An Invitation To Applied Category Theory

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An Invitation To Applied Category Theory

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Author : Brendan Fong
language : en
Publisher: Cambridge University Press
Release Date : 2019-07-18

An Invitation To Applied Category Theory written by Brendan Fong and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-18 with Computers categories.

Category theory reveals commonalities between structures of all sorts. This book shows its potential in science, engineering, and beyond.

Handbook Of Model Based Systems Engineering

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Author : Azad M. Madni
language : en
Publisher: Springer Nature
Release Date : 2023-07-25

Handbook Of Model Based Systems Engineering written by Azad M. Madni and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-25 with Technology & Engineering categories.

This handbook brings together diverse domains and technical competences of Model Based Systems Engineering (MBSE) into a single, comprehensive publication. It is intended for researchers, practitioners, and students/educators who require a wide-ranging and authoritative reference on MBSE with a multidisciplinary, global perspective. It is also meant for those who want to develop a sound understanding of the practice of systems engineering and MBSE, and/or who wish to teach both introductory and advanced graduate courses in systems engineering. It is specifically focused on individuals who want to understand what MBSE is, the deficiencies in current practice that MBSE overcomes, where and how it has been successfully applied, its benefits and payoffs, and how it is being deployed in different industries and across multiple applications. MBSE engineering practitioners and educators with expertise in different domains have contributed chapters that address various uses of MBSE and related technologies such as simulation and digital twin in the systems lifecycle. The introductory chapter reviews the current state of practice, discusses the genesis of MBSE and makes the business case. Subsequent chapters present the role of ontologies and meta-models in capturing system interdependencies, reasoning about system behavior with design and operational constraints; the use of formal modeling in system (model) verification and validation; ontology-enabled integration of systems and system-of-systems; digital twin-enabled model-based testing; system model design synthesis; model-based tradespace exploration; design for reuse; human-system integration; and role of simulation and Internet-of-Things (IoT) within MBSE.

Monoidal Category Theory

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Author : Noson S. Yanofsky
language : en
Publisher: MIT Press
Release Date : 2024-11-05

Monoidal Category Theory written by Noson S. Yanofsky and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-05 with Computers categories.

A comprehensive, cutting-edge, and highly readable textbook that makes category theory and monoidal category theory accessible to students across the sciences. Category theory is a powerful framework that began in mathematics but has since expanded to encompass several areas of computing and science, with broad applications in many fields. In this comprehensive text, Noson Yanofsky makes category theory accessible to those without a background in advanced mathematics. Monoidal Category Theorydemonstrates the expansive uses of categories, and in particular monoidal categories, throughout the sciences. The textbook starts from the basics of category theory and progresses to cutting edge research. Each idea is defined in simple terms and then brought alive by many real-world examples before progressing to theorems and uncomplicated proofs. Richly guided exercises ground readers in concrete computation and application. The result is a highly readable and engaging textbook that will open the world of category theory to many. Makes category theory accessible to non-math majors Uses easy-to-understand language and emphasizes diagrams over equations Incremental, iterative approach eases students into advanced concepts A series of embedded mini-courses cover such popular topics as quantum computing, categorical logic, self-referential paradoxes, databases and scheduling, and knot theory Extensive exercises and examples demonstrate the broad range of applications of categorical structures Modular structure allows instructors to fit text to the needs of different courses Instructor resources include slides

Starting Category Theory

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Author : Paolo Perrone
language : en
Publisher: World Scientific
Release Date : 2024-04-08

Starting Category Theory written by Paolo Perrone and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-08 with Mathematics categories.

One of the central highlights of this work is the exploration of the Yoneda lemma and its profound implications, during which intuitive explanations are provided, as well as detailed proofs, and specific examples. This book covers aspects of category theory often considered advanced in a clear and intuitive way, with rigorous mathematical proofs. It investigates universal properties, coherence, the relationship between categories and graphs, and treats monads and comonads on an equal footing, providing theorems, interpretations and concrete examples. Finally, this text contains an introduction to monoidal categories and to strong and commutative monads, which are essential tools in current research but seldom found in other textbooks.Starting Category Theory serves as an accessible and comprehensive introduction to the fundamental concepts of category theory. Originally crafted as lecture notes for an undergraduate course, it has been developed to be equally well-suited for individuals pursuing self-study. Most crucially, it deliberately caters to those who are new to category theory, not requiring readers to have a background in pure mathematics, but only a basic understanding of linear algebra.

Mathematical Modelling By Help Of Category Theory

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Author : Dmitrii Legatiuk
language : en
Publisher: Springer Nature
Release Date : 2025-03-19

Mathematical Modelling By Help Of Category Theory written by Dmitrii Legatiuk and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-19 with Mathematics categories.

This monograph offers a novel structural perspective on the modelling of engineering problems, utilizing abstract mathematics in the form of category theory. Specifically, the book aims to enhance the understanding of mathematical modelling by developing a category theory-based framework. Category theory is employed to establish clear relationships between mathematical models and their complexities. The theory is then extended to encompass coupled mathematical models, incorporating more advanced categorical structures. To bridge theory and practice, the book presents engineering applications of the abstract categorical framework, providing various modelling examples from real-world engineering scenarios. Additionally, it introduces initial concepts for automatic model generation and error detection in modelling. The theory developed here demonstrates the practical utility of category theory, making this book a valuable resource for researchers in applied mathematics and engineering, particularly those focused on theoretical foundations of modelling.

Alternative Approaches To Economic Theory

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Author : Victor A. Beker
language : en
Publisher: Routledge
Release Date : 2019-06-11

Alternative Approaches To Economic Theory written by Victor A. Beker and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-11 with Business & Economics categories.

The 2007–2008 financial crisis exposed the shortcomings of mainstream economic theory with economists unprepared to deal with it. In the face of this, a major rethinking of economics seems necessary and in presenting alternative approaches to economic theory, this book contributes to the rebuilding of the discipline. This volume brings together contributions from different perspectives and theoretical approaches that address the challenge of updating the economic theory corpus and seek to recover prestige for this discipline after the failure of neoclassical economics. It addresses a range of topics, including the complexity approach to economics, category theory, the Post-Keynesian approach to micro and macroeconomics, financialisation, multidimensional analysis and ecological economics. The book is aimed at economics scholars, researchers, academics and practitioners, as well as upper undergraduates and graduates in this area of knowledge. It may also be of interest for people interested in methodological issues in economics and the relationship between economic theory and the real world.

Artificial General Intelligence

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Author : Patrick Hammer
language : en
Publisher: Springer Nature
Release Date : 2023-05-23

Artificial General Intelligence written by Patrick Hammer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-23 with Computers categories.

This book constitutes the refereed proceedings of the 16th International Conference on Artificial General Intelligence, AGI 2023, held in Stockholm, Sweden in June 2023. The 35 full papers and one short paper presented in this book were carefully reviewed and selected from 72 submissions. The papers cover topics from foundations of AGI, to AGI approaches and AGI ethics, to the roles of systems biology, goal generation, and learning systems, and so much more.

Modal Homotopy Type Theory

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Author : David Corfield
language : en
Publisher: Oxford University Press
Release Date : 2020-02-06

Modal Homotopy Type Theory written by David Corfield and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-06 with Philosophy categories.

"The old logic put thought in fetters, while the new logic gives it wings." For the past century, philosophers working in the tradition of Bertrand Russell - who promised to revolutionise philosophy by introducing the 'new logic' of Frege and Peano - have employed predicate logic as their formal language of choice. In this book, Dr David Corfield presents a comparable revolution with a newly emerging logic - modal homotopy type theory. Homotopy type theory has recently been developed as a new foundational language for mathematics, with a strong philosophical pedigree. Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy offers an introduction to this new language and its modal extension, illustrated through innovative applications of the calculus to language, metaphysics, and mathematics. The chapters build up to the full language in stages, right up to the application of modal homotopy type theory to current geometry. From a discussion of the distinction between objects and events, the intrinsic treatment of structure, the conception of modality as a form of general variation to the representation of constructions in modern geometry, we see how varied the applications of this powerful new language can be.

All The Math You Missed

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Author : Thomas A. Garrity
language : en
Publisher: Cambridge University Press
Release Date : 2021-07

All The Math You Missed written by Thomas A. Garrity and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07 with Business & Economics categories.

Fill in any gaps in your knowledge with this overview of key topics in undergraduate mathematics, now with four new chapters.

Mathematics Of Public Health

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Author : Jummy David
language : en
Publisher: Springer Nature
Release Date : 2023-12-30

Mathematics Of Public Health written by Jummy David and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-30 with Mathematics categories.

This volume addresses SDG 3 from a mathematical standpoint, sharing novel perspectives of existing communicable disease modelling technologies of the next generation and disseminating new developments in modelling methodologies and simulation techniques. These methodologies are important for training and research in communicable diseases and can be applied to other threats to human health. The contributions contained in this collection/book cover a range of modelling techniques that have been and may be used to support decision-making on critical health related issues such as: Resource allocation Impact of climate change on communicable diseases Interaction of human behaviour change, and disease spread Disease outbreak trajectories projection Public health interventions evaluation Preparedness and mitigation of emerging and re-emerging infectious diseases outbreaks Development of vaccines and decisions around vaccine allocation and optimization The diseases and public health issues in this volume include, but are not limited to COVID-19, HIV, Influenza, antimicrobial resistance (AMR), the opioid epidemic, Lyme Disease, Zika, and Malaria. In addition, this volume compares compartmental models, agent-based models, machine learning and network. Readers have an opportunity to learn from the next generation perspective of evolving methodologies and algorithms in modelling infectious diseases, the mathematics behind them, the motivation for them, and some applications to supporting critical decisions on prevention and control of communicable diseases. This volume was compiled from the weekly seminar series organized by the Mathematics for Public Health (MfPH) Next Generation Network. This network brings together the next generation of modellers from across Canada and the world, developing the latest mathematical models, modeling methodologies, and analytical and simulation tools for communicable diseases of global public health concerns. The weekly seminar series provides a unique forum for this network and their invited guest speakers to share their perspectives on the status and future directions of mathematics of public health.