Related papers: Finding attracting sets using combinatorial multiv…
Multiway datasets are commonly analyzed using unsupervised matrix and tensor factorization methods to reveal underlying patterns. Frequently, such datasets include timestamps and could correspond to, for example, health-related measurements…
This paper presents regional attraction of line segment maps, and hereby poses the problem of line segment detection (LSD) as a problem of region coloring. Given a line segment map, the proposed regional attraction first establishes the…
We announce the discovery of a diffeomorphism of a three-dimensional manifold with boundary which has two disjoint attractors. Each attractor attracts a set of positive $3$-dimensional Lebesgue measure whose points of Lebesgue density are…
The structure of invariant regions and globally attracting regions is fundamental to understanding the dynamical properties of reaction network models. We describe an explicit construction of the minimal invariant regions and minimal…
Coherent and dissipative couplings, respectively characterised by energy level repulsion and attraction, each have different applications for quantum information processing. Thus, a system in which both coherent and dissipative couplings…
Modeling heterogeneous correlated time series requires the ability to learn hidden dynamic relationships between component time series with possibly varying periodicities and generative processes. To address this challenge, we formulate and…
The dynamics by iteration of a function on a compact metric space, sometimes called a cascade, can be extended to the dynamics of a closed relation on such a space. Here we apply this relation dynamics to study semiflows (and their relation…
In this work, a new class of vector-valued phase field models is presented, where the values of the phase parameters are constrained by a convex set. The generated phase fields feature the partition of the domain into patches of distinct…
This paper presents a region-partition based attraction field dual representation for line segment maps, and thus poses the problem of line segment detection (LSD) as the region coloring problem. The latter is then addressed by learning…
We describe a computational method for constructing a coarse combinatorial model of some dynamical system in which the macroscopic states are given by elementary cycling motions of the system. Our method is in particular applicable to time…
A large class of real $3$-dimensional nilpotent polynomial vector fields of arbitrary degree is considered. The aim of this work is to present general properties of the discrete and continuous dynamical systems induced by these vector…
The combination of complex networks and dynamic systems research is poised to yield some of the most interesting theoretic and applied scientific results along the forthcoming decades. The present work addresses a particularly important…
Many PDEs (Burgers' equation, KdV, Camassa-Holm, Euler's fluid equations,...) can be formulated as infinite-dimensional Lie-Poisson systems. These are Hamiltonian systems on manifolds equipped with Poisson brackets. The Poisson structure is…
Recent progress about "modular localization" reveals that, as a result of the S-Matrix in its role of a "relative modular invariant of wedge-localization, one obtains a new non-perturbative constructive setting of local quantum physicis…
Using Conley theory we show that local attractors remain (past) attractors under small non-autonomous perturbations. In particular, the attractors of the perturbed systems will have positive invariant neighborhoods and converge upper…
Framed combinatorial topology is a recent approach to tame geometry which expresses higher-dimensional stratified spaces via tractable combinatorial data. The resulting theory of spaces is well-behaved and computable. In this paper we…
Recent experiments on convection in binary mixtures have shown that the interaction between localized waves (pulses) can be repulsive as well as {\it attractive} and depends strongly on the relative {\it orientation} of the pulses. It is…
In this study, we introduce Convolutional Transformer Neural Collaborative Filtering (CTNCF), a novel approach aimed at enhancing recommendation systems by effectively capturing high-order structural information in user-item interactions.…
Platooning on highways with connected and automated vehicles (CAVs) has attracted considerable attention, while how to mange and coordinate platoons in urban networks remains largely an open question. This scientific gap mainly results from…
Matrix factorization (MF) is a versatile learning method that has found wide applications in various data-driven disciplines. Still, many MF algorithms do not adequately scale with the size of available datasets and/or lack…