Distance k-Sectors Exist

The bisector of two nonempty sets P and Q in a metric space is the set of all points with equal distance to P and to Q. A distance k-sector of P and Q, where k is an integer, is a (k-1)-tuple (C_1, C_2, ..., C_{k-1}) such that C_i is the bisector of C_{i-1} and C_{i+1} for every i = 1, 2, ..., k-1, where C_0 = P and C_k = Q. This notion, for the case where P and Q are points in Euclidean plane, was introduced by Asano, Matousek, and Tokuyama, motivated by a question of Murata in VLSI design. They established the existence and uniqueness of the distance trisector in this special case. We prove the existence of a distance k-sector for all k and for every two disjoint, nonempty, closed sets P and Q in Euclidean spaces of any (finite) dimension, or more generally, in proper geodesic spaces (uniqueness remains open). The core of the proof is a new notion of k-gradation for P and Q, whose existence (even in an arbitrary metric space) is proved using the Knaster-Tarski fixed point theorem, by a method introduced by Reem and Reich for a slightly different purpose.Comment: 10 pages, 5 figure

Zone Diagrams in Euclidean Spaces and in Other Normed Spaces

Zone diagram is a variation on the classical concept of a Voronoi diagram. Given n sites in a metric space that compete for territory, the zone diagram is an equilibrium state in the competition. Formally it is defined as a fixed point of a certain "dominance" map. Asano, Matousek, and Tokuyama proved the existence and uniqueness of a zone diagram for point sites in Euclidean plane, and Reem and Reich showed existence for two arbitrary sites in an arbitrary metric space. We establish existence and uniqueness for n disjoint compact sites in a Euclidean space of arbitrary (finite) dimension, and more generally, in a finite-dimensional normed space with a smooth and rotund norm. The proof is considerably simpler than that of Asano et al. We also provide an example of non-uniqueness for a norm that is rotund but not smooth. Finally, we prove existence and uniqueness for two point sites in the plane with a smooth (but not necessarily rotund) norm.Comment: Title page + 16 pages, 20 figure

Laminin γ2 fragments are increased in the circulation of patients with early phase acute lung injury

Katayama, M., Ishizaka, A., Sakamoto, M. et al. Intensive Care Med (2010) 36: 479. https://doi.org/10.1007/s00134-009-1719-

Role of Prostaglandin D2 and Its Receptors in the Pathophysiology of Asthma

Prostaglandin D2 (PGD2) is one of the most abundant lipid mediators present in the airways of asthmatics. However, little was known of the role it plays in the pathophysiology of asthma, until the identification of DP (DP1, PTGDR) and CRTH2 (DP2), two PGD2-specific transmembrane receptors with different distribution and intracellular signaling. Pharmacological tools, such as receptor-specific agonists and antagonists, and genetically-engineered mice, which lack either DP or CRTH2, have helped understand the complex effects of PGD2 in allergic inflammation of the airways. Furthermore, genetic association studies have shown a positive linkage of the genetic polymorphisms in DP and CRTH2, with asthma phenotypes from specific ethnic backgrounds, further highlighting the importance of PGD2 and its receptors in the pathophysiology of asthma

Development and Psychometric Evaluation of a Japanese Version of Newly Graduated Nurses’ Difficulties with End-of-Life Care for Cancer Patients (NDEC Scale)

(1) Background: End-of-life care (EoL care) for cancer patients is stressful for nurses and can easily lead to burnout. Newly graduated nurses (NGNs) have a particularly difficult time, but no scale or inventory has been designed to evaluate their difficulties. This study developed and tested the reliability and validity of a scale to measure NGNs’ difficulties with EoL care for cancer patients (NDEC scale). (2) Methods: This study population consisted of 1000 NGNs and 1000 nurses with at least five years of clinical experience (GNs) that were working in hospitals in Japan. The initial scale consisted of six factors and 28 items. The reliability and validity of the scale were tested. (3) Results: A total of 171 NGNs and 194 GNs responded to the survey. The scale consisted of five factors and 25 items with the factors including “Feeling painful”, “Can’t deal with patients and their families”, “Don’t know the answer”, “Cannot afford”, and “Being afraid of death”. The criteria validity, known population validity, and internal consistency were confirmed. (4) Conclusions: The scale was validated to have a certain level of reliability and validity. The NDEC scale is expected to be used for self-care for NGNs and as an effectiveness indicator for educational programs

Crystallization behavior of the Li2S–P2S5 glass electrolyte in the LiNi1/3Mn1/3Co1/3O2 positive electrode layer

Abstract Sulfide-based all-solid-state lithium batteries are a next-generation power source composed of the inorganic solid electrolytes which are incombustible and have high ionic conductivity. Positive electrode composites comprising LiNi1/3Mn1/3Co1/3O2 (NMC) and 75Li2S·25P2S5 (LPS) glass electrolytes exhibit excellent charge–discharge cycle performance and are promising candidates for realizing all-solid-state batteries. The thermal stabilities of NMC–LPS composites have been investigated by transmission electron microscopy (TEM), which indicated that an exothermal reaction could be attributed to the crystallization of the LPS glass. To further understand the origin of the exothermic reaction, in this study, the precipitated crystalline phase of LPS glass in the NMC–LPS composite was examined. In situ TEM observations revealed that the β-Li3PS4 precipitated at approximately 200 °C, and then Li4P2S6 and Li2S precipitated at approximately 400 °C. Because the Li4P2S6 and Li2S crystalline phases do not precipitate in the single LPS glass, the interfacial contact between LPS and NMC has a significant influence on both the LPS crystallization behavior and the exothermal reaction in the NMC–LPS composites

Reduced gray matter volume in the default-mode network associated with insulin resistance

<p>Insulin resistance may lead to structural and functional abnormalities of the human brain. However, the mechanism by which insulin resistance impairs the brain remains elusive. In this study, we used two large neuroimaging databases to investigate the brain regions where insulin resistance was associated with the gray matter volume and to examine the resting-state functional connectivity between these brain regions and each hypothalamic nucleus. Insulin resistance was associated with reduced gray matter volume in the regions of the default-mode and limbic networks in the cerebral cortex in older adults. Resting-state functional connectivity was prominent between these networks and the paraventricular nucleus of the hypothalamus, a hypothalamic interface connecting functionally with the cerebral cortex. Furthermore, we found a significant correlation in these networks between insulin resistance-related gray matter volume reduction and network paraventricular nucleus of the hypothalamus resting-state functional connectivity. These results suggest that insulin resistance-related gray matter volume reduction in the default-mode and limbic networks emerged through metabolic homeostasis mechanisms in the hypothalamus.</p><p>Funding provided by: Japan Society for the Promotion of Science<br>Crossref Funder Registry ID: https://ror.org/00hhkn466<br>Award Number: JP22K07334</p><p>Funding provided by: Japan Society for the Promotion of Science<br>Crossref Funder Registry ID: https://ror.org/00hhkn466<br>Award Number: JP21K07255</p><p>Funding provided by: Japan Society for the Promotion of Science<br>Crossref Funder Registry ID: https://ror.org/00hhkn466<br>Award Number: JP23H02783</p><p>Data from the Bunkyo Health Study, which aimed to prevent diseases requiring long-term care in older people, was used in the present study. Of 1629 participants in the database, insulin-dependent T2DM patients were excluded, and then the data of 1609 without any missing data were analyzed. We analyzed the gray matter volumes using a VBM software implemented in SPM12 and insulin resistance (HOMA-IR) was calculated using fasting blood sampling data.</p> <p>We also analyzed the functional connectivity between the HOMA-IR-related cerebral region and the hypothalamic nuclei. For this analysis, we used the data of resting-state functional images of HCP (N = 418).</p&gt

Laminin gamma2 fragments are increased in the circulation of patients with early phase acute lung injury.

ObjectiveLaminin-5, a cell adhesive molecule expressed solely by epithelium, is known to enhance epithelial cell migration and repair of injured epithelium, after its essential component gamma2-chain is processed proteolytically. Our previous study revealed circulating levels of amino-terminal fragment of laminin gamma2-chain (G2F) reflect epithelial tumor invasiveness in carcinoma patients, but its physiological role in alveolar epithelial injury remains unknown.DesignSampling of epithelial lining fluids or pulmonary edema fluids from patients with acute lung injury (ALI) or related diseases was performed. Plasma samples were obtained from them at the time of disease onset or later. G2F concentrations were determined by immunoassay constructed by ourselves.ResultsWe found a significantly higher amount of G2F in pulmonary edema and epithelial lining fluids of patients with ALI, as compared with those with the other respiratory diseases. Their plasma levels were also elevated significantly early at the onset of ALI (mean +/- SD; 147 +/- 82 ng/ml in non-surviving and 90 +/- 56 in surviving patients) as compared with those in the patients with cardiogenic pulmonary edema (59 +/- 36) or idiopathic pulmonary fibrosis (37 +/- 17), indicating alveolar epithelium rapidly secrete laminin-5 in ALI. At 5 days after onset, non-surviving patients maintained higher plasma concentrations (152 +/- 84), but in contrast, the levels in surviving patients declined (71 +/- 35), suggesting secretion of laminin-5 was suppressed, associated with recovery from ALI.ConclusionCirculating G2F may be a biomarker for alveolar laminin-5 secreted early at disease onset in ALI, potentially regulating alveolar re-epithelialization