The paper deals with resilient state estimation of cyber-physical systems subject to switching signal attacks and fake measurement injection. In particular, the random set paradigm is adopted in order to model the switching nature of the signal attack and the fake measurement injection via Bernoulli and/or Poisson random sets. The problem of jointly detecting a signal attack and estimating the ...

In general, wavelet coefficients are composed of a few large coefficients and a lot of small ones. Therefore, each wavelet coefficient is efficiently modeled as a random variable of a Bernoulli-Gaussian mixture distribution with unknown parameters. The Bernoulli-Gaussian mixture is composed of the multiplication of the Bernoulli random variable and the Gaussian mixture random variable. In this ...

Bernoullicity is the strongest mixing property that a measuretheoretic dynamical system can have. This is known to be intimately connected to the so-called d̄ metric on processes, introduced by Ornstein. In this paper, we consider families of measures arising in a number of contexts and give conditions under which the measures depend d̄-continuously on the parameters. At points where there is d̄-c...

Following is a study of percolation in the hyperbolic plane H and on regular tilings in the hyperbolic plane. The processes discussed include Bernoulli site and bond percolation on planar hyperbolic graphs, invariant dependent percolations on such graphs, and Poisson-Voronoi-Bernoulli percolation. We prove the existence of three distinct nonempty phases for the Bernoulli processes. In the first...

Recently, λ-Bernoulli and λ-Euler numbers are studied in [5, 10]. The purpose of this paper is to present a systematic study of some families of the q-extensions of the λBernoulli and the λ-Euler numbers by using the bosonic p-adic q-integral and the fermionic p-adic q-integral. The investigation of these λ-q-Bernoulli and λ-q-Euler numbers leads to interesting identities related to these objec...

The three fundamental properties of the Bernoulli numbers, namely, the theorem of von Staudt-Clausen, von Staudt’s second theorem, and Kummer’s original congruence, are generalized to new numbers that we call generalized Bernoulli-Hurwitz numbers. These are coefficients of power series expansion of a higher genus algebraic function with respect to suitable variable. Our generalization strongly ...

In this paper we consider a (possibly continuous) space of Bernoulli experiments. We assume that the Bernoulli distributions are correlated. All evidence data comes in the form of successful or failed experiments at different points. Current state-ofthe-art methods for expressing a distribution over a continuum of Bernoulli distributions use logistic Gaussian processes or Gaussian copula proces...