“…Applying an innovative approach based on the algebraic topology of graphs, we analyse higher-order topological complexes consisting of mutually interwoven cliques of a high order to which the identified functional connections organise. …”
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“…Specifically, we explore the use of simplicial complexes: a structure developed in the field of mathematics known as algebraic topology, of increasing applicability to real data due to a rapidly growing computational toolset. …”
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“…This work integrates mathematics (i.e., algebraic topology) and deep learning (MathDL) to provide a reliable ranking of the binding affinities of 137 SARS-CoV-2 M(pro) inhibitor structures. …”
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“…Unlike traditional graph analysis, algebraic topology was introduced to analyze the topological structures of the E. coli‐PPI‐Network, including high‐dimensional cavities and cycles. …”
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“…Topology is a large subject with several branches, broadly categorized as algebraic topology, point-set topology, and geometric topology. …”
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“…The aim of this volume is to prepare students with a knowledge of elementary algebraic topology to study recent developments in stable homotopy theory, such as the nilpotence and periodicity theorems. …”
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“…This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. …”
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“…This is followed by chapters on topological inference and random algebraic topology, both of which provide applications of the main results.…”
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“…Aimed at advanced graduate students and researchers in algebraic topology and related fields, the book assumes knowledge of basic algebraic topology and group actions. .…”
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“…It is accessible to readers with a minimal background in classical algebraic topology and operad theory.…”
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“…The purpose of the book is to give an exposition of generalized (co)homology theories that can be read by a wide group of mathematicians who are not experts in algebraic topology. It starts with basic notions of homotopy theory and then introduces the axioms of generalized (co)homology theory. …”
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“…This account is a study of twofold symmetry in algebraic topology.…”
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“…This book will be of great interest to researchers into algebraic topology.…”
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“…Self-contained: no background in algebraic topology is necessary.…”
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“…"This book is a jewel- it explains important, useful and deep topics in Algebraic Topology that you won't find elsewhere, carefully and in detail." …”
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“…Cobordism is one of the most basic notions of algebraic topology. This book is devoted to spectral sequences related to cobordism theory: the spectral sequence of a singularity, the Adams-Novikov spectral sequence, and applications of these and other sequences to the investigation of cobordism rings.…”
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“…The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering spaces and deck transformations. …”
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“…It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. …”
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“…It supplies important material essential to understand topics in algebra, algebraic geometry and algebraic topology. Each section comes with exercises providing practice problems for students as well as additional important results for specialists. …”
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“…Here we introduce element- and site-specific persistent homology (a new branch of algebraic topology) to simplify the structural complexity of protein–protein complexes and embed crucial biological information into topological invariants. …”
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