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This paper addresses the inverse scattering problem in a domain ε. The input data, measured out- side ε, involve the waves generated by the interaction of plane waves with various directions and unknown scatterers fully occluded inside ε. The output of this problem is the spatially dielectric constant of these scatterers. Our approach to solving this problem consists of two primary stages. Initially, we eliminate the unknown dielectric constant from the governing equation, resulting in a system of partial di!erential equations. Subsequently, we develop the Carleman contraction mapping method to e!ectively tackle this system. It is noteworthy to highlight this method’s ro- bustness. It does not request a precise initial guess of the true solution, and its computational cost is not expensive. Some numerical examples are presented. 

Distributional drift detection is important in medical applications as it helps ensure the accuracy and reliability of models by identifying changes in the underlying data distribution that could affect the prediction results of machine learning models. However, current methods have limitations in detecting drift, for example, the inclusion of abnormal datasets can lead to unfair comparisons. This paper presents an accurate and sensitive approach to detect distributional drift in CT-scan medical images by leveraging data-sketching and fine-tuning techniques. We developed a robust baseline library model for real-time anomaly detection, allowing for efficient comparison of incoming images and identification of anomalies. Additionally, we fine-tuned a pre-trained Vision Transformer model to extract relevant features, using mammography as a case study, significantly enhancing model accuracy to 99.11%. Combining with data-sketches and fine-tuning, our feature extraction evaluation demonstrated that cosine similarity scores between similar datasets provide greater improvements, from around 50% increased to 99.1%. Finally, the sensitivity evaluation shows that our solutions are highly sensitive to even 1% salt-and-pepper and speckle noise, and it is not sensitive to lighting noise (e.g., lighting conditions have no impact on data drift). The proposed methods offer a scalable and reliable solution for maintaining the accuracy of diagnostic models in dynamic clinical environments. 

Abstract Cancer is an umbrella term that includes a wide spectrum of disease severity, from those that are malignant, metastatic, and aggressive to benign lesions with very low potential for progression or death. The ability to prognosticate patient outcomes would facilitate management of various malignancies: patients whose cancer is likely to advance quickly would receive necessary treatment that is commensurate with the predicted biology of the disease. Former prognostic models based on clinical variables (age, gender, cancer stage, tumor grade, etc.), though helpful, cannot account for genetic differences, molecular etiology, tumor heterogeneity, and important host biological mechanisms. Therefore, recent prognostic models have shifted toward the integration of complementary information available in both molecular data and clinical variables to better predict patient outcomes: vital status (overall survival), metastasis (metastasis-free survival), and recurrence (progression-free survival). In this article, we review 20 survival prediction approaches that integrate multi-omics and clinical data to predict patient outcomes. We discuss their strategies for modeling survival time (continuous and discrete), the incorporation of molecular measurements and clinical variables into risk models (clinical and multi-omics data), how to cope with censored patient records, the effectiveness of data integration techniques, prediction methodologies, model validation, and assessment metrics. The goal is to inform life scientists of available resources, and to provide a complete review of important building blocks in survival prediction. At the same time, we thoroughly describe the pros and cons of each methodology, and discuss in depth the outstanding challenges that need to be addressed in future method development. 

Abstract Accurate knowledge of the phase transitions and thermoelastic properties of candidate iron alloys, such as Fe‐Si alloys, is essential for understanding the nature and dynamics of planetary cores. The phase diagrams of some Fe‐Si alloys between 1 atm and 16 GPa have been back‐extrapolated from higher pressures, but the resulting phase diagram of Fe_83.6Si_16.4(9 wt.% Si) is inconsistent with temperature‐induced changes in its electrical resistivity between 6 and 8 GPa. This study reports in situ synchrotron X‐ray diffraction (XRD) measurements on pre‐melted and powder Fe_83.6Si_16.4samples from ambient conditions to 60 GPa and 900 K using an externally heated diamond‐anvil cell. Upon compression at 300 K, thebccphase persisted up to ∼38 GPa. Thehcpphase appeared near 8 GPa in the pre‐melted sample, and near 17 GPa in the powder sample. The appearance of thehcpphase in the pre‐melted sample reconciles the reported changes in electrical resistivity of a similar sample, thus resolving the low‐pressure region of the phase diagram. The resulting high‐temperature Birch‐Murnaghan equation of state (EoS) and thermal EoS based on the Mie‐Gruneisen‐Debye model of thebccandhcpstructures are consistent with, and complement the literature data at higher pressures. The calculated densities based on the thermal EoS of Fe‐9wt.%Si indicate that bothbccandhcpphases agree with the reported core density estimates for the Moon and Mercury.