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Structured population models are transport-type equations often applied to describe evolution of heterogeneous populations of biological cells, animals or humans, including phenomena such as crowd dynamics or pedestrian flows. This book introduces the mathematical underpinnings of these applications, providing a comprehensive analytical framework for structured population models in spaces of Radon measures. The unified approach allows for the study of transport processes on structures that are not vector spaces (such as traffic flow on graphs) and enables the analysis of the numerical algorithms used in applications. Presenting a coherent account of over a decade of research in the area, the text includes appendices outlining the necessary background material and discusses current trends in the theory, enabling graduate students to jump quickly into research.

Population --- Functions of bounded variation. --- Lipschitz spaces. --- Metric spaces. --- Radon measures. --- Biology --- Mathematical models. --- Biological models --- Biomathematics --- Measures, Radon --- Measure theory --- Vector-valued measures --- Spaces, Metric --- Generalized spaces --- Set theory --- Topology --- Hölder spaces --- Function spaces --- Bounded variables, Functions of --- Bounded variation, Functions of --- BV functions --- Functions of bounded variables --- Functions of real variables

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"This book introduces researchers and students to the concepts and generalized linear models for analyzing quantitative random variables that have one or more bounds. Examples of bounded variables include the percentage of a population eligible to vote (bounded from 0 to 100), or reaction time in milliseconds (bounded below by 0). The human sciences deal in many variables that are bounded. Ignoring bounds can result in misestimation and improper statistical inference. Michael Smithson and Yiyun Shou's book brings together material on the analysis of limited and bounded variables that is scattered across the literature in several disciplines, and presents it in a style that is both more accessible and up-to-date. The authors provide worked examples in each chapter using real datasets from a variety of disciplines. The software used for the examples include R, SAS, and Stata. The data, software code, and detailed explanations of the example models are available on an accompanying website at www.sagepub.com/smithsonshou"--

Linear models (Statistics) --- Random variables --- Functions of bounded variation --- Quantitative research --- Data analysis (Quantitative research) --- Exploratory data analysis (Quantitative research) --- Quantitative analysis (Research) --- Quantitative methods (Research) --- Research --- Bounded variables, Functions of --- Bounded variation, Functions of --- BV functions --- Functions of bounded variables --- Functions of real variables --- Chance variables --- Stochastic variables --- Probabilities --- Variables (Mathematics) --- Models, Linear (Statistics) --- Mathematical models --- Mathematical statistics --- Statistics --- #SBIB:303H10 --- #SBIB:303H520 --- Methoden en technieken: algemene handboeken en reeksen --- Methoden sociale wetenschappen: techniek van de analyse, algemeen --- Functions of bounded variation. --- Linear models (Statistics). --- Quantitative research. --- Random variables. --- Multivariate analysis.

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Functions of bounded variation. --- Functions of several real variables. --- Fonctions à variation bornée --- Fonctions d'une variable réelle --- Fonctions de plusieurs variables réelles --- Lebesgue, Intégrale de --- Espaces de lebesgue --- Espaces de lebesgue

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Functions of several real variables. --- Functions of bounded variation. --- Fonctions de plusieurs variables réelles --- Fonctions à variation bornée --- Fonctions d'une variable réelle --- Lebesgue, Intégrale de --- Espaces de lebesgue --- Espaces de lebesgue

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Fonctions à variation bornée --- Functions of bounded variation. --- Applications conformes --- Représentation des surfaces. --- Conformal mapping --- Surfaces, Representation of --- Fonctions d'une variable complexe --- Fonctions entieres --- Fonctions d'une variable complexe --- Fonctions entieres