arXiv subjects

Deependra Singh

Publications and source records attributed to Deependra Singh.

4 recordsLinked to original sources

arXiv2026

Towards minimal conditions for ergotropy injection in open quantum systems

Interactions between a quantum system and its environment can inject ergotropy into the system, raising the question of the minimal dimensionality and physical resources required for such injection. We first show that ergotropy injection is impossible under thermal operations when both the system and environment are qubits, whereas it becomes possible when the environment is enlarged to a qutrit. We further show that already in the qubit-qubit setting, relaxing environmental thermality and allowing interactions between system and environment allows ergotropy increment under energy-conserving unitaries. To elucidate the role of interactions, we consider a two-qubit isotropic XY interaction Hamiltonian and identify its distinct degeneracy regimes. We show that, in the central-block regime, when both the initial system and environmental states are incoherent, no ergotropic gain is possible when the environment is initially thermal, irrespective of the interaction strength. In contrast, environmental athermality in the form of population inversion, while retaining incoherence, enables ergotropic injection. We derive the optimal ergotropic gain and show that environmental coherence can enhance it, while system coherence alone need not be beneficial and can even reduce the gain. We further consider the double-degenerate regime, characterized by a finite interaction strength, and demonstrate positive ergotropic gain even for a thermal environment.

quant-ph↗

arXiv2025

Retinal Fundus Multi-Disease Image Classification using Hybrid CNN-Transformer-Ensemble Architectures

Our research is motivated by the urgent global issue of a large population affected by retinal diseases, which are evenly distributed but underserved by specialized medical expertise, particularly in non-urban areas. Our primary objective is to bridge this healthcare gap by developing a comprehensive diagnostic system capable of accurately predicting retinal diseases solely from fundus images. However, we faced significant challenges due to limited, diverse datasets and imbalanced class distributions. To overcome these issues, we have devised innovative strategies. Our research introduces novel approaches, utilizing hybrid models combining deeper Convolutional Neural Networks (CNNs), Transformer encoders, and ensemble architectures sequentially and in parallel to classify retinal fundus images into 20 disease labels. Our overarching goal is to assess these advanced models' potential in practical applications, with a strong focus on enhancing retinal disease diagnosis accuracy across a broader spectrum of conditions. Importantly, our efforts have surpassed baseline model results, with the C-Tran ensemble model emerging as the leader, achieving a remarkable model score of 0.9166, surpassing the baseline score of 0.9. Additionally, experiments with the IEViT model showcased equally promising outcomes with improved computational efficiency. We've also demonstrated the effectiveness of dynamic patch extraction and the integration of domain knowledge in computer vision tasks. In summary, our research strives to contribute significantly to retinal disease diagnosis, addressing the critical need for accessible healthcare solutions in underserved regions while aiming for comprehensive and accurate disease prediction.

cs.CV↗

arXiv2024

Machine Learning Approaches to the Shafarevich-Tate Group of Elliptic Curves

We train machine learning models to predict the order of the Shafarevich-Tate group of an elliptic curve over $\mathbb{Q}$. Building on earlier work of He, Lee, and Oliver, we show that a feed-forward neural network classifier trained on subsets of the invariants arising in the Birch--Swinnerton-Dyer conjectural formula yields higher accuracies ($> 0.9$) than any model previously studied. In addition, we develop a regression model that may be used to predict orders of this group not seen during training and apply this to the elliptic curve of rank 29 recently discovered by Elkies and Klagsbrun. Finally we conduct some exploratory data analyses and visualizations on our dataset. We use the elliptic curve dataset from the L-functions and modular forms database (LMFDB).

math.NT↗

arXiv2024

Admissible groups over number fields

Given a field K, one may ask which finite groups are Galois groups of field extensions L/K such that L is a maximal subfield of a division algebra with center K. This connection between inverse Galois theory and division algebras was first explored by Schacher in the 1960s. In this manuscript we consider this problem when K is a number field. For the case when L/K is assumed to be tamely ramified, we give a complete classification of number fields for which every solvable Sylow-metacyclic group is admissible, extending J. Sonn's result over the field of rational numbers. For the case when L/K is allowed to be wildly ramified, we give a characterization of admissible groups over several classes of number fields, and partial results in other cases.

math.NT↗