Related papers: Weak Disorder in Fibonacci Sequences
We analyse the so-called Marginal Instability of linear switching systems, both in continuous and discrete time. This is a phenomenon of unboundedness of trajectories when the Lyapunov exponent is zero. We disprove two recent conjectures of…
One of the most challenging problems in microbiology is to understand how a small fraction of microbes that resists killing by antibiotics can emerge in a population of genetically identical cells, the phenomenon known as persistence or…
Motivated by the study of pattern avoidance in the context of permutations and ordered partitions, we consider the enumeration of weak-ordering chains obtained as leaves of certain restricted rooted trees. A tree of order $n$ is generated…
We explore the impact of weak disorder on the dynamics of classical particles in a periodically oscillating lattice. It is demonstrated that the disorder induces a hopping process from diffusive to regular motion i.e. we observe the…
We study a recursion that generates real sequences depending on a parameter $x$. Given a negative $x$ the growth of the sequence is very difficult to estimate due to canceling terms. We reduce the study of the recursion to a problem about a…
We present a certain generalization of a recent result of M. I. Cirnu on linear recurrence relations with coefficient in progressions [2]. We provide some interesting examples related to some well-known integer sequences, such as Fibonacci…
We investigate general properties of number sequences which allow explicit representation in terms of products. We find that such sequences form whole families of number sequences sharing similar recursive identities. Restricting to the…
This work is a follow-up to our previous work "A numerical approach related to defect-type theories for some weakly random problems in homogenization" (preprint available on this archive). It extends and complements, both theoretically and…
Using the resonant-state expansion for leaky optical modes of a planar Bragg microcavity, we investigate the influence of disorder on its fundamental cavity mode. We model the disorder by randomly varying the thickness of the Bragg-pair…
The dynamical behaviour of a weakly diluted fully-inhibitory network of pulse-coupled spiking neurons is investigated. Upon increasing the coupling strength, a transition from regular to stochastic-like regime is observed. In the…
In this paper, we give precise rates of convergence in the strong invariance principle for stationary sequences of bounded real-valued random variables satisfying weak dependence conditions. One of the main ingredients is a new Fuk-Nagaev…
We obtain the first results on convergence rates in the Prokhorov metric for the weak invariance principle (functional central limit theorem) for deterministic dynamical systems. Our results hold for uniformly expanding/hyperbolic (Axiom A)…
We investigate the effects of weak disorder on the time evolution of a wave packet in an array of optical waveguides with parity-symmetric evanescent coupling and, open or periodic boundary conditions. For an open array, when the disorder…
Weak superimposed codes are combinatorial structures related closely to generalized cover-free families, superimposed codes, and disjunct matrices in that they are only required to satisfy similar but less stringent conditions. This class…
We consider the problem of the approximation of the solution of a one-dimensional SDE with non-globally Lipschitz drift and diffusion coefficients behaving as $x^\alpha$, with $\alpha>1$. We propose an (semi-explicit) exponential-Euler…
The optical properties of materials are strongly influenced by disorder. Control of disorder in photonic materials can unveil interesting optical properties. We have found an engineered photonic structure for which the average light…
We report a numerical investigation of the fluctuations of the Lyapunov exponent of a two dimensional non-interacting disordered system. While the ratio of the mean to the variance of the Lyapunov exponent is not constant, as it is in one…
We consider statistical learning question for $\psi$-weakly dependent processes, that unifies a large class of weak dependence conditions such as mixing, association,$\cdots$ The consistency of the empirical risk minimization algorithm is…
We investigate the effect of topological disorder on a system of forced threshold elements, where each element is arranged on top of complex heterogeneous networks. Numerical results indicate that the response of the system to a weak signal…
The system size dependence of the multifractal spectrum $f(\alpha)$ and its singularity strength $\alpha$ is investigated numerically. We focus on one-dimensional (1D) and 2D disordered systems with long-range random hopping amplitudes in…