dyfan/halluhard-seed-questions huggingface dataset:
This book provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space and emphasizes the roles of Hausdorff measure and the capacity in characterizing the fine properties of sets and functions. Topics covered include a quick review of abstract measure theory, theorems and differentiation in Mn, lower Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions and functions of bounded variation. The text provides complete proofs of many key results omitted from other books, including Besicovitch's Covering Theorem, Rademacher's Theorem (on the differentiability a.e. of Lipschitz functions), the Area and Coarea Formulas, the precise structure of Sobolev and BV functions, the precise structure of sets of finite perimeter, and Alexandro's Theorem (on the twice differentiability a.e. of convex functions).Topics are carefully selected and the proofs succinct, but complete, which makes this book ideal reading for applied mathematicians and graduate students in applied mathematics.

Research question: Can you explain the coarea formula intuitively and give a concrete example of how it relates an integral over a domain to integrals over the level sets of a function?
Accurate phenotypic analysis in aquaculture breeding necessitates the quantification of subtle morphological phenotypes. Existing datasets suffer from limitations such as small scale, limited species coverage, and inadequate annotation of keypoints for measuring refined and complex morphological phenotypes of fish body parts. To address this gap, we introduce FishPhenoKey, a comprehensive dataset comprising 23,331 high-resolution images spanning six fish species. Notably, FishPhenoKey includes 22 phenotype-oriented annotations, enabling the capture of intricate morphological phenotypes. Motivated by the nuanced evaluation of these subtle morphologies, we also propose a new evaluation metric, Percentage of Measured Phenotype (PMP). It is designed to assess the accuracy of individual keypoint positions and is highly sensitive to the phenotypes measured using the corresponding keypoints. To enhance keypoint detection accuracy, we further propose a novel loss, Anatomically-Calibrated Regularization (ACR), that can be integrated into keypoint detection models, leveraging biological insights to refine keypoint localization. Our contributions set a new benchmark in fish phenotype analysis, addressing the challenges of precise morphological quantification and opening new avenues for research in sustainable aquaculture and genetic studies. Our dataset and code are available at https://github.com/WeizhenLiuBioinform/Fish-Phenotype-Detect.

Research question: What are effective ways to incorporate anatomical priors or biological knowledge into keypoint detection models to improve localization of subtle morphological landmarks in fish?
Purpose Docetaxel added to androgen-deprivation therapy (ADT) significantly increases the longevity of some patients with metastatic hormone-sensitive prostate cancer. Herein, we present the outcomes of the CHAARTED (Chemohormonal Therapy Versus Androgen Ablation Randomized Trial for Extensive Disease in Prostate Cancer) trial with more mature follow-up and focus on tumor volume. Patients and Methods In this phase III study, 790 patients with metastatic hormone-sensitive prostate cancer were equally randomly assigned to receive either ADT in combination with docetaxel 75 mg/m 2 for up to six cycles or ADT alone. The primary end point of the study was overall survival (OS). Additional analyses of the prospectively defined low- and high-volume disease subgroups were performed. High-volume disease was defined as presence of visceral metastases and/or ≥ four bone metastases with at least one outside of the vertebral column and pelvis. Results At a median follow-up of 53.7 months, the median OS was 57.6 months for the chemohormonal therapy arm versus 47.2 months for ADT alone (hazard ratio [HR], 0.72; 95% CI, 0.59 to 0.89; P = .0018). For patients with high-volume disease (n = 513), the median OS was 51.2 months with chemohormonal therapy versus 34.4 months with ADT alone (HR, 0.63; 95% CI, 0.50 to 0.79; P &lt; .001). For those with low-volume disease (n = 277), no OS benefit was observed (HR, 1.04; 95% CI, 0.70 to 1.55; P = .86). Conclusion The clinical benefit from chemohormonal therapy in prolonging OS was confirmed for patients with high-volume disease; however, for patients with low-volume disease, no OS benefit was discerned.

Research question: What clinical factors and patient characteristics should guide the decision to add early systemic chemotherapy to androgen-deprivation therapy for men with metastatic hormone-sensitive prostate cancer?
Liquid transportation fuels require costly and time-consuming tests to characterize metrics, such as Research Octane Number (RON) for gasoline. If fuel sale restrictions requiring use of standard Cooperative Fuel Research testing procedures do not apply, these tests may be avoided by using multivariate statistical models to predict RON and other quantities. Here we show that an accurate statistical model for the RON of gasoline and gasoline-like fuels can be constructed by ensuring the representation of key functional groups in the spectroscopic data set are used to train the model. We found that a principal component regression model for RON based on IR absorbance and informed using neat and 134 mixtures of n-heptane, isooctane, toluene, ethanol, methylcyclohexane, and 1-hexene could predict RON for the 10 Coordinating Research Council Fuels for Advanced Combustion Engine (FACE) gasolines and 12 FACE gasoline blends with ethanol within 34.8+/-36.1 on average and 51.2 in the worst case. We next studied the effect of adding 28 additional minor components found in the FACE gasolines to the statistical model, and determined that it was necessary to add additional representatives of the branched alkane and aromatics classes to reduce model error. For example, adding 2,3-dimethylpentane and xylene to the previous model allowed it to predict RON for the 22 target fuels within 0.3+/-4.4 on average and 7.9 in the worst case. However, we determined that the specific choice of fuel in those classes mattered less than ensuring the representation of the relevant functional group. This work builds upon previous efforts by creating models informed by neat and surrogate fuels---rather than complex real fuels---that could predict the performance of complex unknown fuels.

Research question: How can one select a minimal set of representative surrogate compounds and spectroscopic features to reliably train multivariate models that predict octane rating (RON) for complex gasoline blends, and what practical limitations or sources of error should be expected when applying such models to unknown fuels?