相关论文: Digital Shy Maps
The clandestine nature of covert networks makes reliable data difficult to obtain and leads to concerns with missing data. We explore the use of network models to represent missingness mechanisms. Exponential random graph models provide a…
In this study, we performed comprehensive morphological investigations of the spontaneous formations of effective network structures among elements in coupled logistic maps, specifically with a delayed connection change. Our proposed model…
In simulations of a model with topological sectors, algorithms which proceed in small update steps tend to get stuck in one sector, especially on fine lattices. This distorts the numerical results; in particular it is not straightforward to…
One can see deep-learning models as compositions of functions within the so-called tame geometry. In this expository note, we give an overview of some topics at the interface of tame geometry (also known as o-minimality), optimization…
We extend the topological field theory (``itsy bitsy topological field theory"') of our previous work from mod-2 to twisted coefficients. This topological field theory is derived from sutured Floer homology but described purely in terms of…
This paper is concerned with the study of various notions of shadowing of dynamical systems induced by a sequence of maps, so-called time varying maps, on a metric space. We define and study the shadowing, h-shadowing, limit shadowing,…
For digital images, there is an established homotopy equivalence relation which parallels that of classical topology. Many classical homotopy equivalence invariants, such as the Euler characteristic and the homology groups, do not remain…
Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths…
This research is motivated by studying image processing algorithms through a topological lens. The images we focus on here are those that have been segmented by digital Jordan curves as a means of image compression. The algorithms of…
High-definition maps provide precise environmental information essential for prediction and planning in autonomous driving systems. Due to the high cost of labeling and maintenance, recent research has turned to online HD map construction…
Local properties of the fundamental group of a path-connected topological space can pose obstructions to the applicability of covering space theory. A generalized covering map is a generalization of the classical notion of covering map…
It is shown that a surjective monotone map $X\to Y$ between finite $T_0$-spaces induces a surjective map on homology. As such a map turns out to be a sequence of edge contractions in the Hasse diagram of $X$, followed by a homeomorphism,…
In this paper, some generalized metric properties in strongly topological gyrogroups are studied.
Open discrete mappings with a modulus condition in metric spaces are considered. Some results related to local behavior of mappings as well as theorems about continuous extension to a boundary are proved.
We use a well known problem in discrete and computational geometry (partitions of measures by $k$-fans) as a motivation and as a point of departure to illustrate many aspects, both theoretical and computational, of the problem of…
In this paper, by reviewing the concept of subcovering and semicovering maps, we extend the notion of subcovering map to subsemicovering map. We present some necessary or sufficient conditions for a local homeomorphism to be a…
Special generic maps are smooth maps at each singular point of which we can represent as $(x_1, \cdots, x_m) \mapsto (x_1,\cdots,x_{n-1},\sum_{k=n}^{m}{x_k}^2)$ for suitable coordinates. Morse functions with exactly two singular points on…
In this paper we characterise graph inverse semigroups which admit only discrete locally compact semigroup topology. This characterization provides a complete answer on the question of Z. Mesyan, J. D. Mitchell, M. Morayne and Y. H.…
We give an idiosyncratic overview of applications of topology to cyber research, spanning the analysis of variables/assignments and control flow in computer programs, a brief sketch of topological data analysis in one dimension, and the use…
This paper concerns a theoretical approach that combines topological data analysis (TDA) and sheaf theory. Topological data analysis, a rising field in mathematics and computer science, concerns the shape of the data and has been proven…