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Mathematical Neuroscience
Mathematical Neuroscience is a book for mathematical biologists seeking to discover the complexities of brain dynamics in an integrative way. It is the first research monograph devoted exclusively to the theory and methods of nonlinear analysis of infinite systems based on functional analysis techniques arising in modern mathematics. Neural models that describe the spatio-temporal evolution of coarse-grained variables—such as synaptic or firing rate activity in populations of neurons —and often take the form of integro-differential equations would not normally reflect an integrative approach. This book examines the solvability of infinite systems of reaction diffusion type equations in p...
Biophysics Of Consciousness: A Foundational Approach
The problem of how the brain produces consciousness, subjectivity and 'something it is like to be' remains one of the greatest challenges to a complete science of the natural world. While various scientists and philosophers approach the problem from their own unique perspectives and in the terms of their own respective fields, Biophysics of Consciousness: A Foundational Approach attempts a consilience across disparate disciplines to explain how it is possible that an objective brain produces subjective experience.This volume unites the crème de la crème of physicists, neuroscientists, and psychiatrists in the attempt to understand consciousness through a foundational approach encompassing ontological, evolutionary, neurobiological, and Freudian interpretations with the focus on conscious phenomena occurring in the brain. By integrating the perspectives of these diverse disciplines with the latest research and theories on the biophysics of the brain, the book tries to explain how consciousness can be an adaptive and causal element in the natural world.
Quantum Boundaries of Life
Quantum Boundaries of Life, Volume 82 in the Advances in Quantum Chemistry series, presents current topics in this rapidly developing field that have emerged at the cross section of mathematics, physics, chemistry and biology. Topics covered include Quantum Considerations of Neural Memory, Functional Neural Electron Transport, Plasmon-polariton mechanism of the saltatory conduction in myelinated axons, Quantum Field Theory Formulation of Brain Dynamics: Nonequilibrium, Multi Field Theory Formulation of Brain Dynamics, Quantum Protein Folding, Classical-Quantum Interplay in Living Neural Tissue Function, Quantum Effects in Life Dynamics, Quantum transport and utilization of free energy in pro...
Modeling in the Neurosciences
With contributions from more than 40 renowned experts, Modeling in the Neurosciences: From Ionic Channels to Neural Networks is essential for those interested in neuronal modeling and quantitative neiroscience. Focusing on new mathematical and computer models, techniques and methods, this monograph represents a cohesive and comprehensive treatment
The Relativistic Brain
In this monograph, a mathematician and a neurobiologist join forces to address one of the most crucial and controversial scientific questions of our times: can the exquisite capacities of the human brain be simulated by any digital computer? By combining mathematical, computational, neurobiological and evolutionary arguments, Ronald Cicurel and Miguel Nicolelis refute the possibility that any Turing machine will ever succeed in such a simulation. As part of their argument, the authors propose a new theory for brain function: the Relativistic Brain Theory. This theory accounts for decades of neurophysiological and psychological findings and observations that until now have challenged the domi...
Modeling in the Neurosciences
Computational models of neural networks have proven insufficient to accurately model brain function, mainly as a result of simplifications that ignore the physical reality of neuronal structure in favor of mathematically tractable algorithms and rules. Even the more biologically based "integrate and fire" and "compartmental" styles of modeling suff
Putting Ourselves Back in the Equation
Distant galaxies, dark matter, black holes – elusive, incomprehensible and inhospitable – these are the building blocks of modern physics. But where do we fit in this picture? For centuries, we have separated mind from matter. While physicists have pursued a theory of ‘everything’ with single-minded purpose, the matter of the mind, of human consciousness, has been conveniently sidestepped and ignored – consigned to priests, philosophers and poets. With the ambition of Stephen Hawking, Carlo Rovelli and Brian Cox, Putting Ourselves Back in the Equation sets out a bold new vision for theoretical physics, unrestricted by sleek equations and neat formulations. Combining cutting-edge neuroscience with the latest in quantum mechanics, acclaimed writer Musser offers a new interpretation of human consciousness. From bizarre cognitive phenomena, like lucid dreaming and self-taught synaesthesia, to the latest technological developments in AI, Musser asks: what can physics teach us about what it means to be human?
Psychoanalytic Defense Mechanisms in Cognitive Multi-Agent Systems
Human cognitive processes and defense mechanisms, as described in psychoanalysis, bring about new notions and paradigms for artificial intelligence systems. One key reason is that the human cognitive processes and defense mechanisms in question can accomplish conflict detection functionalities, filter functionalities, and other system stabilizing tasks within artificial intelligence systems. Yet artificial cognitive architectures lack the capability to analyze complex situations as well as the universal competencies needed to orientate themselves in complex environments in various domains. Psychoanalytic Defense Mechanisms in Cognitive Multi-Agent Systems addresses this dilemma by exploring ...
On the Contexts of Things Human
The study of isoperimetric inequalities involves a fascinating interplay of analysis, geometry and the theory of partial differential equations. Several conjectures have been made and while many have been resolved, a large number still remain open. One of the principal tools in the study of isoperimetric problems, especially when spherical symmetry is involved, is Schwarz symmetrization, which is also known as the spherically symmetric and decreasing rearrangement of functions. The aim of this book is to give an introduction to the theory of Schwarz symmetrization and study some of its applications. The book gives an modern and up-to-date treatment of the subject and includes several new results proved recently. Effort has been made to keep the exposition as simple and self-contained as possible. A knowledge of the existence theory of weak solutions of elliptic partial differential equations in Sobolev spaces is, however, assumed. Apart from this and a general mathematical maturity at the graduate level, there are no other prerequisites.
