Preface -- Introduction -- Basic Concept of Ca2+ Signaling in Cells and Tissues (M. J. Sanderson) -- Modeling IP-3-Dependent Calcium Dynamics in Non-Excitable Cells (J. Sneyd) -- Integrated Calcium Management in Cardiac Myocytes (T. R. Shannon) -- Mechanisms and Models of Cardiac Excitation-Contraction Coupling (R. L. Winslow, R. Hinch, J. L. Greenstein) -- Mathematical Analysis of the Generati…
Preface -- A. Friedman: Introduction to Neurons -- D. Terman: An Introduction to Dynamical Systems and Neuronal Dynamics -- B. Ermentrout: Neural Oscillators -- A. Borisyuk: Physiology and Mathematical Modeling of the Auditory System.This volume introduces some basic theories on computational neuroscience. Chapter 1 is a brief introduction to neurons, tailored to the subsequent chapters. Chapte…
Markov Models in Molecular Evolution -- to Applications of the Likelihood Function in Molecular Evolution -- to Markov Chain Monte Carlo Methods in Molecular Evolution -- Population Genetics of Molecular Evolution -- Practical Approaches for Data Analysis -- Maximum Likelihood Methods for Detecting Adaptive Protein Evolution -- HyPhy: Hypothesis Testing Using Phylogenies -- Bayesian Analysis of…
Probability Theory (i): One Random Variable -- Probability Theory (ii): Many Random Variables -- Statistics (i): An Introduction to Statistical Inference -- Stochastic Processes (i): Poisson Processes and Markov Chains -- The Analysis of One DNA Sequence -- The Analysis of Multiple DNA or Protein Sequences -- Stochastic Processes (ii): Random Walks -- Statistics (ii): Classical Estimation Theor…
Two Classical Optimization Problems -- Gauss’ Question -- What Does Solution Mean? -- Network Design Problems -- A New Challenge: The Phylogeny -- An Analysis of Steiner’s Problem in Phylogenetic Spaces -- Tree Building Algorithms.The problem of "Shortest Connectivity" has a long and convoluted history: given a finite set of points in a metric space, search for a network that connects these…
Dynamique qualitative et théorie des oscillations -- La théorie de la stabilité -- La théorie des bifurcations -- La théorie classique des perturbations et les perturbations singulières -- Systèmes d’oscillateurs couplés -- Solutions ondes stationnaires et systèmes dynamiques -- Electrophysiologie, synchronisation et oscillations en salves.Par sa nature pluridisciplinaire, ce livre s…
The Theory of Stochastic Processes -- Fundamentals of Probability -- Stochastic Processes -- The Itô Integral -- Stochastic Differential Equations -- The Applications of Stochastic Processes -- Applications to Finance and Insurance -- Applications to Biology and Medicine.This concisely written book is a rigorous and self-contained introduction to the theory of continuous-time stochastic proces…
Stochastic Methods in Statistical Physics -- Coarse-Graining Techniques for (Random) Kac Models -- Euclidean Gibbs Measures of Quantum Crystals: Existence, Uniqueness and a Priori Estimates -- Some Jump Processes in Quantum Field Theory -- Gibbs Measures on Brownian Paths: Theory and Applications -- Spectral Theory for Nonstationary Random Potentials -- A Survey of Rigorous Results on Random Sc…
Summary -- Background -- Fundamental Theorem -- Trudinger-Moser Inequality -- The Green’s Function -- Equilibrium States -- Blowup Analysis for Stationary Solutions -- Multiple Existence -- Dynamical Equivalence -- Formation of Collapses -- Finiteness of Blowup Points -- Concentration Lemma -- Weak Solution -- Hyperparabolicity -- Quantized Blowup Mechanism -- Theory of Dual Variation.This bo…
Biology in a Nutshell -- Words -- Word Distributions and Occurrences -- Physical Mapping of DNA -- Genome Rearrangements -- Sequence Alignment -- Rapid Alignment Methods: FASTA and BLAST -- DNA Sequence Assembly -- Signals in DNA -- Similarity, Distance, and Clustering -- Measuring Expression of Genome Information -- Inferring the Past: Phylogenetic Trees -- Genetic Variation in Populations -- …