With sharp increasing in biological sequences, the traditional sequence alignment methods become unsuitable and infeasible. It motivates a surge of fast alignment-free techniques for sequence analysis. Among these methods, many sorts of feature vector methods are established and applied to reconstruction of species phylogeny. The vectors basically consist of some typical numerical features for certain biological problems. The features may come from the primary sequences, secondary or three dimensional structures of macromolecules. In this study, we propose a novel numerical vector based on only primary sequences of organism to build their phylogeny. Three chemical and physical properties of primary sequences: purine, pyrimidine and keto are also incorporated to the vector. Using each property, we convert the nucleotide sequence into a new sequence consisting of only two kinds of letters. Therefore, three sequences are constructed according to the three properties. For each letter of each sequence we calculate the number of the letter, the average position of the letter and the variation of the position of the letter appearing in the sequence. Tested on several datasets related to mammals, viruses and bacteria, this new tool is fast in speed and accurate for inferring the phylogeny of organisms.

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We investigate local properties of the Green function of the complement of a compact set$E$υ[0,1] with respect to the extended complex plane. We demonstrate, that if the Green function satisfies the 1/2-Hölder condition locally at the origin, then the density of$E$at 0, in terms of logarithmic capacity, is the same as that of the whole interval [0, 1]..

The cosmological observations provide a strong evidence that there is a positive cosmological constant in our universe and thus the spacetime is asymptotical de Sitter space. The conjecture of gravity as the weakest force in the asymptotical dS space leads to a lower bound on the U(1) gauge coupling $g$, or equivalently, the positive cosmological constant gets an upper bound $\rho_V \leq g^2 M_p^4$ in order that the U(1) gauge theory can survive in four dimensions. This result has a simple explanation in string theory, i.e. the string scale $\sqrt{\alpha '}$ should not be greater than the size of the cosmic horizon. Our proposal in string theory can be generalized to U(N) gauge theory and gives a guideline to the microscopic explanation of the de Sitter entropy. The similar results are also obtained in the asymptotical anti-de Sitter space.

Rapid and reliable detection and identification of unknown chemical substances are critical to homeland security. It is challenging to identify chemical components from a wide range of explosives. There are two key steps involved. One is a non-destructive and informative spectroscopic technique for data acquisition. The other is an associated library of reference features along with a computational method for feature matching and meaningful detection within or beyond the library.