scholarly journals Optimal Poisson Cognitive System with Markov Learning Model

2021 ◽  
Vol 25 (6) ◽  
pp. 45-52
Author(s):  
A. A. Solodov
Keyword(s):  
Transition Probabilities ◽  
Stochastic Matrix ◽  
Learning Model ◽  
Interesting Case ◽  
Cognitive System ◽  
Correct Identification ◽  
Fixed Probability ◽  
Stochastic Learning ◽  
Intuitive Idea ◽  
Analytical Expressions

The aim of the study is to develop a mathematical model of the trained Markov cognitive system in the presence of discrete training and interfering random stimuli arising at random times at its input. The research method consists in the application of the simplest Markov learning model of Estes with a stochastic matrix with two states, in which the transition probabilities are calculated in accordance with the optimal Neуman-Pearson algorithm for detecting stimuli affecting the system. The paper proposes a model of the random appearance of images at the input of the cognitive system (in terms of learning theory, these are stimuli to which the system reacts). The model assumes an exponential distribution of the system’s response time to stimuli that is widely used to describe intellectual work, while their number is distributed according to the Poisson law. It is assumed that the cognitive system makes a decision about the presence or absence of a stimulus at its input in accordance with the Neуman-Pearson optimality criterion, i.e. maximizes the probability of correct detection of the stimulus with a fixed probability of false detection. The probabilities calculated in this way are accepted as transition probabilities in the stochastic learning matrix of the system. Thus, the following assumptions are accepted in the work, apparently corresponding to the behavior of the system assuming human reactions, i.e. the cognitive system.The images analyzed by the system arise at random moments of time, while the duration of time between neighboring appearances of images is distributed exponentially.The system analyzes the resulting images and makes a decision about the presence or absence of an image at its input in accordance with the optimal Neуman-Pearson algorithm that maximizes the probability of correct identification of the image with a fixed probability of false identification.The system is trainable in the sense that decisions about the presence or absence of an image are made sequentially on a set of identical situations, and the probability of making a decision depends on the previous decision of the system.The new results of the study are analytical expressions for the probabilities of the system staying in each of the possible states, depending on the number of steps of the learning process and the intensities of useful and interfering stimuli at the input of the system. These probabilities are calculated for an interesting case in which the discreteness of the appearance of stimuli in time is clearly manifested and the corresponding graphs are given. Stationary probabilities are also calculated, i.e. for an infinite number of training steps, the probabilities of the system staying in each of the states and the corresponding graph is presented.In conclusion, it is noted that the presented graphs of the behavior of the trained system correspond to an intuitive idea of the reaction of the cognitive system to the appearance of stimuli. Some possible directions of further research on the topic mentioned in the paper are indicated.

Two-Dimensional Rigid-Body Collisions With Friction

1992 ◽  
Vol 59 (3) ◽  
pp. 635-642 ◽  
Author(s):  
Yu Wang ◽  
Matthew T. Mason
Keyword(s):  
Rigid Body ◽  
Graphical Method ◽  
Correct Identification ◽  
Two Dimensional ◽  
Contact Mode ◽  
New Class ◽  
Tangential Impact ◽  
Approach Velocity ◽  
Conservation Principles ◽  
Analytical Expressions

This paper presents an analysis of a two-dimensional rigid-body collision with dry friction. We use Routh’s graphical method to describe an impact process and to determine the frictional impulse. We classify the possible modes of impact, and derive analytical expressions for impulse, using both Poisson’s and Newton’s models of restitution. We also address a new class of impacts, tangential impact, with zero initial approach velocity. Some methods for rigid-body impact violate energy conservation principles, yielding solutions that increase system energy during an impact. To avoid such anomalies, we show that Poisson’s hypothesis should be used, rather than Newton’s law of restitution. In addition, correct identification of the contact mode of impact is essential.

Learning models with continuous time parameter and multivariate point processes

1983 ◽  
Vol 20 (4) ◽  
pp. 884-890 ◽  
Author(s):  
Helmut Pruscha
Keyword(s):  
Point Process ◽  
Continuous Time ◽  
Point Processes ◽  
Transition Probabilities ◽  
Learning Model ◽  
Time Parameter ◽  
Learning Models ◽  
Random System ◽  
Multivariate Point ◽  
Multivariate Point Processes

The concept of a learning model (or random system with complete connections) with continuous time parameter is introduced on the basis of the notion of a multivariate point process possessing an intensity. The stepwise transition probabilities in terms of the intensity are derived and a Monte Carlo method for simulating a sample is presented. By modelling the intensity process various types of learning models can be built. We propose a linear learning model which comprises the continuous-time Markov process as well as Hawkes's mutually exciting point process. We study the asymptotic behaviour of this linear model in terms of explosion or extinction and of convergence of some estimates. We close with some numerical results from computer simulations.

Dielectronic recombination and satellite line spectra of highly charged tungsten ions1This article is part of a Special Issue on the 10th International Colloquium on Atomic Spectra and Oscillator Strengths for Astrophysical and Laboratory Plasmas.

2011 ◽  
Vol 89 (5) ◽  
pp. 581-589 ◽  
Author(s):  
U.I. Safronova ◽  
A.S. Safronova ◽  
P. Beiersdorfer
Keyword(s):  
Perturbation Theory ◽  
Excited States ◽  
Transition Probabilities ◽  
Dielectronic Recombination ◽  
Rate Coefficients ◽  
Atomic Data ◽  
Correct Identification ◽  
Many Body ◽  
International Colloquium ◽  
Many Body Perturbation Theory

We present our recent progress on theoretical studies that involve auto-ionizing states of highly charged tungsten ions. Such auto-ionizing states have two channels for decay, which requires that both radiative and auto-ionization atomic data be calculated and combined in a detailed study of the dielectronic recombination (DR). Three atomic codes are used to produce relativistic atomic data (energy levels, radiative transition probabilities, and auto-ionization rates). These are the relativistic many-body perturbation theory (RMBPT) code, the multiconfiguration relativistic Hebrew University Lawrence Livermore atomic code (HULLAC), and the Hartree–Fock relativistic (Cowan) code. Branching ratios relative to the first threshold and intensity factors are calculated for satellite lines, and DR rate coefficients are determined for the excited states. The total DR rate coefficient is derived as a function of electron temperature, and it is shown that the contribution of the highly excited states is very important for the calculation of the total DR rates. Synthetic dielectronic satellite spectra are constructed, and the atomic properties specific to the relevant tungsten ions are highlighted. First, we will consider the results for Na-like tungsten (W63+) and Mg-like tungsten (W62+) using all three codes. Then, we move to even higher ionization states and present the results in Li-like W (W71+). For this we use the RMBPT code as well as the quasi-relativistic many-body perturbation theory (MZ) code. The inclusion of the DR process is essential for correct identification of the lines in impurity spectra and for understanding the main contributions to the total radiation losses.

scholarly journals Markov chain properties in terms of column sums of the transition matrix

2012 ◽  
Vol 16 (1) ◽  
pp. 33-51
Author(s):  
Jeffrey J. Hunter
Keyword(s):  
Markov Chain ◽  
Transition Matrix ◽  
Transition Probabilities ◽  
Stochastic Matrix ◽  
Discrete Time Markov Chain ◽  
Mean First Passage Times ◽  
Generalized Matrix ◽  
The Mean ◽  
Generalized Matrix Inverse ◽  
Passage Times

Questions are posed regarding the influence that the column sums of the transition probabilities of a stochastic matrix (with row sums all one) have on the stationary distribution, the mean first passage times and the Kemeny constant of the associated irreducible discrete time Markov chain. Some new relationships, including some inequalities, and partial answers to the questions, are given using a special generalized matrix inverse that has not previously been considered in the literature on Markov chains.

Learning in Neural Networks with Material Synapses

1994 ◽  
Vol 6 (5) ◽  
pp. 957-982 ◽  
Author(s):  
Daniel J. Amit ◽  
Stefano Fusi
Keyword(s):  
Stochastic Process ◽  
Associative Memory ◽  
Electronic Device ◽  
Transition Probabilities ◽  
Variable Number ◽  
Stable States ◽  
Neural Activities ◽  
Stochastic Learning ◽  
Long Time

We discuss the long term maintenance of acquired memory in synaptic connections of a perpetually learning electronic device. This is affected by ascribing each synapse a finite number of stable states in which it can maintain for indefinitely long periods. Learning uncorrelated stimuli is expressed as a stochastic process produced by the neural activities on the synapses. In several interesting cases the stochastic process can be analyzed in detail, leading to a clarification of the performance of the network, as an associative memory, during the process of uninterrupted learning. The stochastic nature of the process and the existence of an asymptotic distribution for the synaptic values in the network imply generically that the memory is a palimpsest but capacity is as low as log N for a network of N neurons. The only way we find for avoiding this tight constraint is to allow the parameters governing the learning process (the coding level of the stimuli; the transition probabilities for potentiation and depression and the number of stable synaptic levels) to depend on the number of neurons. It is shown that a network with synapses that have two stable states can dynamically learn with optimal storage efficiency, be a palimpsest, and maintain its (associative) memory for an indefinitely long time provided the coding level is low and depression is equilibrated against potentiation. We suggest that an option so easily implementable in material devices would not have been overlooked by biology. Finally we discuss the stochastic learning on synapses with variable number of stable synaptic states.

scholarly journals Short communication: Insect detection using a machine learning model

2021 ◽  
Vol 13 (1) ◽  
Author(s):  
Yash Munnalal Gupta ◽  
SOMJIT HOMCHAN
Keyword(s):  
Machine Learning ◽  
Short Communication ◽  
Learning Model ◽  
Acheta Domesticus ◽  
Supervised Machine Learning ◽  
Correct Identification ◽  
Species Classification ◽  
Still Images ◽  
Machine Learning Model ◽  
Biological Studies

Abstract. Homchan S, Gupta YM. 2020. Short communication: Insect detection using a machine learning model. Nusantara Bioscience 13: 69-73. The key step in characterizing any organisms and their gender highly relies on correct identification of specimens. Here we aim to classify insect and their sex by supervised machine learning (ML) model. In the present preliminary study, we used a newly developed graphical user interface (GUI) based platform to create a machine learning model for classifying two economically important cricket species. This study aims to develop ML model for Acheta domesticus and Gryllus bimaculatus species classification and sexing. An experimental investigation was conducted to use Google teachable machine GTM for preliminary cricket species detection and sexing using pre-processed 2646 still images. An alternative method for image processing is used to extract still images from high-resolution video for optimum accuracy. Out of the 2646 images, 2247 were used for training ML model and 399 were used for testing the trained model. The prediction accuracy of trained model had 100 % accuracy to identify both species and their sex. The developed trained model can be integrated into the mobile application for cricket species classification and sexing. The present study may guide professionals in the field of life science to develop ML models based on image classification, and serve as an example for researchers and taxonomists to employ machine learning for species classification and sexing in the preliminary analysis. Apart from our main goals, the paper also intends to provide the possibility of ML models in biological studies and to conduct the preliminary assessment of biodiversity.

Learning models with continuous time parameter and multivariate point processes

1983 ◽  
Vol 20 (04) ◽  
pp. 884-890
Author(s):  
Helmut Pruscha
Keyword(s):  
Point Process ◽  
Continuous Time ◽  
Point Processes ◽  
Transition Probabilities ◽  
Learning Model ◽  
Time Parameter ◽  
Learning Models ◽  
Random System ◽  
Multivariate Point ◽  
Multivariate Point Processes

The concept of a learning model (or random system with complete connections) with continuous time parameter is introduced on the basis of the notion of a multivariate point process possessing an intensity. The stepwise transition probabilities in terms of the intensity are derived and a Monte Carlo method for simulating a sample is presented. By modelling the intensity process various types of learning models can be built. We propose a linear learning model which comprises the continuous-time Markov process as well as Hawkes's mutually exciting point process. We study the asymptotic behaviour of this linear model in terms of explosion or extinction and of convergence of some estimates. We close with some numerical results from computer simulations.

Mathematical Study of the Blood Coagulation Phenomenon

1975 ◽  
Author(s):  
R. Pieptea ◽  
D. Pieptea ◽  
M. Pieptea
Keyword(s):  
Blood Coagulation ◽  
Mathematical Analysis ◽  
Inflection Point ◽  
Arbitrary Point ◽  
Correct Identification ◽  
Coagulation Parameter ◽  
Mathematical Study ◽  
Coagulation Process ◽  
Analytical Expressions

Mathematical analysis of the coagulation process by means of thrombodynamogram made it possible to establish some new and important graphical elements (2) and the analytical expressions (1) of this phenomenon (F[x]):where a = quantic coagulation parameter (a ≃ ym); λ = coagulation rhythm parameter = thrombodynamic center (inflection point of the curve); = arbitrary point on the descending slope. Correct identification and interpretation of these elements raises the expressivity of the thrombodynamogram for evaluating coagulation phenomena.

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