Related papers: Finding attracting sets using combinatorial multiv…
Dependence of magnetic field generation on the rotation rate is explored by direct numerical simulation of magnetohydrodynamic convective attractors in a plane layer of conducting fluid with square periodicity cells for the Taylor number…
We review some relations occurring between the combinatorial intersection theory on the moduli spaces of stable curves and the asymptotic behavior of the 't Hooft-Kontsevich matrix integrals. In particular, we give an alternative proof of…
The algebraic structure of the attractors in a dynamical system determine much of its global dynamics. The collection of all attractors has a natural lattice structure, and this structure can be detected through attracting neighborhoods,…
It is believed that some stars have two or more convection zones in close proximity near to the stellar photosphere. These zones are separated by convectively stable regions that are relatively narrow. Due to the close proximity of these…
There exists a variety of physically interesting situations described by continuous maps that are nondifferentiable on some surface in phase space. Such systems exhibit novel types of bifurcations in which multiple coexisting attractors can…
I investigate a class of dynamical systems in which finite pieces of spacetime contain finite amounts of information. Most of the guiding principles for designing these systems are drawn from general relativity: the systems are…
Time series motifs play an important role in the time series analysis. The motif-based time series clustering is used for the discovery of higher-order patterns or structures in time series data. Inspired by the convolutional neural network…
Dynamical systems are found in innumerable forms across the physical and biological sciences, yet all these systems fall naturally into universal equivalence classes: conservative or dissipative, stable or unstable, compressible or…
We consider the Maxwell-Bloch system which is a finite-dimensional approximation of the coupled nonlinear Maxwell-Schr\"odinger equations. The approximation consists of one-mode Maxwell field coupled to two-level molecule. We construct…
Learning and understanding car-following (CF) behaviors are crucial for microscopic traffic simulation. Traditional CF models, though simple, often lack generalization capabilities, while many data-driven methods, despite their robustness,…
We introduce a class of theories called metastable, including the theory of algebraically closed valued fields (ACVF) as a motivating example. The key local notion is that of definable types dominated by their stable part. A theory is…
This work presents a purely data-driven, wavelet-based framework for modal identification and reduced-order modeling of mechanical systems with assumed linear dynamics characterized by closely spaced modes with classical or non-classical…
We study the entanglement in momentum space of the ground state of a disordered one-dimensional fermion lattice model with attractive interaction. We observe two components in the entanglement spectrum, one of which is related to…
We propose a new framework for the study of continuous time dynamical systems on networks. We view such dynamical systems as collections of interacting control systems. We show that a class of maps between graphs called graph fibrations…
Correlation Filters (CFs) are a class of classifiers which are designed for accurate pattern localization. Traditionally CFs have been used with scalar features only, which limits their ability to be used with vector feature representations…
In this paper, we develop a comprehensive framework to estimate regions of attraction of equilibria for dynamics associated with general vector fields. This framework combines Koopman operator-based methods with rigorous validation…
Symbolic dynamics, which partitions an infinite number of finite-length trajectories into a finite number of trajectory sets, describes the dynamics of a system in a simplified and coarse-grained way with a limited number of symbols. The…
In this paper we explore how to describe a bulk moving particle in the dual conformal field theories (CFTs). One aspect of this problem is to construct the dual state of the moving particle. On the other hand one should find the…
Let $X$ be a Banach space and $f,g:X\rightarrow X$ be contractions. We investigate the set $$ C_{f,g}:=\{w\in X:\m{ the attractor of IFS }\F_w=\{f,g+w\}\m{ is connected}\}. $$ The motivation for our research comes from papers of Mihail and…
Topology based analysis of time-series data from dynamical systems is powerful: it potentially allows for computer-based proofs of the existence of various classes of regular and chaotic invariant sets for high-dimensional dynamics.…