Prediction Possibility in the Fractal Overlap Model of Earthquakes

The two-fractal overlap model of earthquake shows that the contact area distribution of two fractal surfaces follows power law decay in many cases and this agrees with the Guttenberg-Richter power law. Here, we attempt to predict the large events (earthquakes) in this model through the overlap time-series analysis. Taking only the Cantor sets, the overlap sizes (contact areas) are noted when one Cantor set moves over the other with uniform velocity. This gives a time series containing different overlap sizes. Our numerical study here shows that the cumulative overlap size grows almost linearly with time and when the overlapsizes are added up to a pre-assigned large event (earthquake) and then reset to `zero' level, the corresponding cumulative overlap sizes grows upto some discrete (quantised) levels. This observation should help to predict the possibility of `large events' in this (overlap) time series.Comment: 6 pages, 6 figures. To be published as proc. NATO conf. CMDS-10, Soresh, Israel, July 2003. Eds. D. J. Bergman & E. Inan, KLUWER PUB

Patterns in high-frequency FX data: Discovery of 12 empirical scaling laws

We have discovered 12 independent new empirical scaling laws in foreign exchange data-series that hold for close to three orders of magnitude and across 13 currency exchange rates. Our statistical analysis crucially depends on an event-based approach that measures the relationship between different types of events. The scaling laws give an accurate estimation of the length of the price-curve coastline, which turns out to be surprisingly long. The new laws substantially extend the catalogue of stylised facts and sharply constrain the space of possible theoretical explanations of the market mechanisms.Comment: 26 pages, 3 figures, 23 tables,2nd version (text made more concise and readable, algorithm pseudocode, results unchanged), 5-year datasets (USD-JPY, EUR-USD) provided at http://www.olsen.ch/more/datasets

The geometry of fractal percolation

A well studied family of random fractals called fractal percolation is discussed. We focus on the projections of fractal percolation on the plane. Our goal is to present stronger versions of the classical Marstrand theorem, valid for almost every realization of fractal percolation. The extensions go in three directions: {itemize} the statements work for all directions, not almost all, the statements are true for more general projections, for example radial projections onto a circle, in the case $\dim_H >1$, each projection has not only positive Lebesgue measure but also has nonempty interior. {itemize}Comment: Survey submitted for AFRT2012 conferenc

When Models Interact with their Subjects: The Dynamics of Model Aware Systems

A scientific model need not be a passive and static descriptor of its subject. If the subject is affected by the model, the model must be updated to explain its affected subject. In this study, two models regarding the dynamics of model aware systems are presented. The first explores the behavior of "prediction seeking" (PSP) and "prediction avoiding" (PAP) populations under the influence of a model that describes them. The second explores the publishing behavior of a group of experimentalists coupled to a model by means of confirmation bias. It is found that model aware systems can exhibit convergent random or oscillatory behavior and display universal 1/f noise. A numerical simulation of the physical experimentalists is compared with actual publications of neutron life time and {\Lambda} mass measurements and is in good quantitative agreement.Comment: Accepted for publication in PLoS-ON

How a plantar pressure-based, tongue-placed tactile biofeedback modifies postural control mechanisms during quiet standing

The purpose of the present study was to determine the effects of a plantar pressure-based, tongue-placed tactile biofeedback on postural control mechanisms during quiet standing. To this aim, sixteen young healthy adults were asked to stand as immobile as possible with their eyes closed in two conditions of No-biofeedback and Biofeedback. Centre of foot pressure (CoP) displacements, recorded using a force platform, were used to compute the horizontal displacements of the vertical projection the centre of gravity (CoGh) and those of the difference between the CoP and the vertical projection of the CoG (CoP-CoGv). Altogether, the present findings suggest that the main way the plantar pressure-based, tongue-placed tactile biofeedback improves postural control during quiet standing is via both a reduction of the correction thresholds and an increased efficiency of the corrective mechanism involving the CoGh displacements

Impact of Investor's Varying Risk Aversion on the Dynamics of Asset Price Fluctuations

While the investors' responses to price changes and their price forecasts are well accepted major factors contributing to large price fluctuations in financial markets, our study shows that investors' heterogeneous and dynamic risk aversion (DRA) preferences may play a more critical role in the dynamics of asset price fluctuations. We propose and study a model of an artificial stock market consisting of heterogeneous agents with DRA, and we find that DRA is the main driving force for excess price fluctuations and the associated volatility clustering. We employ a popular power utility function, $U(c,\gamma)=\frac{c^{1-\gamma}-1}{1-\gamma}$ with agent specific and time-dependent risk aversion index, $\gamma_i(t)$, and we derive an approximate formula for the demand function and aggregate price setting equation. The dynamics of each agent's risk aversion index, $\gamma_i(t)$ (i=1,2,...,N), is modeled by a bounded random walk with a constant variance $\delta^2$. We show numerically that our model reproduces most of the ``stylized'' facts observed in the real data, suggesting that dynamic risk aversion is a key mechanism for the emergence of these stylized facts.Comment: 17 pages, 7 figure

Mean first-passage times of non-Markovian random walkers in confinement

The first-passage time (FPT), defined as the time a random walker takes to reach a target point in a confining domain, is a key quantity in the theory of stochastic processes. Its importance comes from its crucial role to quantify the efficiency of processes as varied as diffusion-limited reactions, target search processes or spreading of diseases. Most methods to determine the FPT properties in confined domains have been limited to Markovian (memoryless) processes. However, as soon as the random walker interacts with its environment, memory effects can not be neglected. Examples of non Markovian dynamics include single-file diffusion in narrow channels or the motion of a tracer particle either attached to a polymeric chain or diffusing in simple or complex fluids such as nematics \cite{turiv2013effect}, dense soft colloids or viscoelastic solution. Here, we introduce an analytical approach to calculate, in the limit of a large confining volume, the mean FPT of a Gaussian non-Markovian random walker to a target point. The non-Markovian features of the dynamics are encompassed by determining the statistical properties of the trajectory of the random walker in the future of the first-passage event, which are shown to govern the FPT kinetics.This analysis is applicable to a broad range of stochastic processes, possibly correlated at long-times. Our theoretical predictions are confirmed by numerical simulations for several examples of non-Markovian processes including the emblematic case of the Fractional Brownian Motion in one or higher dimensions. These results show, on the basis of Gaussian processes, the importance of memory effects in first-passage statistics of non-Markovian random walkers in confinement.Comment: Submitted version. Supplementary Information can be found on the Nature website : http://www.nature.com/nature/journal/v534/n7607/full/nature18272.htm

Measuring portfolio performance using a modified measure of risk

This paper reports the results of an investigation into the properties of a theoretical modification of beta proposed by Leland (1999) and based on earlier work of Rubinstein (1976). It is shown that when returns are elliptically symmetric, beta is the appropriate measure of risk and that there are other situations in which the modified beta will be similar to the traditional measure based on the capital asset pricing model. For the case where returns have a normal distribution, it is shown that the criterion either does not exist or reduces exactly to the conventional beta. It is therefore conjectured that the modified measure will only be useful for portfolios that have nonstandard return distributions which incorporate skewness. For such situations, it is shown how to estimate the measure using regression and how to compare the resulting statistic with a traditional estimated beta using Hotelling's test. An empirical study based on stocks from the FTSE350 does not find evidence to support the use of the new measure even in the presence of skewness.Journal of Asset Management (2007) 7, 388-403. doi:10.1057/palgrave.jam.225005

Sudden drop of fractal dimension of electromagnetic emissions recorded prior to significant earthquake

The variation of fractal dimension and entropy during a damage evolution process, especially approaching critical failure, has been recently investigated. A sudden drop of fractal dimension has been proposed as a quantitative indicator of damage localization or a likely precursor of an impending catastrophic failure. In this contribution, electromagnetic emissions recorded prior to significant earthquake are analysed to investigate whether they also present such sudden fractal dimension and entropy drops as the main catastrophic event is approaching. The pre-earthquake electromagnetic time series analysis results reveal a good agreement to the theoretically expected ones indicating that the critical fracture is approaching