Matrix-analytic Methods in Stochastic Models

The standard classifications of health systems don't allow for the complexity and variety that exists around the world. Federico Toth sets out a new framework for understanding the many ways in which health systems can be organized and systematically analyses the health systems chosen by 27 OECD countries. He provides a great deal of up-to-date data on financing models, healthcare spending, insurance coverage, methods of organizing providers, healthcare personnel, remuneration methods for doctors and hospitals, development trajectories and recent reforms. For each of the major components of the healthcare system, the organizational models and the possible variants from which individual countries can ideally select are defined. Then, based on the organizational solutions actually adopted, the various national systems are grouped into homogeneous families. With its clear, jargon-free language and concrete examples, this is the most accessible comparative study of international healthcare

The standard classifications of health systems don't allow for the complexity and variety that exists around the world. Federico Toth sets out a new framework for understanding the many ways in which health systems can be organized and systematically analyses the health systems chosen by 27 OECD countries. He provides a great deal of up-to-date data on financing models, healthcare spending, insurance coverage, methods of organizing providers, healthcare personnel, remuneration methods for doctors and hospitals, development trajectories and recent reforms. For each of the major components of the healthcare system, the organizational models and the possible variants from which individual countries can ideally select are defined. Then, based on the organizational solutions actually adopted, the various national systems are grouped into homogeneous families. With its clear, jargon-free language and concrete examples, this is the most accessible comparative study of international healthcare

Using Bishop's work on constructive analysis as a framework, this monograph gives a systematic, detailed and general constructive theory of probability theory and stochastic processes. It is the first extended account of this theory: almost all of the constructive existence and continuity theorems that permeate the book are original. It also contains results and methods hitherto unknown in the constructive and nonconstructive settings. The text features logic only in the common sense and, beyond a certain mathematical maturity, requires no prior training in either constructive mathematics or probability theory. It will thus be accessible and of interest, both to probabilists interested in the foundations of their speciality and to constructive mathematicians who wish to see Bishop's theory applied to a particular field.

Macroevolutionary inference has historically been treated as a two-step process, involving the inference of a tree, and then inference of a macroevolutionary model using that tree. Newer models blend the two steps. These methods make more complete use of fossils than the previous generation of Bayesian phylogenetic models. They also involve many more parameters than prior models, including parameters about which empiricists may have little intuition. In this Element, we set forth a framework for fitting complex, hierarchical models. The authors ultimately fit and use a joint tree and diversification model to estimate a dated phylogeny of the Cincta (Echinodermata), a morphologically distinct group of Cambrian echinoderms that lack the fivefold radial symmetry characteristic of extant members of the phylum. Although the phylogeny of cinctans remains poorly supported in places, this Element shows how models of character change and diversification contribute to understanding patterns of p

A unique text integrating numerics, mathematics and applications to provide a hands-on approach to using optimization techniques, this mathematically accessible textbook emphasises conceptual understanding and importance of theorems rather than elaborate proofs. It allows students to develop fundamental optimization methods before delving into MATLAB®'s optimization toolbox, and to link MATLAB's results with the results from their own code. Following a practical approach, the text demonstrates several applications, from error-free analytic examples to truss (size) optimization, and 2D and 3D shape optimization, where numerical errors are inevitable. The principle of minimum potential energy is discussed to highlight the deep relationship between engineering and optimization. MATLAB code in every chapter illustrates key concepts and the text demonstrates the coupling between MATLAB and SOLIDWORKS® for design optimization. A wide variety of optimization problems are covered including con

Based on the author's forty years of teaching experience, this unique textbook covers both basic and advanced concepts of optimization theory and methods for process systems engineers. Topics covered include continuous, discrete and logic optimization (linear, nonlinear, mixed-integer and generalized disjunctive programming), optimization under uncertainty (stochastic programming and flexibility analysis), and decomposition techniques (Lagrangean and Benders decomposition). Assuming only a basic background in calculus and linear algebra, it enables easy understanding of mathematical reasoning, and numerous examples throughout illustrate key concepts and algorithms. End-of-chapter exercises involving theoretical derivations and small numerical problems, as well as in modeling systems like GAMS, enhance understanding and help put knowledge into practice. Accompanied by two appendices containing web links to modeling systems and models related to applications in PSE, this is an essential

This two-volume work traces the development of series and products from 1380 to 2000 through the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible even to advanced undergraduate students, discusses the development of the fundamental methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 deals with more recent and advanced results, such as Nevanlinna theory and deBranges' work.

Recent advances in statistical approaches called phylogenetic comparative methods (PCMs) have provided paleontologists with a powerful set of analytical tools for investigating evolutionary tempo and mode in fossil lineages. However, attempts to integrate PCMs with fossil data often present workers with practical challenges or unfamiliar literature. This Element presents guides to the theory behind and the application of PCMs with fossil taxa. Based on an empirical dataset of Paleozoic crinoids, example analyses are presented to illustrate common applications of PCMs to fossil data, including investigating patterns of correlated trait evolution and macroevolutionary models of morphological change. The authors emphasize the importance of accounting for sources of uncertainty and discuss how to evaluate model fit and adequacy. Finally, the authors discuss several promising methods for modeling heterogeneous evolutionary dynamics with fossil phylogenies. Integrating phylogeny-based approa

This is the second volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible even to advanced undergraduate students, discusses the development of the methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 examines more recent results, including deBranges' resolution of Bieberbach's conjecture and Nevanlinna's theory of meromorphic functions.

This is the first volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible to even advanced undergraduate students, discusses the development of the methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 treats more recent work, including deBranges' solution of Bieberbach's conjecture, and requires more advanced mathematical knowledge.

The middle of the second until the middle of the first century BCE is one of the most creative periods in the history of human thought, and an important part of this was the interaction between Roman jurists and Hellenistic philosophers. In this highly original book, René Brouwer shows how jurists transformed the study of law into a science with the help of philosophical methods and concepts, such as division, rules and persons, and also how philosophers came to share the jurists' preoccupations with cases and private property. The relevance of this cross-fertilization for present-day law and philosophy cannot be overestimated: in law, its legacy includes the academic study of law and the Western models of dispute resolution, while in philosophy, the method of casuistry and the concept of just property.

Malicious hackers utilize the World Wide Web to share knowledge. Analyzing the online communication of these threat actors can help reduce the risk of attacks. This book shifts attention from the defender environment to the attacker environment, offering a new security paradigm of 'proactive cyber threat intelligence' that allows defenders of computer networks to gain a better understanding of their adversaries by analyzing assets, capabilities, and interest of malicious hackers. The authors propose models, techniques, and frameworks based on threat intelligence mined from the heart of the underground cyber world: the malicious hacker communities. They provide insights into the hackers themselves and the groups they form dynamically in the act of exchanging ideas and techniques, buying or selling malware, and exploits. The book covers both methodology - a hybridization of machine learning, artificial intelligence, and social network analysis methods - and the resulting conclusions, det

By exploring qualitative research through a unique analytic lens, then cumulatively elaborating on methods in each successive chapter, this innovative work cultivates a skill set and literacy base tha

By the award-winning former president of the Linguistic Society of America, this collection of some of John Russell Rickford's pioneering works shows how linguists in sociolinguistics and creole studies can benefit from utilizing data, theories and methods from each other, as they more frequently did in the 1960s and 1970s, when both subfields, in their modern forms at least, were getting started. The volume addresses fundamental sociolinguistic topics such as social class, style, fieldwork, speech community, sociolinguistic competence and language attitudes with data from Guyanese and other Caribbean creoles. Recurrent concepts are also considered including language versatility, variation and change, vernacular use, school success and criminal justice in African America and the Caribbean, using models, case studies and methodologies from sociolinguistics. Theoretical and applied scholars, students apprehensive about sociolinguistic fieldwork, and those considering dynamic methods like

Business Research Methods, 14e, contains stand-alone chapters that reflect research industry practices using real examples from all areas of business. In collaborations with over two dozen industry researchers, Schindler writes a real-world research methods book that distinguishes between big data analytics and small data with an emphasis on decision making. She eloquently covers ethical issues and their solutions, and has added more coverage of process models, sampling how-to, and data preparation.Conscious of the different learning styles of students, Schindler provides appropriate cues for both visual and verbal learners through the use of in-text exhibits, bolded key terms, conceptual photos throughout and research though-leader quotes in PowerPoints for each chapter. She also used various interim GreenBook Research Industry Trends (GRIT) reports to guide the research for this revision. The latest GRIT Report is based on the largest study of research suppliers and users ever conduc

Echinoderms elaborate a calcite skeleton composed of numerous plates with a distinct microstructure (stereom) that can be modelled into different shapes thanks to the use of a transient amorphous calcium carbonate (ACC) precursor phase and the incorporation of an intraorganic matrix during biomineralization. A variety of different types of stereom microarchitecture have been distinguished, each of them optimized for a specific function. For instance, a regular, galleried stereom typically houses collagenous ligaments, whereas an irregular, fine labyrinthic stereom commonly bears muscles. Epithelial tissues, in turn, are usually associated with coarse and dense stereom microfabrics. Stereom can be preserved in fossil echinoderms and a wide array of investigating methods are available. As many case studies have shown, a great deal of important paleobiological and paleoecological information can be decoded by studying the stereom microstructure of extinct echinoderms.

This research textbook, designed for young Human-Computer Interaction (HCI) researchers beginning their careers, surveys the research models and methods in use today and offers a general framework to bring together the disparate concepts. HCI spans many disciplines and professions, including information science, applied psychology, computer science, informatics, software engineering and social science making it difficult for newcomers to get a good overview of the field and the available approaches. The book's rigorous 'approach-and-framework' response is to the challenge of retaining growth and diversification in HCI research by building up a general framework from approaches for Innovation, Art, Craft, Applied, Science and Engineering. This general framework is compared with other HCI frameworks and theories for completeness and coherence, all within a historical perspective of dissemination success. Readers can use this as a model to design and assess their own research frameworks a

China-Africa economic tie has experienced lasting rapid growth since the 2000s, attracting lots of discussion on its nature and effects. A key question is whether Chinese engagements provide an alternative paradigm to existing mainstream models, like Washington Consensus, for developing countries. However, theories on state-market dichotomy can hardly explain the strong momentum of bilateral cooperation. By examining a broad range of practices with solid field research, including trade, infrastructure, agriculture, manufacturing, industrial zones, labor and socio-environmental preservation, this book proposes a new angle of non-linear circular causality to understand Chinese approaches to work with Africa. Guided by the pursuit for sustainable growth rather than by specific models, Chinese actors are able to experiment diverse methods to foster structural transformation in Africa. In particular, the author carefully records mutual influences between Chinese and African stakeholders at

The real world is perceived and broken down as data, models and algorithms in the eyes of physicists and engineers. Data is noisy by nature and classical statistical tools have so far been successful in dealing with relatively smaller levels of randomness. The recent emergence of Big Data and the required computing power to analyse them have rendered classical tools outdated and insufficient. Tools such as random matrix theory and the study of large sample covariance matrices can efficiently process these big data sets and help make sense of modern, deep learning algorithms. Presenting an introductory calculus course for random matrices, the book focusses on modern concepts in matrix theory, generalising the standard concept of probabilistic independence to non-commuting random variables. Concretely worked out examples and applications to financial engineering and portfolio construction make this unique book an essential tool for physicists, engineers, data analysts, and economists.

Cure Models: Methods, Applications and Implementation is the first book in the last 25 years that provides a comprehensive and systematic introduction to the basics of modern cure models, including es

This unique textbook provides an introduction to statistical inference with network data. The authors present a self-contained derivation and mathematical formulation of methods, review examples, and real-world applications, as well as provide data and code in the R environment that can be customised. Inferential network analysis transcends fields, and examples from across the social sciences are discussed (from management to electoral politics), which can be adapted and applied to a panorama of research. From scholars to undergraduates, spanning the social, mathematical, computational and physical sciences, readers will be introduced to inferential network models and their extensions. The exponential random graph model and latent space network model are paid particular attention and, fundamentally, the reader is given the tools to independently conduct their own analyses.

This unique textbook provides an introduction to statistical inference with network data. The authors present a self-contained derivation and mathematical formulation of methods, review examples, and real-world applications, as well as provide data and code in the R environment that can be customised. Inferential network analysis transcends fields, and examples from across the social sciences are discussed (from management to electoral politics), which can be adapted and applied to a panorama of research. From scholars to undergraduates, spanning the social, mathematical, computational and physical sciences, readers will be introduced to inferential network models and their extensions. The exponential random graph model and latent space network model are paid particular attention and, fundamentally, the reader is given the tools to independently conduct their own analyses.

The early modern period is a key historical era for the standardisation of languages in Europe, in which orthographies played an important role. This book traces the development of European spelling systems in the early modern era, and is unique in bringing together several strands of historical research, across a diverse range of Germanic, Romance and Slavic languages, including Polish, German, French, Spanish, Lithuanian, Czech, Croatian and English. Whilst each chapter includes a case study on a particular language or script, the volume in general follows a broad thread of discussion based on models and methods relevant to many languages, showing how empirical approaches can be applied across languages to enrich the field of historical orthography as a whole. The first volume to diachronically explore the standardization of spelling systems from a cross-linguistic perspective, this is an invaluable resource for specialists and those interested in historical European studies more bro

In the age of data-driven problem-solving, applying sophisticated computational tools for explaining substantive phenomena is a valuable skill. Yet, application of methods assumes an understanding of the data, structure, and patterns that influence the broader research program. This Element offers researchers and teachers an introduction to clustering, which is a prominent class of unsupervised machine learning for exploring and understanding latent, non-random structure in data. A suite of widely used clustering techniques is covered in this Element, in addition to R code and real data to facilitate interaction with the concepts. Upon setting the stage for clustering, the following algorithms are detailed: agglomerative hierarchical clustering, k-means clustering, Gaussian mixture models, and at a higher-level, fuzzy C-means clustering, DBSCAN, and partitioning around medoids (k-medoids) clustering.

This state-of-the-art account unifies material developed in journal articles over the last 35 years, with two central thrusts: It describes a broad class of system models that the authors call 'stochastic processing networks' (SPNs), which include queueing networks and bandwidth sharing networks as prominent special cases; and in that context it explains and illustrates a method for stability analysis based on fluid models. The central mathematical result is a theorem that can be paraphrased as follows: If the fluid model derived from an SPN is stable, then the SPN itself is stable. Two topics discussed in detail are (a) the derivation of fluid models by means of fluid limit analysis, and (b) stability analysis for fluid models using Lyapunov functions. With regard to applications, there are chapters devoted to max-weight and back-pressure control, proportionally fair resource allocation, data center operations, and flow management in packet networks. Geared toward researchers and grad

Most textbooks on regression focus on theory and the simplest of examples. Real statistical problems, however, are complex and subtle. This is not a book about the theory of regression. It is about using regression to solve real problems of comparison, estimation, prediction, and causal inference. Unlike other books, it focuses on practical issues such as sample size and missing data and a wide range of goals and techniques. It jumps right in to methods and computer code you can use immediately. Real examples, real stories from the authors' experience demonstrate what regression can do and its limitations, with practical advice for understanding assumptions and implementing methods for experiments and observational studies. They make a smooth transition to logistic regression and GLM. The emphasis is on computation in R and Stan rather than derivations, with code available online. Graphics and presentation aid understanding of the models and model fitting.

Most textbooks on regression focus on theory and the simplest of examples. Real statistical problems, however, are complex and subtle. This is not a book about the theory of regression. It is about using regression to solve real problems of comparison, estimation, prediction, and causal inference. Unlike other books, it focuses on practical issues such as sample size and missing data and a wide range of goals and techniques. It jumps right in to methods and computer code you can use immediately. Real examples, real stories from the authors' experience demonstrate what regression can do and its limitations, with practical advice for understanding assumptions and implementing methods for experiments and observational studies. They make a smooth transition to logistic regression and GLM. The emphasis is on computation in R and Stan rather than derivations, with code available online. Graphics and presentation aid understanding of the models and model fitting.

Data-driven computational neuroscience facilitates the transformation of data into insights into the structure and functions of the brain. This introduction for researchers and graduate students is the first in-depth, comprehensive treatment of statistical and machine learning methods for neuroscience. The methods are demonstrated through case studies of real problems to empower readers to build their own solutions. The book covers a wide variety of methods, including supervised classification with non-probabilistic models (nearest-neighbors, classification trees, rule induction, artificial neural networks and support vector machines) and probabilistic models (discriminant analysis, logistic regression and Bayesian network classifiers), meta-classifiers, multi-dimensional classifiers and feature subset selection methods. Other parts of the book are devoted to association discovery with probabilistic graphical models (Bayesian networks and Markov networks) and spatial statistics with po

Biostatistics with R provides a straightforward introduction on how to analyse data from the wide field of biological research, including nature protection and global change monitoring. The book is centred around traditional statistical approaches, focusing on those prevailing in research publications. The authors cover t-tests, ANOVA and regression models, but also the advanced methods of generalised linear models and classification and regression trees. Chapters usually start with several useful case examples, describing the structure of typical datasets and proposing research-related questions. All chapters are supplemented by example datasets, step-by-step R code demonstrating analytical procedures and interpretation of results. The authors also provide examples of how to appropriately describe statistical procedures and results of analyses in research papers. This accessible textbook will serve a broad audience, from students, researchers or professionals looking to improve their

Biostatistics with R provides a straightforward introduction on how to analyse data from the wide field of biological research, including nature protection and global change monitoring. The book is centred around traditional statistical approaches, focusing on those prevailing in research publications. The authors cover t-tests, ANOVA and regression models, but also the advanced methods of generalised linear models and classification and regression trees. Chapters usually start with several useful case examples, describing the structure of typical datasets and proposing research-related questions. All chapters are supplemented by example datasets, step-by-step R code demonstrating analytical procedures and interpretation of results. The authors also provide examples of how to appropriately describe statistical procedures and results of analyses in research papers. This accessible textbook will serve a broad audience, from students, researchers or professionals looking to improve their

Decision-making in the face of uncertainty is a significant challenge in machine learning, and the multi-armed bandit model is a commonly used framework to address it. This comprehensive and rigorous introduction to the multi-armed bandit problem examines all the major settings, including stochastic, adversarial, and Bayesian frameworks. A focus on both mathematical intuition and carefully worked proofs makes this an excellent reference for established researchers and a helpful resource for graduate students in computer science, engineering, statistics, applied mathematics and economics. Linear bandits receive special attention as one of the most useful models in applications, while other chapters are dedicated to combinatorial bandits, ranking, non-stationary problems, Thompson sampling and pure exploration. The book ends with a peek into the world beyond bandits with an introduction to partial monitoring and learning in Markov decision processes.

Mathematical models of bond markets are of interest to researchers working in applied mathematics, especially in mathematical finance. This book concerns bond market models in which random elements are represented by Lévy processes. These are more flexible than classical models and are well suited to describing prices quoted in a discontinuous fashion. The book's key aims are to characterize bond markets that are free of arbitrage and to analyze their completeness. Nonlinear stochastic partial differential equations (SPDEs) are an important tool in the analysis. The authors begin with a relatively elementary analysis in discrete time, suitable for readers who are not familiar with finance or continuous time stochastic analysis. The book should be of interest to mathematicians, in particular to probabilists, who wish to learn the theory of the bond market and to be exposed to attractive open mathematical problems.

A new and important contribution to the re-emergent field of comparative anthropology, this book argues that comparative ethnographic methods are essential for more contextually sophisticated accounts of a number of pressing human concerns today. The book includes expert accounts from an international team of scholars, showing how these methods can be used to illuminate important theoretical and practical projects. Illustrated with examples of successful inter-disciplinary projects, it highlights the challenges, benefits, and innovative strategies involved in working collaboratively across disciplines. Through its focus on practical methodological and logistical accounts, it will be of value to both seasoned researchers who seek practical models for conducting their own cutting-edge comparative research, and to teachers and students who are looking for first-person accounts of comparative ethnographic research.

A new and important contribution to the re-emergent field of comparative anthropology, this book argues that comparative ethnographic methods are essential for more contextually sophisticated accounts of a number of pressing human concerns today. The book includes expert accounts from an international team of scholars, showing how these methods can be used to illuminate important theoretical and practical projects. Illustrated with examples of successful inter-disciplinary projects, it highlights the challenges, benefits, and innovative strategies involved in working collaboratively across disciplines. Through its focus on practical methodological and logistical accounts, it will be of value to both seasoned researchers who seek practical models for conducting their own cutting-edge comparative research, and to teachers and students who are looking for first-person accounts of comparative ethnographic research.

This must-have manual provides detailed solutions to all of the 300 exercises in Dickson, Hardy and Waters' Actuarial Mathematics for Life Contingent Risks, 3 edition. This groundbreaking text on the modern mathematics of life insurance is required reading for the Society of Actuaries' (SOA) LTAM Exam. The new edition treats a wide range of newer insurance contracts such as critical illness and long-term care insurance; pension valuation material has been expanded; and two new chapters have been added on developing models from mortality data and on changing mortality. Beyond professional examinations, the textbook and solutions manual offer readers the opportunity to develop insight and understanding through guided hands-on work, and also offer practical advice for solving problems using straightforward, intuitive numerical methods. Companion Excel spreadsheets illustrating these techniques are available for free download.

English historical linguistics is a subfield of linguistics which has developed theories and methods for exploring the history of the English language. This Handbook provides an account of state-of-the-art research on this history. It offers an in-depth survey of materials, methods, and language-theoretical models used to study the long diachrony of English. The frameworks covered include corpus linguistics, historical sociolinguistics, historical pragmatics and manuscript studies, among others. The chapters, by leading experts, examine the interplay of language theory and empirical data throughout, critically assessing the work in the field. Of particular importance are the diverse data sources which have become increasingly available in electronic form, allowing the discipline to develop in new directions. The Handbook offers access to the rich and many-faceted spectrum of work in English historical linguistics, past and present, and will be useful for researchers and students intere

Our world is becoming more urban. More than fifty percent of the global population now lives in cities, which poses new challenges for sustainable development. This book integrates theory and methods of sustainability assessment with concepts from systems science to provide guidelines for assessing the sustainability of urban systems. It discusses different aspects of urban sustainability, from energy and housing, to mobility and health, covering social, economic and environmental factors, as well as the various stakeholders and actors involved. The book argues for the need to find models and solutions in order to design sustainable cities of the future in light of the complexity of urban social life. Including diverse case studies from the developed and developing world, this book provides a useful reference for researchers and students from a broad range of disciplines working in the field of sustainability, as well as for environmental consultants and policy makers.

Mathematical analysis is key to the modeling and management of natural resources. By presenting required mathematical methods, classic dynamic models for non-renewable and renewable resources, and by exploring several contemporary problems, this text provides a foundation for advanced research. Topics include seminal models in fishery, forestry and non-renewable resource management, as well as an extensive collection of contemporary applications that include the optimal transition from fossil fuels to clean energy, the optimal timing of interventions to save endangered species, pest control and the optimal management of antibiotic resistance. Deterministic and stochastic models in both discrete and continuous time are covered. The book encourages students to pursue a deeper understanding of the analytics of resource problems and to deploy numerical methods when analytical results prove intractable. The combination of analysis, theory and applications will launch the next generation of

Mathematical analysis is key to the modeling and management of natural resources. By presenting required mathematical methods, classic dynamic models for non-renewable and renewable resources, and by exploring several contemporary problems, this text provides a foundation for advanced research. Topics include seminal models in fishery, forestry and non-renewable resource management, as well as an extensive collection of contemporary applications that include the optimal transition from fossil fuels to clean energy, the optimal timing of interventions to save endangered species, pest control and the optimal management of antibiotic resistance. Deterministic and stochastic models in both discrete and continuous time are covered. The book encourages students to pursue a deeper understanding of the analytics of resource problems and to deploy numerical methods when analytical results prove intractable. The combination of analysis, theory and applications will launch the next generation of

Bringing together contributions on a diverse range of topics, this text explores the relationship between discrete and continuum mechanics as a tool to model new and complex metamaterials. Providing a comprehensive bibliography and historical review of the field, it covers mechanical, acoustic and pantographic metamaterials, discusses Naive Model Theory and Lagrangian discrete models, and their applications, and presents methods for pantographic structures and variational methods for multidisciplinary modeling and computation. The relationship between discrete and continuous models is discussed from both mathematical and engineering viewpoints, making the text ideal for those interested in the foundation of mechanics and computational applications, and innovative viewpoints on the use of discrete systems to model metamaterials are presented for those who want to go deeper into the field. An ideal text for graduate students and researchers interested in continuum approaches to the study