Related papers: Integral Value Transformations: A Class of Discret…
In this contribution I summarize the achievements of separation of variables in integrable quantum systems from the point of view of path integrals. This includes the free motion on homogeneous spaces, and motion subject to a potential…
We construct hierarchies of integrable systems invariant under the two-dimensional Darboux-Toda mapping for noncommuting objects, thus generalizing to the noncommutative case the integrable mapping approach to nonlinear dynamical systems.…
Dynamical phase transitions (DPT) are characterized by nonanalytical time evolution of the dynamical free energy. For general 2-band systems in one and two dimensions (eg. SSH model, Kitaev-chain, Haldane model, p+ip superconductor, etc.),…
Recently, deep-learning based approaches have achieved impressive performance for autonomous driving. However, end-to-end vision-based methods typically have limited interpretability, making the behaviors of the deep networks difficult to…
In this paper, we consider the variational regularization of manifold-valued data in the inverse problems setting. In particular, we consider TV and TGV regularization for manifold-valued data with indirect measurement operators. We provide…
We define a class of transformations of the dependent and independent variables in an ordinary difference scheme. The transformations leave the solution set of the system invariant and reduces to a group of contact transformations in the…
Dynamical system theory is a widely used technique in the analysis of cosmological models. Within this framework, the equations describing the dynamics of a model are recast in terms of dimensionless variables, which evolve according to a…
It is shown that in the case of multicomponent integrable systems connected with algebras $A_n$, the discrete transformation $T$ possesses the fine structure and can be represented in the form $T=\prod T_i^{l_i}$, where $T_i$ are n…
We give an algorithm to determine if the dynamical system generated by a positive automorphism of the free group can also be generated by a self-induced interval exchange transformation. The algorithm effectively yields the interval…
This book provides an introduction to the theory of digital (molecular) spaces (TDS). Digital spaces are combinatorial models of continuous spaces. TDS is one of alternative branches of digital topology that studies constructing and…
Solving partial differential equations (PDEs) by learning the solution operators has emerged as an attractive alternative to traditional numerical methods. However, implementing such architectures presents two main challenges: flexibility…
We introduce a new dynamical indicator of stability based on the Extreme Value statistics showing that it provides an insight on the local stability properties of dynamical systems. The indicator perform faster than other based on the…
Though vision transformers (ViTs) have achieved state-of-the-art performance in a variety of settings, they exhibit surprising failures when performing tasks involving visual relations. This begs the question: how do ViTs attempt to perform…
Simulations of nano- to micro-meter scale fluidic systems under thermal gradients require consistent mesoscopic methods accounting for both hydrodynamic interactions and proper transport of energy. One such method is dissipative particle…
Discrete-time regulatory networks are dynamical systems on directed graphs, with a structure inspired on natural systems of interacting units. There is a natural notion of determination amongst vertices, which we use to classify the nodes…
Motivated by the correspondence between the vertex and IRF models in statistical mechanics, we define and study a notion of vertex-IRF transformation for dynamical twists that generalizes a usual gauge transformation. We use vertex-IRF…
The groundbreaking performance of transformers in Natural Language Processing (NLP) tasks has led to their replacement of traditional Convolutional Neural Networks (CNNs), owing to the efficiency and accuracy achieved through the…
We show that a noncommutative dynamical system of the type that occurs in quantum theory can often be associated with a dynamical principle; that is, an infinitesimal structure that completely determines the dynamics. The nature of these…
Discrete-value time series are sequences of measurements where each measurement is a discrete (categorical or integer) value. These time series are widely used in various fields, and their classification and clustering are essential for…
Vision Transformers (VTs) are becoming a valuable alternative to Convolutional Neural Networks (CNNs) when it comes to problems involving high-dimensional and spatially organized inputs such as images. However, their Transfer Learning (TL)…