Related papers: Symmetric Distributions from Shallow Circuits
We describe a general approach of determining the distribution of spanning subgraphs in the random graph $\G(n,p)$. In particular, we determine the distribution of spanning subgraphs of certain given degree sequences, which is a…
The action of a noise operator on a code transforms it into a distribution on the respective space. Some common examples from information theory include Bernoulli noise acting on a code in the Hamming space and Gaussian noise acting on a…
Fourier analysis and representation of circular distributions in terms of their Fourier coefficients, is quite commonly discussed and used for model-free inference such as testing uniformity and symmetry etc. in dealing with 2-dimensional…
Implementations of the Bruggeman and Maxwell Garnett homogenization formalisms were developed to estimate the relative permittivity dyadic of a homogenized composite material (HCM), namely $\underline{\underline{\epsilon}}^{\rm HCM}$,…
A metric probability space $(\Omega,d)$ obeys the ${\it concentration\; of\; measure\; phenomenon}$ if subsets of measure $1/2$ enlarge to subsets of measure close to 1 as a transition parameter $\epsilon$ approaches a limit. In this paper…
The distribution of reversible programs tends to a limit as their size increases. For problems with a Hamming distance fitness function the limiting distribution is binomial with an exponentially small chance (but non~zero) chance of…
Homogeneous rotation symmetric Boolean functions have been extensively studied in recent years because of their applications in cryptography. Little is known about the basic question of when two such functions are affine equivalent. The…
Assume that $m,s\in\mathbb N$, $m>1$, while $f$ is a polynomial with integer coefficients, $\text{deg}~f>1$, $f^{(i)}$ is the $i$th iteration of the polynomial $f$, $\kappa_n$ has a discrete uniform distribution on the set $\{0,1,\ldots,m^n…
The scattering of quantum particles by non-hermitian (generally nonlocal) potentials in one dimension may result in asymmetric transmission and/or reflection from left and right incidence. Eight generalized symmetries based on the discrete…
A Boolean function of n bits is balanced if it takes the value 1 with probability 1/2. We exhibit a balanced Boolean function with a randomized evaluation procedure (with probability 0 of making a mistake) so that on uniformly random…
We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional…
We initiate the study of \emph{inverse} problems in approximate uniform generation, focusing on uniform generation of satisfying assignments of various types of Boolean functions. In such an inverse problem, the algorithm is given uniform…
We investigate the weight distribution of random binary linear codes. For $0<\lambda<1$ and $n\to\infty$ pick uniformly at random $\lambda n$ vectors in $\mathbb{F}_2^n$ and let $C \le \mathbb{F}_2^n$ be the orthogonal complement of their…
We consider Boolean functions f:{-1,1}^n->{-1,1} that are close to a sum of independent functions on mutually exclusive subsets of the variables. We prove that any such function is close to just a single function on a single subset. We also…
The determination of weight distribution of cyclic codes involves evaluation of Gauss sums and exponential sums. Despite of some cases where a neat expression is available, the computation is generally rather complicated. In this note, we…
This paper primarily concerns the variance estimate of zeros of systems of random holomorphic sections associated with a sequence of smooth Hermitian holomorphic line bundles on a compact Kahler manifold X. The probability measures taken…
We propose a family of four-parameter distributions that contain the K-distribution as special case. The family is derived as a mixture distribution that uses the three-parameter reflected Gamma distribution as parental and the…
The multiplicity distributions produced by the variation of time-dependent gravitational fields in a conformally flat background geometry belong to the same class of infinitely divisible distributions found, for fixed centre of mass…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes…