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OverviewThis introductory guide provides a thorough explanation of the mathematics and algorithms used in standard data analysis techniques within systems biology, biochemistry, and biophysics. Each part of the book covers the mathematical background and practical applications of a given technique. Readers will gain an understanding of the mathematical and algorithmic steps needed to use these software tools appropriately and effectively, as well how to assess their specific circumstance and choose the optimal method and technology. Ideal for students planning for a career in research, early-career researchers, and established scientists undertaking interdisciplinary research. Full Product DetailsAuthor: Paola Lecca , Bruno CarpentieriPublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: 1st ed. 2023 Weight: 0.582kg ISBN: 9783031365652ISBN 10: 3031365658 Pages: 264 Publication Date: 13 September 2023 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsPart I1. Introduction to graph theory 1.1 Definitions and examples 1.2 Spectral graph theory1.3 Centrality measures 1.3.1 Geometric centralities 1.3.2 Closeness 1.3.3 Path-based centralities 1.3.4 Spectral measures 1.4 Axioms for centrality 1.4.1 The size axiom1.4.2 The density axiom 1.4.3 The score-monotonicity axiom 2. Biological networks2.1 Networks: the representation of a system at the basis of systems biology2.2 Biochemical networks2.2.1 Metabolic networks2.2.2 Protein-protein interaction networks2.2.3 Genetic regulatory networks 2.2.4 Neural networks 2.3 Phylogenetic networks 2.4 Signaling networks2.5 Ecological networks2.6 Challenges in computational network biology 3. Network inference for drug discovery3.1 How network biology helps drug discovery3.2 Computational methods3.2.1 Classifier-based methods3.2.2 Reverse-engineering methods3.2.3 Integrating static and dynamic data: a promising venue Part II4. An introduction to differential and integral calculus4.1 Derivative of a real function4.2 Examples of derivatives4.3 Geometric interpretation of the derivative4.4 The algebra of derivatives4.5 Definition of integral4.6 Relation between integral and derivative4.7 Methods of integration4.7.1 Integration by parts4.7.2 Integration by substitution4.7.3 Integration by partial fraction decomposition4.7.4 The reverse chain rule4.7.5 Using combinations of methods4.8 Ordinary differential equations4.8.1 First-order linear equations4.8.2 Initial value problems4.9 Partial differential equations4.10 Discretization of differential equations4.10.1 The Implicit or Backward Euler Method4.10.2 The Runge-Kutta Method4.11 Systems of differential equations 5. Modelling chemical reactions5.1 Modelling in systems biology5.2 The different types of mathematical models5.3 Chemical kinetics: From diagrams to mathematical equations5.4 Kinetics of chemical reactions5.4.1 The law of mass action5.4.2 Example 1: The Lotka-Volterra System5.4.3 Example 2: The Michaelis-Mentin Reactions5.5 Conservation laws5.6 Markov passes5.7 The master equation5.7.1 The chemical master equation5.8 Molecular approach to chemical kinetics5.8.1 Reactions are collisions5.8.2 Reaction rate5.8.3 Zeroth-, first, and second order reactions5.8.4 Higher-order reactions5.9 Fundamental hypothesis of stochastic chemical kinetics5.10 The reaction probability density function5.11 The stochastic simulation algorithms5.11.1 Direct method5.11.2 First Reaction Method5.11.3 Next Reaction Method5.12 Spatio-temporal simulation algorithms5.13 Ordinary differential equation stochastic models: the Langevin equation5.14 Hybrid algorithms 6. Reaction-diffusion systems6.1 The physics of reaction-diffusion systems6.2 Diffusion of non-charged molecules6.2.1 Intrinsic viscosity and frictional coefficient6.2.2. Calculated second virial coefficient6.3 Algorithm and data structures6.4 Drug release6.4.1 The Higuchi model6.4.2 Systems with different geometries6.4.3 The power-law model6.5 What drug dissolution is6.6 The diffusion layer model (Noyes and Whitney)6.7 The Weibull function in dissolution6.7.1 Inhomogeneous conditions6.7.2 Drug dissolution is a stochastic process6.7.3 The inter-facial barrier model6.7.4 Compartmental model Part III7. Linear Algebra Background7.1 Matrices7.1.1 Introduction7.1.2 Special matrices7.1.3 Operation on matrices7.1.4 Transposition and symmetries7.2 Linear systems7.2.1 Introduction7.2.2 Special linear systems7.2.3 General linear systems7.2.4 The Gaussian Elimination method7.2.5 Gaussian elimination for rectangular systems7.2.6 Consistency of linear systems7.2.7 Homogeneous linear systems7.2.8 Nonhomogeneous linear systems7.3 Least-squares problems7.4 Permutations and determinants7.5 Eigenvalue problems7.5.1 Introduction7.5.2 Computing the eigenvalues and the eigenvectors 8. Regression8.1 Regression as a geometric problem8.1.1 Standard error on regression coefficients8.2 Regression via maximum-likelihood estimation8.3 Regression diagnostic8.4 How to assess the goodness of the model8.5 Other types of regression8.6 Case study 1: Regression analysis of sweat secretion volumes in cystic fibrosis patients8.6.1 The experiments8.6.2 The multilinear model8.6.3 Results8.7 Nonlinear regression8.8 Case study 2: inference of kinetic rate constants8.8.1 Parameter space restriction8.8.2 Variance of the estimated parameters 9. Cardiac electrophysiology9.1 The bidomain model9.2 Adaptive algorithms9.3 Iterative methods for linear systems9.4 Krylov subspace methods9.5 Parallel implementation ReferencesReviewsAuthor InformationPaola Lecca, Assistant Professor, Faculty of Engineering, Free University of Bozen-Bolzano, ItalyBruno Carpentieri, Associate Professor, Faculty of Engineering, Free University of Bozen-Balzano, Italy Tab Content 6Author Website:Countries AvailableAll regions |
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