A stochastic theory for temporal fluctuations in self-organized critical systems

A stochastic theory for the toppling activity in sandpile models is developed, based on a simple mean-field assumption about the toppling process. The theory describes the process as an anti-persistent Gaussian walk, where the diffusion coefficient is proportional to the activity. It is formulated as a generalization of the It\^{o} stochastic differential equation with an anti-persistent fractional Gaussian noise source. An essential element of the theory is re-scaling to obtain a proper thermodynamic limit, and it captures all temporal features of the toppling process obtained by numerical simulation of the Bak-Tang-Wiesenfeld sandpile in this limit.Comment: 9 pages, 4 figure

Hawking Radiation in the Dilaton Gravity with a Non-Minimally Coupled Scalar Field

We discuss the two-dimensional dilaton gravity with a scalar field as the source matter where the coupling with the gravity is given, besides the minimal one, through an external field. This coupling generalizes the conformal anomaly in the same way as those found in recent literature, but with a diferent motivation. The modification to the Hawking radiation is calculated explicity and shows an additional term that introduces a dependence on the (effective) mass of the black-hole.Comment: 13 pages, latex file, no figures, to be published in IJM

The Devil is in the Detail: Hints for Practical Optimisation

Finding the minimum of an objective function, such as a least squares or negative log-likelihood function, with respect to the unknown model parameters is a problem often encountered in econometrics. Consequently, students of econometrics and applied econometricians are usually well-grounded in the broad differences between the numerical procedures employed to solve these problems. Often, however, relatively little time is given to understanding the practical subtleties of implementing these schemes when faced with illbehaved problems. This paper addresses some of the details involved in practical optimisation, such as dealing with constraints on the parameters, specifying starting values, termination criteria and analytical gradients, and illustrates some of the general ideas with several instructive examples.gradient algorithms, unconstrained optimisation, generalised method of moments.

Transitions in non-conserving models of Self-Organized Criticality

We investigate a random--neighbours version of the two dimensional non-conserving earthquake model of Olami, Feder and Christensen [Phys. Rev. Lett. {\bf 68}, 1244 (1992)]. We show both analytically and numerically that criticality can be expected even in the presence of dissipation. As the critical level of conservation, $\alpha_c$, is approached, the cut--off of the avalanche size distribution scales as $\xi\sim(\alpha_c-\alpha)^{-3/2}$. The transition from non-SOC to SOC behaviour is controlled by the average branching ratio $\sigma$ of an avalanche, which can thus be regarded as an order parameter of the system. The relevance of the results are discussed in connection to the nearest-neighbours OFC model (in particular we analyse the relevance of synchronization in the latter).Comment: 8 pages in latex format; 5 figures available upon reques

Lattice vibrations and structural instability in Cesium near the cubic to tetragonal transition

Under pressure cesium undergoes a transition from a high-pressure fcc phase (Cs-II) to a collapsed fcc phase (Cs-III) near 4.2GPa. At 4.4GPa there follows a transition to the tetragonal Cs-IV phase. In order to investigate the lattice vibrations in the fcc phase and seek a possible dynamical instability of the lattice, the phonon spectra of fcc-Cs at volumes near the III-IV transition are calculated using Savrasov's density functional linear-response LMTO method. Compared with quasiharmonic model calculations including non-central interatomic forces up to second neighbours, at the volume $V/V_0= 0.44$ ($V_0$ is the experimental volume of bcc-Cs with $a_0$=6.048{\AA}), the linear-response calculations show soft intermediate wavelength $T_{[1\bar{1}0]}[{\xi}{\xi}0]$ phonons. Similar softening is also observed for short wavelength $L[\xi\xi\xi]$ and $L[00\xi]$ phonons and intermediate wavelength $L[\xi\xi\xi]$ phonons. The Born-von K\'{a}rm\'{a}n analysis of dispersion curves indicates that the interplanar force constants exhibit oscillating behaviours against plane spacing $n$ and the large softening of intermediate wavelength $T_{[1\bar{1}0]}[{\xi}{\xi}0]$ phonons results from a negative (110)-interplanar force-constant $\Phi_{n=2}$. The frequencies of the $T_{[1\bar{1}0]}[{\xi}{\xi}0]$ phonons with $\xi$ around 1/3 become imaginary and the fcc structure becomes dynamically unstable for volumes below $0.41V_0$. It is suggested that superstructures corresponding to the $\mathbf{q}{\neq}0$ soft mode should be present as a precursor of tetragonal Cs-IV structure.Comment: 12 pages, 5 figure

Discrete time-series models when counts are unobservable

Count data in economics have traditionally been modeled by means of integer-valued autoregressive models. Consequently, the estimation of the parameters of these models and their asymptotic properties have been well documented in the literature. The models comprise a description of the survival of counts generally in terms of a binomial thinning process and an independent arrivals process usually specified in terms of a Poisson distribution. This paper extends the existing class of models to encompass situations in which counts are latent and all that is observed is the presence or absence of counts. This is a potentially important modification as many interesting economic phenomena may have a natural interpretation as a series of 'events' that are driven by an underlying count process which is unobserved. Arrivals of the latent counts are modeled either in terms of the Poisson distribution, where multiple counts may arrive in the sampling interval, or in terms of the Bernoulli distribution, where only one new arrival is allowed in the same sampling interval. The models with latent counts are then applied in two practical illustrations, namely, modeling volatility in financial markets as a function of unobservable 'news' and abnormal price spikes in electricity markets being driven by latent 'stress'.Integer-valued autoregression, Poisson distribution, Bernoulli distribution, latent factors, maximum likelihood estimation

Ground Beetles (Coleoptera: Carabidae) Inhabiting Stands of Reed Canary Grass Phalaris Arundinacea on Islands in the Lower Chippewa River, Wisconsin

We used pitfall traps to assess ground beetle diversity (Coleoptera:Carabidae) on two islands in the lower Chippewa River, Eau Claire County, Wisconsin, with rapidly expanding populations of reed canary grass, Phalaris arundinaceae. We collected 233 individuals belonging to 17 species over four, 3-9 day sampling periods, May-August 1994. All species have been documented in Wisconsin and most are considered habitat generalists. Agonum fidele, A. extensicolle, Anisodactylus harrisii and Bembidion quadrimaculatum oppositum comprised 70% of all species collected. Seven species were common to both islands, with 13 species collected on Canarygrass Island and 11 species on Ski Jump Island. Carabid species diversity (Shannon’s H=2.01) was greatest on Canarygrass Island