In one scenario of gene evolution, exon shuffling plays a fundamental role in increasing gene diversity. This paper is an appraisal of the biological relevance of categorising proteins by their splicing profiles (exon-intron structures). The central question is whether protein function is more correlated with splicing profiles than sequence similarity, or not. To approach this question, a splic...

We deene the notion of self-concordance of order two for the restriction f of a logarithmic barrier function to a given line. Based on this notion we prove an inner approximation of the domain of f, as well as a lower bound of the distance from a point t to the minimum of f. These results provide the theoretical tools to develop a simple and eecient search step for nding the minimum of the barr...

In this paper, we aim to overcome three major shortcomings of the FDH (Free Disposal Hull) directional distance function through developing two new, named Linear and Fractional CDFDH, complete FDH measures of efficiency. To accomplish this, we integrate the concepts of similarity and FDH directional distance function. We prove that the proposed measures are translation invariant and unit invari...

The ability to accurately predict gene function based on gene sequence is an important tool in many areas of biological research. Such predictions have become particularly important in the genomics age in which numerous gene sequences are generated with little or no accompanying experimentally determined functional information. Almost all functional prediction methods rely on the identification...

We investigate similarity classes of arithmetic lattices in the plane. We introduce a natural height function on the set of such similarity classes, and give asymptotic estimates on the number of all arithmetic similarity classes, semi-stable arithmetic similarity classes, and well-rounded arithmetic similarity classes of bounded height as the bound tends to infinity. We also briefly discuss so...

Since a protein’s amino acid sequence determines 3D structure, which in turn determines protein function, one might think that sequence similarity is also very good predictor of functional similarity, but this turns out to be less the case than with structural similarity. Vastly different amino acid sequences can yield very different structures, and similar sequences can sometimes yield dissimi...

A similarity and a difference between bivariate negative binomial distribution geometric is presented. The of the corresponding characteristic function are

MOTIVATION Importance of accurate automatic protein function prediction is ever increasing in the face of a large number of newly sequenced genomes and proteomics data that are awaiting biological interpretation. Conventional methods have focused on high sequence similarity-based annotation transfer which relies on the concept of homology. However, many cases have been reported that simple tran...

Objective: In pattern recognition and medical diagnosis, similarity measure is an important mathematical tool. To overcome some disadvantages of existing cosine similarity measures of simplified neutrosophic sets (SNSs) in vector space, this paper proposed improved cosine similarity measures of SNSs based on cosine function, including single valued neutrosophic cosine similarity measures and in...

After reviewing the underlying framework required for computational function prediction in the previous chapter, we discuss two advanced sequencebased function prediction methods developed in our group, namely the Protein Function Prediction (PFP) method and the Extended Similarity Group (ESG) method. PFP extends the traditional homology search by incorporating functional associations between p...