Power-law and exponential tails in a stochastic priority-based model queue.

We derive exact asymptotic results for a stochastic queueing model in which tasks are executed according to a continuous-valued priority. The distribution P(tau) of the waiting times tau of executed tasks for this model is shown to behave asymptotically as a power law, P(tau) approximately tau(-3/2), when the average rates of task arrival lambda and execution micro satisfy microlambda, P(tau) approximately tau(-5/2)exp[-(sqrt[micro]-sqrt[lambda])2tau].

Biased diffusion and universality in model queues.

We study the structure and robustness of universality classes for queueing, deriving analytic results for priority-based models with continuous-valued priorities. By mapping one model onto the problem of biased diffusion, we show that its distribution of waiting times, P(tau), decreases for large times tau as P(tau) approximately tau;{-3/2} or as P(tau) approximately tau;{-5/2}exp(-tau/tau_{0}) in different parameter regimes. In a second model, introducing a cost for switching between different classes of tasks substantially changes the asymptotic behavior of P(tau).

Relationship between gene expression and observed intensities in DNA microarrays--a modeling study.

A theoretical study of the physical properties which determine the variation in signal strength from probe to probe on a microarray is presented. A model which incorporates probe-target hybridization, as well as the subsequent dissociation which occurs during stringent washing of the microarray, is introduced and shown to reasonably describe publicly available spike-in experiments carried out at Affymetrix. In particular, this model suggests that probe-target dissociation during the stringent wash plays a critical role in determining the observed hybridization intensities. In addition, it is demonstrated that non-specific hybridization introduces uncertainties which significantly limit the ability of any model to accurately quantify absolute gene expression levels while, in contrast, target folding appears to have little effect on these results. Finally, for data from target spike-in experiments, our model is shown to compare favorably with an existing statistical model in determining target concentration levels.

Escape or switching at short times.

In the standard Arrhenius picture [S. Arrhenius, Z. Phys. Chem., Stoechiom. Verwandtschaftsl. 4, 226 (1889); L. Néel, Ann. Geophys. (C.N.R.S.) 5, 99 (1949)] of thermal switching or escape from a metastable to a stable state, the escape probability per unit time P(s)(t) decreases monotonically with time t as P(s)(t) approximately e(-t/tau(D)), where the decay time tau(D) = tau0e(U/k(B)T), with U the energy barrier, k(B)T the thermal energy, and tau0 the time between escape attempts. Here, we extend the Arrhenius picture to shorter times by deriving general conditions under which P(s)(t) is peaked rather than monotonic, and showing that in the simplest scenario the peak time tau(P) diverges with tau(D) as ln(tau(D)).

How white noise generates power-law switching in bacterial flagellar motors.

The clockwise (CW) or counterclockwise (CCW) spinning of a bacterial flagellar motor is controlled by the concentration [Y] of a phosphorylated protein, CheY-P. Representing the stochastic switching behavior of the motor by a dynamical two-state (CW and CCW) model, whose energy levels fluctuate in time (t) as [Y](t) fluctuates, we show that temporal fluctuations in [Y](t) can generate a power-law distribution for the durations of the CCW states, in agreement with recent experiments. Correlations between the duration times of nearby CCW (CW) intervals are predicted by our model, and shown to exist in the experimental data and to affect the power spectrum for motor switching.

Coarse graining in micromagnetics.

Numerical solutions of the micromagnetic Landau-Lifshitz-Gilbert equations provide valuable information at low temperatures (T), but produce egregious errors at higher T. For example, Curie temperatures are often overestimated by an order of magnitude. We show that these errors result from the use of block or coarse-grained variables, without a concomitant renormalization of the system parameters to account for the block size. Renormalization solves the problem of the Curie-point anomaly and improves the accuracy of more complicated micromagnetic simulations, even at low T.

Modeling of DNA microarray data by using physical properties of hybridization.

A method of analyzing DNA microarray data based on the physical modeling of hybridization is presented. We demonstrate, in experimental data, a correlation between observed hybridization intensity and calculated free energy of hybridization. Then, combining hybridization rate equations, calculated free energies of hybridization, and microarray data for known target concentrations, we construct an algorithm to compute transcript concentration levels from microarray data. We also develop a method for eliminating outlying data points identified by our algorithm. We test the efficacy of these methods by comparing our results with an existing statistical algorithm, as well as by performing a cross-validation test on our model.

Low-frequency magnetic noise in micron-scale magnetic tunnel junctions.

We have observed low-frequency noise due to quasiequilibrium thermal magnetization fluctuations in micron-scale magnetic tunnel junctions (MTJs). This strongly field-dependent magnetic noise occurs within the magnetic hysteresis loops, either as 1/f or Lorentzian (random telegraph) noise. We attribute it to the thermally excited hopping of magnetic domain walls between pinning sites. Our results show that magnetic stability is a crucial factor in reducing the low-frequency noise in small MTJs.

Thermally assisted magnetization reversal in submicron-sized magnetic thin films

We have measured the rate of thermally assisted magnetization reversal of submicron-sized magnetic thin films. For fields H just less than the zero-temperature switching field H(C), the probability of reversal, P(exp)(s)(t), increases for short times t, achieves a maximum value, and then decreases exponentially. Micromagnetic simulations exhibit the same behavior and show that the reversal proceeds through the annihilation of two domain walls that move from opposite sides of the sample. The behavior of P(exp)(s)(t) can be understood through a simple "energy-ladder" model of thermal activation.

Virtual design prototyping applied to medical facilities.

Over the past five years, MITRE has developed rapid 3D modeling and immersive environment capabilities that supports the application of virtual environment technology to many traditional and non-traditional domains [1]. This paper provides background information on these capabilities and describes the application of this technology to the experimental design prototyping of operating rooms of the future and to the design and retrofit of existing or proposed medical facilities. These capabilities employ contemporary commercial hardware and software and exploit stereoscopic projection displays and headsets. A unique user interface facilitates object manipulation within these immersive environments and addresses two key areas: 1) Visualization of the contents on the model server or library in a catalog form; and 2) Natural interaction and immersion of the user with the visualized catalog and selected visualized objects in a 3D synthetic environment. A brief discussion of two developing applications of this technology will be presented. In one application example, the modeling environment can be used to synthesize physical replicas (potentially full stereo scale) of actual surgical rooms used for training of medical personnel. Alternatively, it can be employed as the infrastructure for a new form of collaborative interactive visualization, namely, telesurgery. In another example, the rapid modeling capability provides designers, architects and medical personnel with a means of rapidly developing synthetic renderings of (potentially interactive and remotely operative) proposed medical facilities prior to construction. We also discuss key issues needing to be resolved for successful model interchange.

Singular Lyapunov spectra and conservation laws.

We give analytic arguments and numerical evidence to show that the presence of conservation laws can produce a singularity in the spectrum of Lyapunov exponents for extended dynamical systems of low spatial dimensionality. This phenomenon can be used, e.g., for finding hidden conservation laws. (c) 1995 American Institute of Physics.