Browsing Mathematics (MA) by Title
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HandMovement Prediction Using LFP Data
(20110808)The last decade has seen a surge in the development of BrainMachine Interfaces (BMI) as assistive neural devices for paralysis patients. Current BMI research typically involves a subject performing movements by controlling ... 
Homogeneous Operators
(20180613)A bounded operator T on a complex separable Hilbert space is said to be homogeneous if '(T ) is unitarily equivalent to T for all ' in M•ob, where M•ob is the M•obius group. A complete description of all homogeneous weighted ... 
Homogeneous Operators and Some Irreducible Representations of the Mobius Group
In this report, after recalling the definition of the M¨obius group, we define homogeneous operators, that is, operators T with the property '(T) is unitarily equivalent to T for all ' in the M¨obius group and prove some ... 
Homogenization of Optimal Control Problems in a Domain with Oscillating Boundary
(20171127)Mathematical theory of homogenization of partial differential equations is relatively a new area of research (3040 years or so) though the physical and engineering applications were well known. It has tremendous applications ... 
Inferences on Structure and Function of Proteins from Sequence Data : Development of Methods and Applications
(20180723)Structural and functional annotation of sequences of putative proteins encoded in the newly sequenced genomes pose an important challenge. While much progress has been made towards high throughput experimental techniques ... 
Infinitely Divisible Metrics, Curvature Inequalities And Curvature Formulae
(20140630)The curvature of a contraction T in the CowenDouglas class is bounded above by the curvature of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. ... 
An Introduction to Minimal Surfaces
(20171210)In the first chapter of this report, our aim is to introduce harmonic maps between Riemann surfaces using the Energy integral of a map. Once we have the desired prerequisites, we move on to show how to continuously deform ... 
Irreducible Representations Of The Symmetric Group And The General Linear Group
(20130131)Representation theory is the study of abstract algebraic structures by representing their elements as linear transformations or matrices. It provides a bridge between the abstract symbolic mathematics and its explicit ... 
Joint Eigenfunctions On The Heisenberg Group And Support Theorems On Rn
(20140407)This work is concerned with two different problems in harmonic analysis, one on the Heisenberg group and other on Rn, as described in the following two paragraphs respectively. Let Hn be the (2n + 1)dimensional Heisenberg ... 
Kinetic Theory Based Numerical Schemes for Incompressible Flows
(20180207)Turbulence is an open and challenging problem for mathematical approaches, physical modeling and numerical simulations. Numerical solutions contribute significantly to the understand of the nature and effects of turbulence. ... 
LpAsymptotics of Fourier Transform Of Fractal Measures
(20180608)One of the basic questions in harmonic analysis is to study the decay properties of the Fourier transform of measures or distributions supported on thin sets in Rn. When the support is a smooth enough manifold, an almost ... 
Matchings Between Point Processes
(20140620) 
Mechanising knot Theory
(20180131)Mechanisation of Mathematics refers to use of computers to generate or check proofs in Mathematics. It involves translation of relevant mathematical theories from one system of logic to another, to render these theories ... 
Minimal Crystallizations of 3 and 4 Manifolds
(20180611)A simplicial cell complex K is the face poset of a regular CW complex W such that the boundary complex of each cell is isomorphic to the boundary complex of a simplex of same dimension. If a topological space X is homeomorphic ... 
Mixed Norm Estimates in Dunkl Setting and Chaotic Behaviour of Heat Semigroups
(20180103)This thesis is divided into three parts. In the first part we study mixed norm estimates for Riesz transforms associated with various differential operators. First we prove the mixed norm estimates for the Riesz transforms ... 
Multiscale Modelling of HLA Diversity and Its Effect on Cytotoxic Immune Responses in Influenza H1N1 Infection
(20180606)Cytotoxic Tlymphocytes (CTLs) are important components of the adaptive immune system and function by scanning the intracellular environment so as to detect and destroy infected cells. CTL responses play a major role in ... 
A Multiscale Modeling Study of Iron Homeostasis in Mycrobacterium Tuberculosis
(20180510)Mycobacterium tuberculosis (M.tb), the causative agent of tuberculosis (TB), has remained the largest killer among infectious diseases for over a century. The increasing emergence of drug resistant varieties such as the ...