Analytical Solutions of Singular Isothermal Quadrupole Lens

Using analytical method, we study the Singular Isothermal Quadrupole (SIQ) lens system, which is the simplest lens model that can produce four images. In this case, the radial mass distribution is in accord with the profile of the Singular Isothermal Sphere (SIS) lens, and the tangential distribution is given by adding a quadrupole on the monopole component. The basic properties of the SIQ lens have been studied in this paper, including deflection potential, deflection angle, magnification, critical curve, caustic, pseudo-caustic and transition locus. Analytical solutions of the image positions and magnifications for the source on axes are derived. As have been found, naked cusps will appear when the relative intensity $k$ of quadrupole to monopole is larger than 0.6. According to the magnification invariant theory of the SIQ lens, the sum of the signed magnifications of the four images should be equal to unity \citep{dal98}. However, if a source lies in the naked cusp, the summed magnification of the left three images is smaller than the invariant 1. With this simple lens system, we study the situations that a point source infinitely approaches a cusp or a fold. The sum of magnifications of cusp image triplet is usually not equal to 0, and it is usually positive for major cusp while negative for minor cusp. Similarly, the sum of magnifications of fold image pair is usually neither equal to 0. Nevertheless, the cusp and fold relations are still equal to 0, in that the sum values are divided by infinite absolute magnifications by definition.Comment: 12 pages, 2 figures, accepted for publication in ApJ

Searching for a preferred direction with Union2.1 data

A cosmological preferred direction was reported from the type Ia supernovae (SNe Ia) data in recent years. We use the Union2.1 data to give a simple classification of such studies for the first time. Because the maximum anisotropic direction is independent of isotropic dark energy models, we adopt two cosmological models ($\Lambda$CDM, $w$CDM) for the hemisphere comparison analysis and $\Lambda$CDM model for dipole fit approach. In hemisphere comparison method, the matter density and the equation of state of dark energy are adopted as the diagnostic qualities in the $\Lambda$CDM model and $w$CDM model, respectively. In dipole fit approach, we fit the fluctuation of distance modulus. We find that there is a null signal for the hemisphere comparison method, while a preferred direction ($b=-14.3^\circ \pm 10.1^\circ, l=307.1^\circ \pm 16.2^\circ$) for the dipole fit method. This result indicates that the dipole fit is more sensitive than the hemisphere comparison method.Comment: 8 pages, 2 figures, accepted for publication in MNRA

On Providing Downlink Services in Collocated Spectrum-Sharing Macro and Femto Networks

Femtocells have been considered by the wireless industry as a cost-effective solution not only to improve indoor service providing, but also to unload traffic from already overburdened macro networks. Due to spectrum availability and network infrastructure considerations, a macro network may have to share spectrum with overlaid femtocells. In spectrum-sharing macro and femto networks, inter-cell interference caused by different transmission powers of macrocell base stations (MBS) and femtocell access points (FAP), in conjunction with potentially densely deployed femtocells, may create dead spots where reliable services cannot be guaranteed to either macro or femto users. In this paper, based on a thorough analysis of downlink (DL) outage probabilities (OP) of collocated spectrum-sharing orthogonal frequency division multiple access (OFDMA) based macro and femto networks, we devise a decentralized strategy for an FAP to self-regulate its transmission power level and usage of radio resources depending on its distance from the closest MBS. Simulation results show that the derived closed-form lower bounds of DL OPs are tight, and the proposed decentralized femtocell self-regulation strategy is able to guarantee reliable DL services in targeted macro and femto service areas while providing superior spatial reuse, for even a large number of spectrum-sharing femtocells deployed per cell site

A nonalcoholic fatty liver disease cirrhosis model in gerbil:the dynamic relationship between hepatic lipid metabolism and cirrhosis

Nonalcoholic fatty liver disease (NAFLD) usually takes decades to develop into cirrhosis, which limits the longitudinal study of NAFLD. This work aims at developing a NAFLD-caused cirrhosis model in gerbil and examining the dynamic relationship between hepatic lipid metabolism and cirrhosis. We fed gerbil a high-fat and high-cholesterol diet (HFHCD) for 24 weeks, and recorded the gerbil's phenotype at 3, 6, 9, 12, 15, 18, 21, 24 weeks. The model's pathological process, lipid metabolism, oxidative stress, liver collagen deposition and presence of relevant cytokines were tested and evaluated during the full-time frame of disease onset. The gerbil model can induce nonalcoholic steatohepatitis (NASH) within 9 weeks, and can develop cirrhosis after 21 weeks induction. The model's lipids metabolism disorder is accompanied with the liver damage development. During the NAFLD progression, triglycerides (TG) and free fatty acids (FFA) have presented distinct rise and fall tendency, and the turning points are at the fibrosis stage. Besides that, the ratios of total cholesterol (CHO) to high-density lipoprotein cholesterol (HDL-C) exhibited constant growth tendency, and have a good linear relationship with hepatic stellate cells (HSC) (R-2 = 0.802, P <0.001). The gerbil NAFLD cirrhosis model has been developed and possesses positive correlation between lipids metabolism and cirrhosis. The compelling rise and fall tendency of TG and FFA indicated that the fibrosis progression can lead to impairment in lipoprotein synthesis and engender decreased TG level. CHO/HDL-C ratios can imply the fibrosis progress and be used as a blood indicator for disease prediction and prevention

Superoxide dismutase alterations in COVID-19: implications for disease severity and mortality prediction in the context of omicron variant infection

BackgroundIn the few reports to date, the changes in superoxide dismutase (SOD), a key factor in cellular protection against superoxide, in COVID-19 have been very inconsistent and contradictory. There is also a lack of data on COVID-19 induced by Omicron variant. Further investigation is warranted to figure out SOD alterations in COVID-19, particularly within the context of ongoing Omicron variant infection, which may provide clues to its role within COVID-19 pathogenesis and open up new avenues for COVID-19 treatment.MethodsSOD activity in 109 COVID-19 patients (including 46 severe cases and 63 mild to moderate cases) and 30 matched healthy controls were quantified. Demographic data, blood cell counts, biochemical indicators, coagulation indicators, and inflammatory markers were also recorded.ResultsSOD, an important key node, experienced a significant decrease in COVID-19, with the severe patients exhibiting lower activity compared to the mild to moderate patients and control healthy. Notably, severe patients who deceased had the lowest SOD activity. Correlation analysis revealed significant correlations between SOD and inflammatory markers, organ injury markers, coagulation dysfunction indicators, nutritional markers, and lymphocytes counts. The ROC curve also showed good performance for the differentiation of severe cases and the prediction of death.ConclusionSOD activity was significantly decreased in COVID-19 infected with Omicron variant and significantly correlated with systemic changes, and could be used as a biomarker to assess disease severity and predict mortality in COVID-19 clinical pathway management. Additionally, this finding will contribute to exploring new potential direction for the treatment of severe COVID-19 patients