Related papers: Distribution of the absolute indicator of random B…
In this paper we give an improvement of the degree of the homogeneous linear recurrence with integer coefficients that exponential sums of symmetric Boolean functions satisfy. This improvement is tight. We also compute the asymptotic…
We consider an estimation problem of expected functionals of a general random element that values in a metric space. If the functional forms an explicit function of some unknown parameters, we can estimate it by plugging-in a suitable…
Semi-bent Boolean functions are interesting from a cryptographic standpoint, since they possess several desirable properties such as having a low and flat Walsh spectrum, which is useful to resist linear cryptanalysis. In this paper, we…
The periodogram is a popular tool that tests whether a signal consists only of noise or if it also includes other components. The main issue of this method is to define a critical detection threshold that allows identification of a…
Suppose that f is a boolean function from F_2^n to {0,1} with spectral norm (that is the sum of the absolute values of its Fourier coefficients) at most M. We show that f may be expressed as +/- 1 combination of at most 2^(2^(O(M^4)))…
The aim of sequential change-point detection is to issue an alarm when it is thought that certain probabilistic properties of the monitored observations have changed. This work is concerned with nonparametric, closed-end testing procedures…
The global clustering coefficient is an effective measure for analyzing and comparing the structures of complex networks. The random annulus graph is a modified version of the well-known Erd\H{o}s-R\'{e}nyi random graph. It has been…
We present an algorithm for testing halfspaces over arbitrary, unknown rotation-invariant distributions. Using $\tilde O(\sqrt{n}\epsilon^{-7})$ random examples of an unknown function $f$, the algorithm determines with high probability…
We determine a connection between the weight of a Boolean function and the total weight of its first-order derivatives. The relationship established is used to study some cryptographic properties of Boolean functions. We establish a…
Estimating the proportion of signals hidden in a large amount of noise variables is of interest in many scientific inquires. In this paper, we consider realistic but theoretically challenging settings with arbitrary covariance dependence…
In this paper, a technique on constructing nonlinear resilient Boolean functions is described. By using several sets of disjoint spectra functions on a small number of variables, an almost optimal resilient function on a large even number…
We consider the breakdown of conformal and scale invariance in random systems with strongly random critical points. Extending previous results on one-dimensional systems, we provide an example of a three-dimensional system which has a…
Composites are often created to facilitate the work of decision-makers. Therefore, practical or theoretical considerations may lead to a priori weights of the indicators forming a composite. Composites that are created a weighted aggregates…
This paper presents a framework for abstracting uncertain or non-polynomial components of dynamical systems using polynomial constraints. This enables the application of polynomial-based analysis tools, such as sum-of-squares programming,…
A new measure of non-classical correlations is introduced and characterized. It tests the ability of using a state {\rho} of a composite system AB as a probe for a quantum illumination task [e.g. see S. Lloyd, Science 321, 1463 (2008)], in…
We consider very general "random integers" and (attempt to) prove that many multiplicative and additive functions of such integers have limiting distributions. These integers include, for instance, the curvatures of Apollonian circle…
This paper introduces a statistical method to decide whether two blocks in a pair of of images match reliably. The method ensures that the selected block matches are unlikely to have occurred "just by chance." The new approach is based on…
Recognizing, quantifying and visualizing associations between two variables is increasingly important. This paper investigates how a new function-valued measure of dependence, the quantile dependence function, can be used to construct tests…
Detection of the number of signals corrupted by high-dimensional noise is a fundamental problem in signal processing and statistics. This paper focuses on a general setting where the high-dimensional noise has an unknown complicated…
Recently, $b$-symbol codes are proposed to protect against $b$-symbol errors in $b$-symbol read channels. It is an interesting subject of study to consider the complete $b$-symbol weight distribution of cyclic codes since $b$-symbol metric…