Books in the SpringerBriefs in Mathematical Methods series

This book covers the application to two mutation models: single step mutation for microsatellite loci and single-base substitutions.

This book presents a concise introduction to piecewise deterministic Markov processes (PDMPs), with particular emphasis on their applications to biological models.

The book also demonstrates the methods on the WikiLeaks Afghan War Diary, the results showing that this approach allows deeper insights into conflict dynamics and allows a strikingly statistically accurate forward prediction of armed opposition group activity in 2010, based solely on data from preceding years.

In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the theory of persistence which is indispensable for applications, e.g.

This book develops continuum modeling skills and approaches the topic from three sides: (1) derivation of global integral laws together with the associated local differential equations, (2) design of constitutive laws and (3) modeling boundary processes.

This is the first book to focus on the topological index, the Harary index, of a graph, including its mathematical properties, chemical applications and some related and attractive open problems.

The contents of the book consist of three parts: (i) basic theory of stochastic control and formulation of various option pricing models, (ii) design of finite volume, finite difference and penalty-based algorithms for solving the models and (iii) stability and convergence analysis of the algorithms.