Molecular Dynamics of Comminution in Ball Mills

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 theses force chains explains the spatial distribution of comminution efficiency in ball mills as measured experimentally by Rothkegel and Rolf. For animated sequences of our simulations see http://summa.physik.hu-berlin.de/~kies/Research/RotatingCylinder/rotatingcylind er.htmlComment: 15 pages, 13 figure

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 payed 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 S.O. Rice the related phase velocity is termed 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.Comment: to appear in the Chaos focus issue on "Control, communication, and synchronization in chaotic dynamical systems

Festschrift on the occasion of Ulrike Feudel’s 60th birthday

Peer reviewedPostprin

Phase locking below rate threshold in noisy model neurons

The property of a neuron to phase-lock to an oscillatory stimulus before adapting its spike rate to the stimulus frequency plays an important role for the auditory system. We investigate under which conditions neurons exhibit this phase locking below rate threshold. To this end, we simulate neurons employing the widely used leaky integrate-and-fire (LIF) model. Tuning parameters, we can arrange either an irregular spontaneous or a tonic spiking mode. When the neuron is stimulated in both modes, a significant rise of vector strength prior to a noticeable change of the spike rate can be observed. Combining analytic reasoning with numerical simulations, we trace this observation back to a modulation of interspike intervals, which itself requires spikes to be only loosely coupled. We test the limits of this conception by simulating an LIF model with threshold fatigue, which generates pronounced anticorrelations between subsequent interspike intervals. In addition we evaluate the LIF response for harmonic stimuli of various frequencies and discuss the extension to more complex stimuli. It seems that phase locking below rate threshold occurs generically for all zero mean stimuli. Finally, we discuss our findings in the context of stimulus detection

Dissimilarity analysis based on diffusion maps

Compositional measurements from species assemblages define a high dimensional dataspace in which the data can form complex structures, termed manifolds. Comparing assemblages in this dataspace is difficult because the data is often sparse relative to its dimensionality and the complex structure of the manifold introduces bias and error in measurements of distance. Here, we apply diffusion maps, a manifold learning method, to find and characterize manifolds in high‐dimensional compositional data. We show that diffusion maps embed the data in reduced dimensions in which the Euclidean distance between data points approximates the distance between them along the manifold. This is especially useful when species turnover is high, as it provides a way to measure meaningful distances between assemblages even when they harbor disjoint sets of species. We anticipate diffusion maps will therefore be particularly useful for characterizing community change over large spatial and temporal scales.</jats:p

Finite-sample frequency distributions originating from an equiprobability distribution

Given an equidistribution for probabilities p(i)=1/N, i=1..N. What is the expected corresponding rank ordered frequency distribution f(i), i=1..N, if an ensemble of M events is drawn?Comment: 4 pages, 4 figure

How to decide whether small samples comply with an equidistribution

Abstract The decision whether a measured distribution complies with an equidistribution is a central element of many biostatistical methods. High throughput differential expression measurements, for instance, necessitate to judge possible over-representation of genes. The reliability of this judgement, however, is strongly affected when rarely expressed genes are pooled. We propose a method that can be applied to frequency ranked distributions and that yields a simple but efficient criterion to assess the hypothesis of equiprobable expression levels. By applying our technique to surrogate data we exemplify how the decision criterion can differentiate between a true equidistribution and a triangular distribution. The distinction succeeds even for small sample sizes where standard tests of significance (e.g. χ 2 ) fail. Our method will have a major impact on several problems of computational biology where rare events baffle a reliable assessment of frequency distributions. The program package is available upon request from the authors

Improved Mass Accuracy and Isotope Confirmation through Alignment of Ultrahigh-Resolution Mass Spectra of Complex Natural Mixtures

Fourier-transform ion cyclotron resonance mass spectrometry (FT-ICR-MS) is one of the state-of-the-art methods to analyze complex natural organic mixtures. The precision of detected masses is crucial for molecular formula attribution. Random errors can be reduced by averaging multiple measurements of the same mass, but because of limited availability of ultrahigh-resolution mass spectrometers, most studies cannot afford analyzing each sample multiple times. Here we show that random errors can be eliminated also by averaging mass spectral data from independent environmental samples. By averaging the spectra of 30 samples analyzed on our 15 T instrument we reach a mass precision comparable to a single spectrum of a 21 T instrument. We also show that it is possible to accurately and reproducibly determine isotope ratios with FT-ICR-MS. Intensity ratios of isotopologues were improved to a degree that measured deviations were within the range of natural isotope fractionation effects. In analogy to δ13C in environmental studies, we propose Δ13C as an analytical measure for isotope ratio deviances instead of widely employed C deviances. In conclusion, here we present a simple tool, extensible to Orbitrap-based mass spectrometers, for postdetection data processing that significantly improves mass accuracy and the precision of intensity ratios of isotopologues at no extra cost