Stochastic Processes Crossing from Ballistic to Fractional Diffusion with Memory: Exact Results

We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation we demonstrate how to choose the memory kernel to exactly respect the two different asymptotics of the diffusion process. Having done so we solve for the probability distribution function (pdf) as a continuous function which evolves inside a ballistically expanding domain. This general solution agrees for long times with the pdf obtained within the continuous random walk approach but it is much superior to this solution at shorter times where the effect of the ballistic regime is crucial

The 6-vertex model of hydrogen-bonded crystals with bond defects

It is shown that the percolation model of hydrogen-bonded crystals, which is a 6-vertex model with bond defects, is completely equivalent with an 8-vertex model in an external electric field. Using this equivalence we solve exactly a particular 6-vertex model with bond defects. The general solution for the Bethe-like lattice is also analyzed.Comment: 13 pages, 6 figures; added references for section

The determinants of gene order conservation in yeasts

Current intergene distance is shown to be consistently the strongest predictor of synteny conservation as expected under a simple null model, and other variables are of lesser importance

the Action of Water and Saline Solutions Upon Certain Slightly Soluble Phosphates. 1

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How biologically relevant are interaction-based modules in protein networks?

By applying a graph-based algorithm to yeast protein-interaction networks we have extracted modular structures and show that they can be validated using information from the phylogenetic conservation of the network components. We show that the module cores, the parts with the highest intramodular connectivity, are biologically relevant components of the networks. These constituents correlate only weakly with other levels of organization. We also discuss how such structures could be used for finding targets for antimicrobial drugs

Roughness and Finite Size Effect in the NYSE Stock-Price Fluctuations

We consider the roughness properties of NYSE (New York Stock Exchange) stock-price fluctuations. The statistical properties of the data are relatively homogeneous within the same day but the large jumps between different days prevent the extension of the analysis to large times. This leads to intrinsic finite size effects which alter the apparent Hurst (H) exponent. We show, by analytical methods, that finite size effects always lead to an enhancement of H. We then consider the effect of fat tails on the analysis of the roughness and show that the finite size effects are strongly enhanced by the fat tails. The non stationarity of the stock price dynamics also enhances the finite size effects which, in principle, can become important even in the asymptotic regime. We then compute the Hurst exponent for a set of stocks of the NYSE and argue that the interpretation of the value of H is highly ambiguous in view of the above results. Finally we propose an alternative determination of the roughness in terms of the fluctuations from moving averages with variable characteristic times. This permits to eliminate most of the previous problems and to characterize the roughness in useful way. In particular this approach corresponds to the automatic elimination of trends at any scale.Comment: 13 pages, 11 fugure

Exact Results for the Roughness of a Finite Size Random Walk

We consider the role of finite size effects on the value of the effective Hurst exponent H. This problem is motivated by the properties of the high frequency daily stock-prices. For a finite size random walk we derive some exact results based on Spitzer's identity. The conclusion is that finite size effects strongly enhance the value of H and the convergency to the asymptotic value (H=1/2) is rather slow. This result has a series of conceptual and practical implication which we discuss.Comment: 5 pages, 3 figure