We apply persistent homology, the dominant tool from field of topological data analysis, to study electoral redistricting. begin by combining geographic and a districting plan produce persistence diagram. Then, see beyond particular understand possibilities afforded choices made in redistricting, we build methods visualize analyze large ensembles alternative plans. Our detailed case studies use...

The amount of data that our digital society collects is unprecedented. This represents a valuable opportunity to improve our quality of life by gaining insights about complex problems related to neuroscience, medicine and biology among others. Topological methods, in combination with classical statistical ones, have proven to be a precious resource in understanding and visualizing data. Multidi...

in this article, we show the existence of certain exact sequences with respect to two homology theories, called d-homology and extended d-homology. we present sufficient conditions for the existence of long exact extended d- homology sequence. also we give some illustrative examples.

introduction: the purpose of this study was to investigate the role of patience and its components (transcendence, tolerance, contentment, persistence, and hesitation) in predicting bullying among primary school children in shiraz, iran. another purpose was to compare patience and bullying between male and female students. method: the participants were 317 elementary school students (169 female...

background and objectives: hepatitis c virus (hcv) is a major public health problem worldwide. replication and persistence of hcv genome have been described in the liver tissue as well as b cells lymphocyte. several investigations have reported that long-term persistence of hcv in b cells may result in hodgkin and non-hodgkin lymphoma. this study was aimed to determine frequency of hcv rna in h...

We develop some aspects of the homological algebra persistence modules, in both one-parameter and multi-parameter settings, considered as either sheaves or graded modules. The two theories are different. consider module sheaf tensor product Hom bifunctors well their derived functors, Tor Ext, give explicit computations for interval a classification injective, projective, flat state Kunneth theo...

Motivated by the recent surge of criminal activities with cross-cryptocurrency trades, we introduce a new topological perspective to structural anomaly detection in dynamic multilayer networks. We postulate that anomalies underlying blockchain transaction graph are composed multiple layers likely also be manifested anomalous patterns network shape properties. As such, invoke machinery clique pe...

In this paper we present ideas from computational topology, applicable in analysis of point cloud data. In particular, the point cloud can represent a feature space of a collection of objects such as images or text documents. Computing persistence homology reveals the global structure of similarities between the data. Furthermore, we argue that it is essential to incorporate higher-degree relat...

Topological data analysis is a relatively new branch of machine learning that excels in studying high-dimensional data, and theoretically known to be robust against noise. Meanwhile, objects with mixed numeric categorical attributes are ubiquitous real-world applications. However, topological methods usually applied point cloud the best our knowledge there no available framework for classificat...

In this paper we present an approach to determine the smallest possible number of neurons in a layer neural network such way that topology input space can be learned sufficiently well. We introduce general procedure based on persistent homology investigate topological invariants manifold which suspect data set. specify required dimensions precisely, assuming there is smooth or near are located....