The second part of this two-volume set contains advanced aspects of the quantitative theory of the dynamics of neurons. It begins with an introduction to the effects of reversal potentials on response to synaptic input. It then develops the theory of action potential generation based on the seminal Hodgkin-Huxley equations and gives methods for their solution in the space-clamped and nonspaceclamped cases. The remainder of the book discusses stochastic models of neural activity and ends with a statistical analysis of neuronal data with emphasis on spike trains. The mathematics is more complex...

The human brain contains billions of nerve cells whose activity plays a critical role in the way we behave, feel, perceive, and think. This two-volume set explains the basic properties of a neuron--an electrically active nerve cell--and develops mathematical theories for the way neurons respond to the various stimuli they receive. Volume 1 contains descriptions and analyses of the principle mathematical models that have been developed for neurons in the past thirty years. It provides a brief review of the basic neuroanatomical and neurophysiological facts that will form the focus of the...

This book provides a clear and concise summary of the fluid dynamics of the locomotion of living organisms. The biological phenomena described in detail range from the swimming of bacteria and fish to the flying of insects and birds. The breadth of treatment requires the study of two basic fluid-dynamical regimes. In the first case, that of small organisms, the viscosity of the fluid is paramount in deciding the most effective swimming strategy. However, for larger insects, birds, and most fish, the viscosity of the air or water may be treated as if it were zero, and resulting mechanisms of...

This introduction to mathematical methods that are useful for studying population phenomena is intended for advanced undergraduate and graduate students, and will be accessible to scientists who do not have a strong mathematics background. The material is graded in mathematical difficulty. The earlier parts of the book involve elementary diference equations while later chapters present topics that require more mathematical preparation. Models of total population and population age structure are first derived and studied, and then models of random population events are presented in terms of...

Professor Cronin offers, for the first time, a synthesis of the work of Hodgkin and Huxley on nerve conduction. This information has previously been scattered throughout various media and difficult to retrieve. In this book the author thoroughly describes and analyzes their mathematical models (nonlinear ordinary and partial differential equations) and later models.

Although Ovid is currently enjoying a new wave of popularity, most critics withhold from his poetry the close word-by-word readings that are necessary for a thorough understanding of it. Ovid twice treated the myth of Persephone, and Hinds's book is at first a historical inquiry--the most extensive yet done--into the double transformation in Metamorphosis 5 and Fasti 4 of the rape of Persephone, one of the great Graeco-Roman myths. The study continues as a critical exploration of Ovid's self-conscious delight in language and in writing manifested in these twin narratives, providing a feast...

This volume develops a unifying approach to population studies that emphasizes the interplay between modeling and experimentation and that will provide mathematicians and biologists with a framework within which population dynamics can be fully explored and understood. A unique feature of the book is that deterministic and stochastic models are considered together; spatial effects are investigated by developing models that highlight the consequences that geographical restriction and species mobility may have on population development. Model-based simulations of processes are used to explore...

In this new edition, Brian Charlesworth provides a comprehensive review of the basic mathematical theory of the demography and genetics of age-structured populations. The author aims to avoid complicated mathematics, but gives full derivations of major theoretical results for the edification of the reader.

The chemostat is a basic piece of laboratory apparatus, yet it has begun to occupy an increasingly central role in ecological studies. The ecological environment created by a chemostat is one of the few completely controlled experimental systems for testing microbial growth and competition. As a tool in biotechnology, the chemostat plays an important role in bioprocessing. This book presents the theory of the chemostat as a model for larger ecological problems such as food chains, competition along a gradient, competition in the presence of an inhibitor, and the effects of time varying...

The massive research effort known as the Human Genome Project is an attempt to record the sequence of the three trillion nucleotides that make up the human genome and to identify individual genes within this sequence. The description and classification of sequences is heavily dependent on mathematical and statistical models. This short textbook presents a brief description of several ways in which mathematics and statistics are being used in genome analysis and sequencing.