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A Brief Treatise On Bayesian Inverse Regression., Debashis Chatterjee Dr.
A Brief Treatise On Bayesian Inverse Regression., Debashis Chatterjee Dr.
Doctoral Theses
Inverse problems, where in a broad sense the task is to learn from the noisy response about some unknown function, usually represented as the argument of some known functional form, has received wide attention in the general scientific disciplines. However, apart from the class of traditional inverse problems, there exists another class of inverse problems, which qualify as more authentic class of inverse problems, but unfortunately did not receive as much attention.In a nutshell, the other class of inverse problems can be described as the problem of predicting the covariates corresponding to given responses and the rest of the data. …
Secret Sharing And Its Variants, Matroids,Combinatorics., Shion Samadder Chaudhury Dr.
Secret Sharing And Its Variants, Matroids,Combinatorics., Shion Samadder Chaudhury Dr.
Doctoral Theses
The main focus of this thesis is secret sharing. Secret Sharing is a very basic and fundamental cryptographic primitive. It is a method to share a secret by a dealer among different parties in such a way that only certain predetermined subsets of parties can together reconstruct the secret while some of the remaining subsets of parties can have no information about the secret. Secret sharing was introduced independently by Shamir [139] and Blakely [20]. What they introduced is called a threshold secret sharing scheme. In such a secret sharing scheme the subsets of parties that can reconstruct a secret …
Some Contributions To Free Probability And Random Matrices., Sukrit Chakraborty Dr.
Some Contributions To Free Probability And Random Matrices., Sukrit Chakraborty Dr.
Doctoral Theses
No abstract provided.
Some Topics In Leavitt Path Algebras And Their Generalizations., Mohan R. Dr.
Some Topics In Leavitt Path Algebras And Their Generalizations., Mohan R. Dr.
Doctoral Theses
The purpose of this section is to motivate the historical development of Leavitt algebras, Leavitt path algebras and their various generalizations and thus provide a context for this thesis. There are two historical threads which resulted in the definition of Leavitt path algebras. The first one is about the realization problem for von Neumann regular rings and the second one is about studying algebraic analogs of graph C ∗ -algebras. In what follows we briefly survey these threads and also introduce important concepts and terminology which will recur throughout.
Scaling Limits Of Some Random Interface Models., Biltu Dan Dr.
Scaling Limits Of Some Random Interface Models., Biltu Dan Dr.
Doctoral Theses
In this thesis, we study some probabilistic models of random interfaces. Interfaces between different phases have been topic of considerable interest in statistical physics. These interfaces are described by a family of random variables, indexed by the ddimensional integer lattice, which are considered as a height configuration, namely they indicate the height of the interface above a reference hyperplane. The models are defined in terms of an energy function (Hamiltonian), which defines a Gibbs measure on the set of height configurations. More formally, letÏ• = {Ï•x}x∈Z dbe a collection of real numbers indexed by the d-dimensional integer lattice Z d. …
On The Inertia Conjecture And Its Generalizations., Soumyadip Das Dr.
On The Inertia Conjecture And Its Generalizations., Soumyadip Das Dr.
Doctoral Theses
This thesis concerns problems related to the ramification behaviour of the branched Galois covers of smooth projective connected curves defined over an algebraically closed field of positive characteristic. Our first main problem is the Inertia Conjecture proposed by Abhyankar in 2001. We will show several new evidence for this conjecture. We also formulate a certain generalization of it which is our second problem, and we provide evidence for it. We give a brief overview of these problems in this introduction and reserve the details for Chapter 4.Let k be an algebraically closed field, and U be a smooth connected affine …
Commuting Isometries And Invariant Subspaces In Several Variables., Sankar T. R. Dr.
Commuting Isometries And Invariant Subspaces In Several Variables., Sankar T. R. Dr.
Doctoral Theses
A very general and fundamental problem in the theory of bounded linear operators on Hilbert spaces is to find invariants and representations of commuting families of isometries.In the case of single isometries this question has a complete and explicit answer: If V is an isometry on a Hilbert space â„‹, then there exists a Hilbert space Hu and a unitary operator U on â„‹u such that V on â„‹u and[ S ⊗ IW 0 0 U] ∈ B((l 2 (ℤ+) ⊗ W) ⊕ â„‹u),are unitarily equivalent, whereW = ker V∗ ,is the wandering subspace for V and S is the …
Essays In Behavioral Social Choice Theory., Sarvesh Bandhu Dr.
Essays In Behavioral Social Choice Theory., Sarvesh Bandhu Dr.
Doctoral Theses
This thesis comprises four essays on social choice theory. The first three essays/chapters consider models where voters follow “non-standard” rules for decision making. The last chapter considers the binary social choice model and analyzes the consequences of a new axiom. The first chapter introduces a new axiom for manipulability when voters incur a cost if they misreport their true preference ordering. The second chapter considers the random voting model with strategic voters where standard stochastic dominance strategy-proofness is replaced by strategy-proofness under two lexicographic criteria. The third chapter also considers the random voting model but from a non-strategic perspective. It …
On Tests Of Independence Among Multiplerandom Vectors Of Arbitrary Dimensions., Angshuman Roy Dr.
On Tests Of Independence Among Multiplerandom Vectors Of Arbitrary Dimensions., Angshuman Roy Dr.
Doctoral Theses
Measures of dependence among several random vectors and associated tests of independence play a major role in different statistical applications. Blind source separation or independent component analysis (see, e.g., Hyv¨arinen et al., 2001; Shen et al., 2009), feature selection and feature extraction (see, e.g., Li et al., 2012), detection of serial correlation in time series (see, e.g., Ghoudi et al., 2001) and finding the causal relationships among the variables (see, e.g., Chakraborty and Zhang, 2019) are some examples of their wide-spread applications. Tests of independence has vast applications in other areas of sciences as well. For instance, to characterize the …
Quantum Symmetries In Noncommutative Geometry., Suvrajit Bhattacharjee Dr.
Quantum Symmetries In Noncommutative Geometry., Suvrajit Bhattacharjee Dr.
Doctoral Theses
No abstract provided.
Quantum Markov Maps: Structureand Asymptotics., Vijaya Kumar U. Dr.
Quantum Markov Maps: Structureand Asymptotics., Vijaya Kumar U. Dr.
Doctoral Theses
No abstract provided.
Essays In Social Choice Theory., Dipjyoti Majumdar Dr.
Essays In Social Choice Theory., Dipjyoti Majumdar Dr.
Doctoral Theses
The purpose of this thesis is to explore some issues in social choice theory and decision theory. Social choice theory provides the theoretical foundations for the field of public choice and welfare economics. It tries to bring together normative aspects like perspective value judgements and positive aspects, like strategic con- siderations. The second feature which is our focus, is closely related to the problem of providing appropriate incentives to agents, an issue of prime importance in eco- nomics.Consider for example, a set of agents who must elect one among a set of can- didates. These candidates may be physical agents …
Studies On Polynomial Rings Through Locally Nilpotient Derivations., Nikhilesh Dasgupta Dr.
Studies On Polynomial Rings Through Locally Nilpotient Derivations., Nikhilesh Dasgupta Dr.
Doctoral Theses
No abstract provided.
Higher Chow Cycles On The Jacobian Of Curves., Subham Sarkar Dr.
Higher Chow Cycles On The Jacobian Of Curves., Subham Sarkar Dr.
Doctoral Theses
The following formula, usually called Beilinson’s formula — though independently due to Deligne as well — describes the motivic cohomology group of a smooth projective variety X over a number field as the group of extensions in a conjectured abelian category of mixed motives, MMQ.The aim of this thesis is to describe this construction in the case of the motivic cohomology group of the Jacobian of a curve. The first work in this direction is due to Harris [Har83] and Pulte [Pul88], [Hai87]. They showed that the Abel-Jacobi image of the modified diagonal cycle on the triple product of a …
Characterization Of Eigenfunctions Of The Laplace-Beltrami Operator Through Radial Averages On Rank One Symmetric Spaces., Muna Naik Dr.
Characterization Of Eigenfunctions Of The Laplace-Beltrami Operator Through Radial Averages On Rank One Symmetric Spaces., Muna Naik Dr.
Doctoral Theses
Let X be a rank one Riemannian symmetric space of noncompact type and ∆ be the Laplace–Beltrami operator of X. The space X can be identified with the quotient space G/K where G is a connected noncompact semisimple Lie group of real rank one with finite centre and K is a maximal compact subgroup of G. Thus G acts naturally on X by left translations. Through this identification, a function or measure on X is radial (i.e. depends only on the distance from eK), when it is invariant under the left-action of K. We consider right-convolution operators Θ on functions …
A Study Of Operators On The Discrete Analogue Of Hardy Spaces On Homogeneous Trees And On Other Structures., P. Muthukumar Dr.
A Study Of Operators On The Discrete Analogue Of Hardy Spaces On Homogeneous Trees And On Other Structures., P. Muthukumar Dr.
Doctoral Theses
In analytic function theory, the study of multiplication and composition operators has a rich structure for various analytic function spaces of the unit disk D = {z ∈ C : |z| < 1} such as the Hardy spaces Hp, the Bergman spaces Ap and the Bloch space B. This theory connects the operator theoretic properties such as boundedness, compactness, spectrum, invertibility, isometry with that of the function theoretic properties of the inducing map (symbol) such as bijectivity, boundary behaviour and vise versa In Chapter 2, we define discrete analogue of generalized Hardy spaces (Tp) and their separable subspaces (Tp,0) on a homogenous rooted tree and study some of their properties such as completeness, inclusion relations with other spaces, separability and growth estimate for functions in these spaces and their consequences. In Chapter 3, we obtain equivalent conditions for multiplication operators Mψ on Tp and Tp,0 to be bounded and compact. Furthermore, we discuss point spectrum, approximate point spectrum and spectrum of multiplication operators and discuss when a multiplication operator is an isometry. In Chapter 4, we give an equivalent conditions for the composition operator Cφ to be bounded on Tp and on Tp,0 spaces and compute their operator norms. We have considered the composition operators induced by special symbols such as univalent and multivalent maps and automorphism of a homogenous tree. We also characterize invertible composition operators and isometric composition operators on Tp and on Tp,0 spaces. Also, we discuss the compactness of Cφ on Tp spaces and finally we prove that there are no compact composition operators on Tp,0 spaces. In Chapter 5, we consider the composition operators on the Hardy-Dirichlet space H2, the space of Dirichlet series with square summable coefficients. By using the Schur test, we give some upper and lower estimates on the norm of a composition operator on H2 , for the affine-like inducing symbol ϕ(s) = c1 + cqq −s , where q ≥ 2 is a fixed integer. We also give an estimate for approximation numbers of a composition operators in our H2 setting. In Chapter 6, we study the weighted composition operators preserving the class Pα. Some of its consequences and examples of certain special cases are presented. Furthermore, we discuss about the fixed points of weighted composition operators.
On Free-Type Rigid C*-Tensor Categories And Their Annular Representations., B. Madhav Reddy Dr.
On Free-Type Rigid C*-Tensor Categories And Their Annular Representations., B. Madhav Reddy Dr.
Doctoral Theses
No abstract provided.
Orbit Spaces Of Unimodular Rows Over Smooth Real Affine Algebras., Soumi Tikader Dr.
Orbit Spaces Of Unimodular Rows Over Smooth Real Affine Algebras., Soumi Tikader Dr.
Doctoral Theses
Let R be a commutative, Noetherian ring of (Krull) dimension d. It is well known that the set of isomorphism classes of (oriented, if d is even) stably free R-modules of rank d carries the structure of an abelian group. This group can be identified with the orbit space of unimodular rows namely, Umd+1(R)/SLd+1(R). The prime objective of this thesis is to provide the complete computation of this group, when X = Spec(R) be a smooth real affine variety of dimension d ≥ 2 (with the assumption that the set of real points of X is non-empty and orientable). In …
Infinite Mode Quantum Gaussian States., Tiju Cherian John Dr.
Infinite Mode Quantum Gaussian States., Tiju Cherian John Dr.
Doctoral Theses
No abstract provided.
Essays On Economic Behaviour And Regulation., Subrato Banerjee Dr.
Essays On Economic Behaviour And Regulation., Subrato Banerjee Dr.
Doctoral Theses
To sum up, this thesis looks at agent behaviour in the laboratory, in the field, and in the market. Firstly, we impose a requirement in the laboratory (Chapter 2) that mimics a regulatory environment (similar to the introduction of a maximum retail price, or a legal fare subject to which an economic transaction must take place), and study individual behaviour subject to our (imposed) requirements. We then study the effect of real-life regulation on the behaviour of economic agents in the field. While the effect of regulation is seen in the field (that is, we see that many auto drivers …
On Rational Subgroups Of Exceptional Groups., Neha Hooda Dr.
On Rational Subgroups Of Exceptional Groups., Neha Hooda Dr.
Doctoral Theses
The main theme of this thesis is the study of exceptional algebraic groups via their subgroups. This theme has been widely explored by various authors (Martin Leibeck, Gary Seitz, Adam Thomas, Donna Testerman to mention a few), mainly for split groups ([26], [27], [28], [60] ). When the field of definition k of the concerned algebraic groups is not algebraically closed, the classification of k-subgroups is largely an open problem. In the thesis, we mainly handle the cases of simple groups of type F4 and G2 defined over an arbitrary field. These may not be split over k. We first …
Infinite Color Urn Models., Debleena Thacker Dr.
Infinite Color Urn Models., Debleena Thacker Dr.
Doctoral Theses
In recent years, there has been a wide variety of work on random reinforcement models of various kinds. Urn models form an important class of random reinforcement models, with numerous applications in engineering and informatics and bioscience. In recent years there have been several works on different kinds of urn models and their generalizations. For occupancy urn models, where one considers recursive addition of balls into finite or infinite number of boxes, there are some works which introduce models with infinitely many colors, typically represented by the boxes.As observed in [51], the earliest mentions of urn models are in the …
Inference On Time-To-Event Distribution From Retrospective Data With Imperfect Recall., Sedigheh Salehabadi Dr.
Inference On Time-To-Event Distribution From Retrospective Data With Imperfect Recall., Sedigheh Salehabadi Dr.
Doctoral Theses
Time-to-event data arises from measurements of time till the occurrence of an event of interest. Such data are common in the fields of biology, epidemiology, pub- lic health, medical research, economics and industry. The event of interest can be the death of a human being (Klein and Moeschberger, 2003), failure of a machine (Zhiguo et al., 2007), onset of menarche in adolescent and young adult females (Bergsten-Brucefors, 1976; Chumlea et al., 2003; Mirzaei, Sengupta and Das, 2015), onset (or relapse) of a disease (Klein and Moeschberger, 2003), dental develop- ment (Demirjian, Goldstien and Tanner, 1973; Eveleth and Tanner, 1990), breast …
Nonparametric Methods For Data In Infinite Dimensional Space., Anirvan Chakraborty Dr.
Nonparametric Methods For Data In Infinite Dimensional Space., Anirvan Chakraborty Dr.
Doctoral Theses
For univariate as well as finite dimensional multivariate data, there is an extensive literature on nonparametric statistical methods. One of the reasons for the popularity of nonparametric methods is that it is often difficult to justify the assumptions (e.g., Gaussian distribution of the data) made in the models used in parametric methods. Nonparametric procedures use more flexible models, which involve less assumptions. So, they are more robust against possible departures from the model assumptions, and are applicable to a wide variety of data. Nonparametric methods outperform their parametric competitors in many situations, where the assumptions required for the parametric methods …
Foliations With Geometric Structures: An Approach Through H-Principle., Sauvik Mukherjee Dr.
Foliations With Geometric Structures: An Approach Through H-Principle., Sauvik Mukherjee Dr.
Doctoral Theses
A foliation on a manifold M can be informally thought of as a partition of M into injectively immersed submanifolds, called leaves. In this thesis we study foliations whose leaves carry some specific geometric structures.The thesis consists of two parts. In the first part we classify foliations on open manifolds whose leaves are either locally conformal symplectic or contact manifolds. These foliations can be described by some higher geometric structures - namely the Poisson and the Jacobi structures. In the second part of the thesis, we consider foliations on open contact manifolds whose leaves are contact submanifolds of the ambient …
On The Analysis Of Some Recursive Equations In Probability., Arunangshu Biswas Dr.
On The Analysis Of Some Recursive Equations In Probability., Arunangshu Biswas Dr.
Doctoral Theses
This thesis deals with recursive systems used in theoretical and applied probability. Recursive systems are stochastic processes {Xn}n≥1 where the Xn depends on the earlier Xn−1 and also on some increment process which is uncorrelated with the process Xn. The simplest example of a recursive system is the Random Walk, whose properties have been extensively studied. Mathematically a recursive system takes the form Xn = f(Xn−1, n), is the increment/ innovation procedure and f(·, ·) is a function on the product space of xn and n. We first consider a recursive system called Self-Normalized sums (SNS) corresponding to a sequence …
Some Issues In Unsupervised Feature Selection Using Similarity., Partha Pratim Kundu Dr.
Some Issues In Unsupervised Feature Selection Using Similarity., Partha Pratim Kundu Dr.
Doctoral Theses
Pattern recognition is what humans do most of the time, without any conscious effort, and fortunately excel in. Information is received through various sensory organs, processed simultaneously in the brain, and its source is instantaneously identified without any perceptible effort. The interesting issue is that recognition occurs even under non-ideal conditions, i.e., when information is vague, imprecise or incomplete. In reality, most human activities depend on the success in performing various pattern recognition tasks. Let us consider an example. Before boarding a train or bus, we first select the appropriate one by identifying either the route number or its destination …
Wavelet Analysis On Local Fields Of Positive Characteristic., Quiser Jahan Dr.
Wavelet Analysis On Local Fields Of Positive Characteristic., Quiser Jahan Dr.
Doctoral Theses
In this chapter, we will give a brief history of wavelet analysis on R. We will also list some bask results on local felds which will be used in subvequent chapters.1.1 Wavelets on RWe fiest start with a brief history of wavelets und some basic defnitions and results conceming the orthonormal wavekts on R.1.1.1 A brief historyIn the last few decades vaveler theory has growa extensively and has drawn great atlention sot only in mathematies bu also in engineering, pitysics, computer science and many other fields. In signal and image processing, wavelets play a very important role.In 1910, A. Haar …
Euler Class Groups Of Polynomial And Sub Integral Extensions Of A Noetherian Ring., Md. Ali Zinna Dr.
Euler Class Groups Of Polynomial And Sub Integral Extensions Of A Noetherian Ring., Md. Ali Zinna Dr.
Doctoral Theses
ObjectiveThe main objectives of this thesis are the following:(i) To investigate the behaviour of the Euler class groups under integral and subintegral extensions. More precisely, given a subintegral (or integral) extension R+ S of Noetherian rings, we are interested in finding out the relationship between the Euler class group of R and the Euler class group of S.(ii) To develop a theory (namely, an extension of the theory of Euler class group to the Euler class group of R[T) relative to a projective R[T|-module L of rank 1) in order to detect the precise obstruction for a projective R[T]-module P …
Some Problems In Differential And Subdifferential Calculus Of Matrices., Priyanka Grover Dr.
Some Problems In Differential And Subdifferential Calculus Of Matrices., Priyanka Grover Dr.
Doctoral Theses
A central problem in many subjects like matrix analysis, perturbation theory, numerical analysis and physics is to study the effect of small changes in a matrix A on a function f(A). Among much studied functions on the space of matrices are trace, determinant, permanent, eigenvalues, norms. These are real or complex valued functions. In addition, there are some interesting functions that are matrix valued. For example, the (matrix) absolute value, tensor power, antisymmetric tensor power, symmetric tensor power.When a function is differentiable, one of the ways to study the above problem is by using the derivative of f at A, …