This thesis contains three chapters on individual decision-making and choice. The
first chapter introduces a general model of decision-making where alternatives are sequentially
examined by a decision maker. Our main object of study is a decision rule
that maps infinite sequence...
Cancellations in Short Sums related to Hecke-Cusp Forms
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In number theory, a problem which arises in a variety of contexts is getting non-
trivial cancellation for the general correlation problem, specially when we assume
that they are short sums related to Hecke-cusp forms. In my thesis, I have studied
the cancellation ...
Bilateral Trade and Partnership with Loss Averse Agents
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This thesis consists of three essays on bilateral trading and partnership with loss averse agents. All the three essays consider the same model where two loss averse agents (Tversky and Kahneman (1991), K ̈oszegi and Rabin (2006)) hold some shares of an asset and now want...
Applications of Exponential Maps to Epimorphism and Cancellation Problems
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Throughout this talk k will denote a field. The talk is primarily divided into
two parts. In the first part we will discuss one of the formidable open problems in
the area of Affine Algebraic Geometry, called the Epimorphism Problem.
Question 1. If k[X1,...,Xn]...
On Combinatorial Constructions of Mutually Unbiased Bases (MUBs) with Approximations
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Construction of Mutually Unbiased Bases (MUBs) is a very challenging combinatorial problem in the domain of quantum information theory with several long-standing open questions. The basic definition considers two orthonormal bases in the d-dimensional complex Hilbert space with a fixed specific...
This thesis consists of two essays on allocation theory and one on voting theory. The
first chapter analyses preference domains (called priority domains) where every strategy proof, non-bossy and neutral allocation rule is a priority rule. It considers two versions of neutrality: ...
Some Contributions to Multiple Hypotheses Testing under Dependence
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Large-scale multiple testing problems in various scientific disciplines often study correlated
variables simultaneously. However, the existing literature lacks a study of the performances of
FWER controlling procedures under dependence. This thesis concentrates mainly on FWER
and generalized F...
Classification of Alzheimer's Disease by Machine Learning methods using MRI and fMRI data
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Large Sample Inference in Finite Population Problems
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In sample survey, estimation of different finite population parameters like, mean,
median, variance, coefficient of variation, correlation and regression coefficients, interquartile
range, measure of skewness, etc. was considered extensively in the past.
However, comparison of different estimators&...
Design and Analysis of Some Symmetric Key Schemes for Encryption and Authentication
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This thesis mainly focuses on the design and analysis of tweakable enciphering schemes
(TESs) and message authentication codes (MACs).
Tweakable enciphering schemes are length preserving encryption schemes that
provide security of a strong tweakable pseudorandom permutation. There are sev...