On Entropy-Based Molecular Descriptors: Statistical Analysis of Real and Synthetic Chemical Structures

This paper presents an analysis of entropy-based molecular descriptors. Specifically, we use real chemical structures, as well as synthetic isomeric structures, and investigate properties of and among descriptors with respect to the used data set by a statistical analysis. Our numerical results provide evidence that synthetic chemical structures are notably different to real chemical structures and, hence, should not be used to investigate molecular descriptors. Instead, an analysis based on real chemical structures is favorable. Further, we find strong hints that molecular descriptors can be partitioned into distinct classes capturing complementary information.

Structural information content of networks: Graph entropy based on local vertex functionals

In this paper we define the structural information content of graphs as their corresponding graph entropy. This definition is based on local vertex functionals obtained by calculating-spheres via the algorithm of Dijkstra. We prove that the graph entropy and, hence, the local vertex functionals can be computed with polynomial time complexity enabling the application of our measure for large graphs. In this paper we present numerical results for the graph entropy of chemical graphs and discuss resulting properties. (C) 2007 Elsevier Ltd. All rights reserved.

Entanglement entropy dynamics of Heisenberg chains

By means of the time dependent density matrix renormalization group algorithm we study the zero-temperature dynamics of the Von Neumann entropy of a block of spins in a Heisenberg chain after a sudden quench in the anisotropy parameter. In the absence of any disorder the block entropy increases linearly with time and then saturates. We analyse the velocity of propagation of the entanglement as a function of the initial and final anisotropies and compare our results, wherever possible, with those obtained by means of conformal field theory. In the disordered case we find a slower ( logarithmic) evolution which may signal the onset of entanglement localization.

Pan-STARRS1 DISCOVERY OF TWO ULTRALUMINOUS SUPERNOVAE AT(z) approximate to 0.9

We present the discovery of two ultraluminous supernovae (SNe) at z approximate to 0.9 with the Pan-STARRS1 Medium Deep Survey. These SNe, PS1-10ky and PS1-10awh, are among the most luminous SNe ever discovered, comparable to the unusual transients SN 2005ap and SCP 06F6. Like SN 2005ap and SCP 06F6, they show characteristic high luminosities (M-bol approximate to -22.5 mag), blue spectra with a few broad absorption lines, and no evidence for H or He. We have constructed a full multi-color light curve sensitive to the peak of the spectral energy distribution in the rest-frame ultraviolet, and we have obtained time series spectroscopy for these SNe. Given the similarities between the SNe, we combine their light curves to estimate a total radiated energy over the course of explosion of (0.9-1.4) x 10(51) erg. We find photospheric velocities of 12,000-19,000 km s(-1) with no evidence for deceleration measured across similar to 3 rest-frame weeks around light curve peak, consistent with the expansion of an optically thick massive shell of material. We show that, consistent with findings for other ultraluminous SNe in this class, radioactive decay is not sufficient to power PS1-10ky, and we discuss two plausible origins for these events: the initial spin-down of a newborn magnetar in a core-collapse SN, or SN shock breakout from the dense circumstellar wind surrounding a Wolf-Rayet star.