Related papers: On Sloane's persistence problem
In this paper we examine the use of topological methods for multivariate statistics. Using persistent homology from computational algebraic topology, a random sample is used to construct estimators of persistent homology. This estimation…
Approximating nonlinear dynamics with a truncated perturbative expan- sion may be accurate for a while, but it in general breaks down at a long time scale that is one over the small expansion parameter. There are interesting occasions in…
The existence of stationary distributions to distribution dependent stochastic differential equations are investigated by using the ergodicity of the associated decoupled equation and the Schauder fixed point theorem. By using Zvonkin's…
We present an exact field theoretical representation of the statistical mechanics of classical hard-core Coulomb systems. This approach generalizes the usual sine-Gordon theory valid for point-like charges or lattice systems to continuous…
Persistence diagrams, which summarize the birth and death of homological features extracted from data, are employed as stable signatures for applications in image analysis and other areas. Besides simply considering the multiset of…
We consider a control problem for a heterogeneous population composed of agents able to switch at any time between different options. The controller aims to maximize an average gain per time unit, supposing that the population is of…
This thesis determines some of the implications of non-universal and emergent universal statistics on arithmetic correlations and fluctuations of arithmetic functions, in particular correlations amongst prime numbers and the variance of the…
The theory of the effect of external fluctuation force on the stability and spatial distribution of mutually interacting and slowly evaporating charged drops, levitated in an electrodynamic balance, is presented using classical…
Let $X=(X_1,\ldots,X_n)$ be a vector of i.i.d. random variables where $X_i$'s take values over $\mathbb{N}$. The purpose of this paper is to study the number of weakly increasing subsequences of $X$ of a given length $k$, and the number of…
We study the long time statistics of a two-dimensional Hamiltonian system in the presence of Gaussian white noise. While the original dynamics is known to exhibit finite time explosion, we demonstrate that under the impact of the stochastic…
This paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mechanics. We adopt a new point of view which has emerged progressively in recent years, and which takes…
Let G be a reductive algebraic group over Q, and suppose that Gamma is an arithmetic subgroup of G(R) defined by congruence conditions. A basic problem in arithmetic is to determine the multiplicities of discrete series representations in…
Expanding upon our prior findings on the proximity of dynamics between integrable and non-integrable systems within the framework of nonlinear Schr\"odinger equations, we examine this phenomenon for the focusing Discrete Gross-Pitaevskii…
We give continued fraction algorithms for a particular class of Fuchsian triangle groups. In particular, we give an explicit form of each such group that is a subgroup of the Hilbert modular group of its trace field and provide an interval…
Quasi-invariant measures for non-discrete groups of diffeomorphisms containing a Morse-Smale dynamics are studied. The assumption concerning the presence of a Morse-Smale dynamics allows us to extend to higher dimensions a number of…
In this paper, we discuss long-time behavior of sample paths for a wide range of regime-switching diffusions. Firstly, almost sure asymptotic stability is concerned (i) for regime-switching diffusions with finite state spaces by the…
We consider a walker that at each step keeps the same direction with a probabilitythat depends on the time already spent in the direction the walker is currently moving. In this paper, we study some asymptotic properties of this persistent…
A monotone self-mapping of the nonnegative orthant induces a monotone discrete-time dynamical system which evolves on the same orthant. If with respect to this system the origin is attractive then there must exists points whose image under…
We consider linear, time-dependent and skew-adjoint perturbations of periodic transport equations on the one-dimensional torus. We describe the long-time behavior of solutions for all non-degenerate perturbations in resonant regime, proving…
We introduce a family of area-preserving maps representing a (non-trivial) two-dimensional extension of the Pomeau-Manneville family in one dimension. We analyze the long-time behavior of recurrence time distributions and correlations,…