scholarly journals An Efficient Coding Technique for Stochastic Processes

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 65
Author(s):  
Jesús E. Garca ◽  
Verónica A. González-López ◽  
Gustavo H. Tasca ◽  
Karina Y. Yaginuma
Keyword(s):  
Dna Sequences ◽  
Coding Theory ◽  
Transition Probabilities ◽  
Real Data ◽  
Finite Alphabet ◽  
Real Problem ◽  
Huffman Code ◽  
Efficient Coding ◽  
Codeword Length ◽  
Hand Modeling

In the framework of coding theory, under the assumption of a Markov process (Xt) on a finite alphabet A, the compressed representation of the data will be composed of a description of the model used to code the data and the encoded data. Given the model, the Huffman’s algorithm is optimal for the number of bits needed to encode the data. On the other hand, modeling (Xt) through a Partition Markov Model (PMM) promotes a reduction in the number of transition probabilities needed to define the model. This paper shows how the use of Huffman code with a PMM reduces the number of bits needed in this process. We prove the estimation of a PMM allows for estimating the entropy of (Xt), providing an estimator of the minimum expected codeword length per symbol. We show the efficiency of the new methodology on a simulation study and, through a real problem of compression of DNA sequences of SARS-CoV-2, obtaining in the real data at least a reduction of 10.4%.

scholarly journals Efficient Coding of the Embedded Signal in Steganographic Systems with Multiple Access

2021 ◽  
Vol 2(50) ◽  
Author(s):  
Ala Kobozeva ◽  
◽  
Arteom Sokolov ◽  
Keyword(s):  
Theoretical Basis ◽  
Multiple Access ◽  
Hadamard Transform ◽  
Huffman Code ◽  
Constant Amplitude ◽  
Efficient Coding ◽  
Codeword Length ◽  
Transform Coefficients ◽  
Walsh Hadamard Transform ◽  
The Given

Today, steganographic systems with multiple access are of considerable importance. In such sys-tems, the orthogonal Walsh-Hadamard transform is most often used for multiplexing and divid-ing channels, which leads to the need for efficient coding of the Walsh-Hadamard transform coefficients for the convenience of their subsequent embedding. The purpose of the research is to develop a theoretical basis for efficient coding of the embedded signal in steganographic sys-tems with multiple access with an arbitrary number of users N, based on MC-CDMA technology. This purpose was fulfilled by forming the theoretical basis for constructing effective codes de-signed to encode the embedded signal in steganographic systems with multiple access. The most important results obtained are the proposed and proven relations that determine both the possible values of the Walsh-Hadamard transform coefficients, for a given value of the number of divid-ed channels, and the probability of occurrence of the given values of the Walsh-Hadamard transform coefficients, which allow the construction of effective codes to represent the embed-ded signal. In the case of the number of divided channels N=4, we propose to use a constant amplitude code that provides a smaller value of the average codeword length in comparison with the Huffman code, while the constructed code has correcting capabilities. The significance of the obtained results is determined by the possibility of using the developed theoretical basis when constructing effective codes for encoding the embedded signal in steganographic systems with multiple access at an arbitrary value of the number of divided channels N.

scholarly journals An assembly-free method of phylogeny reconstruction using short-read sequences from pooled samples without barcodes

2021 ◽  
Author(s):  
Thomas K. F. Wong ◽  
Teng Li ◽  
Louis Ranjard ◽  
Steven Wu ◽  
Jeet Sukumaran ◽  
...  
Keyword(s):  
Dna Sequences ◽  
Dna Barcode ◽  
Real Data ◽  
Reference Sequence ◽  
Nucleotide Polymorphisms ◽  
Data Set ◽  
Single Nucleotide ◽  
Short Read ◽  
Pooled Samples ◽  
Haplotype Information

AbstractA current strategy for obtaining haplotype information from several individuals involves short-read sequencing of pooled amplicons, where fragments from each individual is identified by a unique DNA barcode. In this paper, we report a new method to recover the phylogeny of haplotypes from short-read sequences obtained using pooled amplicons from a mixture of individuals, without barcoding. The method, AFPhyloMix, accepts an alignment of the mixture of reads against a reference sequence, obtains the single-nucleotide-polymorphisms (SNP) patterns along the alignment, and constructs the phylogenetic tree according to the SNP patterns. AFPhyloMix adopts a Bayesian model of inference to estimates the phylogeny of the haplotypes and their relative frequencies, given that the number of haplotypes is known. In our simulations, AFPhyloMix achieved at least 80% accuracy at recovering the phylogenies and frequencies of the constituent haplotypes, for mixtures with up to 15 haplotypes. AFPhyloMix also worked well on a real data set of kangaroo mitochondrial DNA sequences.

scholarly journals Time Coordination of Periodic Passenger Train Connections in Conditions of Single-Track Lines

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Filip Lorenz ◽  
Vit Janos ◽  
Dusan Teichmann ◽  
Michal Dorda
Keyword(s):  
Mathematical Model ◽  
Mathematical Programming ◽  
Real Data ◽  
Real Problem ◽  
Single Track ◽  
Railway Stations ◽  
Optimization Software ◽  
Proposed Model ◽  
The Individual ◽  
The Given

The article addresses creation of a mathematical model for a real problem regarding time coordination of periodic train connections operated on single-track lines. The individual train connections are dispatched with a predefined tact, and their arrivals at and departures to predefined railway stations (transfer nodes) need to be coordinated one another. In addition, because the train connections are operated on single-track lines, trains that pass each other in a predefined railway stations must be also coordinated. To optimize the process, mathematical programming methods are used. The presented article includes a mathematical model of the given task, and the proposed model is tested with real data. The calculation experiments were implemented using optimization software Xpress-IVE.

scholarly journals Stereoscopic depth adaptation from binocularly correlated versus anti-correlated noise: Test of an efficient coding theory of stereopsis

2020 ◽  
Vol 166 ◽  
pp. 60-71 ◽  
Author(s):  
Frederick A.A. Kingdom ◽  
Karl-Christopher Yared ◽  
Paul B. Hibbard ◽  
Keith A. May
Keyword(s):  
Coding Theory ◽  
Stereoscopic Depth ◽  
Correlated Noise ◽  
Efficient Coding ◽  
Noise Test

scholarly journals On Determining the Order of Markov Dependence of an Observed Process Governed by a Hidden Markov Model

2002 ◽  
Vol 10 (3) ◽  
pp. 241-251 ◽  
Author(s):  
R.J. Boys ◽  
D.A. Henderson
Keyword(s):  
Markov Chain ◽  
Markov Models ◽  
Transition Probabilities ◽  
Hidden Markov ◽  
Real Data ◽  
Information Criteria ◽  
Monte Carlo Algorithm ◽  
Model Parameters ◽  
Markov Dependence ◽  
Finite State

This paper describes a Bayesian approach to determining the order of a finite state Markov chain whose transition probabilities are themselves governed by a homogeneous finite state Markov chain. It extends previous work on homogeneous Markov chains to more general and applicable hidden Markov models. The method we describe uses a Markov chain Monte Carlo algorithm to obtain samples from the (posterior) distribution for both the order of Markov dependence in the observed sequence and the other governing model parameters. These samples allow coherent inferences to be made straightforwardly in contrast to those which use information criteria. The methods are illustrated by their application to both simulated and real data sets.

scholarly journals Scene statistics and noise determine the relative arrangement of receptive field mosaics

2021 ◽  
Vol 118 (39) ◽  
pp. e2105115118
Author(s):  
Na Young Jun ◽  
Greg D. Field ◽  
John Pearson
Keyword(s):  
Neural Coding ◽  
Coding Theory ◽  
Receptive Fields ◽  
Optimal Arrangement ◽  
Efficient Coding ◽  
Natural Stimuli ◽  
Signal Stimulus ◽  
Theoretical Predictions ◽  
On And Off Pathways ◽  
Contrast Response

Many sensory systems utilize parallel ON and OFF pathways that signal stimulus increments and decrements, respectively. These pathways consist of ensembles or grids of ON and OFF detectors spanning sensory space. Yet, encoding by opponent pathways raises a question: How should grids of ON and OFF detectors be arranged to optimally encode natural stimuli? We investigated this question using a model of the retina guided by efficient coding theory. Specifically, we optimized spatial receptive fields and contrast response functions to encode natural images given noise and constrained firing rates. We find that the optimal arrangement of ON and OFF receptive fields exhibits a transition between aligned and antialigned grids. The preferred phase depends on detector noise and the statistical structure of the natural stimuli. These results reveal that noise and stimulus statistics produce qualitative shifts in neural coding strategies and provide theoretical predictions for the configuration of opponent pathways in the nervous system.

scholarly journals A hybrid landmark Aalen-Johansen estimator for transition probabilities in partially non-Markov multi-state models

2021 ◽  
Author(s):  
Niklas Maltzahn ◽  
Rune Hoff ◽  
Odd O. Aalen ◽  
Ingrid S. Mehlum ◽  
Hein Putter ◽  
...  
Keyword(s):  
Statistical Power ◽  
Transition Probabilities ◽  
Real Data ◽  
Testing Procedure ◽  
Data Application ◽  
Stratification Method ◽  
Model Complex ◽  
Markov Assumption ◽  
State Models ◽  
Disability Education

AbstractMulti-state models are increasingly being used to model complex epidemiological and clinical outcomes over time. It is common to assume that the models are Markov, but the assumption can often be unrealistic. The Markov assumption is seldomly checked and violations can lead to biased estimation of many parameters of interest. This is a well known problem for the standard Aalen-Johansen estimator of transition probabilities and several alternative estimators, not relying on the Markov assumption, have been suggested. A particularly simple approach known as landmarking have resulted in the Landmark-Aalen-Johansen estimator. Since landmarking is a stratification method a disadvantage of landmarking is data reduction, leading to a loss of power. This is problematic for “less traveled” transitions, and undesirable when such transitions indeed exhibit Markov behaviour. Introducing the concept of partially non-Markov multi-state models, we suggest a hybrid landmark Aalen-Johansen estimator for transition probabilities. We also show how non-Markov transitions can be identified using a testing procedure. The proposed estimator is a compromise between regular Aalen-Johansen and landmark estimation, using transition specific landmarking, and can drastically improve statistical power. We show that the proposed estimator is consistent, but that the traditional variance estimator can underestimate the variance of both the hybrid and landmark estimator. Bootstrapping is therefore recommended. The methods are compared in a simulation study and in a real data application using registry data to model individual transitions for a birth cohort of 184 951 Norwegian men between states of sick leave, disability, education, work and unemployment.

scholarly journals Active efficient coding explains the development of binocular vision and its failure in amblyopia

2020 ◽  
Vol 117 (11) ◽  
pp. 6156-6162
Author(s):  
Samuel Eckmann ◽  
Lukas Klimmasch ◽  
Bertram E. Shi ◽  
Jochen Triesch
Keyword(s):  
Eye Movements ◽  
Binocular Vision ◽  
Coding Theory ◽  
Critical Period ◽  
Receptive Fields ◽  
Efficient Coding ◽  
Coding Efficiency ◽  
Vision Development ◽  
Neural Representations ◽  
Active Binocular Vision

The development of vision during the first months of life is an active process that comprises the learning of appropriate neural representations and the learning of accurate eye movements. While it has long been suspected that the two learning processes are coupled, there is still no widely accepted theoretical framework describing this joint development. Here, we propose a computational model of the development of active binocular vision to fill this gap. The model is based on a formulation of the active efficient coding theory, which proposes that eye movements as well as stimulus encoding are jointly adapted to maximize the overall coding efficiency. Under healthy conditions, the model self-calibrates to perform accurate vergence and accommodation eye movements. It exploits disparity cues to deduce the direction of defocus, which leads to coordinated vergence and accommodation responses. In a simulated anisometropic case, where the refraction power of the two eyes differs, an amblyopia-like state develops in which the foveal region of one eye is suppressed due to inputs from the other eye. After correcting for refractive errors, the model can only reach healthy performance levels if receptive fields are still plastic, in line with findings on a critical period for binocular vision development. Overall, our model offers a unifying conceptual framework for understanding the development of binocular vision.

scholarly journals Integrated Transformer Health Estimation Methodology Based on Markov Chains and Evidential Reasoning

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Srdjan Milosavljevic ◽  
Aleksandar Janjic
Keyword(s):  
Markov Chains ◽  
Distribution System ◽  
Transition Probabilities ◽  
Diagnostic Technique ◽  
Real Data ◽  
Evidential Reasoning ◽  
Dempster Shafer Theory ◽  
The Status ◽  
Shafer Theory ◽  
Available Information

Due to the large number of power transformers (ETs) in the distribution system, there is a need for a relatively simple representation of the status of each unit in order to more easily determine where and how to allocate the budget for preventive and corrective maintenance. In recent years, the concept of the transformer health index (HI) as an integral part of resource management was adopted for the condition assessment and ranking of ETs. HI algorithms take different forms and can be determined based on a large number of specific parameters. However, the main problem in HI methodology or any modern diagnostic technique is the existence of regular measurements and inspections and accurate test results. The paper proposes a solution in the form of the upgraded HI and the novel methodology for ET ranking including the value of available information to describe ET current state. The confidence to the measurement results is calculated using evidential reasoning (ER) algorithm based on Dempster–Shafer theory. The contribution to the ER methodology is the calculation of the initial degrees of belief using Markov chains. The aging process of an ET and transition probabilities from state to state are modelled using the statistical data for the population of 300 ETs and 20 years monitoring data. The proposed methodology is tested on the real data for 110/35 kV transformer, and in the second case, compared to the sample of 30 110/x kV transformers with traditional HI calculation.

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