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Qixuan Hu

Publications and source records attributed to Qixuan Hu.

8 recordsLinked to original sources
arXiv2026

Scalar curvature growth on nonnegatively curved three-manifolds

Let $(M^3,g)$ be a complete, connected, noncompact Riemannian three-manifold without boundary and with nonnegative sectional curvature. We prove that its scalar-curvature integral over geodesic balls, divided by the radius, has a limit. In the one-ended case, \[ \lim_{r\to\infty}\frac1r\int_{B_p(r)}\operatorname{Scal}\,d V =8π\bigl(χ(M)-V_M\bigr)\le8π(1-V_M), \] where $V_M$ is the asymptotic volume ratio. In the one-ended case, we show that $χ(M)\in\{0,1\}$. Thus positive asymptotic volume ratio gives the value $8π(1-V_M)$, while in the collapsed case the value is determined by the topology of the end. No pole or scalar-curvature bound is assumed. The proof combines separate smooth approximations of the Busemann and distance functions, integrable negative curvature errors, and a determinant estimate on the level surfaces. An averaged boundary estimate then gives convergence of the integrated extrinsic curvature. In the two-ended case, the splitting theorem gives the exact limit $8πχ(N)$ for the compact surface factor $N$. The one-ended upper bound is attained for every prescribed asymptotic volume ratio in $[0,1]$, and the two-ended bound is also sharp.

math.DG↗
arXiv2026

A quadratic comparison of Neumann eigenvalues on thin convex domains in arbitrary dimenstion

Let $Ω\subset\mathbb R^n$ be a bounded convex domain that is thin around a chosen diameter segment. We compare its Neumann spectrum with the spectrum of that segment weighted by the $(n-1)$-dimensional volumes of its perpendicular sections. We prove an $O(\varepsilon^2)$ comparison of the mean-zero inverse operators and, consequently, an $O(\varepsilon^2)$ eigenvalue comparison for every fixed index in every dimension $n\ge2$. The constants depend only on the dimension and the eigenvalue index. Thin rectangles show that the quadratic exponent is optimal.

math.SP↗
arXiv2026

CBT-Audio: Evaluating Audio Language Models for Patient-Side Distress Intensity Estimation in CBT Session Recordings

Cognitive behavioural therapy is widely used to help patients understand and manage psychological distress. It is often delivered through spoken conversation, where therapists attend not only to what patients say, but also to how they say it, because these cues can help therapists decide how to respond and adapt treatment. Progress in building AI systems for CBT remains largely limited to text, partly because most available datasets are text based and shareable spoken CBT data are scarce under ethical and privacy constraints. This creates a blind spot because text based models and evaluations cannot capture the mismatch between the transcript and the patient's voice, even though therapists often rely on this mismatch to understand patient distress. We introduce CBT-Audio, a dataset for evaluating patient distress estimation from spoken CBT sessions with audio language models. CBT-Audio contains 1,802 patient turns from 96 publicly available CBT recordings, with turn-level distress labels validated on an experts-annotated subset. We evaluate 10 open source audio language models under three input conditions, where models receive only patient audio, only the transcript, or both audio and transcript. Our results show that audio can provide useful information beyond text, especially when combined with transcripts. Adding audio to transcript input improves distress estimation over using the transcript alone in 8 of 10 model families, with significant gains in 4, and case studies show the clearest benefit when verbal content and vocal delivery diverge. CBT-Audio makes spoken patient behaviour measurable for AI evaluation in CBT-related tasks and supports future work on audio language models for mental health interaction.

cs.AI↗
arXiv2025

Multiple eigenvalues and the width

We obtain the simplicity of the first Neumann eigenvalue of convex thin domain with boundary in $R^n$ and compact thin manifolds with non-negative Ricci curvature. For convex thin domain in $R^2$, we get the simplicity of the first k Neumann eigenvalues. The number k depends on the ratio of the corresponding width over the diameter of the domain. For convex thin domain in $R^n$, we obtain the eigenvalue comparison with collapsing segment.

math.SP↗
arXiv2025

Some aspects of Cheng-Yau gradient estimates

In this note, we extend the rigidity of Cheng-Yau gradient estimate in \cite{HXY} to surfaces with lower Ricci curvature bound. Motivated by these sharp Cheng-Yau gradient estimates, pointwise Cheng-Yau gradient estimates for higher dimensional Riemannian manifolds are obtained, and as their applications, monotonicity formulas for positive harmonic functions are obtained.

math.DG↗
arXiv2025

A novel language model for predicting serious adverse event results in clinical trials from their prospective registrations

Objectives: With accurate estimates of expected safety results, clinical trials could be better designed and monitored. We evaluated methods for predicting serious adverse event (SAE) results in clinical trials using information only from their registrations prior to the trial. Material and Methods: We analyzed 22,107 two-arm parallel interventional clinical trials from ClinicalTrials.gov with structured summary results. Two prediction models were developed: a classifier predicting whether a greater proportion of participants in an experimental arm would have SAEs (area under the receiver operating characteristic curve; AUC) compared to the control arm, and a regression model to predict the proportion of participants with SAEs in the control arms (root mean squared error; RMSE). A transfer learning approach using pretrained language models (e.g., ClinicalT5, BioBERT) was used for feature extraction, combined with a downstream model for prediction. To maintain semantic representation in long trial texts exceeding localized language model input limits, a sliding window method was developed for embedding extraction. Results: The best model (ClinicalT5+Transformer+MLP) had 77.6% AUC when predicting which trial arm had a higher proportion of SAEs. When predicting SAE proportion in the control arm, the same model achieved RMSE of 18.6%. The sliding window approach consistently outperformed direct comparisons. Across 12 classifiers, the average absolute AUC increase was 2.00%, and absolute RMSE reduction was 1.58% across 12 regressors. Discussion: Summary results data from ClinicalTrials.gov remains underutilized. Predicted results of publicly reported trials provides an opportunity to identify discrepancies between expected and reported safety results.

cs.CL↗
arXiv2022

The rigidity and stability of gradient estimates

In this note, we obtain the rigidity of the sharp Cheng-Yau gradient estimate for positive harmonic functions on surfaces with nonegative Gaussian curvature, the rigidity of the sharp Li-Yau gradient estimate for positive solutions to heat equations and the related estimates for Dirichlet Green's functions on Riemannian manifolds with nonnegative Ricci curvature. Moreover, we also obtain the corresponding stability results.

math.DG↗