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2. Frontiers in Industrial and Applied Mathematics : FIAM-2021, Punjab, India, December 21–22
- Author
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Rajesh Kumar Sharma, Lorenzo Pareschi, Abdon Atangana, Bikash Sahoo, Vijay Kumar Kukreja, Rajesh Kumar Sharma, Lorenzo Pareschi, Abdon Atangana, Bikash Sahoo, and Vijay Kumar Kukreja
- Subjects
- Mathematical models, Mathematics—Data processing, Dynamical systems, Probabilities, Stochastic processes
- Abstract
This book publishes select papers presented at the 4th International Conference on Frontiers in Industrial and Applied Mathematics (FIAM-2021), held at the Sant Longowal Institute of Engineering and Technology, Longowal, Punjab, India, from 21–22 December 2021. Most of the papers deal with mathematical theory embedded with its applications to engineering and sciences. This book illustrates numerical simulation of scientific problems and the state-of-the-art research in industrial and applied mathematics, including various computational and modeling techniques with case studies and concrete examples. Graduate students and researchers, who are interested in real applications of mathematics in the areas of computational and theoretical fluid dynamics, solid mechanics, optimization and operations research, numerical analysis, bio-mathematics, fuzzy, control and systems theory, dynamical systems and nonlinear analysis, algebra and approximation theory, will find the book useful.
- Published
- 2023
3. Mathematical Modelling and Computational Intelligence Techniques : ICMMCIT-2021, Gandhigram, India February 10–12
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P. Balasubramaniam, Kuru Ratnavelu, Grienggrai Rajchakit, G. Nagamani, P. Balasubramaniam, Kuru Ratnavelu, Grienggrai Rajchakit, and G. Nagamani
- Subjects
- Neural networks (Computer science), Mathematical models, Control engineering, Coding theory, Information theory, Probabilities, Graph theory, Differential equations
- Abstract
This book collects papers presented at the International Conference on Mathematical Modelling and Computational Intelligence Techniques (ICMMCIT) 2021, held at the Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram, Tamil Nadu, India, from 10–12 February 2021. Significant contributions from renowned researchers from fields of applied analysis, mathematical modelling and computing techniques have been received for this conference. Chapters emphasize on the research of computational nature focusing on new algorithms, their analysis and numerical results, as well as applications in physical, biological, social, and behavioural sciences. The accepted papers are organized in topical sections as mathematical modelling, image processing, control theory, graphs and networks, and inventory control.
- Published
- 2022
4. Topics in Applied Analysis and Optimisation : Partial Differential Equations, Stochastic and Numerical Analysis
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Michael Hintermüller, José Francisco Rodrigues, Michael Hintermüller, and José Francisco Rodrigues
- Subjects
- Differential equations, Mathematical optimization, Mathematical models, Probabilities, Numerical analysis, Mathematical physics
- Abstract
This volume comprises selected, revised papers from the Joint CIM-WIAS Workshop, TAAO 2017, held in Lisbon, Portugal, in December 2017. The workshop brought together experts from research groups at the Weierstrass Institute in Berlin and mathematics centres in Portugal to present and discuss current scientific topics and to promote existing and future collaborations. The papers include the following topics: PDEs with applications to material sciences, thermodynamics and laser dynamics, scientific computing, nonlinear optimization and stochastic analysis.
- Published
- 2019
5. Modeling, Stochastic Control, Optimization, and Applications
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George Yin, Qing Zhang, George Yin, and Qing Zhang
- Subjects
- Probabilities, Mathematical optimization, Calculus of variations, Mathematical models
- Abstract
This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.
- Published
- 2019
6. Complex Systems
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E. Goles, Servet Martínez, E. Goles, and Servet Martínez
- Subjects
- Mathematical models, System theory, Control theory, Computer science, Statistics, Computer science—Mathematics, Discrete mathematics
- Abstract
This volume contains the courses given at the Sixth Summer School on Complex Systems held at Facultad de Ciencias Fisicas y Maternaticas, Universidad de Chile at Santiago, Chile, from 14th to 18th December 1998. This school was addressed to graduate students and researchers working on areas related with recent trends in Complex Systems, including dynamical systems, cellular automata, complexity and cutoff in Markov chains. Each contribution is devoted to one of these subjects. In some cases they are structured as surveys, presenting at the same time an original point of view and showing mostly new results. The paper of Pierre Arnoux investigates the relation between low complex systems and chaotic systems, showing that they can be put into relation by some re normalization operations. The case of quasi-crystals is fully studied, in particular the Sturmian quasi-crystals. The paper of Franco Bagnoli and Raul Rechtman establishes relations be tween Lyapunov exponents and synchronization processes in cellular automata. The principal goal is to associate tools, usually used in physical problems, to an important problem in cellularautomata and computer science, the synchronization problem. The paper of Jacques Demongeot and colleagues gives a presentation of at tractors of dynamical systems appearing in biological situations. For instance, the relation between positive or negative loops and regulation systems.
- Published
- 2012
7. Transactions on Computational Science VII
- Subjects
- Mathematics—Data processing, Computer science—Mathematics, Mathematical statistics, Mathematical models, Differential equations, Numerical analysis, Discrete mathematics
- Abstract
The LNCS journal Transactions on Computational Science reflects recent developments in the field of Computational Science, conceiving the field not as a mere ancillary science but rather as an innovative approach supporting many other scientific disciplines. The journal focuses on original high-quality research in the realm of computational science in parallel and distributed environments, encompassing the facilitating theoretical foundations and the applications of large-scale computations and massive data processing. It addresses researchers and practitioners in areas ranging from aerospace to biochemistry, from electronics to geosciences, from mathematics to software architecture, presenting verifiable computational methods, findings and solutions and enabling industrial users to apply techniques of leading-edge, large-scale, high performance computational methods. The 7th issue of the Transactions on Computational Science journal is devoted to core computational science techniques, such as grid computing, advanced numerical methods, and stochastic systems. It has been divided into two parts. The five papers in Part I focus on computations of stochastic systems and the four papers in Part II focus on computational methods for complex systems.
- Published
- 2010
8. Seminaire De Probabilites XXVII
- Author
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Jaques Azema, Paul A. Meyer, Marc Yor, Jaques Azema, Paul A. Meyer, and Marc Yor
- Subjects
- Probabilities, Mathematical models, Mathematical physics, Functions of real variables
- Abstract
This volume represents a part of the main result obtained by a group of French probabilists, together with the contributions of a number of colleagues, mainly from the USA and Japan. All the papers present new results obtained during the academic year 1991-1992. The main themes of the papers are: quantum probability (P.A. Meyer and S. Attal), stochastic calculus (M. Nagasawa, J.B. Walsh, F. Knight, to name a few authors), fine properties of Brownian motion (Bertoin, Burdzy, Mountford), stochastic differential geometry (Arnaudon, Elworthy), quasi-sure analysis (Lescot, Song, Hirsch). Taken all together, the papers contained in this volume reflect the main directions of the most up-to-date research in probability theory. FROM THE CONTENTS: J.P. Ansal, C. Stricker: Unicite et existence de la loi minimale.- K. Kawazu, H. Tanaka: On the maximum of a diffusion process in a drifted Brownian environment.- P.A. Meyer: Representation de martingales d'operateurs, d'apres Parthasarathy-Sinha.- K. Burdzy: Excursion laws and exceptional points on Brownian paths.- X. Fernique: Convergence en loi de variables aleatoires et de fonctions aleatoires, proprietes de compacite des lois, II.- M. Nagasawa: Principle ofsuperposition and interference of diffusion processes.- F. Knight: Some remarks on mutual windings.- S. Song: Inegalites relatives aux processus d'Ornstein-Ulhenbeck a n-parametres et capacite gaussienne c (n,2).- S. Attal, P.A. Meyer: Interpretation probabiliste et extension des integrales stochastiques non commutatives.- J. Azema, Th. Jeulin, F. Knight,M. Yor: Le theoreme d'arret en une fin d'ensemble previsible.
- Published
- 2006
9. Mittag-Leffler Functions, Related Topics and Applications
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Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, Sergei Rogosin, Rudolf Gorenflo, Anatoly A. Kilbas, Francesco Mainardi, and Sergei Rogosin
- Subjects
- Mathematical physics, Special functions, Mathematical models, Integral equations, Probabilities
- Abstract
The 2nd edition of this book is essentially an extended version of the 1st and provides a very sound overview of the most important special functions of Fractional Calculus. It has been updated with material from many recent papers and includes several surveys of important results known before the publication of the 1st edition, but not covered there.As a result of researchers'and scientists'increasing interest in pure as well as applied mathematics in non-conventional models, particularly those using fractional calculus, Mittag-Leffler functions have caught the interest of the scientific community. Focusing on the theory of Mittag-Leffler functions, this volume offers a self-contained, comprehensive treatment, ranging from rather elementary matters to the latest research results. In addition to the theory the authors devote some sections of the work to applications, treating various situations and processes in viscoelasticity, physics, hydrodynamics, diffusion and wave phenomena, as well as stochastics. In particular, the Mittag-Leffler functions make it possible to describe phenomena in processes that progress or decay too slowly to be represented by classical functions like the exponential function and related special functions.The book is intended for a broad audience, comprising graduate students, university instructors and scientists in the field of pure and applied mathematics, as well as researchers in applied sciences like mathematical physics, theoretical chemistry, bio-mathematics, control theory and several other related areas.
- Published
- 2020
10. Seminal Contributions to Modelling and Simulation : 30 Years of the European Council of Modelling and Simulation
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Khalid Al-Begain, Andrzej Bargiela, Khalid Al-Begain, and Andrzej Bargiela
- Subjects
- Digital computer simulation, Mathematical models, Computer simulation
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Marking the 30th anniversary of the European Conference on Modelling and Simulation (ECMS), this inspirational text/reference reviews significant advances in the field of modelling and simulation, as well as key applications of simulation in other disciplines. The broad-ranging volume presents contributions from a varied selection of distinguished experts chosen from high-impact keynote speakers and best paper winners from the conference, including a Nobel Prize recipient, and the first president of the European Council for Modelling and Simulation (also abbreviated to ECMS). This authoritative book will be of great value to all researchers working in the field of modelling and simulation, in addition to scientists from other disciplines who make use of modelling and simulation approaches in their work.
- Published
- 2016
11. Advances in Stochastic Simulation Methods
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N. Balakrishnan, V.B. Melas, S. Ermakov, N. Balakrishnan, V.B. Melas, and S. Ermakov
- Subjects
- Mathematical statistics--Data processing, Mathematical models, Computer simulation
- Abstract
This is a volume consisting of selected papers that were presented at the 3rd St. Petersburg Workshop on Simulation held at St. Petersburg, Russia, during June 28-July 3, 1998. The Workshop is a regular international event devoted to mathematical problems of simulation and applied statistics organized by the Department of Stochastic Simulation at St. Petersburg State University in cooperation with INFORMS College on Simulation (USA). Its main purpose is to exchange ideas between researchers from Russia and from the West as well as from other coun tries throughout the World. The 1st Workshop was held during May 24-28, 1994, and the 2nd workshop was held during June 18-21, 1996. The selected proceedings of the 2nd Workshop was published as a special issue of the Journal of Statistical Planning and Inference. Russian mathematical tradition has been formed by such genius as Tchebysh eff, Markov and Kolmogorov whose ideas have formed the basis for contempo rary probabilistic models. However, for many decades now, Russian scholars have been isolated from their colleagues in the West and as a result their mathe matical contributions have not been widely known. One of the primary reasons for these workshops is to bring the contributions of Russian scholars into lime light and we sincerely hope that this volume helps in this specific purpose.
- Published
- 2012
12. Applied Probability and Stochastic Processes
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J. George Shanthikumar, Ushio Sumita, J. George Shanthikumar, and Ushio Sumita
- Subjects
- Probabilities, Operations research, Mathematical models
- Abstract
Applied Probability and Stochastic Processes is an edited work written in honor of Julien Keilson. This volume has attracted a host of scholars in applied probability, who have made major contributions to the field, and have written survey and state-of-the-art papers on a variety of applied probability topics, including, but not limited to: perturbation method, time reversible Markov chains, Poisson processes, Brownian techniques, Bayesian probability, optimal quality control, Markov decision processes, random matrices, queueing theory and a variety of applications of stochastic processes. The book has a mixture of theoretical, algorithmic, and application chapters providing examples of the cutting-edge work that Professor Keilson has done or influenced over the course of his highly-productive and energetic career in applied probability and stochastic processes. The book will be of interest to academic researchers, students, and industrial practitioners who seek to use the mathematics of applied probability in solving problems in modern society.
- Published
- 2012
13. Semi-Markov Chains and Hidden Semi-Markov Models Toward Applications : Their Use in Reliability and DNA Analysis
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Vlad Stefan Barbu, Nikolaos Limnios, Vlad Stefan Barbu, and Nikolaos Limnios
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- DNA, Reproducible research, Probabilities, Mathematical models, DNA--Analysis--Mathematics, DNA--Mathematical models, Markov processes, Reliability (Engineering)--Mathematical models, Stochastic processes, Public health, Medical care, Nucleic acids, Statistics
- Abstract
This book is concerned with the estimation of discrete-time semi-Markov and hidden semi-Markov processes. Semi-Markov processes are much more general and better adapted to applications than the Markov ones because sojourn times in any state can be arbitrarily distributed, as opposed to the geometrically distributed sojourn time in the Markov case. Another unique feature of the book is the use of discrete time, especially useful in some specific applications where the time scale is intrinsically discrete. The models presented in the book are specifically adapted to reliability studies and DNA analysis. The book is mainly intended for applied probabilists and statisticians interested in semi-Markov chains theory, reliability and DNA analysis, and for theoretical oriented reliability and bioinformatics engineers. It can also serve as a text for a six month research-oriented course at a Master or PhD level. The prerequisites are a background in probability theory and finite state space Markov chains. Vlad Stefan Barbu is associate professor in statistics at the University of Rouen, France, Laboratory of Mathematics ‘Raphaël Salem.'His research focuses basically on stochastic processes and associated statistical problems, with a particular interest in reliability and DNA analysis. He has published several papers in the field. Nikolaos Limnios is a professor in Applied Mathematics at the University of Technology of Compiègne. His research interest concerns stochastic processes and statistics with application to reliability. He is the co-author of the books: Semi-Markov Processes and Reliability (Birkhäuser, 2001 with G. Oprisan) and Stochastic Systems in Merging Phase Space (World Scientific, 2005, with V.S. Koroliuk).
- Published
- 2008
14. Seminaire De Probabilites XXVIII
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Jacques Azema, Paul-Andre Meyer, Marc Yor, Jacques Azema, Paul-Andre Meyer, and Marc Yor
- Subjects
- Probabilities, Mathematical models, Mathematical physics
- Abstract
In this volume of original research papers, the main topics discussed relate to the asymptotic windings of planar Brownian motion, structure equations, closure properties of stochastic integrals. The contents of the volume represent an important fraction of research undertaken by French probabilists and their collaborators from abroad during the academic year 1992-1993.
- Published
- 2006
15. Petri Net Primer : A Compendium on the Core Model, Analysis, and Synthesis
- Author
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Eike Best, Raymond Devillers, Eike Best, and Raymond Devillers
- Subjects
- Computer science—Mathematics, Discrete mathematics, Dynamical systems, Mathematical models, Stochastic models
- Abstract
Petri nets model concurrent and distributed systems where active components communicate through the production and absorption of various kinds of resources. Although the dynamic properties of such systems may be very complex, they may sometimes be connected to the static structure of a Petri net. Many properties are decidable, but their complexity may be huge. It is often opportune to restrict oneself to classes of systems, to partial algorithms, and to similar but simpler properties. Instead of analysing a given system, it is also possible to search for a system satisfying some desired properties by construction. This comprehensive textbook/reference presents and discusses these issues in-depth in the context of one of the most fundamental Petri net models, called place/transition nets. The presentation is fortified by means of many examples and worked exercises. Among topics addressed: • In which order may actions may be generated and scheduled? • What states and configurations may be reached in a concurrent system? • Which interesting classes of systems can be analysed relatively efficiently? • Is it possible to synthesise a system of some class from its behaviour? • How can systems be represented algebraically, compositionally, and concisely? This unique text, based on introductory as well as on advanced courses on distributed systems, will serve as an invaluable guide for students and (future) researchers interested in theoretical—as well as in practical—aspects of Petri nets and related system models. Eike Best has been a full professor (now retired) affiliated to Carl von Ossietzky Universität Oldenburg, Germany. Raymond Devillers has been a full professor (now retired) affiliated to Université Libre de Bruxelles, Belgium. The authors have a long record as collaborators in the fields of Petri nets and the semantics of concurrency.
- Published
- 2024
16. Data-driven Modelling and Scientific Machine Learning in Continuum Physics
- Author
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Krishna Garikipati and Krishna Garikipati
- Subjects
- Mathematical models, Artificial intelligence—Data processing, Machine learning
- Abstract
This monograph takes the reader through recent advances in data-driven methods and machine learning for problems in science—specifically in continuum physics. It develops the foundations and details a number of scientific machine learning approaches to enrich current computational models of continuum physics, or to use the data generated by these models to infer more information on these problems. The perspective presented here is drawn from recent research by the author and collaborators. Applications drawn from the physics of materials or from biophysics illustrate each topic. Some elements of the theoretical background in continuum physics that are essential to address these applications are developed first. These chapters focus on nonlinear elasticity and mass transport, with particular attention directed at descriptions of phase separation. This is followed by a brief treatment of the finite element method, since it is the most widely used approach to solve coupled partial differential equations in continuum physics. With these foundations established, the treatment proceeds to a number of recent developments in data-driven methods and scientific machine learning in the context of the continuum physics of materials and biosystems. This part of the monograph begins by addressing numerical homogenization of microstructural response using feed-forward as well as convolutional neural networks. Next is surrogate optimization using multifidelity learning for problems of phase evolution. Graph theory bears many equivalences to partial differential equations in its properties of representation and avenues for analysis as well as reduced-order descriptions--all ideas that offer fruitful opportunities for exploration. Neural networks, by their capacity for representation of high-dimensional functions, are powerful for scale bridging in physics--an idea on which we present a particular perspective in the context of alloys. One of the most compelling ideas in scientific machine learning is the identification of governing equations from dynamical data--another topic that we explore from the viewpoint of partial differential equations encoding mechanisms. This is followed by an examination of approaches to replace traditional, discretization-based solvers of partial differential equations with deterministic and probabilistic neural networks that generalize across boundary value problems. The monograph closes with a brief outlook on current emerging ideas in scientific machine learning.
- Published
- 2024
17. Mathematical and Statistical Approaches for Anaerobic Digestion Feedstock Optimization
- Author
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Federico Moretta, Giulia Bozzano, Federico Moretta, and Giulia Bozzano
- Subjects
- Electric power production, Mathematical models, Chemical engineering, Statistics
- Abstract
This book examines biomass mixture modeling and optimization. The book discusses anaerobic digestion and related fermentative processes and explains their compositional dynamics. Early chapter examine macromolecules, elemental fractions, and their direct influence on methane production. Supported by an extensive data bank of substrates obtained from research, the book points out correlations that enable the estimation of global methane production for diverse biomass mixtures. Furthermore, it provides valuable insights into discerning the optimal composition capable of yielding the utmost methane output.The book integrates cutting-edge machine learning techniques and shows how the programming language Python and Julia can be used for analysis and to optimize processes. It has many graphs, figures, and visuals.
- Published
- 2024
18. Reliability Engineering
- Author
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Youchao Sun, Longbiao Li, Dmytro Tiniakov, Youchao Sun, Longbiao Li, and Dmytro Tiniakov
- Subjects
- Industrial engineering, Production engineering, Aerospace engineering, Astronautics, Probabilities, Engineering design, Statistics, Mathematical models
- Abstract
This textbook covers the fundamentals of reliability theory and its application for engineering processes, especially for aircraft units and systems. Reliability basis was explained for the best understanding of reliability analysis application for engineering systems in aviation industry. Several approaches for the reliability analysis and their application with examples are presented. It also introduces main trends in the modern reliability theory development.This book will be interested for university students and early-career engineers of aviation industry majors.
- Published
- 2023
19. Dynamic Time Series Models Using R-INLA : An Applied Perspective
- Author
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Nalini Ravishanker, Balaji Raman, Refik Soyer, Nalini Ravishanker, Balaji Raman, and Refik Soyer
- Subjects
- R (Computer program language), Laplace transformation, Time-series analysis, Bayesian statistical decision theory, Mathematical models
- Abstract
Dynamic Time Series Models using R-INLA: An Applied Perspective is the outcome of a joint effort to systematically describe the use of R-INLA for analysing time series and showcasing the code and description by several examples. This book introduces the underpinnings of R-INLA and the tools needed for modelling different types of time series using an approximate Bayesian framework.The book is an ideal reference for statisticians and scientists who work with time series data. It provides an excellent resource for teaching a course on Bayesian analysis using state space models for time series.Key Features: Introduction and overview of R-INLA for time series analysis. Gaussian and non-Gaussian state space models for time series. State space models for time series with exogenous predictors. Hierarchical models for a potentially large set of time series. Dynamic modelling of stochastic volatility and spatio-temporal dependence.
- Published
- 2023
20. Modern Deep Learning for Tabular Data : Novel Approaches to Common Modeling Problems
- Author
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Andre Ye, Zian Wang, Andre Ye, and Zian Wang
- Subjects
- Mathematical models, Machine learning
- Abstract
Deep learning is one of the most powerful tools in the modern artificial intelligence landscape. While having been predominantly applied to highly specialized image, text, and signal datasets, this book synthesizes and presents novel deep learning approaches to a seemingly unlikely domain – tabular data. Whether for finance, business, security, medicine, or countless other domain, deep learning can help mine and model complex patterns in tabular data – an incredibly ubiquitous form of structured data. Part I of the book offers a rigorous overview of machine learning principles, algorithms, and implementation skills relevant to holistically modeling and manipulating tabular data. Part II studies five dominant deep learning model designs – Artificial Neural Networks, Convolutional Neural Networks, Recurrent Neural Networks, Attention and Transformers, and Tree-Rooted Networks – through both their ‘default'usage and their application to tabular data. Part III compounds the power of the previously covered methods by surveying strategies and techniques to supercharge deep learning systems: autoencoders, deep data generation, meta-optimization, multi-model arrangement, and neural network interpretability. Each chapter comes with extensive visualization, code, and relevant research coverage. Modern Deep Learning for Tabular Data is one of the first of its kind – a wide exploration of deep learning theory and applications to tabular data, integrating and documenting novel methods and techniques in the field. This book provides a strong conceptual and theoretical toolkit to approach challenging tabular data problems.What You Will LearnImportant concepts and developments in modern machine learning and deep learning, with a strong emphasis on tabular data applications.Understand the promising links between deep learning and tabular data, and when a deep learning approach is or isn't appropriate.Apply promising research and unique modeling approaches in real-world data contexts.Explore and engage with modern, research-backed theoretical advances on deep tabular modelingUtilize unique and successful preprocessing methods to prepare tabular data for successful modelling. Who This Book Is ForData scientists and researchers of all levels from beginner to advanced looking to level up results on tabular data with deep learning or to understand the theoretical and practical aspects of deep tabular modeling research. Applicable to readers seeking to apply deep learning to all sorts of complex tabular data contexts, including business, finance, medicine, education, and security.
- Published
- 2023
21. An Introduction to Statistical Learning : With Applications in Python
- Author
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Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani, Jonathan Taylor, Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani, and Jonathan Taylor
- Subjects
- Mathematical statistics, Mathematical models, Python (Computer program language)
- Abstract
An Introduction to Statistical Learning provides an accessible overview of the field of statistical learning, an essential toolset for making sense of the vast and complex data sets that have emerged in fields ranging from biology to finance, marketing, and astrophysics in the past twenty years. This book presents some of the most important modeling and prediction techniques, along with relevant applications. Topics include linear regression, classification, resampling methods, shrinkage approaches, tree-based methods, support vector machines, clustering, deep learning, survival analysis, multiple testing, and more. Color graphics and real-world examples are used to illustrate the methods presented. This book is targeted at statisticians and non-statisticians alike, who wish to use cutting-edge statistical learning techniques to analyze their data. Four of the authors co-wrote An Introduction to Statistical Learning, With Applications in R(ISLR), which has become a mainstay of undergraduate and graduate classrooms worldwide, as well as an important reference book for data scientists. One of the keys to its success was that each chapter contains a tutorial on implementing the analyses and methods presented in the R scientific computing environment. However, in recent years Python has become a popular language for data science, and there has been increasing demand for a Python-based alternative to ISLR. Hence, this book (ISLP) covers the same materials as ISLR but with labs implemented in Python. These labs will be useful both for Python novices, as well as experienced users.
- Published
- 2023
22. Proceedings of the 8th International Conference on the Applications of Science and Mathematics : SCIEMATHIC 2022; 17—19 Oct; Malaysia
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Aida Mustapha, Norzuria Ibrahim, Hatijah Basri, Mohd Saifullah Rusiman, Syed Zuhaib Haider Rizvi, Aida Mustapha, Norzuria Ibrahim, Hatijah Basri, Mohd Saifullah Rusiman, and Syed Zuhaib Haider Rizvi
- Subjects
- Mathematical physics, Statistics, Mathematical models, Chemistry, Physical and theoretical, Sustainability
- Abstract
This book presents peer-reviewed articles and recent advances on the potential applications of Science and Mathematics for future technologies, from the 8th International Conference on the Applications of Science and Mathematics (SCIEMATHIC 2022), held in Malaysia. It provides an insight about the leading trends in sustainable Science and Technology. Topics included in this proceedings are in the areas of Mathematics and Statistics, including Natural Science, Engineering and Artificial Intelligence.
- Published
- 2023
23. Modeling Change and Uncertainty : Machine Learning and Other Techniques
- Author
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William P. Fox, Robert E. Burks, William P. Fox, and Robert E. Burks
- Subjects
- Mathematical models, Mathematical analysis
- Abstract
This book offers a problem-solving approach. The authors introduce a problem to help motivate the learning of a particular mathematical modeling topic. The problem provides the issue or what is needed to solve using an appropriate modeling technique.
- Published
- 2022
24. Modeling Biomaterials
- Author
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Josef Málek, Endre Süli, Josef Málek, and Endre Süli
- Subjects
- Mathematical models, Stochastic models, Markov processes, Numerical analysis, Continuum mechanics, Biomaterials
- Abstract
The investigation of the role of mechanical and mechano-chemical interactions in cellular processes and tissue development is a rapidly growing research field in the life sciences and in biomedical engineering. Quantitative understanding of this important area in the study of biological systems requires the development of adequate mathematical models for the simulation of the evolution of these systems in space and time. Since expertise in various fields is necessary, this calls for a multidisciplinary approach.This edited volume connects basic physical, biological, and physiological concepts to methods for the mathematical modeling of various materials by pursuing a multiscale approach, from subcellular to organ and system level. Written by active researchers, each chapter provides a detailed introduction to a given field, illustrates various approaches to creating models, and explores recent advances and future research perspectives. Topics covered include molecular dynamics simulations of lipid membranes, phenomenological continuum mechanics of tissue growth, and translational cardiovascular modeling. Modeling Biomaterials will be a valuable resource for both non-specialists and experienced researchers from various domains of science, such as applied mathematics, biophysics, computational physiology, and medicine.
- Published
- 2022
25. Introduction to Statistical Modelling and Inference
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Murray Aitkin and Murray Aitkin
- Subjects
- Mathematical statistics, Mathematical models
- Abstract
The complexity of large-scale data sets (“Big Data”) has stimulated the development of advanced computational methods for analysing them. There are two different kinds of methods to aid this. The model-based method uses probability models and likelihood and Bayesian theory, while the model-free method does not require a probability model, likelihood or Bayesian theory. These two approaches are based on different philosophical principles of probability theory, espoused by the famous statisticians Ronald Fisher and Jerzy Neyman.Introduction to Statistical Modelling and Inference covers simple experimental and survey designs, and probability models up to and including generalised linear (regression) models and some extensions of these, including finite mixtures. A wide range of examples from different application fields are also discussed and analysed. No special software is used, beyond that needed for maximum likelihood analysis of generalised linear models. Students are expected to have a basic mathematical background in algebra, coordinate geometry and calculus.Features• Probability models are developed from the shape of the sample empirical cumulative distribution function (cdf) or a transformation of it.• Bounds for the value of the population cumulative distribution function are obtained from the Beta distribution at each point of the empirical cdf.• Bayes's theorem is developed from the properties of the screening test for a rare condition.• The multinomial distribution provides an always-true model for any randomly sampled data.• The model-free bootstrap method for finding the precision of a sample estimate has a model-based parallel – the Bayesian bootstrap – based on the always-true multinomial distribution.• The Bayesian posterior distributions of model parameters can be obtained from the maximum likelihood analysis of the model.This book is aimed at students in a wide range of disciplines including Data Science. The book is based on the model-based theory, used widely by scientists in many fields, and compares it, in less detail, with the model-free theory, popular in computer science, machine learning and official survey analysis. The development of the model-based theory is accelerated by recent developmentsin Bayesian analysis.
- Published
- 2022
26. Escape From Model Land : How Mathematical Models Can Lead Us Astray and What We Can Do About It
- Author
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Erica Thompson and Erica Thompson
- Subjects
- Modeling, Mathematical models
- Abstract
Why mathematical models are so often wrong, and how we can make better decisions by accepting their limits Whether we are worried about the spread of COVID-19 or making a corporate budget, we depend on mathematical models to help us understand the world around us every day. But models aren't a mirror of reality. In fact, they are fantasies, where everything works out perfectly, every time. And relying on them too heavily can hurt us. In Escape from Model Land, statistician Erica Thompson illuminates the hidden dangers of models. She demonstrates how models reflect the biases, perspectives, and expectations of their creators. Thompson shows us why understanding the limits of models is vital to using them well. A deeper meditation on the role of mathematics, this is an essential book for helping us avoid either confusing the map with the territory or throwing away the map completely, instead pointing to more nuanced ways to Escape from Model Land.
- Published
- 2022
27. The Nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology, Volume I : Overcoming the Curse of Dimensionality: Linear Systems
- Author
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Dan Gabriel Cacuci and Dan Gabriel Cacuci
- Subjects
- Mathematical physics, Computer simulation, Mathematical models, Statistics, Energy policy, Energy and state, Engineering mathematics, Engineering—Data processing, Nuclear physics
- Abstract
The computational models of physical systems comprise parameters, independent and dependent variables. Since the physical processes themselves are seldom known precisely and since most of the model parameters stem from experimental procedures which are also subject to imprecisions, the results predicted by these models are also imprecise, being affected by the uncertainties underlying the respective model. The functional derivatives (also called “sensitivities”) of results (also called “responses”) produced by mathematical/computational models are needed for many purposes, including: (i) understanding the model by ranking the importance of the various model parameters; (ii) performing “reduced-order modeling” by eliminating unimportant parameters and/or processes; (iii) quantifying the uncertainties induced in a model response due to model parameter uncertainties; (iv) performing “model validation,” by comparing computations to experiments to address the question “does the modelrepresent reality?” (v) prioritizing improvements in the model; (vi) performing data assimilation and model calibration as part of forward “predictive modeling” to obtain best-estimate predicted results with reduced predicted uncertainties; (vii) performing inverse “predictive modeling”; (viii) designing and optimizing the system. This 3-Volume monograph describes a comprehensive adjoint sensitivity analysis methodology, developed by the author, which enables the efficient and exact computation of arbitrarily high-order sensitivities of model responses in large-scale systems comprising many model parameters. The qualifier “comprehensive” is employed to highlight that the model parameters considered within the framework of this methodology also include the system's uncertain boundaries and internal interfaces in phase-space. The model's responses can be either scalar-valued functionals of the model's parameters and state variables (e.g., as customarily encountered in optimization problems) or general function-valued responses. Since linear operators admit bona-fide adjoint operators, responses of models that are linear in the state functions (i.e., dependent variables) can depend simultaneously on both the forward and the adjoint state functions. Hence, the sensitivity analysis of such responses warrants the treatment of linear systems in their own right, rather than treating them as particular cases of nonlinear systems. This is in contradistinction to responses for nonlinear systems, which can depend only on the forward state functions, since nonlinear operators do not admit bona-fide adjoint operators (only a linearized form of a nonlinear operator may admit an adjoint operator). Thus, Volume 1 of this book presents the mathematical framework of the nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (abbreviated as “nth-CASAM-L”), which is conceived for the most efficient computation of exactly obtained mathematical expressions of arbitrarily-high-order (nth-order) sensitivities of a generic system response with respect to all of the parameters underlying the respective forward/adjoint systems. Volume 2 of this book presents the application of the nth-CASAM-L to perform a fourth-order sensitivity and uncertainty analysis of an OECD/NEA reactor physics benchmark which is representative of a large-scale model comprises many (21,976) uncertain parameters, thereby amply illustrating the unique potential of the nth-CASAM-L to enable the exact and efficient computation of chosen high-order response sensitivities to model parameters. Volume 3 of this book presents the “nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (abbreviation: nth-CASAM-N) for the practical, efficient, and exact computation of arbitrarily-high orderse
- Published
- 2022
28. Proceedings of the 7th International Conference on the Applications of Science and Mathematics 2021 : Sciemathic 2021
- Author
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Aida Binti Mustapha, Suhadir Shamsuddin, Syed Zuhaib Haider Rizvi, Saliza Binti Asman, Siti Suhana Jamaian, Aida Binti Mustapha, Suhadir Shamsuddin, Syed Zuhaib Haider Rizvi, Saliza Binti Asman, and Siti Suhana Jamaian
- Subjects
- Mathematical physics, Statistics, Sustainability, Mathematical models, Chemistry, Physical and theoretical, Materials science
- Abstract
This book presents peer-reviewed articles and recent advances on the potential applications of Science and Mathematics for future technologies, from the 7th International Conference on the Applications of Science and Mathematics (SCIEMATHIC 2021), held in Malaysia. It provides an insight about the leading trends in sustainable Science and Technology. The world is looking for sustainable solutions to problems more than ever. The synergistic approach of mathematicians, scientists and engineers has undeniable importance for future technologies. With this viewpoint, SCIEMATHIC 2021 has the theme “Quest for Sustainable Science and Mathematics for Future Technologies”. The conference brings together physicists, mathematicians, statisticians and data scientists, providing a platform to find sustainable solutions to major problems around us. The works presented here are suitable for professionals and researchers globally in making the world a better and sustainable place.
- Published
- 2022
29. Recent Developments in Mathematical, Statistical and Computational Sciences : The V AMMCS International Conference, Waterloo, Canada, August 18–23, 2019
- Author
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D. Marc Kilgour, Herb Kunze, Roman Makarov, Roderick Melnik, Xu Wang, D. Marc Kilgour, Herb Kunze, Roman Makarov, Roderick Melnik, and Xu Wang
- Subjects
- Mathematical models, Probabilities, Biomathematics, Mathematics, Social sciences, Biometry
- Abstract
This book constitutes an up-to-date account of principles, methods, and tools for mathematical and statistical modelling in a wide range of research fields, including medicine, health sciences, biology, environmental science, engineering, physics, chemistry, computation, finance, economics, and social sciences. It presents original solutions to real-world problems, emphasizes the coordinated development of theories and applications, and promotes interdisciplinary collaboration among mathematicians, statisticians, and researchers in other disciplines.Based on a highly successful meeting, the International Conference on Applied Mathematics, Modeling and Computational Science, AMMCS 2019, held from August 18 to 23, 2019, on the main campus of Wilfrid Laurier University, Waterloo, Canada, the contributions are the results of submissions from the conference participants. They provide readers with a broader view of the methods, ideas and tools used in mathematical, statistical andcomputational sciences.
- Published
- 2021
30. Mathematical Modeling and Computation of Real-Time Problems : An Interdisciplinary Approach
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Rakhee Kulshrestha, Chandra Shekhar, Madhu Jain, Srinivas R. Chakravarthy, Rakhee Kulshrestha, Chandra Shekhar, Madhu Jain, and Srinivas R. Chakravarthy
- Subjects
- Mathematical models, Operations research, Stochastic processes, Mathematical optimization
- Abstract
This book covers an interdisciplinary approach for understanding mathematical modeling by offering a collection of models, solved problems related to the models, the methodologies employed, and the results using projects and case studies with insight into the operation of substantial real-time systems. The book covers a broad scope in the areas of statistical science, probability, stochastic processes, fluid dynamics, supply chain, optimization, and applications. It discusses advanced topics and the latest research findings, uses an interdisciplinary approach for real-time systems, offers a platform for integrated research, and identifies the gaps in the field for further research. The book is for researchers, students, and teachers that share a goal of learning advanced topics and the latest research in mathematical modeling.
- Published
- 2021
31. Explanatory Model Analysis : Explore, Explain, and Examine Predictive Models
- Author
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Przemyslaw Biecek, Tomasz Burzykowski, Przemyslaw Biecek, and Tomasz Burzykowski
- Subjects
- Mathematical models
- Abstract
Explanatory Model Analysis Explore, Explain and Examine Predictive Models is a set of methods and tools designed to build better predictive models and to monitor their behaviour in a changing environment. Today, the true bottleneck in predictive modelling is neither the lack of data, nor the lack of computational power, nor inadequate algorithms, nor the lack of flexible models. It is the lack of tools for model exploration (extraction of relationships learned by the model), model explanation (understanding the key factors influencing model decisions) and model examination (identification of model weaknesses and evaluation of model's performance). This book presents a collection of model agnostic methods that may be used for any black-box model together with real-world applications to classification and regression problems.
- Published
- 2021
32. The Elements of Hawkes Processes
- Author
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Patrick J. Laub, Young Lee, Thomas Taimre, Patrick J. Laub, Young Lee, and Thomas Taimre
- Subjects
- Mathematical models, Mathematical statistics
- Abstract
Hawkes processes are studied and used in a wide range of disciplines: mathematics, social sciences, and earthquake modelling, to name a few. This book presents a selective coverage of the core and recent topics in the broad field of Hawkes processes. It consists of three parts. Parts I and II summarise and provide an overview of core theory (including key simulation methods) and inference methods, complemented by a selection of recent research developments and applications. Part III is devoted to case studies in seismology and finance that connect the core theory and inference methods to practical scenarios. This book is designed primarily for applied probabilists, statisticians, and machine learners. However, the mathematical prerequisites have been kept to a minimum so that the content will also be of interest to undergraduates in advanced mathematics and statistics, as well as machine learning practitioners. Knowledge of matrix theory with basics of probability theory, including Poisson processes, is considered a prerequisite. Colour-blind-friendly illustrations are included.
- Published
- 2021
33. An Introduction to Statistical Learning : With Applications in R
- Author
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Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani, Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani
- Subjects
- Mathematical statistics, Mathematical models, R (Computer program language)
- Abstract
An Introduction to Statistical Learning provides an accessible overview of the field of statistical learning, an essential toolset for making sense of the vast and complex data sets that have emerged in fields ranging from biology to finance to marketing to astrophysics in the past twenty years. This book presents some of the most important modeling and prediction techniques, along with relevant applications. Topics include linear regression, classification, resampling methods, shrinkage approaches, tree-based methods, support vector machines, clustering, deep learning, survival analysis, multiple testing, and more. Color graphics and real-world examples are used to illustrate the methods presented. Since the goal of this textbook is to facilitate the use of these statistical learning techniques by practitioners in science, industry, and other fields, each chapter contains a tutorial on implementing the analyses and methods presented in R, an extremely popular open source statistical software platform.Two of the authors co-wrote The Elements of Statistical Learning (Hastie, Tibshirani and Friedman, 2nd edition 2009), a popular reference book for statistics and machine learning researchers. An Introduction to Statistical Learning covers many of the same topics, but at a level accessible to a much broader audience. This book is targeted at statisticians and non-statisticians alike who wish to use cutting-edge statistical learning techniques to analyze their data. The text assumes only a previous course in linear regression and no knowledge of matrix algebra.This Second Edition features new chapters on deep learning, survival analysis, and multiple testing, as well as expanded treatments of naïve Bayes, generalized linear models, Bayesian additive regression trees, and matrix completion. R code has been updated throughout to ensure compatibility.
- Published
- 2021
34. Advances on Links Between Mathematics and Industry : CTMI 2019
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Peregrina Quintela Estévez, Bartomeu Coll, Rosa M. Crujeiras, José Durany, Laureano Escudero, Peregrina Quintela Estévez, Bartomeu Coll, Rosa M. Crujeiras, José Durany, and Laureano Escudero
- Subjects
- Mathematical models, Statistics, Computer science--Mathematics, Applied mathematics, Engineering mathematics
- Abstract
This book results from the talks presented at the First Conference on Transfer between Mathematics & Industry (CTMI 2019). Its goal is to promote and disseminate the mathematical tools for Statistics & Big Data, MSO (Modeling, Simulation and Optimization) and their industrial applications. In this volume, the reader will find innovative advances in the automotive, energy, railway, logistics, and materials sectors. In addition, Advances CTMI 2019 promotes the opening of new research lines aiming to provide suitable solutions for the industrial and societal challenges. Fostering effective interaction between Academia and Industry is our main purpose with this book. CTMI conferences are one of the main forums where significant advances in industrial mathematics are presented, bringing together outstanding leaders from business, science and Academia to promote the use of mathematics for an innovative industry.
- Published
- 2021
35. Stochastic Benchmarking : Theory and Applications
- Author
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Alireza Amirteimoori, Biresh K. Sahoo, Vincent Charles, Saber Mehdizadeh, Alireza Amirteimoori, Biresh K. Sahoo, Vincent Charles, and Saber Mehdizadeh
- Subjects
- Operations research, Stochastic models, Mathematical models, Mathematical optimization
- Abstract
This book introduces readers to benchmarking techniques in the stochastic environment, primarily stochastic data envelopment analysis (DEA), and provides stochastic models in DEA for the possibility of variations in inputs and outputs. It focuses on the application of theories and interpretations of the mathematical programs, which are combined with economic and organizational thinking. The book's main purpose is to shed light on the advantages of the different methods in deterministic and stochastic environments and thoroughly prepare readers to properly use these methods in various cases. Simple examples, along with graphical illustrations and real-world applications in industry, are provided for a better understanding. The models introduced here can be easily used in both theoretical and real-world evaluations. This book is intended for graduate and PhD students, advanced consultants, and practitioners with an interest in quantitative performance evaluation.
- Published
- 2021
36. Advanced Mathematical Modeling with Technology
- Author
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William P. Fox, Robert E. Burks, William P. Fox, and Robert E. Burks
- Subjects
- Mathematical models, Decision making--Mathematical models, Mathematics--Data processing
- Abstract
Mathematical modeling is both a skill and an art and must be practiced in order to maintain and enhance the ability to use those skills. Though the topics covered in this book are the typical topics of most mathematical modeling courses, this book is best used for individuals or groups who have already taken an introductory mathematical modeling course. This book will be of interest to instructors and students offering courses focused on discrete modeling or modeling for decision making.
- Published
- 2021
37. Modelling with Ordinary Differential Equations : A Comprehensive Approach
- Author
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Alfio Borzì and Alfio Borzì
- Subjects
- Differential equations, Mathematical models
- Abstract
Modelling with Ordinary Differential Equations: A Comprehensive Approach aims to provide a broad and self-contained introduction to the mathematical tools necessary to investigate and apply ODE models. The book starts by establishing the existence of solutions in various settings and analysing their stability properties. The next step is to illustrate modelling issues arising in the calculus of variation and optimal control theory that are of interest in many applications. This discussion is continued with an introduction to inverse problems governed by ODE models and to differential games.The book is completed with an illustration of stochastic differential equations and the development of neural networks to solve ODE systems. Many numerical methods are presented to solve the classes of problems discussed in this book.Features: Provides insight into rigorous mathematical issues concerning various topics, while discussing many different models of interest in different disciplines (biology, chemistry, economics, medicine, physics, social sciences, etc.) Suitable for undergraduate and graduate students and as an introduction for researchers in engineering and the sciences Accompanied by codes which allow the reader to apply the numerical methods discussed in this book in those cases where analytical solutions are not available
- Published
- 2020
38. Advances in Photometric 3D-Reconstruction
- Author
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Jean-Denis Durou, Maurizio Falcone, Yvain Quéau, Silvia Tozza, Jean-Denis Durou, Maurizio Falcone, Yvain Quéau, and Silvia Tozza
- Subjects
- Computer vision, Mathematical models, Machine learning
- Abstract
This book presents the latest advances in photometric 3D reconstruction. It provides the reader with an overview of the state of the art in the field, and of the latest research into both the theoretical foundations of photometric 3D reconstruction and its practical application in several fields (including security, medicine, cultural heritage and archiving, and engineering). These techniques play a crucial role within such emerging technologies as 3D printing, since they permit the direct conversion of an image into a solid object. The book covers both theoretical analysis and real-world applications, highlighting the importance of deepening interdisciplinary skills, and as such will be of interest to both academic researchers and practitioners from the computer vision and mathematical 3D modeling communities, as well as engineers involved in 3D printing. No prior background is required beyond a general knowledge of classical computer vision models, numerical methods for optimization, and partial differential equations.
- Published
- 2020
39. Accuracy of Mathematical Models : Dimension Reduction, Homogenization, and Simplification
- Author
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Sergey I. Repin, Stefan A. Sauter, Sergey I. Repin, and Stefan A. Sauter
- Subjects
- Mathematical models
- Abstract
The expansion of scientific knowledge and the development of technology are strongly connected with quantitative analysis of mathematical models. Accuracy and reliability are the key properties we wish to understand and control. This book presents a unified approach to the analysis of accuracy of deterministic mathematical models described by variational problems and partial differential equations of elliptic type. It is based on new mathematical methods developed to estimate the distance between a solution of a boundary value problem and any function in the admissible functional class associated with the problem in question. The theory is presented for a wide class of elliptic variational problems. It is applied to the investigation of modelling errors arising in dimension reduction, homogenization, simplification, and various conversion methods (penalization, linearization, regularization, etc.). A collection of examples illustrates the performance of error estimates.
- Published
- 2020
40. Robust Integration of Model-Based Fault Estimation and Fault-Tolerant Control
- Author
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Jianglin Lan, Ronald J. Patton, Jianglin Lan, and Ronald J. Patton
- Subjects
- Control engineering, System theory, Control theory, Robust statistics, Mathematical models
- Abstract
Robust Integration of Model-Based Fault Estimation and Fault-Tolerant Control is a systematic examination of methods used to overcome the inevitable system uncertainties arising when a fault estimation (FE) function and a fault-tolerant controller interact as they are employed together to compensate for system faults and maintain robustly acceptable system performance. It covers the important subject of robust integration of FE and FTC with the aim of guaranteeing closed-loop stability. The reader's understanding of the theory is supported by the extensive use of tutorial examples, including some MATLAB®-based material available from the Springer website and by industrial-applications-based material. The text is structured into three parts:Part I examines the basic concepts of FE and FTC, providing extensive insight into the importance of and challenges involved in their integration;Part II describes five effective strategiesfor the integration of FE and FTC: sequential, iterative, simultaneous, adaptive-decoupling, and robust decoupling; andPart III begins to extend the proposed strategies to nonlinear and large-scale systems and covers their application in the fields of renewable energy, robotics and networked systems. The strategies presented are applicable to a broad range of control problems, because in the absence of faults the FE-based FTC naturally reverts to conventional observer-based control. The book is a useful resource for researchers and engineers working in the area of fault-tolerant control systems, and supplementary material for a graduate- or postgraduate-level course on fault diagnosis and FTC.Advances in Industrial Control reports and encourages the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control.
- Published
- 2020
41. Mathematical Modelling in Health, Social and Applied Sciences
- Author
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Hemen Dutta and Hemen Dutta
- Subjects
- Mathematical models
- Abstract
This book discusses significant research findings in the field of mathematical modelling, with particular emphasis on important applied-sciences, health, and social issues. It includes topics such as model on viral immunology, stochastic models for the dynamics of influenza, model describing the transmission of dengue, model for human papillomavirus (HPV) infection, prostate cancer model, realization of economic growth by goal programming, modelling of grazing periodic solutions in discontinuous systems, modelling of predation system, fractional epidemiological model for computer viruses, and nonlinear ecological models. A unique addition in the proposed areas of research and education, this book is a valuable resource for graduate students, researchers and educators associated with the study of mathematical modelling of health, social and applied-sciences issues. Readers interested in applied mathematics should also find this book valuable.
- Published
- 2020
42. Probability and Simulation
- Author
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Giray Ökten and Giray Ökten
- Subjects
- Probabilities, Mathematical models
- Abstract
This undergraduate textbook presents an inquiry-based learning course in stochastic models and computing designed to serve as a first course in probability. Its modular structure complements a traditional lecture format, introducing new topics chapter by chapter with accompanying projects for group collaboration. The text addresses probability axioms leading to Bayes'theorem, discrete and continuous random variables, Markov chains, and Brownian motion, as well as applications including randomized algorithms, randomized surveys, Benford's law, and Monte Carlo methods. Adopting a unique application-driven approach to better study probability in action, the book emphasizes data, simulation, and games to strengthen reader insight and intuition while proving theorems. Additionally, the text incorporates codes and exercises in the Julia programming language to further promote a hands-on focus in modelling. Students should have prior knowledge of single variable calculus.Giray Ökten received his PhD from Claremont Graduate University. He has held academic positions at University of Alaska Fairbanks, Ball State University, and Florida State University. He received a Fulbright U.S. Scholar award in 2015. He is the author of an open access textbook in numerical analysis, First Semester in Numerical Analysis with Julia, published by Florida State University Libraries, and a co-author of a children's math book, The Mathematical Investigations of Dr. O and Arya, published by Tumblehome. His research interests include Monte Carlo methods and computational finance.
- Published
- 2020
43. Mathematical Modelling in Real Life Problems : Case Studies From ECMI-Modelling Weeks
- Author
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Ewald Lindner, Alessandra Micheletti, Cláudia Nunes, Ewald Lindner, Alessandra Micheletti, and Cláudia Nunes
- Subjects
- Discrete mathematics, Computer science--Mathematics, Engineering mathematics, Mathematical models, Probabilities, Biomathematics, Mathematical optimization
- Abstract
This book is intended to be a useful contribution for the modern teaching of applied mathematics, educating Industrial Mathematicians that will meet the growing demand for such experts. It covers many applications where mathematics play a fundamental role, from biology, telecommunications, medicine, physics, finance and industry. It is presented in such a way that can be useful in Modelation, Simulation and Optimization courses, targeting master and PhD students. Its content is based on many editions from the successful series of Modelling Weeks organized by the European Consortium of Mathematics in Industry (ECMI). Each chapter addresses a particular problem, and is written in a didactic way, providing the description of the problem, the particular way of approaching it and the proposed solution, along with the results obtained.
- Published
- 2020
44. Parameter Redundancy and Identifiability
- Author
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Diana Cole and Diana Cole
- Subjects
- Ecology--Statistical methods, Ecology--Mathematical models, Parameter estimation, Mathematical models
- Abstract
Statistical and mathematical models are defined by parameters that describe different characteristics of those models. Ideally it would be possible to find parameter estimates for every parameter in that model, but, in some cases, this is not possible. For example, two parameters that only ever appear in the model as a product could not be estimated individually; only the product can be estimated. Such a model is said to be parameter redundant, or the parameters are described as non-identifiable. This book explains why parameter redundancy and non-identifiability is a problem and the different methods that can be used for detection, including in a Bayesian context. Key features of this book: Detailed discussion of the problems caused by parameter redundancy and non-identifiability Explanation of the different general methods for detecting parameter redundancy and non-identifiability, including symbolic algebra and numerical methods Chapter on Bayesian identifiability Throughout illustrative examples are used to clearly demonstrate each problem and method. Maple and R code are available for these examples More in-depth focus on the areas of discrete and continuous state-space models and ecological statistics, including methods that have been specifically developed for each of these areas This book is designed to make parameter redundancy and non-identifiability accessible and understandable to a wide audience from masters and PhD students to researchers, from mathematicians and statisticians to practitioners using mathematical or statistical models.
- Published
- 2020
45. Statistical Techniques for Modelling Extreme Value Data and Related Applications
- Author
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Haroon M. Barakat, Author, Osama M. Khaled, Author, El-Sayed M. Nigm, Author, Haroon M. Barakat, Author, Osama M. Khaled, Author, and El-Sayed M. Nigm, Author
- Subjects
- Natural disasters--Observations, Mathematical models, Simulation methods, Natural disasters--Mathematical models
- Abstract
This book tackles some modern trends and methods in the modelling of extreme data. Usually such data arise from random phenomena such as floods, hurricanes, air and water pollutants, extreme claim sizes, life spans, and maximum sizes of ecological populations. It provides the latest statistical methods to model these random phenomena to understand and predict them, thus allowing the avoidance of damage or at least minimizing it. In addition, this book sheds light on the mathematical and statistical theories on which applied modelling methods were built. Therefore, it has both an applied and theoretical orientation, and represents a valuable addition to existing literature on the modelling of extreme value data.
- Published
- 2019
46. Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA
- Author
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Elias Krainski, Virgilio Gómez-Rubio, Haakon Bakka, Amanda Lenzi, Daniela Castro-Camilo, Daniel Simpson, Finn Lindgren, Håvard Rue, Elias Krainski, Virgilio Gómez-Rubio, Haakon Bakka, Amanda Lenzi, Daniela Castro-Camilo, Daniel Simpson, Finn Lindgren, and Håvard Rue
- Subjects
- Stochastic processes, Mathematical models, Stochastic differential equations, R (Computer program language), Laplace transformation
- Abstract
Modeling spatial and spatio-temporal continuous processes is an important and challenging problem in spatial statistics. Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA describes in detail the stochastic partial differential equations (SPDE) approach for modeling continuous spatial processes with a Matérn covariance, which has been implemented using the integrated nested Laplace approximation (INLA) in the R-INLA package. Key concepts about modeling spatial processes and the SPDE approach are explained with examples using simulated data and real applications.This book has been authored by leading experts in spatial statistics, including the main developers of the INLA and SPDE methodologies and the R-INLA package. It also includes a wide range of applications:• Spatial and spatio-temporal models for continuous outcomes• Analysis of spatial and spatio-temporal point patterns• Coregionalization spatial and spatio-temporal models• Measurement error spatial models• Modeling preferential sampling• Spatial and spatio-temporal models with physical barriers• Survival analysis with spatial effects• Dynamic space-time regression• Spatial and spatio-temporal models for extremes• Hurdle models with spatial effects• Penalized Complexity priors for spatial modelsAll the examples in the book are fully reproducible. Further information about this book, as well as the R code and datasets used, is available from the book website at http://www.r-inla.org/spde-book.The tools described in this book will be useful to researchers in many fields such as biostatistics, spatial statistics, environmental sciences, epidemiology, ecology and others. Graduate and Ph.D. students will also find this book and associated files a valuable resource to learn INLA and the SPDE approach for spatial modeling.
- Published
- 2019
47. Assessing and Improving Prediction and Classification : Theory and Algorithms in C++
- Author
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Timothy Masters and Timothy Masters
- Subjects
- Data mining, C++ (Computer program language), Mathematical models
- Abstract
Assess the quality of your prediction and classification models in ways that accurately reflect their real-world performance, and then improve this performance using state-of-the-art algorithms such as committee-based decision making, resampling the dataset, and boosting. This book presents many important techniques for building powerful, robust models and quantifying their expected behavior when put to work in your application.Considerable attention is given to information theory, especially as it relates to discovering and exploiting relationships between variables employed by your models. This presentation of an often confusing subject avoids advanced mathematics, focusing instead on concepts easily understood by those with modest background in mathematics.All algorithms include an intuitive explanation of operation, essential equations, references to more rigorous theory, and commented C++ source code. Manyof these techniques are recent developments, still not in widespread use. Others are standard algorithms given a fresh look. In every case, the emphasis is on practical applicability, with all code written in such a way that it can easily be included in any program.What You'll LearnCompute entropy to detect problematic predictorsImprove numeric predictions using constrained and unconstrained combinations, variance-weighted interpolation, and kernel-regression smoothingCarry out classification decisions using Borda counts, MinMax and MaxMin rules, union and intersection rules, logistic regression, selection by local accuracy, maximization of the fuzzy integral, and pairwise couplingHarness information-theoretic techniques to rapidly screen large numbers of candidate predictors, identifying those that are especially promisingUse Monte-Carlo permutation methods to assessthe role of good luck in performance resultsCompute confidence and tolerance intervals for predictions, as well as confidence levels for classification decisionsWho This Book is ForAnyone who creates prediction or classification models will find a wealth of useful algorithms in this book. Although all code examples are written in C++, the algorithms are described in sufficient detail that they can easily be programmed in any language.
- Published
- 2018
48. Compact Extended Linear Programming Models
- Author
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Giuseppe Lancia, Paolo Serafini, Giuseppe Lancia, and Paolo Serafini
- Subjects
- Operations research, Management science, Mathematical models, Data mining
- Abstract
This book provides a handy, unified introduction to the theory of compact extended formulations of exponential-size integer linear programming (ILP) models. Compact extended formulations are equally powerful, but polynomial-sized, models whose solutions do not require the implementation of separation and pricing procedures. The book is written in a general, didactic form, first developing the background theoretical concepts (polyhedra, projections, linear and integer programming) and then delving into the various techniques for compact extended reformulations. The techniques are illustrated through a wealth of examples touching on many application areas, such as classical combinatorial optimization, network design, timetabling, scheduling, routing, computational biology and bioinformatics. The book is intended for graduate or PhD students – either as an advanced course on selected topics or within a more general course on ILP and mathematical programming – as well as for practitionersand software engineers in industry exploring techniques for developing optimization models for their specific problems.
- Published
- 2017
49. Radiation Risk Estimation : Based on Measurement Error Models
- Author
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Sergii Masiuk, Alexander Kukush, Sergiy Shklyar, Mykola Chepurny, Illya Likhtarov, Sergii Masiuk, Alexander Kukush, Sergiy Shklyar, Mykola Chepurny, and Illya Likhtarov
- Subjects
- Radiation--Dosage, Risk assessment, Radiation injuries, Nuclear power plants--Environmental aspects, Nuclear reactors--Containment, Radiation--Physiological effect, Nuclear reactors--Risk assessment, Mathematical models
- Abstract
This monograph discusses statistics and risk estimates applied to radiation damage under the presence of measurement errors. The first part covers nonlinear measurement error models, with a particular emphasis on efficiency of regression parameter estimators. In the second part, risk estimation in models with measurement errors is considered. Efficiency of the methods presented is verified using data from radio-epidemiological studies. Contents: Part I - Estimation in regression models with errors in covariatesMeasurement error modelsLinear models with classical errorPolynomial regression with known variance of classical errorNonlinear and generalized linear models Part II Radiation risk estimation under uncertainty in exposure dosesOverview of risk models realized in program package EPICUREEstimation of radiation risk under classical or Berkson multiplicative error in exposure dosesRadiation risk estimation for persons exposed by radioiodine as a result of the Chornobyl accidentElements of estimating equations theoryConsistency of efficient methodsEfficient SIMEX method as a combination of the SIMEX method and the corrected score methodApplication of regression calibration in the model with additive error in exposure doses
- Published
- 2017
50. Stochastic Modeling
- Author
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Nicolas Lanchier and Nicolas Lanchier
- Subjects
- Probabilities, Mathematical models
- Abstract
Three coherent parts form the material covered in this text, portions of which have not been widely covered in traditional textbooks. In this coverage the reader is quickly introduced to several different topics enriched with 175 exercises which focus on real-world problems. Exercises range from the classics of probability theory to more exotic research-oriented problems based on numerical simulations. Intended for graduate students in mathematics and applied sciences, the text provides the tools and training needed to write and use programs for research purposes. The first part of the text begins with a brief review of measure theory and revisits the main concepts of probability theory, from random variables to the standard limit theorems. The second part covers traditional material on stochastic processes, including martingales, discrete-time Markov chains, Poisson processes, and continuous-time Markov chains. The theory developed is illustrated by a variety of examples surrounding applications such as the gambler's ruin chain, branching processes, symmetric random walks, and queueing systems. The third, more research-oriented part of the text, discusses special stochastic processes of interest in physics, biology, and sociology. Additional emphasis is placed on minimal models that have been used historically to develop new mathematical techniques in the field of stochastic processes: the logistic growth process, the Wright –Fisher model, Kingman's coalescent, percolation models, the contact process, and the voter model. Further treatment of the material explains how these special processes are connected to each other from a modeling perspective as well as their simulation capabilities in C and Matlab™.
- Published
- 2017
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