High dimensional representation drift is commonly quantified using Euclidean or cosine distances, which presuppose fixed coordinates when comparing representations across time, training or preprocessing stages. While effective in many settings, these measures entangle intrinsic changes in the data with variations induced by arbitrary parametrizations. We introduce a projective geometric view of representation drift grounded in the Fubini Study metric, which identifies representations that differ only by gauge transformations such as global rescalings or sign flips. Applying this framework to empirical high dimensional datasets, we explicitly construct representation trajectories and track their evolution through cumulative geometric drift. Comparing Euclidean, cosine and Fubini Study distances along these trajectories reveals that conventional metrics systematically overestimate change whenever representations carry genuine projective ambiguity. By contrast, the Fubini Study metric isolates intrinsic evolution by remaining invariant under gauge-induced fluctuations. We further show that the difference between cosine and Fubini Study drift defines a computable, monotone quantity that directly captures representation churn attributable to gauge freedom. This separation provides a diagnostic for distinguishing meaningful structural evolution from parametrization artifacts, without introducing model-specific assumptions. Overall, we establish a geometric criterion for assessing representation stability in high-dimensional systems and clarify the limits of angular distances. Embedding representation dynamics in projective space connects data analysis with established geometric programs and yields observables that are directly testable in empirical workflows.

Leukemia diagnosis and monitoring rely increasingly on high-throughput image data, yet conventional clustering methods lack the flexibility to accommodate evolving cellular patterns and quantify uncertainty in real time. We introduce Adaptive and Dynamic Neuro-Fuzzy Clustering, a novel streaming-capable framework that combines Convolutional Neural Network-based feature extraction with an online fuzzy clustering engine. ADNF initializes soft partitions via Fuzzy C-Means, then continuously updates micro-cluster centers, densities, and fuzziness parameters using a Fuzzy Temporal Index (FTI) that measures entropy evolution. A topology refinement stage performs density-weighted merging and entropy-guided splitting to guard against over- and under-segmentation. On the C-NMC leukemia microscopy dataset, our tool achieves a silhouette score of 0.51, demonstrating superior cohesion and separation over static baselines. The method's adaptive uncertainty modeling and label-free operation hold immediate potential for integration within the INFANT pediatric oncology network, enabling scalable, up-to-date support for personalized leukemia management.

We're finally reading the secrets of Herculaneum's lost library A whole library's worth of papyri owned by Julius Caesar's father-in-law were turned to charcoal by the eruption of Vesuvius. Deep within a particle accelerator, theoretical physicist Giorgio Angelotti is hard at work. He sets a black cylinder on a mount, bolts it down, then runs through some safety checks before retreating from the chamber, known as "the hatch". "You have to be sure there's no one in the hatch before you close the door," he says. That's because he is about to blast the sample with a super-powerful beam of X-rays.

This is particularly true for language tasks that are culture-dependent.

Misinformation in healthcare, from vaccine hesitancy to unproven treatments, poses risks to public health and trust in medical systems. While machine learning and natural language processing have advanced automated fact-checking, validating biomedical claims remains uniquely challenging due to complex terminology, the need for domain expertise, and the critical importance of grounding in scientific evidence. We introduce CER (Combining Evidence and Reasoning), a novel framework for biomedical fact-checking that integrates scientific evidence retrieval, reasoning via large language models, and supervised veracity prediction. By integrating the text-generation capabilities of large language models with advanced retrieval techniques for high-quality biomedical scientific evidence, CER effectively mitigates the risk of hallucinations, ensuring that generated outputs are grounded in verifiable, evidence-based sources. Evaluations on expert-annotated datasets (HealthFC, BioASQ-7b, SciFact) demonstrate state-of-the-art performance and promising cross-dataset generalization. Code and data are released for transparency and reproducibility: https://github.com/PRAISELab-PicusLab/CER

Purpose: This study introduces a novel framework for identifying and exploiting predictive lead-lag relationships in financial markets. We propose an integrated approach that combines advanced statistical methodologies with machine learning models to enhance the identification and exploitation of predictive relationships between equities. Methods: We employed a Gaussian Mixture Model (GMM) to cluster nine prominent stocks based on their mid-range historical volatility profiles over a three-year period. From the resulting clusters, we constructed a multi-stage causal inference pipeline, incorporating the Granger Causality Test (GCT), a customised Peter-Clark Momentary Conditional Independence (PCMCI) test, and Effective Transfer Entropy (ETE) to identify robust, predictive linkages. Subsequently, Dynamic Time Warping (DTW) and a K-Nearest Neighbours (KNN) classifier were utilised to determine the optimal time lag for trade execution. The resulting strategy was rigorously backtested. Results: The proposed volatility-based trading strategy, tested from 8 June 2023 to 12 August 2023, demonstrated substantial efficacy. The portfolio yielded a total return of 15.38%, significantly outperforming the 10.39% return of a comparative Buy-and-Hold strategy. Key performance metrics, including a Sharpe Ratio up to 2.17 and a win rate up to 100% for certain pairs, confirmed the strategy's viability. Conclusion: This research contributes a systematic and robust methodology for identifying profitable trading opportunities derived from volatility-based causal relationships. The findings have significant implications for both academic research in financial modelling and the practical application of algorithmic trading, offering a structured approach to developing resilient, data-driven strategies.

Differential privacy has been proven effective for stochastic gradient descent; however, existing methods often suffer from performance degradation in high-dimensional settings, as the scale of injected noise increases with dimensionality. To tackle this challenge, we propose AdaDPIGU--a new differentially private SGD framework with importance-based gradient updates tailored for deep neural networks. In the pretraining stage, we apply a differentially private Gaussian mechanism to estimate the importance of each parameter while preserving privacy. During the gradient update phase, we prune low-importance coordinates and introduce a coordinate-wise adaptive clipping mechanism, enabling sparse and noise-efficient gradient updates. Theoretically, we prove that AdaDPIGU satisfies $(\varepsilon, δ)$-differential privacy and retains convergence guarantees. Extensive experiments on standard benchmarks validate the effectiveness of AdaDPIGU. All results are reported under a fixed retention ratio of 60%. On MNIST, our method achieves a test accuracy of 99.12% under a privacy budget of $ε= 8$, nearly matching the non-private model. Remarkably, on CIFAR-10, it attains 73.21% accuracy at $ε= 4$, outperforming the non-private baseline of 71.12%, demonstrating that adaptive sparsification can enhance both privacy and utility.

In many robotics applications, it is necessary to compute not only the distance between the robot and the environment, but also its derivative - for example, when using control barrier functions. However, since the traditional Euclidean distance is not differentiable, there is a need for alternative distance metrics that possess this property. Recently, a metric with guaranteed differentiability was proposed [1]. This approach has some important drawbacks, which we address in this paper. We provide much simpler and practical expressions for the smooth projection for general convex polytopes. Additionally, as opposed to [1], we ensure that the distance vanishes as the objects overlap. We show the efficacy of the approach in experimental results. Our proposed distance metric is publicly available through the Python-based simulation package UAIBot.