Mathematical Modelling By Help Of Category Theory
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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.
Mathematical Modelling By Help Of Category Theory
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Author : Dmitrii Legatiuk
language : en
Publisher:
Release Date : 2024*
Mathematical Modelling By Help Of Category Theory written by Dmitrii Legatiuk and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024* with categories.
Solution of any engineering problem starts with a modelling process, which provides a model representing a system under consideration. The critical question for practical use of models is to assess if the model and results of using it can be trusted. To address this question, several approaches have been proposed in the past. However, some of these approaches deal with the practical aspects of models, or in other words, they address correctness of model implementation, while other approaches look at the models from the system engineering point of view, what makes them difficult to transfer to other fields of applications. Moreover, if we look at the modelling process more generally, then we could realise that (physics-based or mathematical) models are created by formalising specific sets of modelling assumptions in terms of mathematical expressions. In this context, if a mistake has been made and one specific modelling assumption has been violated, then the model can be wrong already before even starting using it in concrete applications and computations. Thus, it is necessary to develop tools and methods for detecting such modelling errors related to the conceptualisation of the model as early as possible. This dissertation aims at supporting the understanding of mathematical modelling by proposing a more abstract point of view on models and coupling of models, namely by developing a category theory-based modelling framework. In this context, categories of mathematical models are introduced, and their structure is discussed. In particular, the use of category theory allowed us to introduce clear relations between mathematical models, which are provided by the model property named complexity. Additionally, the notion of model convertibility is introduced, which establish a connection between different model formulations used in practical applications, e.g. integral and differential. After that, all basic notions are uplifted to the case of coupled mathematical models. As expected, coupled models require a more technical treatment, because the structure of categories of coupled mathematical models is more complicated. In particular, it is shown that not every comparison of coupled models makes sense. To support practical applications of the abstract modelling framework, this dissertation presents also engineering perspective on the abstract categorical construction, as well as provides various modelling examples coming from engineering practice. Additionally,based on the category theory-based modelling framework, first ideas towards automatic model generation and conceptual modelling error detection are proposed in this dissertation. Thus, a connection to type theory and functional programming is established in this way. Finally, an extension of the category theory-based modelling framework beyond mathematical models is proposed at the end of the dissertation. This extension sumvi marises knowledge about models gathered by help of category theory-based approach and addresses models from the abstract algebraic point of view. Hence, consideration of very general models is possible in this case. Therefore, this dissertation indicates that category theory and tools of abstract mathematics are indeed useful in practical applications.
Cyber Physical Systems Modelling And Industrial Application
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Author : Alla G. Kravets
language : en
Publisher: Springer Nature
Release Date : 2022-03-26
Cyber Physical Systems Modelling And Industrial Application written by Alla G. Kravets and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-26 with Technology & Engineering categories.
This book discusses the open questions regarding the modelling of cyber-physical systems and their application in different industries. The industry needs new approaches to improve its competitiveness. The concept of cyber-physical systems supports such changes, with the need to find new modelling tools becoming a key challenge. The book contains five-section covering the following topics: cyber-physical systems modelling, IoT and signal processing, cyber-physical systems intelligent control, cyber-physical systems industrial implementation and the production of the new material for cyber-physical systems. These approaches, on the one hand, should ensure the execution of current business processes, and on the other hand, ensure a quick speed of reactions to changes. The target audience of the book are practitioners, enterprises representatives, scientists, PhD and Master students who perform scientific research on modelling and industrial application of cyber-physical systems.
Intelligent Computer Mathematics
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Author : Serge Autexier
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-07-16
Intelligent Computer Mathematics written by Serge Autexier and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-16 with Computers categories.
This book constitutes the joint refereed proceedings of the 9th International Conference on Artificial Intelligence and Symbolic Computation, AISC 2008, the 15th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2008, and the 7th International Conference on Mathematical Knowledge Management, MKM 2008, held in Birmingham, UK, in July/August as CICM 2008, the Conferences on Intelligent Computer Mathematics. The 14 revised full papers for AISC 2008, 10 revised full papers for Calculemus 2008, and 18 revised full papers for MKM 2008, plus 5 invited talks, were carefully reviewed and selected from a total of 81 submissions for a joint presentation in the book. The papers cover different aspects of traditional branches in CS such as computer algebra, theorem proving, and artificial intelligence in general, as well as newly emerging ones such as user interfaces, knowledge management, and theory exploration, thus facilitating the development of integrated mechanized mathematical assistants that will be routinely used by mathematicians, computer scientists, and engineers in their every-day business.
The Philosophical Foundations Of Ecological Civilization
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Author : Arran Gare
language : en
Publisher: Routledge
Release Date : 2016-08-05
The Philosophical Foundations Of Ecological Civilization written by Arran Gare and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-05 with Nature categories.
The global ecological crisis is the greatest challenge humanity has ever had to confront, and humanity is failing. The triumph of the neo-liberal agenda, together with a debauched ‘scientism’, has reduced nature and people to nothing but raw materials, instruments and consumers to be efficiently managed in a global market dominated by corporate managers, media moguls and technocrats. The arts and the humanities have been devalued, genuine science has been crippled, and the quest for autonomy and democracy undermined. The resultant trajectory towards global ecological destruction appears inexorable, and neither governments nor environmental movements have significantly altered this, or indeed, seem able to. The Philosophical Foundations of Ecological Civilization is a wide-ranging and scholarly analysis of this failure. This book reframes the dynamics of the debate beyond the discourses of economics, politics and techno-science. Reviving natural philosophy to align science with the humanities, it offers the categories required to reform our modes of existence and our institutions so that we augment, rather than undermine, the life of the ecosystems of which we are part. From this philosophical foundation, the author puts forth a manifesto for transforming our culture into one which could provide an effective global environmental movement and provide the foundations for a global ecological civilization.
Software Technologies Applications And Foundations
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Author : Martina Seidl
language : en
Publisher: Springer
Release Date : 2018-01-29
Software Technologies Applications And Foundations written by Martina Seidl and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-29 with Computers categories.
This book contains the thoroughly refereed technical papers presented in six workshops collocated with the International Conference on Software Technologies: Applications and Foundations, STAF 2017, held in Marburg, Germany, in July 2017. The 15 full and 22 short papers presented were carefully reviewed and selected from 37 submissions. The events whose papers are included in this volume are: BigMDE 2017: 5th International Workshop on Scalable Model Driven Engineering GCM 2017: 8th International Workshop on Graph Computation Models GRAND 2017: 1st International Workshop on Grand Challenges in Modeling MORSE 2017: 4th International Workshop on Model-driven Robot Software Engineering OCL 2017: 17th International Workshop in OCL and Textual Modeling STAF Projects Showcase 2017: 3rd event dedicated to international and national project dissemination and cooperation
Categories For The Working Philosopher
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Author : Elaine Landry
language : en
Publisher: Oxford University Press
Release Date : 2017-11-17
Categories For The Working Philosopher written by Elaine Landry 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 2017-11-17 with Philosophy categories.
Often people have wondered why there is no introductory text on category theory aimed at philosophers working in related areas. The answer is simple: what makes categories interesting and significant is their specific use for specific purposes. These uses and purposes, however, vary over many areas, both "pure", e.g., mathematical, foundational and logical, and "applied", e.g., applied to physics, biology and the nature and structure of mathematical models. Borrowing from the title of Saunders Mac Lane's seminal work "Categories for the Working Mathematician", this book aims to bring the concepts of category theory to philosophers working in areas ranging from mathematics to proof theory to computer science to ontology, from to physics to biology to cognition, from mathematical modeling to the structure of scientific theories to the structure of the world. Moreover, it aims to do this in a way that is accessible to non-specialists. Each chapter is written by either a category-theorist or a philosopher working in one of the represented areas, and in a way that builds on the concepts that are already familiar to philosophers working in these areas.
Contemporary Natural Philosophy And Philosophies Part 1
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Author : Gordana Dodig-Crnkovic
language : en
Publisher: MDPI
Release Date : 2019-06-11
Contemporary Natural Philosophy And Philosophies Part 1 written by Gordana Dodig-Crnkovic and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-11 with Philosophy categories.
Modern information communication technology eradicates barriers of geographic distances, making the world globally interdependent, but this spatial globalization has not eliminated cultural fragmentation. The Two Cultures of C.P. Snow (that of science–technology and that of humanities) are drifting apart even faster than before, and they themselves crumble into increasingly specialized domains. Disintegrated knowledge has become subservient to the competition in technological and economic race leading in the direction chosen not by the reason, intellect, and shared value-based judgement, but rather by the whims of autocratic leaders or fashion controlled by marketers for the purposes of political or economic dominance. If we want to restore the authority of our best available knowledge and democratic values in guiding humanity, first we have to reintegrate scattered domains of human knowledge and values and offer an evolving and diverse vision of common reality unified by sound methodology. This collection of articles responds to the call from the journal Philosophies to build a new, networked world of knowledge with domain specialists from different disciplines interacting and connecting with other knowledge-and-values-producing and knowledge-and-values-consuming communities in an inclusive, extended, contemporary natural–philosophic manner. In this process of synthesis, scientific and philosophical investigations enrich each other—with sciences informing philosophies about the best current knowledge of the world, both natural and human-made—while philosophies scrutinize the ontological, epistemological, and methodological foundations of sciences, providing scientists with questions and conceptual analyses. This is all directed at extending and deepening our existing comprehension of the world, including ourselves, both as humans and as societies, and humankind.
Topics In Mathematical Analysis And Differential Geometry
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Author : Nicolas K. Laos
language : en
Publisher: World Scientific
Release Date : 1998
Topics In Mathematical Analysis And Differential Geometry written by Nicolas K. Laos and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
This book studies the interplay between mathematical analysis and differential geometry as well as the foundations of these two fields. The development of a unified approach to topological vector spaces, differential geometry and algebraic and differential topology of function manifolds led to the broad expansion of global analysis. This book serves as a self-contained reference on both the prerequisites for further study and the recent research results which have played a decisive role in the advancement of global analysis.
Mathematics Of Information Processing
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Author : Michael Anshel
language : en
Publisher: American Mathematical Soc.
Release Date : 1986
Mathematics Of Information Processing written by Michael Anshel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Features lectures that require a background in the methodologies of discrete mathematics, in particular the elements of algebra, combinatorics and graph theory, discrete probability, logic and the theory of computation. This title covers the two fundamental aspects of the field - database systems and communication networks.