Identifiability And Regression Analysis Of Biological Systems Models
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Identifiability and Regression Analysis of Biological Systems Models
This richly illustrated book presents the objectives of, and the latest techniques for, the identifiability analysis and standard and robust regression analysis of complex dynamical models. The book first provides a definition of complexity in dynamic systems by introducing readers to the concepts of system size, density of interactions, stiff dynamics, and hybrid nature of determination. In turn, it presents the mathematical foundations of and algorithmic procedures for model structural and practical identifiability analysis, multilinear and non-linear regression analysis, and best predictor selection. Although the main fields of application discussed in the book are biochemistry and systems biology, the methodologies described can also be employed in other disciplines such as physics and the environmental sciences. Readers will learn how to deal with problems such as determining the identifiability conditions, searching for an identifiable model, and conducting their own regression analysis and diagnostics without supervision. Featuring a wealth of real-world examples, exercises, and codes in R, the book addresses the needs of doctoral students and researchers in bioinformatics, bioengineering, systems biology, biophysics, biochemistry, the environmental sciences and experimental physics. Readers should be familiar with the fundamentals of probability and statistics (as provided in first-year university courses) and a basic grasp of R.
Identifiability and Regression Analysis of Biological Systems Models
This richly illustrated book presents the latest techniques for the identifiability analysis and standard and robust regression analysis of complex dynamical models, and looks at their objectives. It begins by providing a definition of complexity in dynamic systems, introducing the concepts of system size, density of interactions, stiff dynamics, and the hybrid nature of determination. The discussion then turns to the mathematical foundations of model structural and practical identifiability analysis, multilinear and non-linear regression analysis, and best predictor selection, and their algorithmic procedures. Although the featured examples mainly focus on applications to biochemistry and systems biology, the methodologies described can also be employed in other disciplines such as physics and the environmental sciences. Readers will learn how to determine identifiability conditions, how to search for an identifiable model, and how to conduct their own regression analysis and diagnostics without supervision. This new edition includes a concise, yet comprehensive treatment of the main artificial intelligence methods which can be used for parameter inference in models of complex dynamic biological systems. It emphasizes the most efficient solutions for generating synthetic data that augment the training data and which are indispensable for machine learning procedures. Featuring a wealth of real-world examples, exercises, and R codes, the book addresses the needs of doctoral students and researchers in bioinformatics, bioengineering, systems biology, biophysics, biochemistry, the environmental sciences and experimental physics. Familiarity with the fundamentals of probability and statistics (as provided in first-year university courses) and a basic grasp of R are assumed.
2019-20 MATRIX Annals
MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the ten programs held at MATRIX in 2019 and the two programs held in January 2020: · Topology of Manifolds: Interactions Between High and Low Dimensions · Australian-German Workshop on Differential Geometry in the Large · Aperiodic Order meets Number Theory · Ergodic Theory, Diophantine Approximation and Related Topics · Influencing Public Health Policy with Data-informed Mathematical Models of Infectious Diseases · International Workshop on Spatial Statistics · Mathematics of Physiological Rhythms · Conservation Laws, Interfaces and Mixing · Structural Graph Theory Downunder · Tropical Geometry and Mirror Symmetry · Early Career Researchers Workshop on Geometric Analysis and PDEs · Harmonic Analysis and Dispersive PDEs: Problems and Progress The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.