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Global weather forecast is an important spatial-temporal prediction problem, which can provide numerous societal benefits such as extreme weather forewarning, traffic scheduling, and agricultural planning. Though many spatial-temporal prediction models have been proposed, they suffer from two drawbacks for global weather forecasts, namely 1) ignoring the physical mechanism and spherical characteristics and 2) not effectively exploiting the global and local correlations. To address the above drawbacks, in this paper, we formalize global weather state dynamics as partial differential equations (PDEs) in spherical space and infer the state of the global weather system by solving these PDEs. Specifically, we use Green’s function method to solve the PDEs and find that the solution of the spherical PDEs can be obtained by the spherical convolution. We further proposed a novel Spherical Neural Operator, SNO, which consists of spherical convolution and vanilla convolution. The former is used to solve these PDEs and model the global correlations in spherical space, and the latter is used to capture the local correlations. Upon the operator, a global weather prediction model is developed. Extensive experimental results demonstrate the effectiveness and superiority of our method over state-of-the-art approaches.

Implant-associated infections pose serious threats to patients in terms of morbidity, mortality, and medical costs. This paper focuses on the quantitative assessment of the antimicrobial efficacy of a silver-based prophylactic system for orthopaedic implant applications. The implant system is configured to induce controlled local administration of silver ions via low intensity direct current activation (1–14 µA). We developed a broth-based in vitro testing model to evaluate the effects of important design parameters on the antimicrobial efficacy of the system over a 48-h interval. The time-kill curves obtained with various parameter levels were analyzed through a longitudinal model. Five parameters were investigated independently through one-way factorial experiments (n = 12) against Staphylococcus aureus. In phase 1 of the study, we investigated the effect of cathode material on system performance. We also determined the linear structure of the longitudinal model based on the Akaike information criterion by fitting the empirical data to multiple candidate model structures. The results show that substituting the silver cathode with titanium does not weaken the antimicrobial efficacy of the system (p= 0.9946). In phase 2, a detailed analysis with four design parameters was conducted using the silver–titanium configuration. The performance of the system was found to be independent of the electrode separation distance (p= 0.9926) and the pulsating current frequency (p= 0.9956). However, the anode surface area (p< 0.0001) and the current intensity (p< 0.0001) influenced the antimicrobial efficacy in an interactive manner. Overall, this study characterizes the in vitro antimicrobial efficacy of the proposed system and provides a reference of design parameters for future product engineering.