Topologies on Pseudo-Trees and Applications
Topologies on Pseudo-Trees and Applications

Author: Jacek Nikiel

Publisher: American Mathematical Soc.

Published: 1989

Total Pages: 126

ISBN-13: 0821824791

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A pseudo-tree is a partially ordered set such that the set of all predecessors of any element is linearly ordered. Clearly, each linearly ordered set is a pseudo-tree and pseudo-trees are, in general, much more complicated objects than chains. The aim of this paper is to develop a theory of natural order topologies on pseudo-trees which extends the theories of linearly ordered topological spaces and GO-spaces. Moreover, applications are given for some classes of continua which admit a natural ordering.

Topology of Algebraic Curves
Topology of Algebraic Curves

Author: Alex Degtyarev

Publisher: Walter de Gruyter

Published: 2012-07-04

Total Pages: 412

ISBN-13: 3110258420

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This monograph summarizes and extends a number of results on the topology of trigonal curves in geometrically ruled surfaces. An emphasis is given to various applications of the theory to a few related areas, most notably singular plane curves of small degree, elliptic surfaces, and Lefschetz fibrations (both complex and real), and Hurwitz equivalence of braid monodromy factorizations. The approach relies on a close relation between trigonal curves/elliptic surfaces, a certain class of ribbon graphs, and subgroups of the modular group, which provides a combinatorial framework for the study of geometric objects. A brief summary of the necessary auxiliary results and techniques used and a background of the principal problems dealt with are included in the text. The book is intended to researchers and graduate students in the field of topology of complex and real algebraic varieties.

Operads in Algebra, Topology and Physics
Operads in Algebra, Topology and Physics

Author: Martin Markl

Publisher: American Mathematical Soc.

Published: 2002

Total Pages: 362

ISBN-13: 0821843621

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Operads are mathematical devices which describe algebraic structures of many varieties and in various categories. From their beginnings in the 1960s, they have developed to encompass such areas as combinatorics, knot theory, moduli spaces, string field theory and deformation quantization.

Species Tree Inference
Species Tree Inference

Author: Laura Kubatko

Publisher: Princeton University Press

Published: 2023-03-14

Total Pages: 352

ISBN-13: 0691245150

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An up-to-date reference book on phylogenetic methods and applications for evolutionary biologists The increasingly widespread availability of genomic data is transforming how biologists estimate evolutionary relationships among organisms and broadening the range of questions that researchers can test in a phylogenetic framework. Species Tree Inference brings together many of today’s leading scholars in the field to provide an incisive guide to the latest practices for analyzing multilocus sequence data. This wide-ranging and authoritative book gives detailed explanations of emerging new approaches and assesses their strengths and challenges, offering an invaluable context for gauging which procedure to apply given the types of genomic data and processes that contribute to differences in the patterns of inheritance across loci. It demonstrates how to apply these approaches using empirical studies that span a range of taxa, timeframes of diversification, and processes that cause the evolutionary history of genes across genomes to differ. By fully embracing this genomic heterogeneity, Species Tree Inference illustrates how to address questions beyond the goal of estimating phylogenetic relationships of organisms, enabling students and researchers to pursue their own research in statistically sophisticated ways while charting new directions of scientific discovery.

Situation Theory and Its Applications: Volume 3
Situation Theory and Its Applications: Volume 3

Author: Robin Cooper

Publisher: Center for the Study of Language (CSLI)

Published: 1990

Total Pages: 436

ISBN-13: 9781881526087

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Situation theory is the result of an interdisciplinary effort to create a full-fledged theory of information. Created by scholars and scientists from cognitive science, computer science and AI, linguistics, logic, philosophy, and mathematics, it aims to provide a common set of tools for the analysis of phenomena from all these fields. Unlike Shannon-Weaver type theories of information, which are purely quantitative theories, situation theory aims at providing tools for the analysis of the specific content of a situation (signal, message, data base, statement, or other information-carrying situation). The question addressed is not how much information is carried, but what information is carried.

Basic Algebraic Topology
Basic Algebraic Topology

Author: Anant R. Shastri

Publisher: CRC Press

Published: 2016-02-03

Total Pages: 552

ISBN-13: 1466562447

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Building on rudimentary knowledge of real analysis, point-set topology, and basic algebra, Basic Algebraic Topology provides plenty of material for a two-semester course in algebraic topology. The book first introduces the necessary fundamental concepts, such as relative homotopy, fibrations and cofibrations, category theory, cell complexes, and si

Numerical Methods and Applications
Numerical Methods and Applications

Author: Ivan Dimov

Publisher: Springer

Published: 2015-02-03

Total Pages: 312

ISBN-13: 3319155857

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This book constitutes the thoroughly refereed post-conference proceedings of the 8th International Conference on Numerical Methods and Applications, NMA 2014, held in Borovets, Bulgaria, in August 2014. The 34 revised full papers presented were carefully reviewed and selected from 56 submissions for inclusion in this book. The papers are organized in the following topical sections: Monte Carlo and quasi-Monte Carlo methods; metaheuristics for optimization problems; advanced numerical methods for scientific computing; advanced numerical techniques for PDEs and applications; solving large engineering and scientific problems with advanced mathematical models; numerical simulations and back analysis in civil and mechanical engineering.