scholarly journals First Passage Time Memory Lifetimes for Simple, Multistate Synapses

2017 ◽  
Vol 29 (12) ◽  
pp. 3219-3259 ◽  
Author(s):  
Terry Elliott
Keyword(s):  
Optimality Conditions ◽  
Signal To Noise Ratio ◽  
First Passage Time ◽  
Planck Equation ◽  
Memory Systems ◽  
Passage Time ◽  
Memory Storage ◽  
First Passage ◽  
Firing Properties ◽  
Superior Approach

Memory models based on synapses with discrete and bounded strengths store new memories by forgetting old ones. Memory lifetimes in such memory systems may be defined in a variety of ways. A mean first passage time (MFPT) definition overcomes much of the arbitrariness and many of the problems associated with the more usual signal-to-noise ratio (SNR) definition. We have previously computed MFPT lifetimes for simple, binary-strength synapses that lack internal, plasticity-related states. In simulation we have also seen that for multistate synapses, optimality conditions based on SNR lifetimes are absent with MFPT lifetimes, suggesting that such conditions may be artifactual. Here we extend our earlier work by computing the entire first passage time (FPT) distribution for simple, multistate synapses, from which all statistics, including the MFPT lifetime, may be extracted. For this, we develop a Fokker-Planck equation using the jump moments for perceptron activation. Two models are considered that satisfy a particular eigenvector condition that this approach requires. In these models, MFPT lifetimes do not exhibit optimality conditions, while in one but not the other, SNR lifetimes do exhibit optimality. Thus, not only are such optimality conditions artifacts of the SNR approach, but they are also strongly model dependent. By examining the variance in the FPT distribution, we may identify regions in which memory storage is subject to high variability, although MFPT lifetimes are nevertheless robustly positive. In such regions, SNR lifetimes are typically (defined to be) zero. FPT-defined memory lifetimes therefore provide an analytically superior approach and also have the virtue of being directly related to a neuron's firing properties.

First-Passage Time for Oscillators With Nonlinear Damping

1978 ◽  
Vol 45 (1) ◽  
pp. 175-180 ◽  
Author(s):  
J. B. Roberts
Keyword(s):  
First Passage Time ◽  
Digital Simulation ◽  
Planck Equation ◽  
Passage Time ◽  
Nonlinear Damping ◽  
First Passage ◽  
One Dimensional ◽  
Fokker Planck Equation ◽  
First Passage Failure ◽  
Fokker Planck

A simple numerical scheme is proposed for computing the probability of first passage failure, P(T), in an interval O-T, for oscillators with nonlinear damping. The method depends on the fact that, when the damping is light, the amplitude envelope, A(t), can be accurately approximated as a one-dimensional Markov process. Hence, estimates of P(T) are found, for both single and double-sided barriers, by solving the Fokker-Planck equation for A(t) with an appropriate absorbing barrier. The numerical solution of the Fokker-Planck equation is greatly simplified by using a discrete time random walk analog of A(t), with appropriate statistical properties. Results obtained by this method are compared with corresponding digital simulation estimates, in typical cases.

scholarly journals Thermal dynamic phase transition of Reissner-Nordström Anti-de Sitter black holes on free energy landscape

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Ran Li ◽  
Kun Zhang ◽  
Jin Wang
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Free Energy ◽  
First Passage Time ◽  
Energy Landscape ◽  
Planck Equation ◽  
Passage Time ◽  
Free Energy Landscape ◽  
De Sitter ◽  
First Passage

Abstract We explore the thermodynamics and the underlying kinetics of the van der Waals type phase transition of Reissner-Nordström anti-de Sitter (RNAdS) black holes based on the free energy landscape. We show that the thermodynamic stabilities of the three branches of the RNAdS black holes are determined by the underlying free energy landscape topography. We suggest that the large (small) RNAdS black hole can have the probability to switch to the small (large) black hole due to the thermal fluctuation. Such a state switching process under the thermal fluctuation is taken as a stochastic process and the associated kinetics can be described by the probabilistic Fokker-Planck equation. We obtained the time dependent solutions for the probabilistic evolution by numerically solving Fokker-Planck equation with the reflecting boundary conditions. We also investigated the first passage process which describes how fast a system undergoes a stochastic process for the first time. The distributions of the first passage time switching from small (large) to large (small) black hole and the corresponding mean first passage time as well as its fluctuations at different temperatures are studied in detail. We conclude that the mean first passage time and its fluctuations are related to the free energy landscape topography through barrier heights and temperatures.

First passage time distribution of a Wiener process with drift concerning two elastic barriers

1996 ◽  
Vol 33 (01) ◽  
pp. 164-175 ◽  
Author(s):  
Marco Dominé
Keyword(s):  
Explicit Expression ◽  
Wiener Process ◽  
Time Distribution ◽  
First Passage Time ◽  
Planck Equation ◽  
Passage Time ◽  
Special Choice ◽  
First Passage ◽  
Special Cases ◽  
Reflecting Barriers

We solve the Fokker-Planck equation for the Wiener process with drift in the presence of elastic boundaries and a fixed start point. An explicit expression is obtained for the first passage density. The cases with pure absorbing and/or reflecting barriers arise for a special choice of a parameter constellation. These special cases are compared with results in Darling and Siegert [5] and Sweet and Hardin [15].

scholarly journals Variations on the Theme of Synaptic Filtering: A Comparison of Integrate-and-Express Models of Synaptic Plasticity for Memory Lifetimes

2016 ◽  
Vol 28 (11) ◽  
pp. 2393-2460 ◽  
Author(s):  
Terry Elliott
Keyword(s):  
Synaptic Plasticity ◽  
Parameter Space ◽  
Signal To Noise Ratio ◽  
First Passage Time ◽  
Passage Time ◽  
Memory Storage ◽  
Relevant Parameter ◽  
Filter Model ◽  
Biologically Relevant ◽  
Consecutive Number

Integrate-and-express models of synaptic plasticity propose that synapses integrate plasticity induction signals before expressing synaptic plasticity. By discerning trends in their induction signals, synapses can control destabilizing fluctuations in synaptic strength. In a feedforward perceptron framework with binary-strength synapses for associative memory storage, we have previously shown that such a filter-based model outperforms other, nonintegrative, “cascade”-type models of memory storage in most regions of biologically relevant parameter space. Here, we consider some natural extensions of our earlier filter model, including one specifically tailored to binary-strength synapses and one that demands a fixed, consecutive number of same-type induction signals rather than merely an excess before expressing synaptic plasticity. With these extensions, we show that filter-based models outperform nonintegrative models in all regions of biologically relevant parameter space except for a small sliver in which all models encode memories only weakly. In this sliver, which model is superior depends on the metric used to gauge memory lifetimes (whether a signal-to-noise ratio or a mean first passage time). After comparing and contrasting these various filter models, we discuss the multiple mechanisms and timescales that underlie both synaptic plasticity and memory phenomena and suggest that multiple, different filtering mechanisms may operate at single synapses.

scholarly journals Mean First Passage Memory Lifetimes by Reducing Complex Synapses to Simple Synapses

2017 ◽  
Vol 29 (6) ◽  
pp. 1468-1527 ◽  
Author(s):  
Terry Elliott
Keyword(s):  
Synaptic Plasticity ◽  
First Passage Time ◽  
Passage Time ◽  
Memory Models ◽  
Memory Storage ◽  
First Passage ◽  
Internal States ◽  
Low Pass ◽  
Complex Models ◽  
Low Pass Filters

Memory models that store new memories by forgetting old ones have memory lifetimes that are rather short and grow only logarithmically in the number of synapses. Attempts to overcome these deficits include “complex” models of synaptic plasticity in which synapses possess internal states governing the expression of synaptic plasticity. Integrate-and-express, filter-based models of synaptic plasticity propose that synapses act as low-pass filters, integrating plasticity induction signals before expressing synaptic plasticity. Such mechanisms enhance memory lifetimes, leading to an initial rise in the memory signal that is in radical contrast to other related, but nonintegrative, memory models. Because of the complexity of models with internal synaptic states, however, their dynamics can be more difficult to extract compared to “simple” models that lack internal states. Here, we show that by focusing only on processes that lead to changes in synaptic strength, we can integrate out internal synaptic states and effectively reduce complex synapses to simple synapses. For binary-strength synapses, these simplified dynamics then allow us to work directly in the transitions in perceptron activation induced by memory storage rather than in the underlying transitions in synaptic configurations. This permits us to write down master and Fokker-Planck equations that may be simplified under certain, well-defined approximations. These methods allow us to see that memory based on synaptic filters can be viewed as an initial transient that leads to memory signal rise, followed by the emergence of Ornstein-Uhlenbeck-like dynamics that return the system to equilibrium. We may use this approach to compute mean first passage time–defined memory lifetimes for complex models of memory storage.

scholarly journals The flight of the hornbill: drift and diffusion in arboreal avian movement

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ankit Vikrant ◽  
Janaki Balakrishnan ◽  
Rohit Naniwadekar ◽  
Aparajita Datta
Keyword(s):  
Diffusion Coefficients ◽  
Animal Movement ◽  
Anthropogenic Activities ◽  
First Passage Time ◽  
Mechanistic Model ◽  
Planck Equation ◽  
Passage Time ◽  
First Passage ◽  
Human Settlements ◽  
Fokker Planck

AbstractCapturing movement of animals in mathematical models has long been a keenly pursued direction of research1. Any good model of animal movement is built upon information about the animal’s environment and the available resources including whether prey is in abundance or scarce, densely distributed or sparse2. Such an approach could enable the identification of certain quantities or measures from the model that are species-specific characteristics. We propose here a mechanistic model to describe the movement of two species of Asian hornbills in a resource-abundant heterogenous landscape which includes degraded forests and human settlements. Hornbill telemetry data was used to this end. The birds show a bias both towards features of attraction such as nesting and roosting sites as well as possible bias away from points of repulsion such as human presence. These biases are accounted for with suitable potentials. The spatial patterns of movement are analyzed using the Fokker–Planck equation, which helps explain the variation in movement of different individuals. Search times to target locations were calculated using first passage time equations dual to the Fokker–Planck equations. We also find that the diffusion coefficients are larger for breeding birds than for non-breeding ones—a manifestation of repeated switching of directions to move back to the nest from foraging sites. The degree of directedness towards nests and roosts is captured by the drift coefficients. Non-breeding hornbills show similar values of the ratio of the two coefficients irrespective of the fact that their movement data is available from different seasons. Therefore, the ratio of drift to diffusion coefficients is indicative of an individual’s breeding status, as seen from available data. It could possibly also characterize different species. For all individuals, first passage times increase with proximity to human settlements, in agreement with the premise that anthropogenic activities close to nesting/roosting sites are not desirable.

Non-Markovian Fokker-Planck equation: Solutions and first passage time distribution

2006 ◽  
Vol 73 (3) ◽  
Author(s):  
P. C. Assis ◽  
R. P. de Souza ◽  
P. C. da Silva ◽  
L. R. da Silva ◽  
L. S. Lucena ◽  
...  
Keyword(s):  
Time Distribution ◽  
First Passage Time ◽  
Planck Equation ◽  
Passage Time ◽  
First Passage ◽  
Fokker Planck Equation ◽  
Fokker Planck

The mean first passage time and stochastic resonance in gene transcriptional system with time delay

2016 ◽  
Vol 30 (11) ◽  
pp. 1650067 ◽  
Author(s):  
Y. L. Feng ◽  
J. Zhu ◽  
M. Zhang ◽  
L. L. Gao ◽  
Y. F. Liu ◽  
...  
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
First Passage Time ◽  
Planck Equation ◽  
Passage Time ◽  
Noise Correlation ◽  
Mean First Passage Time ◽  
First Passage ◽  
The Mean ◽  
Correlation Strength

In this paper, the gene transcriptional dynamics driven by correlated noises are investigated, where the time delay for the synthesis of transcriptional factor is introduced. The effects of the noise correlation strength and time delay on the stationary probability distribution (SPD), the mean first passage time and the stochastic resonance (SR) are analyzed in detail based on the delay Fokker–Planck equation. It is found that both the time delay and noise correlation strength play important roles in the bistable transcriptional system. The effect of the correlation strength reduces but the time delay enhances the mean first passage time (MFPT). Finally, the SR for this gene transcriptional system is found to be enhanced by the time delay.

Exact propagator for a Fokker-Planck equation, first passage time distribution, and anomalous diffusion

2011 ◽  
Vol 52 (8) ◽  
pp. 083301 ◽  
Author(s):  
A. T. Silva ◽  
E. K. Lenzi ◽  
L. R. Evangelista ◽  
M. K. Lenzi ◽  
H. V. Ribeiro ◽  
...  
Keyword(s):  
Anomalous Diffusion ◽  
Time Distribution ◽  
First Passage Time ◽  
Planck Equation ◽  
Passage Time ◽  
First Passage ◽  
Fokker Planck Equation ◽  
Fokker Planck
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