On the Maximization of Information Flow Between Spiking Neurons

2009 ◽  
Vol 21 (11) ◽  
pp. 2991-3009 ◽  
Author(s):  
Lucas C. Parra ◽  
Jeffrey M. Beck ◽  
Anthony J. Bell
Keyword(s):  
Joint Distribution ◽  
Point Processes ◽  
Joint Probability ◽  
Learning Rule ◽  
Spike Trains ◽  
Spiking Neurons ◽  
Joint Probability Distribution ◽  
Statistical Structure ◽  
Spiking Network ◽  
Efficient Representation

A feedforward spiking network represents a nonlinear transformation that maps a set of input spikes to a set of output spikes. This mapping transforms the joint probability distribution of incoming spikes into a joint distribution of output spikes. We present an algorithm for synaptic adaptation that aims to maximize the entropy of this output distribution, thereby creating a model for the joint distribution of the incoming point processes. The learning rule that is derived depends on the precise pre- and postsynaptic spike timings. When trained on correlated spike trains, the network learns to extract independent spike trains, thereby uncovering the underlying statistical structure and creating a more efficient representation of the incoming spike trains.

Correlation structure of teletraffic measurements from randomly-scanned calls arrival data

1980 ◽  
Vol 17 (01) ◽  
pp. 203-217
Author(s):  
P. A. Lee
Keyword(s):  
Probability Distribution ◽  
Explicit Expression ◽  
Correlation Coefficient ◽  
Point Processes ◽  
Joint Probability ◽  
Correlation Structure ◽  
Arrival Process ◽  
Joint Probability Distribution ◽  
Interarrival Times ◽  
Stochastic Point Processes

In teletraffic measurements, a call arrival process is commonly studied using a method with time-uniform or periodic scanning. The information recorded is the number of calls arrived between the scannings, from which data the number of scans between two successive calls is obtained. These later numbers are used as a measure of the interarrival times. For an exponential call arrival process, except in the case of Poisson scanning, all other scanning schemes yield the number of scans which are not independent in any two interarrival intervals. By treating the problem as an interaction of two stationary stochastic point processes, we determine the exact joint probability distribution of the number of scans in two adjacent and non-adjacent interarrival intervals. An explicit expression for the correlation coefficient is also obtained.

Correlation structure of teletraffic measurements from randomly-scanned calls arrival data

1980 ◽  
Vol 17 (1) ◽  
pp. 203-217
Author(s):  
P. A. Lee
Keyword(s):  
Probability Distribution ◽  
Explicit Expression ◽  
Correlation Coefficient ◽  
Point Processes ◽  
Joint Probability ◽  
Correlation Structure ◽  
Arrival Process ◽  
Joint Probability Distribution ◽  
Interarrival Times ◽  
Stochastic Point Processes

In teletraffic measurements, a call arrival process is commonly studied using a method with time-uniform or periodic scanning. The information recorded is the number of calls arrived between the scannings, from which data the number of scans between two successive calls is obtained. These later numbers are used as a measure of the interarrival times.For an exponential call arrival process, except in the case of Poisson scanning, all other scanning schemes yield the number of scans which are not independent in any two interarrival intervals. By treating the problem as an interaction of two stationary stochastic point processes, we determine the exact joint probability distribution of the number of scans in two adjacent and non-adjacent interarrival intervals. An explicit expression for the correlation coefficient is also obtained.

scholarly journals Joint Fluctuation Theorems for Sequential Heat Exchange

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 763 ◽  
Author(s):  
Jader Santos ◽  
André Timpanaro ◽  
Gabriel Landi
Keyword(s):  
Heat Exchange ◽  
Joint Distribution ◽  
Bubble Chamber ◽  
Joint Probability ◽  
Fluctuation Theorem ◽  
Joint Probability Distribution ◽  
Fluctuation Theorems ◽  
Natural Tendency ◽  
Multiple Collisions ◽  
Heat Exchanges

We study the statistics of heat exchange of a quantum system that collides sequentially with an arbitrary number of ancillas. This can describe, for instance, an accelerated particle going through a bubble chamber. Unlike other approaches in the literature, our focus is on the joint probability distribution that heat Q 1 is exchanged with ancilla 1, heat Q 2 is exchanged with ancilla 2, and so on. This allows us to address questions concerning the correlations between the collisional events. For instance, if in a given realization a large amount of heat is exchanged with the first ancilla, then there is a natural tendency for the second exchange to be smaller. The joint distribution is found to satisfy a Fluctuation theorem of the Jarzynski–Wójcik type. Rather surprisingly, this fluctuation theorem links the statistics of multiple collisions with that of independent single collisions, even though the heat exchanges are statistically correlated.

scholarly journals Surface Temperature Gradients as Diagnostic Indicators of Midlatitude Circulation Dynamics

2012 ◽  
Vol 25 (12) ◽  
pp. 4154-4171 ◽  
Author(s):  
Christina Karamperidou ◽  
Francesco Cioffi ◽  
Upmanu Lall
Keyword(s):  
Surface Temperature ◽  
Joint Distribution ◽  
Large Scale ◽  
Joint Probability ◽  
Temperature Gradients ◽  
Joint Probability Distribution ◽  
Jet Stream ◽  
Climate Conditions ◽  
Atmospheric Circulation Patterns ◽  
Circulation Patterns

Abstract Zonal and meridional surface temperature gradients are considered to be determinants of large-scale atmospheric circulation patterns. However, there has been limited investigation of these gradients as diagnostic aids. Here, the twentieth-century variability in the Northern Hemisphere equator-to-pole temperature gradient (EPG) and the ocean–land temperature contrast (OLC) is explored. A secular trend in decreasing EPG and OLC is noted. Decadal and interannual (ENSO-related) variations in the joint distribution of EPG and OLC are identified, hinting at multistable climate states that may be indigenous to the climate or due to changing boundary forcings. The NH circulation patterns for cases in the tails of the joint distribution of EPG and OLC are also seen to be different. Given this context, this paper extends past efforts to develop insights into jet stream dynamics using the Lorenz-1984 model, which is forced directly and only by EPG and OLC. The joint probability distribution of jet stream and eddy energy, conditional on EPG and OLC scenarios, is investigated. The scenarios correspond to (i) warmer versus colder climate conditions and (ii) polarized ENSO phases. The latter scenario involves the use of a heuristic ENSO model to drive the Lorenz-1984 model via a modulation of the EPG or the OLC. As with GCMs, the low-order model reveals that the response to El Niño forcing is not similar to an anthropogenic warming signature. The potential uses of EPG and OLC as macro-level indicators of climate change and variability and for comparing results across GCMs and observations are indicated.

scholarly journals On the distribution of an arbitrary subset of the eigenvalues for some finite dimensional random matrices

2019 ◽  
Vol 09 (01) ◽  
pp. 2040004
Author(s):  
Marco Chiani ◽  
Alberto Zanella
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Random Matrices ◽  
Probability Distribution Function ◽  
Joint Distribution ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Arbitrary Subset ◽  
Finite Dimensional ◽  
Joint Probability Distribution Function

We present some new results on the joint distribution of an arbitrary subset of the ordered eigenvalues of complex Wishart, double Wishart, and Gaussian hermitian random matrices of finite dimensions, using a tensor pseudo-determinant operator. Specifically, we derive compact expressions for the joint probability distribution function of the eigenvalues and the expectation of functions of the eigenvalues, including joint moments, for the case of both ordered and unordered eigenvalues.

JOINT DISTRIBUTIONS OF PORTFOLIO LOSSES AND EXOTIC PORTFOLIO PRODUCTS

2007 ◽  
Vol 10 (04) ◽  
pp. 733-748 ◽  
Author(s):  
FRIEDEL EPPLE ◽  
SAM MORGAN ◽  
LUTZ SCHLOEGL
Keyword(s):  
Probability Distribution ◽  
Joint Distribution ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Market Prices ◽  
Joint Distributions ◽  
Time Horizons ◽  
Path Dependent

The pricing of exotic portfolio products, e.g. path-dependent CDO tranches, relies on the joint probability distribution of portfolio losses at different time horizons. We discuss a range of methods to construct the joint distribution in a way that is consistent with market prices of vanilla CDO tranches. As an example, we show how our loss-linking methods provide estimates for the breakeven spreads of forward-starting tranches. .

scholarly journals Graphical Model Market Maker for Combinatorial Prediction Markets

2018 ◽  
Vol 63 ◽  
pp. 421-460
Author(s):  
Kathryn Blackmond Laskey ◽  
Wei Sun ◽  
Robin Hanson ◽  
Charles Twardy ◽  
Shou Matsumoto ◽  
...  
Keyword(s):  
Probability Distribution ◽  
Joint Distribution ◽  
Graphical Model ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Prediction Markets ◽  
Probability Models ◽  
Prediction Market ◽  
Market Mechanisms ◽  
Inference Algorithms

We describe algorithms for use by prediction markets in forming a crowd consensus joint probability distribution over thousands of related events. Equivalently, we describe market mechanisms to efficiently crowdsource both structure and parameters of a Bayesian network. Prediction markets are among the most accurate methods to combine forecasts; forecasters form a consensus probability distribution by trading contingent securities. A combinatorial prediction market forms a consensus joint distribution over many related events by allowing conditional trades or trades on Boolean combinations of events. Explicitly representing the joint distribution is infeasible, but standard inference algorithms for graphical probability models render it tractable for large numbers of base events. We show how to adapt these algorithms to compute expected assets conditional on a prospective trade, and to find the conditional state where a trader has minimum assets, allowing full asset reuse. We compare the performance of three algorithms: the straightforward algorithm from the DAGGRE (Decomposition-Based Aggregation) prediction market for geopolitical events, the simple block-merge model from the SciCast market for science and technology forecasting, and a more sophisticated algorithm we developed for future markets.

scholarly journals Learning precise spatiotemporal sequences via biophysically realistic learning rules in a modular, spiking network

eLife ◽  
2021 ◽  
Vol 10 ◽  
Author(s):  
Ian Cone ◽  
Harel Z Shouval
Keyword(s):  
Learning And Memory ◽  
Learning Rule ◽  
Brain Regions ◽  
Spiking Neurons ◽  
Variable Order ◽  
Extended Version ◽  
Learning Rules ◽  
Spiking Network ◽  
Discrete Sequences ◽  
Temporal Sequences

Multiple brain regions are able to learn and express temporal sequences, and this functionality is an essential component of learning and memory. We propose a substrate for such representations via a network model that learns and recalls discrete sequences of variable order and duration. The model consists of a network of spiking neurons placed in a modular microcolumn based architecture. Learning is performed via a biophysically realistic learning rule that depends on synaptic ‘eligibility traces’. Before training, the network contains no memory of any particular sequence. After training, presentation of only the first element in that sequence is sufficient for the network to recall an entire learned representation of the sequence. An extended version of the model also demonstrates the ability to successfully learn and recall non-Markovian sequences. This model provides a possible framework for biologically plausible sequence learning and memory, in agreement with recent experimental results.

scholarly journals Impact of Noise on Retinal Coding of Visual Signals

2004 ◽  
Vol 92 (2) ◽  
pp. 1023-1033 ◽  
Author(s):  
Christopher L. Passaglia ◽  
John B. Troy
Keyword(s):  
Visual Cortex ◽  
Probability Distribution ◽  
Information Transmission ◽  
Primary Visual Cortex ◽  
Joint Probability ◽  
Spike Trains ◽  
Visual Signals ◽  
Joint Probability Distribution ◽  
Noise Power ◽  
Neural Noise

Neural noise introduces uncertainty about the signals encoded in neural spike trains. Because of the uncertainty neurons can reliably transmit a limited amount of information. This amount is difficult to quantify for neurons that combine signals and noise in a complex manner, as many trials would be needed to estimate the joint probability distribution of stimulus and neural response accurately. The task is experimentally tractable, however, for neurons that combine signals with additive Gaussian noise. For such neurons, the joint probability distribution is well defined and information transmission rates can be computed from estimates of signal-to-noise ratio. Here we use power spectral analysis to specify the contributions of signal and noise to retinal coding of visual information. We show that in the spike trains of cat ganglion cells noise power is minimal and constant at temporal frequencies from 0.3 to 20 Hz and that it increases at higher frequencies to a plateau level that generally depends on stimulus contrast. We also show that trial-to-trial fluctuations in noise amplitude at different frequencies are uncorrelated and normally distributed. Although the contrast dependence indicates that noise at high temporal frequencies contributes nonlinearly to ganglion cell spike trains, cells in the primary visual cortex are not known to respond to stimulus modulations >20 Hz. Hence, noise in the retinal output would appear additive, white, and Gaussian from their perspective. This greatly simplifies analysis of information transmission from the eye to the primary visual cortex and perhaps other regions of the brain.

scholarly journals Age-dependence and aging-dependence: The case of neuronal loss and lifespan in a C. elegans model of Parkinson’s disease

2017 ◽  
Author(s):  
Javier Apfeld ◽  
Walter Fontana
Keyword(s):  
Parkinson’S Disease ◽  
Parkinson's Disease ◽  
Joint Distribution ◽  
Disease Onset ◽  
Joint Probability ◽  
Neuronal Loss ◽  
Joint Probability Distribution ◽  
Age Dependence ◽  
C Elegans ◽  
Age Dependent

It is often assumed, but not established, that the major neurodegenerative diseases, such as Parkinson’s disease, are not just age-dependent (their incidence changes with time) but actually aging-dependent (their incidence is coupled to the process that determines lifespan). To determine a dependence on the aging process requires the joint probability distribution of disease onset and lifespan. For human Parkinson’s disease, such a joint distribution is not available because the disease cuts lifespan short. To acquire a joint distribution, we resorted to an established C. elegans model of Parkinson’s disease in which the loss of dopaminergic neurons is not fatal. We find that lifespan is not correlated with the loss of neurons and that a lifespan-extending intervention into insulin/IGF1 signaling accelerates neuronal loss, while leaving death and neuronal loss times uncorrelated. This suggests that distinct and compartmentalized instances of the same genetically encoded insulin/IGF1 signaling machinery act independently to control neurodegeneration and lifespan in C. elegans. Although the human context might well be different, our study calls attention to maintaining a rigorous distinction between age-dependence and aging-dependence.

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