Posters should be 120 x 120 as maximum size and will be available for the whole conference.

Hitting time distributions in different time windows in financial market

B. Spagnolo(1,2) and G. Bonanno(1)

(1) Dipartimento di Fisica e Tecnologie Relative, Università degli Studi di Palermo, viale delle Scienze - edificio 18, I-90128 Palermo - Italy
(2) I.N.F.M., Unità di Palermo, viale delle Scienze - ed.18, I-90123 Palermo - Italy

We analise the hitting time distributions of stock price returns in different time windows, characterized by different levels of noise present in the market. The study has been performed on two sets of data from US markets. The first one is composed by daily price of 1071 stocks trade for the 12-year period 1987-1998, the second one is composed by high frequency data for 100 stocks for the 4-year period 1995-1998. We compare the probability ditribution obtained by our empirical analisys with those obtained from different models for stock market evolution.

Path Integrals and Exotic Options: Methods and Numerical Results

G Bormetti, G Montagna, O Nicrosini and N Moreni
Univ. and INFN, Pavia , CERMICS-ENPC, Paris

In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to the option pricing problem is presented. A general formula to price path dependent options with underlying asset composed by several eventually correlated stocks is developed. Various flexible and efficient computational algorithms to evaluate the option fair price and the corresponding Greek letters are presented. As examples, Asian, Barrier Knock Out, Reverse Cliquet and Basket options are considered. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement.

A Nonconservative Earthquake Model of Self-Organized Criticality on a Small World topology

F. Caruso1, V. Latora2, A. Rapisarda2, B. Tadic3
1 Scuola Superiore di Catania, Università di Catania, Catania, Italy
2 Dipartimento di Fisica e Astronomia, Università di Catania, Catania, Italy
and INFN sezione di Catania, Via S. Sofia 64, 95123 Catania, Italy
3 Department for Theoretical Physics, Jožef Stefan Institute, Ljubljan, Slovenia

We numerically investigate the Olami-Feder-Christensen model on a small world topology. Contrary to the case of nearest neighbors model, we find that the small world OFC model exhibits self-organized criticality deep within the non-conservative regime. The probability distribution for avalanche size obeys finite size scaling, with universal critical exponents. Moreover we use the stretched exponential function to fit the pdf's cutoffs and, on approaching the small-world limit, the power-law is practically lost and the stretching becomes more pronounced, because of long-range links.

A model for cascading failures in complex networks

P. Crucitti1, V. Latora2, M. Marchiori3
1 Scuola Superiore di Catania, Università di Catania, Catania, Italy
2 Dipartimento di Fisica e Astronomia, Università di Catania, Catania, Italy 3W3C and Lab for computer science, MIT, Usa, Dipartimento di Informatica, Università di Venezia, Italy

Large but rare cascades triggered by small initial shocks are present in most of the infrastructure networks. Here we present a simple model for cascading failures based on the dynamical redistribution of the flow on the network. We show that the breakdown of a single node is sufficient to collapse the efficiency of the entire system if the node is among the ones with largest load. This is particularly important for real-world networks with an highly hetereogeneous distribution of loads as the Internet and electrical power grids.

Capillary condensation of gases in disordered porous materials: metastability and equilibrium

F.Detcheverry, E. Kierlik, M.L. Rosinberg G. and Tarjus
Laboratoire de Physique Theorique des Liquides, Universite Pierre et Marie Curie, Paris, France

A crucial feature of systems with quenched randomness is their tendency to remain far from equilibrium on experimental time scales. This is usually related to the existence of a complex free energy landscape with a multitude of metastable states separated by large barriers, which make irrelevant thermal fluctuations that could drive the system to equilibrium. The response to an external force or field is then history-dependent and proceeds through avalanches of various sizes corresponding to a collective motion from one local minima to the next. A classical example is the motion of one (or many) magnetic domain walls in ferromagnets as the magnetic field is slowly varied. Relevant theoretical work is usually limited to zero temperature.
A similar behavior is observed in capillary condensation of gases in disordered mesoporous materials such as glasses or silica aerogels. As the pressure of the ambiant vapor is varied, the sorption isotherms are hysteretic and the morphology of the hysteresis loop changes with temperature and porosity. By using a lattice-gas description that incorporates at a coarse-grained level the geometric and energetic disorder of interconnected porous structures and applying local mean-field theory, we propose a comprehensive theoretical description of this phenomenon that relates the observed behaviour to the properties of the underlying free-energy surface [1]. We suggest that the morphology of the hysteresis loop is inuenced by out-of-equilibrium transitions and that desorption may be associated to a depinning process [2, 3, 4].
References
[1] E. Kierlik, P. Monson, M. Rosinberg, G. Tarjus, J.Phys.: Condens. Matter 14, 9295 (2002).
[2] M. Rosinberg, E. Kierlik, G. Tarjus, Europhys. Lett. 62, 377 (2003).
[3] F. Detcheverry, E. Kierlik, M. Rosinberg, G. Tarjus, Phys. Rev. E 68, 61504 (2003).
[4] F. Detcheverry, E. Kierlik, M. Rosinberg, G. Tarjus, "The mechanism of gas adsorption and
desorption in aerogels: the e_ect of temperature." submitted to Langmuir.

Edge of chaos for the classic kicked top

S. Duarte Querios, C. Tsallis
Centro Brasileiro de Pequisas Fisicas, Rio de jeneiro, Brazil

In this work one studies the sensitivity to initial conditions in the classic kicked top 3D map, whose phase space consists of a sphere with unitary radius. Varying kick strength, a, it is possible to define regular and chaotic systems where the distance between trajectories initially separated by an infinitesimally (sensitivity) distance grows respectively linear and exponentially in time. On the boarder of these regions, sensitivity to initial conditions grows in time following a q-exponential law. where q is the entropic index related with non-extensive entropy and lambda_q a generalised Lyapunov coefficient. The value of q, for each alpha, is independent from initial conditions less than 1 and evolves to q=1, when a increases, until saturates corresponding to a full occupation of phase space with chaotic region.

Connection between financial models with varying second order moment and nonextensive statistical mechanics

S. Duarte Querios, C. Tsallis
Centro Brasileiro de Pequisas Fisicas, Rio de jeneiro, Brazil

The GARCH algorithm is the most renowned generalisation of Engle's ARCH linear process. Both processes are characterised for presenting a time dependent and correlated variance. Beyond memory parameter, b, (present in ARCH) and an independent and identically distributed noise, ?, it involves another parameter, c, such that, for c=0, the standard ARCH process is reproduced. We use a generalised noise characterised by an index qn, such that qn recovers the Gaussian distribution. Supported on variance time dependence and on superstatistics we match statistical moments of GARCH distributions with q-Gaussian distribution obtained through maximising non-extensive entropy, basis of nonextensive statistical mechanics we obtained a sole analytical connection between q and (b,c, qn) which seems to be remarkably good when compared with computational simulations. With this result we derive an analytical approximation for the stationary distribution of squared variance (volatility). Using generalised Kullback-Leibler relative entropy we measure the degree of dependence between successive terms of GARCH(1,1) time series quantified by an entropic index, qop. This qop index decreases monotonically with the entropic index q from stationary distributions and seems to be independent from b,c combination used.

Lyapunov Coefficient in the Presence of Noise in Metastable Potentials

A. Fiasconaro(1), Lutz Schimansky-Geier(2), D. Valenti(1) and B. Spagnolo(1)

(1)Dipartimento di Fisica e Tecnologie Relative and INFM Viale delle Scienze, Pad. 18, I-90128 Palermo, Italy
(2) Institut fur Physik, Humboldt University, Newtonstr. 15, 12489 Berlin, Germany

The Lyapunov coefficient for initial unstable nonequilibrium states of an overdamped Brownian particle moving in a metastable cubic potential, in the presence of noise, is analyzed. We observe that the mean Lyapunov coefficient shows a non monotonic behavior with a minimum as a function of the noise intensity. This behavior is related to the noise enhanced stability (NES) of a metastable state, which implies a nonmonotonic behavior of the mean first passage time (MFPT) as a function of the noise intensity.
We also present the theoretical evaluations of MFPT for some initial unstable states in which a local minimum appears. These values are close to the "critical" point below of which MFPT has the divergencies for noise intensity tending to zero.
The spatio temporal evolution of the probability to find the particle within the absorbing boundary is also calculated by means of the Fokker-Planck equation.

Roughness and Growth in a Continuous Fluid Invasion Model

I. Hecht and H. Taitelbaum

Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel


We have studied interface characteristics in a continuous fluid invasion model, first introduced by Cieplak & Robbins [Phys. Rev. Lett. 60, 2042 (1988)]. In this model the interface grows as a response to an applied quasi-static pressure which induces various types of instabilities. We suggest a new variant of the model, which differs from the original model by the order of instabilities treatment. This order represents the relative importance of the physical mechanisms involved in the system. The new variant predicts the existence of a third, intermediate regime, in the behavior of the roughness exponent as a function of the wetting properties of the system. The gradual increase of the roughness exponent in this third regime can explain the scattered experimental data for the roughness exponent in the literature. The growth exponent in this model was found to be around zero, due to the initial rough interface.

q-exponential behavior in the sensitivity to initial conditions for a classical map analog of quantum one-dimensional potential with correlated disorder

H. Hernandez Saldana, F.M. Izrailev, A. Robledo

UNAM, Mexico City, Mexico

The metal-insulator transition in the Anderson model for disordered material with long-range correlations has been associated to unbounded and bounded chaotic behavior in a classical map version of the corresponding discrete Schrodinger equation [1]. We explore the transition states at which the Lyapunov exponent canishes in some simplified versions of the classical map. Both power-law decay and stronger than exponential growth in sensitivuty to initial conditions is found for classical trajectories in such transition states that are characterized by angent or period doubling biforcations depending on the parameter values we take. Both the trajectories and the sensitivity follows exactly a q-exponential form[2] with the known value of q that correspond to the route to chaos we consider[3]. Implications of this behavior in their metal-insulator transition counterpart and the role in tha mobility edges for 1D site potentials with long-range correlations are also analyzad and discussed.

[1]A.A. Krokhin and F.M.Izrailev. Phys Rev Lett 82 ( 1999) 4062; Ann. Phys (Leipzig) 8 (1999) 153.
[2] C. Tsallis, et al . " Nonextensive Statisticla Mechanics and its applications". S. Abe and Y. Okamoto Ed. (Springer Berlag, Heidelberg, 2001).
[3] F. Baldovin, A. Robledo. Europhys. Lett. 60 (2002)518.

Experimental investigation of SOC in a three dimensional pile of rice

K.A. Lörincz, C.M. Aegerter, and R.J. Wijngaarden
Department of Physics and Astronomy, Faculty of Sciences FEW/N&S Vrije Universiteit, Amsterdam, The Netherlands

The natural systems thought to exhibit self-organized criticality (SOC), such as earthquakes, economic markets, biological evolution are difficult to study in a controlled experiment. Therefore we are studying a 3-dimensional pile of rice, with which the predictions of SOC can be tested quantitatively.
We show that the hallmarks of SOC, power-law behavior of the avalanches and finite size scaling are observed in this system. We determine the growth and roughness exponents of the rice surface and show that theoretical [1] scaling relations are observed between these exponents and those for the avalanche behavior. We also study directly the approach to the critical state in terms of the evolution of the maximum slope of the pile (gap). We find that this gap approaches its critical value as a power law, were the experimental characteristic exponent is in agreement with that calculated from the avalanche exponents in the critical state,using the theoretical scaling relation by Paczuski et al. [1]

[1] Paczuski et al. Phys. Rev. E 53 (1996) 414
[2]C.M. Aegerter, K.A. L?ornicz, M.S. Welling, and R.J. Wijngaarden: Extremal dynamics and the approach to the critical state: experiments on a three dimensional pile of rice, Phys. Rev. Lett. 92 (2004) 058702-1

Steady-state visual evoked potentials and phase synchronization in migraine

L.Angelini, M.De Tommaso, M.Guido, D.Marinazzo, G.Nardulli, L.Nitti, M.Pellicoro, S.Stramaglia
TIRES:Centre of Innovative Technologies for Signal Detection and Processing, University of Bari, Italy
Physics Department, University of Bari, Italy
Department of Neurological and Psychiatric Sciences, University of Bari, Italy

We investigate phase synchronization in EEG recordings from migraine patients. We use the analytic signal technique, based on the Hilbert transform, and find that migraine brains are characterized by enhanced alpha band phase synchronization in presence of visual stimuli. Our findings show that migraine patients have an overactive regulatory mechanism that renders them more sensitive to external stimuli.

Rotational Heterogeneities in Supercooled Water

M. G. Mazza1, N. Giovambattista1,F. W. Starr2, H. E. Stanley1

2Department of Physics, Wesleyan University, Middletown, Connecticut, USA
1Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts USA.

We study the rotational dynamics and dynamical heterogeneities of supercooled water by means of molecular dynamics simulation of the extended simple point charge model (SPC/E). We study the system in a range of temperature from 200 K to 350$K. We calculate the analog of the mean squared displacement for the rotational degrees of freedom and calculate the rotational diffusion coefficient Dr. We compare Dr with the translational diffusion coefficient Dt. We find that rotational dynamics is heterogeneous, i.e., there are sets of molecules that rotate more than the average in the system for a given time interval. These sets of molecules form clusters. We study the size and the temporal behavior of the clusters. We also relate this kind of clusters with the ones formed by molecules with larger displacement. We find that those two types of clusters partially overlap and are greatly correlated in space.

Metastability hindering synchronization in HMF and Kuramoto models

A. Pluchino, V. Latora and A. Rapisarda

Dipartimento di Fisica e Astronomia and Infn sezione di Catania, Università di Catania, Italy

We discuss the ubiquity of long-living metastable states in various models (HMF, Kuramoto) just before the crtitical value of the phase transition. These states hinder "sinchronization" and are characterized by a glassy dynamics.

Phase Transitions on Markovian Bipartite Graphs

O. Pulkkinen and J. Merikoski
Department of Physics, University of Jyvaskyla, Finland

We consider the stationary properties of a graph-valued Markov process, where the dynamics of the edge-ends on the vertex set is given by a zero-range process, so that the exponential rate of a restructuring event depends only on the degree of either the initial or the final vertex of the move. The subtleties of the underlying particle system, in particular the condensation phenomena, are most easily incorporated by using a bipartite structure. The existence and the size of the giant component, with critical exponents, are discussed in detail for the most interesting case of the so-called Evans's interaction.

Neural Cryptography

A. Ruttor
Institut fuer Theoretische Physik und Astrophysik Universitaet Wuerzburg, Germany

Neural networks can synchronize by mutual learning. As synchronization is much easier than learning by listening, this phenomenon can be applied to cryptography. Two networks training each other generate a secret key over a public channel. Several attacks on this key-exchange protocol are considered and the security of neural cryptography is analyzed.

Influence of the shape of barrier on diffusion in periodic potentials

A. Safonov

We study the influence of barrier's height and width, tilt and period of tilted piece-wise linear periodic potential profile on diffusion coefficient. Unlike the most part of previous papers dedicated to this problem, we consider potential, where tilt and height of barrier are independent values. It makes possible to investigate the influence of these parameters separately. We have found the great enhancement of diffusion coefficient with respect to the free diffusion for subcritical tilt in such systems. Non-monotonic behavior of diffusion coefficient as function of tilt and period is also observed

Mapping Correlations into Planar Graphs

M. Tumminello (1), R.N. Mantegna(1), T. Aste(2), T. Di Matteo(2)

(1) Dipartimento di Fisica e Tecnologie Relative, Università degli Studi di Palermo, viale delle Scienze - edificio 18, I-90128 Palermo - Italy
(2) Department of Applied Mathematics, Australian National University 0200 Canberra, ACT, Australia

We introduce a novel technique to analyze the collective behavior of complex systems by mapping the cross-correlation structure of the considered elements into a planar graph. The resulting structures presents triangulations on the sphere
which are organized around the strongest correlations. We show that this technique gives a description of the hierarchical organization of the system richer than the one obtaining the minimum spanning tree of the considered elements.

Population dynamics in the presence of noise for different systems

D. Valenti(1), O. Chichigina(2), Lutz Schimansky-Geier(3), A. Fiasconaro(1), B. Spagnolo(1)

(1)Dipartimento di Fisica e Tecnologie Relative and INFM, Group of Interdisciplinary Physics, Università di Palermo
Viale delle Scienze, I-90128 Palermo, Italy
(2)M. V. Lomonosov Moscow State University, 119899 Moscow, Russia
(3)Institut für Physik Humboldt - Universität zu Berlin, Newtonstr. 15, (Adlershof)D-12489 Berlin, Germany

We study population dynamics for three different ecosystems. (i) a Lotka-Volterra system in the presence of a multiplicative noise. The interaction parameter between the species is a random process which obeys a stochastic differential equation with a generalized bistable potential in the presence of a periodic driving term. We derive Signal to Noise Ratio and observe Stochastic Resonance. (ii) a Lotka-Volterra system where the interaction parameter between the species is a stochastic process driven by an autocorrelated dichotomous noise with jump rate (t) and coeherence time? c, in the presence of a periodical driving force. (iii) a population dynamics model with a non Gaussian noise source. The role of this noise on the time evolution of the species is analyzed both for white and colored noise with different value of the autocorrelation, i.e. number of memory steps.