Related papers: Stochastic Comparison of Parallel Systems with Log…
Machine learning systems appear stochastic but are deterministically random, as seeded pseudorandom number generators produce identical realisations across repeated executions. Standard evaluation practice typically treats runs across…
The parallel computational complexity of the quadratic map is studied. A parallel algorithm is described that generates typical pseudotrajectories of length t in a time that scales as log t and increases slowly in the accuracy demanded of…
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…
We study the stochastic block model which is often used to model community structures and study community-detection algorithms. We consider the case of two blocks in regard to its largest connected component and largest biconnected…
In this paper, we study the order of the largest connected component of a random graph having two sources of randomness: first, the graph is chosen randomly from all graphs with a given degree sequence, and then bond percolation is applied.…
The multiplicity distributions measured in proton proton collisions at the LHC exhibit interesting new features. One of them is the appearance of substructures, such as the so-called "shoulder" at large multiplicities. The most natural…
The concept of "stochastic precedence" between two real-valued random variables has often emerged in different applied frameworks. In this paper we consider a slightly more general, and completely natural, concept of stochastic precedence…
The reduced density matrix of many-body systems possessing an additive conserved quantity can be decomposed in orthogonal sectors which can be independently analyzed. Recently, these have been proven to equally contribute to entanglement…
This paper addresses the problem of parallelizing computations to study non-linear dynamics in large networks of non-locally coupled oscillators using heterogeneous computing resources. The proposed approach can be applied to a variety of…
In a $\delta-$shock model, a system subject to randomly occurring shocks, the system fails when the time between two successive shocks lies below a threshold $\delta$. In this note, we study the generalization of this model where such…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
In this article, we revisit the paper by Kundu et al.~(2024), presenting new results and insights for both identical and non-identical independent random variables. We derive sufficient conditions for preserving the hazard rate and reversed…
We investigate stochastic comparisons between exponential family distributions and their mixtures with respect to the usual stochastic order, the hazard rate order, the reversed hazard rate order, and the likelihood ratio order. A general…
Recent studies have shown that a system composed from several randomly interdependent networks is extremely vulnerable to random failure. However, real interdependent networks are usually not randomly interdependent, rather a pair of…
In this article, we introduce finite mixture models (FMMs) renowned for capturing population heterogeneity. Our focus lies in establishing stochastic comparisons between two arithmetic (finite) mixture models, employing the vector…
An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We…
We study the problem of comparing ageing patterns of the lifetime of k-out-of-n systems. Mathematically, this reduces to being able to decide about a stochastic ordering relationship between different order statistics. We discuss such…
We present a scalable methodology to verify stochastic hybrid systems. Using the Mori-Zwanzig reduction method, we construct a finite state Markov chain reduction of a given stochastic hybrid system and prove that this reduced Markov chain…
We consider the problem of sampling $n$ numbers from the range $\{1,\ldots,N\}$ without replacement on modern architectures. The main result is a simple divide-and-conquer scheme that makes sequential algorithms more cache efficient and…
Given two vectors in Euclidean space, how unlikely is it that a random vector has a larger inner product with the shorter vector than with the longer one? When the random vector has independent, identically distributed components, we…