Toru Ohira - Böcker

The educational challenge addressed by this introductory textbook is how to present a sampling of the wide range of mathematical tools available for laboratory research to well-motivated students with a mathematical background limited to an introductory course in calculus.

The second edition of Mathematics as a Laboratory Tool reflects the growing impact that computational science is having on the career choices made by undergraduate science and engineering students.  The focus is on dynamics and the effects of time delays and stochastic perturbations (“noise”) on the regulation provided by feedback control systems.  The concepts are illustrated with applications to gene regulatory networks, motor control, neuroscience and population biology.   The presentation in the first edition has been extended to include discussions of neuronal excitability and bursting, multistability, microchaos, Bayesian inference, second-order delay differential equations, and the semi-discretization method for the numerical integration of delay differential equations. Every effort has been made to ensure that the material is accessible to those with a background in calculus.  The text provides advanced mathematical concepts such as the Laplace and Fourier integral transforms in the form of Tools.   Bayesian inference is introduced using a number of detective-type scenarios including the Monty Hall problem.

The second edition of Mathematics as a Laboratory Tool reflects the growing impact that computational science is having on the career choices made by undergraduate science and engineering students.  The focus is on dynamics and the effects of time delays and stochastic perturbations (“noise”) on the regulation provided by feedback control systems.  The concepts are illustrated with applications to gene regulatory networks, motor control, neuroscience and population biology.   The presentation in the first edition has been extended to include discussions of neuronal excitability and bursting, multistability, microchaos, Bayesian inference, second-order delay differential equations, and the semi-discretization method for the numerical integration of delay differential equations. Every effort has been made to ensure that the material is accessible to those with a background in calculus.  The text provides advanced mathematical concepts such as the Laplace and Fourier integral transforms in the form of Tools.   Bayesian inference is introduced using a number of detective-type scenarios including the Monty Hall problem.

This book presents the most recent mathematical approaches to the growing research area of networks, oscillations, and collective motions in the context of biological systems. Bringing together the results of multiple studies of different biological systems, this book sheds light on the relations among these research themes. Included in this book are the following topics: feedback systems with time delay and threshold of sensing (dead zone), robustness of biological networks from the point of view of dynamical systems, the hardware-oriented neuron modeling approach, a universal mechanism governing the entrainment limit under weak forcing, the robustness mechanism of open complex systems, situation-dependent switching of the cues primarily relied on by foraging ants, and group chase and escape.Research on different biological systems is presented together, not separated by specializations or by model systems. Therefore, the book provides diverse perspectives at the forefront of current mathematical research on biological systems, especially focused on networks, oscillations, and collective motions.This work is aimed at advanced undergraduate, graduate, and postdoctoral students, as well as scientists and engineers. It will also be of great use for professionals in industries and service sectors owing to the applicability of topics such as networks and synchronizations.

This book presents a unique fusion of two different research topics. Although the combination is simple and straightforward, the book describes the emergence of rather intricate behavior, provoking the interest of readers for further developments and applications of related topics.