Theses
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Item Essays on Liberalization and Trade Policy in Developing Economies under Increasing Returns(Indian Statistical Institute, 2026-06-25) Kapoor, ShivamDeveloping countries occupy an important place in the world trade pattern of today. Taking advantage of low wages in these countries, the low technology and labor intensive stages of production in many product lines are outsourced here. Hence participation in Global Value Chains for a developing country on the one hand generates employment in manufacturing thereby helping realize economies of scale arising out of division of labor, on the other hand the gains from trade accruing from such participation may be low due to presence of severe distortions like weak legal and financial institutions, and may cause distributional conflicts. My dissertation studies the role of trade and investment liberalization policies for developing countries in the presence of increasing returns. Chapter 2 of the thesis focuses on trade in both final good and the differentiated varieties of an intermediate input between a capital abundant country and a labor abundant country. The intermediate input sector comprises monopolistically competitive firms of heterogeneous productivity. I analyze the impact on the two countries of moving from autarky to free trade. When trade in varieties is subject to both fixed and variable trade costs, the impact of a bilateral liberalization is studied with the help of a numerical simulation. Chapter 3 considers a small open economy characterized by open urban unemployment and rural-urban migration. The urban sector produces an import-competing (tariff protected) final good and a non-traded input that is subject to increasing returns to scale. The rural sector produces the exportable by combining the input with rural labor. In this structure the policy impacts of a foreign capital inflow and an increase in tariff protection are studied. In Chapter 4, I consider a two country, three sector and one factor model of trade and unemployment. Trade takes place in one homogeneous good (costlessly) and the varieties of two differentiated industrial goods (subject to variable trade cost). Equilibrium unemployment of the Shapiro-Stiglitz type is modeled. In this structure I analyze the impact of a unilateral, sector-specific trade policy on industrial relocation in both the protected and unprotected sectors, and on the employment rates in the two countries. Turning again to the case of a small open economy, in Chapter 5, I combine the production structure studied in Chapter 2 with the assumption that the Home economy imports a fixed number of Foreign varieties at a given price (subject to a tariff). Here I study the productivity and welfare effects of an inflow of foreign capital assuming full repatriation of foreign profits. Summary, conclusions and possible extensions for future research are outlined in Chapter 6.Item Relay Selection and User Scheduling in Reconfigurable Intelligent Surface Assisted Millimeter-wave D2D Communication(Indian Statistical Institute, 2026-06-19) Sau, LakshmikantaReconfigurable intelligent surface (RIS) assisted millimeter wave (mmWave) device to device (D2D) communication has recently been proposed as a viable solution to support the overwhelming data traffic in fifth-generation (5G) and beyond wireless networks. However, due to the substantial propagation and penetration losses of mmWave, a direct line of sight (LoS) link between a pair of proximity devices is required for effective communication. Static obstacles like trees and buildings can easily obstruct the direct LoS connectivity between a device pair. In such cases, RISs help to establish an indirect LoS link between an obstructed device pair by reflecting the signals in the desired direction. In Chapter 2, we propose a set cover-based RIS deployment strategy to serve the maximum number of obstructed device pairs with the minimum number of RISs. In particular, we have demonstrated that double reflections via two consecutive RISs can greatly lower the RIS density in the environment, preventing resource waste and enabling the service of more obstructed device pairs. After the RIS deployment, for information transfer, we also propose an energy-efficient RIS group selection criteria. Moreover, we prove that under some conditions, double reflections are more beneficial than single reflection, which is counter-intuitive. Numerical results show that our approach outperforms a random and a recent deployment strategy. In Chapter 3, assuming that the RISs are already deployed and the positions of the nearby users are known, we propose a double-RIS assisted multihop routing scheme for a device pair. Besides the RISs, the emphasis of this work is to make more use of the existing intermediate users (IUs), which can act as relays. Hence, the density of RIS deployment in the surroundings can be reduced, which leads to the avoidance of resource wastage. However, we cannot solely depend on the IUs because this implies complete dependence on their availability for relaying and as a result, the aspect of reliability in terms of delay-constrained information transfer may not be guaranteed. Moreover, the IUs are considered capable of energy harvesting, and as a result, they do not waste their own energy in the process of volunteering to act as a relay for other users. Numerical results demonstrate the advantage of the proposed scheme over some existing approaches, and lastly, useful insights related to the scheme design are also drawn, where we characterize the maximum acceptable delay at each hop under different set-ups. The previous chapter presented a routing scheme for a particular device pair. For multiple device pairs, a single RIS may be simultaneously requested by several devices to act as a relay for their seamless communications. To deal with such cases, in Chapter 4, we propose a priority-aware, user traffic–dependent, grouping-based multihop user scheduling scheme for RIS-assisted mmWave D2D communication under spatially correlated channels. Specifically, the proposed scheme exploits the priority of the users (based on their respective delay-constrained applications) and the aspect of spatial correlation in the narrowly spaced reflecting elements of the RISs. Here, based on the other users in the neighborhood, their respective traffic characteristics, and the already deployed RISs in the surroundings, we establish a multihop connection for energy-efficient information transfer from one of the users to its intended receiver. In this context, we take into account the impact of considering practical discrete phase shifts at the RIS patches instead of its ideal continuous counterpart. Moreover, we also claim and demonstrate that the existing classic least remaining distance based approach is not always the optimal solution. Finally, the numerical results demonstrate the advantages of the proposed strategy over the existing benchmark schemes in terms of data throughput, energy consumption, and energy efficiency. In the previous chapter, each device pair selects the best energy-efficient group, and in case of multiple pairs selecting the same best group, they are scheduled as per their priorities. However, the best group may lead to a large delay for some of the pairs. Moreover, the energy harvesting aspect is not considered there. In Chapter 5, we investigate various group selection strategies which select the k-th best group by considering self-sustainable RIS with spatially correlated channels. Specifically, we consider both power splitting and time switching configurations of the self-sustainable RIS to analyze the system performance and propose appropriate bounds on the choice of system parameters. The analysis takes into account both linear and non-linear energy harvesting models. Based on the application requirements, we propose various group selection strategies, which schedule the k-th best available group based on the end-to-end signal-to-noise ratio and also the energy harvested at a particular group. Accordingly, by using tools from high-order statistics, we derive analytical expressions for the outage probability of each selection strategy. Moreover, using extreme value theory, we investigate an asymptotic scenario where the number of groups available for selection at an RIS approaches infinity. The nontrivial insights obtained from this approach are especially beneficial in applications like large intelligent surface-aided wireless communication. Finally, the numerical results demonstrate the importance and benefits of the proposed approaches in terms of throughput and outage performance.Item Designing Truthful Mechanisms: A study of Voting and Matching Rules(Indian Statistical Institute, 2026-05-27) Bose, AbhigyanMechanisms are formal procedures used in game theory and economics to aggregate individual preferences into collective outcomes in strategic settings with private information. A truthful or strategy-proof mechanism ensures that agents are best off reporting their true preferences, thereby eliminating incentives for manipulation. Such mechanisms are important for achieving fairness, efficiency, and simplicity in practical applications. In environments without monetary transfers, voting and matching rules are two central classes of mechanisms. Voting rules are typically used for public decision-making, while matching rules allocate private goods among individuals. This thesis studies strategy-proof voting and matching rules under different environments and restrictions on preference domains. The thesis is divided into two parts: the first three chapters focus on voting rules, and the last three on matching rules. The first two chapters analyze voting environments where agents share common beliefs over the preference domain, with the relevant incentive notion being locally robust ordinal Bayesian incentive compatibility (LOBIC). Chapter one corrects a result from the existing literature, while chapter two introduces a model of correlated priors based on a betweenness property. Chapter three studies voting structures in environments where agents are connected through an exogenous graph. In this setting, we introduce incentive-compatible extendable voting rules and characterize them under different graph structures. The remaining chapters focus on matching theory. Under unrestricted preferences, the Top Trading Cycles (TTC) mechanism of Gale is known to be the unique rule satisfying strategy-proofness, individual rationality, and Pareto optimality. However, Bade showed that this uniqueness fails under single peaked preferences. Chapters four and five extend this line of research to broader preference domains: multiple single-peaked preferences and single peaked preferences on trees. In both chapters, we propose new algorithms satisfying strategy-proofness, individual rationality, and Pareto optimality. We further study the stronger notion of obvious strategy-proofness, introduced by Li (2017), proving non-existence results for such matching rules. Finally, chapter six presents general existence results for obviously strategy-proof matching rules within the class of individually rational and Pareto optimal rules.Item C*-Extreme Quantum Instruments; Completion and Disintegration of Completely Positive Maps(2026-06-01) Chongdar, ArghyaThis thesis develops a comprehensive operator-algebraic framework for the study of completely positive (CP) instruments, with contributions spanning convexity theory, integration theory, completion problems, and disintegration theory. We begin by laying the foundational groundwork in the theory of C*-algebras and von Neumann algebras, introducing key structures such as CP maps, positive operator-valued measures (POVMs), and CP instruments, along with their dilation-theoretic properties. Pure and decomposable instruments are characterized via minimal bi-dilations, and CP instruments are realized as bivariate maps, providing a rigorous quantum analogue of classical joint measures. The thesis then investigates convexity-theoretic aspects of instruments. A structural characterization of C*-extreme unital completely positive (UCP) instruments on finite-dimensional Hilbert spaces is established, employing methods from the theory of nest algebras. The interplay between C*-extremality and the marginals of an instrument is studied, yielding results on the spectral nature of POVM marginals and the unique determination of an instrument from a single C*-extreme marginal. A systematic integration theory with respect to CP instruments is then developed, inspired by Bartle's classical vector integration framework. This culminates in a CP-instrument correspondence theorem on compact Hausdorff spaces and, notably, a Krein-Milman type theorem for CP instruments on separable C*-algebras — a result not previously available in the literature. The thesis further addresses the CP completion problem — the extension of partially defined linear maps to fully CP maps on C*-algebras — establishing the existence and uniqueness of minimal CP completions, and generalizing a result of Parzygnat and Russo on almost-everywhere identity maps to the full generality of von Neumann algebras. Finally, the theory of non-commutative disintegration is developed, connecting classical disintegration to the existence of left inverses for CP maps. Structural results for left-invertible normal CP maps on B(H) are obtained, and existence and uniqueness of disintegrations are established in the infinite-dimensional setting.Item Exploring Resource-Efficient Deep Learning for Medical Image Segmentation(2026-05-19) Dutta, PallabiAutomated medical image segmentation improves diagnostic accuracy by au tomating the precise delineation of target anatomical structures in the input images. Artificial Intelligence (AI), and specifically, Deep Learning (DL), has emerged as a state-of-the-art approach for this task. However, the significant computational demands of DL approaches often hinders their deployment. Ad vanced models, including Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs), require substantial processing power and a large memory footprint, limiting their use in resource-constrained settings. This thesis aims to address this challenge by developing a series of novel, resource-efficient DL models that achieve high segmentation accuracy with reduced computational costs. The research follows a logical progression of architectural novelty. First, global context-aware attention frameworks, FuDSA-Net and VoCANet, are in troduced by leveraging multi-scalar features and global-context aware attention for efficient 2D/3D segmentation. The spatial and spectral domains are then integrated using a novel hybrid CNN-ViT framework WaveCoformer for learn ing robust representation of the target structure. The developed model achieves high segmentation accuracy with a lower parameter count. Subsequently, the research investigates a computationally efficient alternative to ViTs for segmen tation, called Vision-xLSTM, by developing the U-VixLSTM model. This is extended to the Rot-UViL architecture, capable of modeling cross-dimensional dependencies in volumetric inputs with its novel rotational attention. Finally, the thesis presents a prompt-driven pruning framework for ViT-based segmenta tion models, called PrATo, which dynamically prunes irrelevant ViT tokens with a parameter-free prompt-driven scoring mechanism. The framework achieves ∼ 35−55% reduction of processed tokens. The frameworks developed in this thesis are validated across multiple publicly available datasets; demonstrating their high segmentation accuracy along with computational efficiency.Item On the Jordan-Chevalley-Dunford Decomposition of Certain Classes of Operators and Convergence of Their Normalized Power Sequences(Indian Statistical Institute, 2026-02-25) Shekhawat, RenuThe classical Jordan–Chevalley decomposition expresses a matrix A ∈ Mn(C) as a unique commuting sum A = D + N, where D is diagonalizable and N is nilpotent. Although this decomposition is algebraic in origin, it encodes significant spectral information and, as shown by Nayak, has an important analytic consequence: the convergence of the normalized power sequence {|A^n|^ 1/n }n∈N ; |A| := (A∗A)^1/2 . In this thesis we study Jordan-Chevalley–type decompositions in infinite-dimensional settings and their connection with the convergence behaviour of normalized power sequences. In particular, we discuss this phenomenon for Dunford’s spectral operators and compact operators on a complex Hilbert space, and further extend the theory to operators affiliated with finite type I von Neumann algebras.Item Essays on Monetary-Fiscal Interactions in Emerging Market and Developing Economies(Indian Statistical Institute, 2025-07-17) Bahl, OjasvitaThis thesis contains three chapters on monetary-fiscal interactions in Emerging Market and Developing Economies. Governments in emerging markets and developing economies (EMDEs) frequently intervene in agricultural markets to stabilize food prices following adverse shocks. These interventions often take the form of large-scale food procurement and redistribution, which we define as a redistributive policy shock. This chapter examines the effects of such shocks on inflation and the distribution of consumption between rich and poor households. We develop a tractable two-sector, two-agent New Keynesian DSGE model and estimate its parameters for the Indian economy using Bayesian methods. Our findings reveal that under an inflation-targeting regime, consumer heterogeneity plays a crucial role in determining whether monetary policy responses to various shocks enhance or reduce aggregate welfare. The second chapter evaluates the welfare implications of redistributive policy shocks under alternative monetary policy regimes. Building on Chapter 1, which finds that redistributive policy shocks are inflationary and expansionary in terms of aggregate output, we assess how different monetary responses alter welfare outcomes. Following Schmitt-Grohe Uribe (2007), we compute consumptionequivalent welfare gains to compare the welfare cost of these shocks under the optimised simple monetary rule and the planner’s solution (Ramsey Optimal Monetary Policy). The optimal rule features no interest rate smoothing, a strong response to inflation, and a limited reaction to output. Our findings demonstrate the critical role of monetary policy in shaping the welfare impact of redistributive shocks. We further compare these welfare effects to those of an agricultural productivity shock and show that the steady-state level of redistribution significantly affects the relative costs of redistribution-driven fluctuations. We find that non-optimised rules lead to significantly higher welfare costs than optimised simple rules. In the third chapter, we study the interactions between informality, underdeveloped financial markets and fiscal consolidation by developing a two-sector, twoagent medium-scale NK-DSGE model that allows public expenditure and private consumption to be either substitutes or complements. While there is a large literature that tries to understand the effects of fiscal consolidation in AEs, there is a relatively small literature on fiscal consolidation in EMDEs. We find that greater informality dampens the reduction in public debt from a contractionary fiscal policy shock. We find tax-based shocks to exhibit greater decline in debt at the cost of a greater contraction in output than spending-based shocks. Our analysis suggests that a fiscal consolidation shock can be expansionary when private consumption and public spending exhibit moderately-high substitutability consistent with the literature on expansionary fiscal consolidations.Item Flexible Modeling of non-Gaussian Longitudinal Data: Some Approaches using Copula(Indian Statistical Institute, Kolkata, 2026-03-16) Chattopadhyay, SubhajitLongitudinal data are common in medical and biological sciences, where measurements are gathered from subjects over time to explore relationships with explanatory variables (covariates) and to uncover the underlying mechanisms of dependence among these measurements. The responses observed at each instance can be either discrete or continuous. One of the primary challenges in longitudinal data analysis lies in the non-Gaussian nature of the response variables. As a result, there are relatively few multivariate models in the literature that effectively address the specific characteristics observed in such datasets. In this dissertation, we address four problems concerning longitudinal data analysis by developing new statistical models. These models specifically address the time-related relationships found in various types of non-Gaussian longitudinal data by employing suitable classes of parametric copulas. In the third chapter of this dissertation, we examine a motivating dataset from a recent HIV-AIDS study conducted in Livingstone district, Zambia. The histogram plots of the repeated measurements at each time point reveal asymmetry in the marginal distributions, and pairwise scatter plots uncover nonelliptical dependence patterns. Traditional linear mixed models, typically used for longitudinal data, struggle to capture these complexities effectively. We introduced skew-elliptical copula based mixed models to analyze this continuous data, where we use generalized linear mixed models (GLMM) for the marginals (e.g., Gamma mixed model), and address the temporal dependence of repeated measurements by utilizing copulas associated with skew-elliptical distributions (such as skew-normal/skew-t). The proposed class of copula-based mixed models addresses asymmetry, between-subject variability, and non-standard temporal dependence simultaneously, thereby extending beyond the limitations of standard linear mixed models based on multivariate normality. We estimate the model parameters using the IFM (inference function of margins) method, and outline the procedure for obtaining standard errors of the parameter estimates. To evaluate the performance of this approach under finite sample conditions, rigorous simulation studies are conducted, encompassing skewed and symmetric marginal distributions along with various copula selections. Finally, we apply these models to the HIV dataset and present the insight gained from the analysis. In the fourth chapter of this dissertation, we introduce factor copula models tailored for unbalanced non-Gaussian longitudinal data. Modeling the joint distribution of such data, where subjects may have varying numbers of repeated measurements and responses can be continuous or discrete, poses practical challenges, especially with numerous measurements per subject. Factor copula models, which are canonical vine copulas, leverage latent variables to elucidate the underlying dependence structure of multivariate data. This approach aids in interpretation and implementation for unbalanced longitudinal datasets, enhancing our ability to model complex dependencies effectively. We develop regression models for continuous, binary and ordinal longitudinal data, incorporating covariates, using factor copula constructions with subject-specific latent variables. With consideration for homogeneous within-subject dependence, the proposed models enable feasible parametric inference in moderate to high dimensional scenarios, employing a two-stage (IFM) estimation method. We also present a method for evaluating the residuals of factor copula models to visually assess the goodness of fit. The performance of the proposed models in finite samples is assessed through extensive simulation studies. In empirical analyses, we apply these models to analyze various longitudinal responses from two real-world datasets. Furthermore, we compare the performance of these models with widely used random effects models using standard selection techniques, revealing significant improvements. Our findings suggest that factor copula models can serve as viable alternatives to random effect models, offering deeper insights into the temporal dependence of longitudinal data across diverse contexts. In the fifth chapter of this dissertation, we address the issue of modeling complex and hidden temporal dependence of count longitudinal data. Multivariate elliptical copulas are typically preferred in statistical literature to analyze dependence between repeated measurements of longitudinal data since they allow for different choices of the correlation structure. But these copulas lack in flexibility to model dependence and inference is only feasible under parametric restrictions. In this chapter, we propose the use of finite mixtures of elliptical copulas to enhance the modeling of temporal dependence in discrete longitudinal data. This approach enables the utilization of distinct correlation matrices within each component of the mixture copula. We theoretically explore the dependence properties of finite mixtures of copulas before employing them to construct regression models for count longitudinal data. Inference for this proposed class of models is based on a composite likelihood approach, and we evaluate the finite sample performance of parameter estimates through extensive simulation studies. To validate the fitting of the proposed models, we extend traditional techniques and introduce the t-plot method to accommodate finite mixtures of elliptical copulas. Finally we apply the proposed models to analyze the temporal dependence within two real-world count longitudinal datasets and demonstrate their superiority over standard elliptical copulas. In the final contributing chapter of this dissertation, we introduce a novel multivariate copula based on the multivariate geometric skew-normal (GSN) distribution. This asymmetric copula serves as an alternative to the skew-normal copula proposed by Azzalini. Unlike the standard skew-normal copula, the multivariate GSN copula retains closure properties under marginalization, which offers computational advantages for modeling multivariate discrete data. In this chapter, we outline the construction of the geometric skew-normal copula and its application in modeling the temporal dependence observed in non-Gaussian longitudinal data. We begin by exploring the theoretical properties of the proposed multivariate copula. Subsequently, we develop regression models tailored for both continuous and discrete longitudinal data using this innovative framework. Notably, the quantile function of this copula remains independent of the correlation matrix of its respective multivariate distribution, offering computational advantages in likelihood inference compared to copulas derived from skew-elliptical distributions proposed by Azzalini. Furthermore, composite likelihood inference becomes feasible for this multivariate copula, allowing for parameter estimation from ordered probit models with the same dependence structure as the geometric skew-normal distribution. We conduct extensive simulation studies to validate the geometric skew-normal copula based models and apply them to analyze the longitudinal dependence of two real-world data sets. Finally, We present our findings in terms of the improvements over regression models based on multivariate Gaussian copulas.Item Development of Some Scalable Pattern Recognition Algorithms for Real Life Data Analysis(2017-11-20) Garai, ParthaA huge amount of data is being generated continuously as a result of recent advancement and wide use of high-throughput technologies. With the rapid increase in size of data distributed worldwide, understanding the data has become critical. In this regard, dimensionality reduction and clustering have become the necessary preprocessing steps of multiple research areas and applications. One of the important problems of real life large data sets is uncertainty. Some of the sources of this uncertainty include imprecision in computation and vagueness in class denitions. The uncertainty may also be present in the denition of class membership function. In this background, the thesis addresses the problem of dimensionality reduction and clustering of real life data sets, in the presence of noise and uncertainty. The thesis rst presents the problem of feature selection using both type-1 and interval type-2 fuzzyrough sets, which are eective for dimensionality reduction of real life data sets when uncertainty is present in the data set. The properties of fuzzy-rough sets allow greater exibility in handling noisy and real valued data. While the concept of lower approximation and boundary region of rough sets deals with uncertainty, incompleteness, and vagueness in class denition, the use of either type-1 or interval type-2 fuzzy sets enables ecient handling of overlapping classes in uncertain environment. Moreover, a new concept of \simultaneous attribute selection and feature extraction" is introduced for dimensionality reduction, integrating judiciously the merits of both feature selection and extraction. A scalable rough-fuzzy clustering algorithm is introduced for large real life data sets, where the theory of rough hypercuboid approach, interval type-2 fuzzy sets, and c-means algorithm are integrated judiciously to handle the uncertainty present in a data set. While the concept of rough hypercuboid approach deals with uncertainty, incompleteness, and vagueness in cluster denition, the use of fuzzy membership of interval type-2 fuzzy sets in the boundary region of a cluster enables ecient handling of overlapping partitions in uncertain environment. Finally, the application of both clustering and feature selection algorithms is demonstrated by grouping functionally similar microRNAs from microarray data. The proposed approach can automatically select the optimum set of features while clustering the microRNAs, making the complexity of the algorithm lower.Item A Study of the SHA-2 Cryptographic Hash Family(Indian Statistical Institute, Kolkata, 2009-02-01) Sanadhya Somitra Kumar