Related papers: Topological characterizations to three types of co…

The Boolean algebra of regular closed sets is prominent in topology, particularly as a dual for the Stone-Cech compactification. This algebra is also central for the theory of geometric computation, as a representation for combinatorial…

We determine the topological complexity of unordered configuration spaces on almost all punctured surfaces (both orientable and non-orientable). We also give improved bounds for the topological complexity of unordered configuration spaces…

We discuss the study of topological characteristics of random fields that are used for numerical simulation of oil and gas reservoirs and numerical algorithms (see arXiv:1302.3669), for computing such characteristics, for which we…

This overview article makes the case for how topological concepts can enrich research in machine learning. Using the Euler Characteristic Transform (ECT), a geometrical-topological invariant, as a running example, I present different use…

This paper describes the functioning of a broad-coverage probabilistic top-down parser, and its application to the problem of language modeling for speech recognition. The paper first introduces key notions in language modeling and…

Departing from a suitable categorical concept of topogenous orders defined relative to the bifibration of subobjects, this note introduces and studies topogenous orders on faithful and amnestic functors. Amongst other things, it is shown…

Circuit topology refers to the arrangement of interactions between objects belonging to a linearly ordered object set. Linearly ordered set of objects are common in nature and occur in a wide range of applications in economics, computer…

Given a collection S of subsets of some set U, and M a subset of U, the set cover problem is to find the smallest subcollection C of S such that M is a subset of the union of the sets in C. While the general problem is NP-hard to solve,…

Polymer networks invariably possess topological inhomogeneities in the form of loops and dangling ends. The macroscopic properties of such materials are directly dependent on the local cyclic topology around nodes and chains. Here, a new…

Inspired by the conventional pooling layers in convolutional neural networks, many recent works in the field of graph machine learning have introduced pooling operators to reduce the size of graphs. The great variety in the literature stems…

Represented spaces form the general setting for the study of computability derived from Turing machines. As such, they are the basic entities for endeavors such as computable analysis or computable measure theory. The theory of represented…

In many areas of applied mathematics, engineering, and social and natural sciences, decentralization of information is a key aspect determining how to approach a problem. In this review article, we study information structures in a…

High-order topological phases of matter refer to the systems of $n$-dimensional bulk with the topology of $m$-th order, exhibiting $(n-m)$-dimensional boundary modes and can be characterized by topological pumping. Here, we experimentally…

The study of irreducible higher-order interactions has become a core topic of study in complex systems. Two of the most well-developed frameworks, topological data analysis and multivariate information theory, aim to provide formal tools…

This expository article describes applications of topological configuration spaces to the control of robotic systems. In particular, we review recent work by the authors on configuration spaces of graphs. These are lovely spaces: we show…

We develop a language for describing the relationship among observations, mathematical models, and the underlying principles from which they are derived. Using Information Geometry, we consider geometric properties of statistical models for…

In this paper, we define a soft somewhat open set using the soft interior operator. We study main properties the class of soft somewhat open sets that is contained in the class soft somewhere dense sets. Then, we introduce the classes of…

The utilization of statistical methods an their applications within the new field of study known as Topological Data Analysis has has tremendous potential for broadening our exploration and understanding of complex, high-dimensional data…

Topology optimization is used to systematically design contact-aided thermo-mechanical regulators, i.e. components whose effective thermal conductivity is tunable by mechanical deformation and contact. The thermo-mechanical interactions are…

We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…