In 2008, Halman showed that for any finite set P⊂Rd and any finite family B of axis-parallel boxes in Rd, if the intersection of P and any subfamily B′⊆B of size at most 2d is non-empty, then the intersection of P and B is also non-empty. Very recently Edwards and Soberón initiated the study of quantitative colorful version for 2d families, (p,q)-type variation for p≥q≥d+1, and other extensions of this Helly-type result by Halman.In this paper, we study the quantitative colorful Halman problem for 2d−1 families as well its (p,q)-type variation for p≥q≥2. Specifically, our main result asserts that for any finite set P and finite families of boxes B1,…,B2d−1 in Rd, where d≥2, if every transversal B for the families has an intersection ⋂B containing at least n points of P, then there exist j∈[2d−1] and a subset of P of size at most2n+⌊n−1d⋅2d−1⌋, such that each box of Bj contains at least n points of this subset.
Purpose Sleep-related symptoms in head and neck cancer are poorly characterized and often under-recognized. We examined symptom trajectories, prevalence of moderate/severe symptoms, and associations between severe sleep-related patient-reported symptoms and overall survival (OS) in oropharyngeal cancer (OPC) patients receiving radiotherapy (RT). Methods This retrospective analysis included a longitudinal cohort of 372 patients with OPC treated with curative-intent RT (± chemotherapy) at a tertiary center. Symptoms were assessed at the earliest available pre-RT baseline, RT start, RT end, and 6 months post-RT using the MD Anderson Symptom Inventory–Head and Neck (MDASI-HN). The sleep-related symptom domains were fatigue, sleep disturbance, and drowsiness. OS was evaluated using Kaplan–Meier and multivariable Cox models. Results Severe fatigue, sleep disturbance, and drowsiness were infrequent at baseline but peaked at RT end (26%, 15%, and 18%, respectively) and returned to near-baseline levels by 6 months (6%, 4%, and 2%). Severe longitudinal fatigue (HR 5.05), sleep disturbance (HR 3.86), and drowsiness (HR 8.24) were independently associated with worse OS. Severe symptoms at RT start were also associated with worse OS (fatigue HR 3.58; sleep disturbance HR 5.08; drowsiness HR 7.76; all p < 0.05). Aside from age, severe average daily symptom scores and severe symptoms at RT start were associated with OS after multivariable adjustment. Conclusion Severe sleep-related symptoms peaked during RT. Severe fatigue, sleep disturbance, and drowsiness, both longitudinally and at RT start, were associated with worse OS. These observational associations do not establish causality; symptom assessment may help identify patients who warrant supportive evaluation.
Surrogate models are central to scientific machine learning, where they enable fast prediction, simulation, inference, and control for complex physical systems. For time-dependent problems, however, accurate interpolation of training trajectories is not sufficient: reliable surrogates should also respect the conservation laws, invariants, admissibility conditions, and dissipative structures that give those trajectories physical meaning. We introduce Physics-conforming Latent Twins, a framework for learning latent surrogate solution operators whose dynamics satisfy selected physical principles by design. The method builds on the Latent Twin formulation by jointly learning an encoder, a decoder, and a latent flow map between arbitrary time-indexed states, while constraining the latent dynamics to preserve or dissipate prescribed structural quantities. We develop a constraint-transfer viewpoint that separates pullback compatibility from latent conformity, connecting physical structure in the original state space with enforceable constraints in latent space, and prove structure-preservation bounds showing how latent enforcement improves control of physical defects after decoding. We also derive algebraic conditions for latent flow maps that preserve linear and quadratic invariants or enforce dissipative inequalities. Numerical experiments on representative ODE and PDE benchmarks demonstrate improved constraint satisfaction, structural fidelity, and qualitative long-time behavior while maintaining accurate surrogate prediction.
Datasets may contain observations with multiple labels. If the labels are not mutually exclusive, and if the labels vary greatly in frequency, obtaining a sample that includes sufficient observations with scarcer labels to make inferences about those labels, and which deviates from the population frequencies in a known manner, creates challenges. In this paper, we consider a multivariate Bernoulli distribution as our underlying distribution of a multi-label problem. We present a novel sampling algorithm that takes label dependencies into account. It uses observed label frequencies to estimate multivariate Bernoulli distribution parameters and calculates weights for each label combination. This approach ensures the weighted sampling acquires target distribution characteristics while accounting for label dependencies. We applied this approach to a variety of datasets, including a sample of research articles from Web of Science labeled with 64 biomedical topic categories. We aimed to preserve category frequency order, reduce frequency differences between most and least common categories, and account for category dependencies. This approach produced a more balanced sub-sample, enhancing the representation of minority categories.
Objective To examine whether gain- versus loss-framed messages affect women’s responses to negative family cancer history (FCH) screening results, and whether these effects differ by race. Methods From March to April 2025, we conducted a two-arm parallel-group randomized online trial of message framing (gain vs. loss), stratified by race (Black, non-Hispanic vs. non-Black), among U.S. women aged 40 years and older who screened negative on FCH (N = 655) recruited through the Ipsos nationally representative consumer panel. Participants were blinded to message-framing condition, completed a baseline survey, then viewed either a gain- or loss-framed message. The primary outcomes were understanding of inherited and general cancer risk, acceptance of the negative FCH screening result, and intentions to undergo mammography and update family history. Chi-square tests, ANOVA, and multivariable regression models examined message effects and race-by-framing interactions. Results Of 655 participants, 61% were Black, non-Hispanic (n = 400) and 39% were non-Black (n = 255). Black participants reported higher mammogram screening intention but lower result understanding and result acceptance than non-Black participants. Message framing was not significantly associated with understanding, acceptance, or behavioral intentions (all p > 0.10), and framing effects did not significantly differ by race (all interaction p-values > 0.34); an exploratory analysis identified a non-significant trend toward higher acceptance of loss-framed messages among Black participants (mean difference = 0.56, p = 0.075). Conclusions In a nationally representative sample in which the majority of participants were Black, brief message framing alone did not influence women’s responses to negative FCH results. As family history risk assessment expands in public health practice, equitable communication of negative results appears to require more than optimizing message wording. Future research should test simple, low cost communication strategies that actively engage patients and address result comprehension in population-based screening settings.
