https://dspace.imsc.res.in/xmlui/handle/123456789/2 IMSc Theses/ Dissertations 2026-08-25T07:20:40Z https://dspace.imsc.res.in/xmlui/handle/123456789/928 NNLO QCD⌐QED corrections to unpolarized and polarized SIDIS [HBNI Th287]  Vaibhav Pathak This thesis focuses on advancing the theoretical understanding of semi-inclusive deep- inelastic scattering (SIDIS) through the high-precision computation of higher-order radiative corrections. In this work, we computated full Next-to-Next-to-Leading Order (NNLO) corrections to SIDIS structure functions in QCD, along with extension of this framework to include both pure Quantum Electrodynamics (QED) effects and their interplay with QCD at the same order of accuracy. Taken together, these results represent the contribution to the precision phenomenology of hadronic physics, and are directly relevant for the physics program of the upcoming Electron-Ion Collider (EIC). 2026-01-01T00:00:00Z https://dspace.imsc.res.in/xmlui/handle/123456789/927 Effect of non-equilibrium fluctuations in transport and escape problems [HBNI Th286]  Vishwajeet Kumar This thesis was broadly divided into two parts. The first part was dedicated to the formulation of the Arrhenius law for interacting diffusive systems, along with an analysis of its inference properties. The second part examined the role of finite intermediate barriers in accelerating the barrier-crossing dynamics of a single Brownian particle. In what follows, we summarize the central results arising from this thesis and outline potential directions for future research. 2026-01-01T00:00:00Z https://dspace.imsc.res.in/xmlui/handle/123456789/926 Parameterized approximation algorithms for Partial Covering and Satisfiability with budget constraints [HBNI Th285] Anannya Upasana This thesis studies parameterized approximation algorithms for partial covering problems through a unified framework centered around Maximum Coverage and CCMaxSat. We investigate two complementary optimization objectives: maximizing the number of satisfied constraints using a bounded number of selected objects, and minimizing the number of selected objects required to satisfy a prescribed number of constraints. We further extend these problems by incorporating fairness constraints on the constraints to be satisfied and matroid constraints on the selected objects, yielding a broad family of generalized optimization problems. 2026-01-01T00:00:00Z https://dspace.imsc.res.in/xmlui/handle/123456789/925 Complexity of regulatory logic and dynamics of Boolean models of biological networks [HBNI Th284] Priyotosh Sil Gene regulatory networks (GRNs) orchestrate cellular behavior through complex combinatorial interactions among genes. Boolean models provide a tractable framework for studying GRN dynamics and have been widely used to analyze stability, multistability, and attractor-based representations of cellular phenotypes. While extensive research has established that biological GRNs are highly constrained in both network topology and regulatory logic, the specific effects of different classes of regulatory logic on global network dynamics have not been systematically characterized. The key objective of this thesis is to develop a systematic understanding of how different classes of Boolean functions (BFs) influence the dynamics of Boolean GRN models across varying network topologies and levels of abstraction, thereby informing principled choices of regulatory logic in Boolean modeling of biological systems. Using both random Boolean networks (RBNs) and reconstructed biological GRNs, we show that regulatory logic plays a central role in determining network stability and dynamical organization. First, we analyze ensembles of RBNs to disentangle the effects of regulatory logic from those of network topology. By systematically varying network size, connectivity, and degree distribution, and by employing multiple notions of dynamical stability, we show that biologically meaningful classes of BFs consistently steer network dynamics toward ordered or near-critical regimes. In contrast, networks governed by random BFs exhibit strong sensitivity to topological parameters and frequently transition toward chaotic behavior with increasing connectivity or size. Across diverse stability measures, biologically meaningful BFs display reduced variability and enhanced robustness. Second, we analyze the effect of BF classes on the stability of reconstructed Boolean GRNs using ensembles in which network structure and biological attractors are held fixed while regulatory logic is varied. Adopting a global state-space perspective, we systematically examine how different classes of BFs shape the structure of the state transition graph (STG). To characterize global dynamical organization, we adapt concepts originally developed in the study of cellular automata (CA) and introduce CA-inspired measures of bushiness and convergence. We find that biologically meaningful BFs lead to faster convergence and more contractive STG structures than random logic. Finally, we critically evaluate threshold majority rules (TMRs), a subclass of threshold functions frequently employed in GRN modeling due to their implementation simplicity. Through a comparative analysis with nested canalyzing functions (NCFs), we show that TMRs exhibit higher complexity and sensitivity, are underrepresented in empirical datasets of regulatory logic, and often fail to recover biological attractors and associated basin sizes. These results indicate that, despite their convenience, TMRs are poorly suited as a modeling choice for biological GRNs. Altogether, this thesis establishes regulatory logic as a key determinant of Boolean GRN dynamics and provides systematic guidance for selecting biologically grounded BFs in the modeling of GRNs. 2026-01-01T00:00:00Z