GPU-computing in econophysics and statistical physics

This article focuses on the analysis of financial time series and their correlations. A method is used for quantifying pattern based correlations of a time series. With this methodology, evidence is found that typical behavioral patterns of financial market participants manifest over short time scales, i.e., that reactions to given price patterns are not entirely random, but that similar price patterns also cause similar reactions. Based on the investigation of the complex correlations in financial time series, the question arises, which properties change when switching from a positive trend to a negative trend. An empirical quantification by rescaling provides the result that new price extrema coincide with a significant increase in transaction volume and a significant decrease in the length of corresponding time intervals between transactions. These findings are independent of the time scale over 9 orders of magnitude, and they exhibit characteristics which one can also find in other complex systems in nature (and in physical systems in particular). These properties are independent of the markets analyzed. Trends that exist only for a few seconds show the same characteristics as trends on time scales of several months. Thus, it is possible to study financial bubbles and their collapses in more detail, because trend switching processes occur with higher frequency on small time scales. In addition, a Monte Carlo based simulation of financial markets is analyzed and extended in order to reproduce empirical features and to gain insight into their causes. These causes include both financial market microstructure and the risk aversion of market participants.     

Editorial - Constraints: From physical principles to molecular simulations and beyond

The two articles in this issue of the European Physical Journal Special Topics cover topics in Econophysics and GPU computing in the last years. In the first article [1], the formation of market prices for financial assets is described which can be understood as superposition of individual actions of market participants, in which they provide cumulative supply and demand. This concept of macroscopic properties emerging from microscopic interactions among the various subcomponents of the overall system is also well-known in statistical physics. The distribution of price changes in financial markets is clearly non-Gaussian leading to distinct features of the price process, such as scaling behavior, non-trivial correlation functions and clustered volatility. This article focuses on the analysis of financial time series and their correlations. A method is used for quantifying pattern based correlations of a time series. With this methodology, evidence is found that typical behavioral patterns of financial market participants manifest over short time scales, i.e., that reactions to given price patterns are not entirely random, but that similar price patterns also cause similar reactions. Based on the investigation of the complex correlations in financial time series, the question arises, which properties change when switching from a positive trend to a negative trend. An empirical quantification by rescaling provides the result that new price extrema coincide with a significant increase in transaction volume and a significant decrease in the length of corresponding time intervals between transactions. These findings are independent of the time scale over 9 orders of magnitude, and they exhibit characteristics which one can also find in other complex systems in nature (and in physical systems in particular). These properties are independent of the markets analyzed. Trends that exist only for a few seconds show the same characteristics as trends on time scales of several months. Thus, it is possible to study financial bubbles and their collapses in more detail, because trend switching processes occur with higher frequency on small time scales. In addition, a Monte Carlo based simulation of financial markets is analyzed and extended in order to reproduce empirical features and to gain insight into their causes. These causes include both financial market microstructure and the risk aversion of market participants.     

Correlated noise-based switches and stochastic resonance in a bistable genetic regulation system

The correlated noise-based switches and stochastic resonance are investigated in a bistable single gene switching system driven by an additive noise (environmental fluctuations), a multiplicative noise (fluctuations of the degradation rate). The correlation between the two noise sources originates from on the lysis-lysogeny pathway system of the λ phage. The steady state probability distribution is obtained by solving the time-independent Fokker-Planck equation, and the effects of noises are analyzed. The effects of noises on the switching time between the two stable states (mean first passage time) is investigated by the numerical simulation. The stochastic resonance phenomenon is analyzed by the power amplification factor. The results show that the multiplicative noise can induce the switching from “on” → “off” of the protein production, while the additive noise and the correlation between the noise sources can induce the inverse switching “off” → “on”. A nonmonotonic behaviour of the average switching time versus the multiplicative noise intensity, for different cross-correlation and additive noise intensities, is observed in the genetic system. There exist optimal values of the additive noise, multiplicative noise and cross-correlation intensities for which the weak signal can be optimal amplified.     

Extracting the exponential behaviors in the market data

We introduce a mathematical criterion defining the bubbles or the crashes in financial market price fluctuations by considering exponential fitting of the given data. By applying this criterion we can automatically extract the periods in which bubbles and crashes are identified. From stock market data of so-called the Internet bubbles it is found that the characteristic length of bubble period is about 100 days.     

Enhancement of oscillation amplitude of cavitation bubble due to acoustic wake effect in multibubble environment

Acoustic cavitation occurs in ultrasonic treatment causing various phenomena such as chemical synthesis, chemical decomposition, and emulsification. Nonlinear oscillations of cavitation bubbles are assumed to be responsible for these phenomena, and the neighboring bubbles may interact each other. In the present study, we numerically investigated the dynamic behavior of cavitation bubbles in multi-bubble systems. The results reveal that the oscillation amplitude of a cavitation bubble surrounded by other bubbles in a multi-bubble system becomes larger compared with that in the single-bubble case. It is found that this is caused by an acoustic wake effect, which reduces the pressure near a bubble surrounded by other bubbles and increases the time delay between the bubble contraction/expansion cycles and sound pressure oscillations. A new parameter, called “cover ratio” is introduced to quantitatively evaluate the variation in the bubble oscillation amplitude, the time delay, and the maximum bubble radius.     

Waiting time distributions in financial markets

We study waiting time distributions for data representing two completely different financial markets that have dramatically different characteristics. The first are data for the Irish market during the 19th century over the period 1850 to 1854. A total of 10 stocks out of a database of 60 are examined. The second database is for Japanese yen currency fluctuations during the latter part of the 20th century (1989-1992). The Irish stock activity was recorded on a daily basis and activity was characterised by waiting times that varied from one day to a few months. The Japanese yen data was recorded every minute over 24 hour periods and the waiting times varied from a minute to a an hour or so. For both data sets, the waiting time distributions exhibit power law tails. The results for Irish daily data can be easily interpreted using the model of a continuous time random walk first proposed by Montroll and applied recently to some financial data by Mainardi, Scalas and colleagues. Yen data show a quite different behaviour. For large waiting times, the Irish data exhibit a cut off; the Yen data exhibit two humps that could arise as result of major trading centres in the World. Received 31 December 2001     

Effectiveness of measures of performance during speculative bubbles

Statistical analysis of financial data mostly focused on testing the validity of Brownian motion (Bm). Analyses performed on several time series have shown deviation from the Bm hypothesis, that is at the base of the evaluation of many financial derivatives. We analyze the behavior of performance measures based on maximum drawdown movements (MDD(T)), testing their stability when the underlying process deviates from the Bm hypothesis. In particular we consider the fractional Brownian motion (fBm), and fluctuations estimated empirically on raw market data. The case study of the rising part of speculative bubbles is reported.     

The cahn—hilliard equation with “frozen-in” fluctuations of mobility

Early time kinetics of a system with conserved order parameter quenched into an unstable two-phase region of the phase diagram is considered. We study the process of phase separation under the influence of random “frozen-in” inhomogencities of mobility. The combined effect of this “frozen-in” randomness and persistent thermal fluctuations on the structure factor is discussed. The maximum instability of the Cahn—Hilliard type shifts to larger wavelengths, which may be interpreted as “coarsening” even for small times.     

The near-extreme density of intraday log-returns

The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by non-stationarity and dependence between increments. Furthermore, the convergence to the limit distributions can be slow, requiring a huge amount of records to obtain significant statistics, and thus limiting its practical applications. Focussing, instead, on the closely related density of “near-extremes”–the distance between a record and the maximal value–can render the statistical methods to be more suitable in the practical applications and/or validations of models. We apply this recently proposed method in the empirical validation of an adapted financial market model of the intraday market fluctuations.     

色交叉关联噪声对基因转录调节系统的影响

研究了受色交叉关联噪声驱动的基因转录调节系统的瞬态性质(平均首通时间).据Novikov定理和Fox近似方法得到相应的Fokker-Planck方程,求出稳态概率分布函数的表达式.在此基础上运用最快下降法得到平均首通时间的近似表达式.经过数值计算,结果表明：在强关联,小关联时间条件下,蛋白质的浓度经历了开→关→开;在弱关联,大关联时间条件下,蛋白质的浓度经历了开→关.在基因转录过程中出现了重入现象. 关键词： 色交叉关联噪声 基因转录调节系统 平均首通时间     

Repulsive bubble–bubble interaction in ultrasonic field

The bubble–bubble interaction(BBI) is attractive in most cases, but also could be repulsive. In the present study,three specific mechanisms of repulsive BBI are given. The great contribution to the repulsive BBI is derived from the large radius of the bubble catching the rebound point of the other bubble. For "elastic" bubble and "inelastic" bubble, with the increase of the phase shift between two bubbles, the BBI changes from attractive to repulsive, and the repulsion can be maintained. For both "elastic" bubbles, the BBI alternates between attractive interaction and repulsive interaction along the direction where the ambient radius of one of bubbles increases. For stimulating bubble and stimulated bubble, the BBI can be repulsive. Its property depends on the ambient radii of bubbles. In addition, the distribution of the radiation forces in ambient radius space shows that the BBI is sensitive to the size of bubble and is complex because the bubbles are not of the same size in an ultrasonic field. Finally, as the distance increases or decreases monotonically with time, the absolute value of the BBI decreases or increases, correspondingly. The BBI can oscillate not only in strength but also in polarity when the distance fluctuates with time.     

Understanding the enhanced synchronization of delay-coupled networks with fluctuating topology

We study the dynamics of networks with coupling delay, from which the connectivity changes over time. The synchronization properties are shown to depend on the interplay of three time scales: the internal time scale of the dynamics, the coupling delay along the network links and time scale at which the topology changes. Concentrating on a linearized model, we develop an analytical theory for the stability of a synchronized solution. In two limit cases, the system can be reduced to an “effective” topology: in the fast switching approximation, when the network fluctuations are much faster than the internal time scale and the coupling delay, the effective network topology is the arithmetic mean over the different topologies. In the slow network limit, when the network fluctuation time scale is equal to the coupling delay, the effective adjacency matrix is the geometric mean over the adjacency matrices of the different topologies. In the intermediate regime, the system shows a sensitive dependence on the ratio of time scales, and on the specific topologies, reproduced as well by numerical simulations. Our results are shown to describe the synchronization properties of fluctuating networks of delay-coupled chaotic maps.     

Particle localization and hyperuniformity of polymer‐grafted nanoparticle materials

The properties of materials largely reflect the degree and character of the localization of the molecules comprising them so that the study and characterization of particle localization has central significance in both fundamental science and material design. Soft materials are often comprised of deformable molecules and many of their unique properties derive from the distinct nature of particle localization. We study localization in a model material composed of soft particles, hard nanoparticles with grafted layers of polymers, where the molecular characteristics of the grafted layers allow us to “tune” the softness of their interactions. Soft particles are particular interesting because spatial localization can occur such that density fluctuations on large length scales are suppressed, while the material is disordered at intermediate length scales; such materials are called “disordered hyperuniform”. We use molecular dynamics simulation to study a liquid composed of polymer‐grafted nanoparticles (GNP), which exhibit a reversible self‐assembly into dynamic polymeric GNP structures below a temperature threshold, suggesting a liquid‐gel transition. We calculate a number of spatial and temporal correlations and we find a significant suppression of density fluctuations upon cooling at large length scales, making these materials promising for the practical fabrication of “hyperuniform” materials.     

Big entropy fluctuations in statistical equilibrium: The macroscopic kinetics

Large entropy fluctuations in the equilibrium steady state of classical mechanics are studied in extensive numerical experiments in a simple strongly chaotic Hamiltonian model with two degrees of freedom described by the modified Arnold cat map. The rise and fall of a large separated fluctuation is shown to be described by the (regular and stable) “macroscopic” kinetics, both fast (ballistic) and slow (diffusive). We abandon a vague problem of the “appropriate” initial conditions by observing (in a long run) a spontaneous birth and death of arbitrarily big fluctuations for any initial state of our dynamical model. Statistics of the infinite chain of fluctuations similar to the Poincaré recurrences is shown to be Poissonian. A simple empirical relationship for the mean period between the fluctuations (the Poincaré “cycle”) is found and confirmed in numerical experiments. We propose a new representation of the entropy via the variance of only a few trajectories (“particles”) that greatly facilitates the computation and at the same time is sufficiently accurate for big fluctuations. The relation of our results to long-standing debates over the statistical “irreversibility” and the “time arrow” is briefly discussed.     

Cellular Vacuum

Couldany universe satisfy the following conditions? (i) Each volume of space contains only a finite amount of information, because space and time come in discrete units. (ii) Over some range of size and speed, the mechanics of this world are approximately classical. Imagine a crystalline world of tiny, discrete “cells,” each knowing only what its nearest neighbors do. In such a universe, we’ll construct analogs of particles and fields, and ask what it would mean for these to satisfy constraints like conservation of momentum. In each case classical mechanics will break down—on scales both small and large—and strange phenomena will emerge: a maximal velocity, a slowing of internal clocks, a bound on simultaneous measurement, and quantumlike effects in very weak or intense fields.     

Risk,randomness, crashes and quants

Market movements, whether short-term fluctuations, long-term trends, or sudden surges or crashes, have an immense and widespread economic impact. These movements are suggestive of the complex behaviour seen in many non-equilibrium physical systems. Not surprisingly, therefore, the characterization of market behaviour presents an inviting challenge to the physical sciences and, indeed, many concepts and methods developed for modelling non-equilibrium natural phenomena have found fertile ground in financial settings. In this review, we begin with the simplest random process, the random walk, and, assuming no prior knowledge of markets, build up to the conceptual and computational machinery used to analyse and model the behaviour of financial systems. We then consider the evidence that calls into question several aspects of the random walk model of markets and discuss some ideas that have been put forward to account for the observed discrepancies. The application of all of these methods is illustrated with examples of actual market data.     

Self field electromagnetism and quantum phenomena

Abstract

Quantum Electrodynamics (QED) has been extremely successful inits predictive capability for atomic phenomena. Thus the greatest hope for any alternative view is solely to mimic the predictive capability of quantum mechanics (QM), and perhaps its usefulness will lie in gaining a better understanding of microscopic phenomena. Many “paradoxes” and problematic situations emerge in QED. To combat the QED problems, the field of Stochastics Electrodynamics (SE) emerged, wherein a random “zero point radiation” is assumed to fill all of space in an attmept to explain quantum phenomena, without some of the paradoxical concerns. SE, however, has greater failings. One is that the electromagnetic field energy must be infinit eto work. We have examined a deterministic side branch of SE, “self field” electrodynamics, which may overcome the probelms of SE. Self field electrodynamics (SFE) utilizes the chaotic nature of electromagnetic emissions, as charges lose energy near atomic dimensions, to try to understand and mimic quantum phenomena. These fields and charges can “interact with themselves” in a non-linear fashion, and may thereby explain many quantum phenomena from a semi-classical viewpoint. Referred to as self fields, they have gone by other names in the literature: “evanesccent radiation”, “virtual photons”, and “vacuum fluctuations”. Using self fields, we discuss the uncertainty principles, the Casimir effects, and the black-body radiation spectrum, diffraction and interference effects, Schrodinger's equation, Planck's constant, and the nature of the electron and how they might be understood in the present framework. No new theory could ever replace QED. The self field view (if correct) would, at best, only serve to provide some understanding of the processes by which strange quantum phenomena occur at the atomic level. We discuss possible areas where experiments might be employed to test SFE, and areas where future work may lie.     

Minimal agent based model for financial markets I

We introduce a minimal agent based model for financial markets to understand the nature and self-organization of the stylized facts. The model is minimal in the sense that we try to identify the essential ingredients to reproduce the most important deviations of price time series from a random walk behavior. We focus on four essential ingredients: fundamentalist agents which tend to stabilize the market; chartist agents which induce destabilization; analysis of price behavior for the two strategies; herding behavior which governs the possibility of changing strategy. Bubbles and crashes correspond to situations dominated by chartists, while fundamentalists provide a long time stability (on average). The stylized facts are shown to correspond to an intermittent behavior which occurs only for a finite value of the number of agents N. Therefore they correspond to finite size effects which, however, can occur at different time scales. We propose a new mechanism for the self-organization of this state which is linked to the existence of a threshold for the agents to be active or not active. The feedback between price fluctuations and number of active agents represents a crucial element for this state of self-organized intermittency. The model can be easily generalized to consider more realistic variants.