grid, and no parameters are duplicated. Hence, it samples the parameter space more efficiently. The procedure to optimize our sampling is described in detail in Ref. [@Petri2015].
The 46 cosmological models sampled are shown in Fig. \[fig:design\]. Other cosmological parameters are held fixed, with $H_0=72$ km/s/Mpc, dark energy equation of state $w=-1$, spectral index $n_s=0.96$, and baryon density $\Omega_b=0.046$. The design can be improved in the future by posterior sampling, where we first run only a few models to generate a low-resolution probability plane, and then sample more densely in the high-probability region.
We select the model that is closest to the standard concordance values of the cosmological parameters (e.g., [@planck2015xiii]) as our fiducial model, with $\Omega_m=0.296$ and $\sigma_8=0.786$. We create two sets of realizations for this model, one for covariance matrix estimation, and another one for parameter interpolation. This fiducial model is circled in red in Fig. \[fig:design\].
![\[fig:design\] The design of cosmological parameters used in our simulations (46 models in total). The fiducial cosmology ($\Omega_m=0.296, \sigma_8=0.786$) is circled in red. The models for which AdvACT-like lensing reconstruction is performed are circled in blue. Other cosmological parameters are fixed at $H_0=72$ km/s/Mpc, $w=-1$, $n_s=0.96$, and $\Omega_b=0.046$.](plot/plot_design.pdf){width="48.00000%"}
$N$-body simulation and ray-tracing {#sec:nbody}
-----------------------------------
We use the public code Gadget-2 to run $N$-body simulations with $N_{\rm particles}=1024^3$ and box size = 600 Mpc/$h$ (corresponding to a mass resolution of $1.4\times10^{10} M_\odot/h$). To initialize each simulation, we first obtain the linear matter power spectrum with the Einstein-Boltzmann code CAMB.[^4] The power spectrum is then fed into the initial condition generator N-GenIC, which generates initial snapshots (the input of Gadget-2) of particle positions at $z=100$. The $N$-body simulation is then run from $z=100$ to $z=0$, and we record snapshots at every 144 Mpc$/h$ in comoving distance between $z\approx45$ and $z=0$. The choice of $z\approx45$ is determined by requiring that the redshift range covers 99% of the $W^{\kappa_{cmb}}D(z)$ kernel, where we use the linear growth factor $D(z)\sim 1/(1+z)$.
We then use the Python code LensTools [@Petri2016] to generate CMB lensing convergence maps. We first slice the simulation boxes to create potential planes (3 planes per box, 200 Mpc/$h$ in thickness), where particle density is converted into gravitational potential using the Poisson equation. We track the trajectories of 4096$^2$ light rays from $z=0$ to $z=1100$, where the deflection angle and convergence are calculated at each potential plane. This procedure automatically captures so-called “post-Born” effects, as we never assume that the deflection angle is small or that the light rays follow unperturbed geodesics.[^5] Finally, we create 1,000 convergence map realizations for each cosmology by randomly rotating/shifting the potential planes [@Petri2016b]. For the fiducial cosmology only, we generate 10,000 realizations for the purpose of estimating the covariance matrix. The convergence maps are 2048$^2$ pixels and 12.25 deg$^2$ in size, with square pixels of side length 0.1025 arcmin. The maps generated at this step correspond to the physical lensing convergence field only, i.e., they have no noise from CMB lensing reconstruction. Therefore, they are labeled as “noiseless” in the following sections and figures.
![\[fig:theory\_ps\] Comparison of the CMB lensing convergence power spectrum from the HaloFit model and that from our simulation (1024$^3$ particles, box size 600 Mpc/$h$, map size 12.25 deg$^2$), for our fiducial cosmology. We also show the prediction from linear theory. Error bars are the standard deviation of 10,000 realizations.](plot/plot_theory_comparison.pdf){width="48.00000%"}
We test the power spectra from our simulated maps against standard theoretical predictions. Fig. \[fig:theory\_ps\] shows the power spectrum from our simulated maps versus that from the HaloFit model [@Smith2003; @Takahashi2012] for our fiducial cosmology. We also show the linear-theory prediction, which deviates from the nonlinear HaloFit result at $\ell \gtrsim 700$. The simulation error bars are estimated using the standard deviation of 10,000 realizations. The simulated and (nonlinear) theoretical results are consistent within the error bars for multipoles $\ell<2,000$, which is sufficient for this work, as current and near-future CMB lensing surveys are limited to roughly this $\ell$ range due to their beam size and noise level (the filtering applied in our analysis below effectively removes all information on smaller angular scales). We find similar consistency between theory and simulation for the other 45 simulated models. We test the impact of particle resolution using a smaller box of 300 Mpc/$h$, while keeping the same number of particles (i.e. 8 times higher resolution), and obtain excellent agreement at scales up to $\ell=3,000$. The lack of power on large angular scales is due to the limited size of our convergence maps, while the missing power on small scales is due to our particle resolution. On very small scales ($\ell \gtrsim 5 \times 10^4$), excess power due to finite-pixelization shot noise arises, but this effect is negligible on the scales considered in our analysis.
CMB lensing reconstruction {#sec:recon}
--------------------------
{width="\textwidth"}
In order to obtain CMB lensing convergence maps with realistic noise properties, we generate lensed CMB temperature maps and reconstruct noisy estimates of the convergence field. First, we generate Gaussian random field CMB temperature maps based on a $\Lambda$CDM concordance model temperature power spectrum computed with CAMB. We compute deflection field maps from the ray-traced convergence maps described in the previous sub-section, after applying a filter that removes power in the convergence maps above $
\ell \approx 4,000$.[^6] These deflection maps are then used to lens the simulated primary CMB temperature maps. The lensing simulation procedure is described in detail in Ref. [@Louis2013].
After obtaining the lensed temperature maps, we apply instrumental effects consistent with specifications for the ongoing AdvACT survey [@Henderson2016]. In particular, the maps are smoothed with a FWHM $=1.4$ arcmin beam, and Gaussian white noise of amplitude 6$\mu$K-arcmin is then added.
We subsequently perform lensing reconstruction on these beam-convolved, noisy temperature maps using the quadratic estimator of Ref. [@HuOkamoto2002], but with the replacement of unlensed with lensed CMB temperature power spectra in the filters, which gives an unbiased reconstruction to higher order [@Hanson2010]. The final result is a noisy estimate of the CMB lensing convergence field, with 1,000 realizations for each cosmological model (10,000 for the fiducial model).
We consider only temperature-based reconstruction in this work, leaving polarization estimators for future consideration. The temperature estimator is still expected to contribute more significantly than the polarization to the signal-to-noise for Stage-III CMB experiments like AdvACT, but polarization will dominate for Stage-IV (via $EB$ reconstruction). For the AdvACT-like experiment considered here, including polarization would increase the predicted signal-to-noise on the lensing power spectrum by $\approx 35$%. More importantly, polarization reconstruction allows the lensing field to be mapped out to smaller scales than temperature reconstruction [@HuOkamoto2002], and is more immune to foreground-related biases at high-$\ell$ [@vanEngelen2014b]. Thus, it could prove extremely useful for higher-order CMB lensing statistics, which are sourced by non-Gaussian structure on small scales. Clearly these points are worthy of future analysis, but we restrict this work to temperature reconstruction for simplicity.
In addition to the fiducial model, we select the nearest eight points in the sampled parameter space (points circled in blue in Fig. \[fig:design\]) for the reconstruction analysis. We determine this selection by first reconstructing the nearest models in parameter space, and then broadening the sampled points until the interpolation is stable and the forecasted contours (see Sec. \[sec:constraints\]) are converged for AdvACT-level noise. At this noise level, the other points in model space are sufficiently distant to contribute negligibly to the forecasted contours. In total, nine models are used to derive parameter constraints from the reconstructed, noisy maps. For completeness, we perform a similar convergence test using forecasted constraints from the noiseless maps, finding excellent agreement between contours derived using all 46 models and using only these nine models.
In Fig. \[fig:sample\_maps\], we show an example of a convergence map from the fiducial cosmology before (“noiseless”) and after (“noisy”) reconstruction. Prominent structures seen in the noiseless maps remain obvious in the reconstructed, noisy maps.
Gaussian random field
---------------------
We also reconstruct a set of Gaussian random fields (GRF) in the fiducial model. We generate a set of GRFs using the average power spectrum of the noiseless $\kappa$ maps. We then lens simulated CMB maps using these GRFs, following the same procedure as outlined above, and subsequently perform lensing reconstruction, just as for the reconstructed $N$-body $\kappa$ maps. These noisy GRF-only reconstructions allow us to examine the effect of reconstruction (in particular the non-Gaussianity of the reconstruction noise itself), as well as to determine the level of non-Gaussianity in the noisy $\kappa$ maps.
Interpolation
-------------
![\[fig:interp\] Fractional differences between interpolated and “true” results for the fiducial power spectrum (top), PDF (middle), and peak counts (bottom). Here, we have built the interpolator using results for the other 45 cosmologies, and then compared the interpolated prediction at the fiducial parameter values to the actual simulated results for the fiducial cosmology. The error bars are scaled by $1/\sqrt{N_{\rm sims}}$, where the number of simulations $N_{\rm sims}=1,000$. The agreement for all three statistics is excellent.](plot/plot_interp.pdf){width="48.00000%"}
To build a model at points where we do not have simulations, we interpolate from the simulated points in parameter space using the Clough-Tocher interpolation scheme [@alfeld1984; @farin1986], which triangulates the input points and then minimizes the curvature of the interpolating surface; the interpolated points are guaranteed to be continuously differentiable. In Fig. \[fig:interp\], we show a test of the interpolation using the noiseless $\kappa$ maps: we build the interpolator using all of the simulated cosmologies except for the fiducial model (i.e., 45 cosmologies), and then compare the interpolated results at the fiducial parameter values with the true, simulated results for that cosmology. The agreement for all three statistics is excellent, with deviations $\lesssim$ few percent (and well within the statistical precision). Finally, to check the robustness of the interpolation scheme, we also run our analysis using linear interpolation, and obtain consistent results.[^7]
Analysis {#sec:analysis}
========
In this section, we describe the analysis of the simulated CMB lensing maps, including the computation of the power spectrum, peak counts, and PDF, and the likelihood estimation for cosmological parameters. These procedures are applied in the same way to the noiseless and noisy (reconstructed) maps.
Power spectrum, PDF, and peak counts
------------------------------------
To compute the power spectrum, we first estimate the two-dimensional (2D) power spectrum of CMB lensing maps ($M_{\kappa}$) using $$\begin{aligned}
\label{eq: ps2d}
C^{\kappa \kappa}(\ellB) = \hat M_{\kappa}(\ellB)^*\hat M_{\kappa}(\ellB) \,,\end{aligned}$$ where $\ellB$ is the 2D multipole with components $\ell_1$ and $\ell_2$, $\hat M_{\kappa}$ is the Fourier transform of $M_{\kappa}$, and the asterisk denotes complex conjugation. We then average over all the pixels within each $|\ellB|\in[\ell-\Delta\ell, \ell+\Delta\ell)$ bin, for 20 log-spaced bins in the range of $100<\ell<2,000$, to obtain the one-dimensional power spectrum.
The one-point PDF is the number of pixels with values between \[$\kappa-\Delta\kappa$, $\kappa+\Delta\kappa$) as a function of $\kappa$. We use 50 linear bins with edges listed in Table \[tab: bins\], and normalize the resulting PDF such that its integral is unity. The PDF is a simple observable (a histogram of the data), but captures the amplitude of all (zero-lag) higher-order moments in the map. Thus, it provides a potentially powerful characterization of the non-Gaussian information.
Peaks are defined as local maxima in a $\kappa$ map. In a pixelized map, they are pixels with values higher than the surrounding 8 (square) pixels. Similar to cluster counts, peak counts are sensitive to the most nonlinear structures in the Universe. For galaxy lensing, they have been found to associate with halos along the line of sight both with simulations [@Yang2011] and observations [@LiuHaiman2016]. We record peaks on smoothed $\kappa$ maps, in 25 linearly spaced bins with edges listed in Table \[tab: bins\].
----------------------- ------------------ -----------------------
Smoothing scale PDF bins edges Peak counts bin edges
(arcmin) (50 linear bins) (25 linear bins)
0.5 (noiseless) \[-0.50, +0.50\] \[-0.18, +0.36\]
1.0 (noiseless) \[-0.22, +0.22\] \[-0.15, +0.30\]
2.0 (noiseless) \[-0.18, +0.18\] \[-0.12, +0.24\]
5.0 (noiseless) \[-0.10, +0.10\] \[-0.09, +0.18\]
8.0 (noiseless) \[-0.08, +0.08\] \[-0.06, +0.12\]
1.0, 5.0, 8.0 (noisy) \[-0.12, +0.12\] \[-0.06, +0.14\]
----------------------- ------------------ -----------------------
: \[tab: bins\] PDF and peak counts bin edges for each smoothing scale (the full-width-half-maximum of the Gaussian smoothing kernel applied to the maps).
Cosmological constraints
------------------------
We estimate cosmological parameter confidence level (C.L.) contours assuming a constant (cosmology-independent) covariance and Gaussian likelihood, $$\begin{aligned}
P (\DB | \pB) = \frac{1}{2\pi|\CB|^{1/2}} \exp\left[-\frac{1}{2}(\DB-\muB)\CB^{-1}(\DB-\muB)\right],\end{aligned}$$ where $\DB$ is the data array, $\pB$ is the input parameter array, $\muB=\muB(\pB)$ is the interpolated model, and $\CB$ is the covariance matrix estimated using the fiducial cosmology, with determinant $|\CB|$. The correction factor for an unbiased inverse covariance estimator [@dietrich2010] is negligible in our case, with $(N_{\rm sims}-N_{\rm bins}-2)/(N_{\rm sims}-1) = 0.99$ for $N_{\rm sims} =10,000$ and $N_{\rm bins}=95$. We leave an investigation of the impact of cosmology-dependent covariance matrices and a non-Gaussian likelihood for future work.
Due to the limited size of our simulated maps, we must rescale the final error contour by a ratio ($r_{\rm sky}$) of simulated map size (12.25 deg$^2$) to the survey coverage (20,000 deg$^2$ for AdvACT). Two methods allow us to achieve this — rescaling the covariance matrix by $r_{\rm sky}$ before computing the likelihood plane, or rescaling the final C.L. contour by $r_{\rm sky}$. These two methods yield consistent results. In our final analysis, we choose the former method.
Results {#sec:results}
=======
Non-Gaussianity in noiseless maps {#sec:non-gauss}
---------------------------------
{width="48.00000%"} {width="48.00000%"}
{width="48.00000%"} {width="48.00000%"}
We show the PDF of noiseless $N$-body $\kappa$ maps (PDF$^\kappa$) for the fiducial cosmology in Fig. \[fig:noiseless\_PDF\], as well as that of GRF $\kappa$ maps (PDF$^{\rm GRF}$) generated from a power spectrum matching that of the $N$-body-derived maps. To better demonstrate the level of non-Gaussianity, we also show the fractional difference of PDF$^\kappa$ from PDF$^{\rm GRF}$. The error bars are scaled to AdvACT sky coverage (20,000 deg$^2$), though note that no noise is present here.
The departure of PDF$^\kappa$ from the Gaussian case is significant for all smoothing scales examined (FWHM = 0.5–8.0 arcmin), with increasing significance towards smaller smoothing scales, as expected. The excess in high $\kappa$ bins is expected as the result of nonlinear gravitational evolution, echoed by the deficit in low $\kappa$ bins.
We show the comparison of the peak counts of $N$-body $\kappa$ maps (${\rm N}^\kappa_{\rm peaks}$) versus that of GRFs (${\rm N}^{\rm GRF}_{\rm peaks}$) in Fig. \[fig:noiseless\_pk\]. The difference between ${\rm N}^\kappa_{\rm peaks}$ and ${\rm N}^{\rm GRF}_{\rm peaks}$ is less significant than the PDF, because the number of peaks is much smaller than the number of pixels — hence, the peak counts have larger Poisson noise. A similar trend of excess (deficit) of high (low) peaks is also seen in $\kappa$ peaks, when compared to the GRF peaks.
Covariance matrix {#sec:covariance}
-----------------
![\[fig:corr\_mat\] Correlation coefficients determined from the full noiseless (top) and noisy (bottom) covariance matrices. Bins 1-20 are for the power spectrum (labeled “PS”); bins 21-70 are for the PDF; and bins 71-95 are for peak counts.](plot/corr_mat.pdf "fig:"){width="48.00000%"} ![\[fig:corr\_mat\] Correlation coefficients determined from the full noiseless (top) and noisy (bottom) covariance matrices. Bins 1-20 are for the power spectrum (labeled “PS”); bins 21-70 are for the PDF; and bins 71-95 are for peak counts.](plot/corr_mat_noisy.pdf "fig:"){width="48.00000%"}
Fig. \[fig:corr\_mat\] shows the correlation coefficients of the total covariance matrix for both the noiseless and noisy maps, $$\begin{aligned}
\rhoB_{ij} = \frac{\CB_{ij}}{\sqrt{\CB_{ii}\CB_{jj}}}\end{aligned}$$ where $i$ and $j$ denote the bin number, with the first 20 bins for the power spectrum, the next 50 bins for the PDF, and the last 25 bins for peak counts.
In the noiseless case, the power spectrum shows little covariance in both its own off-diagonal terms ($<10\%$) and cross-covariance with the PDF and peaks ($<20\%$), hinting that the PDF and peaks contain independent information that is beyond the power spectrum. In contrast, the PDF and peak statistics show higher correlation in both self-covariance (i.e., the covariance within the sub-matrix for that statistic only) and cross-covariance, with strength almost comparable to the diagonal components. They both show strong correlation between nearby $\kappa$ bins (especially in the moderate-$|\kappa|$ regions), which arises from contributions due to common structures amongst the bins (e.g., galaxy clusters). Both statistics show anti-correlation between positive and negative $\kappa$ bins. The anti-correlation may be due to mass conservation — e.g., large amounts of mass falling into halos would result in large voids in surrounding regions.
In the noisy case, the off-diagonal terms are generally smaller than in the noiseless case. Moreover, the anti-correlation seen previously between the far positive and negative $\kappa$ tails in the PDF is now a weak positive correlation — we attribute this difference to the complex non-Gaussianity of the reconstruction noise. Interestingly, the self-covariance of the peak counts is significantly reduced compared to the noiseless case, while the self-covariance of the PDF persists to a reasonable degree.
Effect of reconstruction noise {#sec:recon_noise}
------------------------------
![\[fig:recon\] We demonstrate the effect of reconstruction noise on the power spectrum (top), the PDF (middle), and peak counts (bottom) by using Gaussian random field $\kappa$ maps (rather than $N$-body-derived maps) as input to the reconstruction pipeline. The noiseless (solid curves) and noisy/reconstructed (dashed curves) statistics are shown. All maps used here have been smoothed with a Gaussian kernel of FWHM $= 8$ arcmin.](plot/plot_reconstruction.pdf){width="48.00000%"}
To disentangle the effect of reconstruction noise from that of nonlinear structure growth, we compare the three statistics before (noiseless) and after (noisy) reconstruction, using only the GRF $\kappa$ fields. Fig. \[fig:recon\] shows the power spectra, PDFs, and peak counts for both the noiseless (solid curves) and noisy (dashed curves) GRFs, all smoothed with a FWHM $= 8$ arcmin Gaussian window. The reconstructed power spectrum has significant noise on small scales, as expected (this is dominated by the usual “$N^{(0)}$” noise bias).
The post-reconstruction PDF shows skewness, defined as $$\label{eq.skewdef}
S=\left\langle
\left( \frac {\kappa-\bar{\kappa}}{\sigma_\kappa}\right)^3 \right\rangle,$$ which is not present in the input GRFs. In other words, the reconstructed maps have a non-zero three-point function, even though the input GRF $\kappa$ maps in this case do not. While this may seem surprising at first, we recall that the three-point function of the reconstructed map corresponds to a six-point function of the CMB temperature map (in the quadratic estimator formalism). Even for a Gaussian random field, the six-point function contains non-zero Wick contractions (those that reduce to products of two-point functions). Propagating such terms into the three-point function of the quadratic estimator for $\kappa$, we find that they do not cancel to zero. This result is precisely analogous to the usual “$N^{(0)}$ bias” on the CMB lensing power spectrum, in which the two-point function of the (Gaussian) primary CMB temperature gives a non-zero contribution to the temperature four-point function. The result in Fig. \[fig:recon\] indicates that the similar PDF “$N^{(0)}$ bias” contains a negative skewness (in addition to non-zero kurtosis and higher moments). While it should be possible to derive this result analytically, we defer the full calculation to future work. If we filter the reconstructed $\kappa$ maps with a large smoothing kernel, the skewness in the reconstructed PDF is significantly decreased (see Fig. \[fig:skew\]). We briefly investigate the PDF of the Planck 2015 CMB lensing map [@planck2015xv] and do not see clear evidence of such skewness — we attribute this to the low effective resolution of the Planck map (FWHM $\sim$ few degrees). Finally, we note that a non-zero three-point function of the reconstruction noise could potentially alter the forecasted $\kappa$ bispectrum results of Ref. [@Namikawa2016] (where the reconstruction noise was taken to be Gaussian). The non-Gaussian properties of the small-scale reconstruction noise were noted in Ref. [@HuOkamoto2002], who pointed out that the quadratic estimator at high-$\ell$ is constructed from progressively fewer arcminute-scale CMB fluctuations.
Similarly, the $\kappa$ peak count distribution also displays skewness after reconstruction, although it is less dramatic than that seen in the PDF. The peak of the distribution shifts to a higher $\kappa$ value due to the additional noise in the reconstructed maps. We note that the shape of the peak count distribution becomes somewhat rough when large smoothing kernels are applied to the maps, due to the small number of peaks present in this situation (e.g., $\approx 29$ peaks in a 12.25 deg$^2$ map with FWHM = 8 arcmin Gaussian window).
Non-Gaussianity in reconstructed maps {#sec:non-gauss_recon}
-------------------------------------
{width="48.00000%"} {width="48.00000%"}
{width="48.00000%"} {width="48.00000%"}
We show the PDF and peak counts of the reconstructed $\kappa$ maps in Figs. \[fig:noisyPDF\] and \[fig:noisypk\], respectively. The left panels of these figures show the results using maps with an 8 arcmin Gaussian smoothing window. We further consider a Wiener filter, which is often used to filter out noise based on some known information in a signal (i.e., the noiseless power spectrum in our case). The right panels show the Wiener-filtered results, where we inverse-variance weight each pixel in Fourier space, i.e., each Fourier mode is weighted by the ratio of the noiseless power spectrum to the noisy power spectrum (c.f. Fig. \[fig:recon\]), $$\begin{aligned}
f^{\rm Wiener} (\ell) = \frac{C_\ell^{\rm noiseless}}{C_\ell^{\rm noisy}} \,.\end{aligned}$$
Compared to the noiseless results shown in Figs. \[fig:noiseless\_PDF\] and \[fig:noiseless\_pk\], the differences between the PDF and peaks from the $N$-body-derived $\kappa$ maps and those from the GRF-derived $\kappa$ maps persist, but with less significance. For the Wiener-filtered maps, the deviations of the $N$-body-derived $\kappa$ statistics from the GRF case are 9$\sigma$ (PDF) and 6$\sigma$ (peaks), where we derived the significances using the simulated covariance from the $N$-body maps [^8]. These deviations capture the influence of both nonlinear evolution and post-Born effects.
![\[fig:skew\] Top panel: the skewness of the noiseless (triangles) and reconstructed, noisy (diamonds: $N$-body $\kappa$ maps; circles: GRF) PDFs. Bottom panel: the fractional difference between the skewness of the reconstructed $N$-body $\kappa$ and the reconstructed GRF. The error bars are for our map size (12.25 deg$^2$), and are only shown in the top panel for clarity.](plot/plot_skewness3.pdf){width="48.00000%"}
While the differences between the $N$-body and GRF cases in Figs. \[fig:noisyPDF\] and \[fig:noisypk\] are clear, understanding their detailed structure is more complex. First, note that the GRF cases exhibit the skewness discussed in Sec. \[sec:recon\_noise\], which arises from the reconstruction noise itself. We show the skewness of the reconstructed PDF (for both the $N$-body and GRF cases) compared with that of the noiseless ($N$-body) PDF for various smoothing scales in Fig. \[fig:skew\]. The noiseless $N$-body maps are positively skewed, as physically expected. The reconstructed, noisy maps are negatively skewed, for both the $N$-body and GRF cases. However, the reconstructed $N$-body results are less negatively skewed than the reconstructed GRF results (bottom panel of Fig. \[fig:skew\]), presumably because the $N$-body PDF (and peaks) contain contributions from the physical skewness, which is positive (see Figs. \[fig:noiseless\_PDF\] and \[fig:noiseless\_pk\]). However, the physical skewness is not large enough to overcome the negative “$N^{(0)}$”-type skewness coming from the reconstruction noise. We attribute the somewhat-outlying point at FWHM $=8$ arcmin in the bottom panel of Fig. \[fig:skew\] to a noise fluctuation, as the number of pixels at this smoothing scale is quite low (the deviation is consistent with zero). The decrease in $|S|$ between the FWHM $=2$ arcmin and 1 arcmin cases in the top panel of Fig. \[fig:skew\] for the noisy maps is due to the large increase in $\sigma_{\kappa}$ between these smoothing scales, as the noise is blowing up on small scales. The denominator of Eq. (\[eq.skewdef\]) thus increases dramatically, compared to the numerator.
Comparisons between the reconstructed PDF in the $N$-body case and GRF case are further complicated by the fact that higher-order “biases” arise due to the reconstruction. For example, the skewness of the reconstructed $N$-body $\kappa$ receives contributions from many other terms besides the physical skewness and the “$N^{(0)}$ bias” described above — there will also be Wick contractions involving combinations of two- and four-point functions of the CMB temperature and $\kappa$ (and perhaps an additional bias coming from a different contraction of the three-point function of $\kappa$, analogous to the “$N^{(1)}$” bias for the power spectrum [@Hanson2011]). So the overall “bias” on the reconstructed skewness will differ from that in the simple GRF case. This likely explains why we do not see an excess of positive $\kappa$ values over the GRF case in the PDFs shown in Fig. \[fig:noisyPDF\]. While this excess is clearly present in the noiseless case (Fig. \[fig:noiseless\_PDF\]), and it matches physical intuition there, the picture in the reconstructed case is not simple, because there is no guarantee that the reconstruction biases in the $N$-body and GRF cases are exactly the same. Thus, a comparison of the reconstructed $N$-body and GRF PDFs contains a mixture of the difference in the biases and the physical difference that we expect to see. Similar statements hold for comparisons of the peak counts.
Clearly, a full accounting of all such individual biases would be quite involved, but the key point here is that all these effects are fully present in our end-to-end simulation pipeline. While an analytic understanding would be helpful, it is not necessary for the forecasts we present below.
Cosmological constraints {#sec:constraints}
------------------------
Before we proceed to present the cosmological constraints from non-Gaussian statistics, it is necessary to do a sanity check by comparing the forecasted contour from our simulated power spectra to that from an analytic Fisher estimate, $$\begin{aligned}
\FB_{\alpha \beta}=\frac{1}{2} {\rm Tr}
\left\{\CB^{-1}_{\rm Gauss}
\left[\left(\frac {\partial C_\ell}{\partial p_\alpha} \right)
\left(\frac {\partial C_\ell}{\partial p_\beta}\right)^T+
\left(\alpha\leftrightarrow\beta \right)
\right]\right\},\end{aligned}$$ where $\left\{ \alpha,\beta \right\} = \left\{ \Omega_m,\sigma_8 \right\}$ and the trace is over $\ell$ bins. $\CB_{\rm Gauss}$ is the Gaussian covariance matrix, with off-diagonal terms set to zero, and diagonal terms equal to the Gaussian variance, $$\begin{aligned}
\sigma^2_\ell=\frac{2(C_\ell+N_\ell)^2}{f_{\rm sky}(2\ell+1)\Delta\ell}\end{aligned}$$
We compute the theoretical power spectrum $C_\ell$ using the HaloFit model [@Smith2003; @Takahashi2012], with fractional parameter variations of $+1$% to numerically obtain $\partial C_\ell / \partial p$. $N_\ell$ is the reconstruction noise power spectrum, originating from primordial CMB fluctuations and instrumental/atmospheric noise (note that we only consider white noise here). The sky fraction $f_{\rm sky}=0.485$ corresponds to the 20,000 deg$^2$ coverage expected for AdvACT. $(F^{-1}_{\alpha\alpha})^{\frac{1}{2}}$ is the marginalized error on parameter $\alpha$. Both theoretical and simulated contours use the power spectrum within the $\ell$ range of \[100, 2,000\]. The comparison is shown in Fig. \[fig:contour\_fisher\]. The contour from full $N$-body simulations shows good agreement with the analytical Fisher contour. This result indicates that approximations made in current analytical CMB lensing power spectrum forecasts are accurate, in particular the neglect of non-Gaussian covariances from nonlinear growth. A comparison of the analytic and reconstructed power spectra will be presented in Ref. [@Sherwin2016].
![\[fig:contour\_fisher\] 68% C.L. contours from an AdvACT-like CMB lensing power spectrum measurement. The excellent agreement between the simulated and analytic results confirms that non-Gaussian covariances arising from nonlinear growth and reconstruction noise do not strongly bias current analytic CMB lensing power spectrum forecasts (up to $\ell = 2,000$).](plot/plot_contour_fisher.pdf){width="48.00000%"}
Fig. \[fig:contour\_noiseless\] shows contours derived using noiseless maps for the PDF and peak count statistics, compared with that from the noiseless power spectrum. We compare three different smoothing scales (1.0, 5.0, 8.0 arcmin), and find that smaller smoothing scales have stronger constraining power. However, even with the smallest smoothing scale (1.0 arcmin), the PDF contour is still significantly larger than that of the power spectrum. Peak counts using 1.0 arcmin smoothing show almost equivalent constraining power as the power spectrum. However, we note that 1.0 arcmin smoothing is not a fair comparison to the power spectrum with cutoff at $\ell<2,000$, because in reality, the beam size and instrument noise is likely to smear out signals smaller than a few arcmin scale (see below).
At first, it may seem surprising that the PDF is not at least as constraining as the power spectrum in Fig. \[fig:contour\_noiseless\], since the PDF contains the information in the variance. However, this only captures an overall amplitude of the two-point function, whereas the power spectrum contains scale-dependent information.[^9] We illustrate this in Fig. \[fig:cell\_diff\], where we compare the fiducial power spectrum to that with a 1% increase in $\Omega_m$ or $\sigma_8$ (while keeping other parameters fixed). While $\sigma_8$ essentially re-scales the power spectrum by a factor $\sigma_8^2$, apart from a steeper dependence at high-$\ell$ due to nonlinear growth, $\Omega_m$ has a strong shape dependence. This is related to the change in the scale of matter-radiation equality [@planck2015xv]. Thus, for a noiseless measurement, the shape of the power spectrum contains significant additional information about these parameters, which is not captured by a simple change in the overall amplitude of the two-point function. This is the primary reason that the power spectrum is much more constraining than the PDF in Fig. \[fig:contour\_noiseless\].
{width="48.00000%"} {width="48.00000%"}
![\[fig:cell\_diff\] Fractional difference of the CMB lensing power spectrum after a 1% increase in $\Omega_m$ (thick solid line) or $\sigma_8$ (thin solid line), compared to the fiducial power spectrum. Other parameters are fixed at their fiducial values.](plot/plot_Cell_diff.pdf){width="48.00000%"}
{width="48.00000%"} {width="48.00000%"}
![\[fig:contour\_comb\] 68% C.L. contours derived using two combinations of the power spectrum, PDF, and peak counts, compared to using the power spectrum alone. Reconstruction noise corresponding to an AdvACT-like survey is included. The contours are scaled to AdvACT sky coverage of 20,000 deg$^2$.](plot/plot_contour_noisy_comb_clough.pdf){width="48.00000%"}
Fig. \[fig:contour\_noisy\] shows contours derived using the reconstructed, noisy $\kappa$ maps. We show results for three different filters — Gaussian windows of 1.0 and 5.0 arcmin and the Wiener filter. The 1.0 arcmin contour is the worst among all, as noise dominates at this scale. The 5.0 arcmin-smoothed and Wiener-filtered contours show similar constraining power. Using the PDF or peak counts alone, we do not achieve better constraints than using the power spectrum alone, but the parameter degeneracy directions for the statistics are slightly different. This is likely due to the fact that the PDF and peak counts probe non-linear structure, and thus they have a different dependence on the combination $\sigma_8(\Omega_m)^\gamma$ than the power spectrum does, where $\gamma$ specifies the degeneracy direction.
Combination $\Delta \Omega_m$ $\Delta \sigma_8 $
------------------ ------------------- --------------------
PS only 0.0065 0.0044
PDF + Peaks 0.0076 0.0035
PS + PDF + Peaks 0.0045 0.0030
: \[tab: constraints\] Marginalized constraints on $\Omega_m$ and $\sigma_8$ for an AdvACT-like survey from combinations of the power spectrum (PS), PDF, and peak counts, as shown in Fig. \[fig:contour\_comb\].
The error contour derived using all three statistics is shown in Fig. \[fig:contour\_comb\], where we use the 5.0 arcmin Gaussian smoothed maps. The one-dimensional marginalized errors are listed in Table \[tab: constraints\]. The combined contour shows moderate improvement ($\approx 30\%$ smaller error contour area) compared to the power spectrum alone. The improvement is due to the slightly different parameter degeneracy directions for the statistics, which break the $\sigma_8$-$\Omega_m$ degeneracy somewhat more effectively when combined. It is worth noting that we have not included information from external probes that constrain $\Omega_m$ (e.g., baryon acoustic oscillations), which can further break the $\Omega_m$-$\sigma_8$ degeneracy.
Conclusion {#sec:conclude}
==========
In this paper, we use $N$-body ray-tracing simulations to explore the additional information in CMB lensing maps beyond the traditional power spectrum. In particular, we investigate the one-point PDF and peak counts (local maxima in the convergence map). We also apply realistic reconstruction procedures that take into account primordial CMB fluctuations and instrumental noise for an AdvACT-like survey, with sky coverage of 20,000 deg$^2$, noise level 6 $\mu$K-arcmin, and $1.4$ arcmin beam. Our main findings are:
1. We find significant deviations of the PDF and peak counts of $N$-body-derived $\kappa$ maps from those of Gaussian random field $\kappa$ maps, both in the noiseless and noisy reconstructed cases (see Figs. \[fig:noiseless\_PDF\], \[fig:noiseless\_pk\], \[fig:noisyPDF\], and \[fig:noisypk\]). For AdvACT, we forecast the detection of non-Gaussianity to be $\approx$ 9$\sigma$ (PDF) and 6$\sigma$ (peak counts), after accounting for the non-Gaussianity of the reconstruction noise itself. The non-Gaussianity of the noise has been neglected in previous estimates, but we show that it is non-negligible (Fig. \[fig:recon\]).
2. We confirm that current analytic forecasts for CMB lensing power spectrum constraints are accurate when confronted with constraints derived from our $N$-body pipeline that include the full non-Gaussian covariance (Fig. \[fig:contour\_fisher\]).
3. An improvement of $\approx 30\%$ in the forecasted $\Omega_m$-$\sigma_8$ error contour is seen when the power spectrum is combined with PDF and peak counts (assuming AdvACT-level noise), compared to using the power spectrum alone. The covariance between the power spectrum and the other two non-Gaussian statistics is relatively small (with cross-covariance $< 20\%$ of the diagonal components), meaning the latter is complementary to the power spectrum.
4. For noiseless $\kappa$ maps (i.e., ignoring primordial CMB fluctuations and instrumental/atmospheric noise), a smaller smoothing kernel can help extract the most information from the PDF and peak counts (Fig. \[fig:contour\_noiseless\]). For example, peak counts of 1.0 arcmin Gaussian smoothed maps alone can provide equally tight constraints as from the power spectrum.
5. We find non-zero skewness in the PDF and peak counts of reconstructed GRFs, which is absent from the input noiseless GRFs by definition. This skewness is the result of the quadratic estimator used for CMB lensing reconstruction from the temperature or polarization maps. Future forecasts for non-Gaussian CMB lensing statistics should include these effects, as we have here, or else the expected signal-to-noise could be overestimated.
In this work, we have only considered temperature-based reconstruction estimators, but in the near future polarization-based estimators will have equally (and, eventually, higher) signal-to-noise. Moreover, the polarization estimators allow the lensing field to be mapped out to smaller scales, which suggests that they could be even more useful for non-Gaussian statistics.
In summary, there is rich information in CMB lensing maps that is not captured by two-point statistics, especially on small scales where nonlinear evolution is significant. In order to extract this information from future data from ongoing CMB Stage-III and near-future Stage-IV surveys, such as AdvACT, SPT-3G [@Benson2014], Simons Observatory[^10], and CMB-S4 [@Abazajian2015], non-Gaussian statistics must be studied and modeled carefully. We have shown that non-Gaussian statistics will already contain useful information for Stage-III surveys, which suggests that their role in Stage-IV analyses will be even more important. The payoff of these efforts could be significant, such as a quicker route to a neutrino mass detection.
We thank Nick Battaglia, Francois Bouchet, Simone Ferraro, Antony Lewis, Mark Neyrinck, Emmanuel Schaan, and Marcel Schmittfull for useful discussions. We acknowledge helpful comments from an anonymous referee. JL is supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship under award AST-1602663. This work is partially supported by a Junior Fellowship from the Simons Foundation to JCH and a Simons Fellowship to ZH. BDS is supported by a Fellowship from the Miller Institute for Basic Research in Science at the University of California, Berkeley. This work is partially supported by NSF grant AST-1210877 (to ZH) and by a ROADS award at Columbia University. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by NSF grant ACI-1053575. Computations were performed on the GPC supercomputer at the SciNet HPC consortium. SciNet is funded by the Canada Foundation for Innovation under the auspices of Compute Canada, the Government of Ontario, the Ontario Research Fund — Research Excellence, and the Univ. of Toronto.
[^1]: For example, higher order moments [@Bernardeau1997; @Hui1999; @vanWaerbeke2001; @Takada2002; @Zaldarriaga2003; @Kilbinger2005; @Petri2015], three-point functions [@Takada2003; @Vafaei2010], bispectra [@Takada2004; @DZ05; @Sefusatti2006; @Berge2010], peak counts , Minkowski functionals [@Kratochvil2012; @Shirasakiyoshida2014; @Petri2013; @Petri2015], and Gaussianized power spectrum [@Neyrinck2009; @Neyrinck2014; @Yu2012].
[^2]: <http://wwwmpa.mpa-garching.mpg.de/gadget/>
[^3]: <https://pypi.python.org/pypi/lenstools/>
[^4]: <http://camb.info/>
[^5]: While the number of potential planes could be a limiting factor in our sensitivity to these effects, we note that our procedure uses $\approx 40$-70 planes for each ray-tracing calculation (depending on the cosmology), which closely matches the typical number of lensing deflections experienced by a CMB photon.
[^6]: We find that this filter is necessary for numerical stability (and also because our simulated $\kappa$ maps do not recover all structure on these small scales, as seen in Fig. \[fig:theory\_ps\]), but our results are unchanged for moderate perturbations to the filter scale.
[^7]: Due to our limited number of models, linear interpolation is slightly more vulnerable to sampling artifacts than the Clough-Tocher method, because the linear method only utilizes the nearest points in parameter space. The Clough-Tocher method also uses the derivative information. Therefore, we choose Clough-Tocher for our analysis.
[^8]: We note that the signal-to-noise ratios predicted here are comparable to the $\approx 7\sigma$ bispectrum prediction that would be obtained by rescaling the SPT-3G result from Table I of Ref. [@Pratten2016] to the AdvACT sky coverage (which is a slight overestimate given AdvACT’s higher noise level). The higher significance for the PDF found here could be due to several reasons: (i) additional contributions to the signal-to-noise for the PDF from higher-order polyspectra beyond the bispectrum; (ii) inaccuracy of the nonlinear fitting formula used in Ref. [@Pratten2016] on small scales, as compared to the N-body methods used here; (iii) reduced cancellation between the nonlinear growth and post-Born effects in higher-order polyspectra (for the bispectrum, these contributions cancel to a large extent, reducing the signal-to-noise [@Pratten2016]).
[^9]: Note that measuring the PDF or peak counts for different smoothing scales can recover additional scale-dependent information as well.
[^10]: <http://www.simonsobservatory.org/>
|
Q:
Using "plot for" in gnuplot to vary parameters
I want to use the plot for feature in gnuplot to plot functions with varying parameters. Here an example
par = "1 2" #two values for the parameter
f(x,a) = sin(a*x)
g(x,a) = cos(a*x)
plot for [i=1:words(par)] g(x, word(par,i)), f(x, word(par,i))
What I expect is the plotting of the four functions g(x,1), g(x,2, f(x,1), and f(x,2).
But for whatever reason only three functions are plotted, namely: g(x,1), g(x,2, and f(x,2).
This seems completely arbitrary to me.
Can someone help me out?
A:
You have to repeat the for condition:
plot for [i=1:words(par)] g(x, word(par,i)), for [i=1:words(par)] f(x, word(par,i))
|
Q:
Getting list of Variables of map in BPM Metastorm
I'm trying to get list of variables in some map OUTSIDE program automatically. I know I can find them in .process file, with has xml structure.
I also figured out that "x:object" with variable contains "x:Type" ending with "MboField}".
But unfortunately I need to narrow searching criterias more, because I still can't find the main patern to separate variables from other objects.
This is my current code in c#:
var xdoc = XDocument.Load(patches.ProcessFilePatch);
var xmlns = XNamespace.Get("http://schema.metastorm.com/Metastorm.Common.Markup");
IEnumerable<string> values = from x in xdoc.Descendants(xmlns+"Object")
where x.Attribute(xmlns+"Type").Value.ToString().EndsWith("MboField}")
select x.Attribute(xmlns+"Name").Value.ToString();
VariablesInProcessFile = values.ToList();
Any other ways to find Variables among others?
A:
private void getVariablesInProcessFile()
{
var xdoc = XDocument.Load(patches.ProcessFilePatch);
var xmlns = XNamespace.Get("http://schema.metastorm.com/Metastorm.Common.Markup");
var dane = xdoc.Descendants(xmlns + "Object").Where(x => CheckAttributes(x, xmlns)).ToArray();
IEnumerable<string> valuesE = from x in dane.Descendants(xmlns + "Object")
where x.Attribute(xmlns + "Type").Value.ToString().EndsWith("MboField}")
select x.Attribute(xmlns + "Name").Value.ToString();
VariablesInProcessFile = valuesE.ToList();
}
private bool CheckAttributes(XElement x, XNamespace xmlns)
{
var wynik = x.Attribute(xmlns + "Name");
return wynik != null && (wynik.Value == patches.MapName + "Data" || wynik.Value == patches.altMapName + "Data");
}
Where "patches" is my own class containing patch to .process file and possible names of group of Variables, usually related to name of the map.
|
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Too many people are oblivious to the daily injustices that our systems enforce against our own fellow citizens within the city of San Diego and otherwise. Today, you shed light on the criminal justice system’s flaws and our cultural shortcomings. These systems are perpetuated by, as most things unjust, money changing hands. To get at the root of institutionalized injustice, which already impairs marginalized communities disproportionately, consider investigating the impact of the two, publicly-traded private prison companies who hold contracts with the State of California. The State’s contracts directly impact justice and the lack thereof in San Diego. Specifically, question the lobbying they do with respect to rules around detainment, arrests, convictions and lengths of prison sentences. These two companies and the handful of financial institutions with large holdings in them have assets in multibillions that depend on consistent - or ideally rapid - growth in the number of people in jail.
how many people attended the rallies? Particularly the one on Saturday. Where was it? apparently the NAACP paid for it. Who was the keynote speaker? Where was it on the news on Saturday night or Sunday morning or even Sunday night?
How does the Hispanic community feel about the vilification of Zimmerman? Since the courts found him innocent and the NAACP convicted him yet never referred to him as a Hispanic does this show bias on their part?
He would have been better to say, "Due to the Stand Your Ground law in Florida, what happened to Martin could have happened to any one of us."
I didn't vote for Obama because he's black. I voted for him because I thought he'd do a better job than McCain and Romney. I still do. But for the first time I feel like he's telling us he's not the American president, but a black man.
Still, I understand where he's coming from. I'm a minority, too. But oddly the racist comments I've received in my life have been directed at me by black people, not white. Although some whites have, they were mostly black. And the prejudiced comments directed toward me have been from Mexicans who don't believe I'm Mexican enough. They accuse me of being ashamed of being a Mexican because I'm different than the stereotype.
I think the president would have been better to keep out of this. The law is the law and will remain so until changed.
Obama aside, I don't think the Martin/Zimmerman verdict will have a lasting impact on race relations in San Diego. Mexican-Americans and Asians are always excluded from "conversations about race." From this corner of the country, "race relations" on the national level comes down to Black or White. That's what the media peddles and the public buys.
I agree wholeheartedly with the speakers about the need for greater understanding, so that people of color can experience life without constantly being disrespected. A Black man should be able to ride an elevator with a White woman without being perceived as a threat! This harkens back to the racism that eventually took the life of Emmet Till.
The point about power and the desire to maintain it is so true. Power in this society is still held by a wealthy White majority, and until White privilege stops driving violence like it did that night in Florida -- even though Zimmerman is not ethnically White, he displays as White, and was subjected all his life to the lure of Euro-centrism -- and like it did when the jury decided to acquit him, we will rally, march, and yes PROTEST.
Barbarism and bigotry begin in the home. Younger generations inherited their bigotry from their parents and grandparents. They'll pass those values on to their children. Enlightenment breaks the chain.
Weil asks good questions. Where were they held. Why were they not more widely announced? This is the problem with many of the pro-immigrant rallies. By the time I hear about them, it's too late! Or, they have it in from of the County building at 4pm on a Friday!!!
It's impacted the country badly with very different narratives about the event being a function of race. I have seen little that would seem to lead toward harmonizing those disparate viewpoints. I don't know why it would be different in San Diego.
Barack Obama speaks on behalf of many special interests each and every day. He made the statement as a result of being under intense pressure from 13% of the population. No one has a problem with the innumberable statements he's made on behalf of other special interest groups, domestic or foreign.
"It's impacted the country badly with very different narratives about the event being a function of race. I have seen little that would seem to lead toward harmonizing those disparate viewpoints. I don't know why it would be different in San Diego."
San Diego's African-American population is 6% (in the City with a lower percentage in the County). Looking at the disparities on this comment board, those numbers hold up. Getting a balanced reaction to the verdict in San Diego is statistically impossible. That's why this conversation has to be opened-up to Americans of all ethnic descents. That won't be possible until "racism" is no longer framed solely as Black or White.
"he displays as White". Is this new liberal speak? I have never heard this term before and wonder what kind of mind came up with this. Sad commentary on "civil" society. Racial and ethnic division and separation seems to be the focus instead of racial and ethnic harmony.
DLR is correct, we know how the Korean immigrants viewed African Americans in L.A. Any race or ethnicity can be a bigot or discriminatory toward another. We also know how a lot of people today view Arab-Americans. I remember one time, I was at a gas station downtown. A black man was saying something outloud. I wasn't paying attention. He then drew closer to me and repeated his question. I replied, "Sorry, I didn't realize you were speaking to me." He had an accent which in my educated guess, I would say he was Somali. Anyway, he then said "Oh, I thought you were being racist" or words to that effect. It was obvious to me that he had had some unpleasant encounter.
As for Zimmerman, he is Latino on his mother's side (it usually on the mother's side), but even as a Latino, he can still be classified for statistical purposes as the governemnt puts it, as "white."
Duckster, then "stand your ground laws" are a legal/judicial issue--not a racial one--and should be reconsidered. Take those laws to court.
This whole incident has shown that America seems to prefer segregation (by all sides) rather than inclusion. Perhaps the past is our future, too.
Mission,
Why would the government classify Zimmerman as white? I would assume it would be Hispanic. Just like Obama is black and would never be considered white. Unless he committed a crime against a minority. Funny how that works.
IT IS A SICK SOCIETY which pretends that Trayvon Martin hasn't already received the justice that he deserved, a sick society which calls for George Zimmerman's head --- but then it is a sick, sick society which elects --- and then re-elects --- and re-elects --- scum like Barak Hushpuppy OhBummer, Biden The Magnificent, Nazi Pelosi, Filthy Harry Reid, and NYC Mayor Doomberg. In the best of all possible worlds, they'll all be on a plane which crashes into the NY Times Editorial offices at midmorning, any work day, next week.
The real assassins in the Martin-Zimmerman confrontation are 1] Martin, 2] Barak Hushpuppy OhBummer, who is trying to promote race riots and the assassination of George Zimmerman, 3] Attorney General Eric "Fast and Furious" Holder, who will make sure that Zimmerman is unarmed when OhBummer’s and Holder's proxy assassins come for him, and 4] the fascist Democrat-captured media who are character assassins operating on behalf of the Democrat party and the OhBummer dictatorship.
As well, these media propagandists are actionable as accessories before the fact if they succeed in promoting the injury or assassination of George Zimmerman. Every one of the media who have tried or who will try to cause injury to Zimmerman is a legitimate legal target of people who believe in justice --- the justice which Trayvon Martin earned when he jumped George Zimmerman and attempted to murder him. Two lying fascist sacks of shxt --- OhBummer and Holder --- and of course the usual race hustlers like Sharpton, Farrakhan, and Jackson --- can be counted on to promote racial hysteria and a false narrative on this subject, year-on-year, and decade-on-decade, ad nauseam, ad infinitum.
As for "racism in America," there are millions more black racists than white racists in America today --- and the hundreds of millions of non-racists in America have "nothing" to apologize for --- no "guilt" to feel or adopt --- no "white privilege" to apologize for --- no “reparations” to pay --- no obligation to kowtow to all of the black racists --- or to Unkle Skum --- by which expression I mean “government at any and every level of American society.”
In his call to the police before the incident, Zimmerman was advised by the cops to stay in his vehicle. Critics say that Zimmerman had “a duty” to "follow orders" but the caution issued by the cops was not a lawful command, else he would have been cited by the cops, and he wasn't.
Even corrupt Florida State Attorney Angela Corey --- who hid evidence from the defense and fired the whistleblower who outed her --- did not argue that Zimmerman had a legal obligation to remain in his vehicle --- and he exited his vehicle when Martin disappeared from sight.
Zimmerman called the police before Martin jumped him --- and MSNBC deleted parts of the recorded discussion and broadcast it to make it look like Zimmerman was targeting Martin because Martin was black --- rather than tailing Martin because he was wandering around in the dark in a neighborhood which had recently suffered some break-ins and thwarted other break-ins.
This was MSNBC's attempt to lynch a straw horse, a so-called "white" Hispanic. MSNBC needed a black-white confrontation to promote their own racist, anti-white narrative that America is a "racist" society --- a society wherein whites should be disarmed --- and pay reparations to non-whites for the "privilege" [crime] of being white.
There is no evidence whatever that race played a part in Zimmerman's execution of his duties as the on-duty Neighborhood Watch Volunteer.
It is said with great derision that Zimmerman is or was "a wannabe cop." These critics appear to live in safe neighborhoods, no? There's nothing wrong with the aspiration to be a cop unless one intends to indict all cops for wanting to be cops --- and letting a puddy like Chris Matthews be the nighttime Neighborhood Watch volunteer strikes me as ineffective, to say the least --- although a pretty good way to get rid of Chris Matthews, come to think of it.
Immediately upon the breaking of this story in the media, there was the assumption that the confrontation between Martin and Zimmerman had something to do with Florida's "stand your ground" law. But because Martin jumped Zimmerman and knocked him to the ground and proceeded to beat him in "mixed martial arts" pound-and-ground style, Zimmerman clearly was not "standing his ground" --- in the moment of confrontation, he was on his back with Martin on top of him smashing his nose out of shape and smashing Zimmerman's head on the cement.
The attacks on “stand your ground” laws are being made by opportunists whose real objective is to leave the American citizen defenseless and let the freelance-Democrat scum rule the streets of America.
I say that the American people should be well-armed and well-ammoed and stand their ground against the OhBummer dictatorship and against Unkle Skum --- against American government at every level. We have no obligation whatever to surrender to fascist statism --- or to any other brand of statism, as a matter of fact. That government is best which governs least. It is said that American government rests upon the consent of the governed. Now is the time for all good men and women to withdraw and cancel that consent.
Trayvon Martin has been portrayed in the media as a sweetie-pie. The first published pictures of him that I saw were of Martin at the age of 12, or so, looking relatively mild and not especially bright.
The pictures which Martin published of himself at age 17, online, and before he attacked Zimmerman --- and pictures which others had of him at that age --- showed him at 160 lbs and six feet in height --- a football player who had had some "mixed martial arts" training, in his own website flipping-off the viewer, smoking marijuana, and holding a semiautomatic handgun --- I guess OhBummer would have to call that “an assault weapon,” ay? He'd twice been suspended from school, had been found in possession of stolen property, started fights with other people, was a dopehead, and gave the impression that he was also a dope dealer.
Trayvon Martin was a cheap thug, and it makes perfect sense for Barak Hushpuppy OhBummer to say that if he'd had a son, that his son would look like and be like Trayvon Martin, although, arguably, that son would look more like Trayvon Martin's ally, Rachel Jeantel, who has good reason to wear a hoodie, and probably also a very large trashbag, all things considered.
So let Barak Hushpuppy OhBummer and Eric "Fast and Furious" Holder don their hoodies --- their version of the racist KKK pointy-headed white sheets --- and let them pursue their black racist witch hunt and their campaign of character assassination against George Zimmerman.
I say that the majority of the American people see OhBummer and Holder --- and the Democrat-captured media --- and the whole OhBummer Wrecking Crew --- for what they truly are --- a dictatorship which deserves to be smashed.
"This whole incident has shown that America seems to prefer segregation (by all sides) rather than inclusion."
No it hasn't. When considered relative to other white-on-black justifiable shootings, this case shows that racism is alive and well in the american judicial system.
"Are there are racial disparities in justifiable homicide rulings? Out of 53,000 homicides in the database, 23,000 have a white shooter and a white victim. The shooting is ruled to have been justified in a little more than 2 percent of cases. In states with a SYG law (after enactment), the shooting is ruled to be justified in 3.5 percent of cases, compared to less than 2 percent in non-SYG states. In cases where both the victim and shooter are black, the numbers are almost identical, if slightly lower.
When the shooter and victim are of different races, there are substantial differences in the likelihood a shooting is ruled to be justified. When the shooter is black and the victim is white, the shooting is ruled justified in about 1 percent of cases, and is actually slightly lower in non-SYG states. Between 2005 and 2010, there were 1,210 homicides with a black shooter and a white victim—the shooting was ruled to be justified in just 17 of them (about 1 percent)."
The story is completely different when there is a white shooter and a black victim. In the same time period, there were 2,069 shootings where the shooter was white and the victim black. The homicide was ruled to be justified in 236 cases (11 percent). In SYG states, almost 17 percent of white-on-black shootings were ruled to be justified.
Those statistics as well as data from prisons tell an inconvenient truth. I think "Equal Justice" is the next "Marriage Equality" if done correctly. As with LGBT marriage, the country hasn't yet realized the extent of our institutionalized discrimination.
FLORI-DUH Defender, okay, if it makes you feel better, Zimmerman is Latino even though he's father is NOT. Maybe you should check some of the job applications around town where LATINOS are asked to mark "white" for statistical purposes. |
Q:
Is it possible to know the probability that a trade is successful?
I'm trying to model the distribution of different outcomes of day trading every day for a year. I'm starting with $350 dollars. I'm only doing options trading on Apple stock with a 5% stop loss and a 15% stop gain. And if it doesn't hit one of those stops, I sell before the market closes.
I'm not trying to find a way to control whether I win or lose on the given day, I'm just gonna do my best. But at least in the long run is there a way to use the law of large numbers so that after a year, my average is close to the probability of winning on a given day?
If I flip a coin every day for a year, I can get all heads, yeah, but it's way more likely that I get within 3 or 4 from half heads.
Is there a way to set up my option trade for the day so that it has a specific probability? Or at least on certain days that have certain conditions, will there be a pretty specific probability?
I've tried to learn "the secret to making money on the stock market", but I think for an average joe like me, I'm better off just trying to treat it as much like a coin flip as possible.
And by having certain limits on my orders, I get the impression that a probability can be calculated.
A:
If you had a trading system, and by trading system I mean the criteria setup that you will take a trade on, then once a setup comes up at what price will you open the trade and at what price you will close the trade.
As an example, if you want to buy once price breaks through resistance at $10.00 you might place your buy order at $10.05.
So once you have a written trading system you could do backtesting on this system to get a percentage of win trades to loosing trades, your average win size to average lose size, then from this you could work out your expectancy for each trade that you follow your trading system on.
|
The Jasenovac camp complex consisted of five detention facilities established between August 1941 and February 1942 by the authorities of the so-called Independent State of Croatia. As Germany and its Axis allies invaded and dismembered Yugoslavia in April 1941, the Germans and the Italians endorsed the proclamation of the so-called Independent State of Croatia by the fanatically nationalist, fascist, separatist, and terrorist Ustaša organization on April 10, 1941.
After seizing power, the Ustaša authorities erected numerous concentration camps in Croatia between 1941 and 1945. These camps were used to isolate and murder Jews, Serbs, Roma (also known as Gypsies), and other non-Catholic minorities, as well as Croatian political and religious opponents of the regime. The largest of these centers was the Jasenovac complex, a string of five camps on the bank of the Sava River, about 60 miles south of Zagreb. It is presently estimated that the Ustaša regime murdered between 77,000 and 99,000 people in Jasenovac between 1941 and 1945.
In late August 1941, the Croat authorities established the first two camps of the Jasenovac complex—Krapje and Brocica. These two camps were closed four months later. The other three camps in the complex were: Ciglana, established in November 1941 and dismantled in April 1945; Kozara, established in February 1942 and dismantled in April 1945; and Stara Gradiška, which had been an independent holding center for political prisoners since the summer of 1941 and was converted into a concentration camp for women in the winter of 1942.
The camps were guarded by Croatian political police and personnel of the Ustasa militia, which was the paramilitary organization of the Ustaša movement.
Conditions in the Jasenovac camps were horrendous. Prisoners received minimal food. Shelter and sanitary facilities were totally inadequate. Worse still, the guards cruelly tortured, terrorized, and murdered prisoners at will.
Between its establishment in 1941 and its evacuation in April 1945, Croat authorities murdered thousands of people at Jasenovac. Among the victims were: between 45,000 and 52,000 Serb residents of the so-called Independent State of Croatia; between 12,000 and 20,000 Jews; between 15,000 and 20,000 Roma (Gypsies); and between 5,000 and 12,000 ethnic Croats and Muslims, who were political and religious opponents of the regime.
The Croat authorities murdered between 320,000 and 340,000 ethnic Serb residents of Croatia and Bosnia during the period of Ustaša rule; more than 30,000 Croatian Jews were killed either in Croatia or at Auschwitz-Birkenau.
Between 1941 and 1943, Croat authorities deported Jews from throughout the so-called Independent State to Jasenovac and shot many of them at the nearby killing sites of Granik and Gradina. The camp complex management spared those Jews who possessed special skills or training, such as physicians, electricians, carpenters, and tailors. In two deportation operations, in August 1942 and in May 1943, Croat authorities permitted the Germans to transfer most of Croatia's surviving Jews (about 7,000 in total), including most of those still alive in Jasenovac, to Auschwitz-Birkenau in German-occupied Poland.
As the Partisan Resistance Movement under the command of Communist leader Josip Tito approached Jasenovac in late April 1945, several hundred prisoners rose against the camp guards. Many of the prisoners were killed; a few managed to escape. The guards murdered most of the surviving prisoners before dismantling the last three Jasenovac camps in late April. The Partisans overran Jasenovac in early May 1945.
Determining the number of victims for Yugoslavia, for Croatia, and for Jasenovac is highly problematic, due to the destruction of many relevant documents, the long-term inaccessibility to independent scholars of those documents that survived, and the ideological agendas of postwar partisan scholarship and journalism, which has been and remains influenced by ethnic tension, religious prejudice, and ideological conflict. The estimates offered here are based on the work of several historians who have used census records as well as whatever documentation was available in German, Croat, and other archives in the former Yugoslavia and elsewhere.
As more documents become accessible and more research is conducted into the records of the Ustaša regime, historians and demographers may be able to determine more precise figures than are now available. |
Based out of Los Angeles, we specialize in service and repair of all major home and commercial appliances, A/C and Heating units, including most brands and models. Serving the Greater Los Angeles and San Fernando Valley, see our Service Areas,Our technicians are well experienced and have many years of field work behind them. We offer same day service on most orders. There is no extra charge for evenings, weekends or holidays. We are always in your area, so there is no travel charge! Lastly, we only install brand new, factory recommended parts. |
Teresa Carlson
Teresa Carlson is the current vice president for Amazon Web Services' worldwide public sector business. Prior to working for Amazon, Carlson served as Microsoft's Vice President of Federal Government business. Carlson was named Executive of the Year in 2016 for companies greater than $300 million by the Greater Washington GovCon Awards, which is administered by the Northern Virginia Chamber of Commerce.
Education
Carlson graduated from Western Kentucky University with a bachelor's degree in communications and a master's in speech and language pathology.
References
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Vasoconstrictive effects of human post-hemorrhagic cerebrospinal fluid on cat pial arterioles in situ.
Cat cortical arterioles were exposed in vivo to cerebrospinal fluid (CSF) from four patients with subarachnoid hemorrhage (SAH) due to a ruptured intracranial aneurysm. Pial arteriolar caliber was measured by the television image-splitting technique. There was a consistent vasoconstrictive response to CSF. This effect could be ascribed neither to the pH of the CSF nor to the potassium concentration. The vasoconstriction, which was more pronounced with decreasing arteriolar caliber, could be resolved by the perivascular application of nifedipine. |
Power over Ethernet systems are seeing increasing use in today's society. Power over Ethernet, sometimes abbreviated PoE, refers to providing power to Ethernet devices over an Ethernet line that is also used to communicate data. Thus, power over Ethernet devices do not require separate power supply lines. In some instances, the power may be supplied by a power supply contained within an Ethernet switch. Because the power supply does not generally have the power capability to supply maximum power to every port, there is a limit on the number of power over Ethernet devices that can be connected to a given power supply. A port may be denied power, if it will result in oversubscription of the power supply. Example power over Ethernet devices that can benefit from receiving power over the Ethernet communication lines include an internet protocol telephone, a badge reader, a wireless access point, a video camera, and others.
Traditionally, when a power over Ethernet device is connected to a power supply, the power over Ethernet device is allocated a maximum power class according to IEEE standard 802.3af denoted as class 0 thru 4. These maximum values correspond to the maximum amount of power that will be supplied by the power supply to the power over Ethernet device. IEEE standard 802.3af provides for three levels of 15.4 watts, 7.5 watts, and 4.0 watts for these power over Ethernet devices. In certain circumstances, such allocation prevents the power supply from being utilized to its full capability due to the coarse granularity in class.
A software program referred to as Cisco Discovery Protocol allows for more granular specification of the limit for the power over Ethernet powered devices other than the above-described IEEE levels. However, the power supply still may have unutilized capacity. |
1. Introduction {#sec1}
===============
Health care is changing dynamically in the 2010s. The economic recession and problems with recruiting professionals \[[@B1], [@B2]\], staff retention \[[@B3]\], creating healthy work environments \[[@B4], [@B5]\], and a growing demand for customer orientation \[[@B6]\] pose challenges for nurse managers\' work. More expertise in management is needed to respond to these issues.
One essential area of nurse manager\'s management skills is the use of different leadership styles \[[@B7]\]. Leadership styles can be seen as different combinations of tasks and transaction behaviours that influence people in achieving goals \[[@B8]\]. Earlier studies indicate that nurse manager\'s effective leadership style is affiliated to staff retention \[[@B5]\], work unit climate \[[@B4]\], nurses\' job satisfaction \[[@B9], [@B10]\], nurses\' commitment \[[@B11]\], and patient satisfaction \[[@B12]\].
Transformational leadership style \[[@B5], [@B6], [@B13], [@B14]\] and transactional leadership \[[@B7]\] help to respond to these issues. Transformational leadership refers to the leader\'s skills to influence others towards achieving goals by changing the followers\' beliefs, values, and needs \[[@B7]\]. Transactional leadership complements and enhances the effects of transformational leadership outcomes \[[@B15]\].
There are certain skills required from nurse managers so as to be able to use these effective leadership styles. The skills include the ability to create an organization culture that combines high-quality health care and patient/employee safety and highly developed collaborative and team-building skills \[[@B1]\]. Nurse managers also need to have the readiness to observe their own behaviour \[[@B16]\] and its effects on the work unit; as a result, employees can adjust to a better leadership style. These kinds of skills are related to manager\'s emotional intelligence (EI).
EI is an ability to lead ourselves and our relationships effectively \[[@B17]\]. It has been defined as the ability to observe one\'s own and others\' feelings and emotions, to discriminate among them and to use this information to direct one\'s thinking and actions \[[@B18]\]. EI is composed of personal competence and social competence. Self-awareness and self-management are reflections of personal competence, influencing the way the leader manages him/herself. Social awareness and relationship management reflect social competence, which affects how the leader manages relationships with others \[[@B17]\].
Nurse managers with that skill can easily form relationships with others, read employees\' feelings and responses accurately, and lead successfully \[[@B19]--[@B21]\]. Emotionally intelligent leaders\' behaviour also stimulates the creativity of their employees \[[@B22]\]. Goleman et al. \[[@B23]\] have identified visionary, coaching, affiliate, and democratic styles as resonant, and pacesetting and commanding styles as dissonant leadership styles. Most leaders use both resonant and dissonant leadership styles. The leadership styles of Goleman et al. are applied as the basis of this study because earlier studies refer to the significance of these styles, especially that of EI in manager\'s work. In addition, these leadership styles are one way of aiming to carry out transformational leadership. Especially visionary, coaching, affiliate, and democratic styles include elements that promote transformational leadership. Such elements are for example the leader being visionary and empowering staff \[[@B4]\].
This paper focuses on Finnish nurse managers\' leadership styles. The Finnish health care system is a strong institution where health care services are offered to all citizens and funded by taxes \[[@B24]\]. It has widely recognized that health care services in Finland are of high-quality Despite recent concerns about equity issues, Finns are in general very satisfied with their health care services. \[[@B25]\]. Consequently it is important to explore nurse managers\' leadership styles especially in this context.
2. Materials and Methods {#sec2}
========================
2.1. Aim of the Study {#sec2.1}
---------------------
The intention of this study was to explore nurses\' and supervisors\' perceptions of nurse leaders\' leadership styles. The research questions were as follows: what kind of leadership styles do nurse managers use and what are the factors affected by their leadership styles.
2.2. Participants {#sec2.2}
-----------------
To achieve the aim of this study data were collected through open interviews. The majority of Finnish nurse managers, nurses, and supervisors work in hospitals or long-term facilities. Selection of participants was performed in convenience sampling \[[@B26]\]. Participants were selected paying attention to the fact they were of different ages, working in different wards and units (e.g., psychiatry, internal diseases, gerontology) in either hospitals or long-term facilities, and had worked with more than one nurse manager.
The researcher contacted the participants and asked whether they were interested in taking part in the study. The participants were informed about the aim of the study. Participation was voluntary. Prior to the interviews each participant signed a form where they gave their consent to participate in the study. A total of 11 nurses and 10 supervisors, 20 women and one man, from eight Finnish hospitals and five long-term care facilities participated in the study. The age of the nurses varied between 30 and 53 and their experience in health care between 7 and 25 years. The age of the supervisors varied between 38 and 59 and their experience as supervisors between 5 and 21 years. Both nurses and supervisors had worked with many nurse leaders and they were interviewed about nurse managers in general. They thus had experience of different nurse managers on different wards and they were able to describe leadership styles from various aspects.
2.3. Data Collection and Analysis {#sec2.3}
---------------------------------
Semistructured interviews were used to gather data on the perceptions of nurse managers\' leadership styles and factors affected by leadership styles. Interviews were usually carried out in the office in the participants\' workplace. All interviews were recorded with individual consent. Participants were initially asked to describe their work and earlier study and work history. They were subsequently asked about their perception of leadership styles and asked to describe the leadership styles used by their nurse managers. After that they were asked about factors affected by leadership styles. Each interview was approached individually, guided by participants\' responses. The interview sessions lasted between 30 and 85 minutes. Every interview was transcribed word for word from the recordings. Interviewing was continued until saturation of the data was achieved \[[@B27]\].
Because nurses and supervisors might have differed in their perceptions of leadership styles, the data were first analysed separately in two separate groups, following the same process for each group. Content analysis was chosen because it is a research method for making valid inferences from data to the contexts of their use \[[@B28]\].
The interview texts were read through multiple times, based on the author\'s empirical and theoretical preunderstanding of the professional area of the participating nurses and nurse managers. A structured categorization matrix of leadership styles was developed based on the primal leadership model \[[@B23]\] and research of Vesterinen et al. \[[@B29]\]. When using a structured matrix of analysis, an item of the data that does not fit the categorization frame is used to create its own concept, based on the principles of inductive content analysis \[[@B30]\]. When both the data of nurses and superiors were analysed, the results were compared. The categories and subthemes were congruent and therefore the results are presented together, albeit paying attention to differences and similarities of the perceptions of nurses and superiors.
The data analysis of the factors affected by leadership styles was inductive. All the data of nurses and supervisors were analysed together. This process included open coding, creating categories, and abstraction. A classification framework of the factors was formed inductively by defining categories and sub-themes. The criteria for allocating a unit to a category were formed by asking questions if the unit was suitable to the category. The sub-themes were named using descriptive concepts and classified as "belonging" to a particular category. After that, the categories were given names \[[@B31]\].
2.4. Trustworthiness {#sec2.4}
--------------------
The trustworthiness of this study has been ensured by confirming truth value, consistency, neutrality, and transferability of this study \[[@B32]\].
When considering this study from the viewpoint of trustworthiness, there are some threats that should be taken into consideration. The researcher collected the data and performed the analysis alone and the interpretation could have been affected by her professional history \[[@B33]\]. With interviews there is a risk that respondents try to please the interviewer by reporting things they assume s/he wants to hear. The researcher confirmed the truth value of the study by selecting participants in convenience sampling. The respondents\' age distribution was wide and they worked in different units. Their perspectives and descriptions were broad and gave a diverse picture.
The truth value of this study was also confirmed by analysing data as they emerged based on the interviews. To ensure the trustworthiness of the study quotes from interviews are included in the results.
In view of consistency, the research process is described so that it can be repeated if necessary. This gives a possibility to understand the limitations of the process of data collection and analysis. To ensure neutrality in this study, interpretations were based on original data. This is confirmed by citations from the interview data.
In this study the sample was small, consisting of Finnish nurses and supervisors, and the results only reflect their perceptions of leadership styles. As a result, transferability of results is limited. However, when considering the main objective in this study, it was not transferability of research results, but it was to enhance understanding of leadership styles and use it for future studies.
2.5. Ethical Considerations {#sec2.5}
---------------------------
The data for this study were collected following approval from the administrations of the organizations. All participants were informed of the purpose of the study. They were told that their participation was voluntary and would be treated with confidentiality. Participants were asked to sign a form where they gave their consent to take part in the study.
3. Results and Discussion {#sec3}
=========================
3.1. Results {#sec3.1}
------------
Data analysis identified visionary, coaching, affiliate, democratic, commanding, and isolating leadership styles ([Figure 1](#fig1){ref-type="fig"}). Job satisfaction and commitment as well as operation and development work, cooperation and organizational climate in the work unit were the factors affected by leadership styles.
### 3.1.1. Leadership Styles {#sec3.1.1}
Visionary Leadership StyleSupervisors were of the opinion that today, nurse managers use a more visionary leadership style than previously. In the past, many organizations lacked a vision of their own and had fewer possibilities to engage in development for the future. Even now, the skills of nurse managers to lead visionary development work varied.
Both nurses and supervisors reported that it was characteristic of the visionary nurse manager to emphasize and discuss the vision and provide information to employees. When establishing their vision, some nurse managers provided guidelines for attaining the work unit\'s goals. These nurse managers had a systematic and purposeful leadership style, based on the knowledge of nursing science and practice. They generally worked in organizations with strategies and vision. They had clear goals and rules on how to work. Nurse managers had so-called performance development discussions with every employee once a year. During the discussion, the nurse manager explained and revised the goals and discussed the purpose of the employee\'s work together with each employee. At the same time, they agreed on the goals of the employee for the next year. Visionary nurse managers were described as being assertive and persistent in their attempts to get the work units to achieve their goals. Nurse managers with more recent education were better equipped to search for information than nurse managers with older education. In addition, they often had a clear picture of the development needs in nursing practice.
Supervisors said that sometimes the fact that the organization did not have visions or direction for the future was an obstacle to a visionary leadership style. This was emphasized in cases where changes were introduced to the organization. Some nurse managers worked more on the basis of operation up until the present. The managers were guided by various situations and there were no plans for the future."*"This manager had visions and we had long-term plans, but these plans often changed."*"
Nurses emphasized the importance of making the vision understandable by giving information about current issues of the work unit. Nurse manager\'s skills to provide information objectively and positively influenced the way the personnel reacted to topical issues. It was also important to explain the motivation behind decisions.
Coaching Leadership StyleNurses as well as supervisors felt that nurse managers with a coaching leadership style took into consideration both the professional development of the employees and delegation of work. The employees had resources and were seen as experts and the nurse manager delegated tasks to them. The skills of employees to work independently varied. Some employees needed more coaching while others were satisfied with using their own professional skills independently.
The success of delegation was affected by common instructions. They guided employees so that every employee knew his/her tasks. The employees worked and made decisions independently within the bounds agreed. The nurse managers had a significant role in supporting the employees to cope with the problems at work. They were also responsible for coordinating and organizing work in the unit as a whole."*"A nurse manager draws plans for nursing practice so that there are these areas of responsibility and everybody knows what is their area and they answer for that."*"
The nurse manager paid attention to employees\' professional skills and encouraged them to study further. Both personnel\'s competence and leaders\' skills to lead influenced the development work in the unit. It was useful to clarify what kind of needs the work unit and employees had for additional education and to draw up an education plan. This plan was a meaningful basis to guide the employees to necessary training. It was each employee\'s duty to share the new knowledge with other employees. The nurse manager encouraged the employees to collect information without prompting and to think independently. S/he also gave feedback about the professional development of the employee.
Affiliate Leadership StyleNurses as well as supervisors described an affiliate leadership style. Nurse managers with affiliate leadership style emphasized harmony and acceptance of difference. The employees and their best interests were the most important value to the nurse manager. They knew the rules and guidelines of the organization, but they considered the hopes and needs of employees in a flexible manner. The nurse manager had skills to understand the feelings of another person and supported him/her by listening sensitively. Both s/he and his/her personnel trusted each other. Nurses reported that this encouraged the employees to discuss their personal concerns with the nurse manager. "*"The way to act, pay attention to the employee, do you listen to her or not, that is the basic question."*"
On the other hand, supervisors reported that leading could be too solicitous, in a completely motherly way. The basis of the leadership style could be supporting the well-being and job satisfaction of the employees; this might be more important than the development of nursing practise. The purpose---a harmonious atmosphere without conflicts---can be an obstacle to planned changes. "*"When there are big changes in the work unit, nurse manager is present to the employees and listen \[sic\] to them. She tries to support and say \[sic\]: there is no problem and we manage of this."*" "*"When a new employee begins to work, she leads in \[sic\] more paternalistic way and takes care of them all the time."*"
Both nurses and supervisors deemed it important that the nurse manager respects differences and personal characteristics of the employees, not forgetting employees\' equality. A nurse manager who respects and accepts the employees as individuals was easy to approach. On the other hand, nurse manager\'s close friendship with employees could make it more difficult to examine the work unit and its functions objectively."*"There are managers who are very permissive and let the employees behave each in their own way, it is typical that new small managers rise beside them."*"
According to the findings nurse managers sometimes behaved in a manner the employees felt to be unequal."*"It seems that if you are a strong-willed person, you are more likely to get what you want than a person who is adaptable."*"
Democratic Leadership StyleBoth nurses and supervisors reported that it was typical for the democratic nurse manager to emphasize teamwork and commitment to work. All employees\' participation was important to him/her. The nurse manager worked and discussed work together with the personnel. The employees had a possibility to voice their opinions and take part in problem-solving and decision-making. However, the nurse manager was ultimately expected to be a decision-maker. "*"... and find and make the decision by thinking together and listening to opinions of the employees and discussing together; however, she is in some cases the final decision-maker."*"
There were different perceptions of the nurse managers\' positions in this leadership style. On the one hand, they were deemed to be responsible for the work unit and to make reasonable decisions after discussing with the employees. On the other hand, some supervisors felt that some nurse managers did not stand out as managers, but as team members. This meant that the nurse manager\'s own tasks could be of secondary importance."*"... she is working a lot with us and she has difficulties performing her own duties as a nurse manager."*"
Supervisors said that a nurse manager had an important role in cooperation and its development with the members of different professional groups and between work units. His/her skills to get the employees to commit to the common goals were deemed as significant. Planning together with the personnel formed a basis for employees\' commitment to work. That was essential for the development of the operation of the work unit."*"... leadership style influences operation as a whole, for example, how a manager gets employees to commit to common decisions"*"
Commanding Leadership StyleBoth nurses and supervisors identified a commanding leadership style, characterized by an emphasis on compliancy and control. Nurses as well as supervisors reported that it was important to the nurse managers with a commanding leadership style to follow clear directions and advice which they expected to get from others, for example, their own superiors. The employees were expected to obey these orders. The nurse manager could ask employees\' opinions on how to find a solution to a problem in the work unit; usually s/he had already made a decision and it was not changed by the opinions of the employees. The nurse manager did not think it necessary to explain his/her decisions. The leadership style was described as authoritarian, hierarchical, and inflexible."*"Nurse managers who do not have the latest knowledge of leadership, they demand that there should be clear rules and laws for everything and there is no flexibility."*"
Commanding leadership style was more common in the 1970s and 1980s and it was now considered traditional and out-of-date. It was, however, described as a convenient leadership style when employees are inexperienced or when there are big changes in the work unit. Nurse managers were described as controlling the behaviour of the personnel, although observations of that kind have diminished considerably.
Isolating Leadership StyleBoth nurses and supervisors described that nurse managers could isolate themselves from the work unit and retire to their own room where they worked alone without active communication with the employees. In that case the employees felt that they had been left without a leader. Problematic situations like conflicts between employees often arose and they were difficult to repair. Neither the nurse manager nor the employees got the information they needed in their work. "*"The nurse manager is quite isolated, she works alone in her room, we visit her when we have something to discuss with her."*"
### 3.1.2. Factors Affected by Leadership Style {#sec3.1.2}
Both nurses and supervisors reported that nurse manager\'s leadership style affects employees\' job satisfaction and commitment to work. It is felt that nurse manager\'s fairness and trust in the employees promotes their motivation and participation in work. It is important that the employees have a possibility to develop their professional skills. Leadership style contributes to job satisfaction when the nurse manager has skills to prevent and solve conflicts.
All the participants reported that nurse manager\'s skills to lead the work unit and motivate people affect the success of the work unit. Often s/he has to ask for adequate resources. It is important that there are enough trained employees and the employees know and are in charge of their areas of responsibilities. Supervisors remarked on the influence of leadership style on efficiency and economy, because the fluency of operation has an impact on how much money is spent. The nurse manager\'s influence in developing and changing operation is very important. It is important that the employees have a possibility to take part in development work as well. Nurse manager\'s leadership style can promote or hinder development in the work unit.
Supervisors emphasized that nurse managers have a significant role in cooperation within the work unit and outside it. Some nurse managers want to work only inside their own unit, while others take a larger view of the matter. Nurse manager\'s leadership style has an influence on how externally orientated the staff are and whether they have connections outside the work unit. A nurse manager can promote the continuity of patient care by cooperation with other units. S/he is a role model in how to treat nurse students.
Both nurses and supervisors felt that problems in the organizational climate, such as conflicts between the employees or dissatisfaction with the nurse leader are reflected in patient care. The activity or passivity of the nurse manager affects the image of the work unit."*"If there is patient mistreatment, it is the nurse manager whose responsibility it is to decide how to react, for example, "in our unit we treat patients well" or "we do not react at all to this complaint"."*"
All in all, organizational climate, personnel\'s job satisfaction and commitment, work unit\'s operation and development work, and cooperation influence the way patient care succeeds and how a patient experiences the care he/she gets. Leadership style has an effect on patient satisfaction and quality of care. If the nurse manager\'s basic value is good patient care, it influences in many ways his/her leadership style and how s/he organizes things in the work unit.
3.2. Discussion {#sec3.2}
---------------
The discussion is structured around the findings identified above. An isolating leadership style was identified as distinct from the leadership styles that Goleman \[[@B23]\] presented, whereas pace-setting leadership style was not reported. The participants reported that nurse managers used many leadership styles, but normally they had one which they used more than others. Nurses who worked for leaders with resonant leadership styles were more satisfied with supervision and their jobs \[[@B34]\]. Furthermore, visionary leadership style, coaching leadership style, affiliate leadership style, and democratic leadership style seem to promote transformational leadership because they motivate and involve staff. That is why nurse managers should develop themselves in the use of these leadership styles.
Nurse managers\' leadership style depends on many issues, such as organization, situation, and employees. Reynolds and Rogers \[[@B35]\] argue that employees have variable levels of competence depending on the situation. That requires managers to adapt their leadership style. It is important that nurse managers have skills to reflect on their own leadership style and receive feedback about it. That gives them tools to use different leadership styles in different situations.
Health care is meeting ever-increasing new challenges where it has to react rapidly. It is important to the health care organizations to make long-term plans and prepare for the future by paying attention to the needs of inhabitants and the resources needed. The vision is the basis of the goals of the work unit, too. Having knowledge of nursing science and practice gives nurse managers the tools to use a visionary leadership style and make plans for the future. Morjikian et al. \[[@B36]\] argued that communication of future plans, goals, and strategies is important between the nurse manager and the employees. It is important to give information of the vision and explain it regularly to the employees, because sometimes the employees forget the purpose of their work and their working style is not appropriate. When nurse managers work like this they are also carrying out transformational leadership \[[@B4], [@B5]\].
In the future, securing skilled employees will be a big challenge in health care. Vesterinen et al. \[[@B29]\] found that nurse managers with a coaching leadership style appreciated employees\' professional skills and encouraged them to study further. Nurse manager\'s consideration of employees\' profession and educational needs influenced nurse retention positively. Kenmore \[[@B37]\] argued that a coaching leadership style works when the employees are keen to develop and make use of possibilities to do so. Education gave employees tools to work and make decisions independently. Although the nurse manager organizes the work unit as a whole and is responsible for the development work in the unit, his/her support has a significant role in helping employees to cope with the problems they meet in their work. This is also an important part in nurse managers\' role as emotionally intelligent leaders \[[@B10]\].
As a consequence of globalization, both employees and patients come from many different cultures. Their behaviour and habits to express their needs vary. An affiliate leadership style with acceptance of difference could be suited for the multicultural work unit. It is a challenge for the manager to listen sensitively and consider to employees\' personal needs individually and at the same time objectively, not forgetting employees\' equality. This requires an emotionally intelligent nurse manager \[[@B10]\]. The basis of the leadership style could be supporting the well-being and job satisfaction of the employees. As Kenmore \[[@B37]\] argues, if a nurse manager is too concerned with creating harmony, it can lead to evasion of problems.
Because of shortage of employees, nurses have many possibilities to choose and change their workplaces. Democratic leadership style promoted employees\' commitment to work \[[@B29]\]. It is important that the employees can express their opinions and take part in decision-making.
A commanding leadership style prevents the empowerment of the nurses, because they do not have possibilities to participate in work planning \[[@B38]\]. However, there are situations where a commanding leadership style is appropriate. The majority of Finnish nurses will retire in the next few years and there are many nurses with less work experience in the work units. Employees with less work experience may need clear directions, for example, in acute situations when a patient\'s life is in danger.
According to Huston \[[@B1]\], essential nurse manager competencies for the future include the ability to create an organization culture that combines high-quality health care and patient/employee safety and highly developed collaborative and team building skills. As a result of this study, an isolating leadership style was found: the nurse manager worked alone without active communication with the employees. The employees have to work without a leader, and that could cause anxiety for the employees who need support from their leader. A good question in this case is who is really leading the work unit. If the leader does not show consideration towards the employees, it could affect their health and well-being negatively \[[@B39]\]. Nurse managers need support to develop the leadership style. Leaders and their supervisors should be considered collectively to understand how leadership influences employee performance \[[@B40]\].
A nurse manager has an important role in leading the work unit as a whole. A work unit is seen as a reflection of the nurse manager. According to Rosengren et al. \[[@B41]\], nurses reported that nursing leadership was considered "being present and available in daily work," "facilitating professional acknowledgement," "supporting nursing practice" and "improving care both as a team and as individuals." A nurse manager with an emotionally intelligent leadership style creates a favourable work climate characterized by innovation, resilience, and change \[[@B42]\]. Nurse managers have to be flexible in the changes they have directly initiated or by which they have been indirectly affected \[[@B43]\]. Leadership style affects the organizational climate and the ways how information is given and communicated and how questions of the day are discussed. The nurse manager creates the basis for how different opinions are handled and problems solved in the work unit.
Nurse manager\'s leadership style affects the personnel\'s job satisfaction and commitment. It is perceived that nurse manager\'s trust in the employees promotes their motivation and participation in work. Way et al. \[[@B44]\] found that trust and job satisfaction are strong links with greater commitment and intent to stay on at work. Nurse managers create basic preconditions for the operation and for development work.
Leader encourages the employees to develop goals and plan to achieve them. In this way he/she influences the professional development of the personnel \[[@B45]\]. Their skills to build bonds and seek out mutually beneficial relationships affect cooperation in the work unit and around it.
On the other hand, there is no one and only correct leadership style; the same result can be achieved in many ways. A manager who has the ability to reflect on his/her own behaviour, that is, who has high EI, is better able to regulate and estimate his/her leadership style with different employees in different situations. Leadership style influences patient care and its quality at least indirectly. A nurse manager has a significant role in using a leadership style that promotes good patient care.
4. Conclusions {#sec4}
==============
Nurse managers had many leadership styles, but normally they had one that they used more than the others. The nurse managers should consider their leadership style from the point of view of employees, situation factors, and goals of the organization. Leadership styles where employees are seen in a participative, active role have become more common. Together with health care organizations, nursing education programmes should include education of nurse managers to improve their self reflection, through which they are better able to vary their leadership style.
{#fig1}
[^1]: Academic Editor: Linda Moneyham
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Frequency of feeding, weight reduction and energy metabolism.
A study was conducted to investigate the effect of feeding frequency on the rate and composition of weight loss and 24 h energy metabolism in moderately obese women on a 1000 kcal/day diet. During four consecutive weeks fourteen female adults (age 20-58 years, BMI 25.4-34.9 kg/m2) restricted their food intake to 1000 kcal/day. Seven subjects consumed the diet in two meals daily (gorging pattern), the others consumed the diet in three to five meals (nibbling pattern). Body mass and body composition, obtained by deuterium dilution, were measured at the start of the experiment and after two and four weeks of dieting. Sleeping metabolic rate (SMR) was measured at the same time intervals using a respiration chamber. At the end of the experiment 24 h energy expenditure (24 h EE) and diet-induced thermogenesis (DIT) were assessed by a 36 h stay in the respiration chamber. There was no significant effect of the feeding frequency on the rate of weight loss, fat mass loss or fat-free mass loss. Furthermore, fat mass and fat-free mass contributed equally to weight loss in subjects on both gorging and nibbling diet. Feeding frequency had no significant effect on SMR after two or four weeks of dieting. The decrease in SMR after four weeks was significantly greater in subjects on the nibbling diet. 24 h EE and DIT were not significantly different between the two feeding regimens.(ABSTRACT TRUNCATED AT 250 WORDS) |
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Monday, October 13, 2014
Fordham’s First Win over Penn is a Record Breaker
Fordham’s First Win over Penn is a Record Breaker
(Photos by Gary Quintal)
By Howard Goldin
BRONX, NEW YORK, OCTOBER 13- The sixth meeting between the Fordham Rams (6-1, 2-0) and the University of Pennsylvania Quakers (0-4, 0-1) took place at Jack Coffey Field in the Bronx on October 11. The game on Saturday was the first victory of Fordham, 60-22, over the Quakers. The two teams seem to be heading in different directions. The win for Fordham was its fifth straight and 11th consecutive home win, and the loss for Penn was its eighth straight. The 60 points scored by the Rams was the most their Ivy League opponent had surrendered in a single game since its 61-0 defeat by #1 ranked Army on November 17, 1945.
The visitors reached the scoreboard first as Penn quarterback Alek Torgerson threw a 33-yard touchdown pass to Ryan O’Malley at 10:01. To the credit of the Fordham defense, that intercepted two passes and forced two fumbles, the first Penn touchdown was also its last. The last 16 points scored by the Quakers were off the foot of Jimmy Gammil. The junior kicked the point after touchdown and five field goals.
Fordham scored twice on the ground in the first quarter. Harrisburg, Pennsylvania native Chase Edmunds carried the ball three yards for Fordham’s first points. His 11th touchdown of the season, in only six games, has been topped only five times in Fordham history in a single (full). He rushed for 101 yards, the sixth game in which has rushed for triple figures of yards. He is the first Fordham freshman to have a season rushing yardage total above 1,000 (1,011).
Fordham head coach Joe Moorhead, in his third successful season in the Bronx, spoke very highly of the sensational freshman’s work ethic, preparation, and effort, “He’s an old soul. Everything he’s gotten, he’s earned. It’s not a surprise the success he’s had.”
Quarterback Mike Nebrich, a senior, has also been impressed by the freshman running back, “He’s been huge. It [his rushing] opens up the defense. You can lead as a freshman.”
The second Fordham first quarter touchdown came on a recovered fumble and eight-yard run by senior defenseman DeAndre Slate.
Fordham’s defensive onslaught during the remainder of the game was achieved through the air under the leadership and outstanding ability of quarterback Nebrich. The senior from Virginia spoke of how he sees his responsibility during each contest, “My job is to get us going anytime we start sputtering.”
On Saturday, he completed 36 of 47 passes for a Fordham record of 566 yards, which broke the mark of 524 yards he set in 2013. Six of the 36 completions were for touchdowns, tying a Fordham game mark.
Five different receivers caught touchdown tosses from Nebrich. Tubucky Jones Jr., like Nebrich, a University of Connecticut transfer, caught two, one of 37 yards and one of 47 yards. Jones caught 10 for 203 yards, the eighth highest total in Fordham history. Sam Ajala received eight passes for 199 yards, the ninth highest total.
The 730 yards gained by the Fordham offense was a single game school record and the highest total by an NCAA FCS team this season. According to Moorhead, this success stems from good practice habits and game preparation. The coach also praised his players as being good students and fine human beings as well as good athletes. His own college experience at Fordham has obviously imbued in him the knowledge of what a student-athlete should be.
After Fordham’s bye-week the team will travel to Lehigh for its next contest on October 25. The Rams will return to Jack Coffey Field on November 1 to host Colgate. |
Non-equilibrium x-ray spectroscopy using direct quantum dynamics.
Advances in experimental methodology aligned with technological developments, such as 3rd generation light sources, X-ray Free Electron Lasers, and High Harmonic Generation, have led to a paradigm shift in the capability of X-ray spectroscopy to deliver high temporal and spectral resolution on an extremely broad range of samples in a wide array of different environments. Importantly, the complex nature and high information content of this class of techniques mean that detailed theoretical studies are often essential to provide a firm link between the spectroscopic observables and the underlying molecular structure and dynamics. In this paper, we present approaches for simulating dynamical processes in X-ray spectroscopy based upon on-the-fly quantum dynamics with a Gaussian basis set. We show that it is possible to provide a fully quantum description of X-ray spectra without the need of precomputing highly multidimensional potential energy surfaces. It is applied to study two different dynamical situations, namely, the core-hole lifetime dynamics of the water monomer and the dissociation of C F 4 + recently studied using pump-probe X-ray spectroscopy. Our results compare favourably to previous experiments, while reducing the computational effort, providing the scope to apply them to larger systems. |
Q:
highcharts redraw and reflow not working
I am trying to build a dynamic page that has any number between 1-4 graphs on it that can be added or removed as needed but I have run into a huge problem and I can't seem to get the graph to resize after resizing the containing div. for example if I add a graph on the page it will be width 800, then click a button to add another graph it should resize to be 400 a piece but I cannot make it happen. As a very simplistic model I have the following
$(function () {
$('#container').highcharts({
chart: {
type: 'line',
width: 300
},
title: {
text: 'Width is set to 300px'
},
xAxis: {
categories: ['Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun', 'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec']
},
series: [{
data: [29.9, 71.5, 106.4, 129.2, 144.0, 176.0, 135.6, 148.5, 216.4, 194.1, 95.6, 54.4]
}]
});
$('#resize').click(function() {
$('#container').attr('style', 'width: 800px');
$("#container").highcharts().reflow();
console.log($('#container').width());
});
});
now when that is run it will log 800 to the dev tools window in chrome but the graph will not resize. I have tried both redraw() and reflow() as suggested in the documentation for highcharts. I even setup a really quick demo on jsfiddle here, http://jsfiddle.net/7cbsV/
can anyone please help me. It is kind of important. Thank you in advance for the help.
A:
How about using simple chart.setSize(w,h)? See docs.
$("#container").highcharts().setSize(800, height);
|
Ratno Dolne
Ratno Dolne () is a village in the administrative district of Gmina Radków, within Kłodzko County, Lower Silesian Voivodeship, in south-western Poland.
It lies approximately east of Radków, north-west of Kłodzko, and south-west of the regional capital Wrocław.
References
Ratno Dolne |
Successful treatment of radiation induced breast ulcer with hyperbaric oxygen.
The purpose of this report was to investigate the efficacy of hyperbaric oxygen treatment in the management of a persisting radiation induced ulcer following standard breast irradiation. A 57-year-old Caucasian patient was referred following partial mastectomy and axillary node clearance for a T2N0 grade 3 infiltrating ductal carcinoma of the left breast. She received 45 Gy in 25 fractions at 1.8 Gy per fraction to the isocentre to the whole breast using tangential fields and 4 MV photons, in conjunction with intravenous chemotherapy (cyclophosphamide, methotrexate and 5 fluorouracil). Treatment was interrupted for 3.5 weeks because of a grade 4 skin and subcutaneous reaction. Treatment resumed to the tumour bed alone. Chemotherapy was abandoned. The tumour bed received 14 Gy in 7 fractions at 2 Gy per fraction prescribed to the 100% using 10 MeV electrons and a direct field, completing treatment on 7 July 1998. The radiation induced a painful 8x4 cm ulcer which persisted in spite of rigorous treatment including Gentian Violet, Silvazine Cream, Duoderm and antibiotics. The patient received 30 hyperbaric treatments, six times a week, completing treatment on 15 December 1998. The patient required insertion of bilateral ear grommets under local anaesthetic. The breast ulcer showed a response to treatment with early healing after 7-8 days and clinical evidence of re-epithelization. At completion of 30 treatments the patient was left with a small shallow faintly discharging multilocular 3-4 cm ulcer. The ulcer had completely healed by 14 January 1999. The patient has been symptom free since completion of treatment. This report highlights the efficacy of hyperbaric oxygen therapy in the management of persisting radiation-induced ulcers. |
Blunted increase in plasma adenosine levels following dipyridamole stress in dilated cardiomyopathy patients.
Heart failure is characterized by chronically increased adenosine levels, which are thought to express a protective anti-heart failure activation of the adenosinergic system. The aim of the study was to assess whether the activation of adenosinergic system in idiopathic dilated cardiomyopathy (IDC) can be mirrored by a blunted increase in plasma adenosine concentration following dipyridamole stress, which accumulates endogenous adenosine. Two groups were studied: IDC patients (n = 19, seven women, mean age 60 +/- 12 years) with angiographically confirmed normal coronary arteries and left ventricular ejection fraction <35%; and normal controls (n = 15, six women, mean age 68 +/- 5 years). Plasma adenosine was assessed by high-performance liquid chromatography methods in blood samples from peripheral vein at baseline and 12 min after dipyridamole infusion (0.84 mg kg-1 in 10 min). At baseline, IDC patients showed higher plasma adenosine levels than controls (276 +/- 27 nM L-1 vs. 208 +/- 48 nM L-1, P < 0.001). Following dipyridamole, IDC patients showed lower plasma adenosine levels than controls (322 +/- 56 nM L-1 vs. 732 +/- 250 nM L-1, P < 0.001). The dipyridamole-induced percentage increase in plasma adenosine over baseline was 17% in IDC and 251% in controls (P < 0.001). By individual patient analysis, 18 IDC patients exceeded (over the upper limit) the 95% confidence limits for normal plasma adenosine levels at baseline, and all 19 exceeded (below the lower limit) the 95% confidence limits for postdipyridamole plasma adenosine levels found in normal subjects. Patients with IDC have abnormally high baseline adenosine levels and--even more strikingly--blunted plasma adenosine increase following dipyridamole infusion. This is consistent with a chronic activation of the adenosinergic system present in IDC, which can be measured noninvasively in the clinical theatre. |
This invention pertains to speed regulators for direct current DC motors and, more particularly, is concerned with open loop speed regulators for DC motors.
DC motors find numerous applications because of their intrinsic variable speed characteristics and capabilities which offer very high speeds and small size.
The rotating member of a DC motor is named the armature and the stationary member is named the field. The armature has windings and the field can have either windings or permanent magnets.
Some applications have a need for constant speed regardless of torque. A general statement about DC motors is that with an increase in torque, speed will drop and current will increase, assuming a constant input voltage. The amount each parameter varies depends on the type of motor. For a motor with the armature and field winding connected in series the drop in speed will be more pronounced than the increase in current. For motors with shunt connected windings or permanent magnet fields the opposite is true, the speed will be more nearly constant while there is a marked increase in current. There will be some drop in speed however, and this amount may be undesirable in critical applications. For this reason, a number of constant speed controls have been devised over the years.
Speed regulating systems may be classified as either closed loop or open loop. Closed loop systems derive a signal from the actual speed of the motor with a tachometer, for example, and use the signal in a feedback loop.
An open loop system does not measure speed directly but measures some other parameter. In some open loop systems the measured parameter is current.
A well known example of an open loop motor regulating system includes a resistor in series with the input of the motor. The voltage across the resistor corresponds to motor current and is directed to a control circuit. The resistor voltage influences a control circuit which supplies the input voltage to the motor. A change in resistor voltage indicates a change in torque and indirectly indicates a change in speed. In response to the resistor voltage the control circuit adjusts the voltage to the motor thereby supplying the right amount of power required to maintain a constant speed over variations in torque.
The series resistor causes I.sup.2 R power losses particularly when during high torque conditions because current is high. These losses cause heat build-up and a need for a larger power supply capability.
It will be seen that a speed regulator according to the present invention does not require a resistor in series with the motor and is thereby more efficient. |
If you have very poor credit, the cheapest car insurance company is Nationwide. Here, your premium will be more than $435 less than the group average. Compared to the highest credit level, drivers with bad credit pay nearly $1,450 more per year for auto insurance. If you pay off a loan or otherwise improve your credit score, you should shop around for car insurance as your premium should change. Just another reason to keep your score up!
You’ll notice that none of that liability coverage pays for your car or injuries, nor for any injuries your passengers sustain if you cause a wreck. This is why many people — particularly those whose car isn’t yet paid off — want “full coverage” car insurance. This isn’t actually a type of coverage, but instead typically refers to policies that include liability coverage, plus comprehensive and collision coverages.
Auto Insurance is required by law for drivers in most states. Drivers who own a car and drive it often should definitely have auto insurance to cover the risk of damages to their car and personal injury and the liability of harm to other people and property. Otherwise, repairs and medical costs, particularly when you’re liable for an accident, can be very expensive.
Liability auto insurance protects you from that worst case scenario by providing a cushion between your assets and the amount you’re on the hook for. For this reason, choosing the right auto liability limits is the most important part of your car insurance quote comparison. NerdWallet typically recommends having at least as much liability coverage as your net worth.
The best car insurance companies have a few things in common: They have straightforward shopping experiences, take good care of policyholders after a crash and treat their customers with respect and courtesy. That means only insurers with high customer satisfaction scores and relatively few complaints to insurance commissioners make it to the top of our list of the best auto insurance companies.
The key difference in collision vs. comprehensive coverage is that, to a certain extent, the element of the car driver's control. As we have stated before, collision insurance will typically cover events within a motorist's control, or when another vehicle collides with your car. Comprehensive coverage generally falls under "acts of God or nature," that are typically out of your control when driving. These can include such events as a spooked deer, a heavy hailstorm, or a carjacking.
The life insurance market has shrunk by around 4% over the last ten years. Interestingly, the market shrunk after the recession then grew about 51% between 2010 and 2015, though it has since begun to drop in size again. In 2017, life insurance premiums exceeded the amount spent in four of the past five years, but still came short of levels seen in 2008 and 2015. Check out our graph below to see how the market has fluctuated in the last decade. All numbers in billions.
Know when to cut coverage. Don’t strip away coverage just for the sake of cheaper insurance. You’ll need full coverage car insurance to satisfy the terms of an auto loan, and you’ll want it as long as your car would be a financial burden to replace. But for older cars, you can drop comprehensive and collision coverage, which only pay out up to your car’s current value, minus the deductible.
The best companies will also have several supplemental coverage options, or endorsements, that you can add to your homeowners policy. Endorsements can vary, as some provide higher coverage limits for certain types of personal property like jewelry or fine furs; or they can provide supplemental coverage for risks — like water backups, floods, or earthquakes — not covered by home insurance.
If you live in an area with unusual state regulations or heightened risk of weather-related claims, shopping car insurance options will be vital. Not every car insurance company offers policies in every state, which can make pricing less competitive. If you live in storm-prone states like Louisiana or Florida, you might find it harder to get a competitive rate.
If you have very poor credit, the cheapest car insurance company is Nationwide. Here, your premium will be more than $435 less than the group average. Compared to the highest credit level, drivers with bad credit pay nearly $1,450 more per year for auto insurance. If you pay off a loan or otherwise improve your credit score, you should shop around for car insurance as your premium should change. Just another reason to keep your score up!
To calculate the added cost in purchasing comprehensive and/or collision coverage we looked at annual insurance quotes for a 30 year old male from New York across four different insurance companies, and the ten best-selling vehicles in the US. We look at the range of rates you could pay from basic liability to policy plans with comprehensive and collision coverage. Collision typically costs more than comprehensive, although some companies require you to carry both rather than just one. Comparing quotes across at least three companies can get you lower car insurance rates. |
1. Introduction {#sec1}
===============
Soil organic C (SOC) and total N (TN) are very important C and N pools in the terrestrial ecosystems \[[@B1], [@B2]\]. As the components of labile C and N pools in soils, dissolved organic C (DOC) and N (DON) and soil ammonium and nitrate N (NH~4~ ^+^-N and NO~3~ ^−^-N) play crucial roles in the biogeochemistry of C and N and in the nutrient transformation \[[@B3]--[@B5]\]. With the context of climatic warming, how SOC, TN, DOC, DON, NH~4~ ^+^-N, and NO~3~ ^−^-N respond is vital to global C and N cycling \[[@B1], [@B2]\]. However, inconsistent results on the responses of these C and N pools to climatic warming have been observed with respect to vegetation types and initial soil characteristics \[[@B2], [@B3], [@B6]--[@B14]\]. For example, He et al. \[[@B2]\] demonstrated that six-year warming (\~1.4°C increase of 10 cm soil temperature) significantly decreased soil C by 129.3 g m^−2^ in a temperate steppe of Inner Mongolia. In contrast, Li et al. \[[@B7]\] found that two-year warming significantly increased SOC in an alpine meadow (\~2.1°C increase of air temperature) but significantly reduced TN in an alpine swamp meadow (\~2.3°C increase of air temperature) on the Tibetan Plateau. Hagedorn et al. \[[@B13]\] indicated that one-growing-season warming (\~4°C increase of 5 cm soil temperature) did not significantly influence DOC. Song et al. \[[@B1]\] pointed out that six-year warming (\~1.2°C increase of 10 cm soil temperature) significantly reduced DOC in a temperate steppe in Inner Mongolia. Biasi et al. \[[@B15]\] indicated that two-year warming (\~0.9°C increase of 5 cm soil temperature) did not have obvious effects on DON, NH~4~ ^+^-N, NO~3~ ^−^-N, and N~min~ in a lichen-rich dwarf shrub tundra in Siberia. Bai et al. \[[@B14]\] stated that experimental warming (\~0.6--6.7°C in soil temperature) had a significant positive effect on N~min~ but not on TN across all biomes. Therefore, how climatic warming acts on C and N cycling still remains unclear.
More than 70% of the Tibetan Plateau is covered with grasslands \[[@B16]\]. The alpine grasslands of this Plateau are one of the systems most sensitive to global change \[[@B17], [@B18]\]. In alpine grasslands, understanding the responses of SOC, DOC, TN, DON, NH~4~ ^+^-N, and NO~3~ ^−^-N to climatic warming are crucial for predicting future changes in soil fertility and C sequestration. The alpine meadow is one of the most typical grasslands types on the Tibetan Plateau being subjected to climatic warming \[[@B19]\]. Information on how these C and N pools along an elevation gradient respond to climatic warming is scarce on the Tibetan Plateau. Here we set up a warming experiment in an alpine meadow at three elevations (i.e., 4313 m, 4513 m, and 4693 m) on the Northern Tibetan Plateau.
The main objective was to investigate the effects of short-term experimental warming on SOC, TN, DOC, DON, NH~4~ ^+^-N, and NO~3~ ^−^-N. Our previous study indicated that short-term experimental warming could not affect soil microbial biomass \[[@B20]\] and soil microbial activity regulated the balances of soil C and N pools in the alpine meadow \[[@B21]\]. We hypothesized that experimental warming may not affect these C and N pools in this study.
2. Materials and Methods {#sec2}
========================
2.1. Study Area, Experimental Design, and Soil Sampling {#sec2.1}
-------------------------------------------------------
A detailed description of the study area, the warming experimental design, the measurements of microclimate factors (including soil temperature and soil moisture), and the soil sampling are given in Fu et al. \[[@B20], [@B22]\].
Briefly, three alpine meadow sites were established at three elevations (i.e., a low (30°30′N, 91°04′E, and 4313 m), mid- (30°31′N, 91°04′E, and 4513 m), and high (30°32′N, 91°03′E, and 4693 m) elevation) at Damxung Grassland Observation Station of Tibet Autonomous Region in China in May 2010.
Annual mean air temperature and precipitation is 1.3°C and \~476.8 mm, respectively \[[@B20], [@B21]\]. The vegetation is*Kobresia*-dominated alpine meadow and roots are mainly concentrated in the topsoil layer (0--20 cm) \[[@B21], [@B22]\]. The soil is classified as sandy loam, with pH of 6.0--6.7, organic matter of 0.3--11.2%, and total N of 0.03--0.49% \[[@B20], [@B22]\].
Open top chambers (OTCs, 3 mm thick polycarbonate) were used to enhance temperature \[[@B22], [@B23]\]. The bottom and top diameters and the height of OTCs were 1.45 m and 1.00 m and 0.40 m, respectively \[[@B20], [@B22]\]. For each site, four OTCs and their paired control plots (1 m × 1 m) were randomly established in May 2010. There was \~3 m distance between plots.
Daily mean soil temperature (*T* ~*s*~) during the study period of July-September in 2011 inside the OTCs increased by 1.26°C, 0.98°C, and 1.37°C at the low, mid-, and high elevation, respectively, compared to control plots \[[@B20]\]. In contrast, experimental warming decreased daily mean soil moisture (SM) by 0.04 m^3^ m^−3^ in all sites \[[@B20]\]. Daily mean *T* ~*s*~ decreased with increasing elevation from the low to high elevation \[[@B20]\].
We collected topsoil samples (0--20 cm depth) inside each plot using a probe 3.0 cm in diameter on July 7, August 9, and September 10, 2011 \[[@B20]\]. Five soil subsamples were randomly sampled and composited into one soil sample for each plot \[[@B20]\]. Subsamples of the fresh soil were used to measure DOC, DON, NH~4~ ^+^-N, and NO~3~ ^−^-N and other subsamples of the fresh soil were air-dried for the measurements of SOC and TN.
2.2. Soil Analysis {#sec2.2}
------------------
A more detailed description of measurements of soil inorganic N (N~min~, i.e., sum of NH~4~ ^+^-N and NO~3~ ^−^-N), DON, and DOC can be found in Fu et al. \[[@B21]\]. Briefly, soil inorganic N in 20 g fresh soil sample was extracted with 100 mL K~2~SO~4~, filtered through 0.45 *μ*m membrane, and analyzed on a LACHAT Quikchem Automated Ion Analyzer. Dissolved organic C and TN (DTN) in another 20 g fresh soil sample was extracted with 100 mL ultrapure water and filtered through 0.45 membrane. The extractable SOC and TN concentrations in the ultrapure water extracts were measured using a Liqui TOC II elementar analyzer (Elementar Liqui TOC, Elementar Co., Hanau, Germany) and a UV-1700 PharmaSpec visible spectrophotometer (220 nm and 275 nm), respectively. We also analyzed dissolved inorganic N (DIN) in the ultrapure water extracts on a LACHAT Quikchem Automated Ion Analyzer. Then DON was calculated as the difference between DTN and DIN. The potassium dichromate method was used to determine SOC \[[@B24]\]. Soil TN was measured on a CN analyzer (Elementar Variomax CN). Soil microbial biomass (MBC) and N (MBN) data were obtained from Fu et al. \[[@B20]\].
2.3. Statistical Analysis {#sec2.3}
-------------------------
In order to examine the elevation effect, repeated-measures ANOVA with experimental warming and elevation as the between subject factors and with sampling date as the within subject factor was performed for a specific soil property (i.e., SOC, TN, DOC, DON, ratio of DOC to DON (DOC/DON), NH~4~ ^+^-N, NO~3~ ^−^-N, ratio of NH~4~ ^+^-N to NO~3~ ^−^-N(NH~4~ ^+^-N/NO~3~ ^−^-N), and N~min~). At each site, repeated-measures ANOVA with experimental warming (i.e., OTCs versus control) as the between subject factor and with sampling date as the within subject factor was conducted for each soil property. Single factor linear regressions were performed between soil properties and *T* ~*s*~, SM, MBC, and MBN. In addition, multiple stepwise regression analyses were conducted for soil properties to examine the relative importance of *T* ~*s*~, SM, MBC, and MBN in affecting the variations of soil properties. All data were examined for normality and homogeneity before analysis and natural logarithm transformations were made if necessary. The level of significance was *P* \< 0.05. All the statistical tests were performed using the SPSS software (version 16.0; SPSS Inc., Chicago, IL).
3. Results {#sec3}
==========
3.1. Effects of Experimental Warming on Soil Properties {#sec3.1}
-------------------------------------------------------
Regardless of experimental warming, elevation had significant effects on SOC (*F* = 183.19, *P* \< 0.001), TN (*F* = 126.38, *P* \< 0.001), DOC (*F* = 26.42, *P* \< 0.001), DON (*F* = 7.08, *P* \< 0.01), NH~4~ ^+^-N(*F* = 71.98, *P* \< 0.001), NH~4~ ^+^-N/NO~3~ ^−^-N(*F* = 14.01, *P* \< 0.001), and N~min~(*F* = 56.29, *P* \< 0.001) across the three sampling dates. In contrast, there were no significant effects of elevation on NO~3~ ^−^-N and DOC/DON. These C and N pools showed similar seasonal dynamics regardless of experimental warming among the three elevations ([Figure 1](#fig1){ref-type="fig"}).
In line with our initial hypothesis, experimental warming had little effects on SOC, TN, DOC, DON, DOC/DON, and NH~4~ ^+^-N/NO~3~ ^−^-N ([Table 1](#tab1){ref-type="table"}). In contrast, the sensitivity of N~min~ to experimental warming increased with increasing elevation ([Table 1](#tab1){ref-type="table"}). In detail, experimental warming significantly decreased N~min~ by 29.2% and 23.5% at the low and mid-elevation, NO~3~ ^−^-N by 36.4%, 29.5% at the low and mid-elevation, and NH~4~ ^+^-N by 16.7% at the mid-elevation across all the three sampling dates, respectively. In contrast, experimental warming had little effects on NO~3~ ^−^-N and N~min~ at the high elevation.
3.2. Relationships between Soil Properties and Environmental Variables and Soil Microbial Biomass {#sec3.2}
-------------------------------------------------------------------------------------------------
Soil organic C, TN, DOC, NH~4~ ^+^-N, NO~3~ ^−^-N, NH~4~ ^+^-N/NO~3~ ^−^-N, and N~min~ were significantly and positively correlated with SM ([Figure 2](#fig2){ref-type="fig"}). In contrast, SOC, TN, DOC, NH~4~ ^+^-N, and NH~4~ ^+^-N/NO~3~ ^−^-N declined with increasing *T* ~*s*~ ([Table 2](#tab2){ref-type="table"}). The negative correlations of *T* ~*s*~ with DON and N~min~ were relatively lower ([Table 2](#tab2){ref-type="table"}). Soil organic C, TN, DOC, DON, NH~4~ ^+^-N, NH~4~ ^+^-N/NO~3~ ^−^-N, and N~min~ increased significantly with increasing MBC and MBN, while NO~3~ ^−^--N only increased significantly with increasing MBN ([Table 2](#tab2){ref-type="table"}). Nitrate N was not related to MBC and *T* ~*s*~ ([Table 2](#tab2){ref-type="table"}), while DON was not correlated with SM (data not shown). In addition, DOC/DON was not correlated with *T* ~*s*~, SM, MBC, and MBN (data not shown).
The multiple stepwise regression analyses were listed in [Table 3](#tab3){ref-type="table"}. Both SOC and TN were simultaneously affected by MBC and *T* ~*s*~, whereas MBC explained more variation of the two soil properties than *T* ~*s*~. Only MBC was included in the multiple regression equations for DOC, DON, and NH~4~ ^+^-N/NO~3~ ^−^-N, while only MBN was included in the regression equation for NO~3~ ^−^-N. Soil microbial biomass C explained the variation of NH~4~ ^+^-N more than SM. Both MBC and MBN were simultaneously and positively correlated with N~min~. In addition, all the five concerned variables were excluded for DOC/DON.
4. Discussion {#sec4}
=============
4.1. Effects of Experimental Warming on SOC, TN, DOC, and DON {#sec4.1}
-------------------------------------------------------------
Recently, some studies showed that short-term (\<3 years) experimental warming had little effects on SOC, TN, DOC, and/or DON in a tallgrass prairie with a silt loam soil (\~2°C increase of 5 cm soil temperature) in USA \[[@B25]\], in a dragon spruce plantation with a mountain brown soil (\~0.6°C increase of 5 cm soil temperature) on the Tibetan Plateau \[[@B8]\], in an alpine treeline with a sandy Ranker and Podzols soil (\~4°C increase of 5 cm soil temperature) in Switzerland \[[@B13]\], and in a lichen-rich dwarf shrub tundra with Gleyic Cryosols soils (\~0.9°C increase of 5 cm soil temperature) in Siberia \[[@B15]\]. However, other studies with long-term (\>3 years) experimental warming indicated that warming significantly increased or decreased SOC, TN, DOC, and/or DON in a temperate steppe with a Calcic Kastanozems soil in Inner Mongolia (\~1.4°C increase of 10 cm soil temperature) \[[@B2]\], in an alpine meadow (\~3°C increase of 5 cm soil temperature) on the Tibetan Plateau \[[@B3]\], and in a temperate steppe with chestnut soil in Inner Mongolia (\~1.2°C increase of 10 cm soil temperature) \[[@B1]\]. Therefore, the insignificant responses of SOC, TN, DOC, and DON to warming ([Table 1](#tab1){ref-type="table"}) may be due to the short period of warming treatment (14--16 months).
A meta-analysis showed that the effects of experimental warming on N~min~, net N mineralization, and nitrification were significantly and positively correlated with raised soil temperature (\~0.6--6.7°C for N~min~, \~0.6--5.5°C for net mineralization, and \~1.3--5.5°C for net nitrification) across all biomes \[[@B14]\]. Similarly, we found that experimental warming-induced change of soil temperature tended to be negatively correlated with that of TN (*R* ^2^ = 0.43, *P* = 0.057) and positively correlated with that of MBN (*R* ^2^ = 0.43, *P* = 0.056) \[[@B20]\]. In addition, MBN was significantly correlated with SOC, TN, DOC, and DON ([Table 2](#tab2){ref-type="table"}). Therefore, the negligible responses of soil C and N pools to experimental warming ([Table 1](#tab1){ref-type="table"}) may be also due to lower warming magnitude in this alpine meadow.
Microbial activity regulates the production of dissolved organic matter \[[@B5], [@B8], [@B26]\] and experimental warming-induced decline in soil moisture may suppress soil microbial activity \[[@B20], [@B27]\]. Similarly, we also found that soil C and N pools increased with increasing soil microbial biomass and soil moisture ([Figure 2](#fig2){ref-type="fig"}, [Table 2](#tab2){ref-type="table"}). Moreover, short-term experimental warming had little effect on soil microbial biomass in this system \[[@B20]\]. Therefore, the negligible responses of SOC, TN, DOC, and DON to short-term experimental warming may be also related to that of soil microbial biomass \[[@B8], [@B20]\]. Moreover, experimental warming-induced soil drying may also suppress the production of DOC and DON \[[@B8], [@B20]\].
4.2. Effects of Experimental Warming on Soil Inorganic N {#sec4.2}
--------------------------------------------------------
Bai et al. \[[@B14]\] demonstrated that experimental warming did not significantly increase net N nitrification in grasslands. Similarly, experimental warming did not increase net N mineralization in an alpine meadow on the Tibetan Plateau \[[@B28]\]. In the same alpine meadow as this study, the finding that experimental warming did not increase ecosystem photosynthesis and aboveground plant biomass \[[@B22]\] also indirectly supported that experimental warming may not increase soil N availability because it has been observed that plant productivity is positively correlated with net N mineralization \[[@B29]\]. Therefore, the negligible or negative effect of experimental warming on soil inorganic N ([Figure 1](#fig1){ref-type="fig"}, [Table 1](#tab1){ref-type="table"}) may result from the suppression of net N mineralization and nitrification under warming.
The suppression of net N mineralization and nitrification may be owing to decreases in soil moisture and microbial activity because N~min~, NH~4~ ^+^-N, and NO~3~ ^−^-N increased significantly with increasing soil moisture and microbial biomass ([Figure 2](#fig2){ref-type="fig"}, [Table 2](#tab2){ref-type="table"}). Similarly, the experimental warming-induced significant reductions or insignificant changes of inorganic N ([Figure 1](#fig1){ref-type="fig"}, [Table 1](#tab1){ref-type="table"}) were also partly attributed to experimental warming-induced decline in soil microbial biomass \[[@B20]\] and soil drying \[[@B10], [@B29], [@B30]\]. This was in line with the finding that the effect of experimental warming on soil moisture was significantly correlated with that on soil nitrification \[[@B14]\]. On the other hand, microbial biomass was more closely related to soil inorganic N than soil moisture ([Table 3](#tab3){ref-type="table"}). This implied that microbial biomass may dominate the variation of soil inorganic N in this study. However, our previous study showed that short-term experimental warming tended to reduce microbial biomass due to soil drying in the same alpine meadow as this study \[[@B20]\]. Therefore, the experimental warming-induced changes of soil inorganic N, net N mineralization, and nitrification may be directly related to that of microbial activity and indirectly related to that of soil moisture.
The different responses of N~min~ to experimental warming among the three elevations across the sampling dates could be attributed to several probable underlying mechanisms. First, DON is high-quality N source for N mineralization \[[@B8], [@B31]\]. This was supported by the positive relationships between DON and N~min~ and NH~4~ ^+^-N and NO~3~ ^−^-N ([Figure 3](#fig3){ref-type="fig"}). DON under warmed plots tended to be decreased by 10.3% at the low elevation and by 28.7% at the mid-elevation but to be increased by 4.4% at the high elevation across all the three sampling dates, compared to control plots. Second, experimental warming-induced different changes in soil microbial biomass N (MBN) among three elevations \[[@B20]\] could partly explain this phenomenon considering that the production of DON and the immobilization of soil inorganic N were regulated by MBN \[[@B3], [@B32], [@B33]\]. This viewpoint was confirmed by the positive correlations between MBN and DON, N~min~, NH~4~ ^+^-N, and NO~3~ ^−^-N ([Table 2](#tab2){ref-type="table"}). Third, the response of soil N availability to warming could be strongly related to the initial conditions \[[@B8], [@B34]\]. In our system, N~min~, DON, and microbial biomass at the high elevation were significantly larger compared to the low and mid-elevation, whilst there were insignificant differences between the latter two \[[@B20]\].
5. Conclusions {#sec5}
==============
In summary, short-term experimental warming had no obvious effects on topsoil organic C, total N, dissolved organic C, and N pools for the alpine meadow in this study. The insignificant responses of these C and N pools to warming may be due to short-term warming treatment, experiment warming-induced soil drying, and lower warming magnitude. In contrast, the response of soil inorganic N to experimental warming differed among the three elevations, which may be attributed to different response trends of dissolved organic N and microbial biomass and different initial soil inorganic N.
This work was funded by the National Natural Science Foundation of China (no. 41171084) and the National Science and Technology Plan Project of China (no. 2011BAC09B03).
Conflict of Interests
=====================
The authors declare that there is no conflict of interests regarding the publication of this paper.
{#fig1}
{#fig2}
{#fig3}
######
Repeated-measures ANOVA (*F* values) for the main and interactive effects of experimental warming (W) and sampling date (D) on soil organic C (SOC), total N (TN), dissolved organic C (DOC), N (DON), ammonium N (NH~4~ ^+^-N), nitrate N (NO~3~ ^−^-N), the ratio of NH~4~ ^+^-N to NO~3~ ^−^-N (NH~4~ ^+^-N/NO~3~ ^−^-N), and soil inorganic N (N~min~, i.e., sum of NH~4~ ^+^-N and NO~3~ ^−^-N) in an alpine meadow on the Tibetan Plateau at three elevations (*n* = 4).
Elevation Model SOC TN DOC DON DOC/DON NO~3~ ^−^-N NH~4~ ^+^-N NH~4~ ^+^-N/NO~3~ ^−^-N N~min~
----------- ------- -------- ------------- ---------- -------- ------------- ------------- ------------- ------------------------- -----------
4313 m W 0.02 1.58 0.00 0.23 0.70 39.02\*\* 4.22 1.38 26.87\*\*
D 0.31 0.26 16.70\*\*\* 3.66 2.68 55.47\*\*\* 10.98\*\* 10.04\*\* 28.71\*\*\*
W × D 1.04 6.87\* 4.13\* 2.51 1.40 6.32\* 3.44 0.49 5.91\*
4513 m W 1.43 0.03 4.07 5.33 4.52 9.90\* 6.45\* 3.01 10.89\*
D 2.62 0.23 94.06\*\*\* 0.99 5.23 57.26\*\*\* 31.90\*\*\* 13.69\*\*\* 51.19\*\*\*
W × D 0.41 3.35 2.32 6.36\* 6.15\* 11.70\*\* 0.63 8.10\*\* 4.39\*
4693 m W 0.40 2.61 0.07 0.09 0.04 0.26 0.00 0.19 0.14
D 1.96 0.12 0.67 7.80\*\* 0.81 20.22\*\*\* 21.83\*\*\* 3.36 29.26\*\*\*
W × D 0.27 3.89 0.33 3.84 0.34 0.12 2.66 0.88 1.47
\*, \*\*, and \*\*\* indicate *P* \< 0.05, *P* \< 0.01, and *P* \< 0.001, respectively, while no asterisk indicates not significant.
######
Single factor linear regressions between soil properties (soil organic C, SOC; total N, TN; dissolved organic C, DOC; dissolved organic N, DON; nitrate N, NO~3~ ^−^-N; ammonium N, NH~4~ ^+^-N; the ratio of NH~4~ ^+^-N to NO~3~ ^−^-N, NH~4~ ^+^-N/NO~3~ ^−^-N; soil inorganic N, N~min~) and soil temperature (*T* ~*s*~), soil microbial biomass C (MBC), and N (MBN) showing regression parameters (slope, constant, *R* ^2^, and *P*). MBC and MBN data were obtained from Fu et al. \[[@B20]\].
----------------------------------------------------------------------------------------------------------------------------------
Independent\ Regression\ SOC TN DOC DON NO~3~ ^−^-N NH~4~ ^+^-N NH~4~ ^+^-N/NO~3~ ^−^-N N~min~
variable parameters
-------------- ------------- --------- --------- --------- -------- ------------- ------------- ------------------------- --------
*T* ~*s*~ Slope −5.29 −0.32 −7.90 −0.53 −0.03 −1.71 −0.43 −1.74
Constant 100.76 6.81 195.37 13.28 5.73 31.38 7.66 37.11
*R* ^2^ 0.63 0.64 0.38 0.21 0.001 0.31 0.41 0.21
*P* \<0.001 \<0.001 \<0.01 0.057 0.93 \<0.05 \<0.01 0.056
MBC Slope 0.05 0.003 0.10 0.01 0.01 0.03 0.004 0.03
Constant 6.46 1.24 46.29 2.89 3.34 −3.20 0.04 0.14
*R* ^2^ 0.76 0.66 0.70 0.51 0.13 0.92 0.47 0.82
*P* \<0.001 \<0.001 \<0.001 \<0.001 0.139 \<0.001 \<0.01 \<0.001
MBN Slope 0.28 0.01 0.68 0.05 0.06 0.17 0.02 0.23
Constant 10.56 1.58 43.22 2.93 1.60 −3.28 0.41 −1.69
*R* ^2^ 0.43 0.30 0.68 0.42 0.39 0.79 0.25 0.88
*P* \<0.01 \<0.05 \<0.001 \<0.01 \<0.01 \<0.001 \<0.05 \<0.001
----------------------------------------------------------------------------------------------------------------------------------
######
Multiple stepwise regression analyses between soil properties and environmental variables (soil temperature, *T* ~*s*~; soil moisture, SM) and soil microbial biomass (microbial biomass C, MBC; microbial biomass N, MBN) in an alpine meadow on the Tibetan Plateau. MBC and MBN data were obtained from Fu et al. \[[@B20]\].
Soil properties Factors Coefficients *R* ^2^ *P*
------------------------- ---------- -------------- --------- ---------
SOC Constant 49.31 0.003
MBC 0.04 0.76 \<0.001
*T* ~*s*~ −2.69 0.10 0.006
TN Constant 4.28 0.001
MBC 0.002 0.66 0.004
*T* ~*s*~ −0.19 0.14 0.006
DOC Constant 46.29 \<0.001
MBC 0.10 0.70 \<0.001
DON Constant 2.89 0.005
MBC 0.01 0.51 0.001
NH~4~ ^+^-N Constant −4.57 \<0.001
MBC 0.02 0.92 \<0.001
SM 22.39 0.05 \<0.001
NO~3~ ^−^-N Constant 1.60 0.22
MBN 0.06 0.39 0.005
N~min~ Constant −2.24 0.085
MBN 0.15 0.88 \<0.001
MBC 0.01 0.05 0.005
NH~4~ ^+^-N/NO~3~ ^−^-N Constant 0.95 0.036
MBC 0.004 0.47 0.002
[^1]: Academic Editor: Felipe Bastida
|
The authors confirm that all data underlying the findings are fully available without restriction. All relevant data are within the paper.
Introduction {#s1}
============
Mechanical ventilation (MV) has been used in critical care patients for decades. In spite of its life-saving potential, it has several shortcomings. A number of experimental studies have shown that mechanical ventilation may result in the appearance of inflammatory mediators in the lung [@pone.0114247-Uhlig1] and subsequently in oedema. [@pone.0114247-Dreyfuss1] Ventilator-Induced Lung Injury (VILI) causes macro and microscopic unspecific changes[@pone.0114247-Katzenstein1] similar to those found in patients with Acute Respiratory Distress Syndrome (ARDS). As it happens with ARDS, VILI is basically the result of important changes in the permeability of the alveolar-capillary membrane. [@pone.0114247-Dreyfuss2] The potential of mechanical ventilation for triggering or worsening pulmonary damages has been shown in animal models where the application of non-physiological ventilatory parameters (mostly very high tidal volumes) aggravated the condition of animals with a previously injured lung [@pone.0114247-Corbridge1], and even caused an injury in those without a previous pulmonary pathology. [@pone.0114247-Dreyfuss1] The use of low tidal volumes has proved to be a better approach in ARDS patients, survival being improved in strategies based on its usage. [@pone.0114247-Amato1]--[@pone.0114247-Villar1] Interestingly, recent experimental and clinical work has demonstrated that MV with low tidal volume can induce similar pulmonary changes to those noticed for VILI [@pone.0114247-Cobelens1]--[@pone.0114247-Wolthuis1] and that its appearance may be related to MV exposure time. [@pone.0114247-Hegeman1]
Aquaporins are a family of small transmembrane proteins that help water to move fast, selectively and bi-directionally through lipid bi-layers. [@pone.0114247-Kozono1], [@pone.0114247-Ma1] 13 different types have been identified in mammals, [@pone.0114247-Verkman1] from which the lung is known to express four: AQP-1, in the pulmonary capillary endothelium (especially alveolar), and the visceral pleura; AQP-3, in the tracheal epithelium; AQP-4, in the tracheal and bronchial epithelium; and AQP-5, on type I pneumocyte cells of the alveoli, on the membrane adjoining to the alveolar lumen. [@pone.0114247-King1] Their role in the development and resolution of pulmonary oedema gives rise to controversy, although it does seem to play a part in VILI. [@pone.0114247-Hales1]
This research aimed to verify if MV with low or moderately high tidal volumes (10 ml/Kg) sustained over time results in lung injury, subsequently altering pulmonary water content and microvascular permeability, as observed in VILI, and to objectivize what happens with AQP 1 and 5 expression, both types mainly involved in the formation of lung oedema, under the same ventilation conditions.
Material and Methods {#s2}
====================
1. Ethics statement {#s2a}
-------------------
The project was carried out after approval from the Ethics Committee for Animal Experimentation and Wellbeing of the Research Foundation of Valencia\'s Hospital Clínico Universitario.
2. Animal model and monitoring {#s2b}
------------------------------
A total of 30 rats were anaesthetised by intraperitoneal injection of ketamine 80 mg/kg and xylazine 5 mg/kg. 5 rats (group C or controls) were sacrificed by intravenous injection of 100 mg/Kg thiopental. The rest of the animals (n = 25) were performed a surgical tracheostomy, using a teflon cannula (Surflo, 16G). Rats were randomly allocated into two groups. 12 rats were ventilated for 2 hours (group 2H) with a Harvard Rodent Ventilator, model 683 (Harvard Apparatus) with a tidal volume of 10 ml/kg and a respiratory rate of 90 breaths/minute. 13 rats were ventilated with exactly the same parameters for 4 hours (group 4H). The cervical vascular bundle was dissected, and the right internal jugular vein and the right carotid artery were catheterized to continuously monitor heart rate (HR) and mean arterial pressure (MAP). Peak inspiratory pressure and respiratory system compliance were continuously recorded.
Anaesthesia was maintained by continuous intravenous infusion of ketamine and cisatracurium using dosis of 100 mcg/Kg/min and 2--3 mcg/Kg/min, respectively (20 ml of ketamine 5%, 10 ml of cisatracurium 0,2% and 20 ml of saline solution 0,9% at a rate of approximately 0,1 ml/h in the internal jugular vein). Anesthesia was supplemented, in cases in which it was necessary, by administration of an intravenous bolus of 0.1 ml of the mixture. Gasometric samples were taken in all animals in groups 2H and 4H at the beginning of MV and 30 minutes before the end of MV.
Rats were sacrificed by intravenous injection of sodium thiopental. The left lung was used for the determination of lung water content. The right lung of 6 rats from groups 2H and 4H was used for determining AQP 1 and AQP 5 expression. Lungs were either frozen in liquid nitrogen or paraffin-embedded for immunohistochemical sectioning and marking. 2 rats in group C and 4 rats from groups 2H and 4H were used to establish pulmonary macrovascular permeability.
3. Measuring lung oedema {#s2c}
------------------------
Lungs were dried with filter paper and placed on a Petri dish with known weight to obtain lung wet weight (LWW). They were then placed in a drying chamber at 80°C for 96 hours and their dry weight (LDW) was determined.
Two indicators of the amount of oedema were obtained: Lung WW/DW ratio and the proportion of pulmonary water, expressed in percentages (%~water~). The latter parameter was estimated using this formula: % ~water~ = (LWW - LDW)/LWW \* 100
4. Measuring microvascular permeability {#s2d}
---------------------------------------
Microvascular permeability was quantified using Evans Blue Dye. 0.5 ml Evans Blue was injected intravenously (30 mg/Kg) 30 minutes before sacrificing the animal. Rats were sacrificed by exsanguination from the carotid artery, but saline was simultaneously infused via the jugular vein in the same amount as that of the blood extracted.
After death, the right lung was separated and immersed in formamide (5 ml) and homogenised for 2 min. The resulting suspension was incubated at 37°C/18 h and then centrifuged at 5000xg/30 minutes, and the supernatant was measured. Concentration of Evans Blue in the supernatant was spectrophotometrically determined.
5. Study of aquaporin expression {#s2e}
--------------------------------
### 5.1 Western blot {#s2e1}
Proteins were extracted from previously frozen lungs. A Compartmental Protein Extraction Kit (Chemicon International, Temecula CA) was used. 200--400 mg tissue was homogenised in cold buffer C (1 ml/g tissue) and Ultra Turrax (KA, Staufen, Germany). Two protein fractions were obtained for each sample: cytoplasm and membrane, and they were quantified. Proteins in each fraction (100 mg) were separately run on a Tris-HCl/SDS gel, 8% acrylamide, and they were transferred onto a nitrocellulose membrane (Hybond-ECL, Amersham). After washing the membrane with distilled water, it was blocked with a PBS/Tween solution, 0.2%, with 5% skimmed milk. It was then incubated with the primary antibody during 2 hours at room temperature. The antibodies used were Anti-Rat AQP1 (Alpha Diagnostic, San Antonio, TX) and Anti-Rat AQP5 (Alpha Diagnostic, San Antonio, TX), both with a 2 mg/ml concentration. After several washes with PBS/Tween 0.2%, it was incubated with the secondary antibody Anti-Rabbit IgG (DAKO, Glostrup, Denmark) in 1∶2000 dilution. β-actin expression was detected as an internal control, and relative protein content was analysed using the enhanced chemoluminiscence method.
### 5.2 Real-time polymerase chain reaction with reverse transcriptase {#s2e2}
Lungs were cut with a microtome, three sections being obtained for each sample for total RNA extraction with TRIZOL (Reagent InvitrogenTM Life Technologies) as in the phenol extraction method described by Chomczynsky. [@pone.0114247-Chomczynski1] Microsections were added 1 ml TRIZOL and homogenized (Polytron PT 1200, Kinematica AG) and centrifuged at 10.000 rpm/10 min at 4°C. The supernatant was removed and RNA was precipitated by adding 0.1 volumes of sodium acetate 3 M, 2.5 volumes cold ethanol and 0.5 µl glycogen (20 mg/ml). RNA was centrifuged again, air-dried and resuspended in 20 µl Tris/EDTA buffer. RNA was reversely transcribed to cDNA with Superscript II (Invitrogen), by incubation with reverse transcriptase at 50°C for 30 min, followed by amplification with custom primers (Invitrogen), summarised in [Table 1](#pone-0114247-t001){ref-type="table"}. 35 amplification cycles were completed, with denaturalization at 95°C (30 sec), hybridization (30 sec) (temperatures on [Table 1](#pone-0114247-t001){ref-type="table"}) and extension at 72°C (1 min). Following amplification, RT-PCR products were separated in agarose gels at 1% and bands were viewed by ethidium bromide staining, and quantified by band density scanning using Scion Image (Beta 4.02, Scion Corporation). Results were expressed in relation to the level of β-actin mRNA in the same RNA samples.
10.1371/journal.pone.0114247.t001
###### RT-PCR primer sequences and temperature conditions.
{#pone-0114247-t001-1}
Gene Primer (5′-3′) Primer, counterclockwise (5′--3) T (°C)
--------- ---------------------------- ---------------------------------- --------
AQP1 TCTGGAGGCTGTGGTGGCT AAGTGAGTTCTCGAGCAGGGA 60
AQP5 TGGGTCTTCTGGGTAGGGCCTATTGT GCCGGCTTTGGCACTTGAGATACT 50
β-Actin ATCATGTTTGAGACCTTCAACA CATCTCTTGCTCGAAGTCCA 56
### 5.3 Immunohistochemical study {#s2e3}
Sections (4 µm thickness) from the paraffin-embedded lungs were obtained with the microtome. After the sections were dewaxed and hydrated, autoclave pretreatment (10 min, 121°C) for AQP1 and AQP5 antigen retrieval was performed and the sections were incubated in 1% H2O2 for 30 min at room temperature to block endogenous peroxidase activity. After being washed in PBS, the sections were then preincubated with goat serum albumin for 30 min at 37°C, and subsequently incubated with the primary antibodies against AQP1 (1∶500) and AQP5 (1∶300) for 18 h at 4°C. Then, the sections were washed with PBS and stained with Biotin-labelled goat anti-rabbit IgG for 30 min at 37°C. Intervening washes in PBS again were followed by incubation with Horseradish enzyme labelled streptavidin working solution for 30 min at 37°C. The sections were washed in PBS before application of diaminobenzidine (DAB), then were mounted under coverslip and analyzed under light microscope.
6. Statistical analysis {#s2f}
-----------------------
Results were expressed as mean ± standard deviation (SD). To compare results between groups, the non-parametric Kruskall-Wallis and Mann-Whitney tests were used. For the analysis of data within each individual group, the Wilconxon test was applied. Regression analyses for the amount of aquaporins and mRNA and determination coefficients (R^2^) were performed. Values of p\<0.05 were assumed to be statistically significant in all cases.
Results {#s3}
=======
1. Pulmonary oedema {#s3a}
-------------------
No significant differences were found between the three groups for the wet weight-dry weight ratio (group C: 4.72±0.04 vs. group 2H: 4.90±0.33 vs. group 4H: 5.23±0.79) or the percentage of pulmonary water (group C: 78.82±0.16 vs. group 2H: 79.52±1.31 vs. group 4H: 80.55±2.50), though an increasing trend was noticed for both parameters ([Fig. 1](#pone-0114247-g001){ref-type="fig"}).
{#pone-0114247-g001}
2. Ventilatory mechanics and hemodynamic parameters {#s3b}
---------------------------------------------------
Peak inspiratory pressure (PIP) progressively rose in both groups (group 2H and group 4H), higher values being found 90 minutes after the start of the experiment in group 2H and at minute 60 in group 4H ([Fig. 2](#pone-0114247-g002){ref-type="fig"}). No differences were found in the cut-off points of the two groups.
{#pone-0114247-g002}
Pulmonary compliance was reduced gradually in both groups, with significance in respect of the initial value as from minute 30 for group 2H and minute 60 in group 4H ([Fig. 3A](#pone-0114247-g003){ref-type="fig"}). No differences were found between the groups in none of the cut-off points. This decrease in compliance correlated with the peak pressure rise, with an R^2^ value of 0.98, p\<0.01 ([Fig. 3B](#pone-0114247-g003){ref-type="fig"}).
{#pone-0114247-g003}
Rats in both groups were hemodynamically stable. No differences were found in mean arterial pressure (group 2H: 97.95 mmHg ±27.75 vs. group 4H: 104.53 mmHg ±27.54), and the same applies to average heart rate values (group 2H: 341.29 bpm ±66.73 vs. group 4H: 306.52 bpm ±78.11). Mean arterial pressure (MAP) dropped in group 2H progressively compared to the baseline as from minute 60, but this also happened in group 4H as from minute 45. Heart rate also decreased after 120 minutes ([Fig. 4](#pone-0114247-g004){ref-type="fig"}).
{#pone-0114247-g004}
3. Gasometric parameters {#s3c}
------------------------
Gasometric results for groups 2H and 4H are summarised in [Table 2](#pone-0114247-t002){ref-type="table"}. No differences were found for pH, pCO~2~, ABE and lactate values within the study groups, and differences between the two groups were not found either. But a tendency towards mixed acidosis in relation to duration of MV was observed. Oxygenation presented a tendency to pO~2~ and pO~2~/FiO~2~ ratio reduction two hours after MV in group 2H, which was slightly more marked in group 4H after 4 hours.
10.1371/journal.pone.0114247.t002
###### Results of arterial blood gas tests in Group 2H (ventilated for 2 hours, 10 ml/Kg) and Group 4H (ventilated for 4 hours, 10 ml/Kg).
{#pone-0114247-t002-2}
Group 2H (2 hours) Group 4H (4 hours)
-------------- -------------------- --------------------------------------------- -------------- ---------------
**pH** 7,29±0,05 7,21±0,07 7,30±0,05 7,23±0,07
**pCO2** 47,96±3,56 56,87±18,04 47,33±8,51 52,84±7,73
**ABE** −3,96±2,02 −6,70±1,61[\*](#nt102){ref-type="table-fn"} −3,70±2,72 −6,26±4,20
**Lac** 2,08±0,62 1,99±0,66 1,79±0,74 1,91±1,24
**pO2** 93,30±17,72 91,56±16,56 97,28±15,76 83,03±24,27
**pO2/FiO2** 444,38±84,62 436,86±79,17 462,78±74,61 395,22±115,30
Values expressed as mean ± standard deviation.
\* p \<0.05 in relation to baseline.
4. Microvascular permeability {#s3d}
-----------------------------
A significant increase in microvascular permeability was not found. Evans Blue absorbance on lung tissue was as follows: 16.08 ng/mg ±2.45 in group C; 25.96 ng/mg ±9.90 in group 2H and 20.39 ng/mg ±2.20 in group 4H.
5. Expression of aquaporins 1 and 5 {#s3e}
-----------------------------------
AQP 1 steady state levels measured by Western blot in membrane and cytoplasm did not show statistically significant differences in relation to duration of MV ([Figs. 5](#pone-0114247-g005){ref-type="fig"} and [6](#pone-0114247-g006){ref-type="fig"}).
{#pone-0114247-g005}
{#pone-0114247-g006}
AQP-5 steady state levels in cytoplasm and membranes was significantly greater in both groups (2H and 4H) vs. the controls. Besides, AQP-5 expression on cytoplasm and membranes was greater in group 4H than in group 2H (p = 0.027 and p = 0.039, respectively) ([Figs. 5](#pone-0114247-g005){ref-type="fig"} and [7](#pone-0114247-g007){ref-type="fig"}). To better characterize these differences in the expression of AQP 5, a regression analysis of both variables was conducted, which provided a coefficient of determination R^2^ = 0.80 (p = 0.008) and R^2^ = 0.90 (p = 0.001) ([Fig. 8](#pone-0114247-g008){ref-type="fig"}).
{#pone-0114247-g007}
{#pone-0114247-g008}
RT-PCR results show a significant increase in the amount of mRNA for AQP-1 in groups 2H and 4H compared to group C. For AQP 5, an increase was found in the amount of mRNA in group 4H compared to group C ([Fig. 9](#pone-0114247-g009){ref-type="fig"}). The regression analysis of the amount of mRNA showed very significant determination coefficients for alveolar AQP 5 and AQP 1 in relation to duration of MV (R^2^ AQP-5 = 0.71 (p\<0.001) and R^2^ AQP-1 = 0.69 (p\<0.001).
{#pone-0114247-g009}
Immunohistochemical lung preparations of AQP-5 show the membranes of type 1 pneumocytes delimiting the alveolar network. The intensity of the staining increases with duration of MV ([Fig. 10](#pone-0114247-g010){ref-type="fig"}). AQP 1 samples show the network of the alveolar capillaries, as AQP-1 is found in endothelial cells and red blood cells but not in the pneumocytes covering the alveolus. In this case, image analysis does not show an increase in dye intensity in relation to MV time ([Fig. 11](#pone-0114247-g011){ref-type="fig"}).
{#pone-0114247-g010}
{#pone-0114247-g011}
Discussion {#s4}
==========
MV with high tidal volumes or without positive end-expiratory pressure (PEEP) may lead to the appearance of inflammatory mediators in the lung via mechanotransduction. [@pone.0114247-Uhlig1], [@pone.0114247-Tremblay1], [@pone.0114247-Bueno1] MV with tidal volumes over 12 ml/kg is associated with a bad prognosis, while \"lung-protective ventilation\" with low tidal volumes (under 10 ml/kg) and PEEP optimization reduces ventilation-induced injuries. [@pone.0114247-Noauthors1]
However, ventilation with low tidal volumes may result in the appearance of an inflammatory response pattern in the lung. In rats ventilated with low pressures (12 cmH~2~O) and 4 cmH~2~O PEEP during 4 hours, increased activity of myeloperoxidase and macrophage inflammatory protein-2 and interleukin-6 has been reported. [@pone.0114247-Cobelens1] Similarly, mild pro-inflammatory changes have been found in tracheal aspirates and blood of children with healthy lungs ventilated for 2 hours for heart surgery. [@pone.0114247-Plotz1] Likewise, 6 ml/Kg tidal volume MV in Wistar rats has been reported to induce a proinflammatory and profibrogenic response in the lung. [@pone.0114247-Caruso1] And in mechanically ventilated mice at 7.5 ml/Kg for 5 hours, rising levels of IL-6, TNF-α and lung water were found. [@pone.0114247-Wolthuis1] Conversely, some trials have demonstrated MV with tidal volumes of 10 ml/kg during 6 hours not to cause an increase in cytokine expression. [@pone.0114247-Altemeier1] Similarly, no increases in cytokines or mediators were found in previously healthy patients undergoing MV after one hour of exposure, even with tidal volumes of 15 ml/Kg. [@pone.0114247-Wrigge1]
Based on our results, we fail to confirm that MV with scarcely injurious parameters during 4 hours causes acute lung damage or changes in pulmonary permeability with an increase in lung water. A mild trend was observed in our experiments, however. Although levels were not measured for any inflammatory mediator, based on previous studies, inflammatory mediators are likely to be increased by MV even with low tidal volumes.
General anaesthesia and the supine position are known to cause pulmonary atelectasis with predominance in the dependent region. [@pone.0114247-Hedenstierna1] These give the lung a heterogeneous appearance in which atelectasis areas co-exist with aired and even overdistended areas and their corresponding transition zones. [@pone.0114247-Dreyfuss2] Besides, the use of low tidal volumes without PEEP can result in the appearance and maintenance of atelectasis in patients under general anaesthesia and muscular relaxation. [@pone.0114247-Wolthuis1] Regular recruitment with frequent deep insufflations during low tidal volume MV has been reported to improve oxygenation without signs of lung injury in mice mechanically ventilated for hours. [@pone.0114247-Allen1] Therefore, this would explain the worsening observed in the oxygenation of our animals as exposure to MV with low tidal volumes and without PEEP increased.
Our animals may have developed atelectasis in dependent areas, causing different degrees of atelectrauma that would explain the degradation in oxygenation seen in the experiment (*see* [Table 2](#pone-0114247-t002){ref-type="table"}), although it was not statistically significant, as well as the fall in pulmonary compliance and the rise in peak inspiratory pressure (*see* [Figs. 2](#pone-0114247-g002){ref-type="fig"} and [3A](#pone-0114247-g003){ref-type="fig"}). The latter parameters correlated linearly with a coefficient of determination R^2^ of 0.98 in group 4H (animals ventilated for 4 hours) ([Fig. 3B](#pone-0114247-g003){ref-type="fig"}).
Although acid-base parameters are well-known reliable indicators of animal wellbeing, they have only been partially evaluated in murine mechanical ventilation models. [@pone.0114247-Cobelens1], [@pone.0114247-Belperio1], [@pone.0114247-Altemeier1], [@pone.0114247-Tremblay1] In our model, ventilated animals in groups 2H and 4H showed a trend towards mixed acidosis but without significance. As a result of the formation of atelectasis and higher pressures, ventilation might have been less effective, which could account for the rise in pCO~2~ levels, although not significantly. The metabolic component of acidosis can have several causes. Metabolic acidosis in mice can be induced by saline administration, [@pone.0114247-Zuurbier1], [@pone.0114247-Wolthuis1] which in our animals was used for maintenance at very low levels. Yet, metabolic acidosis caused by some hemodynamic failure cannot be totally excluded. This is possibly related to poor compensation for losses rather than potential deficits in venous return and secondary low cardiac output, as a result of the thoracic pressure reversal observed in positive pressure MV. [@pone.0114247-Schwarte1] Similarly, heart rate data showed a significant reduction over time from minute 120 of the experiment, although always within the physiological range of rats. [@pone.0114247-Papadimitriou1]
To date, no research group has explored the expression of AQP 1 and AQP 5 jointly in mechanically ventilated rats with low tidal volumes. However, a study conducted in rats ventilated with very high tidal volumes (40 ml/Kg during 4 hours) showed a reduction in AQP 1 expression. The researchers suggested an inflammatory mediator secondary mechanism, as they managed to mitigate the reduction in AQP 1 by administering a cyclooxygenase 2 inhibitor. [@pone.0114247-Jin1] In another trial, based on an animal model of ARDS induced by smoke inhalation, animals were subjected to MV, finding an increase in mRNA for AQP 1. [@pone.0114247-Schmalstieg1] The shortcoming in these studies is the absence of a control group with non-ventilated animals to study AQP expression.
Our experiments show an increase in AQP 5 expression that became more significant as MV exposure was prolonged and, similarly, an increase in mRNA of AQP 5 which was also greater in group 4H compared to non-ventilated animals. These increases were not accompanied by significant variations in lung water content or microvascular permeability. Although an increase in AQP 1 in the lungs was not found, after 4 h of MV, our study did find a significant increase in mRNA. This is likely to be the previous step to AQP 1 synthesis. It is possibly due to the fact that a longer MV period is needed for an increase in AQP 1 on cytoplasm and membranes to be seen with the Western blot. Different factors have been shown to modulate the amount of AQPs, reducing them under a number of pathological conditions and leading to an increase in pulmonary water and oedema. [@pone.0114247-Wang1]--[@pone.0114247-Jiao1] In addition, the fact that lung injury parameters improve when their expression is induced, assigns AQPs a protective mechanism in the occurrence and development of pulmonary oedema. [@pone.0114247-Cao1]--[@pone.0114247-Dong1] Although some studies with genetically modified animals debate the possible relevant role of AQPs in the reabsorption of alveolar water, they prove the importance of these channels in pulmonary permeability. [@pone.0114247-Bai1], [@pone.0114247-Ma1], [@pone.0114247-Song1] Significant changes in lung water or microvascular permeability were not objectivized in our animals. The explanation for this could be that AQPs, according to some authors, only work in situations of stress. [@pone.0114247-Hales1] Further studies are needed to determine the true role of AQP1 and AQP 5 in MV.
To conclude, in our model prolonged MV and tidal volumes of 10 ml/Kg for 4 hours did not result in increased pulmonary water or changes in microvascular permeability, these being mechanisms involved in ventilation-induced lung injury. Our study found an increase in the protein expression of AQP 5 and its mRNA, correlated with exposure time and mechanical ventilation. Likewise, the amount of mRNA for AQP 1 also increased in correlation with MV time. Apparently, AQP 5 and AQP 1 can have a protective effect against MV-induced pulmonary oedema, but more studies are needed to clarify whether these proteins really play a relevant role in mechanically ventilated lungs under different conditions.
The experiment was carried out in the facilities of the Medical School (University of Valencia).
[^1]: **Competing Interests:**The authors have declared that no competing interests exist.
[^2]: Conceived and designed the experiments: GF JGDLA. Performed the experiments: GF MM EP. Analyzed the data: GF JGDLA BS JC JDA FJB. Contributed reagents/materials/analysis tools: JC BS. Wrote the paper: GF JGDLA BS EP.
|
Sai Shan
Sai Shan () is a hill behind Mayfair Gardens on Tsing Yi Island, Hong Kong. The hill is east of and beneath the northern peak of Tsing Yi Peak. A village, Sai Shan Village is in the valley between Sai Shan and Tsing Yi Peak. A road, Sai Shan Road between Mayfair Gardens and Hong Kong Institute of Vocational Education (Tsing Yi) is named after the hill.
Category:Tsing Yi
Category:Mountains, peaks and hills of Hong Kong |
Q:
How dangerous is it to translate IPs directly via hosts in Windows
Sorry for the inconvenience, as English is not my native.
I use hosts to access some websites as DNS is polluted.
My question is, take www.google.com as an example.
If I am successfully social engineered by an attacker, and changes the translation in hosts into a phishing website.
If I use http, then I am completely screwed, right?
If I use https, then the browser will give a warning, if my PC is not compromised.
For the https case, is it possible that the phishing website just pass a certificate from www.google.com to me to prove it is genuine?
A:
Consider the following statements:
All certificate authorities trusted by your web browser refuse to issue a certificate for examplebank.com to the attacker without proof of domain ownership.
The signing keys of all authorities are securely stored and an unauthorized person cannot issue a certificate to themselves. (See recent Comodo break-in.)
Your web browser correctly checks if the server's SSL certificate is issued by a valid CA, not revoked, valid for use by servers, and issued for the examplebank.com domain.
There is no active malware or a browser bug that causes such checks to be bypassed.
You always open https://examplebank.com, requesting SSL explicitly instead of relying for the website to redirect you.
You actually read the SSL error messages instead of blindly clicking Ignore when you open the website.
If all of the above are true, HTTPS will warn you that you tried to connect to a fake website. However, HTTPS cannot bypass lower-level redirections (such as spoofing examplebank.com by DNS or /etc/hosts), so if you ignore the warnings, your data will be going to the attacker, not to the real bank.
To conclude, yes, it's dangerous.
In response to the edited question:
If you use plain HTTP, you're screwed.
If you use HTTPS, you will receive a big red warning (see first part of the answer).
Every "certificate" has a RSA (sometimes DSA, ECDSA) key pair. The public key of the pair is part of the certificate, while the private key is locked away in the webserver and never sent over the network. Both keys are needed to successfully complete the TLS/SSL handshake.
If the attacker presents a certificate, but does not have the associated private key, they will not be able to decrypt any traffic that goes over TLS. Wikipedia has a description of the TLS handshake.
A:
SSL (HTTPS) will only protect you as long as your client is not compromised.
If someone manages to modify /etc/hosts, he can also manage to modify your browser to not perform the SSL validation of the server you're connecting to, or he can add his fraud server's fake certificate into your system's database of trusted certificates.
If however your client is not compromised and someone manages to redirect your browser to a different IP address (e.g. some kind of DNS-related hack, or cheating you to modify /etc/hosts without anything else), the browser will warn you that something's wrong with the server's certificate, and, provided you don't ignore the warning and proceed, you are safe.
On your second question:
For the https case, is it possible that the phishing website just pass
a certificate from www.google.com to me to prove it is genuine?
No, that is not possible, unless the attacker managed to obtain the server's private key (e.g. by hacking the server itself). Even if a fraud server "passed on" the server's certificate, he will not be able to prove its identity to the client if it does not possess that private key. If he attempted to do that, he will fail and the browser will show a warning.
|
/* Copyright 2019 Google Inc. All Rights Reserved.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
==============================================================================*/
import {Polygon} from '/lib/math/polygon2d.js';
import * as moduleInterface from '/lib/module_interface.js';
import * as moduleTicker from '/client/modules/module_ticker.js';
import * as network from '/client/network/network.js';
import * as peerNetwork from '/client/network/peer.js';
import {easyLog} from '/lib/log.js';
import assert from '/lib/assert.js';
import asset from '/client/asset/asset.js';
import conform from '/lib/conform.js';
import inject from '/lib/inject.js';
import * as stateManager from '/client/state/state_manager.js';
import {TitleCard} from '/client/title_card.js';
import * as time from '/client/util/time.js';
import {delay} from '/lib/promise.js';
function createNewContainer(name) {
var newContainer = document.createElement('div');
newContainer.className = 'container';
newContainer.id = 't-' + time.now();
newContainer.setAttribute('moduleName', name);
return newContainer;
}
export const FadeTransition = {
start(container) {
if (container) {
container.style.opacity = 0.001;
document.querySelector('#containers').appendChild(container);
}
},
async perform(oldModule, newModule, deadline) {
if (newModule.name == '_empty') {
// Fading out.. so fade *out* the *old* container.
oldModule.container.style.transition =
'opacity ' + time.until(deadline).toFixed(0) + 'ms';
oldModule.container.style.opacity = 0.0;
} else {
newModule.container.style.transition =
'opacity ' + time.until(deadline).toFixed(0) + 'ms';
newModule.container.style.opacity = 1.0;
}
// TODO(applmak): Maybe wait until css says that the transition is done?
await delay(time.until(deadline));
}
}
export class ClientModule {
constructor(name, path, config, titleCard, deadline, geo, transition) {
// The module name.
this.name = name;
// The path to the main file of this module.
this.path = path;
// The module config.
this.config = config;
// The title card instance for this module.
this.titleCard = titleCard;
// Absolute time when this module is supposed to be visible. Module will
// actually be faded in by deadline + 5000ms.
this.deadline = deadline;
// The wall geometry.
this.geo = geo;
// The transition to use to transition to this module.
this.transition = transition;
// The dom container for the module's content.
this.container = null;
// Module class instance.
this.instance = null;
// Network instance for this module.
this.network = null;
}
// Deserializes from the json serialized form of ModuleDef in the server.
static deserialize(bits) {
if (bits.module.name == '_empty') {
return ClientModule.newEmptyModule(bits.time);
}
return new ClientModule(
bits.module.name,
bits.module.path,
bits.module.config,
new TitleCard(bits.module.credit),
bits.time,
new Polygon(bits.geo),
FadeTransition,
);
}
static newEmptyModule(deadline = 0, transition = FadeTransition) {
return new ClientModule(
'_empty',
'',
{},
new TitleCard({}),
deadline,
new Polygon([{x: 0, y:0}]),
transition
);
}
// Extracted out for testing purposes.
static async loadPath(path) {
return await import(path);
}
async instantiate() {
this.container = createNewContainer(this.name);
if (!this.path) {
return;
}
const INSTANTIATION_ID =
`${this.geo.extents.serialize()}-${this.deadline}`;
this.network = network.forModule(INSTANTIATION_ID);
let openNetwork = this.network.open();
this.stateManager = stateManager.forModule(network, INSTANTIATION_ID);
const fakeEnv = {
asset,
debug: easyLog('wall:module:' + this.name),
game: undefined,
network: openNetwork,
titleCard: this.titleCard.getModuleAPI(),
state: this.stateManager.open(),
wallGeometry: this.geo,
peerNetwork,
assert,
};
try {
const {load} = await ClientModule.loadPath(this.path);
if (!load) {
throw new Error(`${this.name} did not export a 'load' function!`);
}
const {client} = inject(load, fakeEnv);
conform(client, moduleInterface.Client);
this.instance = new client(this.config);
} catch (e) {
// something went very wrong. Wind everything down.!
this.network.close();
this.network = null;
throw e;
}
}
// Returns true if module is still OK.
async willBeShownSoon() {
if (!this.path) {
return;
}
// Prep the container for transition.
// TODO(applmak): Move the transition smarts out of ClientModule.
this.transition.start(this.container);
try {
await this.instance.willBeShownSoon(this.container, this.deadline);
} catch(e) {
this.dispose();
throw e;
}
}
// Returns true if module is still OK.
beginTransitionIn(deadline) {
if (!this.path) {
return;
}
moduleTicker.add(this.name, this.instance);
try {
this.instance.beginFadeIn(deadline);
} catch (e) {
this.dispose();
throw e;
}
}
finishTransitionIn() {
if (!this.path) {
return;
}
this.titleCard.enter();
this.instance.finishFadeIn();
}
beginTransitionOut(deadline) {
if (!this.path) {
return;
}
this.titleCard.exit();
this.instance.beginFadeOut(deadline);
}
finishTransitionOut() {
if (!this.path) {
return;
}
this.instance.finishFadeOut();
}
async performTransition(otherModule, transitionFinishDeadline) {
await this.transition.perform(otherModule, this, transitionFinishDeadline);
}
dispose() {
if (this.container) {
this.container.remove();
this.container = null;
}
if (!this.path) {
return;
}
this.titleCard.exit(); // Just in case.
moduleTicker.remove(this.instance);
if (this.network) {
this.stateManager.close();
this.stateManager = null;
this.network.close();
this.network = null;
}
}
}
|
Regeneration of elastic fibers by three-dimensional culture on a collagen scaffold and the addition of latent TGF-β binding protein 4 to improve elastic matrix deposition.
The objective of this study was to investigate the effects of latent TGF-β binding protein 4 (LTBP-4) on elastic fiber regeneration in three-dimensional cultures of human dermal fibroblasts (HDFs). Appropriate collagen scaffold for elastic fiber regeneration was also examined. Collagen sponges cross-linked at 120 °C and composed of small pores (25 μm on average) was favorable for elastic fiber regeneration by HDFs. Addition of LTBP-4, followed by culture for 21 days, accelerated elastic fiber accumulation within the scaffolds. Conditioned scaffolds containing either HDFs or LTBP-4-built mature elastic fibers were implanted between the dermis and the cutaneous muscle of mice. The combined use of HDFs and LTBP-4 resulted in thicker tissues containing elastic fibers. These results indicate that weakly cross-linked collagen sponges can be used as scaffolds for regenerating elastic fibers both in vitro and in vivo, and that the addition of LTBP-4 accelerates the deposition of both elastin and fibrillin-1, and increases cell proliferation. These techniques may be useful for generating cutaneous or cardiovascular tissue equivalents; furthermore, they may serve as a useful method for the three-dimensional analyses of drugs used to treat skin diseases or to examine the microstructure of elastin networks. |
Incredibly big tune by Watermat & TAI, building upon an effective piano groove, turning this from catchy house music to a bigger than life future anthem. It’s got main stage written all over it, without falling for the known big room sounds. This is new and highly creative dance music, Frequency setting the standard for house music to come. HUGE!
Expertly layering rich melodic synths with driving yet enchanting vocals, Warriors climaxes in a euphoric drop that creates an uplifting, progressive anthem suitable for any festival main stage. Alongside Nicky, Volt & State have created an anthem portraying a mantra of never giving up and always fighting for what you believe in which can be related to on a universal level. |
Road study gets Sampson’s attention
Chris Berendt/Sampson IndependentEconomic developer John Swope talks business during Monday night's meeting of the Sampson Board of Commissioners.
Photo
Chris Berendt/Sampson IndependentEconomic developer John Swope talks business during Monday night's meeting of the Sampson Board of Commissioners.
Chris Berendt/Sampson IndependentCounty board chairman Jefferson Strickland, standing, flanked by Commissioners Jarvis McLamb, left, and Albert Kirby, talks about an invitation to a reads impact study announcement in Wayne County and what it could mean to Sampson.
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Chris Berendt/Sampson IndependentCounty board chairman Jefferson Strickland, standing, flanked by Commissioners Jarvis McLamb, left, and Albert Kirby, talks about an invitation to a reads impact study announcement in Wayne County and what it could mean to Sampson.
A road economic impact study in Wayne County has drawn the attention of those in Sampson for its future implications — notably the money and jobs it could bring with it.
The U.S. 117/I-795 economic impact assessment study will be unveiled later this month and the Wayne County Transportation Committee sent invitations out to those in surrounding counties interested in learning about the effect of the growth on “citizens, economy, development patterns and lifestyle.”
Sampson County officials were among those invited.
“Many of you are familiar with the new road from Wilson to Goldsboro with a number designation of 795,” Sampson Board of Commissioners chairman Jefferson Strickland told his fellow board members. “The plan is for that road to continue onto Faison and be in Sampson County at the (Interstate) 40/(N.C.) 403 intersection. One of the first meetings to present some of the faces and facts is going to be held in August, and they’ve asked several members of our community to attend.”
Strickland proposed that Jerol Kivett, chairman of the Sampson County Transportation Advocacy Group (TAG), Commissioners Albert Kirby and Billy Lockamy, as well as John Swope, executive director of the Sampson Economic Development Commission, be in attendance at the Aug. 21 meeting at Lane Tree Conference Center in Goldsboro.
The board agreed unanimously.
Interstate 795 is an interstate spur that follows the U.S. 117 corridor from I-95 near Wilson to U.S. 70 in Goldsboro, a length of about 25 miles. There are no other interstates in the eastern portion of North Carolina, east of I-95 and I-40.
Its connectivity with a portion of I-40 in northern Sampson could prove vastly beneficial, local officials attested.
The extension of I-795 southward along the U.S. 117 corridor would connect cities and industrial centers important to national defense, economic growth and job creation, Joe Daughtery, chairman of the Wayne County Transportation Committee, stated in his correspondence to Sampson County and others.
Daughtery cited the potential of $74 million in business and resident cost savings, $520 million in GRP (gross regional product) and nearly $490 million in additional personal income by 2040.
“Employment is projected to grow faster as well, adding about 220 more jobs on average per year along the corridor when compared to not completing the corridor,” he said.
A recently-concluded U.S. 70 Corridor Commission study evaluated the economic development impacts of completing the four-lane freeway bypass system of highways for U.S. 70 from I-40 in Raleigh to the Morehead City State Ports facility; and the conversion of U.S. 117 to I-795 from Goldsboro to I-40.
A U.S. 117 conversion would mean expansion for that road and an impact for I-40 in Sampson, Swope said at the time the study was initiated.
The study team of Cambridge Systematics and the Sanford Holshouser Economic Development Consulting LLC conducted that analysis and are the same team set to conduct the U.S. 117/I-795 economic impact assessment study.
With the Department of Transportation also in the fold, Swope has alluded to exciting possibilities.
“I-795 would be proposed to connect to I-40 near Faison,” Swope said previously. “That would give us a direct route north to I-95, direct access instead of going (west) on I-40 and then catching I-95 North. They would connect to a new I-795, giving people traveling north and south better access than traveling I-40 to I-95.”
State officials said the completion of the highway improvements, has extensive long-term implications for the economic future of eastern North Carolina and the counties along the corridor.
The U.S. 70 Corridor Commission study found that as many as 1,900 jobs could be created each year for communities that rely on the corridor such as Smithfield, Goldsboro, Kinston, New Bern, Havelock and Morehead City. Among other statistics, $1.2 billion could be added to the GRP, including $900 million in additional personal income, and as much as $56 million saved for existing businesses.
Local officials are hoping those positive effects ultimately extend to Sampson.
For years, Swope has sought — and local officials have extended incentives — to attract industries to locate permanently to Exits 348 and 355 off of I-40 in northern Sampson County with mixed success.
Another large interstate would only aid in that pursuit.
“The highest investment value is an interstate,” Swope said last year. “That is what potential investors look for when developing properties. To bring U.S. 117 on as I-795 would be one more strong asset toward improving and strengthening Sampson County’s economy.”
Lockamy said the new road is already getting plenty of use, which bodes well for the counties through which motorists are navigating.
“I traveled that road Saturday evening going into Goldsboro and the traffic was bumper to bumper coming down it,” Lockamy noted. “The traffic is used to it now.”
Chris Berendt can be reached at 910-249-4616. Follow us on twitter @SampsonInd.
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Reminder: Things can go bad even when racing slowly.
Those who enter rallies do so knowing full well there's a solid chance their car might not make it out in one piece. Crashing is just part of the rally game. This YouTube video shows how a handful of rally cars met their doom as they entered one very slick, low-speed corner.
A video shared on YouTube Sunday shows action from last weekend's Śląska Rally in Poland—or more specifically, a handful of rally cars at the rally crashing into a ditch. From the looks of the video, the cars came in hot, but not too hot, from a faster stretch of the rally stage, and were forced to slow down to handle the upcoming corner without going off the course. But because of the stretch of road near the corner is wet and muddy, some of the cars—mostly small European hatchbacks—have trouble making the corner. This, in turn, led to them driving into the ditch next to the course.
Going off a stage in rally happens. The important thing is whether you and the helpful spectators around you manage to push the car right-side-up so you can keep hustling down the course. |
Q:
JavaScript runtime error: Unable to add dynamic content
I'm making a javascript metro app and have some code like this:
<script>
document.writeln(foo());//this line is trouble
</script>
and when I tried to run, it gave me a rather long error:
Unhandled exception at line 20, column 9 in ms-appx://a375ffac-3b69-475a-bd53-ee3c1ccf4c4e/default.html
0x800c001c - JavaScript runtime error: Unable to add dynamic content.
A script attempted to inject dynamic content, or elements previously
modified dynamically, that might be unsafe. For example, using the
innerHTML property to add script or malformed HTML will generate this
exception. Use the toStaticHTML method to filter dynamic content, or
explicitly create elements and attributes with a method such as
createElement. For more information, see
http://go.microsoft.com/fwlink/?LinkID=247104.
How can I get around this?
A:
Windows 8 restricts the content you can set through innerHTML and Writeln, because it's considered unsafe...
The correct way to add content is:
// The untrusted data contains unsafe dynamic content
var unTrustedData = "<img src='http://www.contoso.com/logo.jpg' on-click='calltoUnsafeCode();'/>";
// Safe dynamic content can be added to the DOM without introducing errors
var safeData = window.toStaticHTML(unTrustedData);
// The content of the data is now
// "<img src='http://www.contoso.com/logo.jpg'/>"
// and is safe to add because it was filtered
document.write(safeData);
If your code has some javascript, you can use this function (But microsoft dont recomend it):
MSApp.execUnsafeLocalFunction(function() {
var body = document.getElementsByTagName('body')[0];
body.innerHTML = '<div style="color:' + textColor + '">example</div>';
});
See at:
http://msdn.microsoft.com/en-us/library/windows/apps/Hh767331.aspx
For your case:
MSApp.execUnsafeLocalFunction(function() {
document.writeln(foo());
});
Note that you should only do this if you understand your content is safe; if you don't, I would recommend using the toStaticHTML method.
A:
regarding to the docs I would try :
document.writeln(window.toStaticHTML(foo()));
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Insulin-induced release of plasminogen activator from human blood platelets.
Incubation of washed platelets in Tyrode buffer, pH 7.5, with insulin (200 microU/ml) and CaCl2 (1.2 mM) at 37 degrees C for 3 h resulted in a threefold increase of plasminogen activator activity in the supernatant over the basal level as determined by both the amidolytic assay and the proteolysis of alpha-casein through the formation of plasmin from plasminogen. This plasminogen activator showed no plasmin-like activity and was inhibited by anti-tissue plasminogen activator antibody as well as by type 1 plasminogen activator inhibitor. The substrate specificity and the inhibition of the enzymic activity by various inhibitors indicated that the platelet plasminogen activator (pPA) was related to tissue-type plasminogen activator of relative molecular weight 56,000. Fibrinolytic activity of pPA and its insulin-dependent release were demonstrated by the shortening of euglobulin lysis time and by the clot lysis time of platelet-rich plasma from normal and type I diabetes mellitus patients. Treatment of platelet membranes with insulin also increased the release of pPA. Increased levels of adenosine 3',5'-cyclic monophosphate (cAMP) in platelets by incubation with various agents completely inhibited the insulin-induced release of the activator. On the other hand, inhibition of platelet aggregation by aspirin had no effect on the release of pPA, indicating that the effect of cAMP was not due to the inhibition of platelet aggregation by the nucleotide. |
August 30, 2011
First amendment gives the Press the right to publish news, information and opinions without government interference.
Sixth amendment guarantees that the defendant is tried in a court open to the public before an impartial jury.
The full accommodation of these seemingly over-lapping fundamental rights is rather challenging. The responsibility to establish a balance between the defendant’s right to a fair trial, the media's right to free speech and the public's right to an open court lies squarely on the shoulders of the presiding judge: Michael Pastor, in our case.
There are several measurements that a judge could employ to establish the aforementioned balance in his court. Jury sequestration is one of them.
JURY SEQUESTRATION
Sequestration is the practice of physically keeping the jury together and totally isolated from outside influences during the trial or deliberation stage, or both. This measure is usually taken only for high profile cases, where the massive media coverage may prejudice the jury's verdict, thus, violating the defendant’s six amendment rights.
In its most extreme form, when not in the courtroom hearing the case, jurors are kept under the constant supervision of a guard at an undisclosed location. Their contact with the outsiders including family is eliminated or curtailed. Any outgoing communication, if any allowed, is monitored to ascertain that their communication doesn’t involve the Trial.
It cost the state of California $3 million to sequester OJ Simpson jury for almost 9 months.
Scott Peterson jury was sequestered only during deliberation period for a week. Mark Geragos, Scott Peterson attorney requested full sequestration during the entire trial. Mr. Geragos stated “This gentleman beside me is fighting with one hand tied behind his back. I'm just trying to level the playing field.”Judge Alfred Delucchi denied the total sequestration request, reasoning that “if I was to tell people you can't see your loved ones for five months, you can't watch television, you can't listen to the radio, you're going to be locked away in a hotel somewhere ... it could have a negative effect on people who could get resentful that they've been locked up."JudgeDelucchi remarked that the jurors will be exposed to outside influences regardless and that "the only place this wouldn't happen is if we parked the jury on Mars. We can't do that."
Michael Jackson 2005 Trial was heard by a non-sequestered jury and despite of the intense worldwide coverage of the trial in detriment of Mr. Jackson, jury rendered
a verdict contrary to the media verdict, acquitting him of all 14 counts of charges.
in the court, stating “we would really like the decision to be made based upon
the evidence that is given in this courtroom and the arguments made inside
this courtroom as opposed to what happens on the Nancy Grace Show”
-Michael Flanagan
Judge Pastor asked the prosecution’s stance on the jury sequestration. Deputy Prosecutor David Walgren responded “the court had addressed the issue previously and advised all parties that the court was not inclined to do a sequestering of the jury 24/7. The People were comfortable with the court’s decision. That’s still our position.”
Judge Pastor then declared “at this juncture, I do not feel in any way, shape or form total sequestration of jury is necessary in this case. To have jurors undergo that kind of extraordinary deprivation, quiet frankly, unhealthy to the administration
of justice. I remain confident that jurors follow the law. They follow orders. I feel confident that the jurors understand their responsibility is to follow the evidence and to decide the case on the evidence and not to be influenced by the extraneous materials”. He then advised the defense team to file a motion for his consideration.
On August 18, 2011, Conrad Murray defense team filed a motion requesting jury sequestration. “This is an unusual Trial. There is a reasonable expectation that Dr. Murray’s Trial will be the most publicized in history” stated the motion which then went on to compare Conrad Murray case to Casey Anthony trial. “Television pundits such as Nancy Grace use air time to campaign for the conviction of Ms. Anthony. By feeding on the public anger, Grace’s viewership rose to one and half million per night in June Grace engaged in continuous character assassination with regard to Ms Anthony, the woman she condescendingly referred to as tot mom.”
And then came, in my opinion, highly incendiary and offensive remarks:
“Even if the jurors are instructed not to watch any news coverage, it is unrealistic to expect an unsequestered jury to avoid hearing about the case. Therefore, complete sequestration is necessary to eliminate the high risk of jury contamination. Dr. Murray respectfully asks this court for an order sequestering the jury during the entire trial, including jury deliberations” concluded the defense motion.
On August 25, 2011, Judge Michael Pastor denied the motion to sequester the jury.
Deputy District Attorney David Walgren stated that the prosecution didn’t feel the sequestration was necessary.
“There has to be a level of trust granted to the jurors” ~David Walgren
“Sequestered juries have indicated they have felt like inmates and they feel they were being imprisoned. They are monitored 24/7, they have minimal freedom of movement and they can’t even speak to loved ones without being monitored. Many sequestered jury indicated that they found the sequestration so frustrating, so intimidating and so cruel that it actually interfered with their assessment of the evidence and the law. While I raise the issue of cost, that is not the over-riding consideration. Justice trumps everything" stated judge Michael Pastor.
Ed Chernoff then stated that in Casey Anthony case media pundits offered their interpretation of the evidence and testimonies, acting as a quasi juror. He then requested that the judge ban the Trial from being televised. “I am suggesting that you consider in-court cameras, maybe amend it to prevent that particular problem” Chernoff said.
Judge Pastor responded “by problem, do you mean the exercise of first amendment? The first amendment is one of those cherished fundamental constitutional rights in the United States. That includes the right to comment.
Judge Michael Pastor then denied the motion for jury sequestration: “I expect that the jurors will follow the high road and that means that they will not be in the receipt of or in contact with information regarding this case. I have tremendous faith in the jury system and in the individual promises of jurors. The defense motion is denied."
In summary, Conrad Murray jury won't be sequestered and the Trial will be televised.
PROS OF SEQUESTRING JURY
Preventing exposure of the jurors to prejudicial publicity
Minimizing pressure from public for a particular verdict
Ensuring juror safety from harassment during trial
Promoting a perception of fairness due to no outside influences
CONS OF SEQUESTRING JURY
It is financially costly to the government
If an impartial jury isn’t acquired in the first place then it can’t be maintained by means of sequestering
It doesn't undo prejudice based on pretrial media coverage
It imposes jurors emotional harm if the sequestration period is long
It may be counter to truth-seeking because it:
vCan lead to a non-representative jury because only limited categories
of people are available for a jury that will be sequestered.
vCan cause jurors to rush to judgment to escape sequestration.
vCan cause the jurors to identify with the government (as caretaker) or against the government (as the jury’s jailer).
Marcia Clark on jury sequestration
"When jurors are forced to spend day and night with each other, apart from their families and friends, they become a tribe unto themselves. Because they only have each other for company, and because most people prefer harmony to discord, there’s a natural desire to cooperate, to compromise in order to reach agreement. And they have no safe retreat. If they disagree with their fellow jurors, they can’t go home to a husband, a wife, a friend, where they can regroup and marshal their energies. Make no mistake about it, sequestration is no picnic and I have sympathy and respect for the jurors who put up with that incredible hardship.
We can’t ignore the mental and emotional impact it has on the jurors—an impact that thwarts the whole point of drafting twelve individuals to decide a defendant’s fate"~Marcia Clark, OJ Simpson prosecutor
August 26, 2011
Despite of ardent fan protests and a letter from Michael Jackson Estate Executers,
Global Live Events announced that they are “%100 going ahead”. Yesterday, they announced Ne-Yo as part of their line-up. But would Ne-Yo have agreed to be participate IF he knew that Leonard Rowe is involved in 'Michael Forever Tribute'?
In 2007, LiveNations cancelled Janet Jackson’s Tour. Her dancers had counted on income from the Tour so she reached out to Leonard Rowe asking if he could promote
a 20 concert Tour. “I did not believe that she had the drawing power to tour” Leonard Rowe wrote in his book. He tried his best to convince Michael Jackson to tour as Janet being the opening act but there was no convincing Michael. So Mr. Rowe asked R Kelly to tour with Janet Jackson. R Kelley agreed. Later, Janet thought that R Kelley would steal the spotlight so she changed her mind about touring with R Kelly. Leonard Rowe proceeding planning just an R Kelley Tour. He booked Ne Yo as an opening act for R Kelley. Ultimately, both R Kelley and Ne Yo litigated Leonard Rowe.
Ne-Yo sued Leonard Rowe for breach of contract. Leonard Rowe had dropped Ne-Yo from the Tour without merit. On September 4, 2008, Ne-Yo was awarded $700,320
Fast forward to the present day….
“Latoya was the lead one” said Chris Hunt, President of Global Live Events regarding Jackson Family members backing for ‘Michael Forever Tribute’. Latoya and her company is very much involved & vested in the tribute. Paul Ring, vice president of Ja Tail business development, is also "Head of US Operations, Global Live Events"
Global Live Events CEO, Eric Bute directed Latoya's "Home' song
Ja Tail made a minor change in their website recently. The nature of the change is blaringly evident: to conceal Leonard Rowe involment in 'Michael Forever Tribute'. With his unpleasant history with Rowe, Ne-Yo might have had reservations in performing in the tribute had he known the Rowe connection. So they surreptitiously deleted evidence.
August 24, 2011
"We are %100 going ahead. We will continue to announce names for the line-up.
We are moving forward and now we will try to address issues that have been raised by fans" Global Live Events stated, inviting verified Michael Jackson fanclubs to take part in a conference call on August 30, in which our concerns will be allayed.
We have been Michael Jackson fans and members of fanclubs for our entire lives yet
we are not aware of the "verified fanclub” concept. Do you doubt our fanship? When Mr. Jackson was alive, never once did he limit his communications only to “verified Michael Jackson fanclubs”. We don't hear this utter nonsense from his Estate Executers either. We are ALL verified in the sense that we would walk through fire to make sure that an audacious company doesn’t cheapen Michael Jackson legacy and brand.
We do not want our concerns allayed, we would like them resolved and how can resolution be possible if your very first step towards us is “we are %100 going ahead”?The so-called tribute is taking place during Conrad Murray Trial. Our most pressing concern is the timing. It is futile to elaborate on why the timing is utterly inappropriate
for any decent human-being should be able to connect the dots.
Your invitation to fans is simply a PR stunt in light of adverse media coverage of your event. Your assertion of “we have been listening to the fans” is a bold-faced lie. We started our campaign BECAUSE you refuse to listen to us and consistently delete our comments from your facebook! We learnt from experience and started screen-capping our comments before you delete them. Here is a comment you deleted yesterday:
In a letter dated August 15, 2011, Michael Jackson Estate declared to Global Live Events
"Estate is the only entity that can grant the right to use Michael Jackson’s name, likeness or any of his intellectual property, whether such use is commercial or other purposes. We assume that you do not intend to use any intellectual property controlled by the Estate"
How does your company leap from receiving this communiqué from the Estate Executers
of Michael Jackson to selling tickets to commercialize a brand that is not your property?
Michael Jackson Estate is the single entity who owns and is responsible to protect the integrity of Michael Jackson brand which we believe you are tainting by an exceedingly questionable event marred with negative publicity. Adding insult to injury, you dub this lackluster event as a Michael Jackson “tribute”.Estate Executors communicated with you that “in light of confusion surrounding this ‘event’ we are extremely concerned about Michael’s legacy. We believe Global Live should address our concerns….”
Global Live Events owe Michael Jackson Estate Executers through and through explanation before they proceed. Your failure to seek Estate's approval demonstrates your lack of respect to the very man you are allegedly honoring.Let me remind you that it is your legal and moral obligation to the Estate Executors to resolve every single issue surrounding the event and have their approval before “%100 going ahead”
We realize that your financial interest indeed outweighs integrity. There is nothing decent about exploiting Mr. Jackson’s death for financial gain, doing so during Conrad Murray Trial and exploiting his young children as an advertising tool. We find the exploitation of Michael's children in your terms and conditions document totally abhorrent. Michael Jackson wrote a song about your ilk titled “money”, will that song be in the tribute line up?
Which brings us to another legal issue to be contended with.
Mr. Jackson worked very hard to build one of the most profitable brands of all time. His brand stands for unsurpassed quality and “magic”.There is nothing quality or magical about Michael Forever Tribute which is simply a circus show of has-beens or rookies.
You stated that you have the backing of “overwhelming majority” of the Jackson Family. So what? Jackson Family doesn’t own Michael Jackson brand, his Estate does…solely. Jackson family has no authority to broker Michael image, likeness and songs all of which you declared you will exploit. The Executers clearly communicated to you that you do NOT have their permission to use their intellectual property. Either you intend to violate copyright laws or you are defrauding public by false advertising.
Unless you show willingness to modify terms surrounding Michael Forever Tribute, including but not limited to the timing & unless a representative of Michael Jackson Estate is present, our answer to your conference call is a resounding NO!
We propose that you proceed with the concert but cease and desist the use of Michael Jackson name, likeness & songs. This is a reasonable compromise.
Most of your attendees are fans of the participating artists. Since you are determined to “go ahead” and we are determined not to let that happen with the current terms, why don't we reach an agreement where everyone wins? Our proposal satisfies all parties:
August 22, 2011
Gentlemen, we are writing you once again in regards to the Michael Forever Tribute.
As you know, Michael Jackson worldwide fan community ardently objects and protests the October 2011 tribute. The fans who cherished a very closed-knit relationship with Mr. Jackson would want nothing more than a befitting tribute in his honor…but in due time & organized with utmost care and professionalism.
Under the current circumstances, Michael Forever tribute produces an outcome opposite of what is being marketed. The tribute is simply tasteless, improper, impractical, insensitive and disrespectful. There is no way to resolve the issues we have with this tribute. Since the announcement of this tribute, the fan community has been upset and unable to focus on the upcoming trial. Every day, we wake up hoping for a cancellation and to our dismay, we encounter deafening silence. We've learnt that Michael Forever Tribute facebook is maintained by a ticketing company who doesn't have answers.
Estate Executers had asked you to “address our concerns and those of Michael's loyal fans”. To date, you haven’t communicated with neither the fans nor the Executors of Michael Jackson -you know, the gentelman you are purportedly paying tribute to. If you don’t respect his Estate or his fans then where do you get off monetizing Michael Jackson’s name? You don’t even bother answering simple customer service questions about the event, let alone addressing grave concerns which were made known to you. Yet you proceed to selling tickets nonchalantly. Global Live Events could really benefit from a crash course on business ethics, integrity, professionalism and customer service.
You are prolonging an unpleasant situation to gauge if you could garner enough ticket buyers who are fans of the attending artists. Do you think that the negative media coverage is beneficial for your company reputation or ticket sales?
Since you don't have enough regard for Michael Jackson to cancel out of respect for him, since your corporate aspirations weigh heavier than doing what’s morally right, we propose this compromise: Drop Michael's name and proceed with the concert with the artists you already booked, including the Jacksons. We only request that you don’t use or refer to Mr. Jackson’s name in any shape or form and that the participating artists including the Jacksons don't butcher…I mean attempt to sing Mr. Jackson’s songs.We find this to be a reasonable compromise for all.
We present our offer for your consideration and expect preferably an immediate cancellation or a modification. Look forward to your response as practicable as possible.
August 19, 2011
Thank you for your prompt reaction in regards to the Michael Forever Tribute.
We realize that unlike fans who react with raw emotion, the Estate executors approach matters with composed diplomacy and that there is a legal chain of actions to be followed. The Fan Community is in total agreement with every concern outlined in the letter from the Estate to the Michael Forever Tribute organizers. And whilst we are confident that the Estate will follow through and take the necessary legal actions in the event that the organizers aren’t compliant, we would like to communicate with you our sentiments in regard to some disconcertingissues relevant to the Michael Forever tribute.
Timing: The Fan Community feels that the timing of this event aims to exploit
the Conrad Murray trial. It is exceedingly insensitive, tasteless and improper.
Caliber of artists: We feel that Michael Forever Tribute isn’t a tribute to honor Michael Jackson. It is merely a concert of various artists but the organizers exploit Michael Jackson’s name to garner interest in the event. The participating artists aren’t selected carefully based on the special connection they may have to Mr. Jackson. Rather, Global Live Events extends invitations to any artist who may agree to participate. They are scraping the bottom of the barrel. We feel that the haphazard and sloppy organization so far will not produce a fitting tribute. We would like the official Tribute to come in due time, preferably organized by Michael’s children and sanctioned by his Estate.
Questionable intent: We feel that the intention of the tribute isn’t to pay homage to Michael Jackson but to capitalize on his good name. We don’t feel that a mere concert with mosaic of artists thrown together on the 11th hour is a suitable tribute
Aptitude of Global Live Events: The Company was formed on March 29, 2011. As evidenced by their incompetency so far, we feel that the inexperienced organizers will fall short in organizing a deserving tribute to Michael Jackson.
Paul Ring who is dubbed as "Global Live Events Executive" is also Latoya's employee. This screams conflict of interest. Latoya appears to be the force behind this exploitation of Michael & his children under the guise of a "tribute".
Latoya Jackson 'Starting Over' book, page 340
Global Live Events CEO Eric Bute & Latoya Jackson
Questionable ticketing: We don't get a sense that this tribute is for L.O.V.E.
It is all about money. Fans are required to pledge to charities in addition to the ticket price. Surreptitiously, the organizers use fans’ donations to assert that
the tribute is for a charitable cause. Then why aren’t they donating part of their profits to charities? We don’t even know where the proceedings are going.
Ticketing policy: The organizer declared “If %50 or more of the contracted artists ATTEND OR PERFORM, the concert will take place and NO refunds will be offered”. We believe that the %50 is covered by the Jacksons' appearances and that the announced artists may attend but not necessarily perform. Attending public should receive exactly what the organizers advertised, they shouldn't be short-changed or duped. The promoter aims to cheat the public with fine print. Doing so in Michael's name dishonors Michael's good name & memory.
Gene Simmons:Global Live Events invited someone who not only made public disparaging remarks about Michael but also his children. We feel that the organizer should have been more diligent in carefully selecting artists. We can forgive Mrs. Jackson; due to her age, perhaps she didn’t know who Kiss is or about Gene Simmons remarks but it's hard to believe that Jackson siblings didn’t know about it. We feel that they proceeded despite of the knowledge.
When we TRIED communicating our concerns about Kiss, our voices fell on deaf ears. Promoter deleted our comments from its facebook and tweeted a promotional video nonchalantly. It took a letter from the Estate for them to address this issue. They shut out the very people they are trying to sell tickets to.
After dropping Kiss today from their line-up, the organizer released this statement:
“We have listened to Michael's fans and are grateful to have been alerted to these unfortunate statements by Gene Simmons. Under the circumstances,
we fully agree that even though Kiss is a band Michael admired, we have no choice but to rescind our invitation to them to appear in our tribute”
Whom Global Live Events heard was NOT “Michael’s fans” but a potential lawsuit and the possibility of the Estate Executers throwing a monkey wrench into their event. We are also displeased by their absurd remark that Michael admired Kiss. That is a completely inaccurate nonsense. We do NOT feel right about Global Live Events, we do not trust them, we do not wish to do business with them.
Recent headlines dragged Mr. Jackson’s name in mud so close to the jury selection to the Conrad Murray trial. We feel this may have tainted the potential jury pool. We do not feel that dropping Kiss suffices. The damage is already done. We didn't sense any genuine regret from the statement by Global Live Events.
WE DO NOT ACCEPT THEIR APOLOGY!
Most of the attendees are fans of participating artists. Michael Jackson fans are troubled that his name is used to sell this concert. If they desire to proceed, then they should just market it as a concert event without involving MJ's name into it.
With the upcoming criminal trial, fans would like to focus only on the trial. We find it near impossible to do so because of constant debacles related to this tribute.
It’s Michael Forever Tribute. His mother, siblings and children are involved. The use of Michael Jackson image and likeness is bound to happen.We cordially request that the Estate commence the necessary steps to acertain that this Tribute either doesn’t happen or it doesn’t happen as a Michael Jackson tribute.
We hope that you will attend this matter in a timely manner so that the storm in our community may pass & we may focus on the upcoming Conrad Murray trial.
We, as Michael Jackson's staunch supporters, refuse to support the Michael Forever Tribute, planned by Global Live Events in October, 2011. Even after the removal of Kiss, we feel that the damage is already done. This colossal mistake could have been avoided, had you exerted the diligence required to organize a befitting tribute. You have proven that you will book just any artist who affirms your invitation. This monumental mistake cannot be forgiven, given the magnitude of the damage it caused so close to the criminal trial. Your apology is too little too late and it does not solve the problems we have with this tribute in general.
Since the initial announcement of the event, fans tried communicating with you in regards to our very valid concerns, have we not? Instead of acknowledging, hearing and working together with us, you have deleted “selected” comments from your facebook page, forcing us to form our own facebook Group: Fans Against Michael Forever Tribute.It shouldn't have come to this. Any company who conducts business in Michael Jackson's name should better know that Michael and his fans have cherished a close-knit relationship where we were always heard and communicated with. We refuse to be treated this way by you!
You only addressed the Gene Simmons issue after the Estate's letter. Therefore, the contention that you "listened to Michael's fans" is empty words uttered to save face in the media. Global Live Events rescinded their offer to Kiss only to qualm the media and the Estate. Simply put, the Kiss cancellation is merely a product of the negative media coverage which stood to affect ticket sales and your profit. It was not done out of respect to Michael Jackson. You've no respect for Michael.
The timing of this tribute in the middle of Conrad Murray's trial, ticketing arrangements, faraway location, obscurity over what charities will be receiving the donations, obscurity over who is pocketing the profits, no-guarantee policy of performers.....the issues with this tribute keep piling up, thus, breaking our focus away from the criminal trial. We find this very upsetting. The addition of Gene Simmons, thus, tarnishing Michael Jackson's name was simply the last straw for us. With the damage you caused, it will be us fans having to fix your mistake.
Michael Forever Tribute is not proper at this time for myriad of reasons. We hope we can resolve this matter amicably so that perhaps in the future when a Tribute is planned, you could be part of the production, with more care and diligence.
Understand that we will not rest until this tribute is cancelled. We do NOT care who from the Jackson family is supporting it. We condemn the exploitation of Michael's children & his mother to legitimatize your tribute!!!
We cordially invite you to announce the cancellation of Michael Forever Tribute. |
Quiksilver Technical Figueira da Foz (Portugal), will participate on this year's Kayaksurf & Waveski circuit with two athletes: José Morais (owner of the store) and Gonçalo Duarte (surfkayaker). Meet the team and check the photos. The swell was not so good but was only to present the Team. Both riders belong to the Figueira Kayak Clube. |
Is racial bias built into U.S. immigration law? “The first instance of any kind of visa as we know it for a legal way to come into the system started with the Chinese Exclusion Act of 1884,” according to Jenny Yang, Director of Advocacy and Policy for World Relief’s Refugee and Immigration Program. Scientific data was circulated as evidence that Chinese people were inferior and ought to be kept out. However, immigration law based on race was abolished in 1965. “Still, a lot of reforms are needed.” |
[Rhinoviruses].
Human rhinoviruses (RV) belong to the Picornaviridae and are divided into three species: rhinovirus A, B and C. As causative viruses of upper airway infections (common cold), they possess enormous epidemiological and clinical importance. Furthermore, rhinoviruses are significant pathogens of acute exacerbations of chronic airway diseases such as asthma and chronic obstructive pulmonary disease. Their role as a cofactor in the development of pneumonia and their relevance in critically ill patients is still unclear and the focus of current research. Due to the unspecific clinical symptoms, diagnosis is difficult. Laboratory detection is sophisticated and a distinction between clinically relevant infection and contamination not always possible. Specific therapeutic antiviral strategies against rhinovirus infection do not exist as yet and, due to the large variety of subtypes, the development of vaccines remains a considerable challenge. |
Q:
Apple rejected an app that for use on non public api where there aren't any non pulic apis
This is the message I got from Apple for rejecting my app:
Your app uses or references the following non-public APIs:
didDetermineState:forRegion:
didEnterRegion:
didExitRegion:
The use of non-public APIs is not permitted on the App Store because it can lead to a poor user experience should these APIs change.
I really don't know what to do as there api are clearly public. Anyone got some advise? It would really help.
A:
I think the public apis you are mentioning about are those in CLLocationManagerDelegate. If it is the case, take didEnterRegion:, for example, the api is actually locationManager:didEnterRegion:. However, Apple mentions didEnterRegion: only. That probably means somewhere in your app, you have declared a method with that exact signature, and it happens to have the same signature with a private api method.
My suggestion is to do a search on your whole project for such methods and rename them.
|
// Copyright (c) Microsoft Open Technologies, Inc. All rights reserved. See License.txt in the project root for license information.
namespace System.Data.Entity.TestModels.ProviderAgnosticModel
{
using System;
public enum AllTypesEnum
{
EnumValue0 = 0,
EnumValue1 = 1,
EnumValue2 = 2,
EnumValue3 = 3,
};
public class AllTypes
{
public int Id { get; set; }
public bool BooleanProperty { get; set; }
public byte ByteProperty { get; set; }
public DateTime DateTimeProperty { get; set; }
public decimal DecimalProperty { get; set; }
public double DoubleProperty { get; set; }
public byte[] FixedLengthBinaryProperty { get; set; }
public string FixedLengthStringProperty { get; set; }
public string FixedLengthUnicodeStringProperty { get; set; }
public float FloatProperty { get; set; }
public Guid GuidProperty { get; set; }
public short Int16Property { get; set; }
public int Int32Property { get; set; }
public long Int64Property { get; set; }
public byte[] MaxLengthBinaryProperty { get; set; }
public string MaxLengthStringProperty { get; set; }
public string MaxLengthUnicodeStringProperty { get; set; }
public TimeSpan TimeSpanProperty { get; set; }
public string VariableLengthStringProperty { get; set; }
public byte[] VariableLengthBinaryProperty { get; set; }
public string VariableLengthUnicodeStringProperty { get; set; }
public AllTypesEnum EnumProperty { get; set; }
}
}
|
Cardiac ischemia is a condition that results from insufficient oxygenation to heart muscle and may pose an inherent risk in addition to potentially being a precursor to a life threatening event, such as myocardial infarction (MI). Detecting ischemia may be carried out by a variety of methods, some of which are amendable to implantable monitoring devices. Ischemia, and particularly, unstable ischemia, in a patient may be treated in a clinical setting by a variety of modalities.
A patient with severe unstable ischemia may be a candidate for immediate intervention, such as coronary angioplasty or bypass surgery. However, less severe cases may be treated by pharmaceutical methods as well as others. Even with such treatment modalities available, most ischemic events occur initially outside the clinical environment or at a place or time when such clinical assessment and treatment is not immediately available.
For ICD patients experiencing transient ischemia, standard ventricular pacing therapy in order to increase cardiac output is contraindicated as the increased heart rate induced as a result of the pacing will typically increase the oxygen demand on the heart tissue, and particularly the ischemic heart tissue, which may further exacerbate any damage caused by the ischemia. In addition, generally speaking, a paced rhythm is not as mechanically efficient as a normal sinus rhythm, and, as such, the blood flow output may even be further reduced. Thus, typical single chamber ventricle pacing therapy for an ischemic patient may increase oxygen demand of the heart tissue undergoing ischemic trauma and decrease the pumping efficiency of the heart overall or both.
As such, what has been needed are methods and devices for treating a patient with transient ischemia immediately after onset of the ischemia that do not generate a substantial increase in oxygen consumption by the heart. |
Characterization of the novel HLA-DRB3*03:37 allele by sequencing-based typing.
HLA-DRB3*03:37 differs from HLA-DRB3*03:01:01:01 by one nucleotide substitution in codon 205 in exon 4. |
Q:
Multiplication error in php
I'm building a site where people can exchange coins (site currency) into Bitcoin. The problem I'm having is that for some reason when I multiply the $btcprice with 3 or less the echo is really weird... for your sake this is the code that matters:
<?php
// get 0,01 usd in bitcoins into a variable
$btcprice = file_get_contents('https://blockchain.info/tobtc?currency=USD&value=0.01');
$valueInBTC = 4 * $btcprice;
echo $valueInBTC;
?>
Anything that's 4 or higher will work, but if you try to multiply this with 3 or less it gets weird. For example this:
<?php
// get 0,01 usd in bitcoins into a variable
$btcprice = file_get_contents('https://blockchain.info/tobtc?currency=USD&value=0.01');
$valueInBTC = 3 * $btcprice;
echo $valueInBTC;
?>
Will echo 7.959E-5
I just don't understand what the problem is...
A:
The result you are getting is not an error. It is simply in a formatting you don't expect / know yet. 7.959E-5is exactly the same as 0.00007959 it is just a different way of writing it down. Think of it as 7.959E-5 = 7.959 × (10 ^ (-5)) = 0.00007959. It is called Scientific notation (E notation). In cumputation / science this notation is used, because you can show very large or very small (as in your case) numbers with less digits (it is just shorter to write).
To get the number in other formattings use the php function sprintf().
As you are handling bitcoin values, you shouldn't be formatiing the numbers until just for output. With bitcoins you always deal with very small numbers and you will soon meet precision problems if you try and calculate with formatted floating point numbers.
|
Frithy and Chadacre Woods
Frithy and Chadacre Woods is a 28.7 hectare biological Site of Special Scientific Interest (SSSI) in the parishes of Lawshall and Shimpling in Suffolk, England.
Description
Three ancient and semi-natural woods form the SSSI, namely Frithy Wood in Lawshall parish and Ashen Wood and Bavins Wood on the Chadacre Estate in Shimpling parish.
All three woods are of the wet ash (Fraxinus excelsior) / maple (Acer campestre) type, with hazel (Corylus avellana) also present in considerable quantity. There are pedunculate oak (Quercus robur) trees and other tree and shrub species include aspen (Populus tremula), wild cherry (Prunus avium), midland hawthorn (Crataegus laevigata), hornbeam (Carpinus betulus), crab apple (Malus sylvestris), holly (Ilex aquifolium), spindle (Euonymus europaeus) and common dogwood (Cornus sanguinea). The structure of the woods has been greatly influenced by management of the coppice.
The three woods have a diverse woodland floor vegetation, which is dominated by either dog's mercury (Mercurialis perennis) or brambles (Rubus spp.). They contain a number of plants characteristic of woodlands of this type including herb paris (Paris quadrifolia) in Ashen Wood and wood spurge (Euphorbia amygdaloides), woodruff (Galium odoratum), sanicle (Sanicula europaea) and stinking iris (Iris foetidissima) in Frithy Wood. The SSSI lies within the distribution of oxlip (Primula elatior) and all three woods contain this species. There are many other woodland floor plants including early purple orchid (Orchis mascula), twayblade (Neottia ovata), gromwell (Lithospermum officinale) and bluebell (Hyacinthoides non-scriptus).
There are several well-vegetated rides in the group of woods that support a mixture of woodland and meadow plant species and which attract considerable numbers of common butterflies. Frithy Wood also contains an area of pasture which projects into the wood which is partly shaded by a number of standard trees.
The birdlife of Frithy Wood has been recorded in detail with species including the nightingale, European green woodpecker, great spotted woodpecker and lesser spotted woodpecker which breed regularly.
Roe deer, fallow deer and muntjac can also be seen in the woods but they have caused considerable damage to the ground vegetation.
Forest school
Forest school sessions are held in Frithy Wood by permission of the landowners. The 'school' represents an initiative of All Saints Primary School, Lawshall and the Green Light Trust, an environmental and educational charity.
History
Oliver Rackham has stated that "a wood now called The Frith is almost certain to be pre-conquest, from Old English Fyrhp." In a later book he stated that "an Anglo-Saxon (parallel) is fyrth, a wood, which has given rise to many Frith or Frithy Woods."
There is documentary evidence for the existence of Frithy (formerly Frith) Wood back to 1545 and its Saxon name would imply that the wood is much older than that. All three woods are part of ancient woodland and contain broad boundary banks and ditches typical of coppice woods dating from the medieval period or before.
In more recent times in the twentieth century pigs were kept in Frithy Wood and at one time the wood extended as far as The Street.
Newspaper records
On 31 August 1921 it was reported in the Suffolk Free Press that the remains of George Nunn aged 55 of Lawshall were discovered hanging in Frithy Wood. He had been missing for around 4 months since 22 April and was found a short distance from where he lived.
Access
The woods are not private with easy access.
References
Category:Forests and woodlands of Suffolk
Category:Lawshall
Category:Sites of Special Scientific Interest in Suffolk
Category:Sites of Special Scientific Interest notified in 1987 |
<?php
/**
* Specialized implementation of hook_page_manager_task_tasks(). See api-task.html for
* more information.
*/
function page_manager_contact_user_page_manager_tasks() {
if (!module_exists('contact')) {
return;
}
return array(
// This is a 'page' task and will fall under the page admin UI
'task type' => 'page',
'title' => t('User contact'),
'admin title' => t('User contact'),
'admin description' => t('When enabled, this overrides the default Drupal behavior for displaying the user contact form at <em>user/%user/contact</em>. If no variant is selected, the default Drupal user contact form will be used.'),
'admin path' => 'user/%user/contact',
// Callback to add items to the page managertask administration form:
'task admin' => 'page_manager_contact_user_task_admin',
'hook menu alter' => 'page_manager_contact_user_menu_alter',
// This is task uses 'context' handlers and must implement these to give the
// handler data it needs.
'handler type' => 'context', // handler type -- misnamed
'get arguments' => 'page_manager_contact_user_get_arguments',
'get context placeholders' => 'page_manager_contact_user_get_contexts',
// Allow this to be enabled or disabled:
'disabled' => variable_get('page_manager_contact_user_disabled', TRUE),
'enable callback' => 'page_manager_contact_user_enable',
);
}
/**
* Callback defined by page_manager_contact_user_page_manager_tasks().
*
* Alter the user view input so that user view comes to us rather than the
* normal user view process.
*/
function page_manager_contact_user_menu_alter(&$items, $task) {
if (variable_get('page_manager_contact_user_disabled', TRUE)) {
return;
}
// Override the user view handler for our purpose.
if ($items['user/%user/contact']['page callback'] == 'contact_user_page' || variable_get('page_manager_override_anyway', FALSE)) {
$items['user/%user/contact']['page callback'] = 'page_manager_contact_user';
$items['user/%user/contact']['file path'] = $task['path'];
$items['user/%user/contact']['file'] = $task['file'];
}
else {
// automatically disable this task if it cannot be enabled.
variable_set('page_manager_contact_user_disabled', TRUE);
if (!empty($GLOBALS['page_manager_enabling_contact_user'])) {
drupal_set_message(t('Page manager module is unable to enable user/%user/contact because some other module already has overridden with %callback.', array('%callback' => $items['user/%user/contact']['page callback'])), 'error');
}
}
}
/**
* Entry point for our overridden user view.
*
* This function asks its assigned handlers who, if anyone, would like
* to run with it. If no one does, it passes through to Drupal core's
* user view, which is user_page_view().
*/
function page_manager_contact_user($account) {
// Load my task plugin:
$task = page_manager_get_task('contact_user');
// Load the account into a context.
ctools_include('context');
ctools_include('context-task-handler');
$contexts = ctools_context_handler_get_task_contexts($task, '', array($account));
$output = ctools_context_handler_render($task, '', $contexts, array($account->uid));
if ($output !== FALSE) {
return $output;
}
module_load_include('inc', 'contact', 'contact.pages');
$function = 'contact_user_page';
foreach (module_implements('page_manager_override') as $module) {
$call = $module . '_page_manager_override';
if (($rc = $call('contact_user')) && function_exists($rc)) {
$function = $rc;
break;
}
}
// Otherwise, fall back.
return $function($account);
}
/**
* Callback to get arguments provided by this task handler.
*
* Since this is the node view and there is no UI on the arguments, we
* create dummy arguments that contain the needed data.
*/
function page_manager_contact_user_get_arguments($task, $subtask_id) {
return array(
array(
'keyword' => 'user',
'identifier' => t('User being viewed'),
'id' => 1,
'name' => 'uid',
'settings' => array(),
),
);
}
/**
* Callback to get context placeholders provided by this handler.
*/
function page_manager_contact_user_get_contexts($task, $subtask_id) {
return ctools_context_get_placeholders_from_argument(page_manager_contact_user_get_arguments($task, $subtask_id));
}
/**
* Callback to enable/disable the page from the UI.
*/
function page_manager_contact_user_enable($cache, $status) {
variable_set('page_manager_contact_user_disabled', $status);
// Set a global flag so that the menu routine knows it needs
// to set a message if enabling cannot be done.
if (!$status) {
$GLOBALS['page_manager_enabling_contact_user'] = TRUE;
}
}
|
Our main objective is to characterize the immunological properties and molecular nature of inappropriate antigens detected on SJL/J reticulum cell sarcoma (RCS) and to define the role of these antigens in tumorogenesis. We plan to demonstrate the presence of inappropriate alloantigens on spontaneous, transplantable and cultured RCS cells by cell mediated and complement cytotoxicity, and by immunofluorescence. Furthermore, biochemical analysis of inappropriate antigens will be examined by immune precipitation of NP40 lysed 35S methionine labeled tumor cells with specific alloantisera and characterization of the molecules by SDS gel electrophoresis. The role of inappropriate antigens in host stimulation will be investigated by examining the in vivo response to inappropriate alloantigenic specificities in both cellular and antibody mediated assays. The mechanism by which the immune response promotes tumor escape from immune destruction will be investigated including the role of antigen-antibody complexes in specific anti-tumor-antigen-reactive cell opsonization, modulation of tumor associated antigens by circulating antibody, direct tumor mediated suppression of antigen-reactive cells and activation of suppressor cells. |
Q:
Removal of special characters, a comma separated text, PHP
I got my text variable which is user-specified, normally, user should enter the tags which has to look following:
"food, community, relationship"
but if user type for example
"food;;[]'.'.;@$#community,,,-;,,,relationship"
the script should change it into:
"food, community, relationship".
How can I get this done?
A:
how about:
$str = "-----music,,,,,,,,games;'235@#%@#%media";
$arr = preg_split("/\W+/", $str, -1, PREG_SPLIT_NO_EMPTY);
$str = implode(', ', $arr);
echo $str,"\n";
output:
music, games, 235, media
You could adapt the \W to which characters you need to keep.
|
{
"short_name": "React App",
"name": "Create React App Sample",
"icons": [
{
"src": "favicon.ico",
"sizes": "64x64 32x32 24x24 16x16",
"type": "image/x-icon"
}
],
"start_url": "./index.html",
"display": "standalone",
"theme_color": "#000000",
"background_color": "#ffffff"
}
|
[The rescue station--a multidisciplinary treatment unit in the hospital].
The creation of integrative organizational structures are seen as an objective requirement of medicine characterized by progress of knowledge and specialisation. For emergency cases the rescue station has stood the test as a multidisciplinary unit of the hospital. This thesis is confirmed by experiences obtained from practical work in the Frankfurt/Oder District Hospital and by discussions in the "Working Group Rescue Station" of the "Society of Emergency Medicine of the GDR." In order to realize the function of the rescue chain as well as the multidisciplinary motivation, intensive quantitative and qualitative promotion of rescue stations is required. |
YA/Teen Book Club
The YA/Teen Book Club is now reading In Other Lands by Sarah Rees Brennan.
“Four years in the life of an unloved English schoolboy who’s invited to a secret magical school and learns that even in fantasyland, real life is messier than books. . . . But over the course of four years training among child soldiers, Elliot, unsurprisingly, grows up. His slow development into a genuinely kind person is entirely satisfying, as is his awakening to his own bisexuality and to the colonialism, sexism, and racism of Borderlands society. . . . A stellar . . . wholly rewarding journey.”
―Kirkus Reviews (starred review)
Pick up a copy of In Other Lands today at Griffin Free and then join us on Wednesday, May 30 at 5:30 PM for a lively discussion. |
Q:
CSS minify and rename with gulp
I've a variable like
var files = {
'foo.css': 'foo.min.css',
'bar.css': 'bar.min.css',
};
What I want the gulp to do for me is to minify the files and then rename for me.
But the tasks is currently written as (for one file)
gulp.task('minify', function () {
gulp.src('foo.css')
.pipe(minify({keepBreaks: true}))
.pipe(concat('foo.min.css'))
.pipe(gulp.dest('./'))
});
How to rewrite so it work with my variable files defined above?
A:
You should be able to select any files you need for your src with a Glob rather than defining them in an object, which should simplify your task. Also, if you want the css files minified into separate files you shouldn't need to concat them.
var gulp = require('gulp');
var minify = require('gulp-minify-css');
var rename = require('gulp-rename');
gulp.task('minify', function () {
gulp.src('./*.css')
.pipe(minify({keepBreaks: true}))
.pipe(rename({
suffix: '.min'
}))
.pipe(gulp.dest('./'))
;
});
gulp.task('default', ['minify'], function() {
});
A:
I tried the earlier answers, but I got a never ending loop because I wasn't ignoring the files that were already minified.
First use this code which is similar to other answers:
//setup minify task
var cssMinifyLocation = ['css/build/*.css', '!css/build/*.min.css'];
gulp.task('minify-css', function() {
return gulp.src(cssMinifyLocation)
.pipe(minifyCss({compatibility: 'ie8', keepBreaks:false}))
.pipe(rename({ suffix: '.min' }))
.pipe(gulp.dest(stylesDestination));
});
Notice the '!css/build/*.min.css' in the src (i.e. var cssMinifyLocation)
//Watch task
gulp.task('default',function() {
gulp.watch(stylesLocation,['styles']);
gulp.watch(cssMinifyLocation,['minify-css']);
});
You have to ignore minified files in both the watch and the task.
|
A Lipid Transfer Protein Variant with a Mutant Eight-cysteine Motif Causes Photoperiod-thermo-sensitive Dwarfism in Rice.
Plant height is an important trait for plant architecture patterning and crop yield improvement. Although the pathways involving in gibberellins and brassinosteroid have been well studied, there are still many gaps in the picture of the networks controlling plant height. Here, we revealed that a dominant photoperiod- and thermo-sensitive dwarf mutant is caused by the active role of a mutated gene Ptd1, of which the wild-type gene encodes a non-specific lipid transfer protein (nsLTP). The Ptd1 plants showed severe dwarfism under long-day and low-temperature conditions, but grew nearly normal under short-day and high-temperature conditions; these phenotypic variations were associated with the Ptd1 mRNA level and its protein accumulation. Furthermore, we found that the growth inhibition in Ptd1 might result from the special protein conformation of Ptd1 due to loss of two disulfide bonds in the Eight-cysteine motif (8-CM) that is conserved among nsLTPs. Our findings give new insights into the understanding of the novel function of disulfide bonds in 8-CM, and provide a new strategy for regulation of cell development and plant height, by modifying the amino acid residues involved in protein conformation patterning. |
Comparing alignment methods for inferring the history of the new world lizard genus Mabuya (Squamata: Scincidae).
The rapid increase in the ability to generate molecular data, and the focus on model-based methods for tree reconstruction have greatly advanced the use of phylogenetics in many fields. The recent flurry of new analytical techniques has focused almost solely on tree reconstruction, whereas alignment issues have received far less attention. In this paper, we use a diverse sampling of gene regions from lizards of the genus Mabuya to compare the impact, on phylogeny estimation, of new maximum likelihood alignment algorithms with more widely used methods. Sequences aligned under different optimality criteria are analyzed using partitioned Bayesian analysis with independent models and parameter settings for each gene region, and the most strongly supported phylogenetic hypothesis is then used to test the hypothesis of two colonizations of the New World by African scincid lizards. Our results show that the consistent use of model-based methods in both alignment and tree reconstruction leads to trees with more optimal likelihood scores than the use of independent criteria in alignment and tree reconstruction. We corroborate and extend earlier evidence for two independent colonizations of South America by scincid lizards. Relationships within South American Mabuya are found to be in need of taxonomic revision, specifically complexes under the names M. heathi, M. agilis, and M. bistriata (sensu, M.T. Rodrigues, Papeis Avulsos de Zoologia 41 (2000) 313). |
Hugh Lucas-Tooth
Sir Hugh Vere Huntly Duff Munro-Lucas-Tooth, 1st Baronet (13 January 1903 – 18 November 1985), born and baptised Hugh Vere Huntly Duff Warrand and known as Sir Hugh Vere Huntly Duff Lucas-Tooth, 1st Baronet, from 1920 to 1965, was a Scottish British Conservative politician. Elected to parliament in 1924 at the age of 21, he was the first British MP to have been born in the 20th century.
Family
Warrand's father was Hugh Munro Warrand (8 July 1870 – 11 June 1935, married 24 April 1901), Major in the 3rd Battalion of the Queen's Own Cameron Highlanders, and son of Alexander John Cruikshank Warrand of Bught, Inverness-shire.
Warrand's mother Beatrice Maude Lucas Lucas-Tooth (died 25 June 1944) was a daughter of Sir Robert Lucas-Tooth, 1st Baronet. Warrand's great-grandfather was Robert Tooth, a prominent Australian businessman. His brother Selwyn John Power Warrand (6 February 1904 – 24 May 1941), who married 25 March 1933 to Frena Lingen Crace, daughter of Everard Crace, from Canberra, Australian Capital Territory, by whom he had two children.
Selwyn John Power Warrand was a Commander in the service of the Royal Navy, fought in World War II and was killed in action on board of HMS Hood (51) and his widow remarried in 1947 Henry Richard Charles Humphries. His sister Beatrice Helen Fitzhardinge Warrand (born 1908), married on 27 September 1941 another World War II veteran, Lieutenant Colonel Lyndall Fownes Urwick, Military Cross, Officer of the Order of the British Empire, son of Sir Henry Urwick of Malvern, Worcestershire, Justice of the Peace.
Biography
Warrand was educated at Eton College, and graduated from Balliol College in 1924 with a Bachelor of Arts degree. He adopted the legally changed name Hugh Vere Huntly Duff Lucas-Tooth of Teanich by Royal Licence in 1920 when he gained the recreated baronetcy of his maternal grandfather, the first baronet, whose three sons had died in World War I, being created 1st Baronet Lucas-Tooth, of Bught, County Inverness, in the Baronetage of the United Kingdom on 1 December 1920, with special remainder to the heirs male of the body of his mother.
Lucas-Tooth was first elected to the House of Commons in the 1924 general election as Conservative Member of Parliament for the Isle of Ely from October 1924 to May 1929. Aged 21, he became the youngest MP, known as "Baby of the House". He served as Parliamentary Private Secretary to Arthur Samuel, Secretary for Overseas Trade. Lucas-Tooth was called to the bar in 1933 at Lincoln's Inn entitled to practise as a barrister. He also became a lieutenant colonel in the service of the Queen's Own Cameron Highlanders.
During the 1930s Lucas-Tooth helped established the Lucas-Tooth gymnasium at Tooley Street in south London for the benefit of unemployed men from the Northern coalfields and unemployed areas. A new style of physical exercises helped improve the fitness of these men. It was featured in a British Pathe newsreel in 1938 titled 'Fit – Fitter – Fittest'.
He was defeated in the 1929 general election by the Liberal candidate, James A. de Rothschild. Lucas-Tooth stood again for parliament in the 1945 general election for Hendon South, and was elected, taking his seat in July 1945. He retained the seat in subsequent general elections until 1970 and was Parliamentary Under-Secretary of State for the Home Department between February 1952 and December 1955.
On 3 February 1965 Lucas-Tooth legally changed his name once again by Deed Poll to Hugh Vere Huntly Duff Munro-Lucas-Tooth of Teaninich, to reflect the Scottish lairdship Munro of Teaninich.
He retired from Parliament at the 1970 general election.
Marriage and issue
He married on 10 September 1925 Laetitia Florence Findlay (died 1978), daughter of Sir John Ritchie Findlay, 1st Baronet, of Aberlour; the couple had three children, Laetitia (born 1926), Jennifer (born 1929), and Hugh (born 1932). Hugh succeeded his father as Baronet.
References
External links
Category:1903 births
Category:1985 deaths
Category:People educated at Eton College
Category:Alumni of Balliol College, Oxford
Category:Conservative Party (UK) MPs for English constituencies
Category:Baronets in the Baronetage of the United Kingdom
Category:UK MPs 1924–1929
Category:UK MPs 1945–1950
Category:UK MPs 1950–1951
Category:UK MPs 1951–1955
Category:UK MPs 1955–1959
Category:UK MPs 1959–1964
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Category:UK MPs 1966–1970 |
In aged humans, stroke is a major cause of disability for which no neuroprotective measures are available. In animal studies of focal ischemia, short-term hypothermia often reduces infarct size. Nevertheless, efficient neuroprotection requires long-term, regulated lowering of whole-body temperature. Previously, it is reported that post-stroke exposure to hydrogen sulfide (H2S) effectively lowers whole-body temperature and confers neuroprotection in aged animals. Here we report for the first time that the animals exposed to H2S the normal sleep–wake oscillations are replaced by a low-amplitude EEG dominated by a 4-Hz rhythmicactivity, reminiscent of EEG recordings in hibernating animals. In the present study using magnetic resonance imaging, reverse transcriptase polymerase chain reaction, western blotting and immunofluorescence, we characterized the central nervous system response to H2S -induced hypothermia and report, that annexin A1, a major constituent of peripheral leukocytes that is upregulated after stroke, was consistently downregulated in polymorphonuclear cells in the peri-lesional cortex of post-ischemic, aged rat brain after 48 hours of hypothermia induced by exposure to H2S. This might be due to the reduced kinetics of recruitment, adherence and infiltration of PMN cells by H2S -induced hypothermia. Our findings further suggest that, in contrast to monotherapies that have thus far uniformly failed in clinical practice, prolonged hypothermia has pleiotropic effects on brain physiology that may be necessary for effective protection of the brain after stroke. |
Q:
How to install Visual Studio on Ubuntu 20.04?
Can anyone tell how to install Visual Studio and .NET Framework on Ubuntu 20.04?
Is there any way to Install .NET and Visual Studio in Ubuntu 20.04?
A:
Unfortunately Visual Studio does not available for Linux. But you really want' exactly VS - you should try Wine or any Windows VM.
But I recommend for you one of the following options:
Rider (Cross platform IDE from JetBrains)
Visual Studio Code (Very popular solution for developer on any technology)
Mono Develop
Eclipse
|
IN THE COURT OF CRIMINAL APPEALS
OF TEXAS
NO. PD-1240-10
DAVID CEPEDA JONES, Appellant
v.
THE STATE OF TEXAS
ON APPELLANT’S PETITION FOR DISCRETIONARY REVIEW
FROM THE FOURTH COURT OF APPEALS
BEXAR COUNTY
Per curiam. Keasler, and Hervey, JJ., dissent.
O R D E R
The petition for discretionary review violates Rule of Appellate Procedure 9.3(b) and
68.4(i) because the original petition is not accompanied by 11 copies and the petition does
not contain a complete copy of the opinion of the court of appeals.
The petition is struck. See Rule of Appellate Procedure 68.6.
The petitioner may redraw the petition. The redrawn petition and copies must be filed
in the Court of Criminal Appeals within thirty days after the date of this Order.
Filed: October 6, 2010
Do Not Publish
|
Get affordable prints and increased versatility. Set up, connect, and print right from your mobile device, and produce high-quality photos and everyday documents. Print, scan, and copy with ease. HP Photo and Document All-in-One Printers are designed for families and other home users who want a device capable of printing everything from documents, email and web pages to rich, bright lab-quality photos - with copy and scan tools too. Dynamic security enabled printer. Intended to be used with cartridges using only HP original electronic circuitry. Cartridges with modified or non-HP electronic circuitry may not work, and those that work today may not work in the future.
Get affordable prints and increased versatility. Set up, connect, and print right from your mobile device, and produce high-quality photos and everyday documents. Print, scan, and copy with ease.
HP Photo and Document All-in-One Printers are designed for families and other home users who want a device capable of printing everything from documents, email and web pages to rich, bright lab-quality photos - with copy and scan tools too.
Dynamic security enabled printer. Intended to be used with cartridges using only HP original electronic circuitry. Cartridges with modified or non-HP electronic circuitry may not work, and those that work today may not work in the future. |
Introduction {#s1}
============
Usher syndrome (USH) is an autosomal recessive disorder characterized by hearing loss (HL), retinitis pigmentosa (RP) and vestibular dysfunction. Three clinical subtypes can be distinguished. USH type 1 (USH1) is the most severe among them because of profound HL, absent vestibular responses, and prepubertal onset RP. USH type 2 (USH2) is characterized by congenital moderate to severe HL, with a high-frequency sloping configuration. The vestibular function is normal and onset of RP is in the first or second decade. The onset of the visual symptoms such as night blindness in USH usually occurs several years later than in USH1. USH type 3 (USH3) is characterized by variable onset of progressive HL, variable onset of RP, and variable impairment of vestibular function (normal to absent) [@pone.0090688-Kimberling1], [@pone.0090688-Yan1].
To date, nine genetic loci for USH1(*USH1B-H*, *J*, and *K*) have been mapped to chromosomes 11q13.5, 11p15.1, 10q22.1, 21q21, 10q21-q22, 17q24-q25, 15q22-q23 (*USH1H* and *J*), and 10p11.21--q21.1 [@pone.0090688-Yan1], [@pone.0090688-Jaworek1], [@pone.0090688-Riazuddin1]. Six of the corresponding genes have been identified: the actin-based motor protein myosin VIIa (*MYO7A*, USH1B) [@pone.0090688-Weil1]; two cadherin-related proteins, cadherin 23 (*CDH23*, USH1D) [@pone.0090688-Bork1] and protocadherin 15 (*PCDH15*, USH1F) [@pone.0090688-Ahmed1]; and two scaffold proteins, harmonin (*USH1C*) [@pone.0090688-Verpy1] and sans (*USH1G*) [@pone.0090688-Mustapha1]; the Ca^2+^- and integrin-binding protein (*CIB2*, USH1J) [@pone.0090688-Riazuddin1]. In Caucasian USH1 patients, previous studies showed that mutations in *MYO7A*, *USH1C*, *CDH23*, *PCDH15*, and *USH1G*, were found in 39--55%, 7--14%, 7--35%, 7--11%, and 0--7%, respectively (the frequency of *CIB2* is still unknown) [@pone.0090688-Ouyang1], [@pone.0090688-Bonnet1], [@pone.0090688-LeQuesneStabej1]. In Japanese, Nakanishi et al. showed that *MYO7A* and *CDH23* mutations are present in USH1 patients [@pone.0090688-Nakanishi1], however, the frequency is not yet known. In addition, mutations in three corresponding genes (usherin *USH2A* [@pone.0090688-Eudy1], G protein-coupled receptor 98; *GPR98* [@pone.0090688-Weston1], and deafness, autosomal recessive 31; *DFNB31* [@pone.0090688-Aller1]) have been reported so far in USH2, and USH3 is caused by mutations in the clarin 1 (*CLRN1*) [@pone.0090688-Joensuu1] gene.
Comprehensive molecular diagnosis of USH has been hampered both by genetic heterogeneity and the large number of exons for most of the USH genes. The six USH1 genes collectively contain 180 coding exons [@pone.0090688-Riazuddin1], [@pone.0090688-Mustapha1], [@pone.0090688-Ouyang1] the three USH2 genes comprise 175 coding exons [@pone.0090688-Weston1], [@pone.0090688-Aller1], [@pone.0090688-Nakanishi2], and the USH3 gene has five coding exons [@pone.0090688-Joensuu1]. In addition some of these genes are alternatively spliced ([@pone.0090688-Riazuddin1], [@pone.0090688-Ahmed1], [@pone.0090688-Verpy1], [@pone.0090688-Aller1], [@pone.0090688-Joensuu1] and NCBI database: <http://www.ncbi.nlm.nih.gov/nuccore/>). Thus far, large-scale mutation screening has been performed using direct sequence analysis, but that is both time-consuming and expensive. We thought that targeted exon sequencing of selected genes using the Massively Parallel DNA Sequencing (MPS) technology would enable us to systematically tackle previously intractable monogenic disorders and improve molecular diagnosis.
Therefore, in this study, we have conducted genetic analysis using MPS-based genetic screening to find mutations in nine causative USH genes (except *CIB2*) in Japanese USH1 patients.
Results {#s2}
=======
Mutation analysis of the nine USH genes in 17 unrelated USH1 patients revealed 19 different probable pathogenic variants, of which 14 were novel ([Table 1](#pone-0090688-t001){ref-type="table"}).
10.1371/journal.pone.0090688.t001
###### Possible pathogenic variants found in this study.
{#pone-0090688-t001-1}
Gene Mutation type Nucleotide change Amino acid change exon/intron number Domain control (in 384 alleles) SIFT Score PolyPhen Score Reference
---------- --------------- ------------------- ------------------- -------------------- -------------- -------------------------- ------------ ---------------- --------------------------------
*MYO7A* Frameshift c.1623dup p.Lys542GlnfsX5 Exon 14 \- N/A \- \- Le Quesne Stabej et al. (2012)
c.4482_4483insTG p.Trp1495CysfsX55 Exon 34 \- N/A \- \- This study
c.6205_6206delAT p.Ile2069ProfsX6 Exon 45 \- N/A \- \- This study
Nonsense c.1477C\>T p.Gln493X Exon 13 \- N/A \- \- This study
c.1708C\>T p.Arg570X Exon 15 \- N/A \- \- This study
c.2115C\>A p.Cys705X Exon 18 \- N/A \- \- This study
c.6321G\>A p.Trp2107X Exon 46 \- N/A \- \- This study
Missense c.2074G\>A p.Val692Met Exon 17 Motor domain 0 0.09 0.982 This study
c.2311G\>T p.Ala771Ser Exon 20 IQ 2 0.0026 0.01 0.825 Nakanishi et al. (2010)
c.6028G\>A p.Asp2010Asn Exon 44 FERM 2 0 0 0.925 Jacobson et al. (2009)
*CDH23* Frameshift c.3567delG p.Arg1189ArgfsX5 Exon 30 \- N/A \- \- This study
c.5780_5781delCT p.Ser1927Cysfs16 Exon 44 \- N/A \- \- This study
Splicing c.5821-2A\>G ? Intron 44 \- N/A \- \- This study
Nonsense c.6319C\>T p.Arg2107X Exon 48 \- N/A \- \- Nakanishi et al. (2010)
*PCDH15* Splicing c.158-1G\>A ? Intron 3 \- N/A \- \- This study
Nonsense c.1006C\>T p.Arg336X Exon 10 \- N/A \- \- This study
c.2971C\>T p.Arg991X Exon 22 \- N/A \- \- Roux et al. (2006)
c.3337G\>T p.Glu1113X Exon 25 \- N/A \- \- This study
Missense c.3724G\>A p.Val1242Met Exon 28 Cadherin 11 0 0 1 This study
Computer analysis to predict the effect of missense variants on MYO7A protein function was performed with sorting intolerant from tolerant (SIFT; <http://sift.jcvi.org/>), and polymorphism phenotyping (PolyPhen2; <http://genetics.bwh.harvard.edu/pph2/>).
N/A: not applicable.
All mutations were detected in only one patient each and sixteen of the 17 patients (94.1%) carried at least one mutation, while one patient had no mutations. Thirteen of the 16 mutation carriers each had two pathogenic mutations ([Table 2](#pone-0090688-t002){ref-type="table"}).
10.1371/journal.pone.0090688.t002
###### Details of phenotype and genotype of 17 USH1 patients.
{#pone-0090688-t002-2}
Sample No. Age Sex Allele1 Allele2 Hereditary form Onset of night blindness Cataract Hearing Aid Cochlear Implant
--------------------------------------------------------------------------------------------------------------- ----- ----- -------------------------------------------------- -------------------------------------------------- ----------------- -------------------------- ----------- ------------- ------------------
***MYO7A***
1 37 M p.Gln493X p.Trp1495CysfsX55 sporadic 13 no unilateral unilateral
2 41 W p.l2069fsX6 p.l2069fsX6 AR unknown both eyes bilateral no
5 54 M p.Val692Met p.Val692Met AR 5 both eyes no no
6 54 W p.Arg570X p.Arg570X sporadic 6 no no no
8 14 M p.Lys542GlnfsX5 p.Lys542GlnfsX5 sporadic 6 no unilateral unilateral
11 54 M p.Asp2010Asn p.Trp2107X sporadic 13 no no no
17 56 W p.Cys705X p.Cys705X sporadic unknown no no no
***CDH23***
7 12 W p.Arg1189ArglfsX5 p.Arg1189ArglfsX5 sporadic 12 both eyes no bilateral
9 9 M p.Ser1927Cysfs16 c.5821-2A\>G sporadic 8 no unilateral unilateral
15 16 W p.Arg2107X p.Arg2107X sporadic unknown no no no
***PCDH15***
3 47 W p.Glu1113X p.Glu1113X sporadic 5 both eyes no no
16 28 W p.Arg991X p.Arg991X AR 10 no no no
10 62 M p.Arg962Cys unknown sporadic 9 both eyes no no
12 52 M p.Arg336X unknown sporadic 3 no no no
13 51 M p.Val1242Met unknown sporadic 10 no no no
***MYO7A*** [\*](#nt103){ref-type="table-fn"} **^1^** ***/PCDH15*** [\*](#nt103){ref-type="table-fn"} **^2^**
4 21 M p.Ala771Ser[\*](#nt103){ref-type="table-fn"} ^1^ c.158-1G\>A[\*](#nt103){ref-type="table-fn"} ^2^ sporadic 10 no unilateral unilateral
**unknown**
14 64 W unknown unknown sporadic 15 both eyes unilateral no
\*All subjects have congenital deafness and RP.
Nonsense, frame shift, and splice site mutations are all classified as pathogenic, whereas missense mutations are presumed to be probable pathogenic variants based on results of prediction software for evaluation of the pathogenicity of missense variants ([Table 1](#pone-0090688-t001){ref-type="table"}).
Of the 19 probable pathogenic mutations that we found, 17 were detected by MPS. The remaining two (p.Lys542GlnfsX5 in *MYO7A* and c.5821-2A\>G in *CDH23*) were sequenced by direct sequence analysis.
Of our 17 USH patients, seven had *MYO7A* mutations (41.2%), three had *CDH23* mutations (17.6%), and two had *PCDH15* mutations (11.8%). We did not find any probable pathogenic mutations in *USH1C*, *USH1G*, and USH2/3 genes.
Four USH1 patients (Cases \#3, 5, 8, 15) had probable pathogenic mutations in two different USH genes, with one being a biallelic mutation ([Table 3](#pone-0090688-t003){ref-type="table"}). The other heterozygous/homozygous mutations were missense variants. Three of these patients (Cases \#3, 5, 8) presented with earlier RP onset (night blindness) than in the other patients with two pathogenic mutations (Cases \#1, 6, 7, 9, 11, 16) (*p* = 0.007) ([Fig. 1](#pone-0090688-g001){ref-type="fig"}).
{#pone-0090688-g001}
10.1371/journal.pone.0090688.t003
###### The patients with mutations in two different genes.
{#pone-0090688-t003-3}
Sample Genes with two pathogenic mutations Gene with one heterozygous mutation Nucleotide change Amino acid change control SIFT score PolyPhen score Referense
-------- ------------------------------------- ------------------------------------- ------------------- ------------------------------------------ --------- ------------ ---------------- -------------------------
5 *MYO7A* *CDH23* c.C719T p.P240L[\*](#nt104){ref-type="table-fn"} 0.26 0.06 0.999 Wagatsuma et al. (2007)
8 *MYO7A* *CDH23* c.2568C\>G p.Ile856Met 0 0.08 1 This study
15 *CDH15* *USH1C* c.2437T\>G p.Tyr813Asp 0 0.19 0.932 This study
3 *PCDH15* *USH1G* c.28C\>T p.Arg10Trp 0 0.19 1 This study
\*homozygotes.
One patient (Case \#4) had heterozygote mutations in two USH1 genes (p.Ala771Ser in *MYO7A* and c.158-1G\>A in *PCDH15*). His parents and one brother were found to also be carriers for these mutations. Another brother had no variants ([Fig. 2](#pone-0090688-g002){ref-type="fig"}).
{#pone-0090688-g002}
Discussion {#s3}
==========
For USH1, early diagnosis has many immediate and several long-term advantages for patients and their families [@pone.0090688-Kimberling1]. However, diagnosis in childhood, based on a clinical phenotype, has been difficult because patients appear to have only non-syndromic HL in childhood and RP develops in later years. Although early diagnosis is now possible through DNA testing, performing large-scale mutation screening for USH genes in all non-syndromic HL children has been both time-consuming and expensive. Therefore, the availability of MPS, which facilitates comprehensive large-scale mutation screening [@pone.0090688-Miyagawa1] is a very welcome advance.
MPS technology enabled us to detect pathogenic mutations in USH1 patients efficiently, identifying one or two pathogenic/likely pathogenic mutations in 16 of 17 (94.1%) cases. This was comparable to previous direct sequence analysis results such as Bonnet et al. who detected one or two mutations in 24 out of 27 (89%) USH1 patients [@pone.0090688-Bonnet1] and Le Quesne Stabej et al. who detected one or two mutations in 41 out of 47 (87.2%) USH1 patients [@pone.0090688-LeQuesneStabej1].
In addition, MPS assists in the analysis of disease modifiers and digenic inheritance because it simultaneously investigates many causative genes for a specific disease, such as in our case, USH. Previous reports have described several USH cases with pathogenic mutations in two or three different USH genes [@pone.0090688-Bonnet1], [@pone.0090688-LeQuesneStabej1], [@pone.0090688-Ebermann1]. In our study, four patients had two pathogenic mutations in one gene and missense variants in a different gene ([Table 3](#pone-0090688-t003){ref-type="table"}). We considered the latter to possibly be a disease modifier. For example, *USH1C*:p.Tyr813Asp, which occurred in 0/384 control chromosomes and was predicted to be "probably damaging" by the Polyphen program, was found with a homozygous *CDH23* nonsense mutation (p.Arg2107X) (Case \#15). As for what the variant "modifies", we speculate that for USH1 patients with a disease modifier, RP symptoms such as night blindness show an earlier onset. However, we think that profound HL and the absence of vestibular function in USH1 patients are not affected by modifiers as they are congenital and therefore not progressive.
Ebermann et al. described a USH2 patient with "digenic inheritance." a heterozygous truncating mutation in *GPR98*, and a truncating heterozygous mutation in PDZ domain-containing 7 (*PDZD7*), which is reported to be a cause of USH [@pone.0090688-Ebermann1]. Our USH1 patient (Case \#4) had segregated *MYO7A*:p.Ala771Ser and *PCDH15*:c.158-1G\>A. Molecular analyses in mouse models have shown many interactions among the USH1 proteins [@pone.0090688-Yan1]. In particular, *MYO7A* directly binds to *PCDH15* and both proteins are expressed in an overlapping pattern in hair bundles in a mouse model [@pone.0090688-Senften1]. *PCDH15*:c.158-1G\>A, predicted to alter the splice donor site of intron 3, has been classified as pathogenic. *MYO7A*:p.Ala771Ser is a non-truncating mutation, but was previously reported as disease-causing [@pone.0090688-Nakanishi1]. So, we consider the patient to be the first reported case of *MYO7A*/*PCDH15* digenic inheritance.
However, we should be aware of two limitations of MPS technology. First, the target region of MPS cannot cover all coding exons of USH genes. Actually, the coverage of the target exons was 97.0% in our study. So, it is impossible to detect a mutation in a region which is not covered using this system (Case \#9: c.5821-2A\>G). Secondarily, the MPS system used in this study, is not effective for detecting homo-polymer regions, for example poly C stretch [@pone.0090688-Loman1] (Case \#8: p.Lys542GlnfsX5). In addition, concerning pathogenecity of mutations identified, functional analysis will be necessary to draw the final conclusion in the future.
In UK and US Caucasian USH1 patients, USH1B (*MYO7A*) has been reported as the most common USH1 genetic subtype [@pone.0090688-Bonnet1], [@pone.0090688-LeQuesneStabej1], while USH1F (*PCDH15*) has been reported as the most common USH1 genetic subtype in North American Ashkenazi Jews [@pone.0090688-BenYosef1]. In Japanese, our study revealed that the most common type was *MYO7A* (41.7%), which was similar to the frequency in the above Caucasian patients (46.8∼55%) [@pone.0090688-Bonnet1], [@pone.0090688-LeQuesneStabej1]. However, the small number of USH1 patients in our study might have biased the frequency and further large cohort study will be needed in the future.
In addition, most of our detected mutations were novel. We have previously reported genes responsible for deafness in Japanese patients and observed differences in mutation spectrum between Japanese (who are probably representative of other Asian populations) and populations with European ancestry [@pone.0090688-Usami1].
In conclusion, our study was the first report of USH mutation analysis using MPS and the frequency of USH1 genes in Japanese. Mutation screening using MPS has the potential power to quickly identify mutations of many causative genes such as USH while maintaining cost-benefit performance. In addition, the simultaneous mutation analysis of large numbers of genes was useful for detecting mutations in different genes that are possibly disease modifiers or of digenic inheritance.
Materials and Methods {#s4}
=====================
Subjects {#s4a}
--------
We screened 17 Japanese USH1 patients (aged 9 to 64 years): three from autosomal recessive families (non-affected parents and two or more affected siblings), and 14 from sporadic families. There were 9 males and 8 females. None of the subjects had any other noteworthy symptoms. All subjects or next of kin on the behalf of the minors/children gave prior written informed consent for participation in the project, and the Ethical Committee of Shinshu University approved the study and the consent procedure.
Amplicon Library Preparation {#s4b}
----------------------------
An Amplicon library of the target exons was prepared with an Ion AmpliSeq Custom Panel (Applied Biosystems, Life Technologies, Carlsbad, CA) designed with Ion AmpliSeq Designer (<https://www.ampliseq.com/browse.action>) for nine USH genes by using Ion AmpliSeq Library Kit 2.0 (Applied Biosystems, Life Technologies) and Ion Xpress Barcode Adapter 1--16 Kit (Applied Biosystems, Life Technologies) according to the manufacturers\' procedures.
In brief, DNA concentration was measured with Quant-iT dsDNA HS Assay (Invitrogen, Life Technologies) and Qubit Fluorometer (Invitrogen, Life Technologies) and DNA quality was confirmed by agarose gel electrophoresis. 10 ng of each genomic DNA sample was amplified, using Ion AmpliSeq HiFi Master Mix (Applied Biosystems, Life Technologies) and AmpliSeq Custom primer pools, for 2 min at 99°C, followed by 15 two-step cycles of 99°C for 15 sec and 60°C for 4 min, ending with a holding period at 10°C in a PCR thermal cycler (Takara, Shiga, Japan). After the Multiplex PCR amplification, amplified DNA samples were digested with FuPa enzyme at 50°C for 10 min and 55°C for 10 min and the enzyme was successively inactivated for 60°C for 20 min incubation. After digestion, diluted barcode adapter mix including Ion Xpress Barcode Adapter and Ion P1 adaptor were ligated to the end of the digested amplicons with ligase in the kit for 30 min at 22°C and the ligase was successively inactivated at 60°C for 20 min incubation. Adaptor ligated amplicon libraries were purified with the Agencourt AMPure XP system (Beckman Coulter Genomics, Danvers, MA). The amplicon libraries were quantified by using Ion Library Quantitation Kit (Applied Biosystems, Life Technologies) and the StepOne plus realtime PCR system (Applied Biosystems, Life Technologies) according to the manufacturers\' procedures. After quantification, each amplicon library was diluted to 20 pM and the same amount of the 12 libraries for 12 patients were pooled for one sequence reaction.
Emulsion PCR and Sequencing {#s4c}
---------------------------
The emulsion PCR was carried out with the Ion OneTouch System and Ion OneTouch 200 Template Kit v2 (Life Technologies) according to the manufacturer\'s procedure (Publication Part Number 4478371 Rev. B Revision Date 13 June 2012). After the emulsion PCR, template-positive Ion Sphere Particles were enriched with the Dynabeads MyOne Streptavidin C1 Beads (Life Technologies) and washed with Ion OneTouch Wash Solution in the kit. This process were performed using an Ion OneTouch ES system (Life Technologies).
After the Ion Sphere Particle preparation, MPS was performed with an Ion Torrent Personal Genome Machine (PGM) system using the Ion PGM 200 Sequencing Kit and Ion 318 Chip (Life Technologies) according to the manufacturer\'s procedures.
Base Call and Data Analysis {#s4d}
---------------------------
The sequence data were processed with standard Ion Torrent Suite Software and Torrent Server successively mapped to human genome sequence (build GRCh37/hg19) with Torrent Mapping Alignment Program optimized to Ion Torrent data. The average of 562.33 Mb sequences with about 4,300,000 reads was obtained by one Ion 318 chip. The 98.0% sequences were mapped to the human genome and 94% of them were on the target region. Average coverage of depth in the target region was 314.2 and 93.8% of them were over 20 coverage.
After the sequence mapping, the DNA variant regions were piled up with Torrent Variant Caller plug-in software. Selected variant candidates were filtered with the average base QV (minimum average base quality 25), variant frequency (40--60% for heterozygous mutations and 80--100% for homozygous mutations) and coverage of depth (minimum coverage of depth 10). After the filtrations, variant effects were analyzed with the wANNOVAR web site [@pone.0090688-Wang1], [@pone.0090688-Chang1] (<http://wannovar.usc.edu>) including the functional prediction software for missense variants: Sorting Intolerant from Tolerant (SIFT; <http://sift.jcvi.org/>), and Polymorphism Phenotyping (PolyPhen2; <http://genetics.bwh.harvard.edu/pph2/>). The sequencing data was available in the DNA databank of Japan (Accession number: DRA001273).
Algorithm {#s4e}
---------
Missense, nonsense, and splicing variants were selected among the identified variants. Variants were further selected as less than 1% of: 1) the 1000 genome database (<http://www.1000genomes.org/>), 2) the 5400 exome variants (<http://evs.gs.washington.edu/EVS/>), and 3) the in-house control. Candidate mutations were confirmed by Sanger sequencing and the responsible mutations were identified by segregation analysis using samples from family members of the patients. In addition, the cases with heterozygous or no causative mutation were fully sequenced by Sanger sequencing for USH1 genes in order to verify the MPS results.
Direct Sequence Analysis {#s4f}
------------------------
Primers were designed with the Primer 3 plus web server (<http://www.bioinformatics.nl/cgi-bin/primer3plus/primer3plus.cgi>). Each genomic DNA sample (40 ng) was amplified using Ampli Taq Gold (Life Technologies) for 5 min at 94°C, followed by 30 three-step cycles of 94°C for 30 sec, 60°C for 30 sec, and 72°C for 30 sec, with a final extension at 72°C for 5 min, ending with a holding period at 4°C in a PCR thermal cycler (Takara, Shiga, Japan). The PCR products were treated with ExoSAP-IT (GE Healthcare Bio, Buckinghamshire, UK) and by incubation at 37°C for 60 min, and inactivation at 80°C for 15 min. After the products were purified, we performed standard cycle sequencing reaction with ABI Big Dye terminators in an ABI 3130xl sequencer (Life Technologies).
Accession numbers {#s4g}
-----------------
*MYO7A*, \[NM_000260.3\]; *USH1C*, \[NM\_ 153676.3\]; *CDH23*, \[NM\_ 022124.5\]; *PCDH15*, \[NM\_ 033056.3\]; *USH1G*, \[NM\_ 173477.2\]; *USH2A*, \[NM_206933.2\]; *GPR98*, \[NM\_ 032119.3\]; *DFNB31*, \[NM\_ 015404.3\]; *CLRN1*, \[NM\_ 174878.2\]; *PDZD7*, \[NM\_ 001195263.1\].
We thank A. C. Apple-Mathews for help in preparing the manuscript.
[^1]: **Competing Interests:**The authors have declared that no competing interests exist.
[^2]: Conceived and designed the experiments: HY SI SN SU. Performed the experiments: HY SN. Analyzed the data: HY SN SU. Contributed reagents/materials/analysis tools: HY SI SN KK TT YK HS KN KI TI YN KF CO TK HN SU. Wrote the paper: HY SN SU.
|
---
layout: example
title: Wheat Plot Example
permalink: /examples/wheat-plot/index.html
spec: wheat-plot
image: /examples/img/wheat-plot.png
---
A [wheat plot](http://www.perceptualedge.com/articles/visual_business_intelligence/the_datavis_jitterbug.pdf) is an alternative to standard dot plots and histograms that incorporates aspects of both. The x-coordinate of a point is based on its exact value. The y-coordinate is determined by grouping points into histogram bins, then stacking them based on their rank order within each bin. While not scalable to large numbers of data points, wheat plots allow inspection of (and interaction with) individual points without overplotting. For a related approach, see [beeswarm plots](../beeswarm-plot/).
{% include example spec=page.spec %}
|
Q:
can't select all elements with classList API
I'm having a problem selecting all the LI tags when converting jQuery code to HTML5 javascript
code. I have applied the click event to the parent UL, and the click event is being applied to the correct clicked target LI. The class "selected" is also being applied. The problem is that I need all classes to be cleared from the LI tags before the "selected" class is applied, as I only want it applied to the current event target. In jQuery it is simply a matter of removing classes from the LI's, but I am having problems targeting all the LI tags and removing the class in javascript. I suspect the problem is how I am iterating over the node list returned from QuerySelectorAll. I have also tried amongst other things, document.GetElementsByTagName, and iterating over these.
I am getting an "Uncaught TypeError: Cannot read property 'contains' of undefined" on the myFunc function.
I would be very happy if someone could point out my error.
<div id='button'></div>
<ul id='swatches'>
<li></li>
<li></li>
<li></li>
<li></li>
</ul>
The jQuery code
$('li').on('click', function(){
$('li').removeClass('selected');
$(this).toggleClass('selected');
});
Using the classList API
var swatch = document.getElementById('swatches'),
$li = document.querySelectorAll('#swatches li');
swatch.addEventListener('click', myFunc, false);
function myFunc(e){
var target = e.target;
for(var i=0; i<$li.length; i++){
if($li.classList.contains('selected')){
$li.classList.remove('selected');
}
}
if(target.nodeName.toLowerCase() === 'li'){
e.target.classList.toggle('selected');
}
}
A:
I suspect the problem is how I am iterating over the node list returned from QuerySelectorAll.
Yes. You forget the indices. It should be
for (var i=0; i<$li.length; i++)
if ($li[i].classList.contains('selected'))
// ^^^
$li[i].classList.remove('selected');
// ^^^
However, two points:
You don't need to test for contains() before calling remove() unless you need the information explicitly. Trying to remove a class that doesn't exist just does nothing.
You might not need to iterate the whole $li collection on every click. Since there is only one <li> with the .selected class at a time, you might simply store a reference to the currently-selected element, or use
var cur = swatch.querySelector("li.selected");
if (cur) cur.classList.remove('selected');
(which could work with an id as well).
|
[Treatment of bladder neoplasm: vesical instillation of BCG vaccine in microdoses].
We administered BCG at microdoses (1 mg) to 34 patients after surgical operation for bladder cancer, from 1981 to 1989. A 9% recurrency rate was observed during a 42 month follow up period. This is not significantly different from that observed with 120 mg doses, which are associated to known complications. |
Helderberg Escarpment
The Helderberg Escarpment, also known as the Helderberg Mountains, is an escarpment and mountain range in eastern New York, United States, roughly west of the city of Albany. The escarpment rises steeply from the Hudson Valley below, with an elevation difference of approximately 700 feet (from 400 to 1,100 feet) over a horizontal distance of approximately 2,000 feet. Much of the escarpment is within John Boyd Thacher State Park, and has views of the Hudson Valley and the Albany area.
Geology
The escarpment is geologically related to three other escarpments, the Niagara Escarpment,
the Black River Escarpment, and the Onondaga Escarpment.
The rocks exposed in the escarpment date back to the Middle Ordovician to Early Devonian.
In 1934 the Schenectady Gazette described how the Tory Cave, one of the limestone caves to be found in the escarpment, routinely had stalagmites of ice in the springtime.
Transmission towers
Most of the Capital District's television stations installed their transmission towers at the escarpment to take advantage of its high ground. In 2003 a tower was built on the highest point of the escarpment, for transmitting digital television signals.
History
Dutch settlers first homesteaded the plateau above the escarpment in the 17th century. Helderberg is a Dutch name meaning "clear mountain".
The Open Space Institute and the Mohawk Hudson Land Conservancy are working to keep escarpment lands from being developed for housing or industrial uses.
Farmers farming land near the escarpment can apply to sell their development rights, to help make sure that land is not developed. In 2003 the Ten Eyck family, owners of the Indian Ladder Farm just below the escarpment, sold the development rights to their farm for $848,000. Two real estate assessment were done, one on the value of the property as a working farm, the other on its value as a potential site for urban development. The Ten Eycks were paid the difference in return for agreeing to keep the property as a working farm. They were the first property owners to sell their development rights in Albany County.
References
Category:Landforms of New York (state)
Category:Escarpments of the United States
Category:Landforms of Albany County, New York
Category:Mountains of Albany County, New York
Category:Mountains of New York (state) |
A nonsurgical approach to low back pain.
Low back pain, a leading cause of disability in the United States, has a significant economic impact not only on lost productivity but also on healthcare expenditures. Approximately a fifth of patients will see multiple physicians in their quest for relief of low back pain. Primary care physicians therefore play a crucial role in the initial approach to these patients. A thorough history and physical examination directed toward the neurologic, orthopedic, and osteopathic evaluation are essential. This article reviews the diagnosis and assessment of pain levels and a triad system of therapy involving cortical, spinal, and peripheral levels. Options include antidepressants, neuroleptics, neurostimulants, and osteopathic manipulative treatment (OMT) (cortical level); opiates, tramadol hydrochloride, and transcutaneous electrical nerve stimulators (spinal level); and nonsteroidal anti-inflammatory drugs, epidural injections, spinal blocks, antispasmodics, physical therapy, muscle relaxants, exercise, and OMT (peripheral level), By choosing a modality directed at each level, the clinician may provide the patient with a pain management program that will maximize the chosen mode of therapy and restore function and mobility. |
Association between pediatric asthma care quality and morbidity and English language proficiency in Ohio.
Limited English proficiency can be a barrier to asthma care and is associated with poor outcomes. This study examines whether pediatric patients in Ohio with limited English proficiency experience lower asthma care quality or higher morbidity. We used electronic health records for asthma patients aged 2-17 years from a regional, urban, children's hospital in Ohio during 2011-2015. Community-level demographics were included from U.S. Census data. By using chi-square and t-tests, patients with limited English proficiency and bilingual English-speaking patients were compared with English-only patients. Five asthma outcomes-two quality and three morbidity measures-were modeled using generalized estimating equations. The study included 15 352 (84%) English-only patients, 1744 (10%) patients with limited English proficiency, and 1147 (6%) bilingual patients. Pulmonary function testing (quality measure) and multiple exacerbation visits (morbidity measure) did not differ by language group. Compared with English-only patients, bilingual patients had higher odds of ever having an exacerbation visit (morbidity measure) (adjusted odds ratio [aOR], 1.4; 95% confidence interval [CI], 1.2-1.6) but lower odds of admission to intensive care (morbidity measure) (aOR, 0.3; 95% CI, 0.2-0.7), while patients with limited English proficiency did not differ on either factor. Recommended follow-up after exacerbation (quality measure) was higher for limited English proficiency (aOR, 1.8; 95% CI, 1.4-2.3) and bilingual (aOR, 1.6; 95% CI, 1.3-2.1), compared with English-only patients. In this urban, pediatric population with reliable interpreter services, limited English proficiency was not associated with worse asthma care quality or morbidity. |
In general, customers using an online order processing system may order products using a local computer (e.g., a client) over a connection to a vendor, such as by dialing in over a modem to a computer network, such as the Internet, to the vendor's computer (e.g., server). Typically, the customer can enter in ordering information into a user interface provided by the vendor's order processing software over the connection which is displayed on a visual display of the customer's computer. For example, the customer can begin by entering in the customer's name and address if the customer is interested in a particular product, and the customer can enter in the name and/or model number of the product that the customer is considering ordering. The customer can then receive product information including pricing information, configuration information, and so on.
After receiving this product information over the network connection, the customer can decide whether to place the order or to hold off submitting the order until a later time. If placing the order, the customer can indicate that the customer wishes to submit the order by further manipulating the computer display provided by the vendor's computer. The vendor's order processing software may require the customer to submit additional information, such as a purchase order number and shipping address. After entering this information, the order processing software processes this information and accepts (or rejects) the order. If the order is accepted, the vendor's computer indicates the acceptance and typically provides the customer with verification information, such as a confirmation number or order number, that the customer writes down on a piece of paper or prints out on a printer connected to the customers' local client computer.
If the customer is not sure of the product to be ordered, the customer can request information from the vendor's order processing software, which is then displayed on the customer's client computer as one or more screens of information provided over the network connection by the order processing software. The customer can then read through the displayed screens, or print them out to read the hard copies of the information for comparison with the customer's requirements and needs. If the customer is a business (e.g., wholesaler, distributor, value added reseller or VAR, original equipment manufacturer or OEM, or other business), then the customer can check or compare its own inventory, requests from its customers (e.g., its retail customers) and other information against the information provided by the vendor's computer to determine what products and configurations of those products to order from the vendor. In addition, the customer can use the ordering information (from a display screen or printout) and then enter (e.g., type in at a keyboard or copy and paste using a mouse) this information into an ordering application or other application (e.g., customer's inventory application) that the customer maintains at its own local computer.
In another conventional approach, a customer can log onto a vendor's web site over the Internet, and view information about products for sale at the web site provided by the vendor's order processing software from the vendor's web server. The customer can select products from displays on the web site for an order and can then submit the order through the web site. The web site then displays a confirmation number to the customer, who can print it out if desired. |
The Miami Art Museum and Miami Art Central announced last week that they are forming a partnership in presenting exhibitions of original art works to the public. The move comes as plans by the Miami Art Museum move ahead for creation of an expanded museum. In six months, the two organizations plan to evaluate a possible merger. Whatever the outcome, the development means added impetus to the campaign to build a new museum in downtown Miami and heralds expanded relationships between public and private art institutions here.
Playing a key role in the partnership is Ella Fontanals-Cisneros, who founded Miami Art Central with the objective, she says, of stimulating an active dialogue with the community through exhibitions and education programs reflecting the interests of the local community.
The facility of Cuba-born Mrs. Cisneros is in a 1940s building in South Miami formerly occupied by Southern Bell Co., renovated under the direction of Italian architect Alessandro Fiorentino. It features 20,000 square feet of exhibition space on two floors where five major exhibitions per year and special events are staged.
Mrs. Cisneros was interviewed by Miami Today international editor Michael Hayes before the partnership announcement as she prepared special events at Miami Art Central in conjunction with the Art Basel Miami Beach art fair earlier this month. This is an excerpt from the weekly profile article published in Miami Today. To read the entire article in full, order this issue or subscribe to the print edition of Miami Today. |
Atomic Scala - blearyeyed
http://www.atomicscala.com/book
======
thebluesky
Glad to see Bruce Eckel involved. It's interesting to see just how many Scala
books have been cranked out in the last 6-12 months or are currently in
progress.
------
Toshio
<p>You can download the first 25% of the book <strong>here</strong>.</p>
Ummm ... where?
~~~
thebluesky
Seems he forgot the link. Another excellent book for learning Scala is Scala
for the Impatient. The first 9 chapters are free:
<http://horstmann.com/scala/>
~~~
michaels0620
The link is now working.
|
Prep for Changing Brake Pad Material
Should I fully sand my rotors if Im changing pad material?
I understand the basics of disc brakes in that a little bit of the pad material imbeds itsself in the rotors as part of the normal process of braking. This would lead me to believe sanding is necessary. The problem is of course that Im a little lazy.
If it matters, I would be coming off EBC Red pads, which they say are a type of organic material, and moving back to the stock Shimano sintered pads.
I originally left the Shimano pads as they were howlingly loud and had ok success with the EBC's. They are starting to wear fast however, and I now have at least 4 brand new sets of the Shimano's laying around, so I figure I'll try them again rather than spending more money.
Frankly I don't think that's necessary. I would suggest simply changing them out for new pads of whatever compound and then breaking them in. Whenever you change brake pads, independent of compound, you must break them in again.
For God's Sake!
Do NOT sand your rotors. Clean them with isopropyl alcohol, wipe dry with a nice clean rag and keep your greasy, KFC-eatin' fingers offa them. Change out the pads, making sure to center them correctly and then go ride your bike.
Well, I know I would need to break in the new pads, but doing that on top of the older material and mixing the 2 is what I was questioning.
The actuall process of breaking in pads is where through application of the brakes the pad material imbeds in the rotor surface gradually getting you up to full braking performance.
What I dont know is: will the new pad material just push out the old with no problem? Or will they mix and decrease braking performance?
It would be highly unusual for the use of one pad material to interfere with the efficacy of another material on a standard metal rotor in such a way as to noticeably affect braking performance, particularly if the rotor were thoroughly cleaned beforehand. That's my opinion. There may be some kind of materials scientist out there who may know about something going on in the meso-scale that I don't who may disagree with what I just said, but I don't think so.
As far as I'm concerned there's no need to do anything to the rotor when switching between different types of pads. I have a set of older Shimano XTs where I switch to the stock metallic pads when riding up at my friends cottage and use organic ones when riding in the city. I just drop the pads in and they work just fine, no need to clean the rotors or pads. I've switched back & forth many times over the years and I've never had any problems.
It would be highly unusual for the use of one pad material to interfere with the efficacy of another material on a standard metal rotor in such a way as to noticeably affect braking performance, particularly if the rotor were thoroughly cleaned beforehand. That's my opinion. There may be some kind of materials scientist out there who may know about something going on in the meso-scale that I don't who may disagree with what I just said, but I don't think so.
All cleaning them with alcohol will do is remove oils, dirt, etc.
IF the previous pad material should in fact be removed to optimize performance, alcohol isn't going to do it.
IF the previous pad material should in fact be removed to optimize performance, alcohol isn't going to do it.
The rotor has micropores in it that may have captured some pad material, maybe several micrograms at most. If you are being told by a manufacturer or dealer someplace that such an infinitesimally small amount of previous material will somehow interfere with the performance of your new brake pads (which it won't), then you probably need to find a new brand of rotor, brake and pad. The bottom line is this: there is no credible reason to believe that removal of previous pad material is necessary unless you have done something highly unusual with your brakes or are using them for some highly unusual application or there is some highly unusual condition that you are not mentioning in this forum. |
Cadmium phytoremediation potential of turnip compared with three common high Cd-accumulating plants.
Phytoextraction is a phytoremediation technique used for remediating polluted soils and it greatly relies on the plants' capacities to accumulate contaminants. Turnip is a high cadmium (Cd)-accumulating plant. We compared the Cd tolerance, growth, and Cd accumulation characteristics of two turnip landraces with three additional commonly known high Cd-accumulating species to systematically estimate its Cd phytoremediation potential. Results showed that the turnips could tolerate relatively lower Cd concentrations than other plants. Growth characteristics analyses indicated that the turnips initially grew rapidly and then gradually slowed down, and their photosynthetic parameters indicated that biomass accumulation was easily affected by light. However, the Cd uptake and translocation capacities of the two turnip landraces were higher than those of Phytolacca americana Linn. and Bidens pilosa Linn. but close to that of Brassica napus Linn.. Ultimately, large amounts of Cd accumulated in turnips during early growth and slightly increased as the fleshy roots increased in size. Based on these findings, the present turnip landraces have potential for soil remediation, but additional research is needed before these landraces can be practically used. Moreover, turnips are good candidates for studying the molecular mechanism of high Cd accumulation in plants. |
---
abstract: 'We continue our study of Cartan schemes and their Weyl groupoids. The results in this paper provide an algorithm to determine connected simply connected Cartan schemes of rank three, where the real roots form a finite irreducible root system. The algorithm terminates: Up to equivalence there are exactly 55 such Cartan schemes, and the number of corresponding real roots varies between $6$ and $37$. We identify those Weyl groupoids which appear in the classification of Nichols algebras of diagonal type.'
address:
- 'Michael Cuntz, Fachbereich Mathematik, Universität Kaiserslautern, Postfach 3049, D-67653 Kaiserslautern, Germany'
- 'István Heckenberger, Philipps-Universität Marburg, Fachbereich Mathematik und Informatik, Hans-Meerwein-Straße, D-35032 Marburg, Germany'
author:
- 'M. Cuntz'
- 'I. Heckenberger'
bibliography:
- 'quantum.bib'
title: Finite Weyl groupoids of rank three
---
Introduction
============
Root systems associated with Cartan matrices are widely studied structures in many areas of mathematics, see [@b-BourLie4-6] for the fundaments. The origins of the theory of root systems go back at least to the study of Lie groups by Lie, Killing and Cartan. The symmetry of the root system is commonly known as its Weyl group. Root systems associated with a family of Cartan matrices appeared first in connection with Lie superalgebras [@a-Kac77 Prop.2.5.6] and with Nichols algebras [@a-Heck06a], [@a-Heck08a]. The corresponding symmetry is not a group but a groupoid, and is called the Weyl groupoid of the root system.
Weyl groupoids of root systems properly generalize Weyl groups. The nice properties of this more general structure have been the main motivation to develop an axiomatic approach to the theory, see [@a-HeckYam08], [@a-CH09a]. In particular, Weyl groupoids are generated by reflections and Coxeter relations, and they satisfy a Matsumoto type theorem [@a-HeckYam08]. To see more clearly the extent of generality it would be desirable to have a classification of finite Weyl groupoids.[^1] However, already the appearance of a large family of examples of Lie superalgebras and Nichols algebras of diagonal type indicated that a classification of finite Weyl groupoids is probably much more complicated than the classification of finite Weyl groups. Additionally, many of the usual classification tools are not available in this context because of the lack of the adjoint action and a positive definite bilinear form.
In previous work, see [@a-CH09b] and [@p-CH09a], we have been able to determine all finite Weyl groupoids of rank two. The result of this classification is surprisingly nice: We found a close relationship to the theory of continued fractions and to cluster algebras of type $A$. The structure of finite rank two Weyl groupoids and the associated root systems has a natural characterization in terms of triangulations of convex polygons by non-intersecting diagonals. In particular, there are infinitely many such groupoids.
At first view there is no reason to assume that the situation for finite Weyl groupoids of rank three would be much different from the rank two case. In this paper we give some theoretical indications which strengthen the opposite point of view. For example in Theorem \[cartan\_6\] we show that the entries of the Cartan matrices in a finite Weyl groupoid cannot be smaller than $-7$. Recall that for Weyl groupoids there is no lower bound for the possible entries of generalized Cartan matrices. Our main achievement in this paper is to provide an algorithm to classify finite Weyl groupoids of rank three. Our algorithm terminates within a short time, and produces a finite list of examples. In the appendix we list the root systems characterizing the Weyl groupoids of the classification: There are $55$ of them which correspond to pairwise non-isomorphic Weyl groupoids. The number of positive roots in these root systems varies between $6$ and $37$. Among our root systems are the usual root systems of type $A_3$, $B_3$, and $C_3$, but for most of the other examples we don’t have yet an explanation.
It is remarkable that the number $37$ has a particular meaning for simplicial arrangements in the real projective plane. An arrangement is the complex generated by a family of straight lines not forming a pencil. The vertices of the complex are the intersection points of the lines, the edges are the segments of the lines between two vertices, and the faces are the connected components of the complement of the set of lines generating the arrangement. An arrangement is called simplicial, if all faces are triangles. Simplicial arrangements have been introduced in [@a-Melchi41]. The classification of simplicial arrangements in the real projective plane is an open problem. The largest known exceptional example is generated by $37$ lines. Grünbaum conjectures that the list given in [@a-Gruenb09] is complete. In our appendix we provide some data of our root systems which can be used to compare Grünbaum’s list with Weyl groupoids. There is an astonishing analogy between the two lists, but more work has to be done to be able to explain the precise relationship. This would be desirable in particular since our classification of finite Weyl groupoids of rank three does not give any evidence for the range of solutions besides the explicit computer calculation.
In order to ensure the termination of our algorithm, besides Theorem \[cartan\_6\] we use a weak convexity property of certain affine hyperplanes, see Theorem \[convex\_diff2\]: We can show that any positive root in an affine hyperplane “next to the origin” is either simple or can can be written as the sum of a simple root and another positive root. Our algorithm finally becomes practicable by the use of Proposition \[pr:suminR\], which can be interpreted as another weak convexity property for affine hyperplanes. It is hard to say which of these theorems are the most valuable because avoiding any of them makes the algorithm impracticable (unless one has some replacement).
The paper is organized as follows. We start with two sections proving the necessary theorems to formulate the algorithm: The results which do not require that the rank is three are in Section \[gen\_res\], the obstructions for rank three in Section \[rk3\_obst\]. We then describe the algorithm in the next section. Finally we summarize the resulting data and make some observations in the last section.
**Acknowledgement.** We would like to thank B. M[ü]{}hlherr for pointing out to us the importance of the number $37$ for simplicial arrangements in the real projective plane.
Cartan schemes and Weyl groupoids {#gen_res}
=================================
We mainly follow the notation in [@a-CH09a; @a-CH09b]. The fundaments of the general theory have been developed in [@a-HeckYam08] using a somewhat different terminology. Let us start by recalling the main definitions.
Let $I$ be a non-empty finite set and $\{{\alpha }_i\,|\,i\in I\}$ the standard basis of ${\mathbb{Z}}^I$. By [@b-Kac90 §1.1] a generalized Cartan matrix ${C}=({c}_{ij})_{i,j\in I}$ is a matrix in ${\mathbb{Z}}^{I\times I}$ such that
1. ${c}_{ii}=2$ and ${c}_{jk}\le 0$ for all $i,j,k\in I$ with $j\not=k$,
2. if $i,j\in I$ and ${c}_{ij}=0$, then ${c}_{ji}=0$.
Let $A$ be a non-empty set, ${\rho }_i : A \to A$ a map for all $i\in I$, and ${C}^a=({c}^a_{jk})_{j,k \in I}$ a generalized Cartan matrix in ${\mathbb{Z}}^{I \times I}$ for all $a\in A$. The quadruple $${\mathcal{C}}= {\mathcal{C}}(I,A,({\rho }_i)_{i \in I}, ({C}^a)_{a \in A})$$ is called a *Cartan scheme* if
1. ${\rho }_i^2 = \id$ for all $i \in I$,
2. ${c}^a_{ij} = {c}^{{\rho }_i(a)}_{ij}$ for all $a\in A$ and $i,j\in I$.
Let ${\mathcal{C}}= {\mathcal{C}}(I,A,({\rho }_i)_{i \in I}, ({C}^a)_{a \in A})$ be a Cartan scheme. For all $i \in I$ and $a \in A$ define ${\sigma }_i^a \in
\operatorname{Aut}({\mathbb{Z}}^I)$ by $$\begin{aligned}
{\sigma }_i^a ({\alpha }_j) = {\alpha }_j - {c}_{ij}^a {\alpha }_i \qquad
\text{for all $j \in I$.}
\label{eq:sia}
\end{aligned}$$ The *Weyl groupoid of* ${\mathcal{C}}$ is the category ${\mathcal{W}}({\mathcal{C}})$ such that ${\mathrm{Ob}}({\mathcal{W}}({\mathcal{C}}))=A$ and the morphisms are compositions of maps ${\sigma }_i^a$ with $i\in I$ and $a\in A$, where ${\sigma }_i^a$ is considered as an element in $\operatorname{Hom}(a,{\rho }_i(a))$. The category ${\mathcal{W}}({\mathcal{C}})$ is a groupoid in the sense that all morphisms are isomorphisms. The set of morphisms of ${\mathcal{W}}({\mathcal{C}})$ is denoted by $\operatorname{Hom}({\mathcal{W}}({\mathcal{C}}))$, and we use the notation $$\Homsfrom{a}=\mathop{\cup }_{b\in A}\operatorname{Hom}(a,b) \quad
\text{(disjoint union)}.$$ For notational convenience we will often neglect upper indices referring to elements of $A$ if they are uniquely determined by the context. For example, the morphism ${\sigma }_{i_1}^{{\rho }_{i_2}\cdots {\rho }_{i_k}(a)}
\cdots \s_{i_{k-1}}^{{\rho }_{i_k(a)}}{\sigma }_{i_k}^a\in \operatorname{Hom}(a,b)$, where $k\in {\mathbb{N}}$, $i_1,\dots,i_k\in I$, and $b={\rho }_{i_1}\cdots {\rho }_{i_k}(a)$, will be denoted by ${\sigma }_{i_1}\cdots {\sigma }_{i_k}^a$ or by ${\mathrm{id}}_b{\sigma }_{i_1}\cdots \s_{i_k}$. The cardinality of $I$ is termed the *rank of* ${\mathcal{W}}({\mathcal{C}})$. A Cartan scheme is called *connected* if its Weyl groupoid is connected, that is, if for all $a,b\in A$ there exists $w\in \operatorname{Hom}(a,b)$. The Cartan scheme is called *simply connected*, if $\operatorname{Hom}(a,a)=\{{\mathrm{id}}_a\}$ for all $a\in A$.
Let ${\mathcal{C}}$ be a Cartan scheme. For all $a\in A$ let $${(R\re)^{a}}=\{ {\mathrm{id}}_a {\sigma }_{i_1}\cdots \s_{i_k}({\alpha }_j)\,|\,
k\in {\mathbb{N}}_0,\,i_1,\dots,i_k,j\in I\}\subset {\mathbb{Z}}^I.$$ The elements of the set ${(R\re)^{a}}$ are called *real roots* (at $a$). The pair $({\mathcal{C}},({(R\re)^{a}})_{a\in A})$ is denoted by ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$. A real root ${\alpha }\in {(R\re)^{a}}$, where $a\in A$, is called positive (resp. negative) if ${\alpha }\in {\mathbb{N}}_0^I$ (resp. ${\alpha }\in -{\mathbb{N}}_0^I$). In contrast to real roots associated to a single generalized Cartan matrix, ${(R\re)^{a}}$ may contain elements which are neither positive nor negative. A good general theory, which is relevant for example for the study of Nichols algebras, can be obtained if ${(R\re)^{a}}$ satisfies additional properties.
Let ${\mathcal{C}}={\mathcal{C}}(I,A,({\rho }_i)_{i\in I},({C}^a)_{a\in A})$ be a Cartan scheme. For all $a\in A$ let $R^a\subset {\mathbb{Z}}^I$, and define $m_{i,j}^a= |R^a \cap (\ndN_0 {\alpha }_i + \ndN_0 {\alpha }_j)|$ for all $i,j\in
I$ and $a\in A$. We say that $${\mathcal{R}}= {\mathcal{R}}({\mathcal{C}}, (R^a)_{a\in A})$$ is a *root system of type* ${\mathcal{C}}$, if it satisfies the following axioms.
1. $R^a=R^a_+\cup - R^a_+$, where $R^a_+=R^a\cap \ndN_0^I$, for all $a\in A$.
2. $R^a\cap \ndZ{\alpha }_i=\{{\alpha }_i,-{\alpha }_i\}$ for all $i\in I$, $a\in A$.
3. ${\sigma }_i^a(R^a) = R^{{\rho }_i(a)}$ for all $i\in I$, $a\in A$.
4. If $i,j\in I$ and $a\in A$ such that $i\not=j$ and $m_{i,j}^a$ is finite, then $({\rho }_i{\rho }_j)^{m_{i,j}^a}(a)=a$.
The axioms (R2) and (R3) are always fulfilled for ${\mathcal{R}}{^\mathrm{re}}$. The root system ${\mathcal{R}}$ is called *finite* if for all $a\in A$ the set $R^a$ is finite. By [@a-CH09a Prop.2.12], if ${\mathcal{R}}$ is a finite root system of type ${\mathcal{C}}$, then ${\mathcal{R}}={\mathcal{R}}{^\mathrm{re}}$, and hence ${\mathcal{R}}{^\mathrm{re}}$ is a root system of type ${\mathcal{C}}$ in that case.
In [@a-CH09a Def.4.3] the concept of an *irreducible* root system of type ${\mathcal{C}}$ was defined. By [@a-CH09a Prop.4.6], if ${\mathcal{C}}$ is a Cartan scheme and ${\mathcal{R}}$ is a finite root system of type ${\mathcal{C}}$, then ${\mathcal{R}}$ is irreducible if and only if for all $a\in A$ the generalized Cartan matrix $C^a$ is indecomposable. If ${\mathcal{C}}$ is also connected, then it suffices to require that there exists $a\in A$ such that $C^a$ is indecomposable.
Let ${\mathcal{C}}={\mathcal{C}}(I,A,({\rho }_i)_{i\in I},({C}^a)_{a\in A})$ be a Cartan scheme. Let $\Gamma $ be a nondirected graph, such that the vertices of $\Gamma $ correspond to the elements of $A$. Assume that for all $i\in I$ and $a\in A$ with ${\rho }_i(a)\not=a$ there is precisely one edge between the vertices $a$ and ${\rho }_i(a)$ with label $i$, and all edges of $\Gamma $ are given in this way. The graph $\Gamma $ is called the *object change diagram* of ${\mathcal{C}}$.
![The object change diagram of a Cartan scheme of rank three (nr. 15 in Table 1)[]{data-label="fig:14posroots"}](wg14){width="6cm"}
In the rest of this section let $\cC={\mathcal{C}}(I,A,({\rho }_i)_{i\in I}, (C^a)_{a\in A})$ be a Cartan scheme such that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite root system. For brevity we will write $R^a$ instead of ${(R\re)^{a}}$ for all $a\in A$. We say that a subgroup $H\subset {\mathbb{Z}}^I$ is a *hyperplane* if ${\mathbb{Z}}^I/H\cong {\mathbb{Z}}$. Then ${\mathrm{rk}}\,H=\#I-1$ is the rank of $H$. Sometimes we will identify ${\mathbb{Z}}^I$ with its image under the canonical embedding ${\mathbb{Z}}^I\to {\mathbb{Q}}\otimes _{\mathbb{Z}}{\mathbb{Z}}^I\cong {\mathbb{Q}}^I$.
\[le:hyperplane\] Let $a\in A$ and let $H\subset {\mathbb{Z}}^I$ be a hyperplane. Suppose that $H$ contains ${\mathrm{rk}}\,H$ linearly independent elements of $R^a$. Let $\mathfrak{n}_H$ be a normal vector of $H$ in ${\mathbb{Q}}^I$ with respect to a scalar product $(\cdot ,\cdot )$ on ${\mathbb{Q}}^I$. If $(\mathfrak{n}_H,{\alpha })\ge 0$ for all ${\alpha }\in R^a_+$, then $H$ contains ${\mathrm{rk}}\,H$ simple roots, and all roots contained in $H$ are linear combinations of these simple roots.
The assumptions imply that any positive root in $H$ is a linear combination of simple roots contained in $H$. Since $R^a=R^a_+\cup -R^a_+$, this implies the claim.
Let $a\in A$ and let $H\subset {\mathbb{Z}}^I$ be a hyperplane. Suppose that $H$ contains ${\mathrm{rk}}\,H$ linearly independent elements of $R^a$. Then there exist $b\in A$ and $w\in \operatorname{Hom}(a,b)$ such that $w(H)$ contains ${\mathrm{rk}}\,H$ simple roots. \[le:hyperplane2\]
Let $(\cdot ,\cdot )$ be a scalar product on ${\mathbb{Q}}^I$. Choose a normal vector $\mathfrak{n}_H$ of $H$ in ${\mathbb{Q}}^I$ with respect to $(\cdot ,\cdot )$. Let $m=\# \{{\alpha }\in R^a_+\,|\,(\mathfrak{n}_H,{\alpha })<0\}$. Since ${\mathcal{R}}\re
({\mathcal{C}})$ is finite, $m$ is a nonnegative integer. We proceed by induction on $m$. If $m=0$, then $H$ contains ${\mathrm{rk}}\,H$ simple roots by Lemma \[le:hyperplane\]. Otherwise let $j\in I$ with $(\mathfrak{n}_H,{\alpha }_j)<0$. Let $a'={\rho }_j(a)$ and $H'=\s_j^a(H)$. Then $\s_j^a(\mathfrak{n}_H)$ is a normal vector of $H'$ with respect to the scalar product $(\cdot ,\cdot )'=
(\s_j^{{\rho }_j(a)}(\cdot ),\s_j^{{\rho }_j(a)}(\cdot ))$. Since $\s_j^a:R^a_+\setminus \{{\alpha }_j\}\to R^{a'}_+\setminus \{{\alpha }_j\}$ is a bijection and $\s_j^a({\alpha }_j)=-{\alpha }_j$, we conclude that $$\begin{aligned}
\# \{\beta \in R^{a'}_+\,|\,(\s^a_j(\mathfrak{n}_H),\beta )'<0\}=
\# \{{\alpha }\in R^a_+\,|\,(\mathfrak{n}_H,{\alpha })<0\}-1.
\end{aligned}$$ By induction hypothesis there exists $b\in A$ and $w'\in \operatorname{Hom}(a',b)$ such that $w'(H')$ contains ${\mathrm{rk}}\,H'={\mathrm{rk}}\,H$ simple roots. Then the claim of the lemma holds for $w=w'\s_j^a$.
The following “volume” functions will be useful for our analysis. Let $k\in {\mathbb{N}}$ with $k\le \#I$. By the Smith normal form there is a unique left ${\mathrm{GL}}({\mathbb{Z}}^I)$-invariant right ${\mathrm{GL}}({\mathbb{Z}}^k)$-invariant function ${\mathrm{Vol}}_k:({\mathbb{Z}}^I)^k\to {\mathbb{Z}}$ such that $$\begin{aligned}
{\mathrm{Vol}}_k(a_1{\alpha }_1,\dots,a_k{\alpha }_k)=|a_1\cdots a_k| \quad
\text{for all $a_1,\dots,a_k\in {\mathbb{Z}}$,}\end{aligned}$$ where $|\cdot |$ denotes absolute value. In particular, if $k=1$ and $\beta \in {\mathbb{Z}}^I\setminus \{0\}$, then $\Vol
_1(\beta )$ is the largest integer $v$ such that $\beta =v\beta '$ for some $\beta '\in {\mathbb{Z}}^I$. Further, if $k=\#I$ and $\beta _1,\dots,\beta _k\in {\mathbb{Z}}^I$, then ${\mathrm{Vol}}_k(\beta _1,\dots,\beta _k)$ is the absolute value of the determinant of the matrix with columns $\beta _1,\dots,\beta _k$.
Let $a\in A$, $k\in \{1,2,\dots,\#I\}$, and let $\beta _1,\dots,\beta _k\in R^a$ be linearly independent elements. We write $V^a(\beta _1,\dots,\beta _k)$ for the unique maximal subgroup $V\subseteq {\mathbb{Z}}^I$ of rank $k$ which contains $\beta _1,\dots,\beta _k$. Then ${\mathbb{Z}}^I/V^a(\beta _1,\dots,\beta _k)$ is free. In particular, $V^a(\beta _1,\dots,\beta _{\#I})={\mathbb{Z}}^I$ for all $a\in A$ and any linearly independent subset $\{\beta _1,\dots,\beta _{\#I}\}$ of $R^a$.
\[de:base\] Let $W\subseteq {\mathbb{Z}}^I$ be a cofree subgroup (that is, ${\mathbb{Z}}^I/W$ is free) of rank $k$. We say that $\{\beta _1,\dots,\beta _k\}$ is a *base for $W$ at $a$*, if $\beta _i\in W$ for all $i\in \{1,\dots,k\}$ and $W\cap R^a\subseteq \sum _{i=1}^k{\mathbb{N}}_0\beta _i\cup
-\sum _{i=1}^k{\mathbb{N}}_0\beta _i$.
Now we discuss the relationship of linearly independent roots in a root system. Recall that ${\mathcal{C}}$ is a Cartan scheme such that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite root system of type ${\mathcal{C}}$.
\[th:genposk\] Let $a\in A$, $k\in \{1,\dots,\#I\}$, and let $\beta _1,\dots,\beta _k\in R^a$ be linearly independent roots. Then there exist $b\in A$, $w\in \operatorname{Hom}(a,b)$, and a permutation $\tau $ of $I$ such that $$w(\beta _i)\in {\mathrm{span}}_{\mathbb{Z}}\{{\alpha }_{\tau (1)},
\ldots ,{\alpha }_{\tau (i)}\} \cap R^b_+$$ for all $i\in \{1,\dots,k\}$.
Let $r=\#I$. Since $R^a$ contains $r$ simple roots, any linearly independent subset of $R^a$ can be enlarged to a linearly independent subset of $r$ elements. Hence it suffices to prove the theorem for $k=r$. We proceed by induction on $r$. If $r=1$, then the claim holds.
Assume that $r>1$. Lemma \[le:hyperplane2\] with $H=V^a(\beta _1,\dots,\beta _{r-1})$ tells that there exist $d\in A$ and $v\in \operatorname{Hom}(a,d)$ such that $v(H)$ is spanned by simple roots. By multiplying $v$ from the left with the longest element of ${\mathcal{W}}({\mathcal{C}})$ in the case that $v(\beta _r)\in -{\mathbb{N}}_0^I$, we may even assume that $v(\beta _r)\in {\mathbb{N}}_0^I$. Now let $J$ be the subset of $I$ such that $\#J=r-1$ and ${\alpha }_i\in v(H)$ for all $i\in J$. Consider the restriction ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})|_{J}$ of ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ to the index set $J$, see [@a-CH09a Def. 4.1]. Since $v(\beta _i)\in H$ for all $i\in \{1,\dots,r-1\}$, induction hypothesis provides us with $b\in A$, $u\in \operatorname{Hom}(d,b)$, and a permutation $\tau '$ of $J$ such that $u$ is a product of simple reflections $\s_i$, where $i\in J$, and $$uv(\beta _n)\in
{\mathrm{span}}_{\mathbb{Z}}\{{\alpha }_{\tau '(j_1)}, \ldots ,{\alpha }_{\tau '(j_n)}\}
\cap R^b_+$$ for all $n\in \{1,2,\dots,r-1\}$, where $J=\{j_1,\dots,j_{r-1}\}$. Since $v(\beta _r)\notin v(H)$ and $v(\beta _r)\in {\mathbb{N}}_0^I$, the $i$-th entry of $v(\beta _r)$, where $i\in I\setminus J$, is positive. This entry does not change if we apply $u$. Therefore $uv(\beta _r)\in {\mathbb{N}}_0^I$, and hence the theorem holds with $w=uv\in \operatorname{Hom}(a,b)$ and with $\tau $ the unique permutation with $\tau (n)=\tau '(j_n)$ for all $n\in \{1,\dots,r-1\}$.
\[simple\_rkk\] Let $a\in A$, $k\in \{1,\dots,\#I\}$, and let $\beta _1,\dots,\beta _k\in R^a$ be linearly independent elements. Then $\{\beta _1,\dots,\beta _k\}$ is a base for $V^a(\beta _1,\dots,\beta _k)$ at $a$ if and only if there exist $b\in A$, $w\in \operatorname{Hom}(a,b)$, and a permutation $\tau $ of $I$ such that $w(\beta _i)={\alpha }_{\tau (i)}$ for all $i\in \{1,\dots,k\}$. In this case ${\mathrm{Vol}}_k(\beta _1,\dots,\beta _k)=1$.
The if part of the claim holds by definition of a base and by the axioms for root systems.
Let $b,w$ and $\tau $ be as in Theorem \[th:genposk\]. Let $i\in
\{1,\dots,k\}$. The elements $w(\beta _1),\dots,w(\beta _i)$ are linearly independent and are contained in $V^b({\alpha }_{\tau (1)}, \dots ,
{\alpha }_{\tau (i)})$. Thus ${\alpha }_{\tau (i)}$ is a rational linear combination of $w(\beta _1),\dots,w(\beta _i)$. Now by assumption, $\{w(\beta _1),\dots,w(\beta _k)\}$ is a base for $V^b(w(\beta _1),\dots,w(\beta _k))$ at $b$. Hence ${\alpha }_{\tau
(i)}$ is a linear combination of the positive roots $w(\beta _1),\dots,w(\beta _i)$ with nonnegative integer coefficients. This is possible only if $\{w(\beta _1),\dots,w(\beta _i)\}$ contains ${\alpha }_{\tau (i)}$. By induction on $i$ we obtain that ${\alpha }_{\tau (i)}=w(\beta _i)$.
In the special case $k=\#I$ the above corollary tells that the bases of $\ndZ
^I$ at an object $a\in A$ are precisely those subsets which can be obtained as the image, up to a permutation, of the standard basis of ${\mathbb{Z}}^I$ under the action of an element of ${\mathcal{W}}({\mathcal{C}})$.
In [@p-CH09a] the notion of an ${\mathcal{F}}$-sequence was given, and it was used to explain the structure of root systems of rank two. Consider on ${\mathbb{N}}_0^2$ the total ordering $\le _{\mathbb{Q}}$, where $(a_1,a_2)\le _{\mathbb{Q}}(b_1,b_2)$ if and only if $a_1 b_2\le a_2 b_1$. A finite sequence $(v_1,\dots ,v_n)$ of vectors in ${\mathbb{N}}_0^2$ is an ${\mathcal{F}}$-sequence if and only if $v_1<_{\mathbb{Q}}v_2
<_{\mathbb{Q}}\cdots <_{\mathbb{Q}}v_n$ and one of the following holds.
- $n=2$, $v_1=(0,1)$, and $v_2=(1,0)$.
- $n>2$ and there exists $i\in \{2,3,\dots,n-1\}$ such that $v_i=v_{i-1}+v_{i+1}$ and $(v_1,\dots,v_{i-1}.v_{i+1},\dots,v_n)$ is an ${\mathcal{F}}$-sequence.
In particular, any ${\mathcal{F}}$-sequence of length $\ge 3$ contains $(1,1)$.
\[pr:R=Fseq\] [@p-CH09a Prop.3.7] Let ${\mathcal{C}}$ be a Cartan scheme of rank two. Assume that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite root system. Then for any $a\in A$ the set $R^a_+$ ordered by $\le _\QQ$ is an ${\mathcal{F}}$-sequence.
\[pr:sumoftwo\] [@p-CH09a Cor. 3.8] Let ${\mathcal{C}}$ be a Cartan scheme of rank two. Assume that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite root system. Let $a\in A$ and let $\beta \in R^a_+$. Then either $\beta $ is simple or it is the sum of two positive roots.
\[co:r2conv\] Let $a\in A$, $n\in {\mathbb{N}}$, and let ${\alpha },\beta \in R^a$ such that $\beta -n{\alpha }\in R^a$. Assume that $\{{\alpha },\beta -n{\alpha }\}$ is a base for $V^a({\alpha },\beta )$ at $a$. Then $\beta -k{\alpha }\in R^a$ for all $k\in \{1,2,\dots ,n\}$.
By Corollary \[simple\_rkk\] there exist $b\in A$, $w\in \operatorname{Hom}(a,b)$, and $i,j\in I$ such that $w({\alpha })={\alpha }_i$, $w(\beta -n{\alpha })={\alpha }_j$. Then $n{\alpha }_i+{\alpha }_j=w(\beta )\in R^b_+$. Hence $(n-k){\alpha }_i+{\alpha }_j\in R^b$ for all $k\in \{1,2,\dots,n\}$ by Proposition \[pr:sumoftwo\] and (R2). This yields the claim of the corollary.
\[co:cij\] Let $a\in A$, $k\in {\mathbb{Z}}$, and $i,j\in I$ such that $i\not=j$. Then ${\alpha }_j+k{\alpha }_i\in R^a$ if and only if $0\le k\le -c^a_{i j}$,
Axiom (R1) tells that ${\alpha }_j+k{\alpha }_i\notin R^a$ if $k<0$. Since $c^{{\rho }_i(a)}_{i j}=c^a_{i j}$ by (C2), Axiom (R3) gives that $\al
_j-c^a_{i j}{\alpha }_i=\sigma _i^{{\rho }_i(a)}({\alpha }_j)\in R^a$ and that ${\alpha }_j+k{\alpha }_i\notin R^a$ if $k>-c^a_{i j}$. Finally, if $0<k<-c^a_{i j}$ then ${\alpha }_j+k{\alpha }_i\in R^a$ by Corollary \[co:r2conv\] for ${\alpha }={\alpha }_i$, $\beta ={\alpha }_j-c^a_{i j}{\alpha }_i$, and $n=-c^a_{i j}$.
Proposition \[pr:sumoftwo\] implies another important fact.
\[root\_is\_sum\] Let ${\mathcal{C}}$ be a Cartan scheme. Assume that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite root system of type ${\mathcal{C}}$. Let $a\in A$ and ${\alpha }\in R^a_+$. Then either ${\alpha }$ is simple, or it is the sum of two positive roots.
Assume that ${\alpha }$ is not simple. Let $i\in I$, $b\in A$, and $w\in \operatorname{Hom}(b,a)$ such that ${\alpha }=w({\alpha }_i)$. Then $\ell(w)>0$. We may assume that for all $j\in I$, $b'\in A$, and $w'\in \operatorname{Hom}(b',a)$ with $w'(\alpha_j)={\alpha }$ we have $\ell(w')\ge\ell(w)$. Since $w(\alpha_i)\in {\mathbb{N}}_0^I$, we obtain that $\ell(w\s_i)>\ell(w)$ [@a-HeckYam08 Cor. 3]. Therefore, there is a $j\in I\setminus \{i\}$ with $\ell(w\s_j)<\ell(w)$. Let $w=w_1w_2$ such that $\ell(w)=\ell(w_1)+\ell(w_2)$, $\ell(w_1)$ minimal and $w_2=\ldots \s_i\s_j\s_i\s_j^b$. Assume that $w_2=\s_i\cdots \s_i\s_j^b$ — the case $w_2=\s_j\cdots \s_i \s_j^b$ can be treated similarly. The length of $w_1$ is minimal, thus $\ell(w_1\s_j)>\ell(w_1)$, and $\ell(w)=\ell(w_1)+\ell(w_2)$ yields that $\ell(w_1\s_i)>\ell(w_1)$. Using once more [@a-HeckYam08 Cor. 3] we conclude that $$\begin{aligned}
\label{eq:twopos}
w_1(\alpha_i)\in {\mathbb{N}}_0^I,\quad w_1(\alpha_j)\in {\mathbb{N}}_0^I.\end{aligned}$$ Let $\beta=w_2(\alpha_i)$. Then $\beta \in \NN_0 \alpha_i+\NN_0 \alpha_j$, since $\ell (w_2\s_i)>\ell (w_2)$. Moreover, $\beta $ is not simple. Indeed, $\alpha=w(\alpha_i)=w_1(\beta)$, so $\beta$ is not simple, since $\ell(w_1)<\ell(w)$ and $\ell(w)$ was chosen of minimal length. By Proposition \[pr:sumoftwo\] we conclude that $\beta$ is the sum of two positive roots $\beta_1$, $\beta_2\in {\mathbb{N}}_0{\alpha }_i+{\mathbb{N}}_0{\alpha }_j$. It remains to check that $w_1(\beta_1)$, $w_1(\beta_2)$ are positive. But this follows from .
Obstructions for Weyl groupoids of rank three {#rk3_obst}
=============================================
In this section we analyze the structure of finite Weyl groupoids of rank three. Let ${\mathcal{C}}$ be a Cartan scheme of rank three, and assume that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite irreducible root system of type ${\mathcal{C}}$. In this case a hyperplane in ${\mathbb{Z}}^I$ is the same as a cofree subgroup of rank two, which will be called a *plane* in the sequel. For simplicity we will take $I=\{1,2,3\}$, and we write $R^a$ for the set of positive real roots at $a\in A$.
Recall the definition of the functions ${\mathrm{Vol}}_k$, where $k\in \{1,2,3\}$, from the previous section. As noted, for three elements ${\alpha },\beta,\gamma\in\ZZ^3$ we have ${\mathrm{Vol}}_3(\alpha,\beta,\gamma )=1$ if and only if $\{\alpha,\beta,\gamma\}$ is a basis of ${\mathbb{Z}}^3$. Also, we will heavily use the notion of a base, see Definition \[de:base\].
\[rootmultiple\] Let $a\in A$ and $\alpha,\beta \in R^a$. Assume that ${\alpha }\not=\pm \beta $ and that $\{{\alpha },\beta\}$ is not a base for $V^a({\alpha },\beta )$ at $a$. Then there exist $k,l\in {\mathbb{N}}$ and $\delta \in R^a$ such that $\beta -k{\alpha }=l\delta $ and $\{{\alpha },\delta \}$ is a base for $V^a({\alpha },\beta )$ at $a$.
The claim without the relation $k>0$ is a special case of Theorem \[th:genposk\]. The relation $\beta \not=\delta $ follows from the assumption that $\{{\alpha },\beta \}$ is not a base for $V^a({\alpha },\beta )$ at $a$.
Let $a\in A$ and $\alpha,\beta \in R^a$ such that ${\alpha }\not=\pm \beta $. Then $\{{\alpha },\beta \}$ is a base for $V^a(\al, \beta )$ if and only if ${\mathrm{Vol}}_2({\alpha },\beta )=1$ and ${\alpha }-\beta \notin R^a$. \[le:base2\]
Assume first that $\{{\alpha },\beta \}$ is a base for $V^a({\alpha },\beta )$ at $a$. By Corollary \[simple\_rkk\] we may assume that ${\alpha }$ and $\beta $ are simple roots. Therefore ${\mathrm{Vol}}_2({\alpha },\beta )=1$ and ${\alpha }-\beta \notin R^a$.
Conversely, assume that ${\mathrm{Vol}}_2({\alpha },\beta )=1$, ${\alpha }-\beta \notin R^a$, and that $\{{\alpha },\beta \}$ is not a base for $V^a({\alpha },\beta )$ at $a$. Let $k,l,\delta $ as in Lemma \[rootmultiple\]. Then $$1={\mathrm{Vol}}_2({\alpha },\beta )={\mathrm{Vol}}_2({\alpha },\beta -k{\alpha })=l{\mathrm{Vol}}_2({\alpha },\delta ).$$ Hence $l=1$, and $\{{\alpha },\delta \}=\{{\alpha },\beta -k{\alpha }\}$ is a base for $V^a({\alpha },\beta )$ at $a$. Then $\beta -{\alpha }\in R^a$ by Corollary \[co:r2conv\] and since $k>0$. This gives the desired contradiction to the assumption ${\alpha }-\beta \notin R^a$.
Recall that a semigroup ordering $<$ on a commutative semigroup $(S,+)$ is a total ordering such that for all $s,t,u\in S$ with $s<t$ the relations $s+u<t+u$ hold. For example, the lexicographic ordering on ${\mathbb{Z}}^I$ induced by any total ordering on $I$ is a semigroup ordering.
\[posrootssemigroup\] Let $a\in A$, and let $V\subset {\mathbb{Z}}^I$ be a plane containing at least two positive roots of $R^a$. Let $<$ be a semigroup ordering on ${\mathbb{Z}}^I$ such that $0<\gamma $ for all $\gamma \in R^a_+$, and let ${\alpha },\beta $ denote the two smallest elements in $V\cap R^a_+$ with respect to $<$. Then $\{{\alpha },\beta \}$ is a base for $V$ at $a$.
Let ${\alpha }$ be the smallest element of $V\cap R^a_+$ with respect to $<$, and let $\beta $ be the smallest element of $V\cap (R^a_+\setminus \{{\alpha }\})$. Then $V=V^a(\al, \beta )$ by (R2). By Lemma \[rootmultiple\] there exists $\delta \in V\cap
R^a$ such that $\{{\alpha },\delta \}$ is a base for $V$ at $a$. First suppose that $\delta <0$. Let $m\in {\mathbb{N}}_0$ be the smallest integer with $\delta +(m+1){\alpha }\notin R^a$. Then $\delta +n{\alpha }<0$ for all $n\in {\mathbb{N}}_0$ with $n\le m$. Indeed, this holds for $n=0$ by assumption. By induction on $n$ we obtain from $\delta +n{\alpha }<0$ and the choice of ${\alpha }$ that $\delta +n{\alpha }<-{\alpha }$, since $\delta $ and ${\alpha }$ are not collinear. Hence $\delta +(n+1){\alpha }<0$. We conclude that $-(\delta +m{\alpha })>0$. Moreover, $\{{\alpha },-(\delta +m{\alpha })\}$ is a base for $V$ at $a$ by Lemma \[le:base2\] and the choice of $m$. Therefore, by replacing $\{{\alpha },\delta \}$ by $\{{\alpha },-(\delta +m{\alpha })\}$, we may assume that $\delta >0$. Since $\beta >0$, we conclude that $\beta =k{\alpha }+l\delta $ for some $k,l\in
{\mathbb{N}}_0$. Since $\beta $ is not a multiple of ${\alpha }$, this implies that $\beta =\delta $ or $\beta >\delta $. Then the choice of $\beta $ and the positivity of $\delta $ yield that $\delta =\beta $, that is, $\{{\alpha },\beta \}$ is a base for $V$ at $a$.
\[le:badroots\] Let $k\in {\mathbb{N}}_{\ge 2}$, $a\in A$, ${\alpha }\in R^a_+$, and $\beta \in {\mathbb{Z}}^I$ such that ${\alpha }$ and $\beta $ are not collinear and ${\alpha }+k\beta \in R^a$. Assume that ${\mathrm{Vol}}_2({\alpha },\beta )=1$ and that $(-{\mathbb{N}}{\alpha }+{\mathbb{Z}}\beta )
\cap {\mathbb{N}}_0^I=\emptyset $. Then $\beta \in R^a$ and ${\alpha }+l\beta \in R^a$ for all $l\in \{1,2,\dots,k\}$.
We prove the claim indirectly. Assume that $\beta \notin R^a$. By Lemma \[posrootssemigroup\] there exists a base $\{\gamma _1,\gamma
_2\}$ for $V^a({\alpha },\beta )$ at $a$ such that $\gamma _1,\gamma _2\in R^a_+$. The assumptions of the lemma imply that there exist $m_1,l_1\in {\mathbb{N}}_0$ and $m_2,l_2\in {\mathbb{Z}}$ such that $\gamma _1=m_1{\alpha }+m_2\beta $, $\gamma _2=l_1{\alpha }+l_2\beta $. Since $\beta \notin R^a$, we obtain that $m_1\ge 1$ and $m_2\ge 1$. Therefore relations ${\alpha },{\alpha }+k\beta \in R^a_+$ imply that $\{{\alpha },{\alpha }+k\beta \}=\{\gamma _1,\gamma _2\}$. The latter is a contradiction to ${\mathrm{Vol}}_2(\gamma _1,\gamma _2)=1$ and ${\mathrm{Vol}}_2({\alpha },{\alpha }+k\beta )=k>1$. Thus $\beta \in R^a$. By Lemma \[rootmultiple\] we obtain that $\{\beta ,{\alpha }-m\beta \}$ is a base for $V^a({\alpha },\beta )$ at $a$ for some $m\in {\mathbb{N}}_0$. Then Corollary \[co:r2conv\] and the assumption that ${\alpha }+k\beta \in R^a$ imply the last claim of the lemma.
We say that a subset $S$ of ${\mathbb{Z}}^3$ is *convex*, if any rational convex linear combination of elements of $S$ is either in $S$ or not in ${\mathbb{Z}}^3$. We start with a simple example.
\[le:square\] Let $a\in A$. Assume that $c^a_{12}=0$.
\(1) Let $k_1,k_2\in {\mathbb{Z}}$. Then ${\alpha }_3+k_1{\alpha }_1+k_2{\alpha }_2\in R^a$ if and only if $0\le k_1\le -c^a_{13}$ and $0\le k_2\le -c^a_{23}$.
\(2) Let $\gamma \in ({\alpha }_3+{\mathbb{Z}}{\alpha }_1+{\mathbb{Z}}{\alpha }_2)\cap R^a$. Then $\gamma -{\alpha }_1\in R^a$ or $\gamma +{\alpha }_1\in R^a$. Similarly $\gamma -{\alpha }_2\in R^a$ or $\gamma +{\alpha }_2\in R^a$.
\(1) The assumption $c^a_{12}=0$ implies that $c^{{\rho }_1(a)}_{23}=c^a_{23}$, see [@a-CH09a Lemma4.5]. Applying ${\sigma }_1^{{\rho }_1(a)}$, ${\sigma }_2^{{\rho }_2(a)}$, and ${\sigma }_1{\sigma }_2^{{\rho }_2{\rho }_1(a)}$ to ${\alpha }_3$ we conclude that ${\alpha }_3-c^a_{13}{\alpha }_1$, ${\alpha }_3-c^a_{23}{\alpha }_2$, ${\alpha }_3-c^a_{13}\al
_1-c^a_{23}{\alpha }_2\in R^a_+$. Thus Lemma \[le:badroots\] implies that ${\alpha }_3+m_1{\alpha }_1+m_2{\alpha }_2\in R^a$ for all $m_1,m_2\in {\mathbb{Z}}$ with $0\le m_1\le -c^a_{13}$ and $0\le m_2\le -c^a_{23}$. Further, (R1) gives that ${\alpha }_3+k_1{\alpha }_1+k_2{\alpha }_2\notin R^a$ if $k_1<0$ or $k_2<0$. Applying again the simple reflections ${\sigma }_1$ and ${\sigma }_2$, a similar argument proves the remaining part of the claim. Observe that the proof does not use the fact that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is irreducible.
\(2) Since $c^a_{12}=0$, the irreducibility of ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ yields that $c^a_{13},c^a_{23}<0$ by [@a-CH09a Def.4.5, Prop.4.6]. Hence the claim follows from (1).
\[pr:suminR\] Let $a\in A$ and let $\gamma _1,\gamma _2,\gamma _3\in R^a$. Assume that ${\mathrm{Vol}}_3(\gamma _1,\gamma _2,\gamma _3)=1$ and that $\gamma _1-\gamma _2,\gamma _1-\gamma _3\notin R^a$. Then $\gamma _1+\gamma _2\in R^a$ or $\gamma _1+\gamma _3\in R^a$.
Since $\gamma _1-\gamma _2\notin R^a$ and ${\mathrm{Vol}}_3(\gamma _1,\gamma
_2,\gamma _3)=1$, Theorem \[th:genposk\] and Lemma \[le:base2\] imply that there exists $b\in A$, $w\in \operatorname{Hom}(a,b)$ and $i_1,i_2,i_3\in I$ such that $w(\gamma _1)={\alpha }_{i_1}$, $w(\gamma _2)={\alpha }_{i_2}$, and $w(\gamma _3)={\alpha }_{i_3}+k_1{\alpha }_{i_1}+k_2{\alpha }_{i_2}$ for some $k_1,k_2\in {\mathbb{N}}_0$. Assume that $\gamma _1+\gamma _2\notin R^a$. Then $c^b_{i_1i_2}=0$. Since $\gamma _3-\gamma _1\notin R^a$, Lemma \[le:square\](2) with $\gamma =w(\gamma _3)$ gives that $\gamma _3+\gamma _1\in R^a$. This proves the claim.
\[le:root\_diffs1\] Assume that $R^a\cap ({\mathbb{N}}_0{\alpha }_1+{\mathbb{N}}_0{\alpha }_2)$ contains at most $4$ positive roots.
\(1) The set $S_3:=({\alpha }_3+{\mathbb{Z}}{\alpha }_1+{\mathbb{Z}}{\alpha }_2)\cap R^a$ is convex.
\(2) Let $\gamma \in S_3$. Then $\gamma ={\alpha }_3$ or $\gamma -{\alpha }_1\in R^a$ or $\gamma -{\alpha }_2\in R^a$.
Consider the roots of the form $w^{-1}({\alpha }_3)\in R^a$, where $w\in \Homsfrom{a}$ is a product of reflections ${\sigma }_1^b$, ${\sigma }_2^b$ with $b\in A$. All of these roots belong to $S_3$. Using Lemma \[le:badroots\] the claims of the lemma can be checked case by case, similarly to the proof of Lemma \[le:square\].
The lemma can be proven by elementary calculations, since all nonsimple positive roots in $({\mathbb{Z}}{\alpha }_1+{\mathbb{Z}}{\alpha }_2)\cap R^a$ are of the form say ${\alpha }_1+k{\alpha }_2$, $k\in {\mathbb{N}}$. We will see in Theorem \[th:class\] that the classification of connected Cartan schemes of rank three admitting a finite irreducible root system has a finite set of solutions. Thus it is possible to check the claim of the lemma for any such Cartan scheme. Using computer calculations one obtains that the lemma holds without any restriction on the (finite) cardinality of $R^a\cap ({\mathbb{N}}_0{\alpha }_1+{\mathbb{N}}_0{\alpha }_2)$.
\[le:root\_diffs2\] Let ${\alpha },\beta ,\gamma \in R^a$ such that ${\mathrm{Vol}}_3({\alpha },\beta ,\gamma )=1$. Assume that ${\alpha }-\beta $, $\beta -\gamma $, ${\alpha }-\gamma \notin R^a$ and that $\{{\alpha },\beta ,\gamma \}$ is not a base for ${\mathbb{Z}}^I$ at $a$. Then the following hold.
\(1) There exist $w\in \Homsfrom{a}$ and $n_1,n_2\in {\mathbb{N}}$ such that $w({\alpha })$, $w(\beta )$, and $w(\gamma -n_1{\alpha }-n_2\beta )$ are simple roots.
\(2) None of the vectors ${\alpha }-k\beta $, ${\alpha }-k\gamma $, $\beta -k{\alpha }$, $\beta -k\gamma $, $\gamma -k{\alpha }$, $\gamma -k\beta $, where $k\in {\mathbb{N}}$, is contained in $R^a$.
\(3) ${\alpha }+\beta $, ${\alpha }+\gamma $, $\beta +\gamma \in R^a$.
\(4) One of the sets $\{{\alpha }+2\beta ,\beta +2\gamma ,\gamma +2{\alpha }\}$ and $\{2{\alpha }+\beta ,2\beta +\gamma ,2\gamma +{\alpha }\}$ is contained in $R^a$, the other one has trivial intersection with $R^a$.
\(5) None of the vectors $\gamma -{\alpha }-k\beta $, $\gamma -k{\alpha }-\beta $, $\beta -\gamma -k{\alpha }$, $\beta -k\gamma -{\alpha }$, ${\alpha }-\beta -k\gamma $, ${\alpha }-k\beta -\gamma $, where $k\in {\mathbb{N}}_0$, is contained in $R^a$.
\(6) Assume that ${\alpha }+2\beta \in R^a$. Let $k\in {\mathbb{N}}$ such that ${\alpha }+k\beta \in R^a$, ${\alpha }+(k+1)\beta \notin R^a$. Let ${\alpha }'={\alpha }+k\beta $, $\beta '=-\beta $, $\gamma '=\gamma +\beta $. Then ${\mathrm{Vol}}_3({\alpha }',\beta ',\gamma ')=1$, $\{{\alpha }',\beta ',\gamma '\}$ is not a base for ${\mathbb{Z}}^I$ at $a$, and none of ${\alpha }'-\beta '$, ${\alpha }'-\gamma '$, $\beta '-\gamma '$ is contained in $R^a$.
\(7) None of the vectors ${\alpha }+3\beta $, $\beta +3\gamma $, $\gamma +3{\alpha }$, $3{\alpha }+\beta $, $3\beta +\gamma $, $3\gamma +{\alpha }$ is contained in $R^a$. In particular, $k=2$ holds in (6).
\(1) By Theorem \[th:genposk\] there exist $m_1,m_2,n_1,n_2,n_3\in \ndN
_0$, $i_1,i_2,i_3\in I$, and $w\in \Homsfrom{a}$, such that $w({\alpha })={\alpha }_{i_1}$, $w(\beta )=m_1{\alpha }_{i_1}+m_2{\alpha }_{i_2}$, and $w(\gamma )=n_1{\alpha }_{i_1}+n_2{\alpha }_{i_2}+n_3{\alpha }_{i_3}$. Since $\det w\in
\{\pm 1\}$ and ${\mathrm{Vol}}_3({\alpha },\beta ,\gamma )=1$, this implies that $m_2=n_3=1$. Further, $\beta -{\alpha }\notin R^a$, and hence $w(\beta )={\alpha }_{i_2}$ by Corollary \[co:cij\]. Since $\{{\alpha },\beta ,\gamma \}$ is not a base for ${\mathbb{Z}}^I$ at $a$, we conclude that $w(\gamma )\not={\alpha }_{i_3}$. Then Corollary \[co:cij\] and the assumptions $\gamma -{\alpha }$, $\gamma -\beta
\notin R^a$ imply that $w(\gamma )\notin {\alpha }_{i_3}+{\mathbb{N}}_0{\alpha }_{i_1}$ and $w(\gamma )\notin {\alpha }_{i_3}+{\mathbb{N}}_0{\alpha }_{i_2}$. Thus the claim is proven.
\(2) By (1), $\{{\alpha },\beta \}$ is a base for $V^a({\alpha },\beta )$ at $a$. Thus ${\alpha }-k\beta \notin R^a$ for all $k\in {\mathbb{N}}$. The remaining claims follow by symmetry.
\(3) Suppose that ${\alpha }+\beta \notin R^a$. By (1) there exist $b\in A$, $w\in \operatorname{Hom}(a,b)$, $i_1,i_2,i_3\in I$ and $n_1,n_2\in {\mathbb{N}}$ such that $w({\alpha })={\alpha }_{i_1}$, $w(\beta )={\alpha }_{i_2}$, and $w(\gamma )={\alpha }_{i_3}+n_1{\alpha }_{i_1}+n_2{\alpha }_{i_2}\in R^b_+$. By Theorem \[root\_is\_sum\] there exist $n'_1,n'_2\in {\mathbb{N}}_0$ such that $n'_1\le n_1$, $n'_2\le n_2$, $n'_1+n'_2<n_1+n_2$, and $${\alpha }_{i_3}+n'_1{\alpha }_{i_1}+n'_2{\alpha }_{i_2}\in R^b_+,\quad
(n_1-n'_1){\alpha }_{i_1}+(n_2-n'_2){\alpha }_{i_2}\in R^b_+.$$ Since ${\alpha }+\beta \notin R^a$, Proposition \[pr:R=Fseq\] yields that $R^b_+\cap
{\mathrm{span}}_{\mathbb{Z}}\{{\alpha }_{i_1},{\alpha }_{i_2}\}=\{{\alpha }_{i_1},{\alpha }_{i_2}\}$. Thus $\gamma -{\alpha }\in R^a$ or $\gamma -\beta \in R^a$. This is a contradiction to the assumption of the lemma. Hence ${\alpha }+\beta \in R^a$. By symmetry we obtain that ${\alpha }+\gamma $, $\beta +\gamma \in R^a$.
\(4) Suppose that ${\alpha }+2\beta $, $2{\alpha }+\beta \notin R^a$. By (1) the set $\{{\alpha },\beta \}$ is a base for $V^a({\alpha },\beta )$ at $a$, and ${\alpha }+\beta \in R^a$ by (3). Then Proposition \[pr:R=Fseq\] implies that $R^a\cap {\mathrm{span}}_{\mathbb{Z}}\{{\alpha },\beta \}=\{\pm {\alpha },\pm \beta ,\pm ({\alpha }+\beta
)\}$. Thus (1) and Lemma \[le:root\_diffs1\](2) give that $\gamma -{\alpha }\in
R^a$ or $\gamma -\beta \in R^a$, a contradiction to the initial assumption of the lemma. Hence by symmetry each of the sets $\{{\alpha }+2\beta ,2\al
+\beta \}$, $\{{\alpha }+2\gamma ,2{\alpha }+\gamma \}$, $\{\beta +2\gamma ,2\beta
+\gamma \}$ contains at least one element of $R^a$.
Assume now that $\gamma +2{\alpha }$, $\gamma +2\beta \in R^a$. By changing the object via (1) we may assume that ${\alpha }$, $\beta $, and $\gamma -n_1{\alpha }-n_2\beta $ are simple roots for some $n_1,n_2\in {\mathbb{N}}$. Then Lemma \[le:badroots\] applies to $\gamma +2{\alpha }\in R^a_+$ and $\beta -{\alpha }$, and tells that $\beta
-{\alpha }\in R^a$. This gives a contradiction.
By the previous two paragraphs we conclude that if $\gamma +2{\alpha }\in R^a$, then $\gamma +2\beta \notin R^a$, and hence $\beta +2\gamma \in R^a$. Similarly, we also obtain that ${\alpha }+2\beta \in R^a$. By symmetry this implies (4).
\(5) By symmetry it suffices to prove that $\gamma -({\alpha }+k\beta )\notin R^a$ for all $k\in {\mathbb{N}}_0$. For $k=0$ the claim holds by assumption.
First we prove that $\gamma -({\alpha }+2\beta )\notin R^a$. By (3) we know that $\gamma +{\alpha }$, ${\alpha }+\beta \in R^a$, and $\gamma -\beta \notin R^a$ by assumption. Since ${\mathrm{Vol}}_2(\gamma +{\alpha },{\alpha }+\beta )=1$, Lemma \[le:base2\] gives that $\{\gamma +{\alpha }, {\alpha }+\beta \}$ is a base for $V^a(\gamma +{\alpha },{\alpha }+\beta )$ at $a$. Since $\gamma -({\alpha }+2\beta )=(\gamma +{\alpha })
-2({\alpha }+\beta )$, we conclude that $\gamma -({\alpha }+2\beta )\notin R^a$.
Now let $k\in {\mathbb{N}}$. Assume that $\gamma -({\alpha }+k\beta )\in R^a$ and that $k$ is minimal with this property. Let ${\alpha }'=-{\alpha }$, $\beta '=-\beta $, $\gamma '=\gamma -({\alpha }+k\beta )$. Then ${\alpha }',\beta ',\gamma '\in R^a$ with ${\mathrm{Vol}}_3({\alpha }',\beta ',\gamma ')=1$. Moreover, ${\alpha }'-\beta '\notin
R^a$ by assumption, ${\alpha }'-\gamma '=-(\gamma -k\beta )\notin R^a$ by (2), and $\beta '-\gamma '=-(\gamma -{\alpha }-(k-1)\beta )\notin R^a$ by the minimality of $k$. Further, $\{{\alpha }',\beta ',\gamma '\}$ is not a base for $R^a$, since $\gamma =\gamma '-{\alpha }'-k\beta '$. Hence Claim (3) holds for $\al
',\beta ',\gamma '$. In particular, $$\gamma '+\beta '=\gamma -({\alpha }+(k+1)\beta )\in R^a.$$ This and the previous paragraph imply that $k\ge 3$.
We distinguish two cases depending on the parity of $k$. First assume that $k$ is even. Let ${\alpha }'=\gamma +{\alpha }$ and $\beta '=-({\alpha }+k/2\beta )$. Then ${\mathrm{Vol}}_2({\alpha }',\beta ')=1$ and ${\alpha }'+2\beta '=\gamma -({\alpha }+k\beta )\in R^a$. Lemma \[le:badroots\] applied to ${\alpha }',\beta '$ gives that $\gamma
-k/2\beta ={\alpha }'+\beta '\in R^a$, which contradicts (2).
Finally, the case of odd $k$ can be excluded similarly by considering $V^a(\gamma +{\alpha },\gamma -({\alpha }+(k+1)\beta ))$.
\(6) We get ${\mathrm{Vol}}_3({\alpha }',\beta ',\gamma ')=1$ since ${\mathrm{Vol}}_3({\alpha },\beta ,\gamma )=1$ and ${\mathrm{Vol}}_3$ is invariant under the right action of ${\mathrm{GL}}({\mathbb{Z}}^3)$. Further, $\beta '-\gamma '=-(2\beta +\gamma )\notin R^a$ by (4), and ${\alpha }'-\gamma '\notin R^a$ by (5). Finally, $({\alpha }',\beta ',\gamma ')$ is not a base for ${\mathbb{Z}}^I$ at $a$, since $R^a\ni \gamma -n_1{\alpha }-n_2\beta =\gamma '-n_1{\alpha }'+(1+n_2-kn_1)\beta '$, where $n_1,n_2\in {\mathbb{N}}$ are as in (1).
\(7) We prove that $\gamma +3{\alpha }\notin R^a$. The rest follows by symmetry. If $2{\alpha }+\beta \in R^a$, then $\gamma +2{\alpha }\notin R^a$ by (4), and hence $\gamma +3{\alpha }\notin R^a$. Otherwise ${\alpha }+2\beta ,\gamma +2{\alpha }\in R^a$ by (4). Let $k$, ${\alpha }'$, $\beta '$, $\gamma '$ be as in (6). Then (6) and (3) give that $R^a\ni \gamma '+{\alpha }'=\gamma +{\alpha }+(k+1)\beta $. Since $\gamma +{\alpha }\in
R^a$, Lemma \[le:badroots\] implies that $\gamma +{\alpha }+2\beta \in R^a$. Let $w$ be as in (1). If $\gamma +3{\alpha }\in R^a$, then Lemma \[le:badroots\] for the vectors $w(\gamma +{\alpha }+2\beta )$ and $w({\alpha }-\beta )$ implies that $w({\alpha }-\beta )\in R^a$, a contradiction. Thus $\gamma +3{\alpha }\notin R^a$.
Recall that $\cC$ is a Cartan scheme of rank three and ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite irreducible root system of type $\cC$.
\[root\_diffs\] Let $a\in A$ and ${\alpha },\beta,\gamma\in R^a$. If ${\mathrm{Vol}}_3({\alpha },\beta,\gamma)=1$ and none of $\alpha-\beta$, $\alpha-\gamma$, $\beta-\gamma$ are contained in $R^a$, then $\{{\alpha },\beta,\gamma \}$ is a base for ${\mathbb{Z}}^I$ at $a$.
Assume to the contrary that $\{{\alpha },\beta ,\gamma \}$ is not a base for ${\mathbb{Z}}^I$ at $a$. Exchanging ${\alpha }$ and $\beta $ if necessary, by Lemma \[le:root\_diffs2\](4) we may assume that ${\alpha }+2\beta \in R^a$. By Lemma \[le:root\_diffs2\](6),(7) the triple $({\alpha }+2\beta
,-\beta , \gamma +\beta )$ satisfies the assumptions of Lemma \[le:root\_diffs2\], and $({\alpha }+2\beta )+2(-\beta )={\alpha }\in R^a$. Hence $2{\alpha }+3\beta =2({\alpha }+2\beta )+(-\beta )\notin R^a$ by Lemma \[le:root\_diffs2\](4). Thus $V^a({\alpha },\beta )\cap R^a=\{\pm {\alpha },
\pm ({\alpha }+\beta ),\pm ({\alpha }+2\beta ), \pm \beta \}$ by Proposition \[pr:R=Fseq\], and hence, using Lemma \[le:root\_diffs2\](1), we obtain from Lemma \[le:root\_diffs1\](2) that $\gamma -{\alpha }\in R^a$ or $\gamma -\beta \in R^a$. This is a contradiction to our initial assumption, and hence $\{{\alpha },\beta ,\gamma \}$ is a base for ${\mathbb{Z}}^I$ at $a$.
\[convex\_diff2\] Let $a\in A$ and $\gamma _1,\gamma _2,{\alpha }\in R^a$. Assume that $\{\gamma _1,\gamma _2\}$ is a base for $V^a(\gamma _1,\gamma _2)$ at $a$ and that ${\mathrm{Vol}}_3(\gamma _1,\gamma _2,{\alpha })=1$. Then either $\{\gamma _1,\gamma _2,{\alpha }\}$ is a base for ${\mathbb{Z}}^I$ at $a$, or one of ${\alpha }-\gamma _1$, $\al-\gamma _2$ is contained in $R^a$.
For the proof of Theorem \[th:class\] we need a bound for the entries of the Cartan matrices of ${\mathcal{C}}$. To get this bound we use the following.
\[le:someroots\] Let $a\in A$.
\(1) At most one of $c^a_{12}$, $c^a_{13}$, $c^a_{23}$ is zero.
\(2) ${\alpha }_1+{\alpha }_2+{\alpha }_3\in R^a$.
\(3) Let $k\in {\mathbb{Z}}$. Then $k{\alpha }_1+{\alpha }_2+{\alpha }_3\in R^a$ if and only if $k_1\le k\le k_2$, where $$\begin{aligned}
k_1=
\begin{cases}
0 & \text{if $c^a_{23}<0$,}\\
1 & \text{if $c^a_{23}=0$,}
\end{cases}
\quad
k_2=
\begin{cases}
-c^a_{12}-c^a_{13} & \text{if $c^{{\rho }_1(a)}_{23}<0$,}\\
-c^a_{12}-c^a_{13}-1 & \text{if $c^{{\rho }_1(a)}_{23}=0$.}
\end{cases}
\end{aligned}$$
\(4) We have $2{\alpha }_1+{\alpha }_2+{\alpha }_3\in R^a$ if and only if either $c^a_{12}+c^a_{13}\le -3$ or $c^a_{12}+c^a_{13}=-2$, $c^{\rfl
_1(a)}_{23}<0$.
\(5) Assume that $$\begin{aligned}
\#(R^a_+\cap ({\mathbb{Z}}{\alpha }_1+{\mathbb{Z}}{\alpha }_2))\ge 5.
\label{eq:Rbig}
\end{aligned}$$ Then there exist $k\in {\mathbb{N}}_0$ such that $k{\alpha }_1+2{\alpha }_2+{\alpha }_3\in R^a$. Let $k_0$ be the smallest among all such $k$. Then $k_0$ is given by the following. $$\begin{aligned}
\begin{cases}
0 & \text{if $c^a_{23}\le -2$,}\\
1 & \text{if $-1\le c^a_{23}\le 0$,
$c^a_{21}+c^a_{23}\le -2$, $c^{{\rho }_2(a)}_{13}<0$,}\\
1 & \text{if $-1\le c^a_{23}\le 0$,
$c^a_{21}+c^a_{23}\le -3$, $c^{{\rho }_2(a)}_{13}=0$,}\\
2 & \text{if $c^a_{21}=c^a_{23}=-1$, $c^{{\rho }_2(a)}_{13}=0$,}\\
2 & \text{if $c^a_{21}=-1$, $c^a_{23}=0$, $c^{{\rho }_2(a)}_{13}\le -2$,}\\
3 & \text{if $c^a_{21}=-1$, $c^a_{23}=0$, $c^{{\rho }_2(a)}_{13}=-1$,
$c^{{\rho }_2(a)}_{12}\le -3$,}\\
3 & \text{if $c^a_{21}=-1$, $c^a_{23}=0$, $c^{{\rho }_2(a)}_{13}=-1$,
$c^{{\rho }_2(a)}_{12}=-2$, $c^{{\rho }_1{\rho }_2(a)}_{23}<0$,}\\
4 & \text{otherwise.}
\end{cases}
\end{aligned}$$ Further, if $c^a_{13}=0$ then $k_0\le 2$.
We may assume that ${\mathcal{C}}$ is connected. Then, since ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is irreducible, Claim (1) holds by [@a-CH09a Def.4.5, Prop.4.6].
\(2) The claim is invariant under permutation of $I$. Thus by (1) we may assume that $c^a_{23}\not=0$. Hence ${\alpha }_2+{\alpha }_3\in
R^a$. Assume first that $c^a_{13}=0$. Then $c^{{\rho }_1(a)}_{13}=0$ by (C2), $c^{{\rho }_1(a)}_{23}\not=0$ by (1), and ${\alpha }_2+{\alpha }_3\in R^{{\rho }_1(a)}_+$. Hence $\s^{{\rho }_1(a)}_1({\alpha }_2+{\alpha }_3)=-c^a_{12}{\alpha }_1+{\alpha }_2+{\alpha }_3\in
R^a$. Therefore (2) holds by Lemma \[le:badroots\] for ${\alpha }={\alpha }_2+{\alpha }_3$ and $\beta ={\alpha }_1$.
Assume now that $c^a_{13}\not=0$. By symmetry and the previous paragraph we may also assume that $c^a_{12},c^a_{23}\not=0$. Let $b={\rho }_1(a)$. If $c^b_{23}=0$ then ${\alpha }_1+{\alpha }_2+{\alpha }_3\in R^b$ by the previous paragraph. Then $$R^a\ni \s^b_1({\alpha }_1+{\alpha }_2+{\alpha }_3)
=(-c^a_{12}-c^a_{13}-1){\alpha }_1+{\alpha }_2+{\alpha }_3,$$ and the coefficient of ${\alpha }_1$ is positive. Further, ${\alpha }_2+{\alpha }_3\in R^a$, and hence (2) holds in this case by Lemma \[le:badroots\]. Finally, if $c^b_{23}\not=0$, then ${\alpha }_2+\al
_3\in R^b_+$, and hence $(-c^a_{12}-c^a_{13}){\alpha }_1+{\alpha }_2+{\alpha }_3\in R^a$. Since $-c^a_{12}-c^a_{13}>0$, (2) follows again from Lemma \[le:badroots\].
\(3) If $c^a_{23}<0$, then ${\alpha }_2+{\alpha }_3\in R^a$ and $-k{\alpha }_1+{\alpha }_2+{\alpha }_3\notin R^a$ for all $k\in {\mathbb{N}}$. If $c^a_{23}=0$, then ${\alpha }_1+{\alpha }_2+{\alpha }_3\in R^a$ by (2), and $-k{\alpha }_1+{\alpha }_2+{\alpha }_3\notin R^a$ for all $k\in {\mathbb{N}}_0$. Applying the same argument to $R^{{\rho }_1(a)}$ and using the reflection $\s^{{\rho }_1(a)}_1$ and Lemma \[le:badroots\] gives the claim.
\(4) This follows immediately from (3).
\(5) The first case follows from Corollary \[co:cij\] and the second and third cases are obtained from (4) by interchanging the elements $1$ and $2$ of $I$. We also obtain that if $k_0$ exists then $k_0\ge 2$ in all other cases. By and Proposition \[pr:R=Fseq\] we conclude that ${\alpha }_1+{\alpha }_2\in R^a$. Then $c^a_{21}<0$ by Corollary \[co:cij\], and hence we are left with calculating $k_0$ if $-1\le c^a_{23}\le 0$, $c^a_{21}+c^a_{23}=-2$, $c^{{\rho }_2(a)}_{13}=0$, or $c^a_{21}=-1$, $c^a_{23}=0$. By (1), if $c^{{\rho }_2(a)}_{13}=0$ then $c^{{\rho }_2(a)}_{23}\not=0$, and hence $c^a_{23}<0$ by (C2). Thus we have to consider the elements $k{\alpha }_1+2{\alpha }_2+{\alpha }_3$, where $k\ge 2$, under the assumption that $$\begin{aligned}
c^a_{21}=c^a_{23}=-1, \, c^{{\rho }_2(a)}_{13}=0 \quad \text{or}\quad
c^a_{21}=-1,\, c^a_{23}=0.
\label{eq:ccond1}
\end{aligned}$$ Since $c^a_{21}=-1$, Condition gives that $$c^{{\rho }_2(a)}_{12}\le -2,$$ see [@a-CH09a Lemma4.8]. Further, the first set of equations in implies that $c^{{\rho }_1{\rho }_2(a)}_{13}=0$, and hence $c^{{\rho }_1{\rho }_2(a)}_{23}<0$ by (1). Since ${\sigma }_2^a(2{\alpha }_1+2{\alpha }_2+{\alpha }_3)=2{\alpha }_1+{\alpha }_3-c^a_{23}\al
_2$, the first set of equations in and (4) imply that $k_0=2$. Similarly, Corollary \[co:cij\] tells that $k_0=2$ under the second set of conditions in if and only if $c^{{\rho }_2(a)}_{13}\le -2$.
It remains to consider the situation for $$\begin{aligned}
c^a_{21}=-1,\,c^a_{23}=0,\,c^{{\rho }_2(a)}_{13}=-1.
\label{eq:ccond2}
\end{aligned}$$ Indeed, equation $c^a_{23}=0$ implies that $c^{{\rho }_2(a)}_{23}=0$ by (C2), and hence $c^{{\rho }_2(a)}_{13}<0$ by (1), Assuming we obtain that ${\sigma }_2^a(3{\alpha }_1+2{\alpha }_2+{\alpha }_3)=3{\alpha }_1+{\alpha }_2+{\alpha }_3$, and hence (3) implies that $k_0=3$ if and only if the corresponding conditions in (5) are valid.
The rest follows by looking at $\sigma _1 \sigma _2^a(4{\alpha }_1+2{\alpha }_2+\al
_3)$ and is left to the reader. The last claim holds since $c^a_{13}=0$ implies that $c^a_{23}\not=0$ by (1). The assumption $\#(R^a_+\cap ({\mathbb{Z}}{\alpha }_1+{\mathbb{Z}}{\alpha }_2))\ge 5$ is needed to exclude the case $c^a_{21}=-1$, $c^{{\rho }_2(a)}_{12}=-2$, $c^{{\rho }_1\rfl
_2(a)}_{21}=-1$, where $R^a_+\cap ({\mathbb{Z}}{\alpha }_1+{\mathbb{Z}}{\alpha }_2)=\{{\alpha }_2,{\alpha }_1+{\alpha }_2,
2{\alpha }_1+{\alpha }_2,{\alpha }_1\}$, by using Proposition \[pr:R=Fseq\] and Corollary \[co:cij\], see also the proof of [@a-CH09a Lemma4.8].
\[cartan\_6\] Let $\cC$ be a Cartan scheme of rank three. Assume that ${\mathcal{R}}{^\mathrm{re}}$ is a finite irreducible root system of type $\cC$. Then all entries of the Cartan matrices of $\cC$ are greater or equal to $-7$.
It can be assumed that ${\mathcal{C}}$ is connected. We prove the theorem indirectly. To do so we may assume that $a\in A$ such that $c^a_{12}\le -8$. Then Proposition \[pr:R=Fseq\] implies that $\# (R^a_+\cap ({\mathbb{Z}}{\alpha }_1+{\mathbb{Z}}{\alpha }_2))\ge 5$. By Lemma \[le:someroots\] there exists $k_0\in \{0,1,2,3,4\}$ such that ${\alpha }:=k_0{\alpha }_1+2{\alpha }_2+{\alpha }_3\in R^a_+$ and ${\alpha }-{\alpha }_1\notin R^a$. By Lemma \[le:base2\] and the choice of $k_0$ the set $\{{\alpha },{\alpha }_1\}$ is a base for $V^a({\alpha },{\alpha }_1)$ at $a$. Corollary \[simple\_rkk\] implies that there exists a root $\gamma \in R^a$ such that $\{{\alpha },{\alpha }_1,\gamma \}$ is a base for ${\mathbb{Z}}^I$ at $a$. Let $d\in A$, $w\in \operatorname{Hom}(a,d)$, and $i_1,i_2,i_3\in I$ such that $w({\alpha })={\alpha }_{i_1}$, $w({\alpha }_1)={\alpha }_{i_2}$, $w(\gamma )={\alpha }_{i_3}$.
Let $b={\rho }_1(a)$. Again by Lemma \[le:someroots\] there exists $k_1\in \{0,1,2,3,4\}$ such that $\beta :=k_1{\alpha }_1+2{\alpha }_2+{\alpha }_3\in R^b_+$. Thus $$R^a_+\ni \s_1^b(\beta )=(-k_1-2c^a_{12}-c^a_{13}){\alpha }_1+2{\alpha }_2+\al
_3.$$ Further, $$-k_1-2c^a_{12}-c^a_{13}-k_0>-c^a_{12}$$ since $k_0\le 2$ if $c^a_{13}=0$. Hence ${\alpha }_{i_1}+(1-c^a_{12}){\alpha }_{i_2}
\in R^d$, that is, $c^d_{i_2 i_1}<c^a_{1 2}\le -8$. We conclude that there exists no lower bound for the entries of the Cartan matrices of ${\mathcal{C}}$, which is a contradiction to the finiteness of ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$. This proves the theorem.
The bound in the theorem is not sharp. After completing the classification one can check that the entries of the Cartan matrices of ${\mathcal{C}}$ are always at least $-6$. The entry $-6$ appears for example in the Cartan scheme corresponding to the root system with number $53$, see Corollary \[co:cij\].
\[Euler\_char\] Let ${\mathcal{C}}$ be an irreducible connected simply connected Cartan scheme of rank three. Assume that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite root system of type ${\mathcal{C}}$. Let $e$ be the number of vertices, $k$ the number of edges, and $f$ the number of ($2$-dimensional) faces of the object change diagram of ${\mathcal{C}}$. Then $e-k+f=2$.
Vertices of the object change diagram correspond to elements of $A$. Since ${\mathcal{C}}$ is connected and ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is finite, the set $A$ is finite. Consider the equivalence relation on $I\times A$, where $(i,a)$ is equivalent to $(j,b)$ for some $i,j\in I$ and $a,b\in A$, if and only if $i=j$ and $b\in \{a,{\rho }_i(a)\}$. (This is also known as the pushout of $I\times A$ along the bijections ${\mathrm{id}}:I\times A\to I\times A$ and ${\rho }:I\times A\to I\times A$, $(i,a)\mapsto (i,{\rho }_i(a))$.) Since ${\mathcal{C}}$ is simply connected, ${\rho }_i(a)\not=a$ for all $i\in I$ and $a\in A$. Then edges of the object change diagram correspond to equivalence classes in $I\times A$. Faces of the object change diagram can be defined as equivalence classes of triples $(i,j,a)\in I\times I\times A\setminus
\{(i,i,a)\,|\,i\in I,a\in A\}$, where $(i,j,a)$ and $(i',j',b)$ are equivalent for some $i,j,i',j'\in I$ and $a,b\in A$ if and only if $\{i,j\}=\{i',j'\}$ and $b\in \{({\rho }_j{\rho }_i)^m(a),
{\rho }_i({\rho }_j{\rho }_i)^m(a)\,|\,m\in {\mathbb{N}}_0\}$. Since ${\mathcal{C}}$ is simply connected, (R4) implies that the face corresponding to a triple $(i,j,a)$ is a polygon with $2m_{i,j}^a$ vertices.
For each face choose a triangulation by non-intersecting diagonals. Let $d$ be the total number of diagonals arising this way. Now consider the following two-dimensional simplicial complex $C$: The $0$-simplices are the objects. The $1$-simplices are the edges and the chosen diagonals of the faces of the object change diagram. The $2$-simplices are the $f+d$ triangles. Clearly, each edge is contained in precisely two triangles. By [@b-tomDieck91 Ch.III, (3.3), 2,3] the geometric realization $X$ of $C$ is a closed $2$-dimensional surface without boundary. The space $X$ is connected and compact.
Any two morphisms of ${\mathcal{W}}({\mathcal{C}})$ with same source and target are equal because ${\mathcal{C}}$ is simply connected. By [@a-CH09a Thm.2.6] this equality follows from the Coxeter relations. A Coxeter relation means for the object change diagram that for the corresponding face and vertex the two paths along the sides of the face towards the opposite vertex yield the same morphism. Hence diagonals can be interpreted as representatives of paths in a face between two vertices, and then all loops in $C$ become homotopic to the trivial loop. Hence $X$ is simply connected and therefore homeomorphic to a two-dimensional sphere by [@b-tomDieck91 Ch.III, Satz 6.9]. Its Euler characteristic is $2=e-(k+d)+(f+d)=e-k+f$.
\[re:planesandfaces\] Assume that ${\mathcal{C}}$ is connected and simply connected, and let $a\in A$. Then any pair of opposite $2$-dimensional faces of the object change diagram can be interpreed as a plane in ${\mathbb{Z}}^I$ containing at least two positive roots ${\alpha },\beta \in R^a_+$. Indeed, let $b\in A$ and $i_1,i_2\in I$ with $i_1\not=i_2$. Since ${\mathcal{C}}$ is connected and simply connected, there exists a unique $w\in \operatorname{Hom}(a,b)$. Then $V^a(w^{-1}({\alpha }_{i_1}),w^{-1}({\alpha }_{i_2}))$ is a plane in ${\mathbb{Z}}^I$ containing at least two positive roots. One can easily check that this plane is independent of the choice of the representative of the face determined by $(i_1,i_2,b)\in I\times I\times A$. Further, let $w_0\in \operatorname{Hom}(b,d)$, where $d\in A$, be the longest element in ${\mathrm{Hom}(b,{\mathcal{W}}({\mathcal{C}}))}$. Let $j_1,j_2\in I$ such that $w_0({\alpha }_{i_n})=-{\alpha }_{j_n}$ for $n=1,2$. Then $(j_1,j_2,d)$ determines the plane $$V^a( (w_0w)^{-1}({\alpha }_{j_1}),(w_0w)^{-1}({\alpha }_{j_2}))=
V^a(w^{-1}({\alpha }_{i_1}),w^{-1}({\alpha }_{i_2})).$$ This way we attached to any pair of ($2$-dimensional) opposite faces of the object change diagram a plane containing at least two positive roots.
![The object change diagram of the last root system of rank three[]{data-label="fig:37posroots"}](wg37){width="9cm"}
Let $<$ be a semigroup ordering on ${\mathbb{Z}}^I$ such that $0<\gamma $ for all $\gamma \in R^a_+$. Let ${\alpha },\beta \in R^a_+$ with ${\alpha }\not=\beta $, and assume that ${\alpha }$ and $\beta $ are the smallest elements in $R^a_+\cap
V^a({\alpha },\beta )$ with respect to $<$. Then $\{{\alpha },\beta \}$ is a base for $V^a({\alpha },\beta )$ at $a$ by Lemma \[posrootssemigroup\]. By Corollary \[simple\_rkk\] there exists $b\in A$ and $w\in \operatorname{Hom}(a,b)$ such that $w({\alpha }),w(\beta )\in R^b_+$ are simple roots. Hence any plane in ${\mathbb{Z}}^I$ containing at least two elements of $R^a_+$ can be obtained by the construction in the previous paragraph.
It remains to show that different pairs of opposite faces give rise to different planes. This follows from the fact that for any $b\in A$ and $i_1,i_2\in I$ with $i_1\not=i_2$ the conditions $$d\in A,\ u\in \operatorname{Hom}(b,d),\ j_1,j_2\in I,\
u({\alpha }_{i_1})={\alpha }_{j_1},\ u({\alpha }_{i_2})={\alpha }_{j_2}$$ have precisely two solutions: $u={\mathrm{id}}_b$ on the one side, and $u=w_0w_{i_1i_2}$ on the other side, where $w_{i_1i_2}=\cdots \s_{i_1}\s_{i_2}\s_{i_1}{\mathrm{id}}_b\in {\mathrm{Hom}(b,{\mathcal{W}}({\mathcal{C}}))}$ is the longest product of reflections ${\sigma }_{i_1}$, ${\sigma }_{i_2}$, and $w_0$ is an appropriate longest element of ${\mathcal{W}}({\mathcal{C}})$. The latter follows from the fact that $u$ has to map the base $\{\al
_{i_1},{\alpha }_{i_2},{\alpha }_{i_3}\}$ for ${\mathbb{Z}}^I$ at $b$, where $I=\{i_1,i_2,i_3\}$, to another base, and any base consisting of two simple roots can be extended precisely in two ways to a base of ${\mathbb{Z}}^I$: by adding the third simple root or by adding a uniquely determined negative root.
It follows from the construction and by [@a-CH09b Lemma 6.4] that the faces corresponding to a plane $V^a({\alpha },\beta )$, where ${\alpha },\beta \in R^a_+$ with ${\alpha }\not=\beta $, have as many edges as the cardinality of $V^a({\alpha },\beta )\cap R^a$ (or twice the cardinality of $V^a({\alpha },\beta )\cap R^a_+$).
\[sum\_rank2\] Let $\cC$ be a connected simply connected Cartan scheme of rank three. Assume that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite irreducible root system of type $\cC$. Let $a\in A$ and let $M$ be the set of planes containing at least two elements of $R^a_+$. Then $$\sum_{V\in M} \#(V\cap R^a_+) = 3(\# M-1).$$
Let $e,k,f$ be as in Proposition \[Euler\_char\]. Then $\#M=f/2$ by Remark \[re:planesandfaces\]. For any vertex $b\in A$ there are three edges starting at $b$, and any edge is bounded by two vertices. Hence counting vertices in two different ways one obtains that $3e=2k$. Proposition \[Euler\_char\] gives that $e-k+f=2$. Hence $2k = 3e = 3(2-f+k)$, that is, $k=3f-6$.
Any plane $V$ corresponds to a face which is a polygon consisting of $2\# (V\cap R^a_+)$ edges, see Remark \[re:planesandfaces\]. Summing up the edges twice over all planes (that is summing up over all faces of the object change diagram), each edge is counted twice. Hence $$2 \sum_{V\in M} 2\#(V\cap R^a_+) = 2k = 2(3f-6),$$ which is the formula claimed in the theorem.
\[ex\_square\] Let $\cC$ be a connected simply connected Cartan scheme of rank three. Assume that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite irreducible root system of type $\cC$. Then there exists an object $a\in A$ and $\alpha,\beta,\gamma\in R^a_+$ such that $\{\alpha,\beta,\gamma\}=\{\al_1,\al_2,\al_3\}$ and $$\label{square_hexagon}
\#(V^a(\alpha,\beta)\cap R^a_+)=2, \quad
\#(V^a(\alpha,\gamma)\cap R^a_+)=3.$$ Further $\alpha+\gamma, \beta +\gamma , \alpha+\beta+\gamma\in R^a_+$.
Let $M$ be as in Thm. \[sum\_rank2\]. Let $a$ be any object and assume $\#(V\cap R^a_+)>2$ for all $V\in M$, then $\sum_{V\in M} \#(V\cap R^a_+) \ge 3\# M$ contradicting Thm. \[sum\_rank2\]. Hence for all objects $a$ there exists a plane $V$ with $\#(V\cap R^a_+)=2$. Now consider the object change diagram and count the number of faces: Let $2q_i$ be the number of faces with $2i$ edges. Then Thm. \[sum\_rank2\] translates to $$\label{thm_trans}
\sum_{i\ge 2} i q_i = -3+3\sum_{i\ge 2} q_i.$$ Assume that there exists no object adjacent to a square and a hexagon. Since ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is irreducible, no two squares have a common edge, see Lemma \[le:someroots\](1). Look at the edges ending in vertices of squares, and count each edge once for both polygons adjacent to it. One checks that there are at least twice as many edges adjacent to a polygon with at least $8$ vertices as edges of squares. This gives that $$\sum_{i\ge 4} 2i \cdot 2q_i \ge 2\cdot 4\cdot 2q_2.$$ By Equation we then have $-3+3\sum_{i\ge 2}q_i\ge 4q_2+2q_2+3q_3$, that is, $q_2 < \sum_{i\ge 4}q_i$. But then in average each face has more than $6$ edges which contradicts Thm. \[sum\_rank2\]. Hence there is an object $a$ such that there exist $\alpha,\beta,\gamma\in R^a_+$ as above satisfying Equation . We have $\alpha+\gamma, \beta +\gamma , \alpha+\beta+\gamma\in R^a_+$ by Lemma \[le:someroots\](1),(2) and Corollary \[co:cij\].
The classification {#sec:class}
==================
In this section we explain the classification of connected simply connected Cartan schemes of rank three such that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite irreducible root system. We formulate the main result in Theorem \[th:class\]. The proof of Theorem \[th:class\] is performed using computer calculations based on results of the previous sections. Our algorithm described below is sufficiently powerful: The implementation in $C$ terminates within a few hours on a usual computer. Removing any of the theorems, the calculations would take at least several weeks.
\(1) Let $\cC$ be a connected Cartan scheme of rank three with $I=\{1,2,3\}$. Assume that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite irreducible root system of type $\cC$. Then there exists an object $a\in A$ and a linear map $\tau \in \operatorname{Aut}({\mathbb{Z}}^I)$ such that $\tau ({\alpha }_i)\in \{{\alpha }_1,{\alpha }_2,{\alpha }_3\}$ for all $i\in I$ and $\tau (R^a_+)$ is one of the sets listed in Appendix \[ap:rs\]. Moreover, $\tau (R^a_+)$ with this property is uniquely determined.
\(2) Let $R$ be one of the $55$ subsets of ${\mathbb{Z}}^3$ appearing in Appendix \[ap:rs\]. There exists up to equivalence a unique connected simply connected Cartan scheme ${\mathcal{C}}(I,A,({\rho }_i)_{i\in I},(C^a)_{a\in A})$ such that $R\cup -R$ is the set of real roots $R^a$ in an object $a\in A$. Moreover ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite irreducible root system of type $\cC
$. \[th:class\]
Let $<$ be the lexicographic ordering on ${\mathbb{Z}}^3$ such that $\al_3<\al_2<\al_1$. Then ${\alpha }>0$ for any ${\alpha }\in {\mathbb{N}}_0^3\setminus \{0\}$.
Let ${\mathcal{C}}$ be a connected Cartan scheme with $I=\{1,2,3\}$. Assume that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is a finite irreducible root system of type ${\mathcal{C}}$. Let $a\in A$. By Theorem \[root\_is\_sum\] we may construct $R^a_+$ inductively by starting with $R^a_+=\{{\alpha }_3,{\alpha }_2,{\alpha }_1\}$, and appending in each step a sum of a pair of positive roots which is greater than all roots in $R^a_+$ we already have. During this process, we keep track of all planes containing at least two positive roots, and the positive roots on them. Lemma \[posrootssemigroup\] implies that for any known root ${\alpha }$ and new root $\beta $ either $V^a({\alpha },\beta )$ contains no other known positive roots, or $\beta $ is not part of the unique base for $V^a({\alpha },\beta )$ at $a$ consisting of positive roots. In the first case the roots ${\alpha },\beta $ generate a new plane. It can happen that ${\mathrm{Vol}}_2({\alpha },\beta )>1$, and then $\{{\alpha },\beta \}$ is not a base for $V^a({\alpha },\beta )$ at $a$, but we don’t care about that. In the second case the known roots in $V^a({\alpha },\beta )\cap R^a_+$ together with $\beta $ have to form an $\cF$-sequence by Proposition \[pr:R=Fseq\].
Sometimes, by some theorem (see the details below) we know that it is not possible to add more positive roots to a plane. Then we can mark it as “finished”.
Remark that to obtain a finite number of root systems as output, we have to ensure that we compute only irreducible systems since there are infinitely many inequivalent reducible root systems of rank two. Hence starting with $\{{\alpha }_3,{\alpha }_2,{\alpha }_1\}$ will not work. However, by Corollary \[ex\_square\], starting with $\{{\alpha }_3,{\alpha }_2,\al_2+\al_3,{\alpha }_1,\al_1+\al_2,\al_1+\al_2+\al_3\}$ will still yield at least one root system for each desired Cartan scheme (notice that any roots one would want to add are lexicographically greater).
In this section, we will call [*root system fragment*]{} (or [*rsf*]{}) the following set of data associated to a set of positive roots $R$ in construction:
- normal vectors for the planes with at least two positive roots
- labels of positive roots on these planes
- Cartan entries corresponding to the root systems of the planes
- an array of flags for finished planes
- the sum $s_R$ of $\#(V\cap R)$ over all planes $V$ with at least two positive roots, see Theorem \[sum\_rank2\]
- for each root $r\in R$ the list of planes it belongs to.
These data can be obtained directly from $R$, but the calculation is faster if we continuously update them.
We divide the algorithm into three parts. The main part is Algorithm 4.4, see below.
The first part updates a root system fragment to a new root and uses Theorems \[root\_diffs\] and \[cartan\_6\] to possibly refuse doing so:
[**Algorithm ..**]{} [**AppendRoot**]{}($\alpha$,$B$,$\tilde B$,$\hat\alpha$)\
[*Append a root to an rsf*]{}.\
[**Input:**]{} a root $\alpha$, an rsf $B$, an empty rsf $\tilde B$, a root $\hat\alpha$.\
[**Output:**]{} $\begin{cases}
0: & \mbox{if } \alpha \mbox{ may be appended, new rsf is then in } \tilde B, \\
1: & \mbox{if } \alpha \mbox{ may not be appended}, \\
2: & \mbox{if $\alpha \in R^a_+$ implies the existence of
$\beta \in R^a_+$}\\
& \mbox{with $\hat\alpha<\beta <\alpha $.}
\end{cases}$\
[**.**]{}
Let $r$ be the number of planes containing at least two elements of $R$. For documentation purposes let $V_1,\dots,V_r$ denote these planes. For any $i\in \{1,\dots,r\}$ let $v_i$ be a normal vector for $V_i$, and let $R_i$ be the $\cF$-sequence of $V_i\cap R$. Set $i \leftarrow 1$, $g \leftarrow 1$, $c\leftarrow [\:]$, $p \leftarrow [\:]$, $d\leftarrow\{\:\}$. During the algorithm $c$ will be an ordered subset of $\{1,\dots,r\}$, $p$ a corresponding list of “positions”, and $d$ a subset of $R$.
\[A1\_2\] If $i\le r$ and $g\ne 0$, then compute the scalar product $g:=(\alpha , v_i)$. (Then $g=\det ({\alpha },\gamma _1,\gamma _2)
=\pm {\mathrm{Vol}}_3({\alpha },\gamma _1,\gamma _2)$, where $\{\gamma _1,\gamma _2\}$ is the basis of $V_i$ consisting of positive roots.) Otherwise go to Step \[A1\_6\].
\[A1\_3\] If $g=0$ then do the following: If $V_i$ is not finished yet, then check if ${\alpha }$ extends $R_i$ to a new ${\mathcal{F}}$-sequence. If yes, add the roots of $R_i$ to $d$, append $i$ to $c$, append the position of the insertion of ${\alpha }$ in $R_i$ to $p$, let $g \leftarrow 1$, and go to Step 5.
If $g^2=1$, then use Corollary \[convex\_diff2\]: Let $\gamma_1$ and $\gamma_2$ be the beginning and the end of the $\cF
$-sequence $R_i$, respectively. (Then $\{\gamma _1,\gamma _2\}$ is a base for $V_i$ at $a$). Let $\delta_1 \leftarrow \alpha - \gamma_1$, $\delta_2 \leftarrow \alpha - \gamma_2$. If $\delta_1,\delta _2\notin R$, then return $1$ if $\delta
_1,\delta _2 \le \hat {\alpha }$ and return $2$ otherwise.
Set $i \leftarrow i+1$ and go to Step \[A1\_2\].
\[A1\_6\] If there is no objection appending $\alpha$ so far, i.e. $g \ne 0$, then copy $B$ to $\tilde B$ and include $\alpha$ into $\tilde B$: use $c,p$ to extend existing ${\mathcal{F}}$-sequences, and use (the complement of) $d$ to create new planes. Finally, apply Theorem \[cartan\_6\]: If there is a Cartan entry lesser than $-7$ then return 1, else return 0. If $g=0$ then return 2.
The second part looks for small roots which we must include in any case. The function is based on Proposition \[pr:suminR\]. This is a strong restriction during the process.
[**Algorithm ..**]{} [**RequiredRoot**]{}($R$,$B$,$\hat\alpha$)\
[*Find a smallest required root under the assumption that all roots $\le \hat
{\alpha }$ are known*]{}.\
[**Input:**]{} $R$ a set of roots, $B$ an rsf for $R$, $\hat \alpha $ a root.\
[**Output:**]{} $\begin{cases}
0 & \mbox{if we cannot determine such a root}, \\
1,\varepsilon & \mbox{if we have found a small missing root $\varepsilon $
with $\varepsilon >\hat \alpha $},\\
2 & \mbox{if the given configuration is impossible}.
\end{cases}$\
[**.**]{}
Initialize the return value $f \leftarrow 0$.
\[A2\_0\] We use the same notation as in Algo. 4.2, step 1. For all $\gamma _1$ in $R$ and all $(j,k)\in \{1,\dots,r\}\times \{1,\dots,r\}$ such that $j\not=k$, $\gamma _1\in R_j\cap R_k$, and both $R_j,R_k$ contain two elements, let $\gamma _2,\gamma _3\in R$ such that $R_j=\{\gamma _1,\gamma _2\}$, $R_k=\{\gamma _1,\gamma _3\}$. If ${\mathrm{Vol}}_3(\gamma _1,\gamma _2,\gamma _3) = 1$, then do Steps \[A2\_a\] to \[A2\_b\].
\[A2\_a\] $\xi_2 \leftarrow \gamma_1+\gamma_2$, $\xi_3 \leftarrow \gamma_1+\gamma_3$.
If $\hat\alpha \ge \xi_2$: If $\hat\alpha \ge \xi_3$ or plane $V_k$ is already finished, then return 2. If $f=0$ or $\varepsilon > \xi_3$, then $\varepsilon \leftarrow \xi_3$, $f\leftarrow 1$. Go to Step \[A2\_0\] and continue loop.
If $\hat\alpha \ge \xi_3$: If plane $V_j$ is already finished, then return 2. If $f=0$ or $\varepsilon > \xi_2$, then $\varepsilon \leftarrow \xi_2$, $f\leftarrow 1$.
\[A2\_b\] Go to Step \[A2\_0\] and continue loop.
Return $f,\varepsilon$.
Finally, we resursively add roots to a set, update the rsf and include required roots:
[**Algorithm ..**]{} [**CompleteRootSystem**]{}($R$,$B$,$\hat\alpha$,$u$,$\beta$)\
[*\[mainalg\]Collects potential new roots, appends them and calls itself again*]{}.\
[**Input:**]{} $R$ a set of roots, $B$ an rsf for $R$, $\hat\alpha$ a lower bound for new roots, $u$ a flag, $\beta$ a vector which is necessarily a root if $u=$ True.\
[**Output:**]{} Root systems containing $R$.\
[**.**]{} \[A3\]
Check Theorem \[sum\_rank2\]: If $s_R = 3(r-1)$, where $r$ is the number of planes containing at least two positive roots, then output $R$ (and continue). We have found a potential root system.
If we have no required root yet, i.e. $u=$ False, then\
$f,\varepsilon:=$RequiredRoot$(R,B,\hat{\alpha })$. If $f=1$, then we have found a required root; we call CompleteRootSystem($R,B,\hat\alpha, True, \varepsilon$) and terminate. If $f=2$, then terminate.
Potential new roots will be collected in $Y\leftarrow \{\:\}$; $\tilde B$ will be the new rsf.
For all planes $V_i$ of $B$ which are not finished, do Steps \[A3\_a\] to \[A3\_b\].
\[A3\_a\] $\nu \leftarrow 0$.
For $\zeta$ in the set of roots that may be added to the plane $V_i$ such that $\zeta> \hat\alpha$, do the following:
- set $\nu \leftarrow \nu+1$.
- If $\zeta \notin Y$, then $Y \leftarrow Y \cup \{\zeta\}$. If moreover $u=$ False or $\beta > \zeta$, then
- $y \leftarrow$ AppendRoot($\zeta,B,\tilde B,\hat\alpha$);
- if $y = 0$ then CompleteRootSystem($R\cup\{\zeta\},\tilde B,\zeta ,
u, \beta$).
- if $y = 1$ then $\nu \leftarrow \nu-1$.
\[A3\_b\] If $\nu = 0$, then mark $V_i$ as finished in $\tilde B$.
if $u =$ True and AppendRoot($\beta,B,\tilde B,\hat\alpha$) = 0, then call\
CompleteRootSystem($R\cup\{\beta\},\tilde B,\beta, \textrm{False},
\beta$).\
Terminate the function call.
Note that we only used necessary conditions for root systems, so after the computation we still need to check which of the sets are indeed root systems. A short program in [Magma]{} confirms that Algorithm 4.4 yields only root systems, for instance using this algorithm:
[**Algorithm ..**]{} [**RootSystemsForAllObjects**]{}($R$)\
[*Returns the root systems for all objects if $R=R^a_+$ determines a Cartan scheme ${\mathcal{C}}$ such that ${\mathcal{R}}{^\mathrm{re}}({\mathcal{C}})$ is an irreducible root system*]{}.\
[**Input:**]{} $R$ the set of positive roots at one object.\
[**Output:**]{} the set of root systems at all objects, or $\{\}$ if $R$ does not yield a Cartan scheme as desired.\
[**.**]{} \[A4\]
$N \leftarrow [R]$, $M \leftarrow \{\}$.
While $|N| > 0$, do steps \[begwhile\] to \[endwhile\].
Let $F$ be the last element of $N$. Remove $F$ from $N$ and include it to $M$.\[begwhile\]
Let $C$ be the Cartan matrix of $F$. Compute the three simple reflections given by $C$.
For each simple reflection $s$, do:\[endwhile\]
- Compute $G:=\{s(v)\mid v\in F\}$. If an element of $G$ has positive and negative coefficients, then return $\{\}$. Otherwise mutliply the negative roots of $G$ by $-1$.
- If $G\notin M$, then append $G$ to $N$.
Return $M$.
We list all $55$ root systems in Appendix \[ap:rs\]. It is also interesting to summarize some of the invariants, which is done in Table 1. Let ${\mathcal O}=\{R^a \mid a \in A\}$ denote the set of different root systems. By identifying objects with the same root system one obtains a quotient Cartan scheme of the simply connected Cartan scheme of the classification. In the fifth column we give the automorphism group of one (equivalently, any) object of this quotient. The last column gives the multiplicities of planes; for example $3^7$ means that there are $7$ different planes containing precisely $3$ positive roots.
Nr. $|R_+^a|$ $|{\mathcal O}|$ $|A|$ $\operatorname{Hom}(a)$ planes
------ ----------- ------------------ ------- --------------------------- --------------------------------------------------------
$1$ $6$ $1$ $24$ $A_3$ $2^{3}, 3^{4}, $
$2$ $7$ $4$ $32$ $A_1\times A_1\times A_1$ $2^{3}, 3^{6}, $
$3$ $8$ $5$ $40$ $B_2$ $2^{4}, 3^{6}, 4^{1}, $
$4$ $9$ $1$ $48$ $B_3$ $2^{6}, 3^{4}, 4^{3}, $
$5$ $9$ $1$ $48$ $B_3$ $2^{6}, 3^{4}, 4^{3}, $
$6$ $10$ $5$ $60$ $A_1\times A_2$ $2^{6}, 3^{7}, 4^{3}, $
$7$ $10$ $10$ $60$ $A_2$ $2^{6}, 3^{7}, 4^{3}, $
$8$ $11$ $9$ $72$ $A_1\times A_1\times A_1$ $2^{7}, 3^{8}, 4^{4}, $
$9$ $12$ $21$ $84$ $A_1\times A_1$ $2^{8}, 3^{10}, 4^{3}, 5^{1}, $
$10$ $12$ $14$ $84$ $A_2$ $2^{9}, 3^{7}, 4^{6}, $
$11$ $13$ $4$ $96$ $G_2\times A_1$ $2^{9}, 3^{12}, 4^{3}, 6^{1}, $
$12$ $13$ $12$ $96$ $A_1\times A_1\times A_1$ $2^{10}, 3^{10}, 4^{3}, 5^{2}, $
$13$ $13$ $2$ $96$ $B_3$ $2^{12}, 3^{4}, 4^{9}, $
$14$ $13$ $2$ $96$ $B_3$ $2^{12}, 3^{4}, 4^{9}, $
$15$ $14$ $56$ $112$ $A_1$ $2^{11}, 3^{12}, 4^{4}, 5^{2}, $
$16$ $15$ $16$ $128$ $A_1\times A_1\times A_1$ $2^{13}, 3^{12}, 4^{6}, 5^{2}, $
$17$ $16$ $36$ $144$ $A_1\times A_1$ $2^{14}, 3^{15}, 4^{6}, 5^{1}, 6^{1}, $
$18$ $16$ $24$ $144$ $A_2$ $2^{15}, 3^{13}, 4^{6}, 5^{3}, $
$19$ $17$ $10$ $160$ $B_2\times A_1$ $2^{16}, 3^{16}, 4^{7}, 6^{2}, $
$20$ $17$ $10$ $160$ $B_2\times A_1$ $2^{16}, 3^{16}, 4^{7}, 6^{2}, $
$21$ $17$ $10$ $160$ $B_2\times A_1$ $2^{18}, 3^{12}, 4^{7}, 5^{4}, $
$22$ $18$ $30$ $180$ $A_2$ $2^{18}, 3^{18}, 4^{6}, 5^{3}, 6^{1}, $
$23$ $18$ $90$ $180$ $A_1$ $2^{19}, 3^{16}, 4^{6}, 5^{5}, $
$24$ $19$ $25$ $200$ $A_1\times A_1\times A_1$ $2^{20}, 3^{20}, 4^{6}, 5^{4}, 6^{1}, $
$25$ $19$ $8$ $192$ $G_2\times A_1$ $2^{21}, 3^{18}, 4^{6}, 6^{4}, $
$26$ $19$ $50$ $200$ $A_1\times A_1$ $2^{20}, 3^{20}, 4^{6}, 5^{4}, 6^{1}, $
$27$ $19$ $25$ $200$ $A_1\times A_1\times A_1$ $2^{20}, 3^{20}, 4^{6}, 5^{4}, 6^{1}, $
$28$ $19$ $8$ $192$ $G_2\times A_1$ $2^{24}, 3^{12}, 4^{6}, 5^{6}, 6^{1}, $
$29$ $20$ $27$ $216$ $B_2$ $2^{20}, 3^{26}, 4^{4}, 5^{4}, 8^{1}, $
$30$ $20$ $110$ $220$ $A_1$ $2^{21}, 3^{24}, 4^{6}, 5^{4}, 7^{1}, $
$31$ $20$ $110$ $220$ $A_1$ $2^{23}, 3^{20}, 4^{7}, 5^{5}, 6^{1}, $
$32$ $21$ $15$ $240$ $B_2\times A_1$ $2^{22}, 3^{28}, 4^{6}, 5^{4}, 8^{1}, $
$33$ $21$ $30$ $240$ $A_1\times A_1\times A_1$ $2^{26}, 3^{20}, 4^{9}, 5^{4}, 6^{2}, $
$34$ $21$ $5$ $240$ $B_3$ $2^{24}, 3^{24}, 4^{9}, 6^{4}, $
$35$ $22$ $44$ $264$ $A_2$ $2^{27}, 3^{25}, 4^{9}, 5^{3}, 6^{3}, $
$36$ $25$ $42$ $336$ $A_1\times A_1\times A_1$ $2^{33}, 3^{34}, 4^{12}, 5^{2}, 6^{3}, 8^{1}, $
$37$ $25$ $14$ $336$ $G_2\times A_1$ $2^{36}, 3^{30}, 4^{9}, 5^{6}, 6^{4}, $
$38$ $25$ $28$ $336$ $A_1\times A_2$ $2^{36}, 3^{30}, 4^{9}, 5^{6}, 6^{4}, $
$39$ $25$ $7$ $336$ $B_3$ $2^{36}, 3^{28}, 4^{15}, 6^{6}, $
$40$ $26$ $182$ $364$ $A_1$ $2^{35}, 3^{39}, 4^{10}, 5^{4}, 6^{3}, 8^{1}, $
$41$ $26$ $182$ $364$ $A_1$ $2^{37}, 3^{36}, 4^{9}, 5^{6}, 6^{3}, 7^{1}, $
$42$ $27$ $49$ $392$ $A_1\times A_1\times A_1$ $2^{38}, 3^{42}, 4^{9}, 5^{6}, 6^{3}, 8^{1}, $
$43$ $27$ $98$ $392$ $A_1\times A_1$ $2^{39}, 3^{40}, 4^{10}, 5^{6}, 6^{2}, 7^{2}, $
$44$ $27$ $98$ $392$ $A_1\times A_1$ $2^{39}, 3^{40}, 4^{10}, 5^{6}, 6^{2}, 7^{2}, $
$45$ $28$ $420$ $420$ $1$ $2^{41}, 3^{44}, 4^{11}, 5^{6}, 6^{2}, 7^{1}, 8^{1}, $
$46$ $28$ $210$ $420$ $A_1$ $2^{42}, 3^{42}, 4^{12}, 5^{6}, 6^{1}, 7^{3}, $
$47$ $28$ $70$ $420$ $A_2$ $2^{42}, 3^{42}, 4^{12}, 5^{6}, 6^{1}, 7^{3}, $
$48$ $29$ $56$ $448$ $A_1\times A_1\times A_1$ $2^{44}, 3^{46}, 4^{13}, 5^{6}, 6^{2}, 8^{2}, $
$49$ $29$ $112$ $448$ $A_1\times A_1$ $2^{45}, 3^{44}, 4^{14}, 5^{6}, 6^{1}, 7^{2}, 8^{1}, $
$50$ $29$ $112$ $448$ $A_1\times A_1$ $2^{45}, 3^{44}, 4^{14}, 5^{6}, 6^{1}, 7^{2}, 8^{1}, $
$51$ $30$ $238$ $476$ $A_1$ $2^{49}, 3^{44}, 4^{17}, 5^{6}, 6^{1}, 7^{1}, 8^{2}, $
$52$ $31$ $21$ $504$ $G_2\times A_1$ $2^{54}, 3^{42}, 4^{21}, 5^{6}, 6^{1}, 8^{3}, $
$53$ $31$ $21$ $504$ $G_2\times A_1$ $2^{54}, 3^{42}, 4^{21}, 5^{6}, 6^{1}, 8^{3}, $
$54$ $34$ $102$ $612$ $A_2$ $2^{60}, 3^{63}, 4^{18}, 5^{6}, 6^{4}, 8^{3}, $
$55$ $37$ $15$ $720$ $B_3$ $2^{72}, 3^{72}, 4^{24}, 6^{10}, 8^{3}, $
[Table 1: Invariants of irreducible root systems of rank three]{}
At first sight, one is tempted to look for a formula for the number of objects in the universal covering depending on the number of roots. There is an obvious one: consider the coefficients of $4/((1-x)^2(1-x^4))$. However, there are exceptions, for example nr. 29 with $20$ positive roots and $216$ objects (instead of $220$).
Rank 3 Nichols algebras of diagonal type with finite irreducible arithmetic root system are classified in [@a-Heck05b Table 2]. In Table 2 we identify the Weyl groupoids of these Nichols algebras.
----------------------------- ---- ---- ---- ---- ---- ---- ---- ---- ----
row in [@a-Heck05b Table 2] 1 2 3 4 5 6 7 8 9
Weyl groupoid 1 5 4 1 5 3 11 1 2
row in [@a-Heck05b Table 2] 10 11 12 13 14 15 16 17 18
Weyl groupoid 2 2 5 13 5 6 7 8 14
----------------------------- ---- ---- ---- ---- ---- ---- ---- ---- ----
Irreducible root systems of rank three {#ap:rs}
======================================
We give the roots in a multiplicative notation to save space: The word $1^x2^y3^z$ corresponds to $x\alpha_3+y\alpha_2+z\alpha_1$.
Notice that we have chosen a “canonical” object for each groupoid. Write $\pi(R^a_+)$ for the set $R^a_+$ where the coordinates are permuted via $\pi\in S_3$. Then the set listed below is the minimum of $\{\pi(R^a_+)\mid a\in A,\:\: \pi\in S_3\}$ with respect to the lexicographical ordering on the sorted sequences of roots.
Nr. $1$ with $6$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $123$\
Nr. $2$ with $7$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $23$, $123$\
Nr. $3$ with $8$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $123$, $1^{2}23$\
Nr. $4$ with $9$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $123$, $1^{2}23$, $1^{2}23^{2}$\
Nr. $5$ with $9$ positive roots:\
$1$, $2$, $3$, $12$, $23$, $1^{2}2$, $123$, $1^{2}23$, $1^{2}2^{2}3$\
Nr. $6$ with $10$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{2}23$, $1^{3}23$\
Nr. $7$ with $10$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $23$, $1^{2}2$, $123$, $1^{2}23$, $1^{2}2^{2}3$\
Nr. $8$ with $11$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{2}23$, $1^{3}23$, $1^{3}2^{2}3$\
Nr. $9$ with $12$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$\
Nr. $10$ with $12$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{2}23$, $1^{3}23$, $1^{2}2^{2}3$, $1^{3}2^{2}3$\
Nr. $11$ with $13$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}2^{2}$, $1^{3}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$\
Nr. $12$ with $13$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}23$, $1^{4}23$, $1^{4}2^{2}3$\
Nr. $13$ with $13$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{2}23$, $1^{3}23$, $1^{2}2^{2}3$, $1^{3}2^{2}3$, $1^{4}2^{2}3$\
Nr. $14$ with $13$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $123$, $13^{2}$, $1^{2}23$, $123^{2}$, $1^{2}23^{2}$, $1^{3}23^{2}$, $1^{3}2^{2}3^{2}$\
Nr. $15$ with $14$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$\
Nr. $16$ with $15$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$\
Nr. $17$ with $16$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$\
Nr. $18$ with $16$ positive roots:\
$1$, $2$, $3$, $12$, $23$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $12^{2}3$, $1^{3}23$, $1^{2}2^{2}3$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{4}2^{3}3$, $1^{4}2^{3}3^{2}$\
Nr. $19$ with $17$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}23$, $1^{4}23$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$\
Nr. $20$ with $17$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{5}2^{2}3^{2}$\
Nr. $21$ with $17$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}23$, $1^{2}2^{2}3$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{5}2^{3}3$, $1^{5}2^{3}3^{2}$, $1^{6}2^{3}3^{2}$\
Nr. $22$ with $18$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{5}2^{3}3$, $1^{6}2^{3}3$\
Nr. $23$ with $18$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $23$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $12^{2}3$, $1^{3}23$, $1^{2}2^{2}3$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{3}2^{3}3$, $1^{4}2^{3}3$, $1^{4}2^{3}3^{2}$\
Nr. $24$ with $19$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{7}2^{3}3^{2}$\
Nr. $25$ with $19$ positive roots:\
$1$, $2$, $3$, $12$, $23$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}23$, $1^{2}2^{2}3$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{6}2^{3}3$, $1^{6}2^{3}3^{2}$\
Nr. $26$ with $19$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $23$, $1^{2}2$, $12^{2}$, $123$, $1^{3}2$, $1^{2}23$, $12^{2}3$, $1^{3}23$, $1^{2}2^{2}3$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{3}2^{3}3$, $1^{4}2^{3}3$, $1^{4}2^{3}3^{2}$\
Nr. $27$ with $19$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $23$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $12^{2}3$, $1^{3}2^{2}$, $1^{3}23$, $1^{2}2^{2}3$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{3}2^{3}3$, $1^{4}2^{3}3$, $1^{4}2^{3}3^{2}$\
Nr. $28$ with $19$ positive roots:\
$1$, $2$, $3$, $12$, $23$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}2^{2}$, $1^{3}23$, $1^{2}2^{2}3$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{3}2^{3}3$, $1^{4}2^{3}3$, $1^{5}2^{3}3$, $1^{6}2^{3}3$, $1^{6}2^{4}3$\
Nr. $29$ with $20$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$\
Nr. $30$ with $20$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{7}2^{3}3^{2}$\
Nr. $31$ with $20$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}2^{2}$, $1^{3}23$, $1^{2}2^{2}3$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{4}2^{3}3$, $1^{5}2^{3}3$, $1^{6}2^{3}3^{2}$\
Nr. $32$ with $21$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{7}2^{3}3^{2}$\
Nr. $33$ with $21$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}2^{2}$, $1^{3}23$, $1^{2}2^{2}3$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{4}2^{3}3$, $1^{5}2^{3}3$, $1^{6}2^{3}3$, $1^{6}2^{3}3^{2}$\
Nr. $34$ with $21$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{5}2^{3}3$, $1^{5}2^{2}3^{2}$, $1^{6}2^{3}3$, $1^{6}2^{3}3^{2}$, $1^{7}2^{3}3^{2}$\
Nr. $35$ with $22$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}2^{2}$, $1^{3}23$, $1^{2}2^{2}3$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{4}2^{3}3$, $1^{5}2^{3}3$, $1^{5}2^{2}3^{2}$, $1^{5}2^{3}3^{2}$, $1^{6}2^{3}3^{2}$\
Nr. $36$ with $25$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{8}2^{3}3^{2}$\
Nr. $37$ with $25$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$\
Nr. $38$ with $25$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $12^{2}$, $123$, $1^{3}2$, $1^{2}23$, $12^{2}3$, $1^{3}23$, $1^{2}2^{2}3$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{3}2^{3}3$, $1^{3}2^{2}3^{2}$, $1^{4}2^{3}3$, $1^{5}2^{3}3$, $1^{4}2^{3}3^{2}$, $1^{5}2^{3}3^{2}$, $1^{6}2^{3}3^{2}$, $1^{7}2^{4}3^{2}$\
Nr. $39$ with $25$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{3}2^{2}$, $1^{3}23$, $1^{2}2^{2}3$, $1^{4}23$, $1^{3}2^{2}3$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{4}2^{3}3$, $1^{5}2^{3}3$, $1^{5}2^{2}3^{2}$, $1^{6}2^{3}3$, $1^{5}2^{3}3^{2}$, $1^{6}2^{3}3^{2}$, $1^{7}2^{3}3^{2}$, $1^{7}2^{4}3^{2}$\
Nr. $40$ with $26$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$\
Nr. $41$ with $26$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$\
Nr. $42$ with $27$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$\
Nr. $43$ with $27$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{5}2^{2}3^{2}$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$\
Nr. $44$ with $27$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{7}2^{2}3^{2}$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$\
Nr. $45$ with $28$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{5}2^{2}3^{2}$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$\
Nr. $46$ with $28$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{5}2^{2}3^{2}$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$, $1^{9}2^{4}3^{2}$\
Nr. $47$ with $28$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{5}2^{2}3^{2}$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$, $1^{11}2^{4}3^{2}$\
Nr. $48$ with $29$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{5}2^{2}3^{2}$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{7}2^{2}3^{2}$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$\
Nr. $49$ with $29$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{5}2^{2}3^{2}$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$, $1^{9}2^{4}3^{2}$\
Nr. $50$ with $29$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{5}2^{2}3^{2}$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$, $1^{11}2^{4}3^{2}$\
Nr. $51$ with $30$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{5}2^{2}3^{2}$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{7}2^{2}3^{2}$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$, $1^{9}2^{4}3^{2}$\
Nr. $52$ with $31$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}23$, $1^{5}2$, $1^{4}23$, $1^{6}2$, $1^{5}23$, $1^{4}2^{2}3$, $1^{6}23$, $1^{5}2^{2}3$, $1^{7}23$, $1^{6}2^{2}3$, $1^{7}2^{2}3$, $1^{8}2^{2}3$, $1^{9}2^{2}3$, $1^{10}2^{2}3$, $1^{9}2^{3}3$, $1^{10}2^{3}3$, $1^{11}2^{3}3$, $1^{10}2^{3}3^{2}$, $1^{11}2^{3}3^{2}$, $1^{12}2^{3}3^{2}$\
Nr. $53$ with $31$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{5}2^{2}3^{2}$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{7}2^{2}3^{2}$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{3}3^{2}$, $1^{9}2^{3}3^{2}$, $1^{9}2^{4}3^{2}$, $1^{11}2^{4}3^{2}$\
Nr. $54$ with $34$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{5}2^{3}3$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{8}2^{4}3$, $1^{8}2^{3}3^{2}$, $1^{9}2^{4}3$, $1^{9}2^{3}3^{2}$, $1^{9}2^{4}3^{2}$, $1^{11}2^{4}3^{2}$, $1^{11}2^{5}3^{2}$, $1^{12}2^{5}3^{2}$\
Nr. $55$ with $37$ positive roots:\
$1$, $2$, $3$, $12$, $13$, $1^{2}2$, $1^{2}3$, $123$, $1^{3}2$, $1^{2}23$, $1^{4}2$, $1^{3}2^{2}$, $1^{3}23$, $1^{4}23$, $1^{3}2^{2}3$, $1^{5}2^{2}$, $1^{5}23$, $1^{4}2^{2}3$, $1^{5}2^{2}3$, $1^{6}2^{2}3$, $1^{5}2^{3}3$, $1^{7}2^{2}3$, $1^{6}2^{3}3$, $1^{7}2^{3}3$, $1^{8}2^{3}3$, $1^{7}2^{3}3^{2}$, $1^{9}2^{3}3$, $1^{8}2^{4}3$, $1^{8}2^{3}3^{2}$, $1^{9}2^{4}3$, $1^{9}2^{3}3^{2}$, $1^{10}2^{4}3$, $1^{9}2^{4}3^{2}$, $1^{11}2^{4}3^{2}$, $1^{11}2^{5}3^{2}$, $1^{12}2^{5}3^{2}$, $1^{13}2^{5}3^{2}$
[^1]: In this introduction by a Weyl groupoid we will mean the Weyl groupoid of a connected Cartan scheme, and we assume that the real roots associated to the Weyl groupoid form an irreducible root system in the sense of [@a-CH09a].
|
7 P.3d 49 (2000)
Donald L. SEGNITZ, Appellant (Defendant),
v.
The STATE of Wyoming, Appellee (Plaintiff).
Donald L. Segnitz, Appellant (Defendant),
v.
The State of Wyoming, Appellee (Plaintiff).
Nos. 99-223, 99-254.
Supreme Court of Wyoming.
June 2, 2000.
*50 Representing Appellant: Donald L. Segnitz, Pro Se.
Representing Appellee: Gay Woodhouse, Attorney General; Paul S. Rehurek, Deputy Attorney General; and D. Michael Pauling, Senior Assistant Attorney General.
Before LEHMAN, C.J., and THOMAS, MACY, GOLDEN, and HILL, JJ.
MACY, Justice.
Appellant Donald L. Segnitz appeals from the denials of two motions he filed in two separate courts to correct his illegal sentences. The cases were consolidated for purposes of appeal.
We affirm in part and reverse in part.
ISSUES
In Case No. 99-223, Segnitz presents the following issues for our review:
1. Did the District Court [err] by denying Appellant's Motion to Correct an Illegal Sentence, which was filed because while orally sentenced to concurrent sentences, the Written Judgement and Sentence, and Mitimus failed to stipulate that sentence was concurrent[?]
2. Did the District Court [err] by denying Appellant's Motion to Correct ... an ILLEGAL Sentence, which was filed because the Court did not award credit for time served in it[]s Judgement and Sentence, nor Mitimus[?] Nor had it been *51 addressed orally by the Court at sentencing.
In Case No. 99-254, Segnitz presents the following issues for our review:
A. Did the District Court sentence the Appellant to an illegal term by not abiding by W.R.Cr.P. 32(c)2(C), (E), and (F)?
B. Did the District Court by denying the Motion to Correct an Illegal Sentence and then changing the original sentence abuse it[]s d[i]scretion?
C. If the change in sentence was proper then should the Appellant [be] afforded due process by the District Court?
FACTS
In November of 1997, Segnitz was sentenced in Sweetwater County to serve a term in the Wyoming State Penitentiary of not less than one year nor more than three years, with credit for the time he served in presentence confinement, for the offense of felony larceny. He was released on parole to Community Alternatives of Casper on June 25, 1998. On July 30, 1998, Segnitz departed from Community Alternatives of Casper without authorization, stealing a car to facilitate his exit. He drove to Wheatland where he abandoned this car and stole another, which he drove to Indiana.
Both the Platte County and Natrona County authorities issued arrest warrants for the crimes committed in their respective counties. The Board of Parole issued an order of arrest because Segnitz had violated the terms of his parole for the Sweetwater County felony larceny conviction. Segnitz was arrested in Indiana on August 1, 1998, and later charged with felony larceny in both Platte County and Natrona County. He pleaded guilty to the charges. Segnitz was sentenced on September 10, 1998, in Platte County to a term of not less than two years nor more than four years in the Wyoming State Penitentiary. The order was silent with regard to whether the sentence was to be served concurrently with or consecutively to any other sentences. On March 5, 1999, Segnitz was orally sentenced in Natrona County to the stipulated prison term of three to four years. The stipulation provided for the sentence to be served concurrently with the sentences imposed in Sweetwater County and Platte County. The written Judgment and Sentence failed to mention that the sentence was to be served concurrently with the other sentences, but, three months later, the district court entered an order nunc pro tunc to that effect.
Segnitz arrived at the Wyoming State Penitentiary on or shortly after March 5, 1999, the date he was sentenced in Natrona County. On April 12, 1999, the Board of Parole revoked his parole for the Sweetwater County offense, crediting him "with all of the time during which he was released."
Segnitz filed motions in the district courts of Platte County and Natrona County to correct illegal sentences. In his Platte County motion, Segnitz asserted that the Judgment and Sentence failed to specify how the sentence was to be served with regard to his other sentences. He also complained that the Judgment and Sentence failed to state the number of days awarded as presentence incarceration credit. In response, the district court issued an order wherein it announced that it intended for the sentence to be served consecutively to the others and that Segnitz was not entitled to presentence incarceration credit. In his Natrona County motion, Segnitz claimed that the Judgment and Sentence failed to reflect the district court's oral pronouncement that made the sentence run concurrently with the others and failed to award any presentence incarceration credit. Although the district court initially denied Segnitz's motion, it later entered the order nunc pro tunc referenced above which ordered the sentence for the Natrona County crime to be served concurrently with the other sentences.
Segnitz appeals to the Wyoming Supreme Court.
DISCUSSION
A. Presentence Incarceration Credit
Segnitz contends that both district courts erred when they refused to award credit for the time he spent confined before he was sentenced. The state counters that Segnitz was on parole and in the legal custody *52 of the Board of Parole during the entire time he was confined on these two charges and that the Board of Parole awarded him credit against his Sweetwater County sentence for all the time he spent on parole when his parole was eventually revoked.
The decision to grant or deny a motion to correct an illegal sentence is usually left to the sound discretion of the district court. Hamill v. State, 948 P.2d 1356, 1358 (Wyo.1997). The district court's decision is given considerable deference unless a rational basis does not exist for it. Id. A criminal defendant is entitled to receive credit against his sentence for the time he was incarcerated prior to sentencing, provided that such confinement was because of his inability and failure to post bond on the offense for which he was awaiting disposition. Smith v. State, 988 P.2d 39, 40 (Wyo.1999). A sentence which does not include credit for presentence incarceration is illegal and constitutes an abuse of discretion. Id. A defendant is not, however, entitled to credit for the time he spent in custody when that confinement would have continued despite his ability to post bond. Id.
The Board of Parole revoked Segnitz's parole for the Sweetwater County conviction after he had been sentenced in the Platte County and Natrona County cases. Had the Board of Parole revoked Segnitz's parole before he was sentenced in the Platte County and Natrona County cases, there would be no argument about the fact that those district courts refused to award presentence incarceration credit. We, however, are not concerned with this order of events and agree with the state's observation that Segnitz should not be allowed to apply the credit to the new sentences "simply because his parole was fortuitously revoked" after, and not before, his convictions for the new crimes. When the Board of Parole awarded Segnitz full credit against his Sweetwater County sentence for the time he spent on parole, it cured any problems that existed as a result of the failures by the district courts in Platte County and Natrona County to do so.
B. Concurrent Sentences
Segnitz contends that the district court erred when it ordered his Platte County sentence to run consecutively to the other sentences. The state concedes that Segnitz is correct in this assertion.
The original order was silent with regard to how the Platte County sentence was intended to run with the other sentences. Eleven months later, the district court clarified the Judgment and Sentence by ordering the sentence to run consecutively to the others. In the meantime, the district court of Natrona County ordered its sentence to run concurrently with the other sentences.
When the district court of Platte County entered its order, Segnitz had not yet been prosecuted in Natrona County nor had his parole been revoked. If a defendant is subject to prosecution in more than one court, the decision regarding how the sentences will run with respect to one another should be made by the last judge to impose a sentence. 24 C.J.S. Criminal Law § 1524 (1989). The underlying rationale for this theory is that a judge cannot require a sentence to be served consecutively to a sentence that has not yet been imposed. Id. We agree with the state that this is the best practice and conclude that the district court of Platte County abused its discretion when it ordered its sentence to run consecutively to the others. The district court of Natrona County was the last court to impose a sentence, and it ordered its sentence to run concurrently with the others. That portion of the order for the Platte County offense which directed the sentence to run consecutively to the others is illegal and is hereby stricken.
Affirmed in part and reversed in part.
|
The relationship of impulsivity, sensation seeking, coping, and substance use in youth gamblers.
This study examines the relationship of impulsivity, sensation seeking, coping, and substance use to disordered gambling in a sample of 1,339 youth (637 males and 702 females), 17-21 years old. Results indicate that males with serious gambling problems were more likely than their peers to abuse substances and to use avoidant stress-coping strategies, such as seeking emotional outlets, distracting themselves with other activities, and using humor. In contrast, female disordered gamblers were less likely to engage in active coping and planning strategies. Overall, substance use, coping through distraction, and impulsivity proved the most predictive of disordered gambling for males, and intensity seeking and impulsivity proved most predictive for females. Implications for prevention, intervention, and education are discussed. |
Q:
Retrieve List of picklist values in a Set
I got the following variables(Custom Labels referring to picklist values), and a get method to retrieve List of picklist values of a field.
I need to retrieve those List of picklist values in a Set. How can I do this ?
public String dailyValue {
get { return System.Label.Daily.toLowerCase().trim(); }
private set;
}
public String weeklyValue {
get { return System.Label.Weekly.toLowerCase().trim(); }
private set;
}
public String monthlyValue {
get { return System.Label.Monthly.toLowerCase().trim(); }
private set;
}
public String quarterlyValue {
get { return System.Label.Quarterly.toLowerCase().trim(); }
private set;
}
public String biannuallyValue {
get { return System.Label.Bi_Annually.toLowerCase().trim(); }
private set;
}
public String annuallyValue {
get { return System.Label.Annually.toLowerCase().trim(); }
private set;
}
//values from the frequency picklist
public List<SelectOption> getMonitoringFrequency(){
List<SelectOption> frequencyTypes = new List<SelectOption>();
Schema.DescribeFieldResult fieldResult = Metric__c.Monitoring_Frequency__c.getDescribe();
List<Schema.PicklistEntry> ple = fieldResult.getPicklistValues();
for( Schema.PicklistEntry f : ple){
frequencyTypes.add(new SelectOption(
f.getValue().toLowerCase(),f.getLabel().toLowerCase()
));
}
return frequencyTypes;
}
A:
Depending on whether you want the label or the value in your set, create a set:
set<String> picklistValues = new set<String>();
set<String> picklistLabels = new set<String>():
and then in your for-loop, add the value or label, as appropriate:
for( Schema.PicklistEntry f : ple){
frequencyTypes.add(new
SelectOption(f.getValue().toLowerCase(),f.getLabel().toLowerCase()));
picklistValues.add(f.getValue());
picklistLabels.add(f.getLabel());
}
|
Fish poisoning may be why Polynesians left paradise
Washington, May 19 (ANI): Scientists have come up with a theory that attributes the historic migrations of the Polynesians from the Cook islands to New Zealand, Easter Island and Hawaii in the 11th to 15th centuries, to fish poisoning.
The theory has been proposed by Teina Rongo, a Cook Island Maori from Rarotonga and a Ph.D. student at the Florida Institute of Technology, and his faculty advisers Professors Robert van Woesik and Mark Bush.
Based on archeological evidence, paleoclimatic data and modern reports of ciguatera poisoning, they theorize that ciguatera outbreaks were linked to climate and that the consequent outbreaks prompted historical migrations of Polynesians.
Ciguatera poisoning is a food-borne disease that can come from eating large, carnivorous reef fish, and causes vomiting, headaches, and a burning sensation upon contact with cold surfaces.
It is known that the historic populations of Cook Islanders was heavily reliant on fish as a source of protein, and the scientists suggest that once their fish resources became inedible, voyaging became a necessity.
Modern Cook Islanders, though surrounded by an ocean teeming with fish, don’t eat fish as a regular part of their diet but instead eat processed, imported foods.
In the late 1990s, lower-income families who could not afford processed foods emigrated to New Zealand and Australia.
The researchers suggest that past migrations had similar roots.
The heightened voyaging from A.D. 1000 to 1450 in eastern Polynesia was likely prompted by ciguatera fish poisoning.
There were few options but to leave once the staple diet of an island nation became poisonous.
According to van Woesik, “Our approach brings us a step closer to solving the mysteries of ciguatera and the storied Polynesian native migrations. We hope it will lead to better forecasting and planning for ciguatera outbreaks.” (ANI) |
Biotechnological production of human milk oligosaccharides.
Human milk contains a large variety of oligosaccharides (HMOs) that have the potential to modulate the gut flora, affect different gastrointestinal functions, and influence inflammatory processes. This review introduces the recent advances in the microbial and coupled enzymatic methods to produce HMOs with grouping them into trisaccharides (sialyllactose and fucosyllactose) and complex oligosaccharides (lacto-N-biose derivatives). The high purity and low cost of HMOs should make their use possible in new fields such as the food or pharmaceutical industries. |
1. Introduction {#sec1-polymers-08-00159}
===============
Phenol-formaldehyde (PF) is a high-performance resin that is synthesized by the copolymerization of phenol with formaldehyde. It is widely applied for industrial uses, including adhesives, impregnating resins, and plastics. The excellent properties of PF resin include high mechanical, thermal, and weather stability \[[@B1-polymers-08-00159]\]. However, the lower curing rate and required higher curing temperature compared to other thermosetting adhesives limit the application of PF resins for use in impregnating resins or adhesives \[[@B2-polymers-08-00159],[@B3-polymers-08-00159]\]. Many attempts have been made to accelerate the curing rate or lower the curing temperature, including testing of various catalysts or additives to alter the reaction kinetics, such as carboxylic acid esters \[[@B4-polymers-08-00159],[@B5-polymers-08-00159]\], anhydrides \[[@B6-polymers-08-00159]\], amides \[[@B7-polymers-08-00159]\], carbonate \[[@B8-polymers-08-00159]\], and metallic ions \[[@B9-polymers-08-00159]\]. Additionally, the effects of the condensation condition on the PF resin structure and properties have been well studied by conventional analytical techniques. For example, various mechanisms of PF resin hardening accelerated by catalysts or additives have been reported \[[@B10-polymers-08-00159]\]. Some additives, such as sodium carbonate, act solely to accelerate the curing reaction, but other additives, such as propylene carbonate, both accelerate the reaction and also increase the average functionality of the PF reaction system to allow a tighter final network \[[@B10-polymers-08-00159]\]. The properties of basic catalysts, such as the valence and ionic radius of hydrated cations, affected the mechanisms and kinetics of PF resin condensation and, thus, the composition of the final products \[[@B9-polymers-08-00159]\]. Some studies also reported that an alkaline catalyst promoted the formation of dimethylene ethers in the polymerization reaction, and that *ortho* to *ortho* (*o*,*o*′) ethers were more stable \[[@B11-polymers-08-00159]\]. However, there has been no comprehensive study about the action of catalysts to increase or decrease the ratio of *ortho*/*para* reaction position or analysis of the corresponding physicochemical properties of the accelerated PF resins.
The aromatic ring of phenol has *ortho* and *para* positions capable of reaction with formaldehyde under certain conditions, but the *para* position has higher reactivity than the *ortho* position. The presence of two *ortho* positions and one *para* position in an aromatic ring generally could lead to a PF resin containing mostly *ortho* hydroxymethyl groups \[[@B2-polymers-08-00159]\]. However, in the process of PF resin synthesis, some catalysts could make more formaldehyde or methylol toward phenol *ortho* positions to increase the ratio of *ortho*/*para* substituted positions \[[@B12-polymers-08-00159]\], leading to more reactive functional groups or more unreacted *para* positions at the curing stage, which may shorten the curing time and increase the cross-linking degree of cured PF resin.
Since metal ions can accelerate the curing of PF resins, we tested the ability of barium hydroxide (Ba(OH)~2~), sodium carbonate (Na~2~CO~3~), lithium hydroxide (LiOH), and zinc acetate ((CH~3~COO)~2~Zn) to decrease curing temperature and accelerate the curing rate of PF resins. To elucidate the chemical structure of the cure-accelerated PF resins, we performed quantitative liquid ^13^C NMR to analyze the structural features. Finally, possible synthesis mechanism of metal-mediated polymerization of PF resins was proposed based on the chemical structure analysis and thermogravimetric (DTG) curve.
2. Materials and Methods {#sec2-polymers-08-00159}
========================
2.1. Materials {#sec2dot1-polymers-08-00159}
--------------
Phenol, formaldehyde (37%), Ba(OH)~2~, Na~2~CO~3~, LiOH, and (CH~3~COO)~2~Zn were obtained from Zhong'an Chemical Industries, Beijing, China and were used directly without further purification, and all other chemicals were AR grade and obtained from Beijing Chemical Industries, Beijing, China.
2.2. Preparation of PF Resins {#sec2dot2-polymers-08-00159}
-----------------------------
The catalyst-accelerated PF resin was synthesized by batch polymerization with phenol and formaldehyde at a molar ratio of 1:2.2, and the additive amount of catalyst was 6% based on the total mass of PF resin. In the first step, phenol was mixed in a flask with one third of the formaldehyde and one third of the catalyst. The mixture was quickly heated to 70 °C, and then the heater was turned off. The temperature of the mixture increased to 90 °C due to the heat produced by polymerization reaction and remained at 93--95 °C for 1 h. In the second step, the remaining formaldehyde and two thirds of the catalyst were added to the flask and the mixture was heated to 90 °C and kept at that temperature for 0.5 h. Finally, the mixture was cooled to 40 °C to yield PF resin. PF resins with different catalysts were synthesized with the same procedure.
2.3. Preparation of Plywood {#sec2dot3-polymers-08-00159}
---------------------------
Three-layer plywood (400 mm × 400 mm × 4.8 mm) was prepared with a single poplar veneer in the middle and two poplar veneers on the top and bottom simulating actual industrial parameters. The middle poplar veneer was coated with 125--150 g/m^2^ resin on each side. Four pieces of three-layer plywood for each catalyst-accelerated resin (including control) were hot-pressed under 1.2 MPa at 100, 110, 120, and 130 °C, respectively. The hot-press time was 7 min, including the first one minute and the last one minute to load and unload the pressure, respectively.
2.4. Characterization of PF Resins {#sec2dot4-polymers-08-00159}
----------------------------------
The solid (non-volatile) content of resol resin was determined in accordance with ASTM standard D4426-01. The viscosity of resin was measured using a Brookfield DV-II viscometer (AMETEK-BROOKFIELD Corporation, Middleboro, MA, USA) using 61\# rotor with spinning rate of 100 rpm. Gel time was defined as the time period from the immersion of the test tube into the oil bath (135 °C) to the beginning of the resin gelation (resin forming a string when a glass rod was lifted from the resin).
2.5. Characterization of the Plywood {#sec2dot5-polymers-08-00159}
------------------------------------
The shear strength was measured as per ASTM D906-98.
2.6. FT-IR Analysis of PF Resins {#sec2dot6-polymers-08-00159}
--------------------------------
The resins were placed in 0.01 MPa vacuum at 60 °C for 4 h to dry to non-volatility. FT-IR spectra of vacuum-dried PF resins were performed in a Nicolet IS10 instrument (Thermo Fisher Scientific Corporation, Waltham, MA, USA). Each spectrum was recorded with 32 scans in a frequency range of 600--4000 cm^−1^ at a spectral resolution of 4 cm^−1^.
2.7. Contact Angle Measurement {#sec2dot7-polymers-08-00159}
------------------------------
The contact angle measurements of the PF resins were performed on the tangential surfaces of wood samples with an optical contact angle apparatus (OCA 20 DataPhysics Instruments GmnH, Filderstadt, Germany). Sessile droplets (3 μL, measured with a microsyringe) of liquid resin were placed on the wood surface. The right and left angles of the drops on the surface were collected at intervals of 0.1 s for a total duration of 60 s, and the average angle was calculated.
2.8. Quantitative Liquid ^13^C NMR Measurement {#sec2dot8-polymers-08-00159}
----------------------------------------------
All of the resins were characterized by quantitative ^13^C NMR spectroscopy with a VARIAN INOUR-300 (JEOL Corporation, Tokyo, Japan) spectrometer with a frequency of 75.51 MHz using the inverse-gated decoupling method. All of the spectra were recorded at room temperature with a delay time of 8 s, a 13 h acquisition time and a 15.4 μs pulse width (90°). About 8000 scans were accumulated to obtain spectra for each spectrum. The chemical shifts of each spectrum were accurate to 0.1 ppm and all the resin samples were directly used for ^13^C NMR measurement.
2.9. Thermogravimetric Analysis (TG) of Resins {#sec2dot9-polymers-08-00159}
----------------------------------------------
Samples were dried at 120 °C for 2 h to evaporate the moisture and then TG was performed in a nitrogen atmosphere within a temperature range from room temperature to 700 °C, with a heating rate of 10 °C/min.
3. Results and Discussion {#sec3-polymers-08-00159}
=========================
3.1. Performance of the Catalyst-Accelerated PF Resin {#sec3dot1-polymers-08-00159}
-----------------------------------------------------
[Table 1](#polymers-08-00159-t001){ref-type="table"} shows the solid content, viscosity, and gel time of the PF resins. We found that the solid contents were similar for all resins, but the viscosity varied greatly for different catalysts. The viscosity of the Na~2~CO~3~-accelerated resin was 153.00 mPa·s, higher than the viscosity of the other catalyst-accelerated PF resins, especially the control resin with a low viscosity of 25.70 mPa·s. Similarly, the gel-time for the catalyst-accelerated resins varied from 11.83 min for the Na~2~CO~3~-accelerated resin to 20.46 min for the control resin. These results indicated that these catalysts were able to accelerate the synthesis reaction to different extents. The ability of the catalysts to accelerate the reactions could be ranked as Na~2~CO~3~ \> (CH~3~COO)~2~Zn \> Ba(OH)~2~ \> LiOH. Under the same reaction conditions, the catalyst Na~2~CO~3~ can dramatically accelerate the synthesis reaction process, increase the viscosity, and decrease the gel time of PF resin.
3.2. Contact Angle of the PF Resins {#sec3dot2-polymers-08-00159}
-----------------------------------
The wettability of PF resin on solid surface is usually evaluated by contact angle \[[@B13-polymers-08-00159]\], which was tested on smoothed wood surface in this study. Due to liquid penetration and spreading on the wood surface, the contact angle changed as a function of time, as shown in [Figure 1](#polymers-08-00159-f001){ref-type="fig"}. The process of adhesive wetting includes three steps \[[@B14-polymers-08-00159]\]: (1) formation of a contact angle at the solid and adhesive interface; (2) spreading of the adhesive over a solid surface; and (3) adhesive penetration into the porous solid substrate, as shown in [Figure 2](#polymers-08-00159-f002){ref-type="fig"}.
As shown in [Figure 1](#polymers-08-00159-f001){ref-type="fig"}, at the initial stage of the wetting process, the contact angle of the resins decreased quickly. As time elapsed, the contact angle decreased more slowly and finally attained relative equilibrium. It was observed that the Na~2~CO~3~-accelerated PF resin showed the largest equilibrium contact angle, and the resins could be ranked as Na~2~CO~3~ \> Ba(OH)~2~ \> LiOH \> (CH~3~COO)~2~Zn \> Control. The results suggested that the Na~2~CO~3~-accelerated PF resin had the largest surface tension, which may be due to its larger viscosity. [Figure 1](#polymers-08-00159-f001){ref-type="fig"} also shows that the (CH~3~COO)~2~Zn-accelerated resin had the fastest rate of contact angle change, which meant that (CH~3~COO)~2~Zn-accelerated resin could spread and penetrate more quickly into the porous structure of wood. Both viscosity and the chemical constitution of PF resin could alter the contact angle change rate. Usually, samples with lower viscosity exhibit a faster contact angle change rate. However, from the data in [Table 1](#polymers-08-00159-t001){ref-type="table"}, (CH~3~COO)~2~Zn-accelerated resin showed higher viscosity than that of the control sample, but had a faster contact angle change rate. Thus, the chemical constitution of (CH~3~COO)~2~Zn-accelerated PF resin may be the main factor altering its contact angle change rate. The hydroxymethyl of PF resin is the main chemical group that can easily connect with the hydroxyl of wood cellulose; thus, our data suggests that (CH~3~COO)~2~Zn-accelerated PF resin may contain more hydroxymethyl.
3.3. FT-IR Spectroscopy {#sec3dot3-polymers-08-00159}
-----------------------
To investigate the structural changes in the PF resins accelerated by different catalysts, FT-IR spectra ([Figure 3](#polymers-08-00159-f003){ref-type="fig"}) were obtained after vacuum-drying the samples. The spectra assignments of the PF resins are shown in [Table 2](#polymers-08-00159-t002){ref-type="table"} \[[@B15-polymers-08-00159],[@B16-polymers-08-00159],[@B17-polymers-08-00159]\].
There were no significant differences between the spectra of the catalyst-accelerated resins and the control sample, which indicated structural similarity. Bands at 1020 cm^−1^ were ascribed to C--O stretching vibration of aliphatic C--OH, aliphatic C--O, and methylol C--OH. Bands at 1600 cm^−1^ were assigned to the elongation of aromatic --C=C--, which were consistent in each reaction system and unaffected by catalyst reaction. Thus, bands at 1600 cm^−1^ could be used as an internal standard for analysis. The ratio of absorption value of 1020 cm^−1^ (variable)/1600 cm^−1^ (constant) was calculated to indicate the degree of hydroxymethyl for phenol in each catalyst accelerated-reaction system, as shown in [Table 3](#polymers-08-00159-t003){ref-type="table"}. The control of PF resins had a relatively larger ratio of 1020 cm^−1^/1600 cm^−1^, which may be explained by the fact that the methylol of catalyst-accelerated PF resin tends to undergo further condensation reactions to form methylene (--CH~2~--). Thus, the control sample had relatively more unreacted methylol. This explanation was confirmed by the fact that the control sample showed the lowest viscosity due to its relatively minimum condensation degree.
3.4. Chemical Structure Analysis {#sec3dot4-polymers-08-00159}
--------------------------------
In order to identify the effect of different catalysts on the functional groups, quantitative ^13^C NMR was used to study the difference of chemical shifts between the control and catalyst-accelerated PF resins. The ^13^C NMR spectra are shown in [Figure 4](#polymers-08-00159-f004){ref-type="fig"}, and their corresponding assignments of groups' signals are shown in [Figure 5](#polymers-08-00159-f005){ref-type="fig"} \[[@B12-polymers-08-00159],[@B18-polymers-08-00159],[@B19-polymers-08-00159],[@B20-polymers-08-00159]\].
The chemical shift of 150.0--158.0 ppm was assigned to phenoxy carbons (C1--OH), which was used as an integral standard and analytical standpoint. 156.2--156.8 ppm and 153.4--156.1 ppm were assigned to *para* alkylated groups and *ortho* alkylated groups, respectively. Usually, phenolic *ortho* and *para* carbons' chemical shifts vary with the sodium hydroxide contents of the resin due to the ionization of phenoxy group and the kind of substituted groups. Substitution with methylol groups in the *para* and *ortho* carbon positions was shown at 129.0--130.4 ppm and 127.0--128.1 ppm. Unsubstituted *para* and *ortho* carbons, the main reactive sites for the methylolation reaction, occurred at 119.2--120.4 ppm and 115.0--116.6 ppm, respectively. The unsubstituted *para* and *ortho* carbon peaks were only present in the control and Ba(OH)~2~-accelerated PF resins, which indicated that Na~2~CO~3~, LiOH, and (CH~3~COO)~2~Zn facilitate the reaction of formaldehyde with phenolic *ortho* and *para* position more than what occurs in the control and Ba(OH)~2~ samples. A sharp peak of methanol was evident around 50 ppm for all resins. Industrial formaldehyde usually contains a small amount of methanol which can also be formed during resin synthesis from the Canizzaro reaction of formaldehyde. The signal peak of methylol is sharper than the methylene peak due to its higher group mobility and less variation in the environment within the polymer structure. Thus, the two peaks at 63.3--65.5 ppm and 61.1--61.5 ppm were assigned to *para* methylol and *ortho* methylol. Theoretically, condensation between two methylols can occur to form methylene ether bridges. However, the data in [Figure 4](#polymers-08-00159-f004){ref-type="fig"} shows no peak between 69 and 74 ppm, indicating that methylene ether bridges were not formed between phenolic units during the synthesis of PF resin. The methylene bridges were easily observed in the range of 34--41 ppm. In a different chemical environment, different methylene linkages showed a different chemical shift, 39.7--41.0 ppm and 34.3--35.7 ppm were assigned to *para*--*para* and *ortho*--*para* methylene bridges, respectively. In order to remove the interference of carbon in CH~3~COO^−^ for ^13^C NMR analysis, the Zn(NO~3~)~2~-accelerated resin was also tested by ^13^C NMR analysis and used as a control for the ^13^C NMR analysis of (CH~3~COO)~2~Zn-accelerated resin.
Further analysis of quantitative ^13^C NMR is needed to elucidate the details of the cure-acceleration effect of different catalysts on the structure and compositions of PF resin. In this study, the ratios of integral values of the substituted position *ortho* (127.0--128.1 ppm)/*para* (129.0--130.4 ppm), *ortho* methylol (61.1--61.5 ppm)/*para* methylol (63.3--65.5 ppm), and methylene bridges *ortho-para* (34.3--35.7 ppm)/*para--para* (39.7--41.0 ppm) were calculated, as shown in [Table 4](#polymers-08-00159-t004){ref-type="table"}. PF resins supplemented with Na~2~CO~3~, LiOH, and especially (CH~3~COO)~2~Zn, possessed higher ratios of *ortho*/*para*-substituted positions than did the control or the PF resin with Ba(OH)~2~. In case of the *ortho*/*para* ratio of methylol, the values of Na~2~CO~3~-accelerated and (CH~3~COO)~2~Zn-accelerated PF resins were not calculated (NC), because their ^13^C NMR spectra showed no signal for *para* methylol. Either Na~2~CO~3~ and (CH~3~COO)~2~Zn promoted the complete *para* methylol condensation reaction or drive formaldehyde toward the phenol *ortho* position exclusively. The ratio of *ortho* methylol/*para* methylol for the Zn(NO~3~)~2~-accelerated resin was much higher than other samples, excluding the Na~2~CO~3~-accelerated and (CH~3~COO)~2~Zn-accelerated PF resins. Usually, *para* methylol groups react more easily with other *para* positions to form *para--para* linkages. However, the data in [Table 5](#polymers-08-00159-t005){ref-type="table"} indicates that *ortho-para* linkages were equal to *para--para* linkages in the Na~2~CO~3~-accelerated, Zn(NO~3~)~2~-accelerated, and (CH~3~COO)~2~Zn-accelerated PF resins, suggesting that Na~2~CO~3~, Zn(NO~3~)~2~, and (CH~3~COO)~2~Zn were able to promote the condensation reaction to form *ortho-para* linkages. These results could be further proved by [Table 1](#polymers-08-00159-t001){ref-type="table"} that Na~2~CO~3~ and Zn(NO~3~)~2~-accelerated PF resins had higher viscosity, indicating that the significant promotion of phenol *ortho* position reactivity made Na~2~CO~3~ and Zn(NO~3~)~2~-accelerated PF resins have a tighter final network.
In conclusion, all the catalysts tested showed accelerating effect to promote phenol *ortho* reactivity. However, (CH~3~COO)~2~Zn and Na~2~CO~3~ were able to significantly promote the reaction activity of phenol *ortho* position and the condensation reaction of *ortho* methylol or directed formaldehyde exclusively toward the phenol *ortho* position.
3.5. Plywood Performance {#sec3dot5-polymers-08-00159}
------------------------
[Figure 6](#polymers-08-00159-f006){ref-type="fig"} shows the bonding strength of the plywood prepared with these different PF resins. Each kind of plywood was prepared at four hot-pressing temperatures, namely 100, 110, 120, and 130 °C. Higher hot-pressed temperatures allowed the resin to cure more completely and, thus, increase the bonding strength. Under the same hot-pressing temperature, the plywood prepared with catalyst-accelerated PF resins exhibited higher bonding strength than the control sample, especially the one with Na~2~CO~3~-accelerated PF resin. The data in [Figure 6](#polymers-08-00159-f006){ref-type="fig"} shows that the plywood prepared with Na~2~CO~3~-accelerated resin at 110 °C yielded almost the same bonding strength of plywood with Ba(OH)~2~-accelerated resin at 120 °C, which is higher than that of the control sample pressed at 120 °C. The reason may be that the Na~2~CO~3~-accelerated PF resin had the highest viscosity among PF resins from [Table 1](#polymers-08-00159-t001){ref-type="table"}, or that Na~2~CO~3~ significantly improved PF resin performance by promoting the reaction activity of phenol *ortho* position.
3.6. Thermal Behavior of the Cured PF Resins {#sec3dot6-polymers-08-00159}
--------------------------------------------
To characterize the thermal stability of the catalyst-accelerated PF resins, TG analysis was performed next, as shown in [Figure 7](#polymers-08-00159-f007){ref-type="fig"}. The temperatures at which the maximum degradation speed took place (*T*~max~) for the different thermal events of cured catalyst-accelerated PF resins are shown in [Table 5](#polymers-08-00159-t005){ref-type="table"}.
It was previously known that phenolic resin degrades in three steps: post-curing, thermal reforming, and ring stripping \[[@B21-polymers-08-00159],[@B22-polymers-08-00159]\]. The mass loss (about 5%) of the first thermal event at the lower temperature range (\<155 °C) contributed to the evaporation of free water. In the second stage, with a temperature range from 230 to 300 °C, mass loss was due to the evaporation of water formed by the condensation reaction of methylol groups. The mass loss in the third event (from 350 to 440 °C) was due to the loss of water formed by the condensation reaction of methylol and phenolic hydrogen, as well as between two hydroxyl functional groups, which could cause further structure change of the cured products to a more tightly cross-linked network. In the fourth event (\>450 °C), the mass loss was due to the loss of carbon monoxide and methane formed by degradation of the methylene linkage. As the temperature further increased, the remaining mass was from 65% to 68% at 700 °C, and that of Ba(OH)~2~, Na~2~CO~3~, and (CH~3~COO)~2~Zn-accelerated PF resins was higher than other samples, indicating that a tighter network and higher thermal stability was possessed by their molecular structure.
[Figure 7](#polymers-08-00159-f007){ref-type="fig"} shows TG (a) and DTG (b) curves of the catalyst-accelerated PF resins. All of the PF resins showed similar thermal stability in the first three stages of thermal events. However, in the final event, the DTG curve of the (CH~3~COO)~2~Zn-accelerated resin showed lower degradation speed than the other PF resins, and had double peaks of degradation speed. According to Pizzi and Mohamed *et al.* \[[@B23-polymers-08-00159],[@B24-polymers-08-00159],[@B25-polymers-08-00159]\], when a benzene ring was blended with a zinc ion, a complex compound between the phenolic nuclei and the zinc ion could be formed by a metal-ligand mode, which can accelerate the initial reaction of formaldehyde toward the phenolic nuclei by forming a carbocation of strong positive charge. As shown in [Scheme 1](#polymers-08-00159-sch001){ref-type="scheme"}, the mobility of the polymer chain was restricted by ion-polymer and ion-interaction, resulting in a higher thermal stability of PF resin than the control sample. Thus, the first of double peaks at 493 °C may indicate the breakage of the metal-ligand bonding mode, and the second peak of the double peaks at 518 °C may indicate the degradation of the methylene linkage.
4. Conclusions {#sec4-polymers-08-00159}
==============
The poly-condensations of PF resins with different catalysts suggested different abilities to accelerate the reaction. In general, the accelerating efficiency of the catalysts was Na~2~CO~3~ \> (CH~3~COO)~2~Zn \> Ba(OH)~2~ \> LiOH.
The addition of Na~2~CO~3~ had a remarkable influence on the performance of PF resin. The viscosity of Na~2~CO~3~-accelerated PF resin increased to around 153 mPa·s quickly, five-fold greater than the viscosity of the control resin. Moreover, the gel time of PF resin decreased significantly and the bonding strength of plywood increased by the addition of Na~2~CO~3~. The quantitative ^13^C NMR analysis showed that the (CH~3~COO)~2~Zn and Na~2~CO~3~ catalysts could significantly promote the reaction activity of the phenol *ortho* position, and favor the condensation reaction of *ortho* methylol or direct formaldehyde toward the phenol *ortho* position exclusively. Compared with Na~2~CO~3~, the catalyst (CH~3~COO)~2~Zn showed a slightly weaker accelerating effect, but the contact angle analysis found that the (CH~3~COO)~2~Zn-accelerated resin showed a faster contact angle change rate, which represents a better wettability on the wood surface. Furthermore, the different peaks in the DTG curve and higher weight residue of TG data indicated that (CH~3~COO)~2~Zn has a different accelerating mechanism to improve the thermal stability of PF resin. That mechanism may include metal-ligand bonding between the benzene ring and zinc ion formed by ion-polymer and ion-interaction.
In conclusion, catalysts such as Na~2~CO~3~ and (CH~3~COO)~2~Zn showed significant accelerating effects to promote the curing of PF resin at lower temperatures and to improve PF resin performance. Thus, good catalyst-accelerated PF resins have promised to overcome the shortcoming of high curing temperature and to broaden their application.
This work was supported by the Chinese National Science and Technology Support Program (2015BAD14B03), the Special Fund for Forestry Research in the Public Interest (Project 201504502), and China Postdoctoral Science Foundation Funded Project (2015M570039).
Zhao Yi contributed to synthesis, test, data analysis, and wrote manuscript. Jizhi Zhang, Jianzhang Li and Wei Zhang suggested and supervised the work and revised the manuscript. Shifeng Zhang, and Qiang Gao provided constructive suggestions about this work.
The authors declare no conflict of interest.
Figures, Scheme and Tables
==========================
{#polymers-08-00159-f001}
{#polymers-08-00159-f002}
{#polymers-08-00159-f003}
{#polymers-08-00159-f004}
{#polymers-08-00159-f005}
{#polymers-08-00159-f006}
{#polymers-08-00159-f007}
{#polymers-08-00159-sch001}
polymers-08-00159-t001_Table 1
######
PF resin characteristics.
Catalyst type Performance
----------------- ------------- -------- -------
Control 43 25.70 20.46
Ba(OH)~2~ 46 73.70 15.57
Na~2~CO~3~ 44 153.00 11.83
LiOH 46 58.30 15.88
(CH~3~COO)~2~Zn 44 81.00 13.98
polymers-08-00159-t002_Table 2
######
Assignments of FT-IR spectra of the PF resin.
Wavenumbers (cm^−1^) Assignment
---------------------- ----------------------------------------------------------------------------------
3,367 --OH stretching vibration
2,900 C--H stretching vibration of methylene
1,600, 1440 The elongation of aromatic --C=C--
1,270 C--O stretching vibration of phenolic C--OH and phenolic C--O
1,020 C--O stretching vibration of aliphatic C--OH, aliphatic C--O, and methylol C--OH
970 C--H stretching vibration of vinyl
polymers-08-00159-t003_Table 3
######
The ratio of absorption value of 1020 cm^−1^ (variable)/1600 cm^−1^ (constant) of the PF resins with different catalysts.
Wavenumbers (cm^−1^) Absorption
---------------------- ------------ ------- ------- ------- -------
1,020 43.46 32.63 33.79 45.43 29.85
1,600 29.75 28.14 29.94 38.54 24.81
Ratio (1,020/1,600) 1.46 1.16 1.13 1.17 1.20
polymers-08-00159-t004_Table 4
######
Liquid ^13^C NMR analysis results of PF resin formed with different catalysts.
PF resin *ortho*/*para* (Substituted position) *ortho*/*para* (Methylol) *ortho-para*/*para--para* (Methylene bridges)
--------------------------------- --------------------------------------- --------------------------------- -----------------------------------------------
   
Control   
Ba(OH)~2~
Na~2~CO~3~
LiOH
(CH~3~COO)~2~Zn
Zn(NO~3~)~2~
polymers-08-00159-t005_Table 5
######
Thermal properties of the cured PF resins.
Catalyst type *T~max~* of Thermal event (°C) Weight residue (%) at 700 °C
----------------- -------------------------------- ------------------------------ ----- ----- ----- ------
Control 155 260 394 507 -- 65.5
Ba(OH)~2~ 156 262 390 503 -- 68.0
Na~2~CO~3~ 153 300 386 512 -- 65.5
LiOH 158 283 381 497 -- 68.0
(CH~3~COO)~2~Zn 155 273 381 493 518 68.0
|
Size:
- 0.1
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Color:
- 0.66
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- 0.94
- 1
Body: Animated
Pose:
- - -0.41426134
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- 8.778018
- - 0.0
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Shape: Cube
|
P21S Carnauba Paste Wax is a non-chalky wax, leaving no powder residue or ugly white stains on rubber or plastic. This unique carnauba-beeswax blend goes on and comes off with incredible ease and delivers a great long lasting shine. You will enhance ...
Product Description LG 5231EL1003B Dryer Lint Filter Assembly with Felt Rim Seal. This part number replaces part number 5231EL1003E. For use with the following LG Electronics models: 5231EL1003B, DLE2512W, DLE2514W, DLE2515S, DLE2516W, DLE3733S, DLE3...
Permatex Dielectric Tune-Up Grease protects electrical connections and wiring from salt, dirt and corrosion. Required for modern high energy ignition systems, dialectric grease extends the life of bulb sockets and prevents voltage leaks around any el...
Both Male and Female buckles are Dual Adjust.Made for thin 1" (25mm) backpack style webbing. SIZING TIP: The size of buckles is measured by the webbing that goes in them, not the O.D. of the buckle. WARNING: This is NOT one size/style fits all. This ...
Both Male and Female buckles are Dual Adjust.Made for thin 1" (25mm) backpack style webbing. SIZING TIP: The size of buckles is measured by the webbing that goes in them, not the O.D. of the buckle. WARNING: This is NOT one size/style fits all. This ...
Both Male and Female buckles are Dual Adjust.Made for thin 1" (25mm) backpack style webbing. SIZING TIP: The size of buckles is measured by the webbing that goes in them, not the O.D. of the buckle. WARNING: This is NOT one size/style fits all. This ...
Both Male and Female buckles are Dual Adjust.Made for thin 1" (25mm) backpack style webbing. SIZING TIP: The size of buckles is measured by the webbing that goes in them, not the O.D. of the buckle. WARNING: This is NOT one size/style fits all. This ...
Both Male and Female buckles are Dual Adjust.Made for thin 1" (25mm) backpack style webbing. SIZING TIP: The size of buckles is measured by the webbing that goes in them, not the O.D. of the buckle. WARNING: This is NOT one size/style fits all. This ... |
The United States and Japan will step up their defence cooperation to deal with the threat from nuclear-armed North Korea as tensions in East Asia remain high, officials from the two allies said on Thursday.
Mr Wright started a relationship with Elizabeth after divorcing three earlier wives.
Olivia is the youngest of Mr Wright's four children but she had a difficult relationship with her father, who was frequently absent and gave little support for her single mother before his death in 2012.
She had not met older siblings Leonie Baldock, Alexandra Burt and Myles Wright prior to his death.
Olivia challenged her father's will because her $3 million trust fund had onerous conditions and could not be accessed until she was the age of 30.
Related Articles
She sought an immediate $12 million share of her father's estate, estimated at more than $1 billion, but in February the WA Supreme Court instead awarded her $25 million, the largest such payout in Australian legal history.
Olivia told the Seven Network's Sunday Night program there had been many personal hurdles during her long legal battle.
While she is ready to contest the appeal, she said she's unsure if she would go through the initial legal battle again. |
Loagan Bunut National Park
The Loagan Bunut National Park () is a national park located in Miri Division, Sarawak, Malaysia, on the Borneo island. The park was named after the Loagan Bunut lake nearby, which is connected to Sungai Bunut (sungai is Malay for river), Sungai Baram and Sungai Tinjar. This park occupies a space of and is well known for its rich biodiversity and unique aquatic ecosystem.
The national park was gazetted on January 1, 1990 and it was opened to public on August 29, 1991.
See also
List of national parks of Malaysia
References
Category:National parks of Malaysia
Category:Protected areas of Sarawak
Category:Miri, Malaysia
Category:1990 establishments in Malaysia |
RALEIGH
Complete with everything from excellent school systems and a thriving local economy to miles of parkland and bountiful culinary & cultural attractions, the greater Raleigh metropolitan area truly has it all. See for yourself why so many families and businesses chose to move here, grow here, and stay here. |
A Delicious Way to Support the Princeton Schools This Weekend at Eno Terra
Noriko and Erik Svenson and their children with Eno Terra server Giovanni Maselli last weekend..
Eno Terra is donating four days of lunch proceeds to the PowerUp! PRS Technology Campaign to benefit the Princeton Regional Schools.
This Saturday and Sunday if you eat lunch at Eno Terra, you will be supporting fundraising efforts to improve technology in the public schools.
The Terra Momo Restaurant Group, owner of Eno Terra, is donating the net proceeds from lunch sale both last weekend and this weekend to the Princeton Education Foundation.
Since 1995, the Princeton Education Foundation has encouraged private philanthropy to enhance public education. Since its inception, PEF has contributed over $1 million to the Princeton Public Schools for capital improvements, educational programs and teacher support.
“The donated funds from Eno Terra will go directly to PowerUp! PRS, our campaign to provide much needed technology upgrades to every school in the district,” said PEF Executive Director Adrienne Rubin. “We are very grateful to Eno Terra for this promotion as well as for their ongoing support of our schools.”
Eno Terra, located on Route 27 in Kingston, recently opened for lunch on the weekends. You can make a reservation for lunch for this Saturday, March 24, or this Sunday, March 25 by calling (609) 497-1777.
Raoul Momo, co-owner Terra Momo Restaurant Group, said that it is crucial that schools find new ways of raising money to ensure a high standard of education for all students in Princeton.
“With all the challenges at the state level with school finances, it is important to look to develop local partnerships with businesses like Eno Terra,” he said. “In the end, our children are our most important investment.” |
Yves Niaré
Yves Niaré (20 July 1977 – 5 December 2012) was a shot putter from France.
Career
Niaré was born in Saint-Maurice, Val-de-Marne. He father was Malian shot putter Namakoro Niaré. His main honor was the silver medal at the 2009 European Indoor Championships with a throw of 20.42 metres. He also finished eleventh at the 1996 World Junior Championships, and fourth at the 2009 Mediterranean Games.
Niaré competed at the 2001 World Championships, the 2006 European Championships, the 2007 World Championships, the 2008 Olympic Games and the 2009 World Championships without reaching the final.
His personal best throw in the shot put was 20.72 metres, a French national record, achieved in May 2008 in Versailles. He also had 63.44 metres in the discus throw, achieved in May 2007 in Chelles.
He is the brother of French High Jumper Gaëlle Niaré.
Death
Niaré was killed on the morning of 5 December 2012 in an automobile accident. A statement regarding his death was issued by the French Athletics Federation. He was 35.
Competition record
References
External links
Category:1977 births
Category:2012 deaths
Category:Sportspeople from Val-de-Marne
Category:French male shot putters
Category:French male discus throwers
Category:Athletes (track and field) at the 2008 Summer Olympics
Category:Olympic athletes of France
Category:Road incident deaths in France
Category:French people of Malian descent |
// DO NOT EDIT.
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import Foundation
import SwiftProtobuf
// If the compiler emits an error on this type, it is because this file
// was generated by a version of the `protoc` Swift plug-in that is
// incompatible with the version of SwiftProtobuf to which you are linking.
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fileprivate struct _GeneratedWithProtocGenSwiftVersion: SwiftProtobuf.ProtobufAPIVersionCheck {
struct _2: SwiftProtobuf.ProtobufAPIVersion_2 {}
typealias Version = _2
}
enum Proto3ArenaUnittest_ForeignEnum: SwiftProtobuf.Enum {
typealias RawValue = Int
case foreignZero // = 0
case foreignFoo // = 4
case foreignBar // = 5
case foreignBaz // = 6
case UNRECOGNIZED(Int)
init() {
self = .foreignZero
}
init?(rawValue: Int) {
switch rawValue {
case 0: self = .foreignZero
case 4: self = .foreignFoo
case 5: self = .foreignBar
case 6: self = .foreignBaz
default: self = .UNRECOGNIZED(rawValue)
}
}
var rawValue: Int {
switch self {
case .foreignZero: return 0
case .foreignFoo: return 4
case .foreignBar: return 5
case .foreignBaz: return 6
case .UNRECOGNIZED(let i): return i
}
}
}
#if swift(>=4.2)
extension Proto3ArenaUnittest_ForeignEnum: CaseIterable {
// The compiler won't synthesize support with the UNRECOGNIZED case.
static var allCases: [Proto3ArenaUnittest_ForeignEnum] = [
.foreignZero,
.foreignFoo,
.foreignBar,
.foreignBaz,
]
}
#endif // swift(>=4.2)
/// This proto includes every type of field in both singular and repeated
/// forms.
struct Proto3ArenaUnittest_TestAllTypes {
// SwiftProtobuf.Message conformance is added in an extension below. See the
// `Message` and `Message+*Additions` files in the SwiftProtobuf library for
// methods supported on all messages.
/// Singular
var optionalInt32: Int32 {
get {return _storage._optionalInt32}
set {_uniqueStorage()._optionalInt32 = newValue}
}
var optionalInt64: Int64 {
get {return _storage._optionalInt64}
set {_uniqueStorage()._optionalInt64 = newValue}
}
var optionalUint32: UInt32 {
get {return _storage._optionalUint32}
set {_uniqueStorage()._optionalUint32 = newValue}
}
var optionalUint64: UInt64 {
get {return _storage._optionalUint64}
set {_uniqueStorage()._optionalUint64 = newValue}
}
var optionalSint32: Int32 {
get {return _storage._optionalSint32}
set {_uniqueStorage()._optionalSint32 = newValue}
}
var optionalSint64: Int64 {
get {return _storage._optionalSint64}
set {_uniqueStorage()._optionalSint64 = newValue}
}
var optionalFixed32: UInt32 {
get {return _storage._optionalFixed32}
set {_uniqueStorage()._optionalFixed32 = newValue}
}
var optionalFixed64: UInt64 {
get {return _storage._optionalFixed64}
set {_uniqueStorage()._optionalFixed64 = newValue}
}
var optionalSfixed32: Int32 {
get {return _storage._optionalSfixed32}
set {_uniqueStorage()._optionalSfixed32 = newValue}
}
var optionalSfixed64: Int64 {
get {return _storage._optionalSfixed64}
set {_uniqueStorage()._optionalSfixed64 = newValue}
}
var optionalFloat: Float {
get {return _storage._optionalFloat}
set {_uniqueStorage()._optionalFloat = newValue}
}
var optionalDouble: Double {
get {return _storage._optionalDouble}
set {_uniqueStorage()._optionalDouble = newValue}
}
var optionalBool: Bool {
get {return _storage._optionalBool}
set {_uniqueStorage()._optionalBool = newValue}
}
var optionalString: String {
get {return _storage._optionalString}
set {_uniqueStorage()._optionalString = newValue}
}
var optionalBytes: Data {
get {return _storage._optionalBytes}
set {_uniqueStorage()._optionalBytes = newValue}
}
var optionalNestedMessage: Proto3ArenaUnittest_TestAllTypes.NestedMessage {
get {return _storage._optionalNestedMessage ?? Proto3ArenaUnittest_TestAllTypes.NestedMessage()}
set {_uniqueStorage()._optionalNestedMessage = newValue}
}
/// Returns true if `optionalNestedMessage` has been explicitly set.
var hasOptionalNestedMessage: Bool {return _storage._optionalNestedMessage != nil}
/// Clears the value of `optionalNestedMessage`. Subsequent reads from it will return its default value.
mutating func clearOptionalNestedMessage() {_uniqueStorage()._optionalNestedMessage = nil}
var optionalForeignMessage: Proto3ArenaUnittest_ForeignMessage {
get {return _storage._optionalForeignMessage ?? Proto3ArenaUnittest_ForeignMessage()}
set {_uniqueStorage()._optionalForeignMessage = newValue}
}
/// Returns true if `optionalForeignMessage` has been explicitly set.
var hasOptionalForeignMessage: Bool {return _storage._optionalForeignMessage != nil}
/// Clears the value of `optionalForeignMessage`. Subsequent reads from it will return its default value.
mutating func clearOptionalForeignMessage() {_uniqueStorage()._optionalForeignMessage = nil}
var optionalImportMessage: ProtobufUnittestImport_ImportMessage {
get {return _storage._optionalImportMessage ?? ProtobufUnittestImport_ImportMessage()}
set {_uniqueStorage()._optionalImportMessage = newValue}
}
/// Returns true if `optionalImportMessage` has been explicitly set.
var hasOptionalImportMessage: Bool {return _storage._optionalImportMessage != nil}
/// Clears the value of `optionalImportMessage`. Subsequent reads from it will return its default value.
mutating func clearOptionalImportMessage() {_uniqueStorage()._optionalImportMessage = nil}
var optionalNestedEnum: Proto3ArenaUnittest_TestAllTypes.NestedEnum {
get {return _storage._optionalNestedEnum}
set {_uniqueStorage()._optionalNestedEnum = newValue}
}
var optionalForeignEnum: Proto3ArenaUnittest_ForeignEnum {
get {return _storage._optionalForeignEnum}
set {_uniqueStorage()._optionalForeignEnum = newValue}
}
var optionalStringPiece: String {
get {return _storage._optionalStringPiece}
set {_uniqueStorage()._optionalStringPiece = newValue}
}
var optionalCord: String {
get {return _storage._optionalCord}
set {_uniqueStorage()._optionalCord = newValue}
}
/// Defined in unittest_import_public.proto
var optionalPublicImportMessage: ProtobufUnittestImport_PublicImportMessage {
get {return _storage._optionalPublicImportMessage ?? ProtobufUnittestImport_PublicImportMessage()}
set {_uniqueStorage()._optionalPublicImportMessage = newValue}
}
/// Returns true if `optionalPublicImportMessage` has been explicitly set.
var hasOptionalPublicImportMessage: Bool {return _storage._optionalPublicImportMessage != nil}
/// Clears the value of `optionalPublicImportMessage`. Subsequent reads from it will return its default value.
mutating func clearOptionalPublicImportMessage() {_uniqueStorage()._optionalPublicImportMessage = nil}
var optionalLazyMessage: Proto3ArenaUnittest_TestAllTypes.NestedMessage {
get {return _storage._optionalLazyMessage ?? Proto3ArenaUnittest_TestAllTypes.NestedMessage()}
set {_uniqueStorage()._optionalLazyMessage = newValue}
}
/// Returns true if `optionalLazyMessage` has been explicitly set.
var hasOptionalLazyMessage: Bool {return _storage._optionalLazyMessage != nil}
/// Clears the value of `optionalLazyMessage`. Subsequent reads from it will return its default value.
mutating func clearOptionalLazyMessage() {_uniqueStorage()._optionalLazyMessage = nil}
var optionalLazyImportMessage: ProtobufUnittestImport_ImportMessage {
get {return _storage._optionalLazyImportMessage ?? ProtobufUnittestImport_ImportMessage()}
set {_uniqueStorage()._optionalLazyImportMessage = newValue}
}
/// Returns true if `optionalLazyImportMessage` has been explicitly set.
var hasOptionalLazyImportMessage: Bool {return _storage._optionalLazyImportMessage != nil}
/// Clears the value of `optionalLazyImportMessage`. Subsequent reads from it will return its default value.
mutating func clearOptionalLazyImportMessage() {_uniqueStorage()._optionalLazyImportMessage = nil}
/// Repeated
var repeatedInt32: [Int32] {
get {return _storage._repeatedInt32}
set {_uniqueStorage()._repeatedInt32 = newValue}
}
var repeatedInt64: [Int64] {
get {return _storage._repeatedInt64}
set {_uniqueStorage()._repeatedInt64 = newValue}
}
var repeatedUint32: [UInt32] {
get {return _storage._repeatedUint32}
set {_uniqueStorage()._repeatedUint32 = newValue}
}
var repeatedUint64: [UInt64] {
get {return _storage._repeatedUint64}
set {_uniqueStorage()._repeatedUint64 = newValue}
}
var repeatedSint32: [Int32] {
get {return _storage._repeatedSint32}
set {_uniqueStorage()._repeatedSint32 = newValue}
}
var repeatedSint64: [Int64] {
get {return _storage._repeatedSint64}
set {_uniqueStorage()._repeatedSint64 = newValue}
}
var repeatedFixed32: [UInt32] {
get {return _storage._repeatedFixed32}
set {_uniqueStorage()._repeatedFixed32 = newValue}
}
var repeatedFixed64: [UInt64] {
get {return _storage._repeatedFixed64}
set {_uniqueStorage()._repeatedFixed64 = newValue}
}
var repeatedSfixed32: [Int32] {
get {return _storage._repeatedSfixed32}
set {_uniqueStorage()._repeatedSfixed32 = newValue}
}
var repeatedSfixed64: [Int64] {
get {return _storage._repeatedSfixed64}
set {_uniqueStorage()._repeatedSfixed64 = newValue}
}
var repeatedFloat: [Float] {
get {return _storage._repeatedFloat}
set {_uniqueStorage()._repeatedFloat = newValue}
}
var repeatedDouble: [Double] {
get {return _storage._repeatedDouble}
set {_uniqueStorage()._repeatedDouble = newValue}
}
var repeatedBool: [Bool] {
get {return _storage._repeatedBool}
set {_uniqueStorage()._repeatedBool = newValue}
}
var repeatedString: [String] {
get {return _storage._repeatedString}
set {_uniqueStorage()._repeatedString = newValue}
}
var repeatedBytes: [Data] {
get {return _storage._repeatedBytes}
set {_uniqueStorage()._repeatedBytes = newValue}
}
var repeatedNestedMessage: [Proto3ArenaUnittest_TestAllTypes.NestedMessage] {
get {return _storage._repeatedNestedMessage}
set {_uniqueStorage()._repeatedNestedMessage = newValue}
}
var repeatedForeignMessage: [Proto3ArenaUnittest_ForeignMessage] {
get {return _storage._repeatedForeignMessage}
set {_uniqueStorage()._repeatedForeignMessage = newValue}
}
var repeatedImportMessage: [ProtobufUnittestImport_ImportMessage] {
get {return _storage._repeatedImportMessage}
set {_uniqueStorage()._repeatedImportMessage = newValue}
}
var repeatedNestedEnum: [Proto3ArenaUnittest_TestAllTypes.NestedEnum] {
get {return _storage._repeatedNestedEnum}
set {_uniqueStorage()._repeatedNestedEnum = newValue}
}
var repeatedForeignEnum: [Proto3ArenaUnittest_ForeignEnum] {
get {return _storage._repeatedForeignEnum}
set {_uniqueStorage()._repeatedForeignEnum = newValue}
}
var repeatedStringPiece: [String] {
get {return _storage._repeatedStringPiece}
set {_uniqueStorage()._repeatedStringPiece = newValue}
}
var repeatedCord: [String] {
get {return _storage._repeatedCord}
set {_uniqueStorage()._repeatedCord = newValue}
}
var repeatedLazyMessage: [Proto3ArenaUnittest_TestAllTypes.NestedMessage] {
get {return _storage._repeatedLazyMessage}
set {_uniqueStorage()._repeatedLazyMessage = newValue}
}
var oneofField: OneOf_OneofField? {
get {return _storage._oneofField}
set {_uniqueStorage()._oneofField = newValue}
}
var oneofUint32: UInt32 {
get {
if case .oneofUint32(let v)? = _storage._oneofField {return v}
return 0
}
set {_uniqueStorage()._oneofField = .oneofUint32(newValue)}
}
var oneofNestedMessage: Proto3ArenaUnittest_TestAllTypes.NestedMessage {
get {
if case .oneofNestedMessage(let v)? = _storage._oneofField {return v}
return Proto3ArenaUnittest_TestAllTypes.NestedMessage()
}
set {_uniqueStorage()._oneofField = .oneofNestedMessage(newValue)}
}
var oneofString: String {
get {
if case .oneofString(let v)? = _storage._oneofField {return v}
return String()
}
set {_uniqueStorage()._oneofField = .oneofString(newValue)}
}
var oneofBytes: Data {
get {
if case .oneofBytes(let v)? = _storage._oneofField {return v}
return SwiftProtobuf.Internal.emptyData
}
set {_uniqueStorage()._oneofField = .oneofBytes(newValue)}
}
var unknownFields = SwiftProtobuf.UnknownStorage()
enum OneOf_OneofField: Equatable {
case oneofUint32(UInt32)
case oneofNestedMessage(Proto3ArenaUnittest_TestAllTypes.NestedMessage)
case oneofString(String)
case oneofBytes(Data)
#if !swift(>=4.1)
static func ==(lhs: Proto3ArenaUnittest_TestAllTypes.OneOf_OneofField, rhs: Proto3ArenaUnittest_TestAllTypes.OneOf_OneofField) -> Bool {
switch (lhs, rhs) {
case (.oneofUint32(let l), .oneofUint32(let r)): return l == r
case (.oneofNestedMessage(let l), .oneofNestedMessage(let r)): return l == r
case (.oneofString(let l), .oneofString(let r)): return l == r
case (.oneofBytes(let l), .oneofBytes(let r)): return l == r
default: return false
}
}
#endif
}
enum NestedEnum: SwiftProtobuf.Enum {
typealias RawValue = Int
case zero // = 0
case foo // = 1
case bar // = 2
case baz // = 3
/// Intentionally negative.
case neg // = -1
case UNRECOGNIZED(Int)
init() {
self = .zero
}
init?(rawValue: Int) {
switch rawValue {
case -1: self = .neg
case 0: self = .zero
case 1: self = .foo
case 2: self = .bar
case 3: self = .baz
default: self = .UNRECOGNIZED(rawValue)
}
}
var rawValue: Int {
switch self {
case .neg: return -1
case .zero: return 0
case .foo: return 1
case .bar: return 2
case .baz: return 3
case .UNRECOGNIZED(let i): return i
}
}
}
struct NestedMessage {
// SwiftProtobuf.Message conformance is added in an extension below. See the
// `Message` and `Message+*Additions` files in the SwiftProtobuf library for
// methods supported on all messages.
/// The field name "b" fails to compile in proto1 because it conflicts with
/// a local variable named "b" in one of the generated methods. Doh.
/// This file needs to compile in proto1 to test backwards-compatibility.
var bb: Int32 = 0
var unknownFields = SwiftProtobuf.UnknownStorage()
init() {}
}
init() {}
fileprivate var _storage = _StorageClass.defaultInstance
}
#if swift(>=4.2)
extension Proto3ArenaUnittest_TestAllTypes.NestedEnum: CaseIterable {
// The compiler won't synthesize support with the UNRECOGNIZED case.
static var allCases: [Proto3ArenaUnittest_TestAllTypes.NestedEnum] = [
.zero,
.foo,
.bar,
.baz,
.neg,
]
}
#endif // swift(>=4.2)
struct Proto3ArenaUnittest_TestPackedTypes {
// SwiftProtobuf.Message conformance is added in an extension below. See the
// `Message` and `Message+*Additions` files in the SwiftProtobuf library for
// methods supported on all messages.
var packedInt32: [Int32] = []
var packedInt64: [Int64] = []
var packedUint32: [UInt32] = []
var packedUint64: [UInt64] = []
var packedSint32: [Int32] = []
var packedSint64: [Int64] = []
var packedFixed32: [UInt32] = []
var packedFixed64: [UInt64] = []
var packedSfixed32: [Int32] = []
var packedSfixed64: [Int64] = []
var packedFloat: [Float] = []
var packedDouble: [Double] = []
var packedBool: [Bool] = []
var packedEnum: [Proto3ArenaUnittest_ForeignEnum] = []
var unknownFields = SwiftProtobuf.UnknownStorage()
init() {}
}
/// Explicitly set packed to false
struct Proto3ArenaUnittest_TestUnpackedTypes {
// SwiftProtobuf.Message conformance is added in an extension below. See the
// `Message` and `Message+*Additions` files in the SwiftProtobuf library for
// methods supported on all messages.
var repeatedInt32: [Int32] = []
var repeatedInt64: [Int64] = []
var repeatedUint32: [UInt32] = []
var repeatedUint64: [UInt64] = []
var repeatedSint32: [Int32] = []
var repeatedSint64: [Int64] = []
var repeatedFixed32: [UInt32] = []
var repeatedFixed64: [UInt64] = []
var repeatedSfixed32: [Int32] = []
var repeatedSfixed64: [Int64] = []
var repeatedFloat: [Float] = []
var repeatedDouble: [Double] = []
var repeatedBool: [Bool] = []
var repeatedNestedEnum: [Proto3ArenaUnittest_TestAllTypes.NestedEnum] = []
var unknownFields = SwiftProtobuf.UnknownStorage()
init() {}
}
/// This proto includes a recusively nested message.
struct Proto3ArenaUnittest_NestedTestAllTypes {
// SwiftProtobuf.Message conformance is added in an extension below. See the
// `Message` and `Message+*Additions` files in the SwiftProtobuf library for
// methods supported on all messages.
var child: Proto3ArenaUnittest_NestedTestAllTypes {
get {return _storage._child ?? Proto3ArenaUnittest_NestedTestAllTypes()}
set {_uniqueStorage()._child = newValue}
}
/// Returns true if `child` has been explicitly set.
var hasChild: Bool {return _storage._child != nil}
/// Clears the value of `child`. Subsequent reads from it will return its default value.
mutating func clearChild() {_uniqueStorage()._child = nil}
var payload: Proto3ArenaUnittest_TestAllTypes {
get {return _storage._payload ?? Proto3ArenaUnittest_TestAllTypes()}
set {_uniqueStorage()._payload = newValue}
}
/// Returns true if `payload` has been explicitly set.
var hasPayload: Bool {return _storage._payload != nil}
/// Clears the value of `payload`. Subsequent reads from it will return its default value.
mutating func clearPayload() {_uniqueStorage()._payload = nil}
var repeatedChild: [Proto3ArenaUnittest_NestedTestAllTypes] {
get {return _storage._repeatedChild}
set {_uniqueStorage()._repeatedChild = newValue}
}
var unknownFields = SwiftProtobuf.UnknownStorage()
init() {}
fileprivate var _storage = _StorageClass.defaultInstance
}
/// Define these after TestAllTypes to make sure the compiler can handle
/// that.
struct Proto3ArenaUnittest_ForeignMessage {
// SwiftProtobuf.Message conformance is added in an extension below. See the
// `Message` and `Message+*Additions` files in the SwiftProtobuf library for
// methods supported on all messages.
var c: Int32 = 0
var unknownFields = SwiftProtobuf.UnknownStorage()
init() {}
}
/// TestEmptyMessage is used to test behavior of unknown fields.
struct Proto3ArenaUnittest_TestEmptyMessage {
// SwiftProtobuf.Message conformance is added in an extension below. See the
// `Message` and `Message+*Additions` files in the SwiftProtobuf library for
// methods supported on all messages.
var unknownFields = SwiftProtobuf.UnknownStorage()
init() {}
}
// MARK: - Code below here is support for the SwiftProtobuf runtime.
fileprivate let _protobuf_package = "proto3_arena_unittest"
extension Proto3ArenaUnittest_ForeignEnum: SwiftProtobuf._ProtoNameProviding {
static let _protobuf_nameMap: SwiftProtobuf._NameMap = [
0: .same(proto: "FOREIGN_ZERO"),
4: .same(proto: "FOREIGN_FOO"),
5: .same(proto: "FOREIGN_BAR"),
6: .same(proto: "FOREIGN_BAZ"),
]
}
extension Proto3ArenaUnittest_TestAllTypes: SwiftProtobuf.Message, SwiftProtobuf._MessageImplementationBase, SwiftProtobuf._ProtoNameProviding {
static let protoMessageName: String = _protobuf_package + ".TestAllTypes"
static let _protobuf_nameMap: SwiftProtobuf._NameMap = [
1: .standard(proto: "optional_int32"),
2: .standard(proto: "optional_int64"),
3: .standard(proto: "optional_uint32"),
4: .standard(proto: "optional_uint64"),
5: .standard(proto: "optional_sint32"),
6: .standard(proto: "optional_sint64"),
7: .standard(proto: "optional_fixed32"),
8: .standard(proto: "optional_fixed64"),
9: .standard(proto: "optional_sfixed32"),
10: .standard(proto: "optional_sfixed64"),
11: .standard(proto: "optional_float"),
12: .standard(proto: "optional_double"),
13: .standard(proto: "optional_bool"),
14: .standard(proto: "optional_string"),
15: .standard(proto: "optional_bytes"),
18: .standard(proto: "optional_nested_message"),
19: .standard(proto: "optional_foreign_message"),
20: .standard(proto: "optional_import_message"),
21: .standard(proto: "optional_nested_enum"),
22: .standard(proto: "optional_foreign_enum"),
24: .standard(proto: "optional_string_piece"),
25: .standard(proto: "optional_cord"),
26: .standard(proto: "optional_public_import_message"),
27: .standard(proto: "optional_lazy_message"),
115: .standard(proto: "optional_lazy_import_message"),
31: .standard(proto: "repeated_int32"),
32: .standard(proto: "repeated_int64"),
33: .standard(proto: "repeated_uint32"),
34: .standard(proto: "repeated_uint64"),
35: .standard(proto: "repeated_sint32"),
36: .standard(proto: "repeated_sint64"),
37: .standard(proto: "repeated_fixed32"),
38: .standard(proto: "repeated_fixed64"),
39: .standard(proto: "repeated_sfixed32"),
40: .standard(proto: "repeated_sfixed64"),
41: .standard(proto: "repeated_float"),
42: .standard(proto: "repeated_double"),
43: .standard(proto: "repeated_bool"),
44: .standard(proto: "repeated_string"),
45: .standard(proto: "repeated_bytes"),
48: .standard(proto: "repeated_nested_message"),
49: .standard(proto: "repeated_foreign_message"),
50: .standard(proto: "repeated_import_message"),
51: .standard(proto: "repeated_nested_enum"),
52: .standard(proto: "repeated_foreign_enum"),
54: .standard(proto: "repeated_string_piece"),
55: .standard(proto: "repeated_cord"),
57: .standard(proto: "repeated_lazy_message"),
111: .standard(proto: "oneof_uint32"),
112: .standard(proto: "oneof_nested_message"),
113: .standard(proto: "oneof_string"),
114: .standard(proto: "oneof_bytes"),
]
fileprivate class _StorageClass {
var _optionalInt32: Int32 = 0
var _optionalInt64: Int64 = 0
var _optionalUint32: UInt32 = 0
var _optionalUint64: UInt64 = 0
var _optionalSint32: Int32 = 0
var _optionalSint64: Int64 = 0
var _optionalFixed32: UInt32 = 0
var _optionalFixed64: UInt64 = 0
var _optionalSfixed32: Int32 = 0
var _optionalSfixed64: Int64 = 0
var _optionalFloat: Float = 0
var _optionalDouble: Double = 0
var _optionalBool: Bool = false
var _optionalString: String = String()
var _optionalBytes: Data = SwiftProtobuf.Internal.emptyData
var _optionalNestedMessage: Proto3ArenaUnittest_TestAllTypes.NestedMessage? = nil
var _optionalForeignMessage: Proto3ArenaUnittest_ForeignMessage? = nil
var _optionalImportMessage: ProtobufUnittestImport_ImportMessage? = nil
var _optionalNestedEnum: Proto3ArenaUnittest_TestAllTypes.NestedEnum = .zero
var _optionalForeignEnum: Proto3ArenaUnittest_ForeignEnum = .foreignZero
var _optionalStringPiece: String = String()
var _optionalCord: String = String()
var _optionalPublicImportMessage: ProtobufUnittestImport_PublicImportMessage? = nil
var _optionalLazyMessage: Proto3ArenaUnittest_TestAllTypes.NestedMessage? = nil
var _optionalLazyImportMessage: ProtobufUnittestImport_ImportMessage? = nil
var _repeatedInt32: [Int32] = []
var _repeatedInt64: [Int64] = []
var _repeatedUint32: [UInt32] = []
var _repeatedUint64: [UInt64] = []
var _repeatedSint32: [Int32] = []
var _repeatedSint64: [Int64] = []
var _repeatedFixed32: [UInt32] = []
var _repeatedFixed64: [UInt64] = []
var _repeatedSfixed32: [Int32] = []
var _repeatedSfixed64: [Int64] = []
var _repeatedFloat: [Float] = []
var _repeatedDouble: [Double] = []
var _repeatedBool: [Bool] = []
var _repeatedString: [String] = []
var _repeatedBytes: [Data] = []
var _repeatedNestedMessage: [Proto3ArenaUnittest_TestAllTypes.NestedMessage] = []
var _repeatedForeignMessage: [Proto3ArenaUnittest_ForeignMessage] = []
var _repeatedImportMessage: [ProtobufUnittestImport_ImportMessage] = []
var _repeatedNestedEnum: [Proto3ArenaUnittest_TestAllTypes.NestedEnum] = []
var _repeatedForeignEnum: [Proto3ArenaUnittest_ForeignEnum] = []
var _repeatedStringPiece: [String] = []
var _repeatedCord: [String] = []
var _repeatedLazyMessage: [Proto3ArenaUnittest_TestAllTypes.NestedMessage] = []
var _oneofField: Proto3ArenaUnittest_TestAllTypes.OneOf_OneofField?
static let defaultInstance = _StorageClass()
private init() {}
init(copying source: _StorageClass) {
_optionalInt32 = source._optionalInt32
_optionalInt64 = source._optionalInt64
_optionalUint32 = source._optionalUint32
_optionalUint64 = source._optionalUint64
_optionalSint32 = source._optionalSint32
_optionalSint64 = source._optionalSint64
_optionalFixed32 = source._optionalFixed32
_optionalFixed64 = source._optionalFixed64
_optionalSfixed32 = source._optionalSfixed32
_optionalSfixed64 = source._optionalSfixed64
_optionalFloat = source._optionalFloat
_optionalDouble = source._optionalDouble
_optionalBool = source._optionalBool
_optionalString = source._optionalString
_optionalBytes = source._optionalBytes
_optionalNestedMessage = source._optionalNestedMessage
_optionalForeignMessage = source._optionalForeignMessage
_optionalImportMessage = source._optionalImportMessage
_optionalNestedEnum = source._optionalNestedEnum
_optionalForeignEnum = source._optionalForeignEnum
_optionalStringPiece = source._optionalStringPiece
_optionalCord = source._optionalCord
_optionalPublicImportMessage = source._optionalPublicImportMessage
_optionalLazyMessage = source._optionalLazyMessage
_optionalLazyImportMessage = source._optionalLazyImportMessage
_repeatedInt32 = source._repeatedInt32
_repeatedInt64 = source._repeatedInt64
_repeatedUint32 = source._repeatedUint32
_repeatedUint64 = source._repeatedUint64
_repeatedSint32 = source._repeatedSint32
_repeatedSint64 = source._repeatedSint64
_repeatedFixed32 = source._repeatedFixed32
_repeatedFixed64 = source._repeatedFixed64
_repeatedSfixed32 = source._repeatedSfixed32
_repeatedSfixed64 = source._repeatedSfixed64
_repeatedFloat = source._repeatedFloat
_repeatedDouble = source._repeatedDouble
_repeatedBool = source._repeatedBool
_repeatedString = source._repeatedString
_repeatedBytes = source._repeatedBytes
_repeatedNestedMessage = source._repeatedNestedMessage
_repeatedForeignMessage = source._repeatedForeignMessage
_repeatedImportMessage = source._repeatedImportMessage
_repeatedNestedEnum = source._repeatedNestedEnum
_repeatedForeignEnum = source._repeatedForeignEnum
_repeatedStringPiece = source._repeatedStringPiece
_repeatedCord = source._repeatedCord
_repeatedLazyMessage = source._repeatedLazyMessage
_oneofField = source._oneofField
}
}
fileprivate mutating func _uniqueStorage() -> _StorageClass {
if !isKnownUniquelyReferenced(&_storage) {
_storage = _StorageClass(copying: _storage)
}
return _storage
}
mutating func decodeMessage<D: SwiftProtobuf.Decoder>(decoder: inout D) throws {
_ = _uniqueStorage()
try withExtendedLifetime(_storage) { (_storage: _StorageClass) in
while let fieldNumber = try decoder.nextFieldNumber() {
switch fieldNumber {
case 1: try decoder.decodeSingularInt32Field(value: &_storage._optionalInt32)
case 2: try decoder.decodeSingularInt64Field(value: &_storage._optionalInt64)
case 3: try decoder.decodeSingularUInt32Field(value: &_storage._optionalUint32)
case 4: try decoder.decodeSingularUInt64Field(value: &_storage._optionalUint64)
case 5: try decoder.decodeSingularSInt32Field(value: &_storage._optionalSint32)
case 6: try decoder.decodeSingularSInt64Field(value: &_storage._optionalSint64)
case 7: try decoder.decodeSingularFixed32Field(value: &_storage._optionalFixed32)
case 8: try decoder.decodeSingularFixed64Field(value: &_storage._optionalFixed64)
case 9: try decoder.decodeSingularSFixed32Field(value: &_storage._optionalSfixed32)
case 10: try decoder.decodeSingularSFixed64Field(value: &_storage._optionalSfixed64)
case 11: try decoder.decodeSingularFloatField(value: &_storage._optionalFloat)
case 12: try decoder.decodeSingularDoubleField(value: &_storage._optionalDouble)
case 13: try decoder.decodeSingularBoolField(value: &_storage._optionalBool)
case 14: try decoder.decodeSingularStringField(value: &_storage._optionalString)
case 15: try decoder.decodeSingularBytesField(value: &_storage._optionalBytes)
case 18: try decoder.decodeSingularMessageField(value: &_storage._optionalNestedMessage)
case 19: try decoder.decodeSingularMessageField(value: &_storage._optionalForeignMessage)
case 20: try decoder.decodeSingularMessageField(value: &_storage._optionalImportMessage)
case 21: try decoder.decodeSingularEnumField(value: &_storage._optionalNestedEnum)
case 22: try decoder.decodeSingularEnumField(value: &_storage._optionalForeignEnum)
case 24: try decoder.decodeSingularStringField(value: &_storage._optionalStringPiece)
case 25: try decoder.decodeSingularStringField(value: &_storage._optionalCord)
case 26: try decoder.decodeSingularMessageField(value: &_storage._optionalPublicImportMessage)
case 27: try decoder.decodeSingularMessageField(value: &_storage._optionalLazyMessage)
case 31: try decoder.decodeRepeatedInt32Field(value: &_storage._repeatedInt32)
case 32: try decoder.decodeRepeatedInt64Field(value: &_storage._repeatedInt64)
case 33: try decoder.decodeRepeatedUInt32Field(value: &_storage._repeatedUint32)
case 34: try decoder.decodeRepeatedUInt64Field(value: &_storage._repeatedUint64)
case 35: try decoder.decodeRepeatedSInt32Field(value: &_storage._repeatedSint32)
case 36: try decoder.decodeRepeatedSInt64Field(value: &_storage._repeatedSint64)
case 37: try decoder.decodeRepeatedFixed32Field(value: &_storage._repeatedFixed32)
case 38: try decoder.decodeRepeatedFixed64Field(value: &_storage._repeatedFixed64)
case 39: try decoder.decodeRepeatedSFixed32Field(value: &_storage._repeatedSfixed32)
case 40: try decoder.decodeRepeatedSFixed64Field(value: &_storage._repeatedSfixed64)
case 41: try decoder.decodeRepeatedFloatField(value: &_storage._repeatedFloat)
case 42: try decoder.decodeRepeatedDoubleField(value: &_storage._repeatedDouble)
case 43: try decoder.decodeRepeatedBoolField(value: &_storage._repeatedBool)
case 44: try decoder.decodeRepeatedStringField(value: &_storage._repeatedString)
case 45: try decoder.decodeRepeatedBytesField(value: &_storage._repeatedBytes)
case 48: try decoder.decodeRepeatedMessageField(value: &_storage._repeatedNestedMessage)
case 49: try decoder.decodeRepeatedMessageField(value: &_storage._repeatedForeignMessage)
case 50: try decoder.decodeRepeatedMessageField(value: &_storage._repeatedImportMessage)
case 51: try decoder.decodeRepeatedEnumField(value: &_storage._repeatedNestedEnum)
case 52: try decoder.decodeRepeatedEnumField(value: &_storage._repeatedForeignEnum)
case 54: try decoder.decodeRepeatedStringField(value: &_storage._repeatedStringPiece)
case 55: try decoder.decodeRepeatedStringField(value: &_storage._repeatedCord)
case 57: try decoder.decodeRepeatedMessageField(value: &_storage._repeatedLazyMessage)
case 111:
if _storage._oneofField != nil {try decoder.handleConflictingOneOf()}
var v: UInt32?
try decoder.decodeSingularUInt32Field(value: &v)
if let v = v {_storage._oneofField = .oneofUint32(v)}
case 112:
var v: Proto3ArenaUnittest_TestAllTypes.NestedMessage?
if let current = _storage._oneofField {
try decoder.handleConflictingOneOf()
if case .oneofNestedMessage(let m) = current {v = m}
}
try decoder.decodeSingularMessageField(value: &v)
if let v = v {_storage._oneofField = .oneofNestedMessage(v)}
case 113:
if _storage._oneofField != nil {try decoder.handleConflictingOneOf()}
var v: String?
try decoder.decodeSingularStringField(value: &v)
if let v = v {_storage._oneofField = .oneofString(v)}
case 114:
if _storage._oneofField != nil {try decoder.handleConflictingOneOf()}
var v: Data?
try decoder.decodeSingularBytesField(value: &v)
if let v = v {_storage._oneofField = .oneofBytes(v)}
case 115: try decoder.decodeSingularMessageField(value: &_storage._optionalLazyImportMessage)
default: break
}
}
}
}
func traverse<V: SwiftProtobuf.Visitor>(visitor: inout V) throws {
try withExtendedLifetime(_storage) { (_storage: _StorageClass) in
if _storage._optionalInt32 != 0 {
try visitor.visitSingularInt32Field(value: _storage._optionalInt32, fieldNumber: 1)
}
if _storage._optionalInt64 != 0 {
try visitor.visitSingularInt64Field(value: _storage._optionalInt64, fieldNumber: 2)
}
if _storage._optionalUint32 != 0 {
try visitor.visitSingularUInt32Field(value: _storage._optionalUint32, fieldNumber: 3)
}
if _storage._optionalUint64 != 0 {
try visitor.visitSingularUInt64Field(value: _storage._optionalUint64, fieldNumber: 4)
}
if _storage._optionalSint32 != 0 {
try visitor.visitSingularSInt32Field(value: _storage._optionalSint32, fieldNumber: 5)
}
if _storage._optionalSint64 != 0 {
try visitor.visitSingularSInt64Field(value: _storage._optionalSint64, fieldNumber: 6)
}
if _storage._optionalFixed32 != 0 {
try visitor.visitSingularFixed32Field(value: _storage._optionalFixed32, fieldNumber: 7)
}
if _storage._optionalFixed64 != 0 {
try visitor.visitSingularFixed64Field(value: _storage._optionalFixed64, fieldNumber: 8)
}
if _storage._optionalSfixed32 != 0 {
try visitor.visitSingularSFixed32Field(value: _storage._optionalSfixed32, fieldNumber: 9)
}
if _storage._optionalSfixed64 != 0 {
try visitor.visitSingularSFixed64Field(value: _storage._optionalSfixed64, fieldNumber: 10)
}
if _storage._optionalFloat != 0 {
try visitor.visitSingularFloatField(value: _storage._optionalFloat, fieldNumber: 11)
}
if _storage._optionalDouble != 0 {
try visitor.visitSingularDoubleField(value: _storage._optionalDouble, fieldNumber: 12)
}
if _storage._optionalBool != false {
try visitor.visitSingularBoolField(value: _storage._optionalBool, fieldNumber: 13)
}
if !_storage._optionalString.isEmpty {
try visitor.visitSingularStringField(value: _storage._optionalString, fieldNumber: 14)
}
if !_storage._optionalBytes.isEmpty {
try visitor.visitSingularBytesField(value: _storage._optionalBytes, fieldNumber: 15)
}
if let v = _storage._optionalNestedMessage {
try visitor.visitSingularMessageField(value: v, fieldNumber: 18)
}
if let v = _storage._optionalForeignMessage {
try visitor.visitSingularMessageField(value: v, fieldNumber: 19)
}
if let v = _storage._optionalImportMessage {
try visitor.visitSingularMessageField(value: v, fieldNumber: 20)
}
if _storage._optionalNestedEnum != .zero {
try visitor.visitSingularEnumField(value: _storage._optionalNestedEnum, fieldNumber: 21)
}
if _storage._optionalForeignEnum != .foreignZero {
try visitor.visitSingularEnumField(value: _storage._optionalForeignEnum, fieldNumber: 22)
}
if !_storage._optionalStringPiece.isEmpty {
try visitor.visitSingularStringField(value: _storage._optionalStringPiece, fieldNumber: 24)
}
if !_storage._optionalCord.isEmpty {
try visitor.visitSingularStringField(value: _storage._optionalCord, fieldNumber: 25)
}
if let v = _storage._optionalPublicImportMessage {
try visitor.visitSingularMessageField(value: v, fieldNumber: 26)
}
if let v = _storage._optionalLazyMessage {
try visitor.visitSingularMessageField(value: v, fieldNumber: 27)
}
if !_storage._repeatedInt32.isEmpty {
try visitor.visitPackedInt32Field(value: _storage._repeatedInt32, fieldNumber: 31)
}
if !_storage._repeatedInt64.isEmpty {
try visitor.visitPackedInt64Field(value: _storage._repeatedInt64, fieldNumber: 32)
}
if !_storage._repeatedUint32.isEmpty {
try visitor.visitPackedUInt32Field(value: _storage._repeatedUint32, fieldNumber: 33)
}
if !_storage._repeatedUint64.isEmpty {
try visitor.visitPackedUInt64Field(value: _storage._repeatedUint64, fieldNumber: 34)
}
if !_storage._repeatedSint32.isEmpty {
try visitor.visitPackedSInt32Field(value: _storage._repeatedSint32, fieldNumber: 35)
}
if !_storage._repeatedSint64.isEmpty {
try visitor.visitPackedSInt64Field(value: _storage._repeatedSint64, fieldNumber: 36)
}
if !_storage._repeatedFixed32.isEmpty {
try visitor.visitPackedFixed32Field(value: _storage._repeatedFixed32, fieldNumber: 37)
}
if !_storage._repeatedFixed64.isEmpty {
try visitor.visitPackedFixed64Field(value: _storage._repeatedFixed64, fieldNumber: 38)
}
if !_storage._repeatedSfixed32.isEmpty {
try visitor.visitPackedSFixed32Field(value: _storage._repeatedSfixed32, fieldNumber: 39)
}
if !_storage._repeatedSfixed64.isEmpty {
try visitor.visitPackedSFixed64Field(value: _storage._repeatedSfixed64, fieldNumber: 40)
}
if !_storage._repeatedFloat.isEmpty {
try visitor.visitPackedFloatField(value: _storage._repeatedFloat, fieldNumber: 41)
}
if !_storage._repeatedDouble.isEmpty {
try visitor.visitPackedDoubleField(value: _storage._repeatedDouble, fieldNumber: 42)
}
if !_storage._repeatedBool.isEmpty {
try visitor.visitPackedBoolField(value: _storage._repeatedBool, fieldNumber: 43)
}
if !_storage._repeatedString.isEmpty {
try visitor.visitRepeatedStringField(value: _storage._repeatedString, fieldNumber: 44)
}
if !_storage._repeatedBytes.isEmpty {
try visitor.visitRepeatedBytesField(value: _storage._repeatedBytes, fieldNumber: 45)
}
if !_storage._repeatedNestedMessage.isEmpty {
try visitor.visitRepeatedMessageField(value: _storage._repeatedNestedMessage, fieldNumber: 48)
}
if !_storage._repeatedForeignMessage.isEmpty {
try visitor.visitRepeatedMessageField(value: _storage._repeatedForeignMessage, fieldNumber: 49)
}
if !_storage._repeatedImportMessage.isEmpty {
try visitor.visitRepeatedMessageField(value: _storage._repeatedImportMessage, fieldNumber: 50)
}
if !_storage._repeatedNestedEnum.isEmpty {
try visitor.visitPackedEnumField(value: _storage._repeatedNestedEnum, fieldNumber: 51)
}
if !_storage._repeatedForeignEnum.isEmpty {
try visitor.visitPackedEnumField(value: _storage._repeatedForeignEnum, fieldNumber: 52)
}
if !_storage._repeatedStringPiece.isEmpty {
try visitor.visitRepeatedStringField(value: _storage._repeatedStringPiece, fieldNumber: 54)
}
if !_storage._repeatedCord.isEmpty {
try visitor.visitRepeatedStringField(value: _storage._repeatedCord, fieldNumber: 55)
}
if !_storage._repeatedLazyMessage.isEmpty {
try visitor.visitRepeatedMessageField(value: _storage._repeatedLazyMessage, fieldNumber: 57)
}
switch _storage._oneofField {
case .oneofUint32(let v)?:
try visitor.visitSingularUInt32Field(value: v, fieldNumber: 111)
case .oneofNestedMessage(let v)?:
try visitor.visitSingularMessageField(value: v, fieldNumber: 112)
case .oneofString(let v)?:
try visitor.visitSingularStringField(value: v, fieldNumber: 113)
case .oneofBytes(let v)?:
try visitor.visitSingularBytesField(value: v, fieldNumber: 114)
case nil: break
}
if let v = _storage._optionalLazyImportMessage {
try visitor.visitSingularMessageField(value: v, fieldNumber: 115)
}
}
try unknownFields.traverse(visitor: &visitor)
}
static func ==(lhs: Proto3ArenaUnittest_TestAllTypes, rhs: Proto3ArenaUnittest_TestAllTypes) -> Bool {
if lhs._storage !== rhs._storage {
let storagesAreEqual: Bool = withExtendedLifetime((lhs._storage, rhs._storage)) { (_args: (_StorageClass, _StorageClass)) in
let _storage = _args.0
let rhs_storage = _args.1
if _storage._optionalInt32 != rhs_storage._optionalInt32 {return false}
if _storage._optionalInt64 != rhs_storage._optionalInt64 {return false}
if _storage._optionalUint32 != rhs_storage._optionalUint32 {return false}
if _storage._optionalUint64 != rhs_storage._optionalUint64 {return false}
if _storage._optionalSint32 != rhs_storage._optionalSint32 {return false}
if _storage._optionalSint64 != rhs_storage._optionalSint64 {return false}
if _storage._optionalFixed32 != rhs_storage._optionalFixed32 {return false}
if _storage._optionalFixed64 != rhs_storage._optionalFixed64 {return false}
if _storage._optionalSfixed32 != rhs_storage._optionalSfixed32 {return false}
if _storage._optionalSfixed64 != rhs_storage._optionalSfixed64 {return false}
if _storage._optionalFloat != rhs_storage._optionalFloat {return false}
if _storage._optionalDouble != rhs_storage._optionalDouble {return false}
if _storage._optionalBool != rhs_storage._optionalBool {return false}
if _storage._optionalString != rhs_storage._optionalString {return false}
if _storage._optionalBytes != rhs_storage._optionalBytes {return false}
if _storage._optionalNestedMessage != rhs_storage._optionalNestedMessage {return false}
if _storage._optionalForeignMessage != rhs_storage._optionalForeignMessage {return false}
if _storage._optionalImportMessage != rhs_storage._optionalImportMessage {return false}
if _storage._optionalNestedEnum != rhs_storage._optionalNestedEnum {return false}
if _storage._optionalForeignEnum != rhs_storage._optionalForeignEnum {return false}
if _storage._optionalStringPiece != rhs_storage._optionalStringPiece {return false}
if _storage._optionalCord != rhs_storage._optionalCord {return false}
if _storage._optionalPublicImportMessage != rhs_storage._optionalPublicImportMessage {return false}
if _storage._optionalLazyMessage != rhs_storage._optionalLazyMessage {return false}
if _storage._optionalLazyImportMessage != rhs_storage._optionalLazyImportMessage {return false}
if _storage._repeatedInt32 != rhs_storage._repeatedInt32 {return false}
if _storage._repeatedInt64 != rhs_storage._repeatedInt64 {return false}
if _storage._repeatedUint32 != rhs_storage._repeatedUint32 {return false}
if _storage._repeatedUint64 != rhs_storage._repeatedUint64 {return false}
if _storage._repeatedSint32 != rhs_storage._repeatedSint32 {return false}
if _storage._repeatedSint64 != rhs_storage._repeatedSint64 {return false}
if _storage._repeatedFixed32 != rhs_storage._repeatedFixed32 {return false}
if _storage._repeatedFixed64 != rhs_storage._repeatedFixed64 {return false}
if _storage._repeatedSfixed32 != rhs_storage._repeatedSfixed32 {return false}
if _storage._repeatedSfixed64 != rhs_storage._repeatedSfixed64 {return false}
if _storage._repeatedFloat != rhs_storage._repeatedFloat {return false}
if _storage._repeatedDouble != rhs_storage._repeatedDouble {return false}
if _storage._repeatedBool != rhs_storage._repeatedBool {return false}
if _storage._repeatedString != rhs_storage._repeatedString {return false}
if _storage._repeatedBytes != rhs_storage._repeatedBytes {return false}
if _storage._repeatedNestedMessage != rhs_storage._repeatedNestedMessage {return false}
if _storage._repeatedForeignMessage != rhs_storage._repeatedForeignMessage {return false}
if _storage._repeatedImportMessage != rhs_storage._repeatedImportMessage {return false}
if _storage._repeatedNestedEnum != rhs_storage._repeatedNestedEnum {return false}
if _storage._repeatedForeignEnum != rhs_storage._repeatedForeignEnum {return false}
if _storage._repeatedStringPiece != rhs_storage._repeatedStringPiece {return false}
if _storage._repeatedCord != rhs_storage._repeatedCord {return false}
if _storage._repeatedLazyMessage != rhs_storage._repeatedLazyMessage {return false}
if _storage._oneofField != rhs_storage._oneofField {return false}
return true
}
if !storagesAreEqual {return false}
}
if lhs.unknownFields != rhs.unknownFields {return false}
return true
}
}
extension Proto3ArenaUnittest_TestAllTypes.NestedEnum: SwiftProtobuf._ProtoNameProviding {
static let _protobuf_nameMap: SwiftProtobuf._NameMap = [
-1: .same(proto: "NEG"),
0: .same(proto: "ZERO"),
1: .same(proto: "FOO"),
2: .same(proto: "BAR"),
3: .same(proto: "BAZ"),
]
}
extension Proto3ArenaUnittest_TestAllTypes.NestedMessage: SwiftProtobuf.Message, SwiftProtobuf._MessageImplementationBase, SwiftProtobuf._ProtoNameProviding {
static let protoMessageName: String = Proto3ArenaUnittest_TestAllTypes.protoMessageName + ".NestedMessage"
static let _protobuf_nameMap: SwiftProtobuf._NameMap = [
1: .same(proto: "bb"),
]
mutating func decodeMessage<D: SwiftProtobuf.Decoder>(decoder: inout D) throws {
while let fieldNumber = try decoder.nextFieldNumber() {
switch fieldNumber {
case 1: try decoder.decodeSingularInt32Field(value: &self.bb)
default: break
}
}
}
func traverse<V: SwiftProtobuf.Visitor>(visitor: inout V) throws {
if self.bb != 0 {
try visitor.visitSingularInt32Field(value: self.bb, fieldNumber: 1)
}
try unknownFields.traverse(visitor: &visitor)
}
static func ==(lhs: Proto3ArenaUnittest_TestAllTypes.NestedMessage, rhs: Proto3ArenaUnittest_TestAllTypes.NestedMessage) -> Bool {
if lhs.bb != rhs.bb {return false}
if lhs.unknownFields != rhs.unknownFields {return false}
return true
}
}
extension Proto3ArenaUnittest_TestPackedTypes: SwiftProtobuf.Message, SwiftProtobuf._MessageImplementationBase, SwiftProtobuf._ProtoNameProviding {
static let protoMessageName: String = _protobuf_package + ".TestPackedTypes"
static let _protobuf_nameMap: SwiftProtobuf._NameMap = [
90: .standard(proto: "packed_int32"),
91: .standard(proto: "packed_int64"),
92: .standard(proto: "packed_uint32"),
93: .standard(proto: "packed_uint64"),
94: .standard(proto: "packed_sint32"),
95: .standard(proto: "packed_sint64"),
96: .standard(proto: "packed_fixed32"),
97: .standard(proto: "packed_fixed64"),
98: .standard(proto: "packed_sfixed32"),
99: .standard(proto: "packed_sfixed64"),
100: .standard(proto: "packed_float"),
101: .standard(proto: "packed_double"),
102: .standard(proto: "packed_bool"),
103: .standard(proto: "packed_enum"),
]
mutating func decodeMessage<D: SwiftProtobuf.Decoder>(decoder: inout D) throws {
while let fieldNumber = try decoder.nextFieldNumber() {
switch fieldNumber {
case 90: try decoder.decodeRepeatedInt32Field(value: &self.packedInt32)
case 91: try decoder.decodeRepeatedInt64Field(value: &self.packedInt64)
case 92: try decoder.decodeRepeatedUInt32Field(value: &self.packedUint32)
case 93: try decoder.decodeRepeatedUInt64Field(value: &self.packedUint64)
case 94: try decoder.decodeRepeatedSInt32Field(value: &self.packedSint32)
case 95: try decoder.decodeRepeatedSInt64Field(value: &self.packedSint64)
case 96: try decoder.decodeRepeatedFixed32Field(value: &self.packedFixed32)
case 97: try decoder.decodeRepeatedFixed64Field(value: &self.packedFixed64)
case 98: try decoder.decodeRepeatedSFixed32Field(value: &self.packedSfixed32)
case 99: try decoder.decodeRepeatedSFixed64Field(value: &self.packedSfixed64)
case 100: try decoder.decodeRepeatedFloatField(value: &self.packedFloat)
case 101: try decoder.decodeRepeatedDoubleField(value: &self.packedDouble)
case 102: try decoder.decodeRepeatedBoolField(value: &self.packedBool)
case 103: try decoder.decodeRepeatedEnumField(value: &self.packedEnum)
default: break
}
}
}
func traverse<V: SwiftProtobuf.Visitor>(visitor: inout V) throws {
if !self.packedInt32.isEmpty {
try visitor.visitPackedInt32Field(value: self.packedInt32, fieldNumber: 90)
}
if !self.packedInt64.isEmpty {
try visitor.visitPackedInt64Field(value: self.packedInt64, fieldNumber: 91)
}
if !self.packedUint32.isEmpty {
try visitor.visitPackedUInt32Field(value: self.packedUint32, fieldNumber: 92)
}
if !self.packedUint64.isEmpty {
try visitor.visitPackedUInt64Field(value: self.packedUint64, fieldNumber: 93)
}
if !self.packedSint32.isEmpty {
try visitor.visitPackedSInt32Field(value: self.packedSint32, fieldNumber: 94)
}
if !self.packedSint64.isEmpty {
try visitor.visitPackedSInt64Field(value: self.packedSint64, fieldNumber: 95)
}
if !self.packedFixed32.isEmpty {
try visitor.visitPackedFixed32Field(value: self.packedFixed32, fieldNumber: 96)
}
if !self.packedFixed64.isEmpty {
try visitor.visitPackedFixed64Field(value: self.packedFixed64, fieldNumber: 97)
}
if !self.packedSfixed32.isEmpty {
try visitor.visitPackedSFixed32Field(value: self.packedSfixed32, fieldNumber: 98)
}
if !self.packedSfixed64.isEmpty {
try visitor.visitPackedSFixed64Field(value: self.packedSfixed64, fieldNumber: 99)
}
if !self.packedFloat.isEmpty {
try visitor.visitPackedFloatField(value: self.packedFloat, fieldNumber: 100)
}
if !self.packedDouble.isEmpty {
try visitor.visitPackedDoubleField(value: self.packedDouble, fieldNumber: 101)
}
if !self.packedBool.isEmpty {
try visitor.visitPackedBoolField(value: self.packedBool, fieldNumber: 102)
}
if !self.packedEnum.isEmpty {
try visitor.visitPackedEnumField(value: self.packedEnum, fieldNumber: 103)
}
try unknownFields.traverse(visitor: &visitor)
}
static func ==(lhs: Proto3ArenaUnittest_TestPackedTypes, rhs: Proto3ArenaUnittest_TestPackedTypes) -> Bool {
if lhs.packedInt32 != rhs.packedInt32 {return false}
if lhs.packedInt64 != rhs.packedInt64 {return false}
if lhs.packedUint32 != rhs.packedUint32 {return false}
if lhs.packedUint64 != rhs.packedUint64 {return false}
if lhs.packedSint32 != rhs.packedSint32 {return false}
if lhs.packedSint64 != rhs.packedSint64 {return false}
if lhs.packedFixed32 != rhs.packedFixed32 {return false}
if lhs.packedFixed64 != rhs.packedFixed64 {return false}
if lhs.packedSfixed32 != rhs.packedSfixed32 {return false}
if lhs.packedSfixed64 != rhs.packedSfixed64 {return false}
if lhs.packedFloat != rhs.packedFloat {return false}
if lhs.packedDouble != rhs.packedDouble {return false}
if lhs.packedBool != rhs.packedBool {return false}
if lhs.packedEnum != rhs.packedEnum {return false}
if lhs.unknownFields != rhs.unknownFields {return false}
return true
}
}
extension Proto3ArenaUnittest_TestUnpackedTypes: SwiftProtobuf.Message, SwiftProtobuf._MessageImplementationBase, SwiftProtobuf._ProtoNameProviding {
static let protoMessageName: String = _protobuf_package + ".TestUnpackedTypes"
static let _protobuf_nameMap: SwiftProtobuf._NameMap = [
1: .standard(proto: "repeated_int32"),
2: .standard(proto: "repeated_int64"),
3: .standard(proto: "repeated_uint32"),
4: .standard(proto: "repeated_uint64"),
5: .standard(proto: "repeated_sint32"),
6: .standard(proto: "repeated_sint64"),
7: .standard(proto: "repeated_fixed32"),
8: .standard(proto: "repeated_fixed64"),
9: .standard(proto: "repeated_sfixed32"),
10: .standard(proto: "repeated_sfixed64"),
11: .standard(proto: "repeated_float"),
12: .standard(proto: "repeated_double"),
13: .standard(proto: "repeated_bool"),
14: .standard(proto: "repeated_nested_enum"),
]
mutating func decodeMessage<D: SwiftProtobuf.Decoder>(decoder: inout D) throws {
while let fieldNumber = try decoder.nextFieldNumber() {
switch fieldNumber {
case 1: try decoder.decodeRepeatedInt32Field(value: &self.repeatedInt32)
case 2: try decoder.decodeRepeatedInt64Field(value: &self.repeatedInt64)
case 3: try decoder.decodeRepeatedUInt32Field(value: &self.repeatedUint32)
case 4: try decoder.decodeRepeatedUInt64Field(value: &self.repeatedUint64)
case 5: try decoder.decodeRepeatedSInt32Field(value: &self.repeatedSint32)
case 6: try decoder.decodeRepeatedSInt64Field(value: &self.repeatedSint64)
case 7: try decoder.decodeRepeatedFixed32Field(value: &self.repeatedFixed32)
case 8: try decoder.decodeRepeatedFixed64Field(value: &self.repeatedFixed64)
case 9: try decoder.decodeRepeatedSFixed32Field(value: &self.repeatedSfixed32)
case 10: try decoder.decodeRepeatedSFixed64Field(value: &self.repeatedSfixed64)
case 11: try decoder.decodeRepeatedFloatField(value: &self.repeatedFloat)
case 12: try decoder.decodeRepeatedDoubleField(value: &self.repeatedDouble)
case 13: try decoder.decodeRepeatedBoolField(value: &self.repeatedBool)
case 14: try decoder.decodeRepeatedEnumField(value: &self.repeatedNestedEnum)
default: break
}
}
}
func traverse<V: SwiftProtobuf.Visitor>(visitor: inout V) throws {
if !self.repeatedInt32.isEmpty {
try visitor.visitRepeatedInt32Field(value: self.repeatedInt32, fieldNumber: 1)
}
if !self.repeatedInt64.isEmpty {
try visitor.visitRepeatedInt64Field(value: self.repeatedInt64, fieldNumber: 2)
}
if !self.repeatedUint32.isEmpty {
try visitor.visitRepeatedUInt32Field(value: self.repeatedUint32, fieldNumber: 3)
}
if !self.repeatedUint64.isEmpty {
try visitor.visitRepeatedUInt64Field(value: self.repeatedUint64, fieldNumber: 4)
}
if !self.repeatedSint32.isEmpty {
try visitor.visitRepeatedSInt32Field(value: self.repeatedSint32, fieldNumber: 5)
}
if !self.repeatedSint64.isEmpty {
try visitor.visitRepeatedSInt64Field(value: self.repeatedSint64, fieldNumber: 6)
}
if !self.repeatedFixed32.isEmpty {
try visitor.visitRepeatedFixed32Field(value: self.repeatedFixed32, fieldNumber: 7)
}
if !self.repeatedFixed64.isEmpty {
try visitor.visitRepeatedFixed64Field(value: self.repeatedFixed64, fieldNumber: 8)
}
if !self.repeatedSfixed32.isEmpty {
try visitor.visitRepeatedSFixed32Field(value: self.repeatedSfixed32, fieldNumber: 9)
}
if !self.repeatedSfixed64.isEmpty {
try visitor.visitRepeatedSFixed64Field(value: self.repeatedSfixed64, fieldNumber: 10)
}
if !self.repeatedFloat.isEmpty {
try visitor.visitRepeatedFloatField(value: self.repeatedFloat, fieldNumber: 11)
}
if !self.repeatedDouble.isEmpty {
try visitor.visitRepeatedDoubleField(value: self.repeatedDouble, fieldNumber: 12)
}
if !self.repeatedBool.isEmpty {
try visitor.visitRepeatedBoolField(value: self.repeatedBool, fieldNumber: 13)
}
if !self.repeatedNestedEnum.isEmpty {
try visitor.visitRepeatedEnumField(value: self.repeatedNestedEnum, fieldNumber: 14)
}
try unknownFields.traverse(visitor: &visitor)
}
static func ==(lhs: Proto3ArenaUnittest_TestUnpackedTypes, rhs: Proto3ArenaUnittest_TestUnpackedTypes) -> Bool {
if lhs.repeatedInt32 != rhs.repeatedInt32 {return false}
if lhs.repeatedInt64 != rhs.repeatedInt64 {return false}
if lhs.repeatedUint32 != rhs.repeatedUint32 {return false}
if lhs.repeatedUint64 != rhs.repeatedUint64 {return false}
if lhs.repeatedSint32 != rhs.repeatedSint32 {return false}
if lhs.repeatedSint64 != rhs.repeatedSint64 {return false}
if lhs.repeatedFixed32 != rhs.repeatedFixed32 {return false}
if lhs.repeatedFixed64 != rhs.repeatedFixed64 {return false}
if lhs.repeatedSfixed32 != rhs.repeatedSfixed32 {return false}
if lhs.repeatedSfixed64 != rhs.repeatedSfixed64 {return false}
if lhs.repeatedFloat != rhs.repeatedFloat {return false}
if lhs.repeatedDouble != rhs.repeatedDouble {return false}
if lhs.repeatedBool != rhs.repeatedBool {return false}
if lhs.repeatedNestedEnum != rhs.repeatedNestedEnum {return false}
if lhs.unknownFields != rhs.unknownFields {return false}
return true
}
}
extension Proto3ArenaUnittest_NestedTestAllTypes: SwiftProtobuf.Message, SwiftProtobuf._MessageImplementationBase, SwiftProtobuf._ProtoNameProviding {
static let protoMessageName: String = _protobuf_package + ".NestedTestAllTypes"
static let _protobuf_nameMap: SwiftProtobuf._NameMap = [
1: .same(proto: "child"),
2: .same(proto: "payload"),
3: .standard(proto: "repeated_child"),
]
fileprivate class _StorageClass {
var _child: Proto3ArenaUnittest_NestedTestAllTypes? = nil
var _payload: Proto3ArenaUnittest_TestAllTypes? = nil
var _repeatedChild: [Proto3ArenaUnittest_NestedTestAllTypes] = []
static let defaultInstance = _StorageClass()
private init() {}
init(copying source: _StorageClass) {
_child = source._child
_payload = source._payload
_repeatedChild = source._repeatedChild
}
}
fileprivate mutating func _uniqueStorage() -> _StorageClass {
if !isKnownUniquelyReferenced(&_storage) {
_storage = _StorageClass(copying: _storage)
}
return _storage
}
mutating func decodeMessage<D: SwiftProtobuf.Decoder>(decoder: inout D) throws {
_ = _uniqueStorage()
try withExtendedLifetime(_storage) { (_storage: _StorageClass) in
while let fieldNumber = try decoder.nextFieldNumber() {
switch fieldNumber {
case 1: try decoder.decodeSingularMessageField(value: &_storage._child)
case 2: try decoder.decodeSingularMessageField(value: &_storage._payload)
case 3: try decoder.decodeRepeatedMessageField(value: &_storage._repeatedChild)
default: break
}
}
}
}
func traverse<V: SwiftProtobuf.Visitor>(visitor: inout V) throws {
try withExtendedLifetime(_storage) { (_storage: _StorageClass) in
if let v = _storage._child {
try visitor.visitSingularMessageField(value: v, fieldNumber: 1)
}
if let v = _storage._payload {
try visitor.visitSingularMessageField(value: v, fieldNumber: 2)
}
if !_storage._repeatedChild.isEmpty {
try visitor.visitRepeatedMessageField(value: _storage._repeatedChild, fieldNumber: 3)
}
}
try unknownFields.traverse(visitor: &visitor)
}
static func ==(lhs: Proto3ArenaUnittest_NestedTestAllTypes, rhs: Proto3ArenaUnittest_NestedTestAllTypes) -> Bool {
if lhs._storage !== rhs._storage {
let storagesAreEqual: Bool = withExtendedLifetime((lhs._storage, rhs._storage)) { (_args: (_StorageClass, _StorageClass)) in
let _storage = _args.0
let rhs_storage = _args.1
if _storage._child != rhs_storage._child {return false}
if _storage._payload != rhs_storage._payload {return false}
if _storage._repeatedChild != rhs_storage._repeatedChild {return false}
return true
}
if !storagesAreEqual {return false}
}
if lhs.unknownFields != rhs.unknownFields {return false}
return true
}
}
extension Proto3ArenaUnittest_ForeignMessage: SwiftProtobuf.Message, SwiftProtobuf._MessageImplementationBase, SwiftProtobuf._ProtoNameProviding {
static let protoMessageName: String = _protobuf_package + ".ForeignMessage"
static let _protobuf_nameMap: SwiftProtobuf._NameMap = [
1: .same(proto: "c"),
]
mutating func decodeMessage<D: SwiftProtobuf.Decoder>(decoder: inout D) throws {
while let fieldNumber = try decoder.nextFieldNumber() {
switch fieldNumber {
case 1: try decoder.decodeSingularInt32Field(value: &self.c)
default: break
}
}
}
func traverse<V: SwiftProtobuf.Visitor>(visitor: inout V) throws {
if self.c != 0 {
try visitor.visitSingularInt32Field(value: self.c, fieldNumber: 1)
}
try unknownFields.traverse(visitor: &visitor)
}
static func ==(lhs: Proto3ArenaUnittest_ForeignMessage, rhs: Proto3ArenaUnittest_ForeignMessage) -> Bool {
if lhs.c != rhs.c {return false}
if lhs.unknownFields != rhs.unknownFields {return false}
return true
}
}
extension Proto3ArenaUnittest_TestEmptyMessage: SwiftProtobuf.Message, SwiftProtobuf._MessageImplementationBase, SwiftProtobuf._ProtoNameProviding {
static let protoMessageName: String = _protobuf_package + ".TestEmptyMessage"
static let _protobuf_nameMap = SwiftProtobuf._NameMap()
mutating func decodeMessage<D: SwiftProtobuf.Decoder>(decoder: inout D) throws {
while let _ = try decoder.nextFieldNumber() {
}
}
func traverse<V: SwiftProtobuf.Visitor>(visitor: inout V) throws {
try unknownFields.traverse(visitor: &visitor)
}
static func ==(lhs: Proto3ArenaUnittest_TestEmptyMessage, rhs: Proto3ArenaUnittest_TestEmptyMessage) -> Bool {
if lhs.unknownFields != rhs.unknownFields {return false}
return true
}
}
|
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