Deterministic And Stochastic Approaches In Computer Modeling And Simulation

In the field of computer modeling and simulation, academic scholars face a pressing challenge—how to navigate the complex landscape of both deterministic and stochastic approaches to modeling. This multifaceted arena demands a unified organizational framework, a comprehensive guide that can seamlessly bridge the gap between theory and practical application. Without such a resource, scholars may struggle to harness the full potential of computer modeling, leaving critical questions unanswered and innovative solutions undiscovered. Deterministic and Stochastic Approaches in Computer Modeling and Simulation serves as the definitive solution to the complex problem scholars encounter. By presenting a comprehensive and unified organizational approach, this book empowers academics to conquer the challenges of computer modeling with confidence. It not only provides a classification of modeling methods but also offers a formalized, step-by-step approach to conducting model investigations, starting from defining objectives to analyzing experimental results. For academic scholars seeking a holistic understanding of computer modeling, this book is the ultimate solution. It caters to the diverse needs of scholars by addressing both deterministic and stochastic approaches. Through its structured chapters, it guides readers from the very basics of computer systems investigation to advanced topics like stochastic analytical modeling and statistical modeling.

"The purpose of this book is to make a summary of the possibilities of modeling research, mainly in the computer field, by discussing the areas of problems in mathematical formalization and abstract description, discrete and probabilistic modeling approaches, computer simulation and the empirical approach of statistical modeling"--

Die Autoren führen auf anschauliche und systematische Weise in die mathematische und informatische Modellierung sowie in die Simulation als universelle Methodik ein. Es geht um Klassen von Modellen und um die Vielfalt an Beschreibungsarten. Aber es geht immer auch darum, wie aus Modellen konkrete Simulationsergebnisse gewonnen werden können. Nach einem kompakten Repetitorium zum benötigten mathematischen Apparat wird das Konzept anhand von Szenarien u. a. aus den Bereichen „Spielen – entscheiden – planen" und „Physik im Rechner" umgesetzt.

Stochastic kinetic methods are currently considered to be the most realistic and elegant means of representing and simulating the dynamics of biochemical and biological networks. Deterministic versus stochastic modelling in biochemistry and systems biology introduces and critically reviews the deterministic and stochastic foundations of biochemical kinetics, covering applied stochastic process theory for application in the field of modelling and simulation of biological processes at the molecular scale. Following an overview of deterministic chemical kinetics and the stochastic approach to biochemical kinetics, the book goes onto discuss the specifics of stochastic simulation algorithms, modelling in systems biology and the structure of biochemical models. Later chapters cover reaction-diffusion systems, and provide an analysis of the Kinfer and BlenX software systems. The final chapter looks at simulation of ecodynamics and food web dynamics. Introduces mathematical concepts and formalisms of deterministic and stochastic modelling through clear and simple examples Presents recently developed discrete stochastic formalisms for modelling biological systems and processes Describes and applies stochastic simulation algorithms to implement a stochastic formulation of biochemical and biological kinetics

This sequel to volume 19 of Handbook on Statistics on Stochastic Processes: Modelling and Simulation is concerned mainly with the theme of reviewing and, in some cases, unifying with new ideas the different lines of research and developments in stochastic processes of applied flavour. This volume consists of 23 chapters addressing various topics in stochastic processes. These include, among others, those on manufacturing systems, random graphs, reliability, epidemic modelling, self-similar processes, empirical processes, time series models, extreme value therapy, applications of Markov chains, modelling with Monte Carlo techniques, and stochastic processes in subjects such as engineering, telecommunications, biology, astronomy and chemistry. particular with modelling, simulation techniques and numerical methods concerned with stochastic processes. The scope of the project involving this volume as well as volume 19 is already clarified in the preface of volume 19. The present volume completes the aim of the project and should serve as an aid to students, teachers, researchers and practitioners interested in applied stochastic processes.

This book presents a brief description of what constitutes computer modeling and simulation with techniques given to get a feel for how some of the simulation software packages involving hundreds of thousands of lines of code were developed.

Appropriately for a book having the title "Computer Simulation Methods in Theoretical Physics", this book begins with a disclai mer. It does not and cannot give a complete introduction to simu lational physics. This exciting field is too new and is expanding too rapidly for even an attempt to be made. The intention here is to present a selection of fundamental techniques that are now being widely applied in many areas of physics, mathematics, chem istry and biology. It is worth noting that the methods are not only applicable in physics. They have been successfully used in other sciences, showing their great flexibility and power. This book has two main chapters (Chaps. 3 and 4) dealing with deterministic and stochastic computer simulation methods. Under the heading "deterministic" are collected methods involving classical dynamics, i.e. classical equations of motion, which have become known as the molecular dynamics simulation method. The se cond main chapter deals with methods that are partly or entirely of a stochastic nature. These include Brownian dynamics and the Monte Carlo method. To aid understanding of the material and to develop intuition, problems are included at the end of each chapter. Upon a first reading, the reader is advised to skip Chapter 2, which is a general introduction to computer simUlation methods.

Although stochastic kinetic models are increasingly accepted as the best way to represent and simulate genetic and biochemical networks, most researchers in the field have limited knowledge of stochastic process theory. The stochastic processes formalism provides a beautiful, elegant, and coherent foundation for chemical kinetics and there is a wealth of associated theory every bit as powerful and elegant as that for conventional continuous deterministic models. The time is right for an introductory text written from this perspective. Stochastic Modelling for Systems Biology presents an accessible introduction to stochastic modelling using examples that are familiar to systems biology researchers. Focusing on computer simulation, the author examines the use of stochastic processes for modelling biological systems. He provides a comprehensive understanding of stochastic kinetic modelling of biological networks in the systems biology context. The text covers the latest simulation techniques and research material, such as parameter inference, and includes many examples and figures as well as software code in R for various applications. While emphasizing the necessary probabilistic and stochastic methods, the author takes a practical approach, rooting his theoretical development in discussions of the intended application. Written with self-study in mind, the book includes technical chapters that deal with the difficult problems of inference for stochastic kinetic models from experimental data. Providing enough background information to make the subject accessible to the non-specialist, the book integrates a fairly diverse literature into a single convenient and notationally consistent source.