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The existing quantitative geography literature contains a dearth of articles that span spatial autocorrelation (SA), a fundamental property of georeferenced data, and spatial optimization, a popular form of geographic analysis. The well-known location–allocation problem illustrates this state of affairs, although its empirical geographic distribution of demand virtually always exhibits positive SA. This latent redundant attribute information alludes to other tools that may well help to solve such spatial optimization problems in an improved, if not better than, heuristic way. Within a proof-of-concept perspective, this paper articulates connections between extensions of the renowned Majority Theorem of the minisum problem and especially the local indices of SA (LISA). The relationship articulation outlined here extends to the p = 2 setting linkages already established for the p = 1 spatial median problem. In addition, this paper presents the foundation for a novel extremely efficient p = 2 algorithm whose formulation demonstratively exploits spatial autocorrelation. 

Police patrolling intends to enhance traffic safety by mitigating the risks associated with vehicle crashes and accidents. From a view of operations, patrolling requires an effective distribution of resources and often involves area delineations for this distribution purpose. Given constraints such as budget and human resources for traffic safety, delineating geographic areas optimally for police patrol areas is an important agenda item. This paper considers two p-median location models using segments on a street network as observational units on which traffic issues such as vehicle crashes occur. It also uses two weight sets to construct an enhanced delineation of police patrol areas in the City of Plano, Texas. The first model for the standard p-median formulation gives attention to the cumulative number of motor vehicle crashes from 2011 to 2021 on the major transportation networks in Plano. The second model, an extension of this first p-median one, uses balancing constraints to achieve balanced spatial coverage across patrol areas. These two models are also solved with network kernel density count estimates (NKDCE) instead of crash counts. These smoothed densities on a network enable consideration of uncertainty affiliated with this aggregation. The analysis results of this paper suggest that the p-median models provide effective specifications, including their capability to define patrol areas that encompass the entire study region while minimizing distance costs. The inclusion of balancing constraints ensures a more equitable distribution of workloads among patrol areas, improving overall efficiency. Additionally, the model with NKDCE results in an improved workload balance among delineated areas for police patrolling activities, thus supporting more informed spatial decision-making processes for public safety. 

Thep‐dispersion problem is a spatial optimization problem that aims to maximize the minimum separation distance among all assigned nodes. This problem is characterized by an innate spatial structure based on distance attributes. This research proposes a novel approach, named thedistance‐based spatially informed property(D‐SIP) method to reduce the problem size of thep‐dispersion instances, facilitating a more efficient solution while maintaining optimality in nearly all cases. The D‐SIP is derived from investigating the underlying spatial characteristics from the behaviors of thep‐dispersion problem in determining the optimal location of nodes. To define the D‐SIP, this research applies Ripley'sK‐function to the different types of point patterns, given that the optimal solutions of thep‐dispersion problem are strongly associated with the spatial proximity among points discovered by Ripley'sK‐function. The results demonstrate that the D‐SIP identifies collective dominances of optimal solutions, leading to buildingthe spatially informed p‐dispersion model. The simulation‐based experiments show that the proposed method significantly diminishes the size of problems, improves computational performance, and secures optimal solutions for 99.9% of instances (999 out of 1,000 instances) under diverse conditions. 

Abstract Advancements in nanofabrication processes have propelled nonvolatile phase change materials (PCMs) beyond storage‐class applications. They are now making headway in fields such as photonic integrated circuits (PIC), free‐space optics, and plasmonics. This shift is owed to their distinct electrical, optical, and thermal properties between their different atomic structures, which can be reversibly switched through thermal stimuli. However, the reliability of PCM‐based optical components is not yet on par with that of storage‐class devices. This is in part due to the challenges in maintaining a uniform temperature distribution across the PCM volume during phase transformation, which is essential to mitigate stress and element segregation as the device size exceeds a few micrometers. Understanding thermal transport in PCM‐based devices is thus crucial as it dictates not only the durability but also the performance and power consumption of these devices. This article reviews recent advances in the development of PCM‐based photonic devices from a thermal transport perspective and explores potential avenues to enhance device reliability. The aim is to provide insights into how PCM‐based technologies can evolve beyond storage‐class applications, maintain their functionality, and achieve longer lifetimes. 

Abstract Nonlinear microscopy provides excellent depth penetration and axial sectioning for 3D imaging, yet widespread adoption is limited by reliance on expensive ultrafast pulsed lasers. This work circumvents such limitations by employing rare‐earth doped upconverting nanoparticles (UCNPs), specifically Yb³⁺/Tm³⁺co‐doped NaYF₄nanocrystals, which exhibit strong multimodal nonlinear optical responses under continuous‐wave (CW) excitation. These UCNPs emit multiple wavelengths at UV (λ ≈ 450 nm), blue (λ ≈ 450 nm), and NIR (λ ≈ 800 nm), whose intensities are nonlinearly governed by excitation power. Exploiting these properties, multi‐colored nonlinear emissions enable functional imaging of cerebral blood vessels in deep brain. Using a simple optical setup, high resolution in vivo 3D imaging of mouse cerebrovascular networks at depths up to 800 µmm is achieved, surpassing performance of conventional imaging methods using CW lasers. In vivo cerebrovascular flow dynamics is also visualized with wide‐field video‐rate imaging under low‐powered CW excitation. Furthermore, UCNPs enable depth‐selective, 3D‐localized photo‐modulation through turbid media, presenting spatiotemporally targeted light beacons. This innovative approach, leveraging UCNPs' intrinsic nonlinear optical characteristics, significantly advances multimodal nonlinear microscopy with CW lasers, opening new opportunities in bio‐imaging, remote optogenetics, and photodynamic therapy.