Parametric CR-umbilical Locus of Ellipsoids in C2\mathbb{C}^2

For every real numbers $a \geqslant 1$, $b \geqslant 1$ with $(a,b) \neq (1,1)$, the curve parametrized by $\theta \in \mathbb{R}$ valued in $\mathbb{C}^2 \cong \mathbb{R}^4$ $$\gamma\, \colon \ \ \ \theta \,\,\,\longmapsto\,\,\, \big( x(\theta)+{\scriptstyle{\sqrt{-1}}}\,y(\theta),\,\, u(\theta)+{\scriptstyle{\sqrt{-1}}}\,v(\theta) \big)$$ with components: $$x(\theta) \,:=\, {\textstyle{\sqrt{\frac{a-1}{a\,(ab-1)}}}}\, \cos\,\theta, \ \ \ \ \ y(\theta) \,:=\, {\textstyle{\sqrt{\frac{b\,(a-1)}{ab-1}}}}\, \sin\,\theta, \ \ \ \ \ u(\theta) \,:=\, {\textstyle{\sqrt{\frac{b-1}{b\,(ab-1)}}}}\, \sin\,\theta, \ \ \ \ \ v(\theta) \,:=\, -\, {\textstyle{\sqrt{\frac{a\,(b-1)}{ab-1}}}}\, \cos\,\theta,$$ has image contained in the CR-umbilical locus: $$\gamma(\mathbb{R}) \,\subset\, {\sf UmbCR} \big({\sf E}_{a,b}\big) \,\subset\, {\sf E}_{a,b}$$ of the ellipsoid ${\sf E}_{a,b} \subset \mathbb{C}^2$ of equation $a\,x^2+y^2+b\,u^2+y^2 = 1$

Improving Heterogeneous Graph Learning with Weighted Mixed-Curvature Product Manifold

In graph representation learning, it is important that the complex geometric structure of the input graph, e.g. hidden relations among nodes, is well captured in embedding space. However, standard Euclidean embedding spaces have a limited capacity in representing graphs of varying structures. A promising candidate for the faithful embedding of data with varying structure is product manifolds of component spaces of different geometries (spherical, hyperbolic, or euclidean). In this paper, we take a closer look at the structure of product manifold embedding spaces and argue that each component space in a product contributes differently to expressing structures in the input graph, hence should be weighted accordingly. This is different from previous works which consider the roles of different components equally. We then propose WEIGHTED-PM, a data-driven method for learning embedding of heterogeneous graphs in weighted product manifolds. Our method utilizes the topological information of the input graph to automatically determine the weight of each component in product spaces. Extensive experiments on synthetic and real-world graph datasets demonstrate that WEIGHTED-PM is capable of learning better graph representations with lower geometric distortion from input data, and performs better on multiple downstream tasks, such as word similarity learning, top-$k$ recommendation, and knowledge graph embedding

A Cosine Similarity-based Method for Out-of-Distribution Detection

The ability to detect OOD data is a crucial aspect of practical machine learning applications. In this work, we show that cosine similarity between the test feature and the typical ID feature is a good indicator of OOD data. We propose Class Typical Matching (CTM), a post hoc OOD detection algorithm that uses a cosine similarity scoring function. Extensive experiments on multiple benchmarks show that CTM outperforms existing post hoc OOD detection methods.Comment: Accepted paper at ICML 2023 Workshop on Spurious Correlations, Invariance, and Stability. 10 pages (4 main + appendix

Serum interleukin 6 concentration in patients with pemphigus

Pemphigus is a rare autoimmune blistering disease that detrimentally affects the integumentary system and decreases patients’ quality of life. Recent studies have shown that interleukin 6 (IL-6) is closedly involved in the immunophathogenesis of pemphigus. Therefore, this study was performed to evaluate the role of IL-6 in the pathogenesis and severity of pemphigus disease. The case-series study was conducted in Ho Chi Minh City Hospital of Dermato-Venereology from January 2022 to August 2022, involving 26 patients with pemphigus vulgaris (PV), 4 patients with pemphigus foliaceus (PF), and 20 healthy volunteers. The serum IL-6 concentrations of patients with PV and PF were significantly higher than those of the healthy volunteers (P < 0.001). Serum IL-6 concentrations were significantly higher in patients with a positive than a negative Nikolsky sign (P < 0.001). A significant correlation was found between the serum IL-6 concentration and the pemphigus disease area index (r = 0.8, P < 0.001). Our results suggest that IL-6 may play an important role in the pathogenesis and severity of pemphigus. Therefore, new therapies targeting IL-6 may be a promising choice for treating pemphigus, especially in its severe forms

Influence of ASE Noise on Performance of DWDM Networks Using Low-power Pumped Raman Amplifiers

We present the results of investigation  for  influence of amplified spontaneous emission (ASE) noise, noise figure (NF) and  chromatic dispersion on the performance of middle-distance Dense-wavelength-division-multiplexing (DWDM) networks using low-power pumped distributed Raman amplifiers (DRAs) in two different pump configurations, i.e., forward and backward pumping. We found that the pumping configurations, ASE noise, and dispersion play an important role for improving network performance by decrease of noise figure and bit error rate (BER) of the system. Simulation results show that the lowest bit error rate and low noise figure were obtained, when using forward pumping configuration. Moreover, we have also compared ASE noise powers of the simulation with these of the experiment. These results conclude that DRA with low pump power  ($1$~W) is the promising key technology for short-- and/or middle-distance DWDM transmission networks

A novel IGHMBP2 variant and clinical diversity in Vietnamese SMARD1 and CMT2S patients

BackgroundPathogenic variants in the IGHMBP2 gene are associated with two distinct autosomal recessive neuromuscular disorders: spinal muscular atrophy with respiratory distress type 1 (SMARD1; OMIM #604320) and Charcot–Marie–Tooth type 2S (CMT2S; OMIM #616155). SMARD1 is a severe and fatal condition characterized by infantile-onset respiratory distress, diaphragmatic palsy, and distal muscular weakness, while CMT2S follows a milder clinical course, with slowly progressive distal muscle weakness and sensory loss, without manifestations of respiratory disorder.MethodsWhole-exome sequencing of the IGHMBP2 gene was performed for eight Vietnamese patients with IGHMBP2-related neuromuscular disorders including five patients with SMARD1 and the others with CMT2S.ResultsWe identified one novel IGHMBP2 variant c.1574T &gt; C (p.Leu525Pro) in a SMARD1 patient. Besides that, two patients shared the same pathogenic variants (c.1235 + 3A &gt; G/c.1334A &gt; C) but presented completely different clinical courses: one with SMARD1 who deceased at 8 months of age, the other with CMT2S was alive at 3 years old without any respiratory distress.ConclusionThis study is the first to report IGHMBP-2-related neuromuscular disorders in Vietnam. A novel IGHMBP2 variant c.1574T &gt; C (p.Leu525Pro) expressing SMARD1 phenotype was detected. The presence of three patients with the same genotype but distinct clinical outcomes suggested the interaction of variants and other factors including relating modified genes in the mechanism of various phenotypes

Policy volatility and growth

The paper aims to examine how fiscal and monetary volatility might affect the balanced economic growth rate using a standard monetary growth model characterized by nominal wage rigidity and productive public spending. The model shows that any type of shock — monetary or fiscal — can generate either a negative or positive relationship between short-run volatility and long-run growth, critically de- pending on the size of government and the elasticity of output with respect to labor/ capital. In particular, given the labor income share, it shows that excessive government spending may cause the impact of fiscal volatility on long-run growth to turn from positive to negative. In addition, a rise in the volatility of the monetary shock is capable of generating either an increase or decrease in the mean of growth. With the range of the labor share values in reality, the model produces results consistent with the fact that the relationship between volatility and growth is generally found empirically to be more negative in developing than in developed countries. The model can be seen as a further explanation for the ambiguous empirical evidence in the existing literature.info:eu-repo/semantics/publishedVersio