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A common feature within coastal cities is small, urbanized watersheds where the time of concentration is short, leading to vulnerability to flash flooding during coastal storms that can also cause storm surge. While many recent studies have provided evidence of dependency in these two flood drivers for many coastal areas worldwide, few studies have investigated their co-occurrence locally in detail or the storm types that are involved. Here we present a bivariate statistical analysis framework with historical rainfall and storm surge and tropical cyclone (TC) and extratropical cyclone (ETC) track data, using New York City (NYC) as a mid-latitude demonstration site where these storm types play different roles. In contrast to prior studies that focused on daily or longer durations of rain, we apply hourly data and study simultaneous drivers and lags between them. We quantify characteristics of compound flood drivers, including their dependency, magnitude, lag time, and joint return periods (JRPs), separately for TCs, ETCs, non-cyclone-associated events, and merged data from all events. We find TCs have markedly different driver characteristics from other storm types and dominate the joint probabilities of the most extreme rain surge compound events, even though they occur much less frequently. ETCs are the predominant source of more frequent moderate compound events. The hourly data also reveal subtle but important spatial differences in lag times between the joint flood drivers. For Manhattan and southern shores of NYC during top-ranked TC rain events, rain intensity has a strong negative correlation with lag time to peak surge, promoting pluvial–coastal compound flooding. However, for the Bronx River in northern NYC, fluvial–coastal compounding is favored due to a 2–6 h lag from the time of peak rain to peak surge. 

We study the implicit bias of gradient flow on linear equivariant steerable networks in group-invariant binary classification. Our findings reveal that the parameterized predictor converges in direction to the unique group-invariant classifier with a maximum margin defined by the input group action. Under a unitary assumption on the input representation, we establish the equivalence between steerable networks and data augmentation. Furthermore, we demonstrate the improved margin and generalization bound of steerable networks over their non-invariant counterparts. 

Abstract Evaporation of droplets composed of insoluble materials provides a low‐cost and facile route for assembling materials and structures in a wide spectrum of functionalities down to the nanoscale and also serves as a basis for innovating ink‐solution‐based future manufacturing technologies. This review summarizes the fundamental mechanics theories of material assembly by droplet drying both on solid and liquid substrates and in a fully suspended air environment. The evolution of assembly patterns, material deformation, and liquid flow during droplet drying and its response to external stimuli ranging from solution surfactant and pH value, surface geometric pattern and wettability, drying temperature, pressure environment, to electrical field have been highlighted to elucidate the coupling mechanisms between solid materials and liquid solutions and the manipulation strategies for material assembly through an either active or passive means. The recent progresses in ink‐based printing technologies with selected examples are also presented to illustrate the immediate applications of droplet drying, with a focus on printing electronic sensors and biomedical devices. The remaining challenges and emerging opportunities are discussed. 

SU-8 is an epoxy-based, negative-tone photoresist that has been extensively utilized to fabricate myriads of devices including biomedical devices in the recent years. This paper first reviews the biocompatibility of SU-8 for in vitro and in vivo applications. Surface modification techniques as well as various biomedical applications based on SU-8 are also discussed. Although SU-8 might not be completely biocompatible, existing surface modification techniques, such as O2 plasma treatment or grafting of biocompatible polymers, might be sufficient to minimize biofouling caused by SU-8. As a result, a great deal of effort has been directed to the development of SU-8-based functional devices for biomedical applications. This review includes biomedical applications such as platforms for cell culture and cell encapsulation, immunosensing, neural probes, and implantable pressure sensors. Proper treatments of SU-8 and slight modification of surfaces have enabled the SU-8 as one of the unique choices of materials in the fabrication of biomedical devices. Due to the versatility of SU-8 and comparative advantages in terms of improved Young’s modulus and yield strength, we believe that SU-8-based biomedical devices would gain wider proliferation among the biomedical community in the future. 

Abstract Magic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands. Several numerical and analytical methods have been applied to understand the correlated phases therein, revealing some similarity with the quantum Hall physics. In this work, we provide a Mott-Hubbard perspective for the TBG system. Employing the large-scale density matrix renormalization group on the lattice model containing the projected Coulomb interactions only, we identify a first-order quantum phase transition between the insulating stripe phase and the quantum anomalous Hall state with the Chern number of ±1. Our results not only shed light on the mechanism of the quantum anomalous Hall state discovered at three-quarters filling, but also provide an example of the topological Mott insulator, i.e., the quantum anomalous Hall state in the strong coupling limit.