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This paper addresses the problem of distributed learning under communication constraints, motivated by distributed signal processing in wireless sensor networks and data mining with distributed databases. After formalizing a general model…

We quantify the presence of direct processes in the S-matrix of chaotic microwave cavities with absorption in the one-channel case. To this end the full distribution P_S(S) of the S-matrix, i.e. S=\sqrt{R}e^{i\theta}, is studied in cavities…

For $G=G_{n, 1/2}$, the Erd\H{o}s--Renyi random graph, let $X_n$ be the random variable representing the number of distinct partitions of $V(G)$ into sets $A_1, \ldots, A_q$ so that the degree of each vertex in $G[A_i]$ is divisible by $q$…

Compositional disorder is common in crystal compounds. In these compounds, some atoms are randomly distributed at some crystallographic sites. For such compounds, randomness forms many non-identical independent structures. Thus, calculating…

We derive and prove the path-kernel formula for the linear response (parameter-derivative of averaged statistics) of SDEs. The parameter may affect the drift coefficient, the diffusion coefficient, and the initial condition. The formula…

Let $b_k(n)$ denote the $k-$regular partitons of a natural number $n$. In this paper, we study the behavior of $b_k(n)$ modulo composite integers $M$ which are coprime to $6$. Specially, we prove that for arbitrary $k-$regular partiton…

This paper proposes a generalisation of the Pearson type II distribution, which shall termed Pearson Type II-Riesz distribution, based in the Kotz-Riesz distribution. Specifically, the central nonsingular matricvariate generalised Pearson…

Let $\mu$ be a probability measure on $\mathbb C$, and let $P_n$ be the random polynomial whose zeros are sampled independently from $\mu$. We study the asymptotic distribution of zeros of high-order derivatives of $P_n$. We show that, for…

I propose kernel ridge regression estimators for nonparametric dose response curves and semiparametric treatment effects in the setting where an analyst has access to a selected sample rather than a random sample; only for select…

We consider orthogonal, unitary, and symplectic ensembles of random matrices with (1/a)(ln x)^2 potentials, which obey spectral statistics different from the Wigner-Dyson and are argued to have multifractal eigenstates. If the coefficient…

Let $G$ be a multiplicative subsemigroup of the general linear group $\Gl(\mathbb{R}^d)$ which consists of matrices with positive entries such that every column and every row contains a strictly positive element. Given a $G$--valued random…

A distribution whose normalization constant is an A-hypergeometric polynomial is called an A-hypergeometric distribution. Such a distribution is in turn a generalization of the generalized hypergeometric distribution on the contingency…

Diaconis and Griffiths (2014) study the multivariate Krawtchouk polynomials orthogonal on the multinomial distribution. In this paper we derive the reproducing kernel orthogonal polynomials Q_n(x,y};N,p) on the multinomial distribution…

We consider the accelerated propagation of solutions to equations with a nonlocal linear dispersion on the real line and monostable nonlinearities (both local or nonlocal, however, not degenerated at $0$), in the case when either of the…

We determine the rank of a random matrix over an arbitrary field with prescribed numbers of non-zero entries in each row and column. As an application we obtain a formula for the rate of low-density parity check codes. This formula…

We are concerned with the behavior of the eigenvalues of renormalized sample covariance matrices of the form C_n=\sqrt{\frac{n}{p}}\left(\frac{1}{n}A_{p}^{1/2}X_{n}B_{n}X_{n}^{*}A_{p}^{1/2}-\frac{1}{n}\tr(B_{n})A_{p}\right) as $p,n\to…

We establish the limiting spectral distribution of Kendall's correlation matrices in the moderate high-dimensional regime where the dimension grows slower than the sample size. Our framework allows observations to be independent but not…

We consider the binomial random set model $[n]_p$ where each element in $\{1,\dots,n\}$ is chosen independently with probability $p:=p(n)$. We show that for essentially all regimes of $p$ and very general conditions for a matrix $A$ and a…

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…

A nonparametric family of conditional distributions is introduced, which generalizes conditional exponential families using functional parameters in a suitable RKHS. An algorithm is provided for learning the generalized natural parameter,…