Intercluster Correlation in Seismicity

Mega et al.(cond-mat/0212529) proposed to use the ``diffusion entropy'' (DE) method to demonstrate that the distribution of time intervals between a large earthquake (the mainshock of a given seismic sequence) and the next one does not obey Poisson statistics. We have performed synthetic tests which show that the DE is unable to detect correlations between clusters, thus negating the claimed possibility of detecting an intercluster correlation. We also show that the LR model, proposed by Mega et al. to reproduce inter-cluster correlation, is insufficient to account for the correlation observed in the data.Comment: Comment on Mega et al., Phys. Rev. Lett. 90. 188501 (2003) (cond-mat/0212529

Nonparametric Markovian Learning of Triggering Kernels for Mutually Exciting and Mutually Inhibiting Multivariate Hawkes Processes

In this paper, we address the problem of fitting multivariate Hawkes processes to potentially large-scale data in a setting where series of events are not only mutually-exciting but can also exhibit inhibitive patterns. We focus on nonparametric learning and propose a novel algorithm called MEMIP (Markovian Estimation of Mutually Interacting Processes) that makes use of polynomial approximation theory and self-concordant analysis in order to learn both triggering kernels and base intensities of events. Moreover, considering that N historical observations are available, the algorithm performs log-likelihood maximization in $O(N)$ operations, while the complexity of non-Markovian methods is in $O(N^{2})$. Numerical experiments on simulated data, as well as real-world data, show that our method enjoys improved prediction performance when compared to state-of-the art methods like MMEL and exponential kernels

Quarter-filled spin density wave states with long-range Coulomb interaction

Spin density wave (SDW) states at quarter-filling, which coexist with charge density wave (CDW) states, have been examined where the critical temperature is calculated for an extended Hubbard model with long range repulsive interactions. Within the mean-field theory, it is shown that the first order transition occurs with decreasing temperature for interactions located around the boundary between SDW state and CDW state.Comment: 4 pages, 5 figures, Proceedings of CREST International Workshop (Nagoya, Japan, 24-26 January, 2000), submitted to J. Phys. Chem. Solid

Experimental band structure of the nearly half-metallic CuCr2_2Se4_4: An optical and magneto-optical study

Diagonal and off-diagonal optical conductivity spectra have been determined form the measured reflectivity and magneto-optical Kerr effect (MOKE) over a broad range of photon energy in the itinerant ferromagnetic phase of CuCr$_2$Se$_4$ at various temperatures down to T=10 K. Besides the low-energy metallic contribution and the lower-lying charge transfer transition at $E$$\approx$2 eV, a sharp and distinct optical transition was observed in the mid-infrared region around $E$$=$0.5 eV with huge magneto-optical activity. This excitation is attributed to a parity allowed transition through the Se-Cr hybridization-induced gap in the majority spin channel. The large off-diagonal conductivity is explained by the high spin polarization in the vicinity of the Fermi level and the strong spin-orbit interaction for the related charge carriers. The results are discussed in connection with band structure calculations

Hierarchy of Temporal Responses of Multivariate Self-Excited Epidemic Processes

We present the first exact analysis of some of the temporal properties of multivariate self-excited Hawkes conditional Poisson processes, which constitute powerful representations of a large variety of systems with bursty events, for which past activity triggers future activity. The term "multivariate" refers to the property that events come in different types, with possibly different intra- and inter-triggering abilities. We develop the general formalism of the multivariate generating moment function for the cumulative number of first-generation and of all generation events triggered by a given mother event (the "shock") as a function of the current time $t$. This corresponds to studying the response function of the process. A variety of different systems have been analyzed. In particular, for systems in which triggering between events of different types proceeds through a one-dimension directed or symmetric chain of influence in type space, we report a novel hierarchy of intermediate asymptotic power law decays $\sim 1/t^{1-(m+1)\theta}$ of the rate of triggered events as a function of the distance $m$ of the events to the initial shock in the type space, where $0 < \theta <1$ for the relevant long-memory processes characterizing many natural and social systems. The richness of the generated time dynamics comes from the cascades of intermediate events of possibly different kinds, unfolding via a kind of inter-breeding genealogy.Comment: 40 pages, 8 figure

Ferromagnetic fluctuation and possible triplet superconductivity in Na_xCoO_2*yH_2O: Fluctuation-exchange study of multi-orbital Hubbard model

Spin and charge fluctuations and superconductivity in a recently discovered superconductor Na_xCoO_2*yH_2O are studied based on a multi-orbital Hubbard model. Tight-binding parameters are determined to reproduce the LDA band dispersions with the Fermi surface, which consist of a large cylindrical one around the Gamma-point and six hole pockets near the K-points. By applying the fluctuation-exchange (FLEX) approximation, we show that the Hund's-rule coupling between the Co t2g orbitals causes ferromagnetic (FM) spin fluctuation. Triplet f_{y(y^2-3x^2)}-wave and p-wave pairings are favored by this FM fluctuation on the hole-pocket band. We propose that, in Na_xCoO_2*yH_2O, the Co t2g orbitals and inter-orbital Hund's-rule coupling play important roles on the triplet pairing, and this compound can be a first example of the triplet superconductor in which the orbital degrees of freedom play substantial roles.Comment: 5 pages, 3 figure