Long-range memory model of trading activity and volatility

Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the same long range memory properties. Here we present a stochastic differential equation as a dynamical model of the observed memory in the financial time series. The continuous stochastic process reproduces the statistical properties of the trading activity and serves as a background model for the modeling waiting time, return and volatility. Empirically observed statistical properties: exponents of the power-law probability distributions and power spectral density of the long-range memory financial variables are reproduced with the same values of few model parameters.Comment: 12 pages, 5 figure

Effective Dielectric Tensor for Electromagnetic Wave Propagation in Random Media

We derive exact strong-contrast expansions for the effective dielectric tensor \epeff of electromagnetic waves propagating in a two-phase composite random medium with isotropic components explicitly in terms of certain integrals over the $n$-point correlation functions of the medium. Our focus is the long-wavelength regime, i.e., when the wavelength is much larger than the scale of inhomogeneities in the medium. Lower-order truncations of these expansions lead to approximations for the effective dielectric constant that depend upon whether the medium is below or above the percolation threshold. In particular, we apply two- and three-point approximations for \epeff to a variety of different three-dimensional model microstructures, including dispersions of hard spheres, hard oriented spheroids and fully penetrable spheres as well as Debye random media, the random checkerboard, and power-law-correlated materials. We demonstrate the importance of employing $n$-point correlation functions of order higher than two for high dielectric-phase-contrast ratio. We show that disorder in the microstructure results in an imaginary component of the effective dielectric tensor that is directly related to the {\it coarseness} of the composite, i.e., local volume-fraction fluctuations for infinitely large windows. The source of this imaginary component is the attenuation of the coherent homogenized wave due to scattering. We also remark on whether there is such attenuation in the case of a two-phase medium with a quasiperiodic structure.Comment: 40 pages, 13 figure

Uncertainty Monitoring May Promote Emergents

We suggest that the phenomenon of uncertainty monitoring in nonhuman animals contributes richly to the conception of nonhuman animals’ self-monitoring. We propose that uncertainty may play a role in the emergence of new forms of behavior that are adaptive. We recommend that Smith et al. determine the extent to which the uncertain response transfers immediately to other test paradigms

Rhesus Monkeys (Macaca mulatta) Maintain Learning Set Despite Second-order Stimulus-response Spatial Discontiguity

In many discrimination-learning tests, spatial separation between stimuli and response loci disrupts performance in rhesus macaques. However, monkeys are unaffected by such stimulusresponse spatial discontiguity when responses occur through joystick-based computerized movement of a cursor. To examine this discrepancy, five monkeys were tested on a learning-set task that required them to touch computer-graphic levers {which differed in location across experimental phases) with a cursor in order to select an associated test stimulus. The task produced both first-order (joystick and lever) and second-order (lever and stimuli) spatial discontiguity between the stimuli to be discriminated and the discriminative response. Performance was significantly better than chance for all lever locations including locations in which selection of the correct lever required moving the cursor away from the positive stimulus. Thus, rhesus macaques do not attend simply to the region around the cursor in these computerized tests, but rather they attend to relevant stimulus loci even when these are discontiguous with response and reward areas

Chimpanzee (Pan troglodytes) Counting in a Computerized Testing Paradigm

Using computer-mediated joystick manipulation, the ability of a common chimpanzee(Pan troglodytes) to select arrays of items equal to a given target number was examined. A random dot condition was included in which all sequence cues were eliminated as a means to reach the target numbers 1 to 4. The participant, Austin, had only the quantity of items already selected as a record of how high the count had progressed. Performance on the random dot trials was found to be significantly above chance and improvement over time was also statistically significant. Results of this experiment provide evidence that Austin behaved with a knowledge that the quantity of items selected was the objective of the task rather than adhering rigidly to any specific pattern of selection. The results indicate that Austin had the ability to discriminate the number of items needed to reach the target number and then select items individually to reach that target quantity

A Markov Chain based method for generating long-range dependence

This paper describes a model for generating time series which exhibit the statistical phenomenon known as long-range dependence (LRD). A Markov Modulated Process based upon an infinite Markov chain is described. The work described is motivated by applications in telecommunications where LRD is a known property of time-series measured on the internet. The process can generate a time series exhibiting LRD with known parameters and is particularly suitable for modelling internet traffic since the time series is in terms of ones and zeros which can be interpreted as data packets and inter-packet gaps. The method is extremely simple computationally and analytically and could prove more tractable than other methods described in the literatureComment: 8 pages, 2 figure

The Composite Fermion Hierarchy: Condensed States of Composite Fermion Excitations?

A composite Fermion hierarchy theory is constructed in a way related to the original Haldane picture by applying the composite Fermion (CF) transformation to quasiparticles of Jain states. It is shown that the Jain theory coincides with the Haldane hierarchy theory for principal CF fillings. Within the Fermi liquid approach for few electron systems on the sphere a simple interpretation of many-quasiparticle spectra is given and provides an explanation of failure of CF hierarchy picture when applied to the hierarchical $4/11$ state.Comment: 6 pages, Revtex, 4 figures in PostScript, submitted to Phys. Rev. Let