Positivity of Partitioned Hermitian Matrices with Unitarily Invariant Norms

We give a short proof of a recent result of Drury on the positivity of a $3\times 3$ matrix of the form $(\|R_i^*R_j\|_{\rm tr})_{1 \le i, j \le 3}$ for any rectangular complex (or real) matrices $R_1, R_2, R_3$ so that the multiplication $R_i^*R_j$ is compatible for all $i, j$, where $\|\cdot\|_{\rm tr}$ denotes the trace norm. We then give a complete analysis of the problem when the trace norm is replaced by other unitarily invariant norms.Comment: 6 page

Eigenvalue continuity and Gersgorin\u27s theorem

Two types of eigenvalue continuity are commonly used in the literature. However, their meanings and the conditions under which continuities are used are not always stated clearly. This can lead to some confusion and needs to be addressed. In this note, the Geršgorin disk theorem is revisited and the issue concerning the proofs of the theorem by continuity is clarified

FAD Mutations in Amyloid Precursor Protein Do Not Directly Perturb Intracellular Calcium Homeostasis

Disturbances in intracellular calcium homeostasis are likely prominent and causative factors leading to neuronal cell death in Alzheimer's disease (AD). Familial AD (FAD) is early-onset and exhibits autosomal dominant inheritance. FAD-linked mutations have been found in the genes encoding the presenilins and amyloid precursor protein (APP). Several studies have shown that mutated presenilin proteins can directly affect calcium release from intracellular stores independently of Aβ production. Although less well established, there is also evidence that APP may directly modulate intracellular calcium homeostasis. Here, we directly examined whether overexpression of FAD-linked APP mutants alters intracellular calcium dynamics. In contrast to previous studies, we found that overexpression of mutant APP has no effects on basal cytosolic calcium, ER calcium store size or agonist-induced calcium release and subsequent entry. Thus, we conclude that mutated APP associated with FAD has no direct effect on intracellular calcium homeostasis independently of Aβ production

Label-Free Proteomics Reveals Decreased Expression of CD18 and AKNA in Peripheral CD4+ T Cells from Patients with Vogt-Koyanagi-Harada Syndrome

Vogt-Koyanagi-Harada (VKH) syndrome is a systemic autoimmune disease. CD4+ T cells have been shown to be involved in autoimmune diseases including VKH syndrome. To screen aberrantly expressed membrane proteins in CD4+ T cell from patients with active VKH syndrome, blood samples were taken from five patients with active VKH syndrome and five healthy individuals. A label-free quantitative proteomic strategy was used to identify the differently expressed proteins between the two groups. The results revealed that the expression of 102 peptides was significantly altered (p<0.05) between two groups and matched amino acid sequences of proteins deposited in the international protein index (ipi.HUMAN.v3.36.fasta). The identified peptides corresponded to 64 proteins, in which 30 showed more than a 1.5-fold difference between the two groups. The decreased expression of CD18 and AKNA transcription factor (AKNA), both being three-fold lower than controls in expression identified by the label-free method, was further confirmed in an additional group of five active VKH patients and six normal individuals using the Western blot technique. A significantly decreased expression of CD18 and AKNA suggests a role for both proteins in the pathogenesis of this syndrome

Graph Learning and Its Applications: A Holistic Survey

Graph learning is a prevalent domain that endeavors to learn the intricate relationships among nodes and the topological structure of graphs. These relationships endow graphs with uniqueness compared to conventional tabular data, as nodes rely on non-Euclidean space and encompass rich information to exploit. Over the years, graph learning has transcended from graph theory to graph data mining. With the advent of representation learning, it has attained remarkable performance in diverse scenarios, including text, image, chemistry, and biology. Owing to its extensive application prospects, graph learning attracts copious attention from the academic community. Despite numerous works proposed to tackle different problems in graph learning, there is a demand to survey previous valuable works. While some researchers have perceived this phenomenon and accomplished impressive surveys on graph learning, they failed to connect related objectives, methods, and applications in a more coherent way. As a result, they did not encompass current ample scenarios and challenging problems due to the rapid expansion of graph learning. Different from previous surveys on graph learning, we provide a holistic review that analyzes current works from the perspective of graph structure, and discusses the latest applications, trends, and challenges in graph learning. Specifically, we commence by proposing a taxonomy from the perspective of the composition of graph data and then summarize the methods employed in graph learning. We then provide a detailed elucidation of mainstream applications. Finally, based on the current trend of techniques, we propose future directions.Comment: 20 pages, 7 figures, 3 table

No Association of PTPN22 Polymorphisms with Susceptibility to Ocular Behcet's Disease in Two Chinese Han Populations

Background: Behcet’s disease is known as a recurrent, multisystem inflammation and immune-related disease. Protein tyrosine phosphatase non-receptor 22 (PTPN22) is a key negative regulator of T lymphocytes and polymorphisms of the PTPN22 gene have been shown to be associated with various immune-related diseases. The present study was performed to assess the association between PTPN22 polymorphisms and Behcet’s disease in two Chinese Han populations. Methodology/Principal Findings: A total of 516 patients with ocular Behcet’s disease and 690 healthy controls from two Chinese Han populations were genotyped by the polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) method for three single nucleotide polymorphisms (SNPs). Hardy-Weinberg equilibrium was tested using the x 2 test. Genotype frequencies were estimated through direct counting. Allele and genotype frequencies were compared between patients and controls using logistic regression analysis. The results revealed that there was no association between the tested three PTPN22 SNPs (rs2488457, rs1310182 and rs3789604) and ocular Behcet’s disease (p.0.05). Categorization analysis according to the clinical features did not show any association of these three polymorphisms with these parameters (p.0.05). Conclusions/Significance: The investigated PTPN22 gene polymorphisms (rs2488457, rs1310182 and rs3789604) were not associated with ocular Behcet’s disease in two Chinese Han populations, and showed that it may be different from othe