Variants of vertex and edge colorings of graphs
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A k-linear coloring of a graph G is an edge coloring of G with k colors so that each
color class forms a linear forest—a forest whose each connected component is a path.
The linear arboricity χ′
l(G) of G is the minimum integer k such that ther...
Embedding problems for the ´etale fundamental group of curves
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Let X be a smooth projective curve over an algebraically closed field k of char-
acteristic p > 0, S be a finite subset of closed points in X. Given an embedding
problem (β : Γ ↠ G, α : π´et
1 (X \S) ↠ G) for the ´etale fundam...
Enhanced Security Approaches for Data Protection: Managing Consent, Data Breach, and Asset Inheritance
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The journey of the Indian data protection framework started in 2018 with the introduction of the initial draft as ``Personal Data Protection Bill (PDPB-2018)''. Subsequently, a revised draft PDPB-2019 was introduced. This went through revisions as PDPB 2021 and Digital Personal Data&...
Algorithms and Applications in Complex Network Representation, Classification and Manipulation
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A complex network is a useful model for many real-world systems. Recently, much effort has been put into studying the insights of the complex network. This thesis is all about the study of complex networks.
Based on the study, this thesis can be broadly divided into...
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: ...