相关论文: Shadowing, average shadowing and transitive proper…

We develop a general framework for reasoning about distances between transition systems with quantitative information. Taking as starting point an arbitrary distance on system traces, we show how this leads to natural definitions of a…

We suggest a combinatorial classification of metric filtrations in measure spaces; a complete invariant of such a filtration is its combinatorial scheme, a measure on the space of hierarchies of the group~$\mathbb Z$. In turn, the notion of…

This paper presents and explores a theory of \emph{multiholomorphic maps}. This group of ideas generalizes the theory of pseudoholomorphic curves in a direction suggested by consideration of the kinds of compatible geometric structures that…

The main purpose of this article is to establish moderate deviation principles for additive functionals of bifurcating Markov chains. Bifurcating Markov chains are a class of processes which are indexed by a regular binary tree. They can be…

We study inferring a tree-structured representation from a single image for object shading. Prior work typically uses the parametric or measured representation to model shading, which is neither interpretable nor easily editable. We propose…

We study Markov multi-maps of the interval from the point of view of topological dynamics. Specifically, we investigate whether they have various properties, including topological transitivity, topological mixing, dense periodic points, and…

Topological behavior, such as chaos, irreducibility, and mixing of a one-sided shift of finite type, is well elucidated. Meanwhile, the investigation of multidimensional shifts, for instance, textile systems is difficult and only a few…

In this paper we introduce and study some stronger forms of transitivity like total transitivity, weakly mixing for maps on G-spaces. We obtain their relationship with the earlier defined notion of strongly mixing for maps on G-spaces. We…

Within the scattering matrix approach to electronic transport, the scattering and transport properties of tight-binding random graphs are analyzed. In particular, we compute the scattering matrix elements, the transmission, the…

The study of networks plays a crucial role in investigating the structure, dynamics, and function of a wide variety of complex systems in myriad disciplines. Despite the success of traditional network analysis, standard networks provide a…

Intermittent dynamics is characterized by long periods of different types of dynamical characteristics, for instance almost periodic dynamics alternated by chaotic dynamics. Critical intermittency is intermittent dynamics that can occur in…

Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…

We give a systematic approach to constructing non-reduced, locally Cohen-Macaulay schemes with reduced support a smooth projective variety. The hierarchy of such structures includes a lot of information about the underlying variety, its…

The marginal maximum a posteriori probability (MAP) estimation problem, which calculates the mode of the marginal posterior distribution of a subset of variables with the remaining variables marginalized, is an important inference problem…

The degree of mixing is a fundamental property of a dynamical system. General multi-dimensional shifts cannot be systematically determined. This work introduces constructive and systematic methods for verifying the degree of mixing, from…

Learning a particular task from a dataset, samples in which originate from diverse contexts, is challenging, and usually addressed by deepening or widening standard neural networks. As opposed to conventional network widening, multi-path…

While exploring desirable properties of hash functions in cryptography, the author was led to investigate three notions of functions with scattering or "diffusive" properties, where the functions map between binary strings of fixed finite…

Characterization of topology and dimensionality of spectral feature spaces provides insight into information content. The objective of this study is to characterize topology and spectral dimensionality of spectral mixing spaces representing…

Few-shot classification aims to recognize novel categories with only few labeled images in each class. Existing metric-based few-shot classification algorithms predict categories by comparing the feature embeddings of query images with…

Given a dynamical system $(X,f)$ we investigate several topological dynamical properties for its Zadeh extension $(\mathcal{F}(X),\hat{f})$ endowed with the endograph metric $d_{E}$. In particular, we prove that for some contractive and…