Some renewal process models for single neuron discharge

1971 ◽  
Vol 8 (4) ◽  
pp. 802-808 ◽  
Author(s):  
Howard G. Hochman ◽  
Stephen E. Fienberg
Keyword(s):  
Single Neuron ◽  
Interspike Interval ◽  
Poisson Processes ◽  
Process Models ◽  
Recurrence Time ◽  
The Laplace Transform ◽  
Mean And Variance ◽  
The Mean ◽  
Interspike Interval Distribution ◽  
Interval Distribution

Leslie (1969) obtained the Laplace transform for the recurrence time of clusters of Poisson processes, which can be thought of as yielding the interspike interval distribution for a neuron that receives Poisson excitatory inputs subject to decay. Here, several extensions of this model are derived, each including Poisson inhibitory inputs. Expressions for the mean and variance are derived for each model, and the results for the different models are compared.

Some renewal process models for single neuron discharge

1971 ◽  
Vol 8 (04) ◽  
pp. 802-808
Author(s):  
Howard G. Hochman ◽  
Stephen E. Fienberg
Keyword(s):  
Single Neuron ◽  
Interspike Interval ◽  
Poisson Processes ◽  
Process Models ◽  
Recurrence Time ◽  
The Laplace Transform ◽  
Mean And Variance ◽  
The Mean ◽  
Interspike Interval Distribution ◽  
Interval Distribution

Leslie (1969) obtained the Laplace transform for the recurrence time of clusters of Poisson processes, which can be thought of as yielding the interspike interval distribution for a neuron that receives Poisson excitatory inputs subject to decay. Here, several extensions of this model are derived, each including Poisson inhibitory inputs. Expressions for the mean and variance are derived for each model, and the results for the different models are compared.

CLASSICAL-LIKE RESONANCE INDUCED BY NOISE IN A FITZHUGH–NAGUMO NEURON MODEL

1999 ◽  
Vol 09 (12) ◽  
pp. 2295-2303 ◽  
Author(s):  
S. RIPOLL MASSANÉS ◽  
C. J. PÉREZ VICENTE
Keyword(s):  
High Frequency ◽  
Interspike Interval ◽  
Low Frequency ◽  
Resonance Phenomenon ◽  
Characteristic Time Scale ◽  
Wide Range ◽  
External Stimuli ◽  
Interspike Interval Distribution ◽  
Stochastic Resonance Phenomenon ◽  
Interval Distribution

We have studied the stochastic behavior of Fitzhugh–Nagumo neuron-like model (FN) induced by subthreshold external stimuli. Our analysis based on three standard measures: the power spectrum, interspike interval distribution (ISI) and autocorrelation function shows that it is possible to define a characteristic time scale which can be identified in the response of the system for a wide range of frequencies. In contrast to previous studies we have focused our attention on high frequency signals which could be of interest for real systems such as nervous fibers in the auditory system. We report behaviors which resemble those of classical deterministic oscillators but never the stochastic resonance phenomenon typical of low frequency signals.

Improvements to the Sensitivity of Gravitational Clustering for Multiple Neuron Recordings

2000 ◽  
Vol 12 (11) ◽  
pp. 2597-2620 ◽  
Author(s):  
Stuart N. Baker ◽  
George L. Gerstein
Keyword(s):  
Interspike Interval ◽  
Simulation Method ◽  
Spike Trains ◽  
The Novel ◽  
Limited Data ◽  
Neuronal Synchrony ◽  
Gravitational Clustering ◽  
Using Data ◽  
Interspike Interval Distribution ◽  
Interval Distribution

We outline two improvements to the technique of gravitational clustering for detection of neuronal synchrony, which are capable of improving the method's detection of weak synchrony with limited data. The advantages of the enhancements are illustrated using data with known levels of synchrony and different interspike interval distributions. The novel simulation method described can easily generate such test data. An important dependence of the sensitivity of gravitational clustering to the interspike interval distribution of the analysed spike trains is described.

scholarly journals Maximum Likelihood Decoding of Neuronal Inputs from an Interspike Interval Distribution

2009 ◽  
Vol 21 (11) ◽  
pp. 3079-3105 ◽  
Author(s):  
Xuejuan Zhang ◽  
Gongqiang You ◽  
Tianping Chen ◽  
Jianfeng Feng
Keyword(s):  
Maximum Likelihood ◽  
Interspike Interval ◽  
Time Windows ◽  
Model Neuron ◽  
Maximum Likelihood Estimates ◽  
Maximum Likelihood Decoding ◽  
First Time ◽  
Lif Neuron ◽  
Interspike Interval Distribution ◽  
Interval Distribution

An expression for the probability distribution of the interspike interval of a leaky integrate-and-fire (LIF) model neuron is rigorously derived, based on recent theoretical developments in the theory of stochastic processes. This enables us to find for the first time a way of developing maximum likelihood estimates (MLE) of the input information (e.g., afferent rate and variance) for an LIF neuron from a set of recorded spike trains. Dynamic inputs to pools of LIF neurons both with and without interactions are efficiently and reliably decoded by applying the MLE, even within time windows as short as 25 msec.

Recurrence times of draft-patterns from reservoirs

1975 ◽  
Vol 12 (03) ◽  
pp. 647-652 ◽  
Author(s):  
G. G. S. Pegram
Keyword(s):  
Markov Chain ◽  
Discrete Time ◽  
Recurrence Time ◽  
Reservoir Model ◽  
Discrete State ◽  
Discrete Time Markov Chain ◽  
Recurrence Times ◽  
Mean And Variance ◽  
The Mean ◽  
Run Theory

Expressions for the mean and variance of the recurrence time of non-overlapping draft-patterns of draft from a Moran Reservoir Model (discrete-state and discrete-time Markov chain) are derived using Feller's Renewal argument. In addition an expression for the mean recurrence time for self-overlapping patterns of draft is derived using run-theory.

scholarly journals Markov-modulated Ornstein–Uhlenbeck processes

2016 ◽  
Vol 48 (1) ◽  
pp. 235-254 ◽  
Author(s):  
G. Huang ◽  
H. M. Jansen ◽  
M. Mandjes ◽  
P. Spreij ◽  
K. De Turck
Keyword(s):  
Markov Process ◽  
Integration Theory ◽  
Background Process ◽  
Finite State ◽  
The Laplace Transform ◽  
Mean And Variance ◽  
The Mean ◽  
Markov Modulated ◽  
Set Up ◽  
Functional Central Limit

Abstract In this paper we consider an Ornstein–Uhlenbeck (OU) process (M(t))t≥0 whose parameters are determined by an external Markov process (X(t))t≥0 on a finite state space {1, . . ., d}; this process is usually referred to as Markov-modulated Ornstein–Uhlenbeck. We use stochastic integration theory to determine explicit expressions for the mean and variance of M(t). Then we establish a system of partial differential equations (PDEs) for the Laplace transform of M(t) and the state X(t) of the background process, jointly for time epochs t = t1, . . ., tK. Then we use this PDE to set up a recursion that yields all moments of M(t) and its stationary counterpart; we also find an expression for the covariance between M(t) and M(t + u). We then establish a functional central limit theorem for M(t) for the situation that certain parameters of the underlying OU processes are scaled, in combination with the modulating Markov process being accelerated; interestingly, specific scalings lead to drastically different limiting processes. We conclude the paper by considering the situation of a single Markov process modulating multiple OU processes.

Haloperidol-induced suppression of carotid chemoreception in vitro

1985 ◽  
Vol 59 (3) ◽  
pp. 814-820 ◽  
Author(s):  
W. F. Nolan ◽  
D. F. Donnelly ◽  
E. J. Smith ◽  
R. E. Dutton
Keyword(s):  
Single Unit ◽  
Interspike Interval ◽  
Dose Dependency ◽  
Nerve Activity ◽  
Serial Dependency ◽  
Endogenous Dopamine ◽  
Reduced Frequency ◽  
Interspike Interval Distribution ◽  
Interval Distribution

Effects of antagonism of endogenous dopamine with haloperidol on single-unit frequency, interspike interval distribution, and interval serial dependency of the cat sinus nerve were tested using an in vitro carotid body-sinus nerve superfusion technique. A dose dependency of inhibition by haloperidol (0.05–2.0 microgram/ml) was observed. Superfusion with 1–2 microgram/ml haloperidol significantly reduced frequency within 5 min (P less than 0.05) and caused a complete cessation of firing within 25 min in 5 of 10 chemoreceptor units. Frequency recovered to control during drug washout. Acetylcholine (10-micrograms/ml superfusion or 500-micrograms bolus) increased sinus nerve activity under control conditions but not during superfusion with haloperidol. No effect of haloperidol on impulse serial dependency was detected. However, interval distribution was significantly altered by haloperidol in five of six chemoreceptor units. Our results suggest an excitatory role for dopamine in carotid chemoreception.

A dynamic role of rubral neurons in contact placing by the adult cat

1986 ◽  
Vol 56 (3) ◽  
pp. 835-856 ◽  
Author(s):  
D. E. Batson ◽  
V. E. Amassian
Keyword(s):  
Firing Rate ◽  
Red Nucleus ◽  
Rubrospinal Tract ◽  
Forelimb Muscles ◽  
The Mean ◽  
Adult Cat ◽  
Withdrawal Phase ◽  
Interspike Interval Distribution ◽  
Interval Distribution

The potential dynamic role of red nucleus in contact placing (CP) was investigated in intact awake cats. The activity of individual rubral neurons was recorded and the timing of their discharges was compared with electrical activity in selected contralateral forelimb muscles and with associated changes in joint angles characteristic of CP of the forelimb or hindlimb. The series included 273 rubral neurons (RN) that were recorded extracellularly in five cats; 62% were identified as rubrospinal tract neurons (RTN). Latencies of antidromic invasion following stimulation in the caudal contralateral medulla ranged from 0.25 to 3.3 ms. In some units, invasion occurred intermittently regardless of the stimulus strength above threshold. Most RN discharged tonically in the absence of obvious movement at, e.g., rates of 5-60 spikes/s. Spike train analyses were performed on 21 RN with stable resting discharge. Although the interspike interval distribution usually resembled that of a gamma process, the discharges were nonrandom. Usually, successive intervals were not independent, long and short intervals tending to be followed by intervals longer and shorter, respectively, than the mean interval. The sequence of intervals often shows episodes of relatively periodic discharge with mean interval differing between episodes. Among 120 RN that altered in firing rate during the first lifting-withdrawal phase of CP, 97 (81%) initially accelerated in rate. Variability in the delay between forepaw contact and the initial RN discharge permitted the distinction between contact-locked responses (53%), which began with a short latency, e.g., 20 ms, after contact and peaked usually within 50 ms. When CP failed to occur to a trial, contact-locked responses were further subdivided into a noncontingent type in which the RN response occurred regardless of whether CP occurred or not (type A) and a contingent type in which the RN response was significantly reduced or even absent when CP failed to occur (type B); delayed movement-locked responses (47%), which could be identified only when CP movements were delayed after contact. Delayed movement-locked responses were either types A or B, according to whether the RN response preceded (e.g., by 40-160 ms), or started during the electromyogram (EMG) response or the movement, respectively. Thus response types 1B and 2A can predict the success or failure of subsequent CP. Among an additional 17 RN initially responding after the paw cleared the top corner of the placing apparatus, the firing rate accelerated.(ABSTRACT TRUNCATED AT 400 WORDS)

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