https://dspace.imsc.res.in/xmlui/handle/123456789/1 IMSc Theses/ Dissertations Thu, 04 Jun 2026 09:07:29 GMT 2026-06-04T09:07:29Z https://dspace.imsc.res.in/xmlui/handle/123456789/919 Utilizing Optimal Transport Theory to Model Peptide Conformational Distributions and Address the Levinthal Problem [HBNI Th275] Vigneshwaran K Peptide conformation studies are essential due to their role in biological functions like cell signaling and drug design, as well as their importance in protein structure prediction. Peptides form secondary structures such as alpha helices and beta hairpins, which can serve as building blocks for predicting three-dimensional protein structures. However, peptides exhibit structural flexibility, adopting a range of conformations, with only specific low-energy conformations being bioactive for particular functions. Constructing conformational distributions for longer peptides is challenging due to limited data from experimental sources like the Protein Data Bank (PDB), which mainly provides information for shorter peptides like dipeptides and tripeptides. In this thesis, we address this challenge by using optimal transport techniques to construct conformational distributions for longer peptides. Starting with dipeptide distributions, we develop a method to generate tetrapeptide conformational distributions by minimizing the expectation value of interaction energy functions. Applying this approach to tetrapeptides composed of alanine and glycine reveals preferences for right-handed alpha helices in alanine-rich sequences (e.g., AAAA, AAAG) and beta turns in glycine-dominated ones (e.g., GGGG, GAGG). Extending this method recursively, we generate conformational probabilities for longer peptides, enabling efficient prediction of their structural behavior. This approach provides an innovative solution for exploring peptide flexibility and bioactive conformations. Wed, 01 Jan 2025 00:00:00 GMT https://dspace.imsc.res.in/xmlui/handle/123456789/919 2025-01-01T00:00:00Z https://dspace.imsc.res.in/xmlui/handle/123456789/918 Quantified CDCL and Dependency Schemes: A proof-theoretic study [HBNI Th278] Abhimanyu Choudhury Quantified Conflict Driven Clause Learning (QCDCL) is one of the main approaches to solving Quantified Boolean Formulas (QBF). Cube-learning is employed in this approach to ensure that true formulas can be verified. Dependency Schemes help to detect spurious dependencies that are implied by the variable ordering in the quantifier prefix of QBFs but are not essential for constructing (counter)models. This detection can provably shorten refutations in specific proof systems, and is expected to speed up runs of QBF solvers. The simplest underlying proof system QCDCL [BB23a], formalises the reasoning in the QCDCL approach on false formulas, when neither cube-learning nor dependency schemes is used. The work of [BPB24] further incorporates cube-learning. This thesis is the first work that incorporates the dependency scheme heuristic in the QCDCL proof system. The usage of dependency schemes in QCDCL proof system with and with- out cube-learning are formalised and these new family of systems, the D1 + QCDCLORD (ClausePol, CubePol) proof systems, which incorporates dependency schemes into the proof system, and show it to be sound and complete. When the decisions are restricted to follow level order, but dependency schemes are used in propagation and learning, in conjunction with cube-learning, the resulting proof systems using the dependency schemes Dstd and Drrs are investigated in detail and their relative strengths are analysed. Thu, 01 Jan 2026 00:00:00 GMT https://dspace.imsc.res.in/xmlui/handle/123456789/918 2026-01-01T00:00:00Z https://dspace.imsc.res.in/xmlui/handle/123456789/917 Light Bending Under General Relativity: A Study of Pulsar–Black Hole Binaries [HBNI Th277] Jyotijwal Debnath Pulsars are precise cosmic clocks whose timing signals enable stringent tests of general relativity. In binary systems, several propagation delays arise due to orbital motion and gravitational effects, including the Romer delay, Shapiro delay, Einstein delay, and an additional geometric delay caused by gravitational light bending.Light bending also modifies the observed rotational phase of the pulsar, producing longitudinal and latitudinal bending delays and potentially distorting the pulse profile. While earlier studies treated these effects using weak-field approximations, this work adopts a more general approach and refers to them collectively as bending delays.These delays are most significant near superior conjunction, when the pulsar is behind its companion relative to the observer. This study investigates bending effects in pulsar–black hole binaries using realistic system parameters. The results are consistent with existing approximate models, except away from superior conjunction where such approximations fail.Both non-rotating (Schwarzschild) and rotating (Kerr) black hole companions are analyzed. The spin of the black hole has negligible impact on overall bending delays, although small frame-dragging contributions (longitudinal and latitudinal FD delays) of nanosecond order are identified, with discontinuities at specific orbital phases.The dependence of bending delays on parameters such as eccentricity, orbital period, and companion mass is also examined. Pulse profile analysis shows that for stellar-mass black holes, the signal strength increases without significant shape change, especially near superior conjunction.In the strong-field case of supermassive black hole companions, both the shape and strength of the pulse profile change significantly due to the Einstein ring exceeding the beam size, consistent with gravitational lensing theory.Overall, this work highlights the importance of light bending effects in pulsar–black hole binaries for precision timing and strong-field tests of gravity. Thu, 01 Jan 2026 00:00:00 GMT https://dspace.imsc.res.in/xmlui/handle/123456789/917 2026-01-01T00:00:00Z https://dspace.imsc.res.in/xmlui/handle/123456789/916 Probing Dense Matter Through f -mode Oscillations of Anisotropic Compact Stars in General Relativity [HBNI Th276] Sushovan Mondal Compact stars, such as neutron stars and quark stars, provide a unique environment for studying matter at extreme densities, though the underlying physics remains uncertain due to limitations in the equations of state (EoS). Gravitational waves (GWs), particularly those arising from quasi-normal modes (QNMs), offer a powerful probe of their internal structure. Among these, the fundamental (f-mode) oscillations are especially significant due to their strong coupling with gravitational radiation and sensitivity to stellar properties.This study presents a fully relativistic analysis of f-mode oscillations in anisotropic compact stars using general relativistic perturbation theory. Unlike earlier approaches based on isotropy or simplifying assumptions such as the Cowling approximation, both fluid and spacetime perturbations are included. Pressure anisotropy, motivated by physical effects such as superfluidity, magnetic fields, and pion condensation, is examined for neutron and quark stars with realistic EoS.Equilibrium configurations are constructed by extending the Tolman–Oppenheimer–Volkoff equations to incorporate anisotropy. The perturbation equations for non-radial oscillations are derived by linearizing Einstein’s field equations and solved numerically with appropriate boundary conditions.The results show that the f-mode frequency retains an approximately linear dependence on the square root of the average density, with anisotropy modifying the relation. Frequency increases with anisotropy at lower masses but decreases at higher masses, while the damping time decreases monotonically. Variations of up to ~20% in frequency and ~300% in damping time are observed compared to isotropic cases. The inverse normalized damping time also shows a linear dependence on compactness.Semi-empirical relations are developed linking frequency and damping time to mass, radius, and anisotropy. The frequency exhibits cubic dependence on anisotropy, while the damping time shows sextic dependence for neutron stars and quartic for quark stars.Overall, this work demonstrates that pressure anisotropy significantly affects the quasi-normal mode spectrum of compact stars and highlights its importance in gravitational wave astronomy and future astrophysical modeling. Wed, 01 Jan 2025 00:00:00 GMT https://dspace.imsc.res.in/xmlui/handle/123456789/916 2025-01-01T00:00:00Z