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See below for a selection of the latest books from Mathematical modelling category. Presented with a red border are the Mathematical modelling books that have been lovingly read and reviewed by the experts at Lovereading. With expert reading recommendations made by people with a passion for books and some unique features Lovereading will help you find great Mathematical modelling books and those from many more genres to read that will keep you inspired and entertained. And it's all free!
This volume offers a collection of carefully selected, peer-reviewed papers presented at the BIOMAT 2018 International Symposium, which was held at the University Hassan II, Morocco, from October 29th to November 2nd, 2018. The topics covered include applications of mathematical modeling in hepatitis B, HIV and Chikungunya infections; tumor cell dynamics; inflammatory processes; chemotherapeutic drug effects; and population dynamics. Also discussing the application of techniques like the generalized stochastic Milevsky-Promislov model, numerical simulations and convergence of discrete and continuous models, it is an invaluable resource on interdisciplinary research in mathematical biology for students, researchers, and professionals. Held every year since 2001, the BIOMAT International Symposium gathers together, in a single conference, researchers from Mathematics, Physics, Biology, and affine fields to promote the interdisciplinary exchange of results, ideas and techniques, promoting truly international cooperation for problem discussion. The 2018 edition of BIOMAT International Symposium received contributions by authors from seventeen countries: Algeria, Brazil, Cameroon, Canada, Chad, Colombia, France, Germany, Hungary, Italy, Mali, Morocco, Nigeria, Poland, Portugal, Russia, and Senegal. Selected papers presented at the 2017 edition of this Symposium were also published by Springer, in the volume Trends in Biomathematics: Modeling, Optimization and Computational Problems (978-3-319-91091-8).
The objective of this textbook is the construction, analysis, and interpretation of mathematical models to help us understand the world we live in. Rather than follow a case study approach it develops the mathematical and physical ideas that are fundamental in understanding contemporary problems in science and engineering. Science evolves, and this means that the problems of current interest continually change. What does not change as quickly is the approach used to derive the relevant mathematical models, and the methods used to analyze the models. Consequently, this book is written in such a way as to establish the mathematical ideas underlying model development independently of a specific application. This does not mean applications are not considered, they are, and connections with experiment are a staple of this book. The book, as well as the individual chapters, is written in such a way that the material becomes more sophisticated as you progress. This provides some flexibility in how the book is used, allowing consideration for the breadth and depth of the material covered. Moreover, there are a wide spectrum of exercises and detailed illustrations that significantly enrich the material. Students and researchers interested in mathematical modelling in mathematics, physics, engineering and the applied sciences will find this text useful. The material, and topics, have been updated to include recent developments in mathematical modeling. The exercises have also been expanded to include these changes, as well as enhance those from the first edition. Review of first edition: The goal of this book is to introduce the mathematical tools needed for analyzing and deriving mathematical models. ... Holmes is able to integrate the theory with application in a very nice way providing an excellent book on applied mathematics. ... One of the best features of the book is the abundant number of exercises found at the end of each chapter. ... I think this is a great book, and I recommend it for scholarly purposes by students, teachers, and researchers. Joe Latulippe, The Mathematical Association of America, December, 2009
Dieses Lehrbuch beinhaltet eine Einfuhrung in die vielfaltige und faszinierende Welt der mathematischen Modellierung und eignet sich ideal fur alle, die auf diesem Gebiet noch keine grossen Erfahrungen sammeln konnten. Insbesondere wurde dabei an die Studierenden im Bachelor-Studium gedacht, die beim Durcharbeiten des Buchs das noetige Rustzeug bekommen, um sich selbststandig an die mathematische Modellierung von realen Anwendungen zu wagen und die in der Spezialliteratur beschriebenen Modelle kreativ anzupassen und einzusetzen. Wahrend der erste Teil des Buchs sich der Methodik des Modellierens und den Aktivitaten im Modellierungszyklus widmet, halt der zweite Teil einen Werkzeugkasten fur die einzelnen Modellierungsschritte parat. Die dritte Saule des Buchs bilden einige Fallstudien, die nach der vorgestellten Methodik und mit den Techniken aus dem Werkzeugkasten bearbeitet werden. Das Modellieren beschrankt sich dabei nicht - und das ist das Besondere an diesem Buch - auf die Modellentwurfe, sondern beinhaltet auch ihre Analyse, numerische Behandlung, Implementierung von Algorithmen, Rechnungen, Visualisierung und Analyse der Ergebnisse. Fur die Implementierung der Berechnungen und die Visualisierung der Ergebnisse wird dabei das Softwarepaket MATLAB(R) eingesetzt, alle Beispiele sind jedoch ebenso in Octave lauffahig. Die vorliegende zweite Auflage wurde in einigen Teilen wesentlich erweitert, um die Bedeutung der mathematischen Modellierung in aktuellen Anwendungen noch deutlicher zu machen. Insbesondere werden jetzt auch wichtige Modellansatze aus dem Bereich des maschinellen Lernens vorgestellt und eine neue Fallstudie uber Computertomographie behandelt die Modellierung von inversen schlecht gestellten Problemen.
This book discusses the modeling and analysis of magnetic resonance imaging (MRI) data acquired from the human brain. The data processing pipelines described rely on R. The book is intended for readers from two communities: Statisticians who are interested in neuroimaging and looking for an introduction to the acquired data and typical scientific problems in the field; and neuroimaging students wanting to learn about the statistical modeling and analysis of MRI data. Offering a practical introduction to the field, the book focuses on those problems in data analysis for which implementations within R are available. It also includes fully worked examples and as such serves as a tutorial on MRI analysis with R, from which the readers can derive their own data processing scripts. The book starts with a short introduction to MRI and then examines the process of reading and writing common neuroimaging data formats to and from the R session. The main chapters cover three common MR imaging modalities and their data modeling and analysis problems: functional MRI, diffusion MRI, and Multi-Parameter Mapping. The book concludes with extended appendices providing details of the non-parametric statistics used and the resources for R and MRI data.The book also addresses the issues of reproducibility and topics like data organization and description, as well as open data and open science. It relies solely on a dynamic report generation with knitr and uses neuroimaging data publicly available in data repositories. The PDF was created executing the R code in the chunks and then running LaTeX, which means that almost all figures, numbers, and results were generated while producing the PDF from the sources.
The mystique of biologically inspired (or bioinspired) paradigms is their ability to describe and solve complex relationships from intrinsically very simple initial conditions and with little or no knowledge of the search space. Edited by two prominent, well-respected researchers, the Handbook of Bioinspired Algorithms and Applications reveals the connections between bioinspired techniques and the development of solutions to problems that arise in diverse problem domains. A repository of the theory and fundamentals as well as a manual for practical implementation, this authoritative handbook provides broad coverage in a single source along with numerous references to the available literature for more in-depth information. The book's two sections serve to balance coverage of theory and practical applications. The first section explains the fundamentals of techniques, such as evolutionary algorithms, swarm intelligence, cellular automata, and others. Detailed examples and case studies in the second section illustrate how to apply the theory in actually developing solutions to a particular problem based on a bioinspired technique. Emphasizing the importance of understanding and harnessing the robust capabilities of bioinspired techniques for solving computationally intractable optimizations and decision-making applications, the Handbook of Bioinspired Algorithms and Applications is an absolute must-read for anyone who is serious about advancing the next generation of computing.
The topic of dynamic models tends to be splintered across various disciplines, making it difficult to uniformly study the subject. Moreover, the models have a variety of representations, from traditional mathematical notations to diagrammatic and immersive depictions. Collecting all of these expressions of dynamic models, the Handbook of Dynamic System Modeling explores a panoply of different types of modeling methods available for dynamical systems. Featuring an interdisciplinary, balanced approach, the handbook focuses on both generalized dynamic knowledge and specific models. It first introduces the general concepts, representations, and philosophy of dynamic models, followed by a section on modeling methodologies that explains how to portray designed models on a computer. After addressing scale, heterogeneity, and composition issues, the book covers specific model types that are often characterized by specific visual- or text-based grammars. It concludes with case studies that employ two well-known commercial packages to construct, simulate, and analyze dynamic models. A complete guide to the fundamentals, types, and applications of dynamic models, this handbook shows how systems function and are represented over time and space and illustrates how to select a particular model based on a specific area of interest.
This book provides a broad yet detailed introduction to neural networks and machine learning in a statistical framework. A single, comprehensive resource for study and further research, it explores the major popular neural network models and statistical learning approaches with examples and exercises and allows readers to gain a practical working understanding of the content. This updated new edition presents recently published results and includes six new chapters that correspond to the recent advances in computational learning theory, sparse coding, deep learning, big data and cloud computing. Each chapter features state-of-the-art descriptions and significant research findings. The topics covered include: * multilayer perceptron; * the Hopfield network; * associative memory models;* clustering models and algorithms; * t he radial basis function network; * recurrent neural networks; * nonnegative matrix factorization; * independent component analysis; *probabilistic and Bayesian networks; and * fuzzy sets and logic. Focusing on the prominent accomplishments and their practical aspects, this book provides academic and technical staff, as well as graduate students and researchers with a solid foundation and comprehensive reference on the fields of neural networks, pattern recognition, signal processing, and machine learning.
Modeling and Inverse Problems in the Presence of Uncertainty collects recent research-including the authors' own substantial projects-on uncertainty propagation and quantification. It covers two sources of uncertainty: where uncertainty is present primarily due to measurement errors and where uncertainty is present due to the modeling formulation itself. After a useful review of relevant probability and statistical concepts, the book summarizes mathematical and statistical aspects of inverse problem methodology, including ordinary, weighted, and generalized least-squares formulations. It then discusses asymptotic theories, bootstrapping, and issues related to the evaluation of correctness of assumed form of statistical models. The authors go on to present methods for evaluating and comparing the validity of appropriateness of a collection of models for describing a given data set, including statistically based model selection and comparison techniques. They also explore recent results on the estimation of probability distributions when they are embedded in complex mathematical models and only aggregate (not individual) data are available. In addition, they briefly discuss the optimal design of experiments in support of inverse problems for given models. The book concludes with a focus on uncertainty in model formulation itself, covering the general relationship of differential equations driven by white noise and the ones driven by colored noise in terms of their resulting probability density functions. It also deals with questions related to the appropriateness of discrete versus continuum models in transitions from small to large numbers of individuals. With many examples throughout addressing problems in physics, biology, and other areas, this book is intended for applied mathematicians interested in deterministic and/or stochastic models and their interactions. It is also s
This book presents a new and original method for the solution of boundary value problems in angles for second-order elliptic equations with constant coefficients and arbitrary boundary operators. This method turns out to be applicable to many different areas of mathematical physics, in particular to diffraction problems in angles and to the study of trapped modes on a sloping beach. Giving the reader the opportunity to master the techniques of the modern theory of diffraction, the book introduces methods of distributions, complex Fourier transforms, pseudo-differential operators, Riemann surfaces, automorphic functions, and the Riemann-Hilbert problem. The book will be useful for students, postgraduates and specialists interested in the application of modern mathematics to wave propagation and diffraction problems.
This monograph aims to provide a rigorous yet accessible presentation of some fundamental concepts used in modeling brain mechanics and give a glimpse of the insights and advances that have arisen as a result of the nascent interaction of the mathematical and neurosurgical sciences. It begins with some historical perspective and a brief synopsis of the biomedical/biological manifestations of the clinical conditions/diseases considered. Each chapter proceeds with a discussion of the various mathematical models of the problems considered, starting with the simplest models and proceeding to more complex models where necessary. A detailed list of relevant references is provided at the end of each chapter. With the beginning research student in mind, the chapters have been crafted to be as self-contained as possible while addressing different clinical conditions and diseases. The book is intended as a brief introduction to both theoreticians and experimentalists interested in brain mechanics, with directions and guidance for further reading, for those who wish to pursue particular topics in greater depth. It can also be used as a complementary textbook in a graduate level course for neuroscientists and neuroengineers.
Galton used quantiles more than a hundred years ago in describing data. Tukey and Parzen used them in the 60s and 70s in describing populations. Since then, the authors of many papers, both theoretical and practical, have used various aspects of quantiles in their work. Until now, however, no one put all the ideas together to form what turns out to be a general approach to statistics. Statistical Modelling with Quantile Functions does just that. It systematically examines the entire process of statistical modelling, starting with using the quantile function to define continuous distributions. The author shows that by using this approach, it becomes possible to develop complex distributional models from simple components. A modelling kit can be developed that applies to the whole model - deterministic and stochastic components - and this kit operates by adding, multiplying, and transforming distributions rather than data. Statistical Modelling with Quantile Functions adds a new dimension to the practice of statistical modelling that will be of value to anyone faced with analyzing data. Not intended to replace classical approaches but to supplement them, it will make some of the traditional topics easier and clearer, and help readers build and investigate models for their own practical statistical problems.
Many methods for analyzing clustered data exist, all with advantages and limitations in particular applications. Compiled from the contributions of leading specialists in the field, Topics in Modelling of Clustered Data describes the tools and techniques for modelling the clustered data often encountered in medical, biological, environmental, and social science studies. It focuses on providing a comprehensive treatment of marginal, conditional, and random effects models using, among others, likelihood, pseudo-likelihood, and generalized estimating equations methods. The authors motivate and illustrate all aspects of these models in a variety of real applications. They discuss several variations and extensions, including individual-level covariates and combined continuous and discrete outcomes. Flexible modelling with fractional and local polynomials, omnibus lack-of-fit tests, robustification against misspecification, exact, and bootstrap inferential procedures all receive extensive treatment. The applications discussed center primarily, but not exclusively, on developmental toxicity, which leads naturally to discussion of other methodologies, including risk assessment and dose-response modelling. Clearly written, Topics in Modelling of Clustered Data offers a practical, easily accessible survey of important modelling issues. Overview models give structure to a multitude of approaches, figures help readers visualize model characteristics, and a generous use of examples illustrates all aspects of the modelling process.