Browsing Mathematics (MA) by Title
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The CaratheodoryFejer Interpolation Problems and the VonNeumann inequality
(20180530)The validity of the vonNeumann inequality for commuting $n$  tuples of $3\times 3$ matrices remains open for $n\geq 3$. We give a partial answer to this question, which is used to obtain a necessary condition for the ... 
Central and Peripheral Correlates of Motor Planning
(20180211)A hallmark of human behaviour is that we can either couple or decouple our thoughts, decision and motor plans from actions. Previous studies have reported evidence of gating of information between intention and action that ... 
Characterization of Brain Signals Across Scales Using Temporally Modulated Visual Stimuli
Electrical signals from the brain can be recorded at several different scales, ranging from spiking activity to local field potential (LFP) in animals to scalp electroencephalogram (EEG) in humans. Each signal represents ... 
Compactness Theorems for The Spaces of Distance Measure Spaces and Riemann Surface Laminations
(20180218)Gromov’s compactness theorem for metric spaces, a compactness theorem for the space of compact metric spaces equipped with the GromovHausdorﬀ distance, is a theorem with many applications. In this thesis, we give a ... 
Computation of Sparse Representations of High Dimensional Time Series Data and Experimental Applications
Obtaining a sparse representation of high dimensional data is often the first step towards its further analysis. Conventional Vector Autoregressive (VAR) modelling methods applied to such data results in noisy, nonsparse ... 
Computational Studies on Structures and Functions of Single and Multidomain Proteins
(20180525)Proteins are essential for the growth, survival and maintenance of the cell. Understanding the functional roles of proteins helps to decipher the working of macromolecular assemblies and cellular machinery of living ... 
A computational systems biology approach for elucidating molecular features of primary and metastatic melanoma
Malignant melanoma, a cancer arising from melanocytes, is reported to have one of the fastest growing incidence rates worldwide, and is considered to be one of the most aggressive human malignancies. According to the ... 
Controlled SemiMarkov Processes With Partial Observation
(20110928) 
Correlation Functions in the Finite Toom Model
This thesis is divided into four chapters. In Chapter 1, we give some basic definitions and results that we need throughout the thesis. In Chapter 2, we describe the pn0;n1qToom model and prove some known results about ... 
Curvature Calculations Of The Operators In CowenDouglas Class
(20140303)In a foundational paper “Operators Possesing an Open Set of Eigenvalues” written several decades ago, Cowen and Douglas showed that an operator T on a Hilbert space ‘H possessing an open set Ω C of eigenvalues determines ... 
Decomposition of the tensor product of Hilbert modules via the jet construction and weakly homogeneous operators
Let ½ Cm be a bounded domain and K :£!C be a sesquianalytic function. We show that if ®,¯ È 0 be such that the functions K® and K¯, defined on £, are nonnegative definite kernels, then theMm(C) valued function ... 
Development of Efficient Computational Methods for Better Estimation of Optical Properties in Diffuse Optical Tomography
(20180402)Diffuse optical tomography (DOT) is one of the promising imaging modalities that pro vides functional information of the soft biological tissues invivo, such as breast and brain tissues. The near infrared (NIR) light ... 
Development Of NMR Methods For Metabolomics And Protein Resonance Assignments
(20170525)Nuclear Magnetic Resonance (NMR) spectroscopy is a quantitative, noninvasive and nondestructive technique useful in biological studies. By manipulating the magnetization of nuclei with nonzero spin, NMR gives insights ... 
Dilation Theory of Contractions and NevanlinnaPick Interpolation Problem
In this article, we give two different proofs of the existence of the minimal isometric dilation of a single contraction. Then using the existence of a unitary dilation of a contraction, we prove the `von Neumann's ... 
Dilations, Functoinal Model And A Complete Unitary Invariant Of A rcontraction.
(20130802)A pair of commuting bounded operators (S, P) for which the set r = {(z 1 +z 2,z 1z 2) : z 1 ≤1, z 2 ≤1} C2 is a spectral set, is called a rcontraction in the literature. For a contraction P and a bounded commutant ... 
Duality for Spaces of Holomorphic Functions into a Locally Convex Topological Vector Space
Consider an open subset O of the complex plane and a function f : O ÝÑ C. We understand the concept of holomorphicity of a complexvalued function. Suppose a function f defined on O takes values in a locally convex ... 
Dynamic Flow Rules in Continuum Viscoplasticity and Damage Models for Polycrystalline Solids
Modelling highly nonlinear, strongly temperature and ratedependent viscoplastic behaviour of polycrystalline solids (e.g., metals and metallic alloys) is one of the most challenging topics of contemporary research ... 
Dynamical Properties of Families of Holomorphic Mappings
(20180608)Thesis Abstract In the first part of the thesis, we study some dynamical properties of skew products of H´enon maps of C2 that are fibered over a compact metric space M . The problem reduces to understanding the dynamical ...