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Yusen Xia

Publications and source records attributed to Yusen Xia.

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A Sharp Diameter-Dependent Lower Bound for the First Nonzero Neumann Eigenvalue of Geodesic Triangles in Space Forms

We prove a sharp lower bound for the first nonzero Neumann eigenvalue of geodesic triangles of given diameter in two-dimensional space forms. The bound is given by the first positive radial Neumann eigenvalue of an one dimensional model; it is approached by degenerating isosceles triangles. When \(K>0\) and \(D=\pi/(2\sqrt K)\), equality is attained precisely by birectangular triangles. We also prove a hot-spots theorem for non-acute spherical triangles of diameter at most \(\pi/2\), and establish antisymmetry and eigenvalue monotonicity for isosceles spherical triangles of diameter \(\pi/2\).

math.DG

On the PPW Conjecture For Hopf-symmetric Sets In Non-compact Rank One Symmetric Space

In this paper, we proved that for a bounded Hopf-symmetric domain $\Omega$ in a noncompact rank one symmetric space $M$, the second Dirichlet eigenvalue $\lambda_2 (\Omega) \leq \lambda_2 (B_1)$ where $B_1$ is a geodesic ball in $M$ such that $\lambda_1 (\Omega) =\lambda_1 (B_1)$. This generalizes the work of Ashbaugh & Benguria, Benguria & Linde for bounded domains in constant curvature spaces.

math.DG

Fairness in Computational Innovations: Identifying Bias in Substance Use Treatment Length of Stay Prediction Models with Policy Implications

Predictive machine learning (ML) models are computational innovations that can enhance medical decision-making, including aiding in determining optimal timing for discharging patients. However, societal biases can be encoded into such models, raising concerns about inadvertently affecting health outcomes for disadvantaged groups. This issue is particularly pressing in the context of substance use disorder (SUD) treatment, where biases in predictive models could significantly impact the recovery of highly vulnerable patients. In this study, we focus on the development and assessment of ML models designed to predict the length of stay (LOS) for both inpatients (i.e., residential) and outpatients undergoing SUD treatment. We utilize the Treatment Episode Data Set for Discharges (TEDS-D) from the Substance Abuse and Mental Health Services Administration (SAMHSA). Through the lenses of distributive justice and socio-relational fairness, we assess our models for bias across variables related to demographics (e.g., race) as well as medical (e.g., diagnosis) and financial conditions (e.g., insurance). We find that race, US geographic region, type of substance used, diagnosis, and payment source for treatment are primary indicators of unfairness. From a policy perspective, we provide bias mitigation strategies to achieve fair outcomes. We discuss the implications of these findings for medical decision-making and health equity. We ultimately seek to contribute to the innovation and policy-making literature by seeking to advance the broader objectives of social justice when applying computational innovations in health care.

cs.CY