Ising Systems with Conflicting Dynamics: Exact Results for Random Interactions and Fields

López-Lacomba, A. I.; Marro, Joaquín

doi:10.1209/0295-5075/25/3/003

Cited by 11 publications

(14 citation statements)

References 12 publications

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“…This generalizes a case in the literature for random S-independent fluctuations (Garrido & Munoz, 1993;Lacomba & Marro, 1994;Marro & Dickman, 1999). In this case, one hasc(±κ; +) =c(±κ; −) and, consequently, α − ij = 0 ∀i, j.…”

Section: Effective Local Fieldssupporting

confidence: 75%

Effects of Fast Presynaptic Noise in Attractor Neural Networks

et al. 2006

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We study both analytically and numerically the effect of presynaptic noise on the transmission of information in attractor neural networks. The noise occurs on a very short timescale compared to that for the neuron dynamics and it produces short-time synaptic depression. This is inspired in recent neurobiological findings that show that synaptic strength may either increase or decrease on a short timescale depending on presynaptic activity. We thus describe a mechanism by which fast presynaptic noise enhances the neural network sensitivity to an external stimulus. The reason is that, in general, presynaptic noise induces nonequilibrium behavior and, consequently, the space of fixed points is qualitatively modified in such a way that the system can easily escape from the attractor. As a result, the model shows, in addition to pattern recognition, class identification and categorization, which may be relevant to the understanding of some of the brain complex tasks.

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Section: Effective Local Fieldssupporting

confidence: 75%

Effects of Fast Presynaptic Noise in Attractor Neural Networks

et al. 2006

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“…One has λ µ = α with α ≡ P N −1 from normalization µ a µ = 1 for equal probability, a µ = P −1 ; cf (20). The fluctuations around the Hebbian rule are then characterized by…”

Section: Exact Results For Symmetric Synapsesmentioning

confidence: 99%

“…As an extension of previous work on disordered systems [16,20,26], we have presented and studied a model for associative memory. This is a generalized, kinetic version of the Hopfield neural network in the sense that the synapse intensities do not remain constant after the learning process but fluctuate with time during neuron activity.…”

Section: Resultsmentioning

confidence: 99%

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Neural networks with fast time-variation of synapses

Torres¹,

Garrido²,

Marro³

1997

J. Phys. A: Math. Gen.

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Abstract. We study a kinetic neural network in which the intensity of synaptic couplings varies on a timescale of order p(1 − p) −1 compared with that for neuron variations. We describe some exact and mean-field results for p → 0. This includes, for example, the Hopfield model with random fluctuations of synapse intensities such that neurons couple each other, on average, according to the Hebbian learning rule. The consequences of such fluctuations on the performance of the network are analysed in detail for some specific choices of the rate and fluctuation distribution, including the case in which couplings are asymmetric.

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“…16,20,24,30, 40 and 60 with periodic boundary conditions and a random initial configuration of the spins. We have analyzed the following values of the parameters: 0.0 < h o < 5.0 and 0.01 < T < 10.0.…”

mentioning

confidence: 99%

Nonequilibrium phase transitions and tricriticality in a three-dimensional lattice system with random-field competing kinetics

Crokidakis

2010

Phys. Rev. E

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We study a nonequilibrium Ising model that stochastically evolves under the simultaneous operation of several spin-flip mechanisms. In other words, the local magnetic fields change sign randomly with time due to competing kinetics. This dynamics models a fast and random diffusion of disorder that takes place in dilute metallic alloys when magnetic ions diffuse. We performe Monte Carlo simulations on cubic lattices up to L = 60. The system exhibits ferromagnetic and paramagnetic steady states. Our results predict first-order transitions at low temperatures and large disorder strengths, which correspond to the existence of a nonequilibrium tricritical point at finite temperature. By means of standard finite-size scaling equations, we estimate the critical exponents in the low-field region, for which our simulations uphold continuous phase transitions.

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Ising Systems with Conflicting Dynamics: Exact Results for Random Interactions and Fields

Cited by 11 publications

References 12 publications

Effects of Fast Presynaptic Noise in Attractor Neural Networks

Effects of Fast Presynaptic Noise in Attractor Neural Networks

Neural networks with fast time-variation of synapses

Nonequilibrium phase transitions and tricriticality in a three-dimensional lattice system with random-field competing kinetics

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