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作者 Hata, Masayoshi, author
書名 Neurons : a mathematical ignition / Masayoshi Hata
出版項 Singapore ; Hackensack, NJ : World Scientific, [2015]
國際標準書號 9789814618618
book jacket
館藏地 索書號 處理狀態 OPAC 訊息 條碼
 數學所圖書室  QA76.87 .H38 2015    在架上    30340200538571
系列 Series on number theory and its applications ; vol. 9
附註 1. Series on number theory and its applications -- 2. Caianiello's equations -- 3. Rotation numbers -- 4. Classification of [symbol] -- 5. Farey series -- 6. Further investigation of [symbols] -- 7. Limit sets [symbol] and [symbol] -- 8. Piecewise linear maps -- 9. Orbital and itinerary functions -- 10. Farey structure -- 11. [symbol] and [symbol]-leaves -- 12. Approximations to Hecke-Mahler series
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
主題 Neural networks (Computer science) -- Mathematics
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