John J. Hopfield

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Computational properties of use of biological organisms or to the construction of computers can emerge as collective properties of systems having a large number of simple equivalent components (or neurons). The physical meaning of content-addressable memory is described by an appropriate phase space flow of the state of a system. A model of such a system is(More)
A model for a large network of "neurons" with a graded response (or sigmoid input-output relation) is studied. This deterministic system has collective properties in very close correspondence with the earlier stochastic model based on McCulloch - Pitts neurons. The content- addressable memory and other emergent collective properties of the original model(More)
Highly-interconnected networks of nonlinear analog neurons are shown to be extremely effective in computing. The networks can rapidly provide a collectively-computed solution (a digital output) to a problem on the basis of analog input information. The problems to be solved must be formulated in terms of desired optima, often subject to constraints. The(More)
A computational model is described in which the sizes of variables are represented by the explicit times at which action potentials occur, rather than by the more usual 'firing rate' of neurons. The comparison of patterns over sets of analogue variables is done by a network using different delays for different information paths. This mode of computation(More)
Cellular functions, such as signal transmission, are carried out by 'modules' made up of many species of interacting molecules. Understanding how modules work has depended on combining phenomenological analysis with molecular studies. General principles that govern the structure and behaviour of modules may be discovered with help from synthetic sciences(More)
We describe how several optimization problems can be rapidly solved by highly interconnected networks of simple analog processors. Analog-to-digital (A/D) conversion was considered as a simple optimization problem, and an A/D converter of novel architecture was designed. A/D conversion is a simple example of a more general class of signal-decision problems(More)
A new conceptual framework and a minimization principle together provide an understanding of computation in model neural circuits. The circuits consist of nonlinear graded-response model neurons organized into networks with effectively symmetric synaptic connections. The neurons represent an approximation to biological neurons in which a simplified set of(More)
The molecular mechanisms underlying long-term potentiation in the hippocampus have received much attention because of the likely functional importance of synaptic plasticity for information storage and the development of neuronal connectivity. Surprisingly, it remains unclear whether activity modifies the strength of individual synapses in a digital(More)
The specificity with which the genetic code is read in protein synthesis, and with which other highly specific biosynthetic reactions take place, can be increased above the level available from free energy differences in intermediates or kinetic barriers by a process defined here as kinetic proofreading. A simple kinetic pathway is described which results(More)
We present evidence that resonance properties of rat vibrissae differentially amplify high-frequency and complex tactile signals. Consistent with a model of vibrissa mechanics, optical measurements of vibrissae revealed that their first mechanical resonance frequencies systematically varied from low (60-100 Hz) in longer, posterior vibrissae to high ((More)