Motion in random fields - an application to stock market data

A new model for stock price fluctuations is proposed, based upon an analogy with the motion of tracers in Gaussian random fields, as used in turbulent dispersion models and in studies of transport in dynamically disordered media. Analytical and numerical results for this model in a special limiting case of a single-scale field show characteristics similar to those found in empirical studies of stock market data. Specifically, short-term returns have a non-Gaussian distribution, with super-diffusive volatility, and a fast-decaying correlation function. The correlation function of the absolute value of returns decays as a power-law, and the returns distribution converges towards Gaussian over long times. Some important characteristics of empirical data are not, however, reproduced by the model, notably the scaling of tails of the cumulative distribution function of returns.Comment: 28 pages, 10 figure

Dynamical Systems on Networks: A Tutorial

We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more complicated scenarios. We briefly motivate why examining dynamical systems on networks is interesting and important, and we then give several fascinating examples and discuss some theoretical results. We also briefly discuss dynamical systems on dynamical (i.e., time-dependent) networks, overview software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than original version, some reorganization and also more pointers to interesting direction

Flatness of tracer density profile produced by a point source in turbulence

The average concentration of tracers advected from a point source by a multivariate normal velocity field is shown to deviate from a Gaussian profile. The flatness (kurtosis) is calculated using an asymptotic series expansion valid for velocity fields with short correlation times or weak space dependence. An explicit formula for the excess flatness at first order demonstrates maximum deviation from a Gaussian profile at time t of the order of five times the velocity correlation time, with a t–1 decay to the Gaussian value at large times. Monotonically decaying forms of the velocity time correlation function are shown to yield negative values for the first order excess flatness, but positive values can result when the correlation function has an oscillatory tail

Implementing Structured Decision Making Procedures in Child Welfare

The University Archives has determined that this item is of continuing value to OSU's history.Session 4: Program Evaluation in Social Work. Presenter: James P. Gleeson, Ph.D., University of Illinois at Chicago - "Implementing Structured Decision Making Procedures in Child Welfare".The Ohio State University College of Social Wor

Combined Effects of Frequency Quantization and Additive Input Noise in a First-order Digital PLL

AbstractA recent work by Gardner [Gardner, F.M., Frequency granularity in digital phase-locked loops, IEEE Trans. Commun., 44 (1996), 749758] on the subject of digital phase-locked loops (DPLLs) investigated, via simulation, the characteristics of the phase-jitter caused by frequency quantization in the numerically-controlled oscillator. Further works by Feely, Teplinsky et al [Feely, O., Rogers, A., and Teplinsky, A., Phase-jitter dynamics of digital phaselocked loops, IEEE Trans. Circuits and Systems, Part I: Fundamental Theory and Applications, 46 (1999), 545–558], [Feely, O., and Teplinsky, A., Phase-jitter dynamics of digital phase-locked loops: Part II, IEEE Trans. Circuits and Systems, Part I: Fundamental Theory and Applications., 47 (2000), 458–473] used the theory of nonlinear dynamics to provide a complete analytical explanation of this phase-jitter.This paper examines in detail the case where the input signal is embedded in additive noise, a scenario earlier investigated by Gardner where no satisfactory method of characterising the phase-jitter was found. Here, further numerical results for the 1-D DPLL are presented and it is shown analytically how the DPLL noise-jitter dynamics may be approximated by a noisy circle rotation map for reasonable levels of additive noise. The noise in this case is unique and highly nonlinear in nature and thus not amenable to traditional analysis. By considering the the probability flow over time, a time-dependent difference-delay equation is derived for the probability density function (PDF) of the phase-jitter. It is shown that this PDF reaches a steady-state and that this state is described by a non-local equation. The solutions of this equation are investigated, both numerically and analytically, and used to explain the interaction between the additive and quantization noise that was previously not understood

An analytical approach to sorting in periodic potentials

There has been a recent revolution in the ability to manipulate micrometer-sized objects on surfaces patterned by traps or obstacles of controllable configurations and shapes. One application of this technology is to separate particles driven across such a surface by an external force according to some particle characteristic such as size or index of refraction. The surface features cause the trajectories of particles driven across the surface to deviate from the direction of the force by an amount that depends on the particular characteristic, thus leading to sorting. While models of this behavior have provided a good understanding of these observations, the solutions have so far been primarily numerical. In this paper we provide analytic predictions for the dependence of the angle between the direction of motion and the external force on a number of model parameters for periodic as well as random surfaces. We test these predictions against exact numerical simulations