Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session D39: Focus Session: Econophysics and Applications Outside of Physics |
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Sponsoring Units: GSNP Chair: Victor Yakovenko, University of Maryland Room: Morial Convention Center 231 |
Monday, March 10, 2008 2:30PM - 2:42PM |
D39.00001: Image Segmentation in Linear Time using the Potts Model Frank W. Bentrem A computational method is described which efficiently segments digital grayscale images using the Q-state Ising (or Potts) model. Since the Ising model was first proposed in 1925, physicists have studied lattice models to gain deep insights into ordered/disordered systems. Some researchers have realized that digital images may be modeled in much the same way as these physical systems (i.e., as a square lattice of numerical values). A major drawback in using this technique for image segmentation is that it processes in exponential time. Advances have been made via certain approximations to reduce the segmentation process to power-law time. However, real-time processing (such as for sonar imagery) requires much greater efficiency. We describe an energy minimization technique using four Potts (Q-Ising) models which processes in linear time. The technique is demonstrated on acoustic seafloor images as well as medical images. [Preview Abstract] |
Monday, March 10, 2008 2:42PM - 2:54PM |
D39.00002: Battles between an insurgent army and an advanced army - focus on strategy Surajit Sen, Linda Shanahan Detailed and aggregate analyses of the outcome of past battles focusing on rates of troop losses or on the ratios of forces on each side is at the heart of present knowledge about battles. Here we present non-equilibrium statistical mechanics based studies of possible outcomes of well matched strategic battles by a ``blue'' army against insurgency based attacks by well matched opponents in a ``red'' army in red territory. We assume that the red army attacks with randomly varying force levels to potentially confuse and drive the blue's strategies. The temporal evolution of the model battles incorporate randomness in the deployment of the reds and hence possess attendant history dependence. Our results reveal that while unpredictable events play a major role in battles, a balance between risk of exposure in a battlefield and the use of short range intelligence is needed in determining whether one side can decimate the other, and hence force a battle to end. [Preview Abstract] |
Monday, March 10, 2008 2:54PM - 3:06PM |
D39.00003: Understanding individual human mobility patterns Marta C. Gonz\'{a}lez, Cesar A. Hidalgo, Albert-L\'{a}szlo Barab\'{a}si Understanding human mobility patterns is of major importance for a number of areas, ranging from urban planning to traffic forecasting, transportation geography, and preventing the spread of biological and mobile viruses. Yet, in the absence of tools to monitor the time resolved location of a large number of individuals, our understanding of the basic laws governing human trajectories remains limited. Here we study the individual mobility pattern of mobile phone users whose position is tracked in a time resolved manner. We find that the displacement distribution of the whole population can be approximated with a truncated L\'{e}vy statistics, in agreement with earlier measurements. We show, however, that the main contribution to the observed distribution comes from the differences in the travel pattern of individuals. Furthermore, we find that the individual trajectories are bounded in space and are highly anisotropic, an effect that increases with the trajectory's radius of gyration. After we correct for differences in the radius of gyration and anisotropy all individuals are described by the same universal mobility pattern. These results open new avenues for modeling human motion, with important impact on agent based modeling, epidemic prevention, emergency response and urban planing. [Preview Abstract] |
Monday, March 10, 2008 3:06PM - 3:18PM |
D39.00004: Epidemics with Multistrain Interactions: Cross Immunity and Antibody-Dependent Enhancement Simone Bianco, Leah Shaw Dynamics of epidemic spread is a problem of global interest. In this work we investigate the dynamical properties of a multistrain disease in a population where the strains interact via antibody-dependent enhancement (ADE) and cross immunity. ADE is a property of some multistrain diseases, such as dengue fever and Ebola, in which the antibodies generated by a primary infection with a strain tend to increase the infectiousness of a secondary infection with a different strain. After a primary infection, cross immunity provides temporary reduced susceptibility to the other strains. The presence of chaotic outbreaks and desynchronization between strains has already been observed in a model with no cross immunity if the ADE is sufficiently strong. The addition of weak cross immunity provides a stabilizing effect, while strong cross immunity leads to large amplitude chaotic outbreaks. A stochastic version of the model is also considered. [Preview Abstract] |
Monday, March 10, 2008 3:18PM - 3:30PM |
D39.00005: Panic reactions and global disease dynamics Rafael Brune, Christian Thiemann, Bernd Blasius, Theo Geisel, Dirk Brockmann We analyze spatially extended disease dynamics in a system in which individuals change their dispersal characteristics in response to the local infection level. The key question is to what extent infectious wave front dynamics and the time course of the global infection change in response to host awareness and individuals trying to avoid infection by increased dispersal. We investigate two qualitatively different responses to the local degree of infection. In one system (panic reaction) the local diffusion coefficient increases with the concentration of infecteds, in the other system (directed reaction) individuals drift proportional to infection level gradients. For both systems we develop a mean field model. Although one expects that the individual rationale of avoiding an epidemic wave mitigates disease dynamics we find extended parameter regimes in which this rationale actually facilitates epidemic spread. Finally we investigate the dynamics of a fully stochastic system in which the effects prevail but which also show an increased extinction probability of the epidemic as a function of increasing dispersal response. [Preview Abstract] |
Monday, March 10, 2008 3:30PM - 3:42PM |
D39.00006: Fractal Hearts are Healthy Hearts---Are Fractal Companies Healthy Companies? Bronson Argyle, Gus Hart Fractal analyses of cardiac rhythms have implied that healthy individuals have complex cardiac behavior whereas aged or unhealthy individuals show either more random or more periodic behavior. Does this marker of ``complexity = health'' show up elsewhere? Can this technique be used in other fields as well? Specifically, does a Detrended Fluctuation Analysis of S{\&}P 500 bid prices reveal long range correlations in volatility, similar to those observed in cardiac interbeat intervals? If such correlations exist, measures of market complexity could be compared with individual securities to assess corporate strength and vitality. [Preview Abstract] |
Monday, March 10, 2008 3:42PM - 4:18PM |
D39.00007: Economic Fluctuations and Statistical Physics: Quantifying Extremely Rare and Much Less Rare Events Invited Speaker: Recent analysis of truly huge quantities of empirical data suggests that classic economic theories not only fail for a few outliers, but that there occur similar outliers of every possible size. In fact, if one analyzes only a small data set (say $10^4$ data points), then outliers appear to occur as ``rare events.'' However, when we analyze orders of magnitude more data ($10^8$ data points!), we find orders of magnitude more outliers---so ignoring them is not a responsible option, and studying their properties becomes a realistic goal. We find that the statistical properties of these ``outliers'' are identical to the statistical properties of everyday fluctuations. For example, a histogram giving the number of fluctuations of a given magnitude $ x$ for fluctuations ranging in magnitude from everyday fluctuations to extremely rare fluctuations that occur with a probability of only $10^{-8}$ is a perfect straight line in a double-log plot. Quantitative analogies between financial fluctuations and earthquakes will be discussed. Two unifying principles that underlie much of the finance analysis we will present are scale invariance and universality [R. N. Mantegna and H. E. Stanley, {\it Introduction to Econophysics: Correlations \& Complexity in Finance\/} (Cambridge U. Press, 2000)]. Scale invariance is a property not about algebraic equations but rather about functional equations, which have as their solutions not numbers but rather functional forms. The key idea of universality is that the identical set of laws hold across diverse markets, and over diverse time periods. This work was carried out in collaboration with a number of students and colleagues, chief among whom are X. Gabaix (MIT and Princeton) and V. Plerou (Boston University). [Preview Abstract] |
Monday, March 10, 2008 4:18PM - 4:30PM |
D39.00008: Nonstationary increments and variable diffusion processes in financial markets Joseph L. McCauley, Kevin E. Bassler, Gemunu H. Gunaratne Fat tailed returns distributions and Hurst exponent scaling for financial markets have been reported for more than a decade. The sliding interval technique used in those analyses implicitly assumes that the increments are stationary, an assumption that generally contradicts the facts that the increments are uncorrelated. We show that the data exhibit nonstationary, uncorrelated increments, implying diffusive dynamics with a variable diffusion coefficient, but there is no evidence for either fat tails or Hurst exponent scaling in daily FX returns. [Preview Abstract] |
Monday, March 10, 2008 4:30PM - 4:42PM |
D39.00009: A Model for Nonstationary Market Dynamics with Nontrivial Dynamical Scaling Min Liu, Kevin E. Bassler In a recent empirical analysis of the Euro/Dollar exchange rate [Bassler, et al., PNAS 104, 17287 (2007)] it was found that during certain periods of the day the market returns scale with Hurst exponents H that are significantly different from 1/2. In some of these periods it is less than 1/2, while in others it is greater than 1/2. In this talk we will propose a possible origin for this behavior and other stylized market facts, including short time negative autocorrelations of returns, in terms of a nonstationary compound Poisson process with a time-dependent intensity rate function that results from a changing bid-ask spread in the microscopic market. The model correctly describes the dynamic scaling behavior of a simple reaction-diffusion model of a limit-order book. That model, like the Euro/Dollar exchange rate, has nonstationary return increments and a Hurst exponent H not equal to 1/2. [Preview Abstract] |
Monday, March 10, 2008 4:42PM - 4:54PM |
D39.00010: path integral approach to closed form pricing formulas in the Heston framework. Damiaan Lemmens, Michiel Wouters, Jacques Tempere, Sven Foulon We present a path integral approach for finding closed form formulas for option prices in the framework of the Heston model. The first model for determining option prices was the Black-Scholes model, which assumed that the logreturn followed a Wiener process with a given drift and constant volatility. To provide a realistic description of the market, the Black-Scholes results must be extended to include stochastic volatility. This is achieved by the Heston model, which assumes that the volatility follows a mean reverting square root process. Current applications of the Heston model are hampered by the unavailability of fast numerical methods, due to a lack of closed-form formulae. Therefore the search for closed form solutions is an essential step before the qualitatively better stochastic volatility models will be used in practice. To attain this goal we outline a simplified path integral approach yielding straightforward results for vanilla Heston options with correlation. Extensions to barrier options and other path-dependent option are discussed, and the new derivation is compared to existing results obtained from alternative path-integral approaches (Dragulescu, Kleinert). [Preview Abstract] |
Monday, March 10, 2008 4:54PM - 5:06PM |
D39.00011: Modeling income distribution as a sum of additive and multiplicative stochastic processes Anand Banerjee, Victor Yakovenko We obtained an analytical stationary solution of the Fokker-Planck equation for a stochastic process that is a sum of the additive and multiplicative processes. The stationary probability distribution function smoothly interpolates between an exponential distribution at the low end and a power law at the high end. It may have different applications in physics. Here we apply it to income distribution in a society by modeling income as a stochastic process. We analyze the personal income distribution data in USA from the Internal Revenue Service. Using just three fitting parameters (the average income in the exponential part, the power-law exponent, and the crossover point between the exponential and the power laws), we obtain very good fits of the IRS data for a range of years. [Preview Abstract] |
Monday, March 10, 2008 5:06PM - 5:18PM |
D39.00012: Power-law behavior and condensation phenomena in disordered urn models: Analysis and its application to macro-economics Jun-ichi Inoue, Jun Ohkubo We investigate equilibrium statistical properties of a disordered urn model. New types of urn models are proposed, in which quenched disorder parameters play an important role in generating power-law behavior. By choosing an arbitrary energy function for each urn, one can construct a lot of urn models, and we assume that the energy function contains a disordered parameters. We evaluate the occupation probability $P(k)$ that an arbitrary urn has $k$ balls by using the concept of statistical physics of disordered systems. In our new disordered urn model, we find that above critical density $\rho_{\rm c}$ for a given temperature, condensation phenomenon occurs and most of the balls are condensed into an urn with the lowest energy level. As the result, the occupation probability changes its scaling behavior from an exponential-law to a heavy tailed power-law in large $k$ regime. We also discuss an application of our results for explaining of macro economy, in particular, emergence of wealth differentials. [Preview Abstract] |
Monday, March 10, 2008 5:18PM - 5:30PM |
D39.00013: The Macro Model of the Inequality Process and the Surging Relative Frequency of Large Wage Incomes John Angle Particles are randomly paired in the Inequality Process (IP), a particle system scattering a positive quantity, wealth. Each particle has a parameter, $\omega$, the fraction of wealth lost in a loss whose probability is 0.5. The stationary distribution of the wealth of particles with $\omega _{\psi}$ is approximated by a $\Gamma $ pdf, the IP's macro model, with shape and scale parameters expressed in terms of $\omega_{\psi }$. The model's dynamics are driven by the product, $\tilde {\omega}_t \mu _t $, where $\tilde {\omega }_t $ is the harmonic mean of the $\omega$'s in the population at time t and $\mu _t$, the population mean of wealth at time t. This $\Gamma $ pdf model fits the annual distribution of annual wage income in the U.S. 1961-2003. These data also confirm that the time-series of scalar statistics of wage income that labor economists think are produced by the U.S. distribution of wage income being ``hollowed out'' (bimodal), the increasing dispersion of wage income and the surging relative frequency of large wage incomes, are produced by the distribution being stretched over larger wage incomes, as implied by the IP's macro model when $\tilde {\omega }_t \mu _t $ increases. The IP's macro model includes wage income distribution dynamics into statistical mechanics. To appear in The Econophysics of Markets and Business Networks. [Preview Abstract] |
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