Abstract

The dynamics exhibited by reaction networks is often a manifestation of their steady states. This dissertation show that there exists endotactic and strongly endotactic dynamical systems that are not weakly reversible and possess a family of infinitely many positive steady states. In addition, for some of these systems we prove that there exist no weakly reversible mass-action systems that are dynamically equivalent to mass-action systems generated by these networks. This extends a result by Boros, Craciun and Yu [1], who proved the existence of weakly reversible dynamical systems with infinitely many steady states. We also investigate the possibility that for any given reaction rate vector k associated with a network G, there exists another network G′ with a corresponding reaction rate vector that reproduces the massaction dynamics generated by (G,k). Our focus is on a particular class of networks for G, where the corresponding network G′ is weakly reversible. In particular, we show that strongly endotactic twodimensional networks with a two-dimensional stoichiometric subspace, as well as certain endotactic networks under additional conditions, exhibit this property. Furthermore, we show that being endotactic is necessary for the dynamics of a network to be included in the dynamics of a weakly reversible network. Additionally, we establish a strong connection between this family of networks and the locus in the space of rate constants in which the corresponding dynamics admits globally stable steady states.

Abstract

Memory allows us to store and recall past experiences, and understanding how this works is key to uncovering the mechanisms behind human cognition. This thesis investigates how temporal context — the background of experiences surrounding a memory — influences recognition in a continuous recognition task. Unlike traditional memory studies that rely heavily on free recall, this research uses the Natural Scenes Dataset (NSD) and functional MRI (fMRI) data to explore how the brain retrieves and uses temporal context. The Temporal Context Model (TCM) suggests that when we remember something, we also bring back the contextual backdrop of that memory. This study tests whether such context retrieval occurs in a continuous recognition task, where participants viewed thousands of images and indicated whether they had seen them before. The dataset’s randomized image presentation ensured minimal strategic recall, making it an excellent environment to examine authentic context retrieval effects. Results show a clear pattern: participants were more likely to correctly recognize an image if it followed another image seen in close temporal proximity. This suggests that when a memory is triggered, the brain retrieves not just the image but also the surrounding temporal context. The closer the images were during encoding, the stronger this effect — a concept known as the temporal gradient. Neural analysis further supports these findings. fMRI data reveal heightened neural similarity in the medial temporal lobe (MTL), particularly in the hippocampus and entorhinal cortex, when recognition was successful. These regions showed patterns consistent with temporal context reinstatement, confirming their central role in memory retrieval. This study contributes compelling evidence that temporal context retrieval is a fundamental aspect of episodic memory, even in scenarios without explicit recall strategies. The findings also provide insights into how the brain’s memory systems work together. Future research could build on these results by exploring how context retrieval operates across different memory tasks or using computational models to further refine the TCM. Ultimately, this study advances our understanding of how we remember our past, offering a clearer picture of the cognitive and neural foundations of memory

Abstract

Error-correcting codes are mathematical objects that are useful for mitigating errors due to noise, but they are also fundamental to other problems, such as designing and ensuring the privacy and efficiency of storage systems. Reed-Muller codes is one such family of codes that is widely used across these diverse applications, but these codes have limited flexibility in parameters like rate and length, which are required in many cases. In this thesis, we propose a new family of codes similar to Reed-Muller codes and study their properties and decoding. We study a family of subcodes of the m-dimensional product code C ⊗m (‘subproduct codes’) that have a recursive Plotkin-like structure, and which include Reed-Muller (RM) codes and Dual Berman codes as special cases. We denote the codes in this family as C ⊗[r,m] , where 0 ≤ r ≤ m is the ‘order’ of the code. These codes allow a ‘projection’ operation that can be exploited in iterative decoding, viz., the sum of two carefully chosen subvectors of any codeword in C ⊗[r,m] belongs to C ⊗[r−1,m−1] . Recursive subproduct codes provide a wide range of rates and block lengths compared to RM codes while possessing several of their structural properties, such as the Plotkin-like design, the projection property, and fast ML decoding of first-order codes. Our simulation results for first-order and secondorder codes, that are based on a belief propagation decoder and a local graph search algorithm, show instances of subproduct codes that perform either better than or within 0.5 dB of comparable RM codes and CRC-aided Polar codes

Abstract

Quadrotors are extensively utilized in applications such as surveillance, mapping, and delivery, owing to their high maneuverability and vertical takeoff and landing (VTOL) capabilities. The deployment of quadrotors in these critical tasks necessitates a high degree of safety and reliability. However, their inherent lack of rotor redundancy poses significant challenges in addressing motor faults, making fault tolerance a crucial concern in their design and operation. This thesis presents a simple method for stabilizing the quadrotor dynamics under complete loss of one actuator using two-stage optimal control. Detailed equilibrium analysis and subsequent selection of the operating point under actuator loss are provided, incorporating constraints on the maximum available thrust. Two distinct cases were considered for equilibrium selection: one in which two actuators have equal inputs, and another in which all actuator inputs are allowed to vary independently. It is shown that when all actuator inputs are allowed to vary independently, the system can track an additional state, thereby enabling attitude tracking. A detailed simulation study using a high-fidelity nonlinear model of the quadrotor is presented, showing the stability and performance of the closed-loop system under complete actuator loss, in the presence of external disturbances. To ensure better maneuverability, the quadrotor under fault may have to shift to multiple equilibrium states along the course of a single flight. This poses a challenge as designing a controller for every equilibrium state across the state space is a tedious task. To address this challenge, a controller capable of stabilizing the quadrotor under fault across multiple equilibrium states was designed by applying Linear Matrix Inequality (LMI) conditions. The controller was tested in simulation using a high-fidelity nonlinear model of the quadrotor. The proposed method not only ensures continued stable flight in fault scenarios but also lays the groundwork for resilient flight control design in safety-critical aerial robotics applications.

Abstract

In this work, we introduce and rigorously characterize a broad class of quantum operations termed quantum ergodic channels. These are completely positive, and trace-preserving (CPTP) maps that possess a unique fixed point toward which any initial quantum state asymptotically evolves. The existence of such a fixed point enables a systematic exploration of ergodicity in quantum dynamics, extending classical notions into the quantum regime. We construct and analyze Lindblad-type master equations governing the evolution under these ergodic channels in arbitrary finite-dimensional Hilbert spaces. These equations describe both Markovian and non-Markovian dynamics, depending on the time dependence and structure of the generator. In particular, the class of ergodic channels considered here encompasses both memoryless and memory-affected evolution, allowing us to explore their differences through established quantitative measures of non-Markovianity. A special focus is placed on the case where the fixed point of the channel is a passive state, i.e., a state from which no work can be extracted via unitary operations. In such settings, evolution under ergodic channels gives rise to non-trivial ergotropy dynamics. Ergotropy is a fundamental thermodynamic quantity that quantifies the maximum extractable work from a quantum state via unitary transformations, assuming no access to additional resources. We show that in the Markovian regime, where the dynamics lack memory, the ergotropy of the system decreases monotonically over time, consistent with the second law of thermodynamics in open systems. However, under non-Markovian dynamics, the situation changes significantly. We demonstrate that ergotropy can temporarily increase during evolution, indicating a backflow of useful energy from the environment into the system. This phenomenon—referred to as ergotropy backflow—is a direct manifestation of memory effects and points to the possibility of temporary reversals in the degradation of thermodynamic resources. Our analysis shows that this backflow is not only physically meaningful but also operationally relevant: it can serve as a dynamical witness or indicator of non-Markovianity. These findings offer a novel perspective on the interplay between non-Markovianity and thermodynamic behavior in open quantum systems. By grounding the discussion in welldefined resource-theoretic and thermodynamic terms, this study deepens our understanding of how memory effects influence the evolution of quantum resources such as ergotropy. In particular, it highlights the role of ergodic channels as a versatile theoretical framework for studying energy dynamics, dissipation, and resource recovery in realistic quantum settings—including potential applications in the design and analysis of quantum batteries. Overall, the results presented here enrich the theoretical framework of open quantum systems and pave the way for future investigations into the thermodynamic implications of quantum memory effects. They suggest practical strategies for identifying, characterizing, and potentially exploiting non-Markovian dynamics to enhance the performance of emerging quantum technologies.

Abstract

The fundamental question of whether advertising revenue compromises editorial independence has long been debated in media studies, yet empirical evidence has remained limited due to the difficulty of systematically analyzing large-scale newspaper content. This thesis investigates the relationship between advertising practices and editorial coverage in Indian print media, examining whether companies that advertise more receive more favorable or extensive news coverage. To conduct this investigation, we developed a scalable computational pipeline employing advanced image processing and Optical Character Recognition (OCR) techniques to systematically extract articles and advertisements from digital versions of print newspapers with high accuracy. This methodology enabled us to process and analyze content on a larger scale, overcoming traditional limitations in media content analysis. Our automated approach successfully parsed newspaper layouts, distinguished between editorial and advertising content, and extracted text with sufficient precision for quantitative analysis. Applying this pipeline to five prominent newspapers that span multiple regions and three languages—English, Hindi, and Telugu—we assembled a comprehensive dataset comprising more than 12,000 editions and several hundred thousand advertisements collected over six years. These newspapers collectively reach a readership exceeding 100 million people, making our analysis representative of India’s diverse print media landscape. The data set includes publications with varying editorial orientations, geographic focus, and readership demographics, providing robust coverage of the Indian print media ecosystem. Our analysis reveals several significant findings on contemporary print advertising practices and their potential influence on editorial content. Despite declining print circulation trends, advertising levels have remained remarkably consistent over the six-year study period, suggesting advertisers continue to value print media’s reach and credibility. We observe systematic patterns in ad placement, with corporate advertisements appearing disproportionately on prominent pages, while government advertisements contribute a substantial portion of overall advertising revenue. The data also reveal temporal patterns in advertising intensity, seasonal variations between different advertiser categories, and regional differences in advertising strategies. Most importantly, our regression analyses provide strong empirical evidence that advertising expenditure is correlated with editorial coverage patterns. Companies that advertise more heavily in a newspaper receive significantly more extensive coverage, and this coverage tends to be more favorable in sentiment compared to non-advertising entities. This relationship remains statistically robust for different model specifications, time periods, and advertiser popularity levels. The effect is particularly pronounced for corporate advertisers, suggesting that commercial relationships may indeed influence editorial decisions in ways that could compromise journalistic independence and potentially mislead readers about the true newsworthiness or merit of covered entities.

Abstract

Training and evaluating large language models (LLMs) on deductive reasoning tasks has attracted much attention in recent times. There have been various attempts at training and evaluating LLMs to perform deductive reasoning tasks. Some among these have shown interesting results which suggest that LLMs behave like humans by displaying content effect, that is, they reason better on reasoning tasks containing rules that align with our everyday beliefs and reason poorly when the rules are beliefviolating. Others, using chain-of-thought prompting, a technique to make LLMs generate intermediate steps before making them arrive at the final conclusion, suggest that LLMs may emulate human-like reasoning thought processes by generating intermediate reasoning steps. On the other hand, there are studies which conclude that language models do not yet demonstrate reliable deductive reasoning, since their performance is shown to decrease upon introduction of perturbations, such as synonym substitution, and attribute their reasoning to artefacts from the training data. In this study, we look at these three distinct attempts at evaluating LLMs on deductive competence tasks, each employing different criteria such as content-based reasoning (Dasgupta et al., 2023 [1]), chain-of-thought prompting (Wei et. al., 2023 [2]), and introduction of perturbations (Yuan et al., 2023 [3]). In order to make sense of these claims concerning genuine reasoning, we introduce a framework developed by Diane Proudfoot using externalist criteria for machine cognition (Proudfoot 2004 [4]), which is based on Wittgenstein’s argument that deductive reasoning involves rule-following which is normative in nature. Based on the notion that deductive competence involves the following of normative rules, the framework proposes the use of the Wittgensteinian distinction between rule-following and quasi rule-following as a method to distinguish genuine deductive competence from quasi-competence. The criteria distinguishing between rule-following and quasi rule-following shall be adapted to analyse whether these LLMs can be said to reason genuinely or are merely imitating reasoning-like behaviour. We propose this use of Proudfoot’s criteria for rule-following as a framework to distinguish genuine deductive competence from quasi deductive competence. In doing so, we also draw attention to the limitations and implications of Proudfoot’s claims regarding machine cognition through the introduction of a thought experiment. This thought experiment enables us to think through Proudfoot’s argument, according to which it is due to pragmatic considerations–and not in principle–that LLMs are unlikely to possess genuine reasoning.

Abstract

With the advent of Industry 4.0, the demands on industrial robots have expanded beyond simple pick-and-place tasks. Future smart factories require robots capable of a wide range of manipulation skills, including the ability to manipulate objects with variety of actions like pushing. This thesis investigates the capabilities of a manipulator and the system to perform fine or controlled non-prehensile manipulation (without grasping the objects), potentially exceeding the robot arm’s reachable workspace. Key contributions of this research include: • Hybrid Planner combining Striking, Pushing and Pick and Place motions. • Development of sophisticated optimal control strategies for generate manipulation of objects to specific target locations with high precision without necessarily grasping. These algorithms calculate the optimal contact point,force and velocity required for each action. • Conducting experiments primarily in a simulation environment to validate the effectiveness of the end-effector design and its control algorithms, complemented by preliminary tests on a real robot. These evaluations demonstrate the practical viability and robustness of the proposed system under controlled conditions. The thesis further explores the vast practical implications of Non-Prehensile manipulation. In warehouse logistics, this technology can significantly optimize sorting, material transfer, and distribution processes by enabling faster and more precise handling of items. By combining optimization and planning strategies, this research provides a comprehensive framework for designing a framework for hybrid manipulation. This interdisciplinary methodology enhances the versatility, adaptability, and performance of robots, ultimately improving efficiency, safety, and productivity in various industrial and operational settings. Keywords: Mobile Manipulation, Non-Prehensile Manipulation, Redundant robot, Trajectory optimization, Robot Arm Control, Action-based Planning, Hybrid Action Planner, Whole body control, Robot Simulation, Rigid body dynamics, Sim-to-real, residual learning, Planning framework.

Abstract

Enabling effective grasping capabilities in unmanned aerial manipulators (UAMs) presents formidable challenges stemming from the intricate coupling forces that emerge between the flying platform and manipulator arm, compounded by parametric uncertainties and environmental disturbances. Current methodologies predominantly fall into two categories: those demanding precise dynamic models of the entire system, and those addressing the aerial and manipulator subsystems as separate entities , both approaches facing substantial limitations when deployed in practical settings. Despite substantial advancement in research on the topic of aerial manipulation, there is a lack of methods that properly address the effect of uncertain interaction forces between the manipulator interacting with the environment and the floating aerial base. These forces tend to be notoriously hard, if not impossible, to model due to uncertainties in payload characteristics and environmental interaction. This thesis proposes a novel adaptive control architecture for an integrated solution for the UAM system combined with a bistable passive gripper to facilitate dependable aerial grasping operations without necessitating prior knowledge of system dynamics or disturbance characteristics. The bistable gripper employs a pre-stressed spring steel band that transitions between two stable states, autonomously initiating object capture upon contact and thereby minimizing alignment precision requirements. Its innovative cable-driven actuation mechanism, powered by a single compact DC motor, enables efficient gripper release without requiring bulky pneumatic components. The developed adaptive control strategy effectively addresses the challenge of unmodeled coupling dynamics and state-dependent uncertainties inherent in aerial manipulation systems. The controller incorporates adaptation mechanisms that dynamically estimate composite uncertainties, encompassing variations in inertial parameters, Coriolis and centrifugal effects, gravitational influences, and external forces, maintaining reliable tracking performance despite the absence of precise system identification. A rigorous Lyapunov stability analysis demonstrates that the closed-loop system achieves uniform ultimate boundedness under practical operating conditions.

Abstract

Many real-world systems can be modeled as dynamic graphs, where nodes and edges evolve with time. Graph Neural Networks (GNNs) excel at modeling relational data. Temporal GNNs capture the dynamics of time-changing data very well. Still, their reliability in risk-sensitive domains where errors in fraud detection, legal judgments, or medical diagnoses carry severe consequences remains limited. Traditional GNNs lack mechanisms to quantify uncertainty or abstain from low-confidence predictions, particularly in dynamic systems where temporal evolution and class imbalance amplify ambiguity. This thesis addresses these gaps by introducing strategic abstention mechanisms into graph learning, helping models to prioritize high-confidence decisions while rejecting uncertain predictions. We unify this approach across dynamic and static graphs, advancing reliability in high-stakes applications through uncertainty-aware frameworks. For the first time, our approach integrates a reject option strategy within the framework of GNNs for continuous-time dynamic graphs. This allows the model to strategically abstain from making predictions when uncertainty is high and confidence is low, minimizing the risk of critical misclassification and enhancing reliability. We propose a coverage-based abstention prediction model to implement the reject option that maximizes predictions within specified coverage. It improves prediction scores for link prediction and node classification tasks. Temporal GNNs deal with skewed datasets for the next state prediction or node classification. In cases of class imbalance, our method can be tuned to provide a higher weight to the minority class. Exhaustive experiments are presented on four datasets for dynamic link prediction and two for dynamic node classification tasks. This demonstrates our approach’s effectiveness in improving reliability and area under the curve (AUC)/average precision (AP) scores for predictions in dynamic graph scenarios. The results highlight our model’s ability to efficiently handle trade-offs between prediction confidence and coverage, making it a dependable solution for applications requiring high precision in dynamic and uncertain environments. Beyond temporal graphs, we extend the concept of classification with the reject option to static graph settings. We reformulate legal judgment prediction (LJP) as node classification on citation networks (ILDC dataset), integrating cost- and coverage-based abstention. Our models (NCwR-Cost/NCwR-Cov) improve accuracy by rejecting uncertain cases, ensuring reliability in legal decision-making. SHAPbased explanations reveal case-specific abstention rationale, enhancing transparency. Further validation on medical datasets (thyroid diagnosis, diabetes prediction) confirms cross-domain validation, with abstention mechanisms reducing misclassification risks in ambiguous cases. This work provides deployable solutions for applications where reliability is non-negotiable.