Multiscaling and Structure Functions in Turbulence: An Alternative Approach

We propose an alternative formulation of structure functions for the velocity field in fully developed turbulence. Instead of averaging moments of the velocity differences as a function of the distance, we suggest to average moments of the distances as a function of the velocity difference. This is like an ``inverted'' structure function, with a different statistics. On the basis of shell model calculations we obtain a new multiscaling spectrum.Comment: 4 pages, REVTex, 4 figure

Inducing phase-locking and chaos in cellular oscillators by modulating the driving stimuli

Inflammatory responses in eucaryotic cells are often associated with oscillations in the nuclear-cytoplasmic translocation of the transcription factor NF-kB. In most laboratory realizations, the oscillations are triggered by a cytokine stimulus, like the tumor necrosis factor alpha, applied as a step change to a steady level. Here we use a mathematical model to show that an oscillatory external stimulus can synchronize the NF-kB oscillations into states where the ratios of the internal to external frequency are close to rational numbers. We predict a specific response diagram of the TNF-driven NF-kB system which exhibits bands of synchronization known as "Arnold tongues". Our model also suggests that when the amplitude of the external stimulus exceeds a certain threshold there is the possibility of coexistence of multiple different synchronized states and eventually chaotic dynamics of the nuclear NF-kB concentration. This could be used as a way of externally controlling immune response, DNA repair and apoptotic pathways.Comment: 12 pages, 3 figure

Moth Species New to Michigan

This is a compilation of moth species previously unrecorded from Michigan. Moore\u27s (1955) publication has been critically examined necessitating some specific changes. All questionable material has been determined by present day specialists in their particular fields. The McDunnough (1938) checklist is followed in the arrangement of the new data together with most of the recent changes in nomenclature as presented by Forbes (1948, 1954, 1960), Hardwick (1970), Hodges (1971), and Covell (1970, 1971). With the advent of more sophisticated collecting equipment and the easier access to Michigan\u27s Upper Peninsula a total of 154 species has been added. Many institutional and private collections have been examined including the large collection at Michigan State University which was not considered in the Moore publication

Entrainment of noise-induced and limit cycle oscillators under weak noise

Theoretical models that describe oscillations in biological systems are often either a limit cycle oscillator, where the deterministic nonlinear dynamics gives sustained periodic oscillations, or a noise-induced oscillator, where a fixed point is linearly stable with complex eigenvalues and addition of noise gives oscillations around the fixed point with fluctuating amplitude. We investigate how each class of model behaves under the external periodic forcing, taking the well-studied van der Pol equation as an example. We find that, when the forcing is additive, the noise-induced oscillator can show only one-to-one entrainment to the external frequency, in contrast to the limit cycle oscillator which is known to entrain to any ratio. When the external forcing is multiplicative, on the other hand, the noise-induced oscillator can show entrainment to a few ratios other than one-to-one, while the limit cycle oscillator shows entrain to any ratio. The noise blurs the entrainment in general, but clear entrainment regions for limit cycles can be identified as long as the noise is not too strong.Comment: 27 pages in preprint style, 12 figues, 2 tabl

Symbolic dynamics of biological feedback networks

We formulate general rules for a coarse-graining of the dynamics, which we term `symbolic dynamics', of feedback networks with monotone interactions, such as most biological modules. Networks which are more complex than simple cyclic structures can exhibit multiple different symbolic dynamics. Nevertheless, we show several examples where the symbolic dynamics is dominated by a single pattern that is very robust to changes in parameters and is consistent with the dynamics being dictated by a single feedback loop. Our analysis provides a method for extracting these dominant loops from short time series, even if they only show transient trajectories.Comment: 4 pages, 4 figure

Inverse Statistics in Economics : The gain-loss asymmetry

Inverse statistics in economics is considered. We argue that the natural candidate for such statistics is the investment horizons distribution. This distribution of waiting times needed to achieve a predefined level of return is obtained from (often detrended) historic asset prices. Such a distribution typically goes through a maximum at a time called the {\em optimal investment horizon}, $\tau^*_\rho$, since this defines the most likely waiting time for obtaining a given return $\rho$. By considering equal positive and negative levels of return, we report on a quantitative gain-loss asymmetry most pronounced for short horizons. It is argued that this asymmetry reflects the market dynamics and we speculate over the origin of this asymmetry.Comment: Latex, 6 pages, 3 figure