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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 …