We derive a tighter inequality than Cauchy-Schwarz Inequality, leverage it to refine Pearson's

To be consistent with accuracy definition, we denote the correctness ofstj for instance t as sim(stj,rt) = ( 2 distance(stj,rt))/ 2 where sim(stj,rt) is in the range [0,1] and distance(stj,rt) is in range [0, 2], 2 is the largest Euclidean distance in the probability simplex. Given a test dataset I, the correctness of a learner SLj on I can be denoted as 2 corrSLj = 1n Pn t=1sim(stj,rt). In this section, we define multiple metrics for consistency, accuracy, and correct-consistency in detail. Figure 1 shows the metrics computation in our experiments. We have created a git repository for this work and will be posted upon the acceptance and publicationofthiswork.

Our analysis further exposes that IGR encourages neurons with the same activation states for natural samples and the corresponding perturbed samples.

We develop a method to generate prediction intervals that have a user-specified coverage level across all regions of feature-space, a property calledconditional coverage.

Australia's beloved weather website got a makeover - and infuriated users It was an unseasonably warm spring day in Sydney on 22 October, with a forecast of 39C (99F) - a real scorcher. The day before, the state of New South Wales had reported its hottest day in over a century, a high of 44.8C in the outback town of Bourke. But little did the team at the national Bureau of Meteorology foresee that they, in particular, would soon be feeling the heat. Affectionately known by Australians as the Bom, the agency's long-awaited website redesign went live that morning, more than a decade after the last update. Within hours, the Bom was flooded with a deluge of complaints.

In addition to its more widely studied cultural movements, American Evangelicalism has a well-developed but less externally visible literary side. Christian Fiction, however, has been little studied, and what scholarly attention there is has focused on the explosively popular Left Behind series. In this work, we use computational tools to provide both a broad topical overview of Christian Fiction as a genre and a more directed exploration of how its authors depict divine acts. Working with human annotators, we first developed a codebook for identifying "acts of God." We then adapted the codebook for use by a recent, lightweight LM with the assistance of a much larger model. The laptop-scale LM is largely capable of matching human annotations, even when the task is subtle and challenging. Using these annotations, we show that significant and meaningful differences exist between divine acts depicted by the Left Behind books and Christian Fiction more broadly.

Shape measures have emerged as promising descriptors of white matter tractography, offering complementary insights into anatomical variability and associations with cognitive and clinical phenotypes. However, conventional methods for computing shape measures are computationally expensive and time-consuming for large-scale datasets due to reliance on voxel-based representations. We propose Tract2Shape, a novel multimodal deep learning framework that leverages geometric (point cloud) and scalar (tabular) features to predict ten white matter tractography shape measures. To enhance model efficiency, we utilize a dimensionality reduction algorithm for the model to predict five primary shape components. The model is trained and evaluated on two independently acquired datasets, the HCP-YA dataset, and the PPMI dataset. We evaluate the performance of Tract2Shape by training and testing it on the HCP-YA dataset and comparing the results with state-of-the-art models. To further assess its robustness and generalization ability, we also test Tract2Shape on the unseen PPMI dataset. Tract2Shape outperforms SOTA deep learning models across all ten shape measures, achieving the highest average Pearson's r and the lowest nMSE on the HCP-YA dataset. The ablation study shows that both multimodal input and PCA contribute to performance gains. On the unseen testing PPMI dataset, Tract2Shape maintains a high Pearson's r and low nMSE, demonstrating strong generalizability in cross-dataset evaluation. Tract2Shape enables fast, accurate, and generalizable prediction of white matter shape measures from tractography data, supporting scalable analysis across datasets. This framework lays a promising foundation for future large-scale white matter shape analysis.