Criticality and Heterogeneity in the Solution Space of Random Constraint Satisfaction Problems

Random constraint satisfaction problems are interesting model systems for spin-glasses and glassy dynamics studies. As the constraint density of such a system reaches certain threshold value, its solution space may split into extremely many clusters. In this paper we argue that this ergodicity-breaking transition is preceded by a homogeneity-breaking transition. For random K-SAT and K-XORSAT, we show that many solution communities start to form in the solution space as the constraint density reaches a critical value alpha_cm, with each community containing a set of solutions that are more similar with each other than with the outsider solutions. At alpha_cm the solution space is in a critical state. The connection of these results to the onset of dynamical heterogeneity in lattice glass models is discussed.Comment: 6 pages, 4 figures, final version as accepted by International Journal of Modern Physics

Heavy-tailed statistics in short-message communication

Short-message (SM) is one of the most frequently used communication channels in the modern society. In this Brief Report, based on the SM communication records provided by some volunteers, we investigate the statistics of SM communication pattern, including the interevent time distributions between two consecutive short messages and two conversations, and the distribution of message number contained by a complete conversation. In the individual level, the current empirical data raises a strong evidence that the human activity pattern, exhibiting a heavy-tailed interevent time distribution, is driven by a non-Poisson nature.Comment: 4 pages, 4 figures and 1 tabl

Spin-one bosons in low dimensional Mott insulating states

We analyze the strong coupling limit of spin-one bosons in low dimensional Mott insulating states. In 1D lattices, for an odd number of bosons per site ($N_0$), the ground state is a dimerized valence bond crystal state with a two-fold degeneracy; the low lying elementary spin excitations carry spin one. For an even number of bosons per site, the ground state is a nondegenerate spin singlet Mott state. We also argue that in a square lattice in a quantum disordered limit the ground states should be dimerized valence bond crystals for an odd integer $N_0$. Finally, we briefly report results for non-integer numbers of bosons per site in one-dimensional lattices.Comment: 5 pages; discussions on non-integer case have been shortene

Vortex-like surface wave and its role in the transient phenomena of meta-material focusing

We show that a slab of meta-material (with $\epsilon=\mu=-1+i\Delta$) possesses a vortex-like surface wave with no ability to transport energy, whose nature is completely different from a localized mode or a standing wave. Through computations based on a rigorous time-dependent Green's function approach, we demonstrate that such a mode inevitably generates characteristic image oscillations in two dimensional focusing with even a monochromatic source, which were observed in many numerical simulations, but such oscillations are weak in three dimensional focusing.Comment: To appear in the March 7th issue of Appl. Phys. Let

Statistical Inference for Time-changed Brownian Motion Credit Risk Models

We consider structural credit modeling in the important special case where the log-leverage ratio of the firm is a time-changed Brownian motion (TCBM) with the time-change taken to be an independent increasing process. Following the approach of Black and Cox, one defines the time of default to be the first passage time for the log-leverage ratio to cross the level zero. Rather than adopt the classical notion of first passage, with its associated numerical challenges, we accept an alternative notion applicable for TCBMs called "first passage of the second kind". We demonstrate how statistical inference can be efficiently implemented in this new class of models. This allows us to compare the performance of two versions of TCBMs, the variance gamma (VG) model and the exponential jump model (EXP), to the Black-Cox model. When applied to a 4.5 year long data set of weekly credit default swap (CDS) quotes for Ford Motor Co, the conclusion is that the two TCBM models, with essentially one extra parameter, can significantly outperform the classic Black-Cox model.Comment: 21 pages, 3 figures, 2 table