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Read e-book online Biomathematics and Related Computational Problems PDF

By Shun-ichi Amari (auth.), Luigi M. Ricciardi (eds.)

ISBN-10: 9400929757

ISBN-13: 9789400929753

ISBN-10: 940107836X

ISBN-13: 9789401078368

Biomathematics emerged and quickly grew as an self sustaining self-discipline within the past due sixties as scientists with numerous backgrounds within the mathematical, organic and actual sciences accrued jointly to shape Departments and Institutes founded round this self-discipline that many at the moment felt may still fall among the cracks of valid technology. for varied purposes a few of these new associations vanished within the mid-seventies, fairly within the U. S. , the most explanation for their loss of life being fiscal. however, strong biomathematical in order that the variety study has been endlessly carried on by way of a number of staff around the world of this job appears to be like now as actually notable: from important and potent mathematical statements approximately difficulties which are firmly rooted within the 'wet' fact of biology to deep theoretical investigations on striking uncomplicated questions. it's also attention-grabbing to keep in mind that a few rules and theories set forth by means of 'paleo-biomathematicians' virtually 1 / 4 of century in the past are actually turning into hugely favored additionally via scientists engaged in really diverse examine fields. for example, neural nets is the new subject in desktop technology nowadays! good conscious of the growing to be curiosity during this particularly new box, years again I geared up a small workshop on Biomathematics: present prestige and destiny views which was once held on the collage of Salerno throughout the center of April, 1980.

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R. Caianiello Universi~ of Salerno Department of Theoretical Physics and SMSA 84100 - Salerno Italy ABSTRACT. The Neuronic Equations, presented by this author in 1961 as part of a model of neural activity which algebrized McCulloch's logic approach, have been since the object of much work; interest in them is now revived by the fact that they describe arbitrary parallel nets, and contain Cellular Automata as particular cases. The present report exhibits, in compact form, the exact solution of the "inverse problem" related to them: given an arbitrary sequence of states, how to construct a net that will perform that sequence during its evolution.

1984]: Springer. Self-organization and Associative Memory, Nakano, K. , SMC-2, 381-388. Takeuchi, A. and Amari, S. [1979] : 'Formation of topographic maps and columnar microstructures', Biol. Cybern. 35, 63-72. von der Malsberg, C. [1973]: 'Self-organization of orientation sensitive cells in the striate cortex', Kybernetik, 14, 85-100. PROBLEMS CONNECTED WITH NEURONIC EQUATIONS E. R. Caianiello Universi~ of Salerno Department of Theoretical Physics and SMSA 84100 - Salerno Italy ABSTRACT. The Neuronic Equations, presented by this author in 1961 as part of a model of neural activity which algebrized McCulloch's logic approach, have been since the object of much work; interest in them is now revived by the fact that they describe arbitrary parallel nets, and contain Cellular Automata as particular cases.

2, 127-153. Holden A;V. (1976) Models of the Stochastic Activity of Neurons. Biomathematics, Vol. 16. Springer-Verlag, Berlin. M. (1968) Diffusion models for the stochastic activity of neurons. R. ) 116-144. Springer-Verlag, Berlin. Lansky F. and Lanska V. (1987) Diffusion approximations of the neuronal model with synaptic reversal potentials. BioI. Cybernetics 56, 19-26. M. and Sacerdote L. (1985 a). Exponential trends of OrnsteinUhlenbeck first-passage-time densities. J Appl. Frob. 22, 346-359.

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Biomathematics and Related Computational Problems by Shun-ichi Amari (auth.), Luigi M. Ricciardi (eds.)


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