I Principles 1 1 Models of Systems 3 1. 1 Systems. Models. and Modeling . . . . . . . . . . . . . . . . . . . . 3 1. 2 Uses of Scientific Models . . . . . . . . . . . . . . . . . . . . . . . . 4 1. 3 Example: Island Biogeography . . . . . . . . . . . . . . . . . . . . . 6 1. 4 Classifications of Models . . . . . . . . . . . . . . . . . . . . . . . . 10 1. 5 Constraints on Model Structure . . . . . . . . . . . . . . . . . . . . . 12 1. 6 Some Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1. 7 Misuses of Models: The Dark Side . . . . . . . . . . . . . . . . . . . 13 1. 8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2 The Modeling Process 17 2. 1 Models Are Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2. 2 Two Alternative Approaches . . . . . . . . . . . . . . . . . . . . . . 18 2. 3 An Example: Population Doubling Time . . . . . . . . . . . . . . . . 24 2. 4 Model Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2. 5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3 Qualitative Model Formulation 32 3. 1 How to Eat an Elephant . . . . . . . . . . . . . . . . . . . . . . . . . 32 3. 2 Forrester Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3. 3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3. 4 Errors in Forrester Diagrams . . . . . . . . . . . . . . . . . . . . . . 44 3. 5 Advantages and Disadvantages of Forrester Diagrams . . . . . . . . . 44 3. 6 Principles of Qualitative Formulation . . . . . . . . . . . . . . . . . . 45 3. 7 Model Simplification . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3. 8 Other Modeling Problems . . . . . . . . . . . . . . . . . . . . . . . . 49 viii Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. 9 Exercises 53 4 Quantitative Model Formulation: I 4. 1 From Qualitative to Quantitative . . . . . . . . . . . . . . . . . Finite Difference Equations and Differential Equations 4. 2 . . . . . . . . . . . . . . . . 4. 3 Biological Feedback in Quantitative Models . . . . . . . . . . . . . . . . . . . . . . . . . . 4. 4 Example Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. 5 Exercises 5 Quantitative Model Formulation: I1 81 . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. 1 Physical Processes 81 . . . . . . . . . . . . . . . 5. 2 Using the Toolbox of Biological Processes 89 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. 3 Useful Functions 96 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. 4 Examples 102 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. 5 Exercises 104 6 Numerical Techniques 107 . . . . . . . . . . . . . . . . . . . . . . . 6. 1 Mistakes Computers Make 107 . . . . . . . . . . . . . . . . . . . . . . . . . . 6. 2 Numerical Integration 110 . . . . . . . . . . . . . . . . 6. 3 Numerical Instability and Stiff Equations 115 . . . . . . . . . . . . . .

This Festschrift volume, published in honor of Carolyn Talcott on the occasion of her 70th birthday, contains a collection of papers presented at a symposium held in Menlo Park, California, USA, in November 2011. Carolyn Talcott is a leading researcher and mentor of international renown among computer scientists. She has made key contributions to a number of areas of computer science including: semantics and verification of progamming languages; foundations of actor-based systems; middleware, meta-architectures, and systems; Maude and rewriting logic; and computational biology. The 21 papers presented are organized in topical sections named: Essays on Carolyn Talcott; actors and programming languages; cyberphysical systems; middleware and meta-architectures; formal methods and reasoning tools; and computational biology.

Investigating Biological Systems Using Modeling describes how to apply software to analyze and interpret data from biological systems. It is written for students and investigators in lay person's terms, and will be a useful reference book and textbook on mathematical modeling in the design and interpretation of kinetic studies of biological systems. It describes the mathematical techniques of modeling and kinetic theory, and focuses on practical examples of analyzing data. The book also uses examples from the fields of physiology, biochemistry, nutrition, agriculture, pharmacology, and medicine. Contains practical descriptions of how to analyze kinetic data Provides examples of how to develop and use models Describes several software packages including SAAM/CONSAM Includes software with working models

This book introduces concepts and practical tools for dynamical mathematical modeling of biological systems. Dynamical models describe the behavior of a system over time as a result of internal feedback loops and external forcing, based on mathematically formulated dynamical laws, similarly to how Newton's laws describe the movement of celestial bodies. Dynamical models are increasingly popular in biology, as they tend to be more powerful than static regression models. This book is meant for undergraduate and graduate students in physics, applied mathematics and data science with an interest in biology, as well as students in biology with a strong interest in mathematical methods. The book covers deterministic models (for example differential equations), stochastic models (for example Markov chains and autoregressive models) and model-independent aspects of time series analysis. Plenty of examples and exercises are included, often taken or inspired from the scientific literature, and covering a broad range of topics such as neuroscience, cell biology, genetics, evolution, ecology, microbiology, physiology, epidemiology and conservation. The book delivers generic modeling techniques used across a wide range of situations in biology, and hence readers from other scientific disciplines will find that much of the material is also applicable in their own field. Proofs of most mathematical statements are included for the interested reader, but are not essential for a practical understanding of the material. The book introduces the popular scientific programming language MATLAB as a tool for simulating models, fitting models to data, and visualizing data and model predictions. The material taught is current as of MATLAB version 2022b. The material is taught in a sufficiently general way that also permits the use of alternative programming languages.

Simulation and Verification of Electronic and Biological Systems provides a showcase for the Circuit and Multi-Domain Simulation Workshop held in San Jose, California, USA, on November 5, 2009. The nine chapters are contributed by experts in the field and provide a broad discussion of recent developments on simulation, modeling and verification of integrated circuits and biological systems. Specific topics include large scale parallel circuit simulation, industrial practice of fast SPICE simulation, structure-preserving model order reduction of interconnects, advanced simulation techniques for oscillator networks, dynamic stability of static memories and biological systems as well as verification of analog integrated circuits. Simulation and verification are fundamental enablers for understanding, analyzing and designing an extremely broad range of engineering and biological circuits and systems. The design of nanometer integrated electronic systems and emerging biomedical applications have stimulated the development of novel simulation and verification techniques and methodologies. Simulation and Verification of Electronic and Biological Systems provides a broad discussion of recent advances on simulation, modeling and verification of integrated circuits and biological systems and offers a basis for stimulating new innovations.

Systems Biology is the systematic study of the interactions between the components of a biological system and studies how these interactions give rise to the function and behavior of the living system. Through this, a life process is to be understood as a whole system rather than the collection of the parts considered separately. Systems Biology is therefore more than just an emerging field: it represents a new way of thinking about biology with a dramatic impact on the way that research is performed. The logical approach provides an intuitive method to provide explanations based on an expressive relational language. This book covers various aspects of logical modeling of biological systems, bringing together 10 recent logic-based approaches to Systems Biology by leading scientists. The chapters cover the biological fields of gene regulatory networks, signaling networks, metabolic pathways, molecular interaction and network dynamics, and show logical methods for these domains based on propositional and first-order logic, logic programming, answer set programming, temporal logic, Boolean networks, Petri nets, process hitting, and abductive and inductive logic programming. It provides an excellent guide for all scientists, biologists, bioinformaticians, and engineers, who are interested in logic-based modeling of biological systems, and the authors hope that new scientists will be encouraged to join this exciting scientific endeavor.

This text looks at different effects on the process of biological phosphorus removal. Topics include: biological phosphorus removal processes; process and molecular ecological studies; and the effect of potassium limitation on biological phosphorus removal.

This book contributes to better understand how lifestyle modulations can effectively halt the emergence and progression of human diseases. The book will allow the reader to gain a better understanding of the mechanisms by which the environment interferes with the bio-molecular regulatory processes underlying the emergence and progression of complex diseases, such as cancer. Focusing on key and early cellular bio-molecular events giving rise to the emergence of degenerative chronic disease, it builds on previous experience on the development of multi-cellular organisms, to propose a mathematical and computer based framework that allows the reader to analyze the complex interplay between bio-molecular processes and the (micro)-environment from an integrative, mechanistic, quantitative and dynamical perspective. Taking the wealth of empirical evidence that exists it will show how to build and analyze models of core regulatory networks involved in the emergence and progression of chronic degenerative diseases, using a bottom-up approach.

Dynamic Systems Biology Modeling and Simuation consolidates and unifies classical and contemporary multiscale methodologies for mathematical modeling and computer simulation of dynamic biological systems – from molecular/cellular, organ-system, on up to population levels. The book pedagogy is developed as a well-annotated, systematic tutorial – with clearly spelled-out and unified nomenclature – derived from the author's own modeling efforts, publications and teaching over half a century. Ambiguities in some concepts and tools are clarified and others are rendered more accessible and practical. The latter include novel qualitative theory and methodologies for recognizing dynamical signatures in data using structural (multicompartmental and network) models and graph theory; and analyzing structural and measurement (data) models for quantification feasibility. The level is basic-to-intermediate, with much emphasis on biomodeling from real biodata, for use in real applications. - Introductory coverage of core mathematical concepts such as linear and nonlinear differential and difference equations, Laplace transforms, linear algebra, probability, statistics and stochastics topics - The pertinent biology, biochemistry, biophysics or pharmacology for modeling are provided, to support understanding the amalgam of "math modeling with life sciences - Strong emphasis on quantifying as well as building and analyzing biomodels: includes methodology and computational tools for parameter identifiability and sensitivity analysis; parameter estimation from real data; model distinguishability and simplification; and practical bioexperiment design and optimization - Companion website provides solutions and program code for examples and exercises using Matlab, Simulink, VisSim, SimBiology, SAAMII, AMIGO, Copasi and SBML-coded models - A full set of PowerPoint slides are available from the author for teaching from his textbook. He uses them to teach a 10 week quarter upper division course at UCLA, which meets twice a week, so there are 20 lectures. They can easily be augmented or stretched for a 15 week semester course - Importantly, the slides are editable, so they can be readily adapted to a lecturer's personal style and course content needs. The lectures are based on excerpts from 12 of the first 13 chapters of DSBMS. They are designed to highlight the key course material, as a study guide and structure for students following the full text content - The complete PowerPoint slide package (~25 MB) can be obtained by instructors (or prospective instructors) by emailing the author directly, at: joed@cs.ucla.edu