Positive Definite Solutions of the Nonlinear Matrix Equation X+AHXˉ−1A=IX+A^{\mathrm{H}}\bar{X}^{-1}A=I

This paper is concerned with the positive definite solutions to the matrix equation $X+A^{\mathrm{H}}\bar{X}^{-1}A=I$ where $X$ is the unknown and $A$ is a given complex matrix. By introducing and studying a matrix operator on complex matrices, it is shown that the existence of positive definite solutions of this class of nonlinear matrix equations is equivalent to the existence of positive definite solutions of the nonlinear matrix equation $W+B^{\mathrm{T}}W^{-1}B=I$ which has been extensively studied in the literature, where $B$ is a real matrix and is uniquely determined by $A.$ It is also shown that if the considered nonlinear matrix equation has a positive definite solution, then it has the maximal and minimal solutions. Bounds of the positive definite solutions are also established in terms of matrix $A$. Finally some sufficient conditions and necessary conditions for the existence of positive definite solutions of the equations are also proposed

Optimal Pole Assignment of Linear Systems by the Sylvester Matrix Equations

The problem of state feedback optimal pole assignment is to design a feedback gain such that the closed-loop system has desired eigenvalues and such that certain quadratic performance index is minimized. Optimal pole assignment controller can guarantee both good dynamic response and well robustness properties of the closed-loop system. With the help of a class of linear matrix equations, necessary and sufficient conditions for the existence of a solution to the optimal pole assignment problem are proposed in this paper. By properly choosing the free parameters in the parametric solutions to this class of linear matrix equations, complete solutions to the optimal pole assignment problem can be obtained. A numerical example is used to illustrate the effectiveness of the proposed approach

GGPPS1 predicts the biological character of hepatocellular carcinoma in patients with cirrhosis

Background: Hepatocellular carcinoma (HCC) has been associated with diabetes and obesity, but a possible connection with the metabolic syndrome (MetS) and its potential interaction with hepatitis and cirrhosis are open to discussion. Our previous investigations have shown that GGPPS1 plays a critical role during hyperinsulinism. In this report, the expression and distribution of GGPPS1 in liver cancer, and its clinical significance were investigated. Methods: 70 patients with hepatocellular carcinoma (HCC) were included in this study. Three different types of tissues from each HCC patient were assembled immediately after surgical resection: tumor-free tissue >5 cm far from tumor edge (TF), adjacent nonmalignant tissue within 2 cm (AT), and tissue from the tumor (TT). Normal liver tissues from 10 liver transplant donors served as healthy control (HC) while 10 patients with liver cirrhosis as cirrhosis control (CC). The expression and distribution of GGPPS1 were detected by immunohistochemistry, western blots, or real-time PCR. The relationship between the expression of GGPPS1 and clinic pathologic index were analyzed. Results: We found that GGPPS1 was intensified mainly in the cytoplasm of liver tumor cells. Both the expression of GGPPS1 mRNA and protein were upregulated in TT comparing to AT or TF. Meanwhile, HCC patients with cirrhosis had relative higher expression of GGPPS1. In addition, many pathologic characters show close correlation with GGPPS1, such as tumor stage, vessel invasion, and early recurrence. Conclusion: GGPPS1 may play a critical role during the development of HCC from cirrhosis and is of clinical significance for predicting biological character of HCC

Hamiltonian type Lie bialgebras

We first prove that, for any generalized Hamiltonian type Lie algebra $L$, the first cohomology group $H^1(L,L \otimes L)$ is trivial. We then show that all Lie bialgebra structures on $L$ are triangular.Comment: LaTeX, 16 page

Identification of optimum scopes of environmental factors for snails using spatial analysis techniques in Dongting Lake Region, China

BACKGROUND: Owing to the harmfulness and seriousness of Schistosomiasis japonica in China, the control and prevention of S. japonica transmission are imperative. As the unique intermediate host of this disease, Oncomelania hupensis plays an important role in the transmission. It has been reported that the snail population in Qiangliang Lake district, Dongting Lake Region has been naturally declining and is slowly becoming extinct. Considering the changes of environmental factors that may cause this phenomenon, we try to explore the relationship between circumstance elements and snails, and then search for the possible optimum scopes of environmental factors for snails. METHODS: Moisture content of soil, pH, temperature of soil and elevation were collected by corresponding apparatus in the study sites. The LISA statistic and GWR model were used to analyze the association between factors and mean snail density, and the values in high-high clustered areas and low-low clustered areas were extracted to find out the possible optimum ranges of these elements for snails. RESULTS: A total of 8,589 snail specimens were collected from 397 sampling sites in the study field. Besides the mean snail density, three environmental factors including water content, pH and temperature had high spatial autocorrelation. The spatial clustering suggested that the possible optimum scopes of moisture content, pH, temperature of the soil and elevation were 58.70 to 68.93%, 6.80 to 7.80, 22.73 to 24.23°C and 23.50 to 25.97 m, respectively. Moreover, the GWR model showed that the possible optimum ranges of these four factors were 36.58 to 61.08%, 6.541 to 6.89, 24.30 to 25.70°C and 23.50 to 29.44 m, respectively. CONCLUSION: The results indicated the association between snails and environmental factors was not linear but U-shaped. Considering the results of two analysis methods, the possible optimum scopes of moisture content, pH, temperature of the soil and elevation were 58.70% to 68.93%, 6.6 to 7.0, 22.73°C to 24.23°C, and 23.5 m to 26.0 m, respectively. The findings in this research will help in making an effective strategy to control snails and provide a method to analyze other factors

Temporal transcriptomic changes in long non-coding RNAs and messenger RNAs involved in the host immune and metabolic response during Toxoplasma gondii lytic cycle

Background: Long non-coding RNAs (lncRNAs) are important regulators of various biological and pathological processes, in particular the inflammatory response by modulating the transcriptional control of inflammatory genes. However, the role of lncRNAs in regulating the immune and inflammatory responses during infection with the protozoan parasite Toxoplasma gondii remains largely unknown. Methods: We performed a longitudinal RNA sequencing analysis of human foreskin fibroblast (HFF) cells infected by T. gondii to identify differentially expressed long non-coding RNAs (lncRNAs) and messenger RNAs (mRNAs), and dysregulated pathways over the course of T. gondii lytic cycle. The transcriptome data were validated by qRT-PCR. Results: RNA sequencing revealed significant transcriptional changes in the infected HFFs. A total of 697, 1234, 1499, 873, 1466, 561, 676 and 716 differentially expressed lncRNAs (DElncRNAs), and 636, 1266, 1843, 2303, 3022, 1757, 3088 and 2531 differentially expressed mRNAs (DEmRNAs) were identified at 1.5, 3, 6, 9, 12, 24, 36 and 48h post-infection, respectively. Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment analysis of DElncRNAs and DEmRNAs revealed that T. gondii infection altered the expression of genes involved in the regulation of host immune response (e.g., cytokine–cytokine receptor interaction), receptor signaling (e.g., NOD-like receptor signaling pathway), disease (e.g., Alzheimer's disease), and metabolism (e.g., fatty acid degradation). Conclusions: These results provide novel information for further research on the role of lncRNAs in immune regulation of T. gondii infection. Graphical Abstract: [Figure not available: see fulltext.

A simulation study on the measurement of D0-D0bar mixing parameter y at BES-III

We established a method on measuring the \dzdzb mixing parameter $y$ for BESIII experiment at the BEPCII $e^+e^-$ collider. In this method, the doubly tagged $\psi(3770) \to D^0 \overline{D^0}$ events, with one $D$ decays to CP-eigenstates and the other $D$ decays semileptonically, are used to reconstruct the signals. Since this analysis requires good $e/\pi$ separation, a likelihood approach, which combines the $dE/dx$, time of flight and the electromagnetic shower detectors information, is used for particle identification. We estimate the sensitivity of the measurement of $y$ to be 0.007 based on a $20fb^{-1}$ fully simulated MC sample.Comment: 6 pages, 7 figure

Classification of gluteal muscle contracture in children and outcome of different treatments

<p>Abstract</p> <p>Background</p> <p>Gluteal muscle contracture (GMC) is a clinical syndrome due to multiple etiologies in which hip movements may be severely limited. The aim of this study was to propose a detailed classification of GMC and evaluate the statistical association between outcomes of different management and patient conditions.</p> <p>Methods</p> <p>One hundred fifty-eight patients, who were treated between January 1995 and December 2004, were reviewed at a mean duration of follow-up of 4.8 years. Statistical analyses were performed using X²and Fisher's exact tests.</p> <p>Results</p> <p>Non-operative management (NOM), as a primary treatment, was effective in 19 of 49 patients (38.8%), while operative management was effective in all 129 patients, with an excellence rating of 83.7% (108/129). The outcome of NOM in level I patients was significantly higher than in level II and III patients (<it>P </it>< 0.05). The results of NOM and operative management in the child group were better than the adolescent group (<it>P </it>< 0.05). Complications in level III were more than in level II.</p> <p>Conclusion</p> <p>NOM was more effective in level I patients than in level II and III patients. Operative management was effective in patients at all levels, with no statistical differences between levels or types. We recommend NOM as primary treatment for level I patients and operative management for level II and III patients. Either NOM or operative management should be carried out as early as possible.</p