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May 21, 2012
05/12

by
John Hertz

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Topics: Neural computers., Neural networks (Neurobiology)

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Jul 20, 2013
07/13

by
Zhaoping Li; John Hertz

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We present a model of a coupled system of the olfactory bulb and cortex. Odor inputs to the epithelium are transformed to oscillatory bulbar activities. The cortex recognizes the odor by resonating to the bulbar oscillating pattern when the amplitude and phase patterns from the bulb match an odor memory stored in the intracortical synapses. We assume a cortical structure which transforms the odor information in the oscillatory pattern to a slow DC feedback signal to the bulb. This feedback...

Source: http://arxiv.org/abs/physics/9902052v1

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Sep 21, 2013
09/13

by
Joanna Tyrcha; John Hertz

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We derive learning rules for finding the connections between units in stochastic dynamical networks from the recorded history of a ``visible'' subset of the units. We consider two models. In both of them, the visible units are binary and stochastic. In one model the ``hidden'' units are continuous-valued, with sigmoidal activation functions, and in the other they are binary and stochastic like the visible ones. We derive exact learning rules for both cases. For the stochastic case, performing...

Source: http://arxiv.org/abs/1301.7274v1

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Sep 18, 2013
09/13

by
Zhaoping Li; John Hertz

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We present a model of an olfactory system that performs odor segmentation. Based on the anatomy and physiology of natural olfactory systems, it consists of a pair of coupled modules, bulb and cortex. The bulb encodes the odor inputs as oscillating patterns. The cortex functions as an associative memory: When the input from the bulb matches a pattern stored in the connections between its units, the cortical units resonate in an oscillatory pattern characteristic of that odor. Further circuitry...

Source: http://arxiv.org/abs/cond-mat/0002289v1

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Sep 22, 2013
09/13

by
Yasser Roudi; John Hertz

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We derive and study dynamical TAP equations for Ising spin glasses obeying both synchronous and asynchronous dynamics using a generating functional approach. The system can have an asymmetric coupling matrix, and the external fields can be time-dependent. In the synchronously updated model, the TAP equations take the form of self consistent equations for magnetizations at time $t+1$, given the magnetizations at time $t$. In the asynchronously updated model, the TAP equations determine the time...

Source: http://arxiv.org/abs/1103.1044v1

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Sep 17, 2013
09/13

by
Zoran Konkoli; John Hertz

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We study a random heteropolymer model with Langevin dynamics, in the supersymmetric formulation. Employing a procedure similar to one that has been used in static calculations, we construct an ensemble in which the affinity of the system for a native state is controlled by a "selection temperature" T0. In the limit of high T0, the model reduces to a random heteropolymer, while for T0-->0 the system is forced into the native state. Within the Gaussian variational approach that we...

Source: http://arxiv.org/abs/cond-mat/0207286v2

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Sep 24, 2013
09/13

by
Silvio Franz; John Hertz

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We study the off-equilibrium relaxational dynamics of the Amit-Roginsky $\phi^3$ field theory, for which the mode coupling approximation is exact. We show that complex phenomena such as aging and ergodicity breaking are present at low temperature, similarly to what is found in long range spin glasses. This is a generalization of mode coupling theory of the structural glass transition to off-equilibrium situations.

Source: http://arxiv.org/abs/cond-mat/9408079v1

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Sep 21, 2013
09/13

by
John Hertz; Alexander Lerchner; Mandana Ahmadi

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We review the use of mean field theory for describing the dynamics of dense, randomly connected cortical circuits. For a simple network of excitatory and inhibitory leaky integrate-and-fire neurons, we can show how the firing irregularity, as measured by the Fano factor, increases with the strength of the synapses in the network and with the value to which the membrane potential is reset after a spike. Generalizing the model to include conductance-based synapses gives insight into the...

Source: http://arxiv.org/abs/q-bio/0402023v1

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Sep 21, 2013
09/13

by
John Hertz; Yasser Roudi; Joanna Tyrcha

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Now that spike trains from many neurons can be recorded simultaneously, there is a need for methods to decode these data to learn about the networks that these neurons are part of. One approach to this problem is to adjust the parameters of a simple model network to make its spike trains resemble the data as much as possible. The connections in the model network can then give us an idea of how the real neurons that generated the data are connected and how they influence each other. In this...

Source: http://arxiv.org/abs/1106.1752v1

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Sep 21, 2013
09/13

by
Alexander Lerchner; Mandana Ahmadi; John Hertz

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Measured responses from visual cortical neurons show that spike times tend to be correlated rather than exactly Poisson distributed. Fano factors vary and are usually greater than 1 due to the tendency of spikes being clustered into bursts. We show that this behavior emerges naturally in a balanced cortical network model with random connectivity and conductance-based synapses. We employ mean field theory with correctly colored noise to describe temporal correlations in the neuronal activity....

Source: http://arxiv.org/abs/q-bio/0402026v1

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Sep 18, 2013
09/13

by
Zoran Konkoli; John Hertz; Silvio Franz

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We study the Langevin dynamics of the standard random heteropolymer model by mapping the problem to a supersymmetric field theory using the Martin-Siggia-Rose formalism. The resulting model is solved non-perturbatively employing a Gaussian variational approach. In constructing the solution, we assume that the chain is very long and impose the translational invariance which is expected to be present in the bulk of the globule by averaging over the center the of mass coordinate. In this way we...

Source: http://arxiv.org/abs/cond-mat/0101406v2

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Sep 18, 2013
09/13

by
John Hertz; Barry Richmond; Kristian Nilsen

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We use mean field theory to study the response properties of a simple randomly-connected model cortical network of leaky integrate-and-fire neurons with balanced excitation and inhibition. The formulation permits arbitrary temporal variation of the input to the network and takes exact account of temporal firing correlations. We find that neuronal firing statistics depend sensitively on the firing threshold. In particular, spike count variances can be either significantly greater than or...

Source: http://arxiv.org/abs/cond-mat/0202145v1

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Sep 21, 2013
09/13

by
Yasser Roudi; Erik Aurell; John Hertz

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Statistical models for describing the probability distribution over the states of biological systems are commonly used for dimensional reduction. Among these models, pairwise models are very attractive in part because they can be fit using a reasonable amount of data: knowledge of the means and correlations between pairs of elements in the system is sufficient. Not surprisingly, then, using pairwise models for studying neural data has been the focus of many studies in recent years. In this...

Source: http://arxiv.org/abs/0905.1410v1

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Sep 22, 2013
09/13

by
Silvia Scarpetta; Zhaoping Li; John Hertz

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We introduce a model of generalized Hebbian learning and retrieval in oscillatory neural networks modeling cortical areas such as hippocampus and olfactory cortex. Recent experiments have shown that synaptic plasticity depends on spike timing, especially on synapses from excitatory pyramidal cells, in hippocampus and in sensory and cerebellar cortex. Here we study how such plasticity can be used to form memories and input representations when the neural dynamics are oscillatory, as is common in...

Source: http://arxiv.org/abs/cond-mat/0111034v1

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Sep 21, 2013
09/13

by
Yasser Roudi; Joanna Tyrcha; John Hertz

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We study pairwise Ising models for describing the statistics of multi-neuron spike trains, using data from a simulated cortical network. We explore efficient ways of finding the optimal couplings in these models and examine their statistical properties. To do this, we extract the optimal couplings for subsets of size up to 200 neurons, essentially exactly, using Boltzmann learning. We then study the quality of several approximate methods for finding the couplings by comparing their results with...

Source: http://arxiv.org/abs/0902.2885v1

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3.0

Jun 30, 2018
06/18

by
Stojan Jovanović; John Hertz; Stefan Rotter

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We derive explicit, closed-form expressions for the cumulant densities of a multivariate, self-exciting Hawkes point process, generalizing a result of Hawkes in his earlier work on the covariance density and Bartlett spectrum of such processes. To do this, we represent the Hawkes process in terms of a Poisson cluster process and show how the cumulant density formulas can be derived by enumerating all possible "family trees", representing complex interactions between point events. We...

Topics: Physics, Quantitative Biology, Statistics, Neurons and Cognition, Mathematics, Statistics Theory,...

Source: http://arxiv.org/abs/1409.5353

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28

Sep 20, 2013
09/13

by
Hans C. Fogedby; John Hertz; Axel Svane

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We present a dynamical description and analysis of non-equilibrium transitions in the noisy one-dimensional Ginzburg-Landau equation for an extensive system based on a weak noise canonical phase space formulation of the Freidlin-Wentzel or Martin-Siggia-Rose methods. We derive propagating nonlinear domain wall or soliton solutions of the resulting canonical field equations with superimposed diffusive modes. The transition pathways are characterized by the nucleations and subsequent propagation...

Source: http://arxiv.org/abs/cond-mat/0404508v1

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Sep 18, 2013
09/13

by
Hans C. Fogedby; John Hertz; Axel Svane

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We present a dynamical description and analysis of non-equilibrium transitions in the noisy Ginzburg-Landau equation based on a canonical phase space formulation. The transition pathways are characterized by nucleation and subsequent propagation of domain walls or solitons. We also evaluate the Arrhenius factor in terms of an associated action and find good agreement with recent numerical optimization studies.

Source: http://arxiv.org/abs/cond-mat/0212546v1

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44

Sep 18, 2013
09/13

by
Hong-Li Zeng; John Hertz; Yasser Roudi

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The couplings in a sparse asymmetric, asynchronous Ising network are reconstructed using an exact learning algorithm. L$_1$ regularization is used to remove the spurious weak connections that would otherwise be found by simply minimizing the minus likelihood of a finite data set. In order to see how L$_1$ regularization works in detail, we perform the calculation in several ways including (1) by iterative minimization of a cost function equal to minus the log likelihood of the data plus an...

Source: http://arxiv.org/abs/1211.3671v1

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38

Sep 21, 2013
09/13

by
Jason Sakellariou; Yasser Roudi; Marc Mezard; John Hertz

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We study how the degree of symmetry in the couplings influences the performance of three mean field methods used for solving the direct and inverse problems for generalized Sherrington-Kirkpatrick models. In this context, the direct problem is predicting the potentially time-varying magnetizations. The three theories include the first and second order Plefka expansions, referred to as naive mean field (nMF) and TAP, respectively, and a mean field theory which is exact for fully asymmetric...

Source: http://arxiv.org/abs/1106.0452v1

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Jul 20, 2013
07/13

by
Joanna Tyrcha; Yasser Roudi; Matteo Marsili; John Hertz

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Neurons subject to a common non-stationary input may exhibit a correlated firing behavior. Correlations in the statistics of neural spike trains also arise as the effect of interaction between neurons. Here we show that these two situations can be distinguished, with machine learning techniques, provided the data are rich enough. In order to do this, we study the problem of inferring a kinetic Ising model, stationary or nonstationary, from the available data. We apply the inference procedure to...

Source: http://arxiv.org/abs/1203.5673v2

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2.0

Jun 30, 2018
06/18

by
Claudia Battistin; John Hertz; Joanna Tyrcha; Yasser Roudi

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We propose a new algorithm for inferring the state of hidden spins and reconstructing the connections in a synchronous kinetic Ising model, given the observed history. Focusing on the case in which the hidden spins are conditionally independent of each other given the state of observable spins, we show that calculating the likelihood of the data can be simplified by introducing a set of replicated auxiliary spins. Belief Propagation (BP) and Susceptibility Propagation (SusP) can then be used to...

Topics: Statistical Mechanics, Data Analysis, Statistics and Probability, Physics, Disordered Systems and...

Source: http://arxiv.org/abs/1412.1727

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Sep 21, 2013
09/13

by
Alexander Lerchner; Cristina Ursta; John Hertz; Mandana Ahmadi; Pauline Ruffiot

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We study the spike statistics of neurons in a network with dynamically balanced excitation and inhibition. Our model, intended to represent a generic cortical column, comprises randomly connected excitatory and inhibitory leaky integrate-and-fire neurons, driven by excitatory input from an external population. The high connectivity permits a mean-field description in which synaptic currents can be treated as Gaussian noise, the mean and autocorrelation function of which are calculated...

Source: http://arxiv.org/abs/q-bio/0402022v1

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Sep 18, 2013
09/13

by
Hong-Li Zeng; Mikko Alava; Erik Aurell; John Hertz; Yasser Roudi

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We describe how the couplings in an asynchronous kinetic Ising model can be inferred. We consider two cases, one in which we know both the spin history and the update times and one in which we only know the spin history. For the first case, we show that one can average over all possible choices of update times to obtain a learning rule that depends only on spin correlations and can also be derived from the equations of motion for the correlations. For the second case, the same rule can be...

Source: http://arxiv.org/abs/1209.2401v3