We consider a randomly forced Ginzburg–Landau equation on an unbounded domain. The forcing is smooth and homogeneous in space and white noise in time. We prove existence and smoothness of solutions, existence of an invariant measure for the corresponding Markov process and we define the spatial densities of topological entropy, of measure-theoretic entropy, and of upper box-counting dimension. ...

We explore a hidden feedback loops effect in online recommender systems. Feedback result degradation of multi-armed bandit (MAB) recommendations to small subset and loss coverage novelty. study how uncertainty noise user interests influence the existence loops. First, we show that an unbiased additive random does not prevent loop. Second, demonstrate non-zero probability resetting is sufficient...

We present a weakly nonlinear analysis of our recently developed model for the formation of crime patterns. Using a perturbative approach, we find amplitude equations that govern the development of crime “hotspot” patterns in our system in both the one-dimensional (1D) and two-dimensional (2D) cases. In addition to the supercritical spots already shown to exist in our previous work, we prove he...

The purpose of this article is to formulate a number of probabilis-tic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the general equivalence of the existence of a hidden variable and the existence of a joint probability distribution of the observable quantities, whether finit...

The purpose of this article is to formulate a number of probabilis-tic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the general equivalence of the existence of a hidden variable and the existence of a joint probability distribution of the observable quantities, whether finit...