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E-raamat: Neurons: A Mathematical Ignition

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(Kyoto Univ, Japan)
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Neurons: A Mathematical IgnitionSuurem pilt
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This unique volume presents a fruitful and beautiful mathematical world hidden in Caianiello's neuronic equations, which describe the instantaneous behavior of a model of a brain or thinking machine. The detailed analysis from a viewpoint of “dynamical systems”, even in a single neuron case, enables us to obtain amazingly good rational approximations to the Hecke–Mahler series with two variables. Some interesting numerical applications of our rational approximations are also discussed.This book is fundamentally self-contained and many topics required in it are explained from the beginning. Each chapter contains a number of instructive and mostly original exercises at various levels.
This unique volume presents a fruitful and beautiful mathematical world
hidden in Caianiello's neuronic equations, which describe the instantaneous
behavior of a model of a brain or thinking machine. The detailed analysis
from a viewpoint of "dynamical systems", even in a single neuron case,
enables us to obtain amazingly good rational approximations to the
Hecke-Mahler series with two variables. Some interesting numerical
applications of our rational approximations are also discussed.This book is
fundamentally self-contained and many topics required in it are explained
from the beginning. Each chapter contains a number of instructive and mostly
original exercises at various levels.
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