Related papers: Framed Combinatorial Topology with Labels in $\inf…
We develop a general approach to finding combinatorial models for cluster algebras. The approach is to construct a labeled graph called a framework. When a framework is constructed with certain properties, the result is a model…
We review, for a general audience, a variety of recent experiments on extracting structure from machine-learning mathematical data that have been compiled over the years. Focusing on supervised machine-learning on labeled data from…
Labelling data is expensive and time consuming especially for domains such as medical imaging that contain volumetric imaging data and require expert knowledge. Exploiting a larger pool of labeled data available across multiple centers,…
Fuzzy Cognitive Maps (FCMs) are considered a soft computing technique combining elements of fuzzy logic and recurrent neural networks. They found multiple application in such domains as modeling of system behavior, prediction of time…
We propose a unifying mathematical framework describing the higher categorical structures formed by topological defects in quantum field theory equipped with tangential structures, such as orientations, framings, or…
To enumerate 3-manifold triangulations with a given property, one typically begins with a set of potential face pairing graphs (also known as dual 1-skeletons), and then attempts to flesh each graph out into full triangulations using an…
We introduce stratified labelings as a novel semantical approach to abstract argumentation frameworks. Compared to standard labelings, stratified labelings provide a more fine-grained assessment of the controversiality of arguments using…
The unprecedented pace of machine learning research has lead to incredible advances, but also poses hard challenges. At present, the field lacks strong theoretical underpinnings, and many important achievements stem from ad hoc design…
This work introduces ``generalized meshes", a type of meshes suited for the discretization of partial differential equations in non-regular geometries. Generalized meshes extend regular simplicial meshes by allowing for overlapping elements…
We introduce probabilistic frames to study finite frames whose elements are chosen at random. While finite tight frames generalize orthonormal bases by allowing redundancy, independent, uniformly distributed points on the sphere…
There are two rather distinct approaches to Morse theory nowadays: smooth and discrete. We propose to study a real valued function by assembling all associated sections in a topological category. From this point of view, Reeb functions on…
More than two decades ago, combinatorial topology was shown to be useful for analyzing distributed fault-tolerant algorithms in shared memory systems and in message passing systems. In this work, we show that combinatorial topology can also…
The cohomology theory known as Tmf, for "topological modular forms," is a universal object mapping out to elliptic cohomology theories, and its coefficient ring is closely connected to the classical ring of modular forms. We extend this to…
Hierarchical classification is significant for complex tasks by providing multi-granular predictions and encouraging better mistakes. As the label structure decides its performance, many existing approaches attempt to construct an excellent…
We use finite group topological lattice gauge theory, also known as the quantum double model, as a lens to explore a notion of topological order enriched by a non-invertible symmetry. For invertible symmetry enriched topological order,…
In this study, we address the complex issue of graph clustering in signed graphs, which are characterized by positive and negative weighted edges representing attraction and repulsion among nodes, respectively. The primary objective is to…
A model category is called combinatorial if it is cofibrantly generated and its underlying category is locally presentable. As shown in recent years, homotopy categories of combinatorial model categories share useful properties, such as…
Some combinatorial properties of fixed boundary rhombus random tilings with octagonal symmetry are studied. A geometrical analysis of their configuration space is given as well as a description in terms of discrete dynamical systems, thus…
Casting neural networks in generative frameworks is a highly sought-after endeavor these days. Contemporary methods, such as Generative Adversarial Networks, capture some of the generative capabilities, but not all. In particular, they lack…
Frames provide redundant, stable representations of data which have important applications in signal processing. We introduce a connection between symplectic geometry and frame theory and show that many important classes of frames have…