Random obtuse triangles and convex quadrilaterals

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 83-85).We intend to discuss in detail two well known geometrical probability problems. The first one deals with finding the probability that a random triangle is obtuse in nature. We initially discuss the various ways of choosing a random triangle. The problem is at first analyzed based on random angles (adding to 180 degrees) and random sides (obeying the triangle inequality) which is a direct modification of the Broken Stick Problem. We then study the effect of shape on the probability that when three random points are chosen inside a figure of that shape they will form an obtuse triangle. Literature survey reveals the existence of the analytical formulae only in the cases of square, circle and rectangle. We used Monte Carlo simulation to solve this problem in various shapes. We intend to show by means of simulation that the given probabilatity will reach its minimum value when the random points are taken inside a circle. We then introduce the concept of Random Walk in Triangles and show that the probability that a triangle formed during the process is obtuse is itself random. We also propose the idea of Differential Equation in Triangle Space and study the variation of angles during this dynamic process. We then propose to extend this to the problem of calculating the probability of the quadrilateral formed by four random points is convex. The effects of shape are distinctly different than those obtained in the random triangle problem. The effort of true random numbers and normally generated pseudorandom numbers are also compared for both the problems considered.by Nirjhar Banerjee.S.M

An algorithm to find similar internal sequence repeats

In recent years, identification of sequence patterns has been given immense importance to understand better their significance with respect to genomic organization and evolutionary processes. To this end, an algorithm has been derived to identify all similar sequence repeats present in a protein sequence. The proposed algorithm is useful to correlate the three-dimensional structure of various similar sequence repeats available in the Protein Data Bank against the same sequence repeats present in other databases like SWISS-PROT, PIR and Genome databases

IMPLEMENTATION OF A COMBINATORIAL AUCTIONING ALGORITHM FOR OPTIMAL DYNAMIC YARD SPACE ALLOCATION IN A CONTAINER PORT

Master'sMASTER OF SCIENCE IN COMPUTATIONAL ENGINEERIN

An algorithm to find distant repeats in a pair of protein sequences

Distant repeats between a pair of protein sequences can be exploited to study the various aspects of proteins such as structure-function relationship, disorders due to protein malfunction, evolutionary analysis, etc. An in-depth analysis of the distant repeats would facilitate to establish a stable evolutionary relation of the repeats with respect to their three-dimensional structure. To this effect, an algorithm has been devised to identify the distant repeats in a pair of protein sequences by essentially using the scores of PAM (Percent Accepted Mutation) matrices. The proposed algorithm will be of much use to researchers involved in the comparative study of various organisms based on the amino-acid repeats in protein sequences. (C) 2010 Elsevier B.V. All rights reserved

weekly meeting

Proteins containing amino acid repeats are considered to be of great importance in evolutionary studies. The principal mechanism of formation of amino acid repeats is by the duplication or recombination of genes. Thus, repeats are found in both nucleotide and protein sequences. In proteins, repeats are involved in protein-protein interactions as well as in binding to other ligands such as DNA and RNA. The study of internal sequence repeats would be helpful to scientists in various fields, including structural biology, enzymology, phylogenetics, genomics and proteomics. Hence an algorithm (Finding All Internal Repeats, FAIR) has been designed utilizing the concepts of dynamic programing to identify the repeats. The proposed algorithm is a faster and more efficient method to detect internal sequence repeats in both protein and nucleotide sequences, than those found in the literature. The algorithm has been implemented in $C^{++}$ and a web-based computing engine, IdentSeek, has been developed to make FAIR accessible to the scientific community. IdentSeek produces a clear, detailed result (including the location of the repeat in the sequence and its length), which can be accessed through the world wide web at the URL http://bioserver1.physics.iisc.ernet.in/ident/

An algorithm to find similar internal sequence repeats

In recent years, identification of sequence patterns has been given immense importance to understand better their significance with respect to genomic organization and evolutionary processes. To this end, an algorithm has been derived to identify all similar sequence repeats present in a protein sequence. The proposed algorithm is useful to correlate the three-dimensional structure of various similar sequence repeats available in the Protein Data Bank against the same sequence repeats present in other databases like SWISS-PROT, PIR and Genome databases