http://hdl.handle.net/123456789/2203 Thesis submitted by MP -2020 batch as part of their course Thu, 23 Apr 2026 09:29:45 GMT 2026-04-23T09:29:45Z http://hdl.handle.net/123456789/2208 Title: Understanding the role of mbd3b in Zebrafish Retina Regeneration/ Authors: Hammad, Syed Mohammad Abstract: Müller glia (MG) helps in regeneration of injured retina in Zebrafish, making it a valuable model system for studying retina regeneration. The exact mechanism of molecular interplay that orchestrates de-differentiation, proliferation and re-differentiation processes occurring during regeneration still remains elusive. These processes are believed to accompany an extensive rearrangement in the genetic and epigenetic landscape of the regenerating retinal cell. Although the roles of many genetic and epigenetic regulators have been studied in the light of regeneration, that of developmentally important gene Mbd3 remains unexplored. Mbd3 is an essential component of the Nucleosome remodeling and Histone Deacetylase complex, and thus exerts an epigenetic control over the cell expression. We investigated the role of Mbd3b, a methyl CpG binding domain containing protein, in different stages of zebrafish retina regeneration. We found that mbd3b levels are regulated during retina regeneration, with higher expression near the injury site at 6dpi. Overexpression of mbd3b has revealed its regulatory role in controlling the proliferation of Müller glia cells, and also suggested its regulation on several Regeneration-associated Genes. Moreover, we found reduction in the level of mbd3b on Verteporfin drug treatment, suggesting its regulation by Hippo signaling pathway. These results suggest that Mbd3b plays a crucial role in zebrafish retina regeneration and holds promise as a potential therapeutic target for retinal diseases like Diabetic Retinopathy. Description: Embargo period Mon, 01 May 2023 00:00:00 GMT http://hdl.handle.net/123456789/2208 2023-05-01T00:00:00Z http://hdl.handle.net/123456789/2207 Title: Introduction to Riemann Surfaces Authors: Jana, Barnali Abstract: I have done my masters thesis on Riemann Surfces . This article provides an introduc- tion to Riemann surfaces, which are locally open sets in the complex plane. The definition is made precise by defining complex charts and structures, and examples of compact Rie- mann surfaces, including the Projective Line P 1 , complex tori, and smooth plane curves, are presented. To determine if a function defined near a point on a Riemann surface is holomor- phic, complex charts are used to transport the function to the neighborhood of a point in the complex plane, and this process is made precise for a variety of properties. The concept of singularity type (removable, pole, essential) for functions of a single variable extends read- ily to functions on a Riemann surface. Several theorems concerning holomorphic maps, including the open mapping theorem, identity theorem, and discreteness of preimages, are immediate consequences of the corresponding theorem for holomorphic functions. Holo- morphic maps between two Riemann surfaces have a standard normal form in some local coordinates, where essentially every map looks like a power map. Holomorphic maps be- tween compact Riemann surfaces exhibit several beautiful properties, including constancy of degree map. The article provides a proof that the sum of orders of a non-constant mero- morphic function on a Riemann surface is zero. The constancy of the degree of a holomor- phic map between compact Riemann surfaces, combined with the theory of Euler numbers, gives an important formula known as Riemann-Hurwitz’s formula. The article also covers gluing of Riemann surfaces, with hyperelliptic Riemann surfaces as an important example, and identifies all automorphism groups of holomorphic functions between complex tori. In the last section, the article discusses group actions on Riemann surfaces, and introduces the basic construction of Riemann surfaces by dividing a known Riemann surface by the action of a group. Description: Embargo period Mon, 01 May 2023 00:00:00 GMT http://hdl.handle.net/123456789/2207 2023-05-01T00:00:00Z http://hdl.handle.net/123456789/2206 Title: Spectral Theory of Normal Operators Authors: Das, Biplab Abstract: We discuss the spectral theory of bounded normal operators on Hilbert Space and functional cal- culus, as well as the Gelfand-Neimark-Segal construction of C ⇤ -algebras, also discuss symmetric extensions of unbounded operators. We begin by introducing the spectral theory for compact self-adjoint operators and then extend it to compact normal operators. We also discuss the idea of the spectrum for Banach algebras and explores complex analysis for operator-valued functions, including integration and Cauchy integral formula. Finally, we discuss the concept of unbounded operators and provides the idea of symmetric self-adjoint extensions of closed symmetric unbounded operators Description: Embargo period Mon, 01 May 2023 00:00:00 GMT http://hdl.handle.net/123456789/2206 2023-05-01T00:00:00Z http://hdl.handle.net/123456789/2204 Title: Markov Decision Process and Its Applications Authors: Mondal, Rishov Abstract: This thesis investigates the potential of Markov decision processes (MDP) as a tool for solving complex decision-making problems in real-life scenarios. The project delves into the application of MDP in stochastic games, specifically by analyzing an inventory duopoly with a yield uncertainty problem as part of the operations research problem. The thesis also explores the role of MDP in analyzing the budget allocation problem in the Voter Model, a popular model in opinion dynamics. The study provides a comprehensive analysis of MDP’s effectiveness in solving real-life problems and highlights its benefits over other decision-making models. The project offers insights into how MDP can be effectively used to analyze and solve real-life problems and provides directions for future research in this area. Description: Embargo period Mon, 01 May 2023 00:00:00 GMT http://hdl.handle.net/123456789/2204 2023-05-01T00:00:00Z