We study spectral moments of the Bures-Hall random matrices ensemble. The main result establishes a recurrence relation for the kth spectral moment valid for a real-valued k, in contrast to prevailing results in the literature of different ensembles of assuming an integer k. The key to establish the recurrence relation is the obtained Christoffel-Darboux formulae of correlation kernels of the ensemble that avoid tedious summations. As an application of our spectral moment results, we re-derive the formulae of average von Neumann entropy and quantum purity of Bures-Hall ensemble conjectured by Ayana Sarkar and Santosh Kumar.
Solar-driven interfacial evaporation has emerged as a highly promising route, leveraging abundant solar energy for efficient desalination. However, many existing solar evaporators still face challenges such as salt accumulation and, crucially, fail to reduce heavy metal concentrations to the ultra-low levels required by drinking water standards. To address this gap, we have developed a room-temperature fabricated graphene oxide/siloxane-PVA hydrogel (GO/SPH) evaporator wherein solar-driven evaporation works in synergy with integrated chelating amino groups to achieve the thorough removal of heavy metal ions concurrent with desalination. The optimized 3.0 wt% GO/SPH composite demonstrates a remarkable evaporation rate of 2.21 kg m- 2 h- 1 under 1 sun irradiation, a two-fold improvement over the pristine SPH. This exceptional dual-function performance is underpinned by its synergistic architecture. For solar evaporation, GO within the matrix acts as a highly efficient photothermal agent, achieving 91.4% conversion efficiency. Concurrently, for heavy metal remediation, amino ligands derived from the APTMS crosslinker enable the selective sequestration of Cu2+, Cr3+, Cd2+, and Pb2+ ions through specific coordination chemistry. Crucially, the entire evaporator is stabilized by a hydrolytically stable Si-O-Si network, which ensures robust multi-cycle performance by retaining over 95% of its initial efficiency and preserving its decontamination integrity over extended operation.
Inspired by the synergistic hydration mechanisms of the elytra of the desert beetle and the lotus leaf, we developed a biomimetic copper foam/ Cu3(BTC)2@hexadecyltrimethoxysilane(CF/HKUST-1@HDTMS) composite membrane via a controllable silane modification strategy. This material was constructed on a copper substrate through a process involving selective oxidation, in-situ chelation, and surface modification, resulting in a surface with a well-defined wettability gradient. Characterization techniques such as scanning electron microscopy and X-ray photoelectron spectroscopy confirmed the heterogeneous structure and chemical composition of the CF/HKUST-1@HDTMS surface. The hydrophilic regions, identified by contact angle measurements, provide optimized nucleation sites for water vapor, promoting rapid condensation. Conversely, the superhydrophobic regions significantly reduce the adhesion force, as quantified by dynamic contact angle analysis, enabling efficient droplet coalescence and shedding. This bio-inspired design replicates nature’s intelligent water management, endowing the CF/HKUST-1@HDTMS membrane with both high condensation efficiency and outstanding self-renewal capability. Furthermore, robustness tests, including mechanical abrasion and environmental exposure, demonstrated the material’s exceptional stability. The CF/HKUST-1@HDTMS membrane thus presents a promising and durable solution for atmospheric water harvesting in arid regions.
Discovering personally identifiable information (PII) in mobile forensic databases is difficult because the relevant table-column regions are unknown, distributed across heterogeneous SQLite schemas, and may contain values embedded in free-text or semi-structured fields. We present a hypothesis-driven framework that treats PII localization as bounded, adaptive search under uncertainty. An agent ranks candidate table-column regions, probes sampled values, and maintains a memory of prior evidence, confidence scores, and decisions to refine subsequent hypotheses. The framework separates lightweight PII exploration from targeted extraction, normalization, and deduplication over validated regions, thereby limiting exhaustive inspection to regions supported by sampled evidence. We evaluate the framework on 25 SQLite databases from 10 Android and iOS applications in the Cellebrite CTF corpus, targeting email addresses, phone numbers, domain names, person names, and postal addresses. Against a corpus-level distinct ground-truth set of 3,751 entities, Gemini 2.5 Pro achieves 94.5
Deep learning models are emerging as strong alternatives to numerical weather prediction, yet their internal representations remain poorly understood. We analyze the latent space of Microsoft’s Aurora model to test whether its embed- dings align with known physical processes. First, we show that land–sea distinctions are strongly captured, with errors mainly at coastlines. Second, we examine extreme surface temperatures using percentile-based thresholds, finding that embeddings reveal a gradient from moderate to severe events, though recall degrades at the rarest percentiles. These results suggest that Aurora’s encoder encodes physically consistent features but underestimates rare extremes. Our study combines deep learning forecasting, interpretable representation learning, and classical ML probing, illustrating how cross-disciplinary AI methods can yield insight into foundation models
