On the spectrum of a stretched spiral vortex

Corrections are found to the k^–5/3 spectrum of Lundgren [Phys. Fluids 25, 2193 (1982)] for a stretched spiral vortex model (a is the stretching strain rate and k the scalar wave number) of turbulent fine scales. These take the form of additional terms arising from the early time evolution, when the stretching of vortex lines is small. For the special case when the spiral takes the form of a rolled-up shear layer, it is shown that the composite spectrum is divergent, thus requiring the introduction of a finite early cutoff time tau1 in the time integral for the nonaxisymmetric contribution. The identity nuomega2 = 2nu[integral]0[infinity]k^2E(k)dk which gives the dissipation is then satisfied self-consistently. Direct numerical calculation of the energy spectrum from the approximate vorticity field for a special choice of spiral structure nevertheless indicates that the one-term k^–5/3-spectrum result is asymptotically valid in the inertial range provided atau1 is O(1) but that the numerically calculated dissipation spectrum appears to lie somewhere between an exp(–B1k2) and an exp(–B2k) form. It is also shown that the stretched, rolled-up shear-layer model predicts asymptotic shell-summed spectra of the energy dissipation and of the square of the vorticity, each asymptotically constant, with no power-law dependence, for k smaller than the Kolmogorov wave number.The corresponding one-dimensional spectra each show –log(k1) behavior for small k1. The extension of the model given by Pullin and Saffman [Phys. Fluids A 5, 126 (1993)] is reformulated by the introduction of a long-time cutoff in the vortex lifetime and an additional requirement that the vortex structures be approximately space filling. This gives a reduction in the number of model free-parameters but introduces a dependence of the calculated Kolmogorov constant and skewness on the ratio of the initial vortex radius to the equivalent Burgers-vortex radius. A scaling for this ratio in terms of the Taylor microscale Reynolds number is proposed in which the stretching strain is assumed to be provided by the large scales with spatial coherence limited to the maximum stretched length of the structures. Postdictions of the fourth-order flatness factor and of higher moments of the longitudinal velocity gradient statistics are compared with numerical simulation

Optimal constraint-based decision tree induction from itemset lattices

International audienceIn this article we show that there is a strong connection between decision tree learning and local pattern mining. This connection allows us to solve the computationally hard problem of finding optimal decision trees in a wide range of applications by post-processing a set of patterns: we use local patterns to construct a global model. We exploit the connection between constraints in pattern mining and constraints in decision tree induction to develop a framework for categorizing decision tree mining constraints. This framework allows us to determine which model constraints can be pushed deeply into the pattern mining process, and allows us to improve the state-of-the-art of optimal decision tree induction

Evolutionary approaches for the reverse-engineering of gene regulatory networks: A study on a biologically realistic dataset

<p>Abstract</p> <p>Background</p> <p>Inferring gene regulatory networks from data requires the development of algorithms devoted to structure extraction. When only static data are available, gene interactions may be modelled by a Bayesian Network (BN) that represents the presence of direct interactions from regulators to regulees by conditional probability distributions. We used enhanced evolutionary algorithms to stochastically evolve a set of candidate BN structures and found the model that best fits data without prior knowledge.</p> <p>Results</p> <p>We proposed various evolutionary strategies suitable for the task and tested our choices using simulated data drawn from a given bio-realistic network of 35 nodes, the so-called insulin network, which has been used in the literature for benchmarking. We assessed the inferred models against this reference to obtain statistical performance results. We then compared performances of evolutionary algorithms using two kinds of recombination operators that operate at different scales in the graphs. We introduced a niching strategy that reinforces diversity through the population and avoided trapping of the algorithm in one local minimum in the early steps of learning. We show the limited effect of the mutation operator when niching is applied. Finally, we compared our best evolutionary approach with various well known learning algorithms (MCMC, K2, greedy search, TPDA, MMHC) devoted to BN structure learning.</p> <p>Conclusion</p> <p>We studied the behaviour of an evolutionary approach enhanced by niching for the learning of gene regulatory networks with BN. We show that this approach outperforms classical structure learning methods in elucidating the original model. These results were obtained for the learning of a bio-realistic network and, more importantly, on various small datasets. This is a suitable approach for learning transcriptional regulatory networks from real datasets without prior knowledge.</p

An ion mobility mass spectrometer coupled with a cryogenic ion trap for recording electronic spectra of charged, isomer-selected clusters

Infrared and electronic spectra are indispensable for understanding the structural and energetic properties of charged molecules and clusters in the gas phase. However, the presence of isomers can potentially complicate the interpretation of spectra, even if the target molecules or clusters are mass-selected beforehand. Here, we describe an instrument for spectroscopically characterizing charged molecular clusters that have been selected according to both their isomeric form and their mass-to-charge ratio. Cluster ions generated by laser ablation of a solid sample are selected according to their collision cross sections with helium buffer gas using a drift tube ion mobility spectrometer and their mass-to-charge ratio using a quadrupole mass filter. The mobility- and mass-selected target ions are introduced into a cryogenically cooled, three-dimensional quadrupole ion trap where they are thermalized through inelastic collisions with an inert buffer gas (He or He/N2 mixture). Spectra of the molecular ions are obtained by tagging them with inert atoms or molecules (Ne and N2), which are dislodged following resonant excitation of an electronic transition, or by photodissociating the cluster itself following absorption of one or more photons. An electronic spectrum is generated by monitoring the charged photofragment yield as a function of wavelength. The capacity of the instrument is illustrated with the resonance-enhanced photodissociation action spectra of carbon clusters (Cn+) and polyacetylene cations (HC2nH+) that have been selected according to the mass-to-charge ratio and collision cross section with He buffer gas and of mass-selected Au2+ and Au2Ag+ clusters