Related papers: Locally Sampleable Uniform Symmetric Distributions
Data uniformity is a concept associated with several semantic data characteristics such as lack of features, correlation and sample bias. This article introduces a novel measure to assess data uniformity and detect uniform pointsets on…
We prove several new results on the Hamming weight of bounded uniform and small-bias distributions. We exhibit bounded-uniform distributions whose weight is anti-concentrated, matching existing concentration inequalities. This construction…
In this paper, we propose efficient probabilistic algorithms for several problems regarding the autocorrelation spectrum. First, we present a quantum algorithm that samples from the Walsh spectrum of any derivative of $f()$. Informally, the…
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…
Let Boolean function $f:\{0,1\}^n\longrightarrow \{0,1\}$ where $|\{x\in\{0,1\}^n| f(x)=1\}|=a\geq 1$. To search for an $x\in\{0,1\}^n$ with $f(x)=1$, by Grover's algorithm we can get the objective with query times $\lfloor…
We establish a comprehensive probability theory for coherent transport of random waves through arbitrary linear media. The transmissivity distribution for random coherent waves is a fundamental B-spline with knots at the transmission…
We introduce new method for generating correlated or uncorrelated Bernoulli random variables by using the binary expansion of a continuous random variable with support on the unit interval. We show that when this variable has a symmetric…
In this work, we study stability of distributed filtering of Markov chains with finite state space, partially observed in conditionally Gaussian noise. We consider a nonlinear filtering scheme over a Distributed Network of Agents (DNA),…
We study the problem of estimating a monotone function $f:\{0,1\}^d\to[0,1]$ from noisy observations at uniformly random vertices of the Boolean hypercube. As a measure of complexity for the target~$f$, we use the total $L^1$-influence…
We develop efficient binary (i.e., 1-bit) and multi-bit coding schemes for estimating the scale parameter of $\alpha$-stable distributions. The work is motivated by the recent work on one scan 1-bit compressed sensing (sparse signal…
We suggest an upper bound on binomial coefficients that holds over the entire parameter range and whose form repeats the form of the de Moivre-Laplace approximation of the symmetric binomial distribution. Using the bound, we estimate the…
We give a geometric characterization of vectorial boolean functions with differential uniformity less or equal to 4.
It is shown that the topologies and nestings of the zero and nodal sets of random (Gaussian) band limited functions have universal laws of distribution. Qualitative features of the supports of these distributions are determined. In…
It is shown that the topologies and nestings of the zero and nodal sets of random (Gaussian) band limited functions have universal laws of distribution. Qualitative features of the supports of these distributions are determined. In…
We study the volume distribution of nodal domains of random band-limited functions on generic manifolds, and find that in the high energy limit a typical instance obeys a deterministic universal law, independent of the manifold. Some of the…
Bialek, Callan and Strong have recently given a solution of the problem of determining a continuous probability distribution from a finite set of experimental measurements by formulating it as a one-dimensional quantum field theory. This…
This article presents an efficient algorithm to generate a discrete uniform distribution on a set of $p$ elements using a biased random source for $p$ prime. The algorithm generalizes Von Neumann's method and improves computational…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
We are interested in fixed points in Boolean networks, {\em i.e.} functions $f$ from $\{0,1\}^n$ to itself. We define the subnetworks of $f$ as the restrictions of $f$ to the subcubes of $\{0,1\}^n$, and we characterizes a class…
We derive a spectral interpretation of the pivot operation on a graph and generalise this operation to hypergraphs. We establish lower bounds on the number of flat spectra of a Boolean function, depending on internal structures, with…