Random homogenization of coercive Hamilton-Jacobi equations in 1d

In this paper, we will prove the random homogenization of general coercive non-convex Hamilton-Jacobi equations in one dimensional case. This extends the result of Armstrong, Tran and Yu when the Hamiltonian has a separable form $H(p,x,\omega)=H(p)+V(x,\omega)$ for any coercive $H(p)$

Small-Deviation Inequalities for Sums of Random Matrices

Random matrices have played an important role in many fields including machine learning, quantum information theory and optimization. One of the main research focuses is on the deviation inequalities for eigenvalues of random matrices. Although there are intensive studies on the large-deviation inequalities for random matrices, only a few of works discuss the small-deviation behavior of random matrices. In this paper, we present the small-deviation inequalities for the largest eigenvalues of sums of random matrices. Since the resulting inequalities are independent of the matrix dimension, they are applicable to the high-dimensional and even the infinite-dimensional cases

New insights for C5a and C5a receptors in sepsis

The complement system plays a central role in inflammation and immunity. Among the complement activation products, C5a is one of the most potent inflammatory peptides with a broad spectrum of functions. There is strong evidence for complement activation including elevated plasma level of C5a in humans and animals with sepsis. C5a exerts its effects through the C5a receptors. Of the two receptors that bind C5a, the C5aR (CD88) is known to mediate signaling activity, whereas the function of another C5a binding receptor, C5L2, remains largely unknown. Here, we review the critical role of C5a in sepsis and summarize evidence indicating that both C5aR and C5L2 act as regulating receptors for C5a during sepsis

Multidimensional Time Series Fuzzy Association Rules Mining

In this paper, we present a new solution, in which the fuzziness of both subsequences and subsequences interval has been taken into consideration for solving the problem of multidimensional time series fuzzy association rules mining. Aimed at dealing with the new conception, this paper has put forward some key algorithms of the solution. Finally, an application example of multidimensional time series fuzzy association rules mining is illustrated. The result shows that rules with fuzzy interval can only be mined out by the above-mentioned new method