Related papers: Asymptotic enumeration of correlation-immune boole…

We introduce a concept of asymptotic principal values which enables us to handle rigorously singular integrals of higher-order poles encountered in the computation of various quantities based on correlation functions of a vacuum. Several…

For N=1,2,..., let S_N be a simple random sample of size n=n_N from a population A_N of size N, where 0<=n<=N. Then with f_N=n/N, the sampling fraction, and 1_A the inclusion indicator that A is in S_N, for any H a subset of A_N of size k>=…

A well known result in the theory of uniform distribution modulo one (which goes back to Fej\'er and Csillag) states that the fractional parts $\{n^\alpha\}$ of the sequence $(n^\alpha)_{n\ge1}$ are uniformly distributed in the unit…

We study the influence of reflective boundaries on time-dependent responses of one-dimensional quantum fluids at zero temperature beyond the low-energy approximation. Our analysis is based on an extension of effective mobile impurity models…

We define and study the complexity of robust polynomials for Boolean functions and the related fault-tolerant quantum decision trees, where input bits are perturbed by noise. We compare several different possible definitions. Our main…

We describe a new class of Boolean functions which provide the presently best known trade-off between low computational complexity, nonlinearity and (fast) algebraic immunity. In particular, for $n\leq 20$, we show that there are functions…

The asymptotic expansion of $n$-dimensional cyclic integrals was expressed as a series of functionals acting on the symmetric function involved in the cyclic integral. In this article, we give an explicit formula for the action of these…

We establish asymptotic formulae for various correlations involving general divisor functions $d_k(n)$ and partial divisor functions $d_l(n,A)=\sum_{q|n:q\leq n^A}d_{l-1}(q)$, where $A\in[0,1]$ is a parameter and $k,l\in\mathbb{N}$ are…

Using the approach formulated in the previous papers of the author, a consistent procedure is developed for calculating non-classical asymptotic power terms in the total and the direct correlation functions of a critical fluid. Analyzing…

When k > 1 and s is sufficiently large in terms of k, we derive an explicit multi-term asymptotic expansion for the number of representations of a large natural number as the sum of s positive integral k-th powers.

In a recent paper (Tran et al., Ann.Phys.311(2004)204), some asymptotic number theoretical results on the partitioning of an integer were derived exploiting its connection to the quantum density of states of a many-particle system. We…

The fundamental task of group testing is to recover a small distinguished subset of items from a large population while efficiently reducing the total number of tests (measurements). The key contribution of this paper is in adopting a new…

Correlation functions in the restricted primitive model are calculated within a field-theoretic approach in the one-loop self-consistent Hartree approximation. The correlation functions exhibit damped oscillatory behavior as found before in…

Observational cohort studies with oversampled exposed subjects are typically implemented to understand the causal effect of a rare exposure. Because the distribution of exposed subjects in the sample differs from the source population,…

Discrete kernel smoothing is now gaining importance in nonparametric statistics. In this paper, we investigate some asymptotic properties of the normalized discrete associated-kernel estimator of a probability mass function. We show, under…

In 2008, Cusick {\it et al.} conjectured that certain elementary symmetric Boolean functions of the form $\sigma_{2^{t+1}l-1, 2^t}$ are the only nonlinear balanced ones, where $t$, $l$ are any positive integers, and…

We study the asymptotic behavior of two statistics defined on the symmetric group S_n when n tends to infinity: the number of elements of S_n having k records, and the number of elements of S_n for which the sum of the positions of their…

This paper considers the problem of approximating a Boolean function $f$ using another Boolean function from a specified class. Two classes of approximating functions are considered: $k$-juntas, and linear Boolean functions. The $n$ input…

We examine a hierarchy of equivalence classes of quasi-random properties of Boolean Functions. In particular, we prove an equivalence between a number of properties including balanced influences, spectral discrepancy, local strong…

Given a Boolean function f, the (Hamming) weight wt(f) and the nonlinearity N(f) are well known to be important in designing functions that are useful in cryptography. The nonlinearity is expensive to compute, in general, so any shortcuts…