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1. The max‐ p ‐compact‐regions problem

   https://doi.org/10.1111/tgis.12874  

   Feng, Xin; Rey, Sergio; Wei, Ran (November 2021, Transactions in GIS)

   Abstract The max‐p‐compact‐regions problem involves the aggregation of a set of small areas into an unknown maximum number (p) of compact, homogeneous, and spatially contiguous regions such that a regional attribute value is higher than a predefined threshold. The max‐p‐compact‐regions problem is an extension of the max‐p‐regions problem accounting for compactness. The max‐p‐regions model has been widely used to define study regions in many application cases since it allows users to specify criteria and then to identify a regionalization scheme. However, the max‐p‐regions model does not consider compactness even though compactness is usually a desirable goal in regionalization, implying ideal accessibility and apparent homogeneity. This article discusses how to integrate a compactness measure into the max‐pregionalization process by constructing a multiobjective optimization model that maximizes the number of regions while optimizing the compactness of identified regions. An efficient heuristic algorithm is developed to address the computational intensity of the max‐p‐compact‐regions problem so that it can be applied to large‐scale practical regionalization problems. This new algorithm will be implemented in the open‐source Python Spatial Analysis Library. One hypothetical and one practical application of the max‐p‐compact‐regions problem are introduced to demonstrate the effectiveness and efficiency of the proposed algorithm. 

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2. Infinite energy harmonic maps from quasi-compact Kähler surfaces

   https://doi.org/10.1515/ans-2023-0122  

   Daskalopoulos, Georgios; Mese, Chikako (February 2024, Advanced Nonlinear Studies)

   Abstract We construct infinite energy harmonic maps from a quasi-compact Kähler surface with a Poincaré-type metric into an NPC space. This is the first step in the construction of pluriharmonic maps from quasiprojective varieties into symmetric spaces of non-compact type, Euclidean and hyperbolic buildings and Teichmüller space. 

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3. Black hole feeding and feedback in a compact galaxy

   https://doi.org/10.1093/mnras/stad1529  

   Di, Yihuan; Li, Yuan; Yuan, Feng; Shi, Fangzheng; Caradonna, Mirielle (May 2023, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT We perform high-resolution hydrodynamical simulations using the framework of MACER to investigate supermassive black hole (SMBH) feeding and feedback in a massive compact galaxy, which has a small effective radius but a large stellar mass, with a simulation duration of 10 Gyr. We compare the results with a reference galaxy with a similar stellar mass but a less concentrated stellar density distribution, as typically found in local elliptical galaxies. We find that about 10 per cent of the time, the compact galaxy develops multiphase gas within a few kpc, but the accretion flow through the inner boundary below the Bondi radius is always a single phase. The inflow rate in the compact galaxy is several times larger than in the reference galaxy, mainly due to the higher gas density caused by the more compact stellar distribution. Such a higher inflow rate results in stronger SMBH feeding and feedback and a larger fountain-like inflow-outflow structure. Compared to the reference galaxy, the star formation rate in the compact galaxy is roughly two orders of magnitude higher but is still low enough to be considered quiescent. Over the whole evolution period, the black hole mass grows by ∼50 per cent in the compact galaxy, much larger than the value of ∼ 3 per cent in the reference galaxy. 

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4. On finite time Type I singularities of the Kähler–Ricci flow on compact Kähler surfaces

   https://doi.org/10.4171/JEMS/1485  

   Cifarelli, Charles; Conlon, Ronan J.; Deruelle, Alix (July 2024, Journal of the European Mathematical Society)

   We show that the underlying complex manifold of a complete non-compact two-dimensional shrinking gradient Kähler-Ricci soliton (M,g,X) with soliton metric g with bounded scalar curvature Rg whose soliton vector field X has an integral curve along which Rg↛0 is biholomorphic to either C×P1 or to the blowup of this manifold at one point. Assuming the existence of such a soliton on this latter manifold, we show that it is toric and unique. We also identify the corresponding soliton vector field. Given these possibilities, we then prove a strong form of the Feldman-Ilmanen-Knopf conjecture for finite time Type I singularities of the Kähler-Ricci flow on compact Kähler surfaces, leading to a classification of the bubbles of such singularities in this dimension. 

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5. Enhanced mRNA FISH with compact quantum dots

   https://doi.org/10.1038/s41467-018-06740-x  

   Liu, Yang; Le, Phuong; Lim, Sung Jun; Ma, Liang; Sarkar, Suresh; Han, Zhiyuan; Murphy, Stephen J.; Kosari, Farhad; Vasmatzis, George; Cheville, John C.; et al (October 2018, Nature Communications)

   Abstract Fluorescence in situ hybridization (FISH) is the primary technology used to image and count mRNA in single cells, but applications of the technique are limited by photophysical shortcomings of organic dyes. Inorganic quantum dots (QDs) can overcome these problems but years of development have not yielded viable QD-FISH probes. Here we report that macromolecular size thresholds limit mRNA labeling in cells, and that a new generation of compact QDs produces accurate mRNA counts. Compared with dyes, compact QD probes provide exceptional photostability and more robust transcript quantification due to enhanced brightness. New spectrally engineered QDs also allow quantification of multiple distinct mRNA transcripts at the single-molecule level in individual cells. We expect that QD-FISH will particularly benefit high-resolution gene expression studies in three dimensional biological specimens for which quantification and multiplexing are major challenges. 

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