RedStone: Curating General, Code, Math, and QA Data for Large Language Models
Paper • 2412.03398 • Published • 2
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Assume $u: \mathbb{R}^N \to \mathbb{R}$ is a smooth function with suitable integrability assumptions. I'm interested in a formal computation, do not worry about integrability properties or smoothness of $u$.
Let $a$ be a constant.
By integration by parts, how can one prove that the identity $$\int_{\mathbb{R}^N}u^a\nab... |
This is a late answer to the question. For an easy typing, i will use the letters $b$ for a root of the polynomial $X^2+2\in\Bbb Q[X]$, and $a$ for a root of the polynomial $X^4 -5X^2-32\in\Bbb Q[X]$.
Note than as a short intermezzo the relation, used in the sequel in blue:$$(a^2-5)^2=a^4-10a^2+25 =(a^4-5a^2-32)-5(a^2-... |
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Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
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Now showing items 1-10 of 18
J/Ψ production and nuclear effects in p-Pb collisions at √sNN=5.02 TeV
(Springer, 2014-02)
Inclusive J/ψ production has been studied with the ALICE detector in p-Pb collisions at the nucleon–nucleon center of mass energy √sNN = 5.02TeV at the CERN LHC. The measurement is performed in... |
let $T$ be a linear operator from a Banach space $X$ to Banach space $Y$.and $X=ker(T)\oplus M_1$ where $M_1$ is closed subspace of $X$.let $M$ be a closed subspce of $X$ then I want to prove that there exist a finite dimensional subspace $M_0$ such that $M=M \cap M_1 +M_0$
If $\dim (Ker(T))= +\infty$ the claim is fals... |
https://doi.org/10.1351/goldbook.A00086
The quantity of light available to molecules at a particular point in the atmosphere and which, on absorption, drives photochemical processes in the atmosphere. It is calculated by integrating the @S05824@ \(L\left (\lambda,\,\theta,\,\varphi \right )\) over all directions of inc... |
$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 4.7}$
Using the projection operator formalism
a) compute the probability of each of the possible outcomes of measuring the first qubit of an arbitrary... |
I calculated correlation function $C(t)=\langle x(t)x(0)\rangle$ for ground state of Simple Harmonic Oscillator (SHO) in two different methods. But the results do not match.
First Attempt:
From Heisenberg equations of motion, $$\mathbf{X}(t)=\mathbf{X}(0)\cos(\omega t)+\frac{\mathbf{P}(0)}{m \omega} \sin(\omega t)$$
So... |
Returns an array of cells for the quick guess, optimal (calibrated) or std. errors of the values of the model's parameters.
Syntax ARMA_PARAM( X, Order, mean, sigma, phi, theta, Type, maxIter) X is the univariate time series data (a one dimensional array of cells (e.g. rows or columns)). Order is the time order in the ... |
Take an elementary convergent integral like:
$\int^\infty_0 e^{- \lambda x} = \frac{1}{\lambda} $
If you series expand it every term and integrate term-by-term every term integrates to infinity. Is there a systematic way to cut-off the integral if you keep the $n^{th}$ term in the series so that you can reasonably appr... |
ISSN:
1937-1632
eISSN:
1937-1179
All Issues
Discrete & Continuous Dynamical Systems - S
March 2009 , Volume 2 , Issue 1
A special issue on
Asymptotic Behavior of Dissipative PDEs
Select all articles
Export/Reference:
Abstract:
This issue consists of ten carefully refereed papers dealing with important qualitative featu... |
Let’s say we have a current wire with a current $I$ flowing. We know there is a field of $B=\frac{\mu_0I}{2\pi r}$ by using Ampère's law, and a simple integration path which goes circularly around the wire. Now if we take the path of integration as so the surface spans doesn’t intercept the wire we trivially get a $B=0... |
For a spin-1 particle at rest, it has three spin states(+1, -1, 0, along the z axis). If we rotate the z axis to -z direction, the spin +1 state will become the spin -1 state. Can we transfer the spin +1 state to the spin 0 state by the frame rotation?
Let $|\pm 1\rangle$ and $|0\rangle$ be the eigenstates of the obser... |
Let's take an aqueous solution of a salt $\ce{NaHA}$ with the initial concentration $C$ when added to water. It will completely dissociate according to the eaquation: $\ce{NaHA(s) \rightarrow Na^+ +HA^-}$.
$\ce{HA^-}$ will participate in three equilibria:
$\ce{2HA^- \leftrightarrows H2A +A^{2-}\quad \quad \quad }$ ${K_... |
My question relates to Chapter 3, Exercise 8 in "Baby Rudin". It states:
If $\sum_n a_n$ converges, and if $\{b_n\}$ is monotonic and bounded, prove that $\sum_n a_n b_n$ converges.
My attempt would have been:
Since $\{b_n\}$ is monotonic and bounded, $\{b_n\}$ converges and it exists $\inf \{b_n\}$ as well as $\sup \{... |
When writing $$\arg(z^n) = n\arg(z) + 2πk$$ and letting $\arg$ denote the principal complex argument of $z$. Is $k$ generally an integer or is it that $0\lt k\lt n$ or $k=[\frac{1}{2}-\frac{n}{2\pi}\arg(z)]$ as some books suggest? Obviously, I don't understand any of this and would appreciate if someone explained this ... |
From Noether's theorem applied to fields we can get the general expression for the stress-energy-momentum tensor for some fields:
$$T^{\mu}_{\;\nu} = \sum_{i} \left(\frac{\partial \mathcal{L}}{\partial \partial_{\mu}\phi_{i}}\partial_{\nu}\phi_{i}\right)-\delta^{\mu}_{\;\nu}\mathcal{L}$$
The EM Lagrangian, in the Weyl ... |
Yeah, this software cannot be too easy to install, my installer is very professional looking, currently not tied into that code, but directs the user how to search for their MikTeX and or install it and does a test LaTeX rendering
Some body like Zeta (on codereview) might be able to help a lot... I'm not sure if he doe... |
In the idealised case, the answer to this is slightly surprising. The fact that the mass of a rocket must include the mass of its fuel is embodied in the rocket equation, $$\Delta v = v_e \ln\frac{m_i}{m_f},$$where $m_i$ is the initial mass of the rocket (including fuel, payload and everything else), and $m_f$ is the f... |
I'll help you answer your second question.
But first, there are some difficulties with the problem you've been given. Firstly your question isn't fully specified: you need to have the Hamiltonian itself so you need at least the potential $V(x)$. The expression for $E_n$ you are given bespeaks either a quantum harmonic ... |
Yeah, this software cannot be too easy to install, my installer is very professional looking, currently not tied into that code, but directs the user how to search for their MikTeX and or install it and does a test LaTeX rendering
Some body like Zeta (on codereview) might be able to help a lot... I'm not sure if he doe... |
Yes, even when
n is known in advance
and
each string-length is $\lceil$log 2(n)$\rceil$ + 1
and
we only care about the state between updates,
not the computation required to perform updates
and
the update procedure can be non-computable
.
For all positive integers n and all elements x of {0,1} n, by [the simpler versio... |
CentralityBin () CentralityBin (const char *name, Float_t low, Float_t high) CentralityBin (const CentralityBin &other) virtual ~CentralityBin () CentralityBin & operator= (const CentralityBin &other) Bool_t IsAllBin () const Bool_t IsInclusiveBin () const const char * GetListName () const virtual void CreateOutputObje... |
I'd like to set
$1024 \times 768$ without any space between the three items. Is this possible? If so, how?
E.g., what I get is:
1024 x 768
and what I want is:
1024x768
TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetting systems. It only takes a minute to si... |
For a test case, I want to determine the velocity profile of a viscously damped standing wave.
By linearizing the density ($\rho=\rho_0+\rho'$) and velocity ($ux=ux'$), the continuity and Navier-Stokes equations result in, respectively:
\begin{align} \partial_t\rho' + \rho_0\partial_xu_x' &= 0 \tag{1} \\ \partial_t^2\r... |
The problem isn't 100% clear, and a full treatment would probably require the use of coupled oscillation techniques that you may or may not have learned yet. But if this is meant to be solved with "basic" techniques, here's how I would think about it:
For a normal pendulum, the tension in the string is largest when the... |
LHCb Collaboration; Bernet, R; Büchler-Germann, A; Bursche, A; Chiapolini, N; De Cian, M; Elsasser, C; Müller, K; Palacios, J; Salzmann, C; Serra, N; Steinkamp, O; Straumann, U; Tobin, M; Vollhardt, A; Anderson, J; Aaij, R; Abellán Beteta, C; Adeva, B; Zvyagin, A (2012).
Measurement of the ratio of prompt $\chi_{c}$ to... |
Does the sequence $\sin(n!)$ diverge(converge)?
It seems the sequence diverges. I tried for a contradiction but with no success. Thanks for your cooperation.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign... |
I have developed a differential equation for the variation of a star's semi-major axis with respect to its eccentricity.
It is as follows:
$$\frac{dy}{dx}=\frac{12}{19}\frac{y\left(1+\left(\frac{73}{24}x^2\right)+\left(\frac{37}{26}x^4\right)\right)}{x\left(1+\left(\frac{121}{304}x^2\right)\right)}$$
Where $y$ is the s... |
Consider the series:
$$\sum_{n=1}^{\infty}\frac{\zeta(2n+1)}{n(2n+1)}$$
We can easily prove that it's a convergent series. My question, is there a way to express this series in terms of zeta constants ?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in r... |
Yeah, this software cannot be too easy to install, my installer is very professional looking, currently not tied into that code, but directs the user how to search for their MikTeX and or install it and does a test LaTeX rendering
Some body like Zeta (on codereview) might be able to help a lot... I'm not sure if he doe... |
Does $\int_1^\infty\sin (\frac{\sin x}{x})\mathrm d x$diverge or not? If it converges, does it converge conditionally or absolutely? I guess that it converges conditionally, also,I think it may be related to $\int_{n\pi}^{(n+1)\pi}\frac{\sin x}{x}\mathrm d x$ , but I do not know how to start? Any help will be appreciat... |
Yes, this presents no difficulty.
As long as you can sample from the full conditionals (and it sounds like you can) then yes.
For a bivariate $(U,V)$ that's just sampling $(V|U=u)$ and $(U|V=v)$. Let's consider a simple case (for which we don't really need Gibbs sampling). Let:
$f_{X,Q}(x,q)= \frac{{n\choose x}} {\math... |
I know that if we move a rectangular wire from no magnetic field to through a magnetic field, there would be an induced voltage because there is change in flux (b∆x). However, if we moved a wire/rod in the same situation, it will also induce a voltage but is it due to the change in flux (b∆x) or charge separation?
The ... |
Yeah, this software cannot be too easy to install, my installer is very professional looking, currently not tied into that code, but directs the user how to search for their MikTeX and or install it and does a test LaTeX rendering
Some body like Zeta (on codereview) might be able to help a lot... I'm not sure if he doe... |
Yeah, this software cannot be too easy to install, my installer is very professional looking, currently not tied into that code, but directs the user how to search for their MikTeX and or install it and does a test LaTeX rendering
Some body like Zeta (on codereview) might be able to help a lot... I'm not sure if he doe... |
The subway train will indeed be hit by light, but it will be hard to see the lights through the window.
The problem in seeing the tunnel light is relativistic aberration, that the angle of the light is changed by your relative velocity. The formula is $$\cos(\theta_2)=\frac{\cos(\theta_1)+\beta}{1+\beta\cos(\theta_1)}$... |
Hello,I am an undergraduate who has taken basic linear algebra and ODE. As for physics, I have taken an online edX quantum mechanics course.I am looking at studying some of the necessary math and physics needed for QFT and particle physics. It looks like I need tensors and group theory...
Hello, I am newish in group th... |
In combinatorics there are quite many such disproven conjectures. The most famous of them are:
1) Tait conjecture:
Any 3-vertex connected planar cubic graph is Hamiltonian
The first counterexample found has 46 vertices. The "least" counterexample known has 38 vertices.
2) Tutte conjecture:
Any bipartite cubic graph is ... |
I'm given series $\sum_{n = 1}^{+\infty} \frac{(-1)^{n}}{(n+1)!}\left(1 + 2! + \cdots + n!\right)$ and I have to find whether it is convergent.
Testing for absolute convergence, we have $a_n = \frac{1}{(n+1)!} + \frac{2}{(n+1)!} + \cdots + \frac{(n-1)!}{(n+1)!} + \frac{n!}{(n+1)!}$ and since last term is $\frac{n!}{(n+... |
Recent developments of CRISPR-Cas9 based homing endonuclease gene drive systems for the suppression or replacement of mosquito populations have generated much interest in their use for control of mosquito-borne diseases (such as dengue, malaria, Chikungunya and Zika). This is because genetic control of pathogen transmi... |
I simply want to calculate the bulk modulus of water at 50C and increasing pressures. I think I am correctly calculating the new specific volume from the original conditions at (25C and 1atm) to 50C and higher pressures. I am rightly getting a decrease in specific volume with increasing pressure at constant temperature... |
The argument for the first question goes as follows:
Consider the Pauli-Lubanski vector $ W_{\mu} = \epsilon_{\mu\nu\rho\sigma}P^{\nu}M^{\rho\sigma}$. Where $P^{\mu}$ are the momenta and $M^{\mu\nu}$ are the Lorentz generators. (The norm of this vector is a Poincare group casimir but this fact will not be needed for th... |
As mentioned in NotAstronaut's answer, objects smaller than 25 meters will typically burn up in the atmosphere. One can very easily see why this should be the case using Newton's impact depth formula. This is based on approximating the problem by assuming that the matter in the path of the object is being pushed at the... |
Find all real numbers $a_1, a_2, a_3, b_1, b_2, b_3$ such that for every $i\in \lbrace 1, 2, 3 \rbrace$ numbers $a_{i+1}, b_{i+1}$ are distinct roots of equation $x^2+a_ix+b_i=0$ (suppose $a_4=a_1$ and $b_4=b_1$).
There are many ways to do it but I've really wanted to finish the following idea:
From Vieta's formulas we... |
I am reading the classical article of A. Salomaa where he gives two axiom systems for regular sets and proofs consistency and completeness.
As I have understood it, an axiomatic system in some logic (lets suppose predicate first order logic) are axioms formulated in the language of the logic, i.e. well-formed formulas ... |
Interpolation and optimal hitting for complete minimal surfaces with finite total curvature 87 Downloads Abstract
We prove that, given a compact Riemann surface \(\Sigma \) and disjoint finite sets \(\varnothing \ne E\subset \Sigma \) and \(\Lambda \subset \Sigma \), every map \(\Lambda \rightarrow \mathbb {R}^3\) exte... |
I have to prove if this function is differentiable.
$$f(x,y)= \begin{cases} \frac{\cos x-\cos y}{x-y} \iff x \neq y \\-\sin x \iff x=y \end{cases}$$
if $x \neq y$ it is continuous, but i want to see if it is continuous in x=y too.
i can rewrite f as $$ f(x,y)= \begin{cases} \frac{g(x)-g(y)}{x-y} \iff x \neq y \\ g'(x)=... |
This is the first entry in what will become an ongoing series on regression analysis and modeling. In this tutorial, we will start with the general definition or topology of a regression model, and then use NumXL program to construct a preliminary model. Next, we will closely examine the different output elements in an... |
You can at least sketch an answer to the "multiply $t,t^2,\dots,t^{m-1}$ where $m$ is the multiplicity" question by considering a family of IVPs where two roots are approaching one another. Consider the IVPs
$$y''-(1+a)y'+ay,y(0)=0,y'(0)=1$$
where $a$ is approaching $1$. Let us solve this whenever $a$ is not $1$. The r... |
Given $a$, $b$ and $c$ are positive real numbers. Prove that:$$\sum \limits_{cyc}\frac {a}{(b+c)^2} \geq \frac {9}{4(a+b+c)}$$
Additional info: We can't use induction. We should mostly use Cauchy inequality. Other inequalities can be used rarely.
Things I have done so far: The inequality look is similar to Nesbitt's in... |
When a symmetry is anomalous, the path integral $Z=\int\mathcal{D}\phi e^{iS[\phi]}$ is not invariant under that group of symmetry transformations $G$. This is because though the classical action $S[\phi]$ is invariant the measure may not be invariant. Since 1PI effective action $\Gamma[\phi_{c}]$ takes quantum correct... |
Noether's theorem states that, for every
continuous symmetry of an action, there exists a conserved quantity, e.g. energy conservation for time invariance, charge conservation for $U(1)$. Is there any similar statement for discrete symmetries?
Noether's theorem states that, for every
migrated from math.stackexchange.co... |
Let's consider $0<\alpha<1/2$ and denote by $W_T^{1-\alpha,\infty}(0,T)$ the space of measurable functions $g:[0,T]\to\Bbb R$ such that $$ ||g||_{1-\alpha,\infty,T}:=\sup_{0<s<t<T}\left[\frac{|g(t)-g(s)|}{(t-s)^{1-\alpha}}+\int_s^t\frac{|g(y)-g(s)|}{(y-s)^{2-\alpha}}\,dy\right]<+\infty\;\;\;. $$
Moreover, we define the... |
I have an ellipse centered at $(h,k)$, with semi-major axis $r_x$, semi-minor axis $r_y$, both aligned with the Cartesian plane.
How do I determine if a circle with center $(x,y)$ and radius $r$ is within the area bounded by the ellipse
Mathematics Stack Exchange is a question and answer site for people studying math a... |
So, for the past few years it's been my goal to create an equation that would give me the position of an object in a gravitational field at time $t$, given it's initial position and velocity. At first the problem was that I didn't know enough to do the math. Now that I can do multivariable calculus I thought that probl... |
I sought-for the equations of motion of an unrestrained rigid body. The equations of motion are readily available in the literature, but my concern is to derive them by Hamilton's principle.
Expressing the position of an infinitesimal particle within the body as:
$$ \vec{R} = \vec{R}_0 + \vec{r} $$
where $\vec{R}_0$ an... |
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Our company has a long history in China to produce
Chips Packaging Machine Manufacturer, Factory Supplierchips packing machine animal food packing machine rice husk powder pac... |
Let $X_n(\Bbb{Z})$ be the simplicial complex whose vertex set is $\Bbb{Z}$ and such that the vertices $v_0,...,v_k$ span a $k$-simplex if and only if $|v_i-v_j| \le n$ for every $i,j$. Prove that $X_n(\Bbb{Z})$ is $n$-dimensional...
no kidding, my maths is foundations (basic logic but not pedantic), calc 1 which I'm pr... |
I'm trying to understand BRST complex in its Lagrangian incarnation i.e. in the form mostly closed to original Faddeev-Popov formulation. It looks like the most important part of that construction (proof of vanishing of higher cohomology groups) is very hard to find in the literature, at least I was not able to do so. ... |
ISSN:
1078-0947
eISSN:
1553-5231
All Issues
Discrete & Continuous Dynamical Systems - A
January 2014 , Volume 34 , Issue 1
Special issue
on Infinite Dimensional Dynamics and Applications
Select all articles
Export/Reference:
Abstract:
The theory of infinite dimensional and stochastic dynamical systems is a rapidly expa... |
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RedStone
Based on the paper "RedStone: Curating General, Code, Math, and QA Data for Large Language Models" and the official GitHub repository, I have replicated the processing of the RedStone-Math dataset in Redstone.
I followed the processing steps outlined in the official repository with minimal modifications.
The final processed dataset is similar in scale to what is presented in the paper, but I have not yet used this data for training to verify its quality.
The release is under the Redstone's license. If any data within it infringes on your copyright, please contact me for removal.
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