Entropy Approach to the Construction of a Measure of Word Symbolic Diverseness and its Application to Clustering of Plant Genomes

2016 ◽  
Vol 11 (1) ◽  
pp. 114-126 ◽  
Author(s):  
Ю.Г. Сметанин ◽  
Y.G. Smetanin
Keyword(s):  
Finite Length ◽  
Translation Operator ◽  
Entropy Function ◽  
Discrete Distributions ◽  
Finite Alphabet ◽  
Information Analysis ◽  
Plant Genomes ◽  
Unit Translation

An approach to the information analysis is considered for the case when the information is presented by words of finite length over a finite alphabet. A method of generating a measure of symbolic diverseness of words based on peak characteristics of a shift entropy function is proposed. The shift entropy function is formally defined using a unit translation operator and the entropy of discrete distributions. A model example is presented together with some results of application of the proposed measure in the clustering of families of plants using the analysis of genome of their representatives.

DISCRETE KNOTS

2002 ◽  
Vol 11 (08) ◽  
pp. 1307-1321 ◽  
Author(s):  
ERNESTO BRIBIESCA
Keyword(s):  
Finite Length ◽  
Finite Alphabet ◽  
Orthogonal Direction ◽  
Chain Code ◽  
Line Segments ◽  
Direction Change ◽  
Straight Line ◽  
Starting Point ◽  
A Chain

A method for representing knots by means of a chain code is presented. Knots which are digitalized and represented by the orthogonal direction change chain code are called discrete knots. Discrete knots are composed of constant straight-line segments using only orthogonal directions. The chain elements represent the orthogonal direction changes of the constant straight-line segments of the discrete knot. There are only five possible orthogonal direction changes for representing any discrete knot. Thus, this chain code only considers relatives directions changes, which allows us to have a unique knot descriptor invariant under translation and rotation. Also, this knot descriptor may be starting point normalized. Finally, this unique knot descriptor produces a numerical string of finite length over a finite alphabet, allows us the usage of grammatical techniques for discrete-knot analysis. Thus, we present some prime discrete knot detection examples within composite discrete knots.

User modelling for intent prediction in information analysis

2003 ◽  
Author(s):  
Eugene Santos ◽  
Hien Nguyen ◽  
Qunhua Zhao ◽  
Hua Wang
Keyword(s):  
User Modelling ◽  
Information Analysis ◽  
Intent Prediction

Unified summation equations and their applications in tribology wear process

2013 ◽  
Vol 61 (2) ◽  
pp. 405-417 ◽  
Author(s):  
K. Wierzcholski
Keyword(s):  
Translation Operator ◽  
Wear Process ◽  
Recurrence Equations ◽  
New Form

Abstract This paper presents some applications of summation equations with regard to the calculation prognosis of micro-bearing wear parameters. Summation equations are presented in a new form of difference and recurrence equations where the unknown micro-bearing wear function occurs as the argument of the reciprocal unified operator of summation (UOS). In this paper the properties of the UOS and reciprocal UOS as well as the unitary translation operator (UTO) are defined and applied to a micro-bearing wear determination. The approach of both dual and interaction between summation and recurrence equations and micro-bearing wear determination, makes this paper unique.

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