scholarly journals A Mathematical Analysis of Memory Lifetime in a Simple Network Model of Memory

2020 ◽  
Vol 32 (7) ◽  
pp. 1322-1354
Author(s):  
Pascal Helson
Keyword(s):  
Markov Chains ◽  
Large Time ◽  
Recurrent Network ◽  
External Signal ◽  
Synaptic Currents ◽  
Probability Of Error ◽  
Initial Signal ◽  
Unique Signal ◽  
External Stimuli ◽  
Simple Network

We study the learning of an external signal by a neural network and the time to forget it when this network is submitted to noise. The presentation of an external stimulus to the recurrent network of binary neurons may change the state of the synapses. Multiple presentations of a unique signal lead to its learning. Then, during the forgetting time, the presentation of other signals (noise) may also modify the synaptic weights. We construct an estimator of the initial signal using the synaptic currents and in this way define a probability of error. In our model, these synaptic currents evolve as Markov chains. We study the dynamics of these Markov chains and obtain a lower bound on the number of external stimuli that the network can receive before the initial signal is considered forgotten (probability of error above a given threshold). Our results are based on a finite-time analysis rather than large-time asymptotic. We finally present numerical illustrations of our results.

Cross-Correlations in High-Conductance States of a Model Cortical Network

2010 ◽  
Vol 22 (2) ◽  
pp. 427-447 ◽  
Author(s):  
John Hertz
Keyword(s):  
Correlation Coefficients ◽  
Neuronal Firing ◽  
Synaptic Conductance ◽  
Synaptic Currents ◽  
High Conductance State ◽  
Systematic Behavior ◽  
Cross Correlations ◽  
Conductance States ◽  
Simple Network ◽  
High Conductance

Neuronal firing correlations are studied using simulations of a simple network model for a cortical column in a high-conductance state with dynamically balanced excitation and inhibition. Although correlations between individual pairs of neurons exhibit considerable heterogeneity, population averages show systematic behavior. When the network is in a stationary state, the average correlations are generically small: correlation coefficients are of order 1/N, where N is the number of neurons in the network. However, when the input to the network varies strongly in time, much larger values are found. In this situation, the network is out of balance, and the synaptic conductance is low, at times when the strongest firing occurs. However, examination of the correlation functions of synaptic currents reveals that after these bursts, balance is restored within a few milliseconds by a rapid increase in inhibitory synaptic conductance. These findings suggest an extension of the notion of the balanced state to include balanced fluctuations of synaptic currents, with a characteristic timescale of a few milliseconds.

Self-Organized Maps on Continuous Bump Attractors

2013 ◽  
Vol 8 (1) ◽  
pp. 234-247 ◽  
Author(s):  
К.П. Соловьева ◽  
K.P. Solovyeva
Keyword(s):  
Neural Network ◽  
Recurrent Neural Network ◽  
Recurrent Network ◽  
External Signal ◽  
Stable States ◽  
Factors Affecting ◽  
One Dimensional ◽  
Self Organized ◽  
The Neural Network ◽  
Winner Takes All

In this article, we describe a simple binary neuron system, which implements a self-organized map. The system consists of R input neurons (R receptors), and N output neurons of a recurrent neural network. The neural network has a quasi-continuous set of attractor states (one-dimensional “bump attractor”). Due to the dynamics of the network, each external signal (i.e. activity state of receptors) imposes transition of the recurrent network into one of its stable states (points of its attractor). That makes our system different from the “winner takes all” construction of T.Kohonen. In case, when there is a one-dimensional cyclical manifold of external signals in R-dimensional input space, and the recurrent neural network presents a complete ring of neurons with local excitatory connections, there exists a process of learning of connections between the receptors and the neurons of the recurrent network, which enables a topologically correct mapping of input signals into the stable states of the neural network. The convergence rate of learning and the role of noises and other factors affecting the described phenomenon has been evaluated in computational simulations.

Minimizing the learning loss in adaptive control of Markov chains under the weak accessibility condition

1991 ◽  
Vol 28 (04) ◽  
pp. 779-790 ◽  
Author(s):  
Rajeev Agrawal
Keyword(s):  
Adaptive Control ◽  
Maximum Likelihood ◽  
Markov Chains ◽  
Upper Bound ◽  
Unknown Parameter ◽  
Learning Loss ◽  
Probability Of Error ◽  
Control Scheme ◽  
Rate Of Decay ◽  
Randomized Control

We consider the adaptive control of Markov chains under the weak accessibility condition with a view to minimizing the learning loss. A certainty equivalence control with a forcing scheme is constructed. We use a stationary randomized control scheme for forcing and compute a maximum likelihood estimate of the unknown parameter from the resulting observations. We obtain an exponential upper bound on the rate of decay of the probability of error. This allows us to choose the rate of forcing appropriately, whereby we achieve a o(f(n) log n) learning loss for any function as .

scholarly journals Sex-specific topology of the nociceptive circuit shapes dimorphic behavior in C. elegans

2021 ◽  
Author(s):  
Vladyslava Pechuk ◽  
Gal Goldman ◽  
Yehuda Salzberg ◽  
Aditi H Chaubey ◽  
R Aaron Bola ◽  
...  
Keyword(s):  
Network Topology ◽  
Neural Circuit ◽  
Sensory Transduction ◽  
Sexually Dimorphic ◽  
Nociceptive Behavior ◽  
C Elegans ◽  
Network Topologies ◽  
External Stimuli ◽  
Dimorphic Behavior ◽  
Simple Network

How sexually dimorphic behavior is encoded in the nervous system is poorly understood. Here, we characterize the dimorphic nociceptive behavior in C. elegans and study the underlying circuits, which are composed of the same neurons but are wired differently. We show that while sensory transduction is similar in the two sexes, the downstream network topology markedly shapes behavior. We fit a network model that replicates the observed dimorphic behavior in response to external stimuli, and use it to predict simple network rewirings that would switch the behavior between the sexes. We then show experimentally that these subtle synaptic rewirings indeed flip behavior. Strikingly, when presented with aversive cues, rewired males were compromised in finding mating partners, suggesting that network topologies that enable efficient avoidance of noxious cues have a reproductive "cost". Our results present a deconstruction of the design of a neural circuit that controls sexual behavior, and how to reprogram it.

Minimizing the learning loss in adaptive control of Markov chains under the weak accessibility condition

1991 ◽  
Vol 28 (4) ◽  
pp. 779-790 ◽  
Author(s):  
Rajeev Agrawal
Keyword(s):  
Adaptive Control ◽  
Maximum Likelihood ◽  
Markov Chains ◽  
Upper Bound ◽  
Unknown Parameter ◽  
Learning Loss ◽  
Probability Of Error ◽  
Control Scheme ◽  
Rate Of Decay ◽  
Randomized Control

We consider the adaptive control of Markov chains under the weak accessibility condition with a view to minimizing the learning loss. A certainty equivalence control with a forcing scheme is constructed. We use a stationary randomized control scheme for forcing and compute a maximum likelihood estimate of the unknown parameter from the resulting observations. We obtain an exponential upper bound on the rate of decay of the probability of error. This allows us to choose the rate of forcing appropriately, whereby we achieve a o(f(n) log n) learning loss for any function as .

Lateral inhibition in a recurrent network

1997 ◽  
Author(s):  
William T. Farrar ◽  
Guy C. Van Orden
Keyword(s):  
Lateral Inhibition ◽  
Recurrent Network

Markov models—Markov chains

2019 ◽  
Vol 16 (8) ◽  
pp. 663-664 ◽  
Author(s):  
Jasleen K. Grewal ◽  
Martin Krzywinski ◽  
Naomi Altman
Keyword(s):  
Markov Chains ◽  
Markov Models

Structured Data Entry for Reliable Acquisition of Pharmacokinetic Data

1996 ◽  
Vol 35 (03) ◽  
pp. 261-264 ◽  
Author(s):  
T. Schromm ◽  
T. Frankewitsch ◽  
M. Giehl ◽  
F. Keller ◽  
D. Zellner
Keyword(s):  
Text Processing ◽  
Data Entry ◽  
Processing System ◽  
Database System ◽  
Structured Data ◽  
Pharmacokinetic Parameters ◽  
Pharmacokinetic Data ◽  
Probability Of Error ◽  
Error Frequency ◽  
Estimated Error

Abstract:A pharmacokinetic database was constructed that is as free of errors as possible. Pharmacokinetic parameters were derived from the literature using a text-processing system and a database system. A random data sample from each system was compared with the original literature. The estimated error frequencies using statistical methods differed significantly between the two systems. The estimated error frequency in the text-processing system was 7.2%, that in the database system 2.7%. Compared with the original values in the literature, the estimated probability of error for identical pharmacokinetic parameters recorded in both systems is 2.4% and is not significantly different from the error frequency in the database. Parallel data entry with a text-processing system and a database system is, therefore, not significantly better than structured data entry for reducing the error frequency.

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