scholarly journals Relation Between Firing Statistics of Spiking Neuron with Delayed Fast Inhibitory Feedback and Without Feedback

2018 ◽  
Vol 17 (01) ◽  
pp. 1850005 ◽  
Author(s):  
Alexander Vidybida ◽  
Olha Shchur
Keyword(s):  
Initial Segment ◽  
General Relation ◽  
Threshold Level ◽  
Interspike Intervals ◽  
Input Stream ◽  
Poisson Input ◽  
Artificial Neurons ◽  
Inhibitory Feedback ◽  
Model Independent ◽  
Probability Density Function Pdf

We consider a class of spiking neuronal models, defined by a set of conditions typical for basic threshold-type models, such as the leaky integrate-and-fire or the binding neuron model and also for some artificial neurons. A neuron is fed with a Poisson process. Each output impulse is applied to the neuron itself after a finite delay [Formula: see text]. This impulse acts as being delivered through a fast Cl-type inhibitory synapse. We derive a general relation which allows calculating exactly the probability density function (pdf) [Formula: see text] of output interspike intervals of a neuron with feedback based on known pdf [Formula: see text] for the same neuron without feedback and on the properties of the feedback line (the [Formula: see text] value). Similar relations between corresponding moments are derived.Furthermore, we prove that the initial segment of pdf [Formula: see text] for a neuron with a fixed threshold level is the same for any neuron satisfying the imposed conditions and is completely determined by the input stream. For the Poisson input stream, we calculate that initial segment exactly and, based on it, obtain exactly the initial segment of pdf [Formula: see text] for a neuron with feedback. That is the initial segment of [Formula: see text] is model-independent as well. The obtained expressions are checked by means of Monte Carlo simulation. The course of [Formula: see text] has a pronounced peculiarity, which makes it impossible to approximate [Formula: see text] by Poisson or another simple stochastic process.

scholarly journals First Passage Time Distribution for Spiking Neuron with Delayed Excitatory Feedback

2019 ◽  
Vol 19 (01) ◽  
pp. 2050005
Author(s):  
Olha Shchur ◽  
Alexander Vidybida
Keyword(s):  
First Passage Time ◽  
General Relation ◽  
Passage Time ◽  
Input Stream ◽  
First Passage ◽  
Exact Relation ◽  
Function Type ◽  
Artificial Neurons ◽  
Poisson Stream ◽  
Probability Density Function Pdf

A class of spiking neuronal models with threshold 2 is considered. It is defined by a set of conditions typical for basic threshold-type models, such as the leaky integrate-and-fire (LIF) or the binding neuron model, and also for some artificial neurons. A neuron is stimulated with a Poisson stream of excitatory impulses. Each output impulse is conveyed through the feedback line to the neuron input after finite delay [Formula: see text]. This impulse is identical to those delivered from the input stream. We have obtained a general relation allowing calculating exactly the probability density function (PDF) [Formula: see text] for distribution of the first passage time of crossing the threshold, which is the distribution of output interspike intervals (ISI) values for this neuron. The calculation is based on known PDF [Formula: see text] for that same neuron without feedback, intensity of the input stream [Formula: see text] and properties of the feedback line. Also, we derive exact relation for calculating the moments of [Formula: see text] based on known moments of [Formula: see text]. The obtained general expression for [Formula: see text] is checked numerically using Monte Carlo simulation for the case of LIF model. The course of [Formula: see text] has a [Formula: see text]-function-type peculiarity. This fact contributes to the discussion about the possibility to model neuronal activity with Poisson process, supporting the “no” answer.

scholarly journals Analysis and evaluation of the functionality of the mass service system on the basis of customs of truck vehicles

2018 ◽  
Vol 19 (6) ◽  
pp. 906-910
Author(s):  
Andrzej Lewiński ◽  
Marta Żurek-Mortka
Keyword(s):  
Service System ◽  
Real Data ◽  
Input Stream ◽  
Analysis And Evaluation ◽  
Poisson Input ◽  
Mass Service ◽  
Random Events ◽  
Service Stations ◽  
Queue Theory ◽  
Service Theory

Paper discussed the modeling of customs processes for truck vehicles using the Markov processes and mass service theory (queue theory), showing the operation of the notification handling system as a system dependent on random events. The system is characterized as a system with Poisson input stream, exponential service time and many service stations. The results are presented in the form of graphs based on real data received from the customs office

scholarly journals Relation Between Firing Statistics of Spiking Neuron with Instantaneous Feedback and Without Feedback

2015 ◽  
Vol 14 (04) ◽  
pp. 1550034 ◽  
Author(s):  
Alexander Vidybida
Keyword(s):  
Neuron Model ◽  
Probability Density Functions ◽  
Density Functions ◽  
Spiking Neuron ◽  
Interspike Intervals ◽  
Neuron Models ◽  
Similar Relation ◽  
Artificial Neurons ◽  
Poisson Stream ◽  
Spiking Neuron Models

We consider a class of spiking neuron models, defined by a set of conditions which are typical for basic threshold-type models like leaky integrate-and-fire, or binding neuron model and also for some artificial neurons. A neuron is fed with a point renewal process. A relation between the three probability density functions (PDF): (i) PDF of input interspike intervals ISIs, (ii) PDF of output interspike intervals of a neuron with a feedback and (iii) PDF for that same neuron without feedback is derived. This allows to calculate any one of the three PDFs provided the remaining two are given. Similar relation between corresponding means and variances is derived. The relations are checked exactly for the binding neuron model stimulated with Poisson stream.

scholarly journals Hydrogeological Study of the Glacial—Fluvioglacial Territory of Grandate (Como, Italy) and Stochastical Modeling of Groundwater Rising

2018 ◽  
Vol 8 (9) ◽  
pp. 1456 ◽  
Author(s):  
Ivana La Licata ◽  
Loris Colombo ◽  
Vincenzo Francani ◽  
Luca Alberti
Keyword(s):  
Threshold Level ◽  
Automatic Calibration ◽  
Underground Structures ◽  
Site Model ◽  
Code Model ◽  
Hydrogeological Study ◽  
Model Independent ◽  
Piezometric Heads ◽  
Hydrogeological Structure ◽  
Monthly Probability

On November 2014, the Municipality of Grandate, near Lake Como, had to deal with a great emergency that was caused by the flooding of factory undergrounds. The authors realized a hydrogeological study to understand the causes of groundwater flooding and to prepare a pre-feasibility study concerning possible actions for groundwater control. The hydrogeological structure is rather complex and required time-consuming reconstruction of the conceptual site model. A transient numerical model was developed to analyse the system behaviour in different scenarios. The flow model was calibrated in a steady and unsteady-state using the automatic calibration code Model-Independent Parameter Estimation (PEST). The study demonstrated that the reason for floods was mainly due to the concurrence of three causes: (1) the hydrogeological structure of the area was recognized as a stagnation zone, (2) groundwater rising, and (3) extremely heavy rainfall in 2014. Through the PEST RandPar function, 100 random rainfall scenarios were generated starting from rainfall data for the last 20 years. The model was used to run 100 1-year long simulations considering the probability distribution of recharge related to the 100 randomly generated rainfall scenarios. Through collecting the piezometric heads that resulted from the simulations, monthly probability curves of groundwater exceeding a threshold level were obtained. The results provided an occurrence probability of groundwater level exceeding the underground structures level between 12% and 15%.

Maternal DDAVP-induced hyponatremia: Threshold level for fetal urinary diuresis

1998 ◽  
Vol 5 (1) ◽  
pp. 151A-151A
Author(s):  
M NIJLAND ◽  
T ROBERTS ◽  
M CURRAN ◽  
M ROSS
Keyword(s):  
Threshold Level

Inhibitory Feedback Loop Induces Anticipated Synchronization in Neuronal Networks

2014 ◽  
Vol 1 ◽  
pp. 636-639
Author(s):  
Fernanda S. Matias ◽  
Pedro V. Carelli ◽  
Claudio R. Mirasso ◽  
Mauro Copelli
Keyword(s):  
Feedback Loop ◽  
Neuronal Networks ◽  
Inhibitory Feedback

OPTIMIZATION OF MARKOV SYSTEMS OF QUEUEING WITH WAITING TIME IN THE MATLAB SYSTEM

2017 ◽  
pp. 39-47
Author(s):  
Viktor Afonin ◽  
Vladimir Valer'evich Nikulin
Keyword(s):  
Queueing System ◽  
Queueing Systems ◽  
Random Variable ◽  
Model Systems ◽  
Queuing Systems ◽  
Input Flow ◽  
Continuous Random Variable ◽  
Input Stream ◽  
Time Intervals ◽  
Markov Systems

The article focuses on attempt to optimize two well-known Markov systems of queueing: a multichannel queueing system with finite storage, and a multichannel queueing system with limited queue time. In the Markov queuing systems, the intensity of the input stream of requests (requirements, calls, customers, demands) is subject to the Poisson law of the probability distribution of the number of applications in the stream; the intensity of service, as well as the intensity of leaving the application queue is subject to exponential distribution. In a Poisson flow, the time intervals between requirements are subject to the exponential law of a continuous random variable. In the context of Markov queueing systems, there have been obtained significant results, which are expressed in the form of analytical dependencies. These dependencies are used for setting up and numerical solution of the problem stated. The probability of failure in service is taken as a task function; it should be minimized and depends on the intensity of input flow of requests, on the intensity of service, and on the intensity of requests leaving the queue. This, in turn, allows to calculate the maximum relative throughput of a given queuing system. The mentioned algorithm was realized in MATLAB system. The results obtained in the form of descriptive algorithms can be used for testing queueing model systems during peak (unchanged) loads.

Modeling and design of role engineering in development of access control for dynamic information systems

2013 ◽  
Vol 61 (3) ◽  
pp. 569-579 ◽  
Author(s):  
A. Poniszewska-Marańda
Keyword(s):  
Information Systems ◽  
Dynamic Information ◽  
Minimal Set ◽  
Distributed Information ◽  
Heterogeneous Information ◽  
System Protection ◽  
Level Model ◽  
Model Independent ◽  
Role Concept ◽  
High Level

Abstract Nowadays, the growth and complexity of functionalities of current information systems, especially dynamic, distributed and heterogeneous information systems, makes the design and creation of such systems a difficult task and at the same time, strategic for businesses. A very important stage of data protection in an information system is the creation of a high level model, independent of the software, satisfying the needs of system protection and security. The process of role engineering, i.e. the identification of roles and setting up in an organization is a complex task. The paper presents the modeling and design stages in the process of role engineering in the aspect of security schema development for information systems, in particular for dynamic, distributed information systems, based on the role concept and the usage concept. Such a schema is created first of all during the design phase of a system. Two actors should cooperate with each other in this creation process, the application developer and the security administrator, to determine the minimal set of user’s roles in agreement with the security constraints that guarantee the global security coherence of the system.

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