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Optimal Area-Sensitive Bounds for Polytope Approximation
No full textApproximating convex bodies is a fundamental problem in geometry. Given a convex body K in Rd for a fixed dimension d, the objective is to minimize the number of facets of an approximating polytope for a given Hausdorff error ε. The best known uniform bound, due to Dudley (1974), shows that O((diam(K)/ε)(d-1)/2) facets suffice. Although this bound is optimal for fat objects, such as Euclidean balls, it is far from optimal for “skinny” convex bodies. Skinniness can be characterized relative to the Euclidean ball. Given a convex body K, define its area radius, arad(K), to be the radius of the Euclidean ball having the same surface area as K. It follows from generalizations of the isoperimetric inequality that diam(K)≥2·arad(K). We show that, given a convex body whose minimum width is at least ε, it is possible to approximate the body by a polytope having O((arad(K)/ε)(d-1)/2) facets. Our approach works by first reducing the problem of approximating convex bodies to that of approximating convex functions. We employ a classical concept from convexity, called Macbeath regions. We demonstrate that there is a polar relationship between the Macbeath regions of a function and the Macbeath regions of its Legendre dual. This is combined with known bounds on the Mahler volume to bound the total size of the approximation.</p
Resonances through subwavelength holes: Theory, computation, and applications
No full textElectromagnetic wave scattering by subwavelength hole structures has received significant research interest in the past two decades, due to the unusual physical phenomena that arise in these media when external radiation is present, such as the extraordinary optical transmission (EOT) and strongly localized optical field at the hole apertures. It turns out that resonances, which are broadly defined as complex eigenvalues of the underlying Maxwell's operator, play a major role in EOT and anomalous field enhancement for such media. These resonances can be induced by the geometry (such as tiny holes) or the medium parameter (such as permittivity values) of the problem, or their collaborative interactions. In this paper, we survey the mathematical theory that has been developed to understand the various resonances in subwavelength hole structures, along with quantitative analyses of their resonant scattering and the induced EOT phenomena. We also review computational methods proposed for modeling resonant wave scattering in these multiscale media and the mathematical frameworks established for applications in sensing and imaging. Finally, we discuss open problems and outstanding mathematical challenges in the field. The mathematical investigation of the resonances for this class of problems provides the fundamental theory as well as computational algorithms for the design of more efficient subwavelength optical devices and their applications. It also sheds light on the studies of other related spectral problems with the differential operators defined over multiscale media.</p
Interactions of metal-phenolic networks with physiological barriers and their advances in diseases management
No full textOrganisms exist widespread physiological barrier systems, including the blood-brain barrier (BBB), gastrointestinal barrier (GIB), pulmonary mucosal barrier, and skin barriers, which act as protectors while also impeding the successful passage of therapeutic drugs. Barriers are mainly made up of tight cell junctions and active transport systems, but different organs have environmentally adapted unique structures, and heterogeneous tumors escape drug interventions by camouflaging the barrier structure. Metal-phenolic networks (MPNs) are an emerging nanodrug platform that has attracted significant attention due to their unique combination of metal and polyphenol properties, especially for trans-barrier transport. MPNs demonstrate diverse biological effects when interacting with physiological barriers, notably in penetration, repair, and regulation, thereby amplifying the therapeutic effects of the nanosystems. Additionally, MPNs exhibit cross-barrier spatiotemporal modulation capabilities, yet comprehensive insights into the interactions of MPNs with physiological barriers are not presently. Therefore, this review systematically covers the core characteristics, production methods, and process control of MPNs. It also details the key microstructural features of various physiological and tumor pathological barriers and summarizes advances in the application of MPNs for the treatment of diseases associated with different barriers. Lastly, it presents an initial overview of the spatiotemporal crosstalk mechanisms of MPNs within the multilevel barrier systems of the body and further highlights the challenges and prospects of MPNs in overcoming physiological barrier challenges.</p
PHIMO-NN: Compact Modeling by Fusing Device Physics and Neural Networks for One-Shot Parameterization
No full textThe complexity of compact device modeling has grown significantly in advanced technologies, including an increase in the number of model parameters, the time-consuming process of parameter extraction, and significant efforts required for model updating with device technology evolutions. To address these challenges, a new methodology by fusing device physics and tiny neural networks (PHIMO-NN) is developed. With the capability of neural networks in the universal approximation to assist compact modeling, e.g., replacing manual fitting functions and/or binning equations, the number of model parameters is reduced while a global coverage is achieved. The well-behaved derivatives of PHIMO-NN outputs to its parameters lead to a desired one-shot parameterization using a back-propagation (BP) training. For FinFET technology data of a 14/16 nm PDK model comprising 5 bins covering the entire gate lengths, PHIMO-NN parameterization takes 20 minutes, resulting in a significant speedup compared with traditional model extractions. Further, model transferring for technology updates is made easier with the continuous learning capability. For example, a PHIMO-NN trained for FinFETs with an error of 0.22% is easily extended for nanosheet GAAFETs with an error of 0.31%. PHIMO-NN combines the advantages of physics-based models (physics-awareness and simplicity) and AI models (parameterization efficiency and accuracy), promising an agile device modeling methodology for advanced/emerging technologies.</p
Time–frequency constrained graph-level representation learning paradigm for real-time mechanical fault diagnosis
No full textAlthough graph neural networks (GNNs) have achieved remarkable success for fault diagnosis, the mainstream node classification paradigm suffers from low efficiency. Furthermore, intrinsic correlations within raw signals are rarely exploited to address the insufficient fault knowledge in model training. To address these issues, a time–frequency constraint-guided graph-level feature representation learning method for few-shot fault diagnosis is proposed. It overcomes the inevitable challenges of graph reconstruction and model retraining associated with node-level diagnosis models, thereby enhancing the real-time responsiveness. Specifically, a feature-enhanced chain graph (FECG) with only a few edges is introduced, which improves the interpretability and efficiency of edge construction in input graphs. Further, a time–frequency constrained graph convolutional network (TFCGCN) is developed, which can guide the gradient descent direction during model training based on the designed time–frequency constraint loss, reducing the model's reliance on labeled faulty samples. To mitigate the attenuation of time–frequency constraints during cross-layer propagation, a node feature transfer technique is proposed, and it also enhances the feature extraction capabilities of graph convolution layers. Through ablation experiments and comparisons with various existing models, the effectiveness and superiority of the proposed FECG-TFCGCN were validated, with several extremely unbalanced training sets on axial flow pumps and machine tool spindles.</p
Plastic threats to coral reefs: A strategic management perspective from Bali's marine protected areas
No full textPlastic pollution remains a significant threat to coral reef ecosystems, even within Marine Protected Areas (MPAs). This study assesses the levels and types of plastic debris, both macroplastics and microplastics, found in coral reef ecosystems at two MPAs in Bali: Karangasem and Nusa Penida. Coral health was evaluated using the Underwater Photo Transect (UPT) method, while plastic particles were identified through field sampling and laboratory analysis, including Raman spectroscopy. Macroplastic accumulation was higher in Karangasem, while microplastic concentrations were comparable between the two regions. Microplastics were detected in coral tissues, and Polyethylene (PET and LDPE) was the dominant polymer. Although Pollution Load Index (PLI) values indicate a low ecological risk, it is evident that both MPAs suffer from coral degradation. Notably, the data suggest that macroplastic may have a more direct impact on coral reefs through physical damage. Despite these threats, both MPAs exhibited high ecological resilience, suggesting strong recovery potential if waste inputs are reduced. The findings highlight the important of improving waste management, especially capacity building and increased funding allocation. Strengthening each strategic approach of the MPAs can reduce plastic leakage into the sea and support coral reef recovery.</p
