Jan A. Freund

Stochastic Processes in Physics, Chemistry, and Biology

Stochastic Transport and Brownian Motion.- Directed Current Without Dissipation: Reincarnation of a Maxwell-Loschmidt Demon.- Molecular Motors and Stochastic Models.- Nonlinearly Coupled Chemical Reactions.- Thermodynamics of Isothermal Brownian Motors.- Rocking Ratchets at High Frequencies.- Defect Dragging in Periodic Structures.- Conduction in an Inhomogeneous Medium.- Theory and Control of Multiple Hopping in Activated Surface Diffusion.- Brownian Motion in a d-Dimensional Space with Fluctuating Friction.- Active Motion of Brownian Particles.- Diffusion in Granular Gases of Viscoelastic Particles.- Stochastic Resonance and Phase Synchronization.- Scaling of Noise and Constructive Aspects of Fluctuations.- Stochastic Resonances in Underdamped Bistable Systems.- Stochastic Resonance in a System of Coupled Asymmetric Resonators.- Optimizing Information Transmission in Model Neuronal Ensembles: The Role of Internal Noise.- Stochastic Resonance with Images and Spatially Correlated Stochastic Patterns.- Adiabatic and Non-adiabatic Resonances in Excitable Systems.- The Lighthouse Model of a Neural Net with Delay.- Noise-enhanced Phase Coherence in Ensembles of Stochastic Resonators.- Estimation of Synchronization from Noisy Data with Application to Human Brain Activity.- Nonequilibrium Thermodynamics and Dynamical Complexity.- Noise-Induced Phase Transitions and Reactive Processes.- Noise-Induced Order in Extended Systems: A Tutorial.- Linear Instability Mechanisms of Noise-Induced Phase Transitions.- Parametric Resonance Revisited.- On Noise-Induced Transitions in Nonlinear Oscillators.- The Kramers Oscillator Revisited.- Reactive Processes in Low Dimensions: Statistical and Dynamical Aspects.- On-Off Intermittency and Stochastic Stability in Nematics Driven by Multiplicative Noise.- Effect of Boundary Condition Fluctuations on Smoluchowski Reaction Rates.- Experimental Studies of Noise-Induced Phenomena in a Tunnel Diode.- Quantum Mechanical Model of Proton Transfer in a Fluctuating Potential Field of the Active Site of ?-Chymotrypsin.- Large Fluctuations and Noise in Chaotic Systems.- A Gentle Introduction to the Integration of Stochastic Differential Equations.- Controlling Large Fluctuations: Theory and Experiment.- Fluctuational Escape from a Chaotic Attractor.- Problems of a Statistical Ensemble Theory for Systems Far from Equilibrium.- Stochastic Approach to Lyapunov Exponents in Coupled Chaotic Systems.- Peculiarities of Nonhyperbolic Chaos.- Information of Open Systems.- Structure Formation.- Nonlinear Spatiotemporal Patterns in Globally Coupled Reaction-Diffusion Systems.- Segregation Effects in Randomly Mixed Diffusion-Controlled Binary Reactions.- Nonlinear Waves on Stochastic Support: Calcium Waves in Astrocyte Syncytia.- Stochastic Field Equation for Amorphous Surface Growth.- Epitaxial Growth with Elastic Interaction: Layer and Cluster Growth.- Stochastic Evolution of a Discrete Line: Numerical Results.- Structures in Planetary Rings- Stability and Gravitational Scattering.

Frequency and phase synchronization in stochastic systems

The phenomenon of frequency and phase synchronization in stochastic systems requires a revision of concepts originally phrased in the context of purely deterministic systems. Various definitions of an instantaneous phase are presented and compared with each other with special attention paid to their robustness with respect to noise. We review the results of an analytic approach describing noise-induced phase synchronization in a thermal two-state system. In this context exact expressions for the mean frequency and the phase diffusivity are obtained that together determine the average length of locking episodes. A recently proposed method to quantify frequency synchronization in noisy potential systems is presented and exemplified by applying it to the periodically driven noisy harmonic oscillator. Since this method is based on a threshold crossing rate pioneered by Rice the related phase velocity is termed the Rice frequency. Finally, we discuss the relation between the phenomenon of stochastic resonance and noise-enhanced phase coherence by applying the developed concepts to the periodically driven bistable Kramers oscillator.

A statistical approach to vehicular traffic

A two-dimensional cellular automaton is introduced to model the flow and jamming of vehicular traffic in cities. Each site of the automaton represents a crossing where a finite number of cars can wait approaching the crossing from each of the four directions. The flow of cars obeys realistic traffic rules. We investigate the dependence of the average velocity of cars on the global traffic density. At a critical threshold for the density the average velocity reduces drastically caused by jamming. For the low-density regime we provide analytical results which agree with the numerical results.

Non-linear EEG analyses predict non-response to rTMS treatment in major depressive disorder

OBJECTIVE Several linear electroencephalographic (EEG) measures at baseline have been demonstrated to be associated with treatment outcome after antidepressant treatment. In this study we investigated the added value of non-linear EEG metrics in the alpha band in predicting treatment outcome to repetitive transcranial magnetic stimulation (rTMS). METHODS Subjects were 90 patients with major depressive disorder (MDD) and a group of 17 healthy controls (HC). MDD patients were treated with rTMS and psychotherapy for on average 21 sessions. Three non-linear EEG metrics (Lempel-Ziv Complexity (LZC); False Nearest Neighbors and Largest Lyapunov Exponent) were applied to the alpha band (7-13 Hz) for two 1-min epochs EEG and the association with treatment outcome was investigated. RESULTS No differences were found between a subgroup of unmedicated MDD patients and the HC. Non-responders showed a significant decrease in LZC from minute 1 to minute 2, whereas the responders and HC showed an increase in LZC. CONCLUSIONS There is no difference in EEG complexity between MDD and HC and the change in LZC across time demonstrated value in predicting outcome to rTMS. SIGNIFICANCE This is the first study demonstrating utility of non-linear EEG metrics in predicting treatment outcome in MDD.

Molecular dynamics of comminution in ball mills

Abstract:We investigate autogenous fragmentation of dry granular material in rotating cylinders using two-dimensional molecular dynamics. By evaluation of spatial force distributions achieved numerically for various rotation velocities we argue that comminution occurs mainly due to the existence of force chains. A statistical analysis of these force chains explains the spatial distribution of comminution efficiency in ball mills as measured experimentally by Rothkegel [1] and Rolf [2]. For animated sequences of our simulations see http://summa.physik.hu-berlin.de/

Noise Induced Order: Stochastic Resonance

\sim kies/mill/bm.html

ENTROPY AND EXTENDED MEMORY IN DISCRETE CHAOTIC DYNAMICS

kies/mill/bm.html

Signal detection enhanced by comodulated noise

Natural sounds often exhibit correlated amplitude modulations at different frequency regions, so-called comodulation. Therefore, the ear might be especially adapted to these kinds of sounds. Two effects have been related to the sensitivity of the auditory system to common modulations across frequency: comodulation detection difference (CDD) and comodulation masking release (CMR). Research on these effects has been done on the psychophysical and on the neurophysiological level in humans and other animals. Until now, models have focused only on one of the effects. In the present study, a simple model based on data from neuronal recordings obtained during CDD experiments with starlings is discussed. This model demonstrates that simple peripheral processing in the ear can go a substantial way to explaining psychophysical signal detection thresholds in response to CDD and CMR stimuli. Moreover, it is largely analytically tractable. The model is based on peripheral processing and incorporates the basic steps frequency filtering, envelope extraction, and compression. Signal detection is performed based on changes in the mean compressed envelope of the filtered stimulus. Comparing the results of the model with data from the literature, the scope of this unifying approach to CDD and CMR is discussed.