Mathematical Models of Video-Sequences of Digital Half-Tone Images

2013 ◽  
pp. 207-241 ◽  
Author(s):  
E.P. Petrov ◽  
I.S. Trubin ◽  
E.V. Medvedeva ◽  
S.M. Smolskiy
Keyword(s):  
Mathematical Models ◽  
Markov Processes ◽  
Fourth Order ◽  
Markov Models ◽  
Video Sequences ◽  
Markov Type ◽  
Computationally Intensive

This chapter is devoted to Mathematical Models (MM) of Digital Half-Tone Images (DHTI) and their video-sequences presented as causal multi-dimensional Markov Processes (MP) on discrete meshes. The difficulties of MM development for DHTI video-sequences of Markov type are shown. These difficulties are related to the enormous volume of computational operations required for their realization. The method of MM-DHTI construction and their statistically correlated video-sequences on the basis of the causal multi-dimensional multi-value MM is described in detail. Realization of such operations is not computationally intensive; Markov models from the second to fourth order demonstrate this. The proposed method is especially effective when DHTI is represented by low-bit (4-8 bits) binary numbers.

Two Markov Models of Neighborhood Housing Turnover

1972 ◽  
Vol 4 (2) ◽  
pp. 133-146 ◽  
Author(s):  
G Gilbert
Keyword(s):  
Mathematical Models ◽  
Markov Processes ◽  
Renewal Process ◽  
Markov Models ◽  
Transition Probabilities ◽  
Markov Renewal Process ◽  
Turnover Process

This paper develops two mathematical models of housing turnover in a neighborhood. The first of these draws upon the theory of non-homogeneous Markov processes and includes the effects of present neighborhood composition upon future turnover probabilities. The second model considers the turnover process as a Markov renewal process and therefore allows the inclusion of length of occupancy as a determinant of transition probabilities. Example calculations for both models are included, and procedures for using the models are outlined.

Hidden Markov Processes

2014 ◽  
Author(s):  
M. Vidyasagar
Keyword(s):  
Hidden Markov Models ◽  
Markov Processes ◽  
Viterbi Algorithm ◽  
Markov Models ◽  
Hidden Markov ◽  
Local Alignment ◽  
Biological Applications ◽  
Standard Material ◽  
Hidden Markov Processes ◽  
Genomics And Proteomics

This book explores important aspects of Markov and hidden Markov processes and the applications of these ideas to various problems in computational biology. It starts from first principles, so that no previous knowledge of probability is necessary. However, the work is rigorous and mathematical, making it useful to engineers and mathematicians, even those not interested in biological applications. A range of exercises is provided, including drills to familiarize the reader with concepts and more advanced problems that require deep thinking about the theory. Biological applications are taken from post-genomic biology, especially genomics and proteomics. The topics examined include standard material such as the Perron–Frobenius theorem, transient and recurrent states, hitting probabilities and hitting times, maximum likelihood estimation, the Viterbi algorithm, and the Baum–Welch algorithm. The book contains discussions of extremely useful topics not usually seen at the basic level, such as ergodicity of Markov processes, Markov Chain Monte Carlo (MCMC), information theory, and large deviation theory for both i.i.d and Markov processes. It also presents state-of-the-art realization theory for hidden Markov models. Among biological applications, it offers an in-depth look at the BLAST (Basic Local Alignment Search Technique) algorithm, including a comprehensive explanation of the underlying theory. Other applications such as profile hidden Markov models are also explored.

scholarly journals SHsearch - a method for fast remote homology detection

2018 ◽  
Author(s):  
Mohamed Baddar
Keyword(s):  
Markov Models ◽  
Sequence Similarity ◽  
Protein Homology ◽  
Homology Detection ◽  
Remote Homology ◽  
Sensitivity Loss ◽  
Computationally Intensive ◽  
Profile Hmm ◽  
Programming Algorithms ◽  
Remote Homology Detection

Remote homology detection is the problem of detecting homology in cases of low sequence similarity. It is a hard computational problem with no approach that works well in all cases. Methods based on profile hidden Markov models (HMM) often exhibit relatively higher sensitivity for detecting remote homologies than commonly used approaches. However, calculating similarity scores in profile HMM methods is computationally intensive as they use dynamic programming algorithms. In this paper we introduce SHsearch: a new method for remote protein homology detection. Our method is implemented as a modification of HHsearch: a remote protein homology detection method based on comparing two profile HMMs. The motivation for modification was to reduce the run time of HHsearch significantly with minimal sensitivity loss. SHsearch focuses on comparing the important submodels of the query and database HMMs instead of comparing the complete models. Hence, SHsearch achieves a significant speedup over HHsearch with minimal loss in sensitivity. On SCOP 1.63, SHsearch achieved 88X speedup with 8.2% loss in sensitivity with respect to HHsearch at error rate of 10%, which deemed to be an acceptable tradeoff.

scholarly journals Testing the Semi Markov Model Using Monte Carlo Simulation Method for Predicting the Network Traffic

2020 ◽  
pp. 713-720
Author(s):  
Shirin Kordnoori ◽  
Hamidreza Mostafaei ◽  
Shaghayegh Kordnoori ◽  
Mohammadmohsen Ostadrahimi
Keyword(s):  
Monte Carlo ◽  
Markov Model ◽  
Markov Processes ◽  
Network Traffic ◽  
Markov Models ◽  
Transition Probabilities ◽  
Simulation Method ◽  
Monte Carlo Algorithm ◽  
Statistical Characteristics ◽  
Semi Markov Processes

Semi-Markov processes can be considered as a generalization of both Markov and renewal processes. One of the principal characteristics of these processes is that in opposition to Markov models, they represent systems whose evolution is dependent not only on their last visited state but on the elapsed time since this state. Semi-Markov processes are replacing the exponential distribution of time intervals with an optional distribution. In this paper, we give a statistical approach to test the semi-Markov hypothesis. Moreover, we describe a Monte Carlo algorithm able to simulate the trajectories of the semi-Markov chain. This simulation method is used to test the semi-Markov model by comparing and analyzing the results with empirical data. We introduce the database of Network traffic which is employed for applying the Monte Carlo algorithm. The statistical characteristics of real and synthetic data from the models are compared. The comparison between the semi-Markov and the Markov models is done by computing the Autocorrelation functions and the probability density functions of the Network traffic real and simulated data as well. All the comparisons admit that the Markovian hypothesis is rejected in favor of the more general semi Markov one. Finally, the interval transition probabilities which show the future predictions of the Network traffic are given.

scholarly journals SHsearch: a method for fast remote homology detection

2018 ◽  
Author(s):  
Mohamed Baddar
Keyword(s):  
Markov Models ◽  
Sequence Similarity ◽  
Protein Homology ◽  
Homology Detection ◽  
Remote Homology ◽  
Sensitivity Loss ◽  
Computationally Intensive ◽  
Profile Hmm ◽  
Programming Algorithms ◽  
Remote Homology Detection

Remote homology detection is the problem of detecting homology in cases of low sequence similarity. It is a hard computational problem with no approach that works well in all cases. Methods based on profile hidden Markov models (HMM) often exhibit relatively higher sensitivity for detecting remote homologies than commonly used approaches. However, calculating similarity scores in profile HMM methods is computationally intensive as they use dynamic programming algorithms. In this paper we introduce SHsearch: a new method for remote protein homology detection. Our method is implemented as a modification of HHsearch: a remote protein homology detection method based on comparing two profile HMMs. The motivation for modification was to reduce the run time of HHsearch significantly with minimal sensitivity loss. SHsearch focuses on comparing the important submodels of the query and database HMMs instead of comparing the complete models. Hence, SHsearch achieves a significant speedup over HHsearch with minimal loss in sensitivity. On SCOP 1.63, SHsearch achieved 88X speedup with 8.2% loss in sensitivity with respect to HHsearch at error rate of 10%, which deemed to be an acceptable tradeoff.

CHAOTIC OSCILLATOR CONFIGURATION USING A FREQUENCY DEPENDENT NEGATIVE RESISTOR

1999 ◽  
Vol 09 (03n04) ◽  
pp. 229-242 ◽  
Author(s):  
A. S. ELWAKIL ◽  
M. P. KENNEDY
Keyword(s):  
Mathematical Models ◽  
Fourth Order ◽  
Chaotic Attractor ◽  
General Purpose ◽  
Chaotic Oscillator ◽  
Topological Equivalence ◽  
Frequency Dependent ◽  
Nonlinear Resistor ◽  
Current Voltage ◽  
Current Voltage Characteristics

Chaos is observed from a fourth-order autonomous circuit inspired by Chua's circuit and obtained by replacing the active symmetric nonlinear resistor (Chua's diode) with a parallel combination of a frequency dependent negative resistor (FDNR) and a general-purpose signal diode. Accordingly, nonlinearity is introduced by a passive device with antisymmetric current-voltage characteristics whereas activity is transferred to the FDNR. The observed chaotic attractor has similar dynamics to the Colpitts chaotic attractor and we show its topological equivalence to the well-known Rossler attractor. Experimental results, PSpice simulations and numerical simulations of the derived mathematical models are included.

Utilization Mathematical and Physical Models Derived Therefrom Real-Time Models for the Optimization of Heating Processes

2013 ◽  
Vol 58 (3) ◽  
pp. 981-985 ◽  
Author(s):  
I. Špička ◽  
M. Heger
Keyword(s):  
Mathematical Models ◽  
Real Time ◽  
Model Simulation ◽  
Optimization Algorithms ◽  
Physical Models ◽  
Simplified Model ◽  
Operating Data ◽  
Reheating Furnace ◽  
Accurate Model ◽  
Computationally Intensive

Abstract Heating of materials is energy and costly operations. On those reasons optimization is highly desirable. One of the possible solutions to optimize heating in real time is to use a large number of fast simulations on the basis of them the optimization algorithms have chosen the most appropriate option of the heating control. This solution implies the use of extremely fast but sufficiently accurate simplified mathematical models of heating, the structure and parameters of them are defined based on accurate modelling using computationally intensive but slower classical mathematical-physical models. Based on the operating data of the reheating furnace was build an accurate model of heating. Using the simplified model simulation of heating was done with different heating conditions with downtime during heating. Proposed algorithms including the simulations show that the proposed strategy leads to verifiable savings during heating.

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