Related papers: An Invariance Principle for the Multi-slice, with …

Inference after model selection presents computational challenges when dealing with intractable conditional distributions. Markov chain Monte Carlo (MCMC) is a common method for sampling from these distributions, but its slow convergence…

Statistical sufficiency formalizes the notion of data reduction. In the decision theoretic interpretation, once a model is chosen all inferences should be based on a sufficient statistic. However, suppose we start with a set of procedures…

The purpose of this short article is to announce, and briefly describe, a Maple package, PARTITIONS, that (inter alia) completely automatically discovers, and then proves, explicit expressions (as sums of quasi-polynomials) for pm(n) for…

Let $\mathcal{M}$ be a set with $M$ elements, let $\psi :\mathcal{M}\to\mathcal{M}$ be a bijective involution, and let~$\boldsymbol{\mathcal{X}}_{\psi}$ be the set of sequences $(x_1,\dots,x_M)\in\mathcal{M}^M$ with the property that…

Let $V$ be a vector space over a finite field $k$. We give a condition on a subset $A \subset V$ that allows for a local criterion for checking when a function $f:A \to k$ is a restriction of a polynomial function of degree $<m$ on $V$. In…

Given graphs H_1,...,H_k, we study the minimum order of a graph G such that for each i, the induced copies of H_i in G cover V(G). We prove a general upper bound of twice the sum of the numbers m_i, where m_i is one less than the order of…

Strong invariance principles describe the error term of a Brownian approximation of the partial sums of a stochastic process. While these strong approximation results have many applications, the results for continuous-time settings have…

A stationary subdivision scheme generates the full space of polynomials of degree up to $k$ if and only if its mask satisfies sum rules of order $k+1$, or its symbol satisfies zero conditions of order $k+1$. This property is often called…

A multiple integral functional is equivalent to a curvilinear integral functional, if the domain is a hyper-parallelepiped, but equivalence is only theoretical. The introduction of this kind of functionals in multitime optimal control…

We consider the question of approximating Max 2-CSP where each variable appears in at most $d$ constraints (but with possibly arbitrarily large alphabet). There is a simple $(\frac{d+1}{2})$-approximation algorithm for the problem. We prove…

Fix an integer k, and let I(l), l=1,2,..., be a sequence of k-dimensional vectors of multiple Wiener-It\^o integrals with respect to a general Gaussian process. We establish necessary and sufficient conditions to have that, as l diverges,…

We prove that permutations with few inversions exhibit a local-global dichotomy in the following sense. Suppose ${\boldsymbol\sigma}$ is a permutation chosen uniformly at random from the set of all permutations of $[n]$ with exactly…

In this paper we show the distributions of sliding block patterns for Bernoulli processes with finite alphabet, which is not based on the induction on sample size. We show a new inclusion-exclusion formula in multivariate generating…

We present a novel verification technique to prove interesting properties of a class of array programs with a symbolic parameter N denoting the size of arrays. The technique relies on constructing two slightly different versions of the same…

The factor graph of an instance of a symmetric constraint satisfaction problem on n Boolean variables and m constraints (CSPs such as k-SAT, k-AND, k-LIN) is a bipartite graph describing which variables appear in which constraints. The…

We study optimization problems in which a linear functional is maximized over probability measures that are dominated by a given measure according to an integral stochastic order in an arbitrary dimension. We show that the following four…

Recent likelihood theory produces $p$-values that have remarkable accuracy and wide applicability. The calculations use familiar tools such as maximum likelihood values (MLEs), observed information and parameter rescaling. The usual…

A system is invariant with respect to an input transformation if we can transform any dynamic input by this function and obtain the same output dynamics after adjusting the initial conditions appropriately. Often, the set of all such input…

The present phase of Machine Learning is characterized by supervised learning algorithms relying on large sets of labeled examples ($n \to \infty$). The next phase is likely to focus on algorithms capable of learning from very few labeled…

Classical algorithms in numerical analysis for numerical integration (quadrature/cubature) follow the principle of approximate and integrate: the integrand is approximated by a simple function (e.g. a polynomial), which is then integrated…