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Spatial optimization problems (SOPs) are characterized by spatial relationships governing the decision variables, objectives, and/or constraint functions. In this article, we focus on a specific type of SOP called spatial partitioning, which is a combinatorial problem due to the presence of discrete spatial units. Exact optimization methods do not scale with the size of the problem, especially within practicable time limits. This motivated us to develop population-based metaheuristics for solving such SOPs. However, the search operators employed by these population-based methods are mostly designed for real-parameter continuous optimization problems. For adapting these methods to SOPs, we apply domain knowledge in designing spatially aware search operators for efficiently searching through the discrete search space while preserving the spatial constraints. To this end, we put forward a simple yet effective algorithm called s warm-based s p atial meme ti c al gorithm (SPATIAL) and test it on the school (re)districting problem. Detailed experimental investigations are performed on real-world datasets to evaluate the performance of SPATIAL. Besides, ablation studies are performed to understand the role of the individual components of SPATIAL. Additionally, we discuss how SPATIAL is helpful in the real-life planning process and its applicability to different scenarios and motivate future research directions. 

With the wide application of electronic health records (EHR) in healthcare facilities, health event prediction with deep learning has gained more and more attention. A common feature of EHR data used for deep-learning-based predictions is historical diagnoses. Existing work mainly regards a diagnosis as an independent disease and does not consider clinical relations among diseases in a visit. Many machine learning approaches assume disease representations are static in different visits of a patient. However, in real practice, multiple diseases that are frequently diagnosed at the same time reflect hidden patterns that are conducive to prognosis. Moreover, the development of a disease is not static since some diseases can emerge or disappear and show various symptoms in different visits of a patient. To effectively utilize this combinational disease information and explore the dynamics of diseases, we propose a novel context-aware learning framework using transition functions on dynamic disease graphs. Specifically, we construct a global disease co-occurrence graph with multiple node properties for disease combinations. We design dynamic subgraphs for each patient's visit to leverage global and local contexts. We further define three diagnosis roles in each visit based on the variation of node properties to model disease transition processes. Experimental results on two real-world EHR datasets show that the proposed model outperforms state of the art in predicting health events. 

Influence blocking maximization (IBM) is crucial in many critical real-world problems such as rumors prevention and epidemic containment. The existing work suffers from: (1) concentrating on uniform costs at the individual level, (2) mostly utilizing greedy approaches to approximate optimization, (3) lacking a proper graph representation for influence estimates. To address these issues, this research introduces a neural network model dubbed Neural Influence Blocking (\algo) for improved approximation and enhanced influence blocking effectiveness. The code is available at https://github.com/oates9895/NIB. 

Despite progress in tomographic imaging of Earth’s interior, a number of critical questions regarding the large-scale structure and dynamics of the mantle remain outstanding. One of those questions is the impact of phase-boundary undulations on global imaging of mantle heterogeneity and on geodynamic (i.e. convection-related) observables. To address this issue, we developed a joint seismic-geodynamic-mineral physical tomographic inversion procedure that incorporates lateral variations in the depths of the 410- and 660-km discontinuities. This inversion includes S-wave traveltimes, SS precursors that are sensitive to transition-zone topography, geodynamic observables/data (free-air gravity, dynamic surface topography, horizontal divergence of tectonic plates and excess core-mantle boundary ellipticity) and mineral physical constraints on thermal heterogeneity. Compared to joint tomography models that do not include data sensitivity to phase-boundary undulations in the transition zone, the inclusion of 410- and 660-km topography strongly influences the inference of volumetric anomalies in a depth interval that encompasses the transition zone and mid-mantle. It is notable that joint tomography inversions, which include constraints on transition-zone discontinuity topography by seismic and geodynamic data, yield more pronounced density anomalies associated with subduction zones and hotspots. We also find that the inclusion of 410- and 660-km topography may improve the fit to the geodynamic observables, depending on the weights applied to seismic and geodynamic data in the inversions. As a consequence, we find that the amplitude of non-thermal density anomalies required to explain the geodynamic data decreases in most of the mantle. These findings underline the sensitivity of the joint inversions to the inclusion of transition-zone complexity (e.g. phase-boundary topography) and the implications for the inferred non-thermal density anomalies in these depth regions. Finally, we underline that our inferences of 410- and 660-km topography avoid a commonly employed approximation that represents the contribution of volumetric heterogeneity to SS-wave precursor data. Our results suggest that this previously employed correction, based on a priori estimates of uppermantle heterogeneity, might be a significant source of error in estimating the 410- and 660-km topography. 

Despite progress in tomographic imaging of Earth's interior, a number of critical questions regarding the large-scale structure and dynamics of the mantle remain outstanding. One of those questions is the impact of phase-boundary undulations on global imaging of mantle heterogeneity and on geodynamic (i.e. convection-related) observables. To address this issue, we developed a joint seismic-geodynamic-mineral physical tomographic inversion procedure that incorporates lateral variations in the depths of the 410- and 660-km discontinuities. This inversion includes S-wave traveltimes, SS precursors that are sensitive to transition-zone topography, geodynamic observables/data (free-air gravity, dynamic surface topography, horizontal divergence of tectonic plates and excess core-mantle boundary ellipticity) and mineral physical constraints on thermal heterogeneity. Compared to joint tomography models that do not include data sensitivity to phase-boundary undulations in the transition zone, the inclusion of 410- and 660-km topography strongly influences the inference of volumetric anomalies in a depth interval that encompasses the transition zone and mid-mantle. It is notable that joint tomography inversions, which include constraints on transition-zone discontinuity topography by seismic and geodynamic data, yield more pronounced density anomalies associated with subduction zones and hotspots. We also find that the inclusion of 410- and 660-km topography may improve the fit to the geodynamic observables, depending on the weights applied to seismic and geodynamic data in the inversions. As a consequence, we find that the amplitude of non-thermal density anomalies required to explain the geodynamic data decreases in most of the mantle. These findings underline the sensitivity of the joint inversions to the inclusion of transition-zone complexity (e.g. phase-boundary topography) and the implications for the inferred non-thermal density anomalies in these depth regions. Finally, we underline that our inferences of 410- and 660-km topography avoid a commonly employed approximation that represents the contribution of volumetric heterogeneity to SS-wave precursor data. Our results suggest that this previously employed correction, based on a priori estimates of upper-mantle heterogeneity, might be a significant source of error in estimating the 410- and 660-km topography.