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The problem of approximating a given probability distribution using a simpler distribution plays an important role in several areas of machine learning, e.g. variational inference and classification. Within this context, we consider the task of learning a mixture of tree distributions. Although mixtures of trees can be... | CommonCrawl |
Frank den Hollander is professor of mathematics at Leiden University in The Netherlands. His research focuses on probability theory, ergodic theory, statistical physics, population dynamics and complex networks. Frank has supervised 13 PhD students and 33 postdocs, has published 150 papers, and is the author of three m... | CommonCrawl |
Abstract. We study the spectral properties of pseudo-differential operators in the semi-classical limit at energies near a non degenerate minimum of the principal symbol $p$. We give precise asymptotics of the non resonant energy levels for a scalar holomorphic $p$, we get explicit expressions in dimension 2. Precise a... | CommonCrawl |
Given a sequence of integers $a_1, a_2, a_3, \ldots , a_ n$, an island in the sequence is a contiguous subsequence for which each element is greater than the elements immediately before and after the subsequence. In the examples below, each island in the sequence has a bracket below it. The bracket for an island contai... | CommonCrawl |
Nothing in Cantor's proof depends on a "list" however defined.
Well, I would say that both an enumeration and a sequence are types of list and that Cantor uses both, but this is now becoming a semantic argument of little importance to people who understand the proof (among whom I include you).
To me, the most elegant f... | CommonCrawl |
where $x=(x_1,\dots , x^n)\in\Omega,$ $\Omega$ is a bounded domain in $R^n,$ $t\in(0, T),$ $0 < T <+\infty,$ $f(x, t)$ and $h(x, t)$ are given functions, $\mu$ is a given real, $m$ is a given natural, and $\Delta$ is necessary due to presence of the additional unknown function $q(x)$), the boundary overdetermination co... | CommonCrawl |
This puzzle replaces all numbers with other symbols.
Your job, as the title suggests, is to find what value fits in the place of $\bigstar$. To get the basic idea down, I recommend you solve Puzzle 1 first.
Each numerical symbol represents integers and only integers. This means fractions and irrational numbers like $\s... | CommonCrawl |
Abstract: This survey is a study of a dynamical system consisting of a massive piston in a cubic container of large size $L$ filled with an ideal gas. The piston has mass $M\sim L^2$ and undergoes elastic collisions with $N\sim L^3$ non-interacting gas particles of mass $m=1$. It is found that under suitable initial co... | CommonCrawl |
Mcdougal littel worksheets for graphing inequalities on the coordinate plane, colorado standards test 2nd grade questions samples, multiplying ,subtracting inters, trinomials and finding the vertex, Simplifying Rational Exponents, worksheets, dictionary: samples of a expressions for math, how to be better at pre algebr... | CommonCrawl |
First we can tell what the idea of a derivative is. But the issue of computing derivatives is another thing entirely: a person can understand the idea without being able to effectively compute, and vice-versa.
Suppose that $f$ is a function of interest for some reason. We can give $f$ some sort of 'geometric life' by t... | CommonCrawl |
Share Email Topic 2 error & uncertainty- part 3 byNoel Gallagher 10606views Uncertainty and equipment error byChris Paine 53746views Calculating Uncertainties bymrjdfield 4559views IB Chemistry on uncertainty error c... If we try to read off the numbers on the speedometer and write them down, there'll be a lot of uncer... | CommonCrawl |
I found this function, and i have problems with the demonstration of truth or falseness of this afirmation, so some one can help me?
Let S and P be the sum and the product of the divisors of a number T $\in$ $\mathbb Z$ and T different of 1.In the case T is a prime number, the roots are +i, -i. In this last case a thin... | CommonCrawl |
If you are new to Facebook, let alone social media, learning how to use Facebook can be an incredibly difficult and frustrating endeavor. Facebook is a very expansive platform, and is nothing like the chat rooms of old where communicating was easy. Simple tasks on Facebook such as finding friends and adding photos can ... | CommonCrawl |
To find a product using the distributive property, you take the coefficent--in this case the 3 outside of the parentheses--and multiply it by each term within the parentheses separately. The first term within the parentheses is $x$, so the first term of the product is $3\times x$, or $3x$. The second term within the pa... | CommonCrawl |
The adsorption of nanoparticles on a surface has interest in fields like heterogeneous catalysts and quantum dots. We simulate the monolayer adsorption of nanoparticles on patterned substrate. We adopted a pattern consisting of equal squares of size $\alpha$ and a distance $\beta$ apart from each other, and characteriz... | CommonCrawl |
Abstract: We generalize recent linear lower bounds for Polynomial Calculus based on binomial ideals. We produce a general hardness criterion (that we call immunity), which is satisfied by a random function, and prove linear lower bounds on the degree of PC refutations for a wide class of tautologies based on immune fun... | CommonCrawl |
Written by Colin+ in basic maths skills.
A question that frequently comes up in the insalubrious sort of place a mathematician might hang around is, what is that value of $0^0$. We generally sigh and answer that the same way every time.
It was nice, then, to see someone ask a more fundamental one: what is $0 \div 0$?
T... | CommonCrawl |
Linköping University, Department of Electrical Engineering, Integrated Circuits and Systems.
This report is about control, design and implementation of a low voltage-fed quasi Z-source three-level inverter. The topology has been interesting for photovoltaic-systems due to its ability to boost the incoming voltage witho... | CommonCrawl |
Ouch! A kitten got stuck on a tree. Fortunately, the tree's branches are numbered. Given a description of a tree and the position of the kitten, can you write a program to help the kitten down?
The input is a description of a single tree. The first line contains an integer $K$, denoting the branch on which the kitten g... | CommonCrawl |
In this problem, we are dividing by a fraction. However, we are never supposed to divide by a fraction. Rather, we must multiply by the reciprocal of the fraction. The reciprocal of a fraction is that fraction with the numerator (top of the fraction) and denominator (bottom of the fraction) switched. Thus, we simplify ... | CommonCrawl |
In neural nets, there is often a weight regularization term in the loss function, which ensures that unnecessarily high weights don't occur. For example, if $C(\theta,x)$ is the baseline loss function, then we have the loss $L(\theta,x)=C(\theta,x)+\sum L(\theta_i)$, (where $L$ is the $L_1$ norm or $L_2$ norm usually).... | CommonCrawl |
Abstract: Spectral emission lines are local features that represent extra emissions of photons in a narrow band of energy. In a statistical model, it is often appropriate to model the emission lines with a narrow Gaussian function or a delta function. In this article, we show how to identify the location of the narrow ... | CommonCrawl |
Abstract: In a traitor tracing scheme, each user is given a different decryption key. A content distributor can encrypt digital content using a public encryption key and each user in the system can decrypt it using her decryption key. Even if a coalition of users combines their decryption keys and constructs some ``pir... | CommonCrawl |
A semitoric integrable Hamiltonian system, briefly a semitoric system, is given by two autonomous Hamiltonian systems on a 4-dimensional manifold whose flows Poisson-commute and induce an $(\mathbb S^1 \times \mathbb R)$-action that has only nondegenerate, nonhyperbolic singularities. Semitoric systems have been symple... | CommonCrawl |
The recursive motif "F +60 F +240 F +60 F" produces the well-known Koch snowflake. Interestingly, for certain choices of angles, this recursive algorithm actually produces an image with finitely many segments and rotational symmetry.
The subdivision of the circle into 360 parts is arbitrary, however. The image above wa... | CommonCrawl |
We reduce a broad class of machine learning problems, usually addressed by EM or sampling, to the problem of finding the $k$ extremal rays spanning the conical hull of a data point set. These $k$ ``anchors'' lead to a global solution and a more interpretable model that can even outperform EM and sampling on generalizat... | CommonCrawl |
概要:二次元乱流を特徴づける性質として, 高レイノルズ数におけるエネルギー密度スペクトル中のエンストロフィーカスケードとエネルギー逆カスケードに対応する領域の出現が挙げられる. 言い換えれば, 二次元乱流とは粘性ゼロ極限における流体のエネルギー保存とエンストロフィー散逸によって特徴付けられる. よって非粘性流体の運動を記述するEuler方程式の解でこのような性質を持つものが存在すれば, 二次元乱流の数学的構造を解析するうえで重要であると考えられる. しかし, 二次元Euler方程式においてエンストロフィー散逸解を直接構成するには数学的な困難が伴う. 本セミナーでは, Euler方程式の正則化方程式である. Euler-$\alpha... | CommonCrawl |
Abstract : The need to compute the intersections between a line and a high-order curve or surface arises in a large number of finite element applications. Such intersection problems are easy to formulate but hard to solve robustly. We introduce a non-iterative method for computing intersections by solving a matrix sing... | CommonCrawl |
The moment problem arises as the result of trying to invert the mapping that takes a measure $μ$ to the sequences of moments, and to resolve the problem of determinacy of such measure.
If all powers of two random variables are uncorrelated, are they independent?
Do orthogonal polynomials determine the moments of their ... | CommonCrawl |
Yesterday was Sam's birthday. The most interesting gift was definitely the chessboard. Sam quickly learned the rules of chess and defeated his father, all his friends, his little sister, and now no one wants to play with him any more.
Sam's chessboard has size $N\times N$. A bishop can move to any distance in any of th... | CommonCrawl |
I'll give a brief account of Hamiltonian dynamical systems whose degrees of freedom are given by a complex-valued sequence $\alpha_n(t)$, and the Hamiltonian is a quartic combination of $\alpha_n$ and its complex conjugate. Such systems arise naturally as weakly nonlinear approximations to a few interesting equations o... | CommonCrawl |
Can you divide one square paper into five equal squares? You have a scissor and glue. You can measure and cut and then attach as well. Only condition is You can't waste any paper.
(where simple means no self intersections and equidecomposable means finitely cut and glued).
For your problem you can take the first polygo... | CommonCrawl |
How do you canonicalize a matrix over column- and row-swap operations?
Or more specifically, does there exist a function f(M) such that f(M)=f(N) iff there is set of column- and row-swap operations (i.e. a permutation matrix A) on M that would transform M into N (i.e. AMA')?
But how to handle this?
432179865 any of ... | CommonCrawl |
Molar conductivity increases with decrease in concentration. This is because the total volume, $V$, of solution containing one mole of electrolyte also increases. It has been found that decrease in $\kappa$ on dilution of a solution is more than compensated by increase in its volume. Physically, it means that at a give... | CommonCrawl |
Induction (recursion actually) will end you up with all finite decimals, but of arbitrary length. This way you'll never end up with infinite decimals.
Induction is how you specify all members of these limits. You can't write them all out.
(c) using a symbol such as "\" or "0" seems to be equivalent to "scratches on a r... | CommonCrawl |
A tatami tiling is an arrangement of $1 \times 2$ dominoes (or mats) in a rectangle with $m$ rows and $n$ columns, subject to the constraint that no four corners meet at a point. For fixed $m$ we present and use Dean Hickerson's combinatorial decomposition of the set of tatami tilings — a decomposition that allows them... | CommonCrawl |
We consider robust optimization problems, where the goal is to optimize in the worst case over a class of objective functions. We develop a reduction from robust improper optimization to stochastic optimization: given an oracle that returns $\alpha$-approximate solutions for distributions over objectives, we compute a ... | CommonCrawl |
A question was just asked about whether or not we still need model categories of spectra (vs working with the $\infty$-category). To me (and Fernando Muro at least), it is reminiscent of a previous question about whether we still need model categories. Both questions already have answers from experts in both methods. I... | CommonCrawl |
A group action on a metric space is called growth tight if the exponential growth rate of the group with respect to the induced pseudo-metric is strictly greater than that of its quotients. A prototypical example is the action of a free group on its Cayley graph with respect to a free generating set. More generally, wi... | CommonCrawl |
This tutorial will provide step-by-step guide for building a Recommendation Engine. We will be recommending conference papers based on their title and abstract. There are two major types of Recommendation Engines: Content Based and Collaborative Filtering Engines.
Content Based recommends only using information about t... | CommonCrawl |
$\alpha$ and $n \alpha$ are two angles and they formed compound angles $(n+1)\alpha$ and $(n-1)\alpha$ by sum and difference. Sine and cosine functions formed a fractional function to represent a quantity in general trigonometric form.
The two sine functions with compound angles are in subtraction form. The subtraction... | CommonCrawl |
The aim of this paper is to find cellular automata (CA) rules that are used to describe S-boxes with good cryptographic properties and low implementation cost. Up to now, CA rules have been used in several ciphers to define an S-box, but in all those ciphers, the same CA rule is used. This CA rule is best known as the ... | CommonCrawl |
Hypoglycemic effect through activity inhibition of $\alpha$-glucosidase and $\alpha$-amylase was evaluated using leaves of Eleutherococcus senticosu, Eleutherococcus gracilistylus, Eleutherococcus sieboldianus and Eleutherococcus sessiliflorus which belong to Acanthopanax sessiliflorus genus. As a result of measuring $... | CommonCrawl |
From the solution, it is clear that $x_t$ cannot become negative. However, it is not so clear from the SDE. In fact, if I do simulations using the SDE, x very frequently becomes negative for certain parameter combinations.
The reason SDE may seem to allow a negative value of x is because dW can be a large negative numb... | CommonCrawl |
) hypothesis while on the other hand very religious people for example have 0 in their priori when it comes to possibility of their religion being made up so they are forced to ignore evidence to the contrary (because bayesian updating breaks for them due to division by zero and mind's way to signal this exception is d... | CommonCrawl |
Chattopadhyay, K and Mukhopadhyay, NK (1990) On the origin of banded microstructure in rapidly solidified alloys: The case of Al-10%Mn quasicrystalline system. In: Journal of Crystal Growth, 106 (2-3). pp. 387-392.
The formation of banded structure with bands perpendicular to the growth direction is reported in the rap... | CommonCrawl |
Mathematical Circles (Russian Experience); Dmitri Fomin, Sergey Genkin, Ilia Itenberg; Translated from Russian by Mark Saul; Volume 7; American Mathematical Society; ISBN 0-8218-0430-8.
Can we draw a closed path made of 9 line segments, each of which intersects exactly one of the others?
Can a convex 13-gon be divided ... | CommonCrawl |
My girlfriend and I have been attending a weekly Dungeons & Dragons night at a local board game cafe, which means that we have been thoroughly immersed in the superstition surrounding the dice. We have heard stories of unlikely strings of bad rolls that ultimately lead to the frustrated fellow adventurer performing the... | CommonCrawl |
Abstract. We consider the Navier-Stokes equation on a two dimensional torus with a random force, white noise in time and analytic in space, for arbitrary Reynolds number $R$. We prove probabilistic estimates for the long time behaviour of the solutions that imply bounds for the dissipation scale and energy spectrum as ... | CommonCrawl |
This notebook proposes a general introduction to goal babbling, and how it differs from motor babbling, in the context of robotics. Goal babbling is a way for robots to discover their body and environment on their own. While representations of those could be pre-programmed, there are many reasons not to do so: environm... | CommonCrawl |
Is there any references on the tensor product of (locally) presentable categories ?
Is there any references that defines it properly and proves the basic properties ?
The canonical reference is Chapter 5 of Greg Bird's thesis.
Not the answer you're looking for? Browse other questions tagged reference-request ct.categor... | CommonCrawl |
This second version doesn't have to pull in extra packages and doesn't create intermediate lists, but mine is shorter and doesn't have explicit recursion. What do you think of my solution in comparison with the library's implementation?
Data.Bifunctor is part of base since 4.8.0.0, so I'm not sure where you get the "ex... | CommonCrawl |
Let $n$ be a whole number. When is it possible to write $n$ as a sum of two squares, say $n=a^2+b^2$, or as a sum of three squares, say $n=a^2+b^2 +c^2$, or as a sum of four squares, and so on? Of course, $a$, $b$, $c$, $\ldots$ are also meant to be whole numbers here. We can also ask whether there is any convenient te... | CommonCrawl |
Hough transform is a widely used shape detection techniques in computer vision and image processing. Hough transform aims to find imperfect instances of objects of within a certain class of shapes by a voting procedure. Essentially, hough transform transform points in the original space to parametric sapce, in which th... | CommonCrawl |
In the first part of this talk I will define a sequence of polynomials resembling the Chebyshev polynomials of the first kind, and present results on their irreducibility and zero distribution. I will also consider $2\times 2$ Hankel determinants of these polynomials, which have interesting zero distributions. Furt... | CommonCrawl |
In this paper, H(sub)$\infty$ depth and course controllers of autonomous underwater vehicles using H(sub)$\infty$ servo control are proposed. An H(sub)$\infty$ servo problem is foumulated to design the controllers satisfying a robust tracking property with modeling errors and disturbances. The solution of the H(sub)$\i... | CommonCrawl |
This is a question I asked on the cognitive science beta, but which never got any answer. I do not know what the policy should be for question migration/reposting (maybe worth discussing in the meta?), but I hoped it might get more answers (i.e. at least one ;)) here.
A rigorous formulation of these axioms can be found... | CommonCrawl |
In this supplemental set of notes we derive some approximations for , when is large, and in particular Stirling's formula. This formula (and related formulae for binomial coefficients will be useful for estimating a number of combinatorial quantities in this course, and also in allowing one to analyse discrete random w... | CommonCrawl |
We complete the picture how the asymptotic behavior of a dynamical system is reflected by properties of the associated Perron-Frobenius operator. Our main result states that strong convergence of the powers of the Perron-Frobenius operator is equivalent to setwise convergence of the underlying dynamic in the measure al... | CommonCrawl |
Residual intersection theory works well for ideals like the ideal of $p\times p$ minors of a generic $p \times (p+1)$ matrix, but fails for some very nice ideals, such as the ideal of $2 \times 2$ minors of a $2\times n$ matrix for n greater than $3$. Poking around for what might be true, Bernd Ulrich and I stumbled on... | CommonCrawl |
Das, Apurba Kumar and Haldar, Debasish and Hegde, Raghurama P and Shamala, N and Banerjee, Arindam (2005) X-ray crystallographic signature of supramolecular triple helix formation from a water soluble synthetic tetrapeptide. In: Chemical Communications (14). pp. 1836-1838.
Single crystal X-ray diffraction studies on th... | CommonCrawl |
Following on from the previous article on Pricing a Call Option with Multi-Step Binomial Trees, we are now going to discuss what happens as we increase the number of steps, $N$. In particular, we will discuss what happens as $N\rightarrow\infty$. Some care must be taken at this stage, as we will be dealing with infinit... | CommonCrawl |
Gavin J Daigle, Karthik Krishnamurthy, Nandini Ramesh, Ian Casci, John Monaghan, Kevin McAvoy, Earl W Godfrey, Dianne C Daniel, Edward M Johnson, Zachary Monahan, Frank Shewmaker, Piera Pasinelli and Udai Bhan Pandey.
Pur-alpha regulates cytoplasmic stress granule dynamics and ameliorates FUS toxicity.. Acta neuropatho... | CommonCrawl |
A set $Q$ is well-quasi-ordered by a relation $\le$ if for every sequence $q_1,q_2,\ldots$ of elements of $Q$ there exist $i<j$ such that $q_i \le q_j$. In their Graph Minors series, Robertson and Seymour prove that graphs are well-quasi-ordered by the minor relation. This result, which is known as the Graph Minor Theo... | CommonCrawl |
Jack and Jill developed a special encryption method, so they can enjoy conversations without worrrying about eavesdroppers. Here is how: let $L$ be the length of the original message, and $M$ be the smallest square number greater than or equal to $L$. Add $(M - L)$ asterisks to the message, giving a padded message with... | CommonCrawl |
If $f(x)$ is $U$-almost-periodic and if $f'(x)$ is uniformly continuous on $(-\infty,\infty)$, then $f'(x)$ is $U$-almost-periodic; the indefinite integral $F(x)=\int_0^xf(t)dt$ is $U$-almost-periodic if $F(x)$ is a bounded function.
Bohr's treatise [a1] is a good reference. An up-to-date reference is [a2].
This page w... | CommonCrawl |
Department of Mathematics, Shahid Chamran University of Ahvaz, P.O. Box: 6135713895, Ahvaz, Iran.
We introduce and study the concept of $\alpha $-semi short modules.
Using this concept we extend some of the basic results of $\alpha $-short modules to $\alpha $-semi short modules.
We observe that if $M$ is an $\alpha $-... | CommonCrawl |
My current research interests focus on developing theoretical and numerical methods for understanding the phase behavior and structures of block copolymers, polymer brushes and polyelectrolytes both in bulk and under geometrical confinements. During the PhD period, my research focus was conducting both experimental and... | CommonCrawl |
Effects of unsteady sheared $\bf E \times B$ flow on drift wave turbulence and heat transport driven by slab ion temperature gradient (ITG) instability are investigated by means of Landau fluid simulations. Here, the $\bf E \times B$ flow, which consists of stationary and time-periodic oscillatory parts, is externally ... | CommonCrawl |
How can we define the limit of a constant function?
In mathematics, a limit is the value that a function(or sequence) "approaches" as the input (or index) "approaches" some value.
What if the function was a constant?! A constant function will not approach anything, so, how would we define the limit of a constant functi... | CommonCrawl |
Many quantum information tasks require measurements to distinguish between different quantum-mechanically entangled states (Bell states) of a particle pair. In practice, measurements are often limited to linear evolution and local measurement (LELM) of the particles. We investigate LELM distinguishability of the Bell s... | CommonCrawl |
Some of the basic probability and statistics concepts. joint probabilities, combinatories; conditional probabilities and independence and their examples; Bayes' rule.
Recall: If A & B are 2 disjoint events, then $P[A\cup B]=P[A]+P[B]$, $P[A\cap B]=P[A]\cdot P[B]$.
If $A\cup B \neq \varnothing$, then $P[A\cap B]=P[A]\cd... | CommonCrawl |
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
This activity investigates how you might make squares and pentominoes from Polydron.
If you had 36 cubes, what different cuboids could you make?
Can you put the $25$ coloured tiles into the $5\times ... | CommonCrawl |
I am trying to construct an example of a ring satisfying the followings.
I know that a local noetherian ring having a height $1$ principal prime ideal is a domain. Actually I wanted to prove this without the local condition. I couldn't prove this hence I am looking for a counterexample. I need some help. Thanks.
As a h... | CommonCrawl |
$R^\wedge \to S^\wedge $ is formally smooth for the $\mathfrak n^\wedge $-adic topology.
Here $R^\wedge $ and $S^\wedge $ are the $\mathfrak m$-adic and $\mathfrak n$-adic completions of $R$ and $S$.
In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by fillin... | CommonCrawl |
What would be the entry for 20 in this list?
20 = ___ . . . ?
Please use and explain the simplest possible rule, not purely mathematical, that accounts for every equivalence from 0 to 99.
Because you gave us a list of equivalences which are more equal than others. So we can assume the remaining numbers are less equal... | CommonCrawl |
Abstract: I provide updates for the theoretical predictions of the muon and electron anomalous magnetic moments, for the shift in the fine structure constant $\alpha(M_Z)$ and for the weak mixing parameter $\sin^2 \Theta_W(M_Z)$. Phenomenological results for Euclidean time correlators, the key objects in the lattice QC... | CommonCrawl |
Abstract: Solutions of the Polchinski exact renormalization group equation in the scalar O(N) theory are studied. Families of regular solutions are found and their relation with fixed points of the theory is established. Special attention is devoted to the limit $N=\infty$, where many properties can be analyzed analyti... | CommonCrawl |
Abstract: We construct a thermal dark matter model with annihilation mediated by a resonance to explain the positron excess observed by PAMELA, Fermi-LAT and AMS-02, while satisfying constraints from cosmic microwave background (CMB) measurements. The challenging requirement is that the resonance has twice the dark mat... | CommonCrawl |
I'm struggling with the concept of the Fatou set because its definition as the largest open set on which the iterates of a map are normal is so abstract. However, on Wikipedia I've caught mentions of "fatou domains", here meaning loosely "largest open set on which the iterates have a certain long term behavior". The Fa... | CommonCrawl |
1 Nguyễn Việt Dũng, Nguyen Van Ninh, The Higher Topological Complexity of Complement of Fiber Type Arrangement, Acta Mathematica Vietnamica, 42 (2017), 249–256, Scopus.
2 Nguyễn Việt Dũng, Tran Quoc Cong, The Homotopy Type of the Complement to a System of Complex Lines in $\mathbb C^2$, Vietnam Journal of Mathematics, ... | CommonCrawl |
Zakaria, Siti Fatimah Binti (2016) Analytic Properties of Potts and Ising Model Partition Functions and the Relationship between Analytic Properties and Phase Transitions in Equilibrium Statistical Mechanics. PhD thesis, University of Leeds.
The Ising and $Q$-state Potts models are statistical mechanical models of spin... | CommonCrawl |
This page describes how to run constant pH replica exchange MD (pH-REMD) in which replicas are run at the same temperature but different pH values. Note, this tutorial is for implicit (Generalized Born) solvent. After you learn how to run CpHMD in explicit solvent (click here for tutorial), you can set up each replica ... | CommonCrawl |
It was the first meeting of the humans and the aliens, and things were going well: The humans and aliens had learned to understand each other's language and found that both were hoping for a peaceful relationship. In this spirit, the alien and human ambassador decided to play a game.
Yes, yes. We know how queens move o... | CommonCrawl |
Is every soft sheaf of countable $\mathbb Q$-vector spaces a direct sum of skyscraper sheaves?
Let $X$ be a finite-dimensional compact metrizable space (these properties might partially be irrelevant; on the other hand, the case $X=[0,1]$ is already interesting to me).
Let $\mathcal F$ be a soft sheaf of $\mathbb Q$-ve... | CommonCrawl |
Hannenhalli and Pevzner gave the first polynomial-time algorithm for computing the inversion distance between two signed permutations, as part of the larger task of determining the shortest sequence of inversions needed to transform one permutation into the other. Their algorithm (restricted to distance calculation) pr... | CommonCrawl |
A financial intermediary is an institution that facilitates the flow of funds between individuals or other economic entities.
A financial intermediary is an institution that facilitates the flow of funds between individuals or other economic entities having a surplus of funds (savers) to those running a deficit of fund... | CommonCrawl |
We study principal bundles for strict Lie $n$-groups over simplicial manifolds. Given a Lie group $G$, one can construct a principal $G$-bundle on a manifold $M$ by taking a cover $U$ of $M$, specifying a transition cocycle, and then quotienting $U\times G$ by the equivalence relation generated by the cocycle. We demon... | CommonCrawl |
Abstract: We prove that a finite-difference centered approximation for the Kolmogorov equation in the whole space preserves the decay properties of continuous solutions as $ t \to \infty $, independently of the mesh-size parameters. This is a manifestation of the property of numerical hypo-coercivity, and it holds both... | CommonCrawl |
You are given an array of $n$ integers. You want to modify the array so that it is increasing, i.e., every element is at least as large as the previous element.
On each turn, you may increase the value of any element by one. What is the minimum number of turns?
The first input line contains an integer $n$: the size of ... | CommonCrawl |
Solubility of beryllium in pseudobinary aluminum-magnesium(2)silicide.
The Al-Mg-Si system is the basis of a major class of heat treatable alloys used for both wrought and cast products. Several heat treatable alloys exhibit age hardening at room temperature after a solution treatment (natural aging), and this property... | CommonCrawl |
Abstract: A polynomial $f(x_1,\ldots,x_n)$ is said to be an identity for $m \times m$ matrices if $f(M_1,\ldots,M_n) = 0$ for all choices of $m \times m$ matrices for $M_i$s.
In the problem of partial function extension, we are given a partial function consisting of a set of $n$ points in a domain and a function value ... | CommonCrawl |
One part of making the solver faster were low-level optimizations in the unit-propagation implementation. I won't go into the details of that, but you can look at the new code. The bigger part were several heuristics that play a big role in making CDCL perform well. Below I will explain each implemented in varisat so f... | CommonCrawl |
Is there any superstable configuration in the game of life?
This question spins off of Gil Kalai's recent question on Conway's game of life for a random initial configuration.
There are numerous configurations in the game of life that are known to be stable---such as blocks, beehives, blinkers and toads---in the sense ... | CommonCrawl |
I had a strange correlation test result between two variables ($y$ = residuals of a linear regression, $x$ = dependent variable).
Oh, ok, I have almost zero correlation!
And rho = -0.11. Cool! It seems that $y_0$ and $x_0$ are correlated in some way.
How can I accept null hypothesis if rho ($\rho$) is nearly -1?
That d... | CommonCrawl |
Volume 32, Number 1B (2004), 939-995.
This paper proves that the scaling limit of a loop-erased random walk in a simply connected domain $Dsubsetneqq\C$ is equal to the radial SLE$_2$ path. In particular, the limit exists and is conformally invariant. It follows that the scaling limit of the uniform spanning tree in a ... | CommonCrawl |
Let's import the numpy module.
The slowest run took 34.86 times longer than the fastest. This could mean that an intermediate result is being cached.
Matrix multiplication is np.dot(A, B) for two 2D arrays.
The .shape attribute contains the dimensionality array as a tuple. So the tuple (5,4,3) means that we're dealing ... | CommonCrawl |
20 Why convolution regularize functions?
17 Suppose that there exist a set $\Gamma$ of positive measure such that $\nabla u=0, a.e.\ x\in\Gamma$.
16 Do diffeomorphisms act transitively on a manifold?
16 Is there no norm in $C^\infty ([a,b])$?
16 How bad can the second derivative of a convex function be? | CommonCrawl |
One special type of real-valued functions that are of interested to study are known as increasing and decreasing (collectively, monotonic) functions which we define below.
Definition: A function $f$ is said to be an Increasing Function on the interval $[a, b]$ if for all $x, y \in [a, b]$ where $x < y$ we have that $f(... | CommonCrawl |
We establish new approximation results, in the sense of Lusin, of Sobolev functions by Lipschitz ones, in some classes of non-doubling metric measure structures. Our proof technique relies upon estimates for heat semigroups and applies to Gaussian and $RCD(K, \infty)$ spaces. As a consequence, we obtain quantitative st... | CommonCrawl |
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