Gupta, Vaibhav

Chronic diseases, especially diabetes, are burdens for the patient since lifelong management is required, and comorbidities can occur as a consequence of insufficient prevention. Hypoglycemia, a medical condition encountered by diabetic individuals, can result in severe symptoms if untreated, necessitating prompt preventive actions. Continuous health monitoring based on data collected with wearables can enable the early prediction of extreme blood glucose states. However, integrating and using data acquired from various sensors is challenging, especially when it comes to maintaining the quality and quantity of data due to inherent noise and missing values. To this end, the review discusses dataset constraints and highlights the temporal behaviour of prominent features in predicting hypoglycemia. It outlines a framework of preprocessing techniques that could be adopted to mitigate dataset limitations. A thorough analysis of the imputation procedures employed in the reviewed studies is conducted. In addition, machine learning imputation techniques applied in other healthcare domains are studied to investigate if they could be adopted to close the longer gaps of missing values in the datasets involved in the prediction of hypoglycemia. Based on a comprehensive evaluation of imputation techniques, a paradigm, Impute-Paradigm, is proposed and validated through a case study, enabling imputation tailored to variable duration time gaps. After analysing the reviewed studies, we recommend studying the rate of change of individual features and conclude that different time gaps of separate features should be treated with multiple imputation techniques.

Forecasting the behaviour of industrial robots, power grids or pandemics under changing external inputs requires accurate dynamical models that can adapt to varying signals and capture long-term effects such as delays or memory. While recent neural approaches address some of these challenges individually, their reliance on computationally intensive solvers and their black-box nature limit their practical utility. In this work, we propose Laplace-Net, a decoupled, solver-free neural framework for learning forced and delay-aware dynamical systems. It uses the Laplace transform to (i) bypass computationally intensive solvers, (ii) enable the learning of delays and memory effects and (iii) decompose each system into interpretable control-theoretic components. Laplace-Net also enhances transferability, as its modular structure allows for targeted re-training of individual components to new system setups or environments. Experimental results on eight benchmark datasets–including linear, nonlinear and delayed systems–demonstrate the method’s improved accuracy and robustness compared to state-of-the-art approaches, particularly in handling complex and previously unseen inputs.

Recent advances in wearable technology have enabled the continuous monitoring of vital physiological signals, essential for predictive modeling and early detection of extreme physiological events. Among these physiological signals, heart rate (HR) plays a central role, as it is widely used in monitoring and managing cardiovascular conditions and detecting extreme physiological events such as hypoglycemia. However, data from wearable devices often suffer from missing values. To address this issue, recent studies have employed various imputation techniques. Traditionally, the effectiveness of these methods has been evaluated using predictive accuracy metrics such as RMSE, MAPE, and MAE, which assess numerical proximity to the original data. While informative, these metrics fail to capture the complex statistical structure inherent in physiological signals. This study bridges this gap by presenting a comprehensive evaluation of four statistical imputation methods, linear interpolation, K Nearest Neighbors (KNN), Piecewise Cubic Hermite Interpolating Polynomial (PCHIP), and B splines, for short term HR data gaps. We assess their performance using both predictive accuracy metrics and statistical distance measures, including the Cohen Distance Test (CDT) and Jensen Shannon Distance (JS Distance), applied to HR data from the D1NAMO dataset and the BIG IDEAs Lab Glycemic Variability and Wearable Device dataset. The analysis reveals limitations in existing imputation approaches and the absence of a robust framework for evaluating imputation quality in physiological signals. Finally, this study proposes a foundational framework to develop a composite evaluation metric to assess imputation performance.

Structural Health Monitoring (SHM) is a fundamental task in the life-cycle assessment and management of civil infrastructures, specifically dams, locks, bridges, and roads. It aids in cost reduction, facilitates the early detection of degradation processes, damages, and structural deficiencies, ensures timely maintenance, and provides early risk warnings. SHM is directly related to the concept of Digital Twin, which is usually defined as a virtual replica of the physical asset. On the one hand, SHM provides the data for the implementation of digital twins, while on the other hand, digital twins can improve the effectiveness of SHM and support data analysis. Together, they represent a powerful combination for managing and maintaining critical infrastructure. A hybrid approach has become increasingly established in recent years, which comprises a combination of physics-based models and data-driven techniques. This approach mitigates the constraints of both models to align the digital twin’s behavior more closely with that of the corresponding physical asset. This study explores the hybrid modeling framework known as physics-enhanced machine learning for forecasting potential structural damage. Among the various hybrid modeling approaches, we focus on physics-informed neural networks (PINNs) and their applications in SHM of civil infrastructures. This study provides a comprehensive classification of research employing the PINNs architecture and critically evaluates its associated limitations. Additionally, we explore advanced deep learning architectures that can integrate PINNs within their computational frameworks to enhance SHM performance by addressing its limitations. This work is a foundational reference for understanding state-of-the-art advancements in PINNs for SHMapplications.

In this dissertation, we are studying abstract algebra; mostly, our focus is on studying Galois theory in depth, and then we will study the proof of our main theorem, "Hilbert Irreducibility Theorem," which states that given any irreducible polynomial g (t_1, t_2,...., t_n, x) over the rational numbers, there are an infinite number of rational n-tuples (a_1, a_2,...., a_n) such that f (a_1, a_2,..., a_n, x) is irreducible over the rational numbers. I have omitted the basics of abstract algebra, such as group, ring, and field theory, and motivated the reader to read a basic book to learn these topics. I have presumed that the reader knows linear algebra. I started my dissertation with an introduction to group characters and then extended our discussion to Galois extension and normal extension to provide the basis for studying the Fundamental Theorem of Galois Theory. Then, we fixed our focus on Kummer Extensions and Cyclotomic Extensions. To end our discussion of Galois' theory, we studied solvable groups. Then some complex analysis theorems have been stated, which we will use in our proof of Hilbert's irreducibility theorem. A whole chapter has been dedicated to studying lemmas to prove our theorem, and then in the last chapter, we have proved our theorem.