منابع مشابه
A spherical Hopfield model
We introduce a spherical Hopfield-type neural network involving neurons and patterns that are continuous variables. We study both the thermodynam-ics and dynamics of this model. In order to have a retrieval phase a quartic term is added to the Hamiltonian. The thermodynamics of the model is exactly solvable and the results are replica symmetric. A Langevin dynamics leads to a closed set of equa...
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In this note, I review some basic properties of the Hopfield model. I closely follow Chapter 2 of Herz, Krogh & Palmer (1991) which is an excellent introductory textbook on the theory of neural networks. I motivate the mean field analysis of the stochastic Hopfield model slightly differently than Herz, Krogh & Palmer (1991) and my derivations are a little longer, filling in some of the gaps in ...
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The Hopfield model in a transverse field is investigated in order to clarify how quantum fluctuations affect the macroscopic behavior of neural networks. Using the Trotter decomposition and the replica method, we find that the α (the ratio of the number of stored patterns to the system size)-∆ (the strength of the transverse field) phase diagram of this model in the ground state resembles the α...
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In 1973, the phenomenon of long-term potentiation (LTP) was discovered. The study of LTP is now a small industry within the field of neuroscience. Among the various forms of LTP, those that depend on the NMDA subtype of glutamate receptor are regarded as “Hebbian.” These forms depend on temporal contiguity of presynaptic and postsy naptic activity. The requirement of temporal contiguity is exp...
متن کاملA Mathematical Model for Indian Ocean Circulation in Spherical Coordinate
In recent years, the Indian Ocean (IO) has been discovered to have a much larger impact on climate variability than previously thought. This paper reviews processes in which the IO is, or appears to be, actively involved. We begin the mathematical model with a pattern for summer monsoon winds. Three dimensional temperature and velocity fields are calculated analytically for the ocean forced by ...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2003
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/36/41/002