Vaishali Aggarwal | Searcharxiv

arXiv2025

Computing the nearest $\Omega$-admissible descriptor dissipative Hamiltonian system

For a given set $\Omega \subseteq \mathbb{C}$, a matrix pair $(E,A)$ is called $\Omega$-admissible if it is regular, impulse-free and its eigenvalues lie inside the region $\Omega$. In this paper, we provide a dissipative Hamiltonian characterization for the matrix pairs that are $\Omega$-admissible where $\Omega$ is an LMI region. We then use these results for solving the nearest $\Omega$-admissible matrix pair problem: Given a matrix pair $(E,A)$, find the nearest $\Omega$-admissible pair $(\tilde E, \tilde A)$ to the given pair $(E,A)$. We illustrate our results on several data sets and compare with the state of the art.

math.NA↗

arXiv2025

Leveraging LLMs for Mental Health: Detection and Recommendations from Social Discussions

Textual data from social platforms captures various aspects of mental health through discussions around and across issues, while users reach out for help and others sympathize and offer support. We propose a comprehensive framework that leverages Natural Language Processing (NLP) and Generative AI techniques to identify and assess mental health disorders, detect their severity, and create recommendations for behavior change and therapeutic interventions based on users' posts on Reddit. To classify the disorders, we use rule-based labeling methods as well as advanced pre-trained NLP models to extract nuanced semantic features from the data. We fine-tune domain-adapted and generic pre-trained NLP models based on predictions from specialized Large Language Models (LLMs) to improve classification accuracy. Our hybrid approach combines the generalization capabilities of pre-trained models with the domain-specific insights captured by LLMs, providing an improved understanding of mental health discourse. Our findings highlight the strengths and limitations of each model, offering valuable insights into their practical applicability. This research potentially facilitates early detection and personalized care to aid practitioners and aims to facilitate timely interventions and improve overall well-being, thereby contributing to the broader field of mental health surveillance and digital health analytics.

cs.SI↗