- Table View
- List View
Model-Based Clustering, Classification, and Density Estimation Using mclust in R (Chapman & Hall/CRC The R Series)
by Chris Fraley Luca Scrucca T. Brendan Murphy Raftery Adrian E.Model-Based Clustering, Classification, and Denisty Estimation Using mclust in R Model-based clustering and classification methods provide a systematic statistical approach to clustering, classification, and density estimation via mixture modeling. The model-based framework allows the problems of choosing or developing an appropriate clustering or classification method to be understood within the context of statistical modeling. The mclust package for the statistical environment R is a widely adopted platform implementing these model-based strategies. The package includes both summary and visual functionality, complementing procedures for estimating and choosing models. Key features of the book: An introduction to the model-based approach and the mclust R package A detailed description of mclust and the underlying modeling strategies An extensive set of examples, color plots, and figures along with the R code for reproducing them Supported by a companion website, including the R code to reproduce the examples and figures presented in the book, errata, and other supplementary material Model-Based Clustering, Classification, and Density Estimation Using mclust in R is accessible to quantitatively trained students and researchers with a basic understanding of statistical methods, including inference and computing. In addition to serving as a reference manual for mclust, the book will be particularly useful to those wishing to employ these model-based techniques in research or applications in statistics, data science, clinical research, social science, and many other disciplines.
Model-Free Prediction and Regression
by Dimitris N. PolitisThe Model-Free Prediction Principle expounded upon in this monograph is based on the simple notion of transforming a complex dataset to one that is easier to work with, e. g. , i. i. d. or Gaussian. As such, it restores the emphasis on observable quantities, i. e. , current and future data, as opposed to unobservable model parameters and estimates thereof, and yields optimal predictors in diverse settings such as regression and time series. Furthermore, the Model-Free Bootstrap takes us beyond point prediction in order to construct frequentist prediction intervals without resort to unrealistic assumptions such as normality. Prediction has been traditionally approached via a model-based paradigm, i. e. , (a) fit a model to the data at hand, and (b) use the fitted model to extrapolate/predict future data. Due to both mathematical and computational constraints, 20th century statistical practice focused mostly on parametric models. Fortunately, with the advent of widely accessible powerful computing in the late 1970s, computer-intensive methods such as the bootstrap and cross-validation freed practitioners from the limitations of parametric models, and paved the way towards the `big data' era of the 21st century. Nonetheless, there is a further step one may take, i. e. , going beyond even nonparametric models; this is where the Model-Free Prediction Principle is useful. Interestingly, being able to predict a response variable Y associated with a regressor variable X taking on any possible value seems to inadvertently also achieve the main goal of modeling, i. e. , trying to describe how Y depends on X. Hence, as prediction can be treated as a by-product of model-fitting, key estimation problems can be addressed as a by-product of being able to perform prediction. In other words, a practitioner can use Model-Free Prediction ideas in order to additionally obtain point estimates and confidence intervals for relevant parameters leading to an alternative, transformation-based approach to statistical inference.
Model-Oriented Design of Experiments (Lecture Notes in Statistics #209)
by Valerii V. Fedorov Peter HacklThis book presents the basic ideas of statistical methods in the design of optimal experiments. This new edition now includes sections on design techniques based on the elemental Fisher information matrices (as opposed to Pearson information/moment matrices), allowing a seamless extension of the design techniques to inferential problems where the shape of distributions is essential for optimal design construction. Topics include designs for nonlinear models, models with random parameters and models with correlated observations, designs for model discrimination and misspecified (contaminated) models, and designs in functional spaces. The authors avoid technical details, assuming a moderate background in calculus, matrix algebra, and statistics. In many places, however, suggestions are made as to how the ideas presented in this book can be extended and elaborated for use in real scientific research and practical engineering problems.
Model-based Geostatistics for Global Public Health: Methods and Applications (Chapman & Hall/CRC Interdisciplinary Statistics)
by Peter J. Diggle Emanuele GiorgiModel-based Geostatistics for Global Public Health: Methods and Applications provides an introductory account of model-based geostatistics, its implementation in open-source software and its application in public health research. In the public health problems that are the focus of this book, the authors describe and explain the pattern of spatial variation in a health outcome or exposure measurement of interest. Model-based geostatistics uses explicit probability models and established principles of statistical inference to address questions of this kind. <P><P>Features: <li>Presents state-of-the-art methods in model-based geostatistics. <li>Discusses the application these methods some of the most challenging global public health problems including disease mapping, exposure mapping and environmental epidemiology. <li>Describes exploratory methods for analysing geostatistical data, including: diagnostic checking of residuals standard linear and generalized linear models; variogram analysis; Gaussian process models and geostatistical design issues. <li>Includes a range of more complex geostatistical problems where research is ongoing. <li>All of the results in the book are reproducible using publicly available R code and data-sets, as well as a dedicated R package. <li>This book has been written to be accessible not only to statisticians but also to students and researchers in the public health sciences. <P><P>The Authors <P><P>Peter Diggle is Distinguished University Professor of Statistics in the Faculty of Health and Medicine, Lancaster University. He also holds honorary positions at the Johns Hopkins University School of Public Health, Columbia University International Research Institute for Climate and Society, and Yale University School of Public Health. His research involves the development of statistical methods for analyzing spatial and longitudinal data and their applications in the biomedical and health sciences. <P><P>Dr Emanuele Giorgi is a Lecturer in Biostatistics and member of the CHICAS research group at Lancaster University, where he formerly obtained a PhD in Statistics and Epidemiology in 2015. His research interests involve the development of novel geostatistical methods for disease mapping, with a special focus on malaria and other tropical diseases. In 2018, Dr Giorgi was awarded the Royal Statistical Society Research Prize "for outstanding published contribution at the interface of statistics and epidemiology." He is also the lead developer of PrevMap, an R package where all the methodology found in this book has been implemented.
Model-free Hedging: A Martingale Optimal Transport Viewpoint (Chapman and Hall/CRC Financial Mathematics Series)
by Pierre Henry-LabordereModel-free Hedging: A Martingale Optimal Transport Viewpoint focuses on the computation of model-independent bounds for exotic options consistent with market prices of liquid instruments such as Vanilla options. The author gives an overview of Martingale Optimal Transport, highlighting the differences between the optimal transport and its martingale counterpart. This topic is then discussed in the context of mathematical finance.
Modeling Behavior and Population Dynamics: Seabirds, Seals, and Marine Iguanas (Interdisciplinary Applied Mathematics #57)
by Jim M. Cushing Shandelle M. Henson James L. HaywardThis monograph summarizes several decades of collaborations between ecologists and mathematicians, presenting novel applications in biological modeling. The authors are among the first researchers to pioneer the use of dynamical systems models to successfully describe and predict animal behavior in relation to environmental changes. The text highlights the biological and mathematical techniques used in the research, including three main components: 1) large data sets on natural populations in the field; 2) mathematical models rigorously tied to data, which describe, explain, and predict behavioral dynamics in relation to environmental variables; and 3) simplified, proof-of-concept models to probe dynamic mechanisms, suggest testable hypotheses, and allow study of the consequences of environmental change and evolving traits. It is a suitable text for field ecologists interested in the modeling procedures and conclusions addressed therein, as well as mathematicians interested in applications to population, ecological, and evolutionary dynamics.
Modeling Binary Correlated Responses using SAS, SPSS and R (ICSA Book Series in Statistics #9)
by Jeffrey R. Wilson Kent A. LorenzStatistical tools to analyze correlated binary data are spread out in the existing literature. This book makes these tools accessible to practitioners in a single volume. Chapters cover recently developed statistical tools and statistical packages that are tailored to analyzing correlated binary data. The authors showcase both traditional and new methods for application to health-related research. Data and computer programs will be publicly available in order for readers to replicate model development, but learning a new statistical language is not necessary with this book. The inclusion of code for R, SAS, and SPSS allows for easy implementation by readers. For readers interested in learning more about the languages, though, there are short tutorials in the appendix. Accompanying data sets are available for download through the book s website. Data analysis presented in each chapter will provide step-by-step instructions so these new methods can be readily applied to projects. Researchers and graduate students in Statistics, Epidemiology, and Public Health will find this book particularly useful.
Modeling Binary Correlated Responses: Using SAS, SPSS, R and STATA (ICSA Book Series in Statistics)
by Jeffrey R. Wilson Kent A. Lorenz Lori P. SelbyThis book is an updated edition of Modeling Binary Correlated Responses Using SAS, SPSS and R, and now it includes the use of STATA. It uses these Statistical tools to analyze correlated binary data, accessible to practitioners in a single volume. Chapters cover recently developed statistical tools and statistical packages, as well as showcase both traditional and new methods for application to health-related research. Data analysis presented in each chapter will provide step-by-step instructions so these new methods can be readily applied to projects. Short tutorials are in the appendix, for readers interested in learning more about the languages. Data and computer programs will be publicly available in order for readers to replicate model development, but learning a new statistical language is not necessary with this book. The inclusion of code for R, SAS, SPSS and STATA, allows for easy implementation by readers. Researchers and graduate students in Statistics, Epidemiology, and Public Health will find this book particularly useful.
Modeling Biomaterials (Nečas Center Series)
by Endre Süli Josef MálekThe 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.
Modeling Calcium Signaling: A Fractional Perspective (SpringerBriefs in Biochemistry and Molecular Biology)
by Sunil Dutt Purohit Ritu Agarwal KritikaThis book features chapters written by renowned scientists from various parts of the world, providing an up-to-date survey of submanifold theory, spanning diverse topics and applications. The book covers a wide range of topics such as Chen–Ricci inequalities in differential geometry, optimal inequalities for Casorati curvatures in quaternion geometry, conformal η-Ricci–Yamabe solitons, submersion on statistical metallic structure, solitons in f(R, T)-gravity, metric-affine geometry, generalized Wintgen inequalities, tangent bundles, and Lagrangian submanifolds. Moreover, the book showcases the latest findings on Pythagorean submanifolds and submanifolds of four-dimensional f-manifolds. The chapters in this book delve into numerous problems and conjectures on submanifolds, providing valuable insights for scientists, educators, and graduate students looking to stay updated with the latest developments in the field. With its comprehensive coverage and detailed explanations, this book is an essential resource for anyone interested in submanifold theory.
Modeling Change and Uncertainty: Machine Learning and Other Techniques (Textbooks in Mathematics)
by William P. Fox Robert E. BurksMathematical modeling is a powerful craft that requires practice. The more practice the better one will become in executing the art. The authors wrote this book to develop the craft of mathematical modeling and to foster a desire for lifelong learning, habits of mind and develop competent and confident problem solvers and decision makers for the 21st century. 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. Then principles are applied to the problem and present the steps in obtaining an appropriate model to solve the problem. Modeling Change and Uncertainty: Covers both linear and nonlinear models of discrete dynamical systems. Introduces statistics and probability modeling. Introduces critical statistical concepts to handle univariate and multivariate data. Establishes a foundation in probability modeling. Uses ordinary differential equations (ODEs) to develop a more robust solution to problems. Uses linear programming and machine learning to support decision making. Introduces the reality of uncertainty and randomness that is all around us. Discusses the use of linear programing to solve common problems in modern industry. Discusses he power and limitations of simulations. Introduces the methods and formulas used in businesses and financial organizations. Introduces valuable techniques using Excel, MAPLE, and R. Mathematical modeling offers a framework for decision makers in all fields. This framework consists of four key components: the formulation process, the solution process, interpretation of the solution in the context of the actual problem, and sensitivity analysis. Modeling Change and Uncertainty will be of interest to mathematics departments offering advanced mathematical modeling courses focused on decision making or discrete mathematical modeling and by undergraduate, graduate students and practitioners looking for an opportunity to develop, practice, and apply the craft of mathematical modeling. Table of Contents 1. Perfect Partners: Combining Models of Change and Uncertainty with Technology2. Modeling Change: Discrete Dynamical Systems (DDS) and Modeling Systems of DDS3. Statistical and Probabilistic Models4. Modeling with Probability5. Differential Equations6. Forecasting with Linear Programming and Machine Learning7. Stochastic Models and Markov Chains8. Linear Programming9. Simulation of Queueing Models10. Modeling of Financial Analysis11. Reliability Models12. Machine Learning and Unconstrained Optimal ProcessDr. William P. Fox is currently a visiting professor of Computational Operations Research at the College of William and Mary. He is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School and teaches a three-course sequence in mathematical modeling for decision making. He received his Ph.D. in Industrial Engineering from Clemson University. He has taught at the United States Military Academy for twelve years until retiring and at Francis Marion University where he was the chair of mathematics for eight years. He has many publications and scholarly activities including twenty plus books and one hundred and fifty journal articles. Colonel (R) Robert E. Burks, Jr., Ph.D. is an Associate Professor in the Defense Analysis Department of the Naval Postgraduate School (NPS) and the Director of the NPS’ Wargaming Center. He holds a Ph.D. in Operations Research from the Air Force Institute of Technology. He is a retired logistics Army Colonel with more than thirty years of military experience in leadership, advanc
Modeling Correlated Outcomes Using Extensions of Generalized Estimating Equations and Linear Mixed Modeling
by George J. KnaflThis book formulates methods for modeling continuous and categorical correlated outcomes that extend the commonly used methods: generalized estimating equations (GEE) and linear mixed modeling. Partially modified GEE adds estimating equations for variance/dispersion parameters to the standard GEE estimating equations for the mean parameters. Fully modified GEE provides alternate estimating equations for mean parameters as well as estimating equations for variance/dispersion parameters. The new estimating equations in these two cases are generated by maximizing a "likelihood" function related to the multivariate normal density function. Partially modified GEE and fully modified GEE use the standard GEE approach to estimate correlation parameters based on the residuals. Extended linear mixed modeling (ELMM) uses the likelihood function to estimate not only mean and variance/dispersion parameters, but also correlation parameters. Formulations are provided for gradient vectors and Hessian matrices, for a multi-step algorithm for solving estimating equations, and model-based and robust empirical tests for assessing theory-based models.Standard GEE, partially modified GEE, fully modified GEE, and ELMM are demonstrated and compared using a variety of regression analyses of different types of correlated outcomes. Example analyses of correlated outcomes include linear regression for continuous outcomes, Poisson regression for count/rate outcomes, logistic regression for dichotomous outcomes, exponential regression for positive-valued continuous outcome, multinomial regression for general polytomous outcomes, ordinal regression for ordinal polytomous outcomes, and discrete regression for discrete numeric outcomes. These analyses also address nonlinearity in predictors based on adaptive search through alternative fractional polynomial models controlled by likelihood cross-validation (LCV) scores. Larger LCV scores indicate better models but not necessarily distinctly better models. LCV ratio tests are used to identify distinctly better models.A SAS macro has been developed for analyzing correlated outcomes using standard GEE, partially modified GEE, fully modified GEE, and ELMM within alternative regression contexts. This macro and code for conducting the analyses addressed in the book are available online via the book’s Springer website. Detailed descriptions of how to use this macro and interpret its output are provided in the book.
Modeling Count Data
by Joseph M. HilbeThis entry-level text offers clear and concise guidelines on how to select, construct, interpret, and evaluate count data. Written for researchers with little or no background in advanced statistics, the book presents treatments of all major models using numerous tables, insets, and detailed modeling suggestions. It begins by demonstrating the fundamentals of linear regression and works up to an analysis of the Poisson and negative binomial models, and to the problem of overdispersion. Examples in Stata, R, and SAS code enable readers to adapt models for their own purposes, making the text an ideal resource for researchers working in public health, ecology, econometrics, transportation, and other related fields.
Modeling Decisions for Artificial Intelligence: 15th International Conference, MDAI 2018, Mallorca, Spain, October 15–18, 2018, Proceedings (Lecture Notes in Computer Science #11144)
by Vicenç Torra Yasuo Narukawa Isabel Aguiló Manuel González-HidalgoThis book constitutes the proceedings of the 15th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2018, held in Mallorca, Spain, in October 2018.The 24 papers presented in this volume were carefully reviewed and selected from 43 submissions. The book also contains one invited talk in full paper length. The papers were organized in topical sections named: aggregation operators, fuzzy measures and integrals; decision making; clustering and classification; and data privacy and security.
Modeling Decisions for Artificial Intelligence: 16th International Conference, MDAI 2019, Milan, Italy, September 4–6, 2019, Proceedings (Lecture Notes in Computer Science #11676)
by Vicenç Torra Yasuo Narukawa Gabriella Pasi Marco VivianiThis book constitutes the refereed proceedings of the 16th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2019, held in Milan, Italy, in September 2019. The 30 papers presented in this volume were carefully reviewed and selected from 50 submissions. They discuss different facets of decision processes in a broad sense and present research in data science, data privacy, aggregation functions, human decision making, graphs and social networks, and recommendation and search. The papers are organized in the following topical sections: aggregation operators and decision making; data science and data mining; and data privacy and security.
Modeling Decisions for Artificial Intelligence: 18th International Conference, MDAI 2021, Umeå, Sweden, September 27–30, 2021, Proceedings (Lecture Notes in Computer Science #12898)
by Vicenç Torra Yasuo NarukawaThis book constitutes the refereed proceedings of the 18th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2021, held in Umeå, Sweden, in September 2021.* The 24 papers presented in this volume were carefully reviewed and selected from 50 submissions. Additionally, 3 invited papers were included. The papers discuss different facets of decision processes in a broad sense and present research in data science, data privacy, aggregation functions, human decision making, graphs and social networks, and recommendation and search. The papers are organized in the following topical sections: aggregation operators and decision making; approximate reasoning; machine learning; data science and data privacy. *The conference was held virtually due to the COVID-19 pandemic.
Modeling Demographic Processes in Marked Populations
by David L. Thomson Michael J. Conroy Evan G. CoochThis book brings together biologists and statisticians in an interdisciplinary synthesis to develop new methods to overcome the most significant challenges and constraints faced by quantitative biologists seeking to model demographic rates. The book is centered on the ten key areas in the field where important problems in demographic analysis are being solved with new statistical methods. Each area presents one overview written by an acknowledged expert in this field, and four original research contributions. The 10 key areas are: - Abundance estimation; direct, proxies and point counts; Population dynamics; - Combining sources of information; - Dispersal movement and migration; - State uncertainty: assignment error and unobservable states; - Robust design: sampling, applications and advances; - Bayesian applications: advances, random effects and hierarchical models; - Evolutionary ecology; - Wildlife and conservation management; - Software developments for the modelling of demographic rates in marked populations.
Modeling Economic Instability: A History of Early Macroeconomics (Springer Studies in the History of Economic Thought)
by Michaël Assous Vincent CarretThis book offers a fresh perspective on the early history of macroeconomics, by examining the macro-dynamic models developed from the late 1920s to the late 1940s, and their treatment of economic instability. It first explores the differences and similarities between the early mathematical business cycle models developed by Ragnar Frisch, Michal Kalecki, Jan Tinbergen and others, which were presented at meetings of the Econometric Society and discussed in private correspondence. By doing so, it demonstrates the diversity of models representing economic phenomena and especially economic crises and instability. Jan Tinbergen emerged as one of the most original and pivotal economists of this period, before becoming a leader of the macro-econometric movement, a role for which he is better known. His emphasis on economic policy was later mirrored in the United States in Paul Samuelson’s early work on business cycles analysis, which, drawing on Alvin Hansen, aimed at interpreting the 1937-1938 recession. The authors then show that the subsequent shift in Samuelson's approach, from the study of business cycle trajectories to the comparison of equilibrium points, provided a response to the econometricians' critique of early Keynesian models. In the early 1940s, Samuelson was able to link together the tools that had been developed by the econometricians and the economic content that was at the heart of the so-called Keynesian revolution. The problem then shifted from business cycle trajectories to the disequilibrium between economic aggregates, and the issues raised by the global stability of full employment equilibrium. This was addressed by Oskar Lange, who presented an analysis of market coordination failures, and Lawrence Klein, Samuelson's first PhD student, who pursued empirical work in this direction. The book highlights the various visions and approaches that were embedded in these macro-dynamic models, and that their originality is of interest to today's model builders as well as to students and anyone interested in how new economic ideas come to be developed.
Modeling Failure and Fracture of Soft Solids and Fluids
by Konstantin VolokhThis book applies approaches of nonlinear continuum mechanics used to model fracture and failures in soft materials. Two physical observations underlie mathematical theories described in this book. First, the energy of molecular bonds is bounded and, consequently, the macroscopic strain energy must be bounded. Second, the broken bonds are diffused and, consequently, highly localized material sink takes place. The first observation allows describing material failure as the damage initiation. The second observation allows modeling cracks as damage localization and propagation. This book builds on the experiences of “Soft Matter Mechanics” by Konstantin Volokh.
Modeling Fixed Income Securities and Interest Rate Options (Chapman and Hall/CRC Financial Mathematics Series)
by Robert JarrowModeling Fixed Income Securities and Interest Rate Options, Third Edition presents the basics of fixed-income securities in a way that, unlike competitive texts, requires a minimum of prerequisites. While other books focus heavily on institutional details of the bond market, all of which could easily be learned "on the job," the third edition of this classic textbook is more focused with presenting a coherent theoretical framework for understanding all basic models. The author’s unified approach—the Heath Jarrow Morton model—under which all other models are presented as special cases, enhances understanding of the material. The author’s pricing model is widely used in today’s securities industry. This new edition offers many updates to align with advances in the research and requires a minimum of prerequisites while presenting the basics of fixed-income securities. Highlights of the Third Edition Chapters 1-16 completely updated to align with advances in research Thoroughly eliminates out-of-date material while advancing the presentation Includes an ample amount of exercises and examples throughout the text which illustrate key concepts .
Modeling Groundwater Flow and Contaminant Transport
by Jacob Bear Alexander H.-D. ChengIn many parts of the world, groundwater resources are under increasing threat from growing demands, wasteful use, and contamination. To face the challenge, good planning and management practices are needed. A key to the management of groundwater is the ability to model the movement of fluids and contaminants in the subsurface. The purpose of this book is to construct conceptual and mathematical models that can provide the information required for making decisions associated with the management of groundwater resources, and the remediation of contaminated aquifers. The basic approach of this book is to accurately describe the underlying physics of groundwater flow and solute transport in heterogeneous porous media, starting at the microscopic level, and to rigorously derive their mathematical representation at the macroscopic levels. The well-posed, macroscopic mathematical models are formulated for saturated, single phase flow, as well as for unsaturated and multiphase flow, and for the transport of single and multiple chemical species. Numerical models are presented and computer codes are reviewed, as tools for solving the models. The problem of seawater intrusion into coastal aquifers is examined and modeled. The issues of uncertainty in model input data and output are addressed. The book concludes with a chapter on the management of groundwater resources. Although one of the main objectives of this book is to construct mathematical models, the amount of mathematics required is kept minimal.
Modeling Hydrologic Change: Statistical Methods
by Richard H. McCuenModeling hydrologic changes and predicting their impact on watersheds is a dominant concern for hydrologists and other water resource professionals, civil and environmental engineers, and urban and regional planners. As such changes continue, it becomes more essential to have the most up-to-date tools with which to perform the proper analyses and m
Modeling Infectious Diseases in Humans and Animals
by Pejman Rohani Matt J. KeelingFor epidemiologists, evolutionary biologists, and health-care professionals, real-time and predictive modeling of infectious disease is of growing importance. This book provides a timely and comprehensive introduction to the modeling of infectious diseases in humans and animals, focusing on recent developments as well as more traditional approaches.Matt Keeling and Pejman Rohani move from modeling with simple differential equations to more recent, complex models, where spatial structure, seasonal "forcing," or stochasticity influence the dynamics, and where computer simulation needs to be used to generate theory. In each of the eight chapters, they deal with a specific modeling approach or set of techniques designed to capture a particular biological factor. They illustrate the methodology used with examples from recent research literature on human and infectious disease modeling, showing how such techniques can be used in practice. Diseases considered include BSE, foot-and-mouth, HIV, measles, rubella, smallpox, and West Nile virus, among others. Particular attention is given throughout the book to the development of practical models, useful both as predictive tools and as a means to understand fundamental epidemiological processes. To emphasize this approach, the last chapter is dedicated to modeling and understanding the control of diseases through vaccination, quarantine, or culling.Comprehensive, practical introduction to infectious disease modelingBuilds from simple to complex predictive modelsModels and methodology fully supported by examples drawn from research literaturePractical models aid students' understanding of fundamental epidemiological processesFor many of the models presented, the authors provide accompanying programs written in Java, C, Fortran, and MATLABIn-depth treatment of role of modeling in understanding disease control
Modeling Information Diffusion in Online Social Networks with Partial Differential Equations (Surveys and Tutorials in the Applied Mathematical Sciences #7)
by Feng Wang Haiyan Wang Kuai XuThe book lies at the interface of mathematics, social media analysis, and data science. Its authors aim to introduce a new dynamic modeling approach to the use of partial differential equations for describing information diffusion over online social networks. The eigenvalues and eigenvectors of the Laplacian matrix for the underlying social network are used to find communities (clusters) of online users. Once these clusters are embedded in a Euclidean space, the mathematical models, which are reaction-diffusion equations, are developed based on intuitive social distances between clusters within the Euclidean space. The models are validated with data from major social media such as Twitter. In addition, mathematical analysis of these models is applied, revealing insights into information flow on social media. Two applications with geocoded Twitter data are included in the book: one describing the social movement in Twitter during the Egyptian revolution in 2011 and another predicting influenza prevalence. The new approach advocates a paradigm shift for modeling information diffusion in online social networks and lays the theoretical groundwork for many spatio-temporal modeling problems in the big-data era.
Modeling MEMS and NEMS
by John A. Pelesko David H. BernsteinDesigning small structures necessitates an a priori understanding of various device behaviors. The way to gain such understanding is to construct, analyze, and interpret the proper mathematical model.Through such models, Modeling MEMS and NEMS illuminates microscale and nanoscale phenomena, thereby facilitating the design and optimization o