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### Sampling from the Birkhoff polytope

The set of $n\times n$ real, nonnegative matrices whose rows and columns sum to one forms the well-known Birkhoff polytope Recently someone asked me if I knew How to sample (in polynomial time) ...
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### Sampling uniformly from all possible line segments of a given length that fit inside a container

Consider that task of randomly placing a line segment of some length $L$ near a plane s.t. a point $p$ at the center of the line segment is at most a distance $H$ from the plane and intersections ...
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### A sampling and learning question

Suppose there is an oracle that returns a number $b \in \mathbb{Z}_{n}$ whenever I press the button. We have $b = a + e$, where $a \in \mathbb{Z}_n$ is a fixed number and $e$ is sampled according to ...
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The setting is as follows: We are given two random variables $X : \Omega \to \mathbb{R}$ and $\Theta : \Omega \to T$ for some 'parameter space' $T \subset \mathbb{R}$, and 1) we know the density of $... 0answers 54 views ### Simulate a graph from a certain distribution I am wondering if anyone can indicate whether the following is a solved problem. I don't care about time of the algorithm currently. Consider a general probability distribution F on simple graphs ... 0answers 67 views ### Stochastic process inference from partial observations Consider a set$U$. My signal is a piece-wise constant "function"$Sig: t \mapsto s$, i.e. the signal at time$t$equals to some subset$s \subset U$. One can see$Sig(t)$as a stochastic process. ... 1answer 128 views ### Monte Carlo estimator with autocorrelated samples Given an integration problem$I=\int{f(x)dx}$, we can construct an ordinary Monte Carlo estimator as$E[I]=\sum\limits_i\frac{f(x_i)}{p(x_i)}$where the samples$x_i$are usually i.i.d. and drawn ... 1answer 435 views ### transform a polynomial into another one upto a constant I have a polynomial$p(x)=a_Nx^N+a_{N-1}x^{N-1}+\dots+a_0$. I want to convert this into another polynomial of same order, say$b_Ny^N+b_{N-1}y^{N-1}+\dots+b_0$. Is it possible to find a transformation ... 1answer 2k views ### Uniform sampling hemisphere and project in a specific direction [closed] Hi, I need to generate a 'uniform sample' over an hemisphere and once done project it in a specific vector direction. I have try the following, but it produce some errors... maybe you have an idea ? ... 0answers 28 views ### Approximating Minkowski Sum of 3 dimensional Convex Polytopes by Sampling Let$P_1,P_2...P_r$be a set of convex polytopes with$n_r$vertices in 3 dimensions. These polytopes basically represent uncertainties of '$r$' number of 3d-points respectively in space. The global ... 0answers 40 views ### Supremum distribution of band-limited functions with random spectrum Consider the properties of band-limited functions$f_N:[-\pi,\pi]\to\mathbb{R}$defined through their Fourier series$f_N(x)=\sum_{n=-N}^N c_n e^{inx}$where$c_n=a_n+i b_n$and both$a_n,b_n\sim\cal{...
As far as I know, the most popular way to sample from a polytope (in H-representation) $$\mathcal{P} := \{z \in \mathbb{R}^n | (Az)_j \le b_j\; \forall j=1,2,\ldots,m\}$$ ...
Sorry for the vague title but I couldn't find a better one. I want to compute the sum $S = \frac{1}{N}\sum_{i=1}^N c_i x_i$ where $c_i$s are known positive constants. The problem is that computing ...