Fractal rotation isolates mechanisms for form-dependent motion in human vision

Here, we describe a motion stimulus in which the quality of rotation is fractal. This makes its motion unavailable to the translationbased motion analysis known to underlie much of our motion perception. In contrast, normal rotation can be extracted through the aggregation of the outputs of translational mechanisms. Neural adaptation of these translation-based motion mechanisms is thought to drive the motion after-effect, a phenomenon in which prolonged viewing of motion in one direction leads to a percept of motion in the opposite direction. We measured the motion after-effects induced in static and moving stimuli by fractal rotation. The after-effects found were an order of magnitude smaller than those elicited by normal rotation. Our findings suggest that the analysis of fractal rotation involves different neural processes than those for standard translational motion. Given that the percept of motion elicited by fractal rotation is a clear example of motion derived from form analysis, we propose that the extraction of fractal rotation may reflect the operation of a general mechanism for inferring motion from changes in form.

Efficient modelling technique for fractal electromagnetic band-gap arrays

An efficient modelling technique is proposed for the analysis of a fractal-element electromagnetic band-gap array. The modelling is based on a method of moments modal analysis in conjunction with an interpolation scheme, which significantly accelerates the computations. The plane-wave and the surface-wave responses of the structure have been studied by means of transmission coefficients and dispersion diagrams. The multiband properties and the compactness of the proposed structure are presented. The technique is general and can be applied to arbitrary-shaped element geometries.

On Entropy-Based Molecular Descriptors: Statistical Analysis of Real and Synthetic Chemical Structures

This paper presents an analysis of entropy-based molecular descriptors. Specifically, we use real chemical structures, as well as synthetic isomeric structures, and investigate properties of and among descriptors with respect to the used data set by a statistical analysis. Our numerical results provide evidence that synthetic chemical structures are notably different to real chemical structures and, hence, should not be used to investigate molecular descriptors. Instead, an analysis based on real chemical structures is favorable. Further, we find strong hints that molecular descriptors can be partitioned into distinct classes capturing complementary information.

From perfect to fractal transmission in spin chains

Perfect state transfer is possible in modulated spin chains [Phys. Rev. Lett. 92, 187902 (2004)], imperfections, however, are likely to corrupt the state transfer. We study the robustness of this quantum communication protocol in the presence of disorder both in the exchange couplings between the spins and in the local magnetic field. The degradation of the fidelity can be suitably expressed, as a function of the level of imperfection and the length of the chain, in a scaling form. In addition the time signal of fidelity becomes fractal. We further characterize the state transfer by analyzing the spectral properties of the Hamiltonian of the spin chain.

Quantitative structure-toxicity relationships for chlorophenols to bioluminescent lux-marked bacteria using atom-based semi-empirical molecular-orbital descriptors

Literature data on the toxicity of chlorophenols for three luminescent bacteria (Vibrio fischeri, and the lux-marked Pseudomonas fluorescens 10586s pUCD607 and Burkholderia spp. RASC c2 (Tn4431)) have been analyzed in relation to a set of computed molecular physico-chemical properties. The quantitative structure-toxicity relationships of the compounds in each species showed marked differences when based upon semi-empirical molecular-orbital molecular and atom based properties. For mono-, di- and tri-chlorophenols multiple linear regression analysis of V. fischeri toxicity showed a good correlation with the solvent accessible surface area and the charge on the oxygen atom. This correlation successfully predicted the toxicity of the heavily chlorinated phenols, suggesting in V. fischeri only one overall mechanism is present for all chlorophenols. Good correlations were also found for RASC c2 with molecular properties, such as the surface area and the nucleophilic super-delocalizability of the oxygen. In contrast the best QSTR for P. fluorescens contained the 2nd order connectivity index and ELUMO suggesting a different, more reactive mechanism. Cross-species correlations were examined, and between V. fischeri and RASC c2 the inclusion of the minimum value of the nucleophilic susceptibility on the ring carbons produced good results. Poorer correlations were found with P. fluorescens highlighting the relative similarity of V. fischeri and RASC c2, in contrast to that of P. fluorescens.

Are power laws that estimate fractal dimension a good descriptor of soil structure and its link to soil biological properties?

The study of interrelationships between soil structure and its functional properties is complicated by the fact that the quantitative description of soil structure is challenging. Soil scientists have tackled this challenge by taking advantage of approaches such as fractal geometry, which describes soil architectural complexity through a scaling exponent (D) relating mass and numbers of particles/aggregates to particle/aggregate size. Typically, soil biologists use empirical indices such as mean weight diameters (MWD) and percent of water stable aggregates (WSA), or the entire size distribution, and they have successfully related these indices to key soil features such as C and N dynamics and biological promoters of soil structure. Here, we focused on D, WSA and MWD and we tested whether: D estimated by the exponent of the power law of number-size distributions is a good and consistent correlate of MWD and WSA; D carries information that differs from MWD and WSA; the fraction of variation in D that is uncorrelated with MWD and WSA is related to soil chemical and biological properties that are thought to establish interdependence with soil structure (e.g., organic C, N, arbuscular mycorrhizal fungi). We analysed observational data from a broad scale field study and results from a greenhouse experiment where arbuscular mycorrhizal fungi (AMF) and collembola altered soil structure. We were able to develop empirical models that account for a highly significant and large portion of the correlation observed between WSA and MWD but we did not uncover the mechanisms that underlie this correlation. We conclude that most of the covariance between D and soil biotic (AMF, plant roots) and abiotic (C. N) properties can be accounted for by WSA and MWD. This result implies that the ecological effects of the fragmentation properties described by D and generally discussed under the framework of fractal models can be interpreted under the intuitive perspective of simpler indices and we suggest that the biotic components mostly impacted the largest size fractions, which dominate MWD, WSA and the scaling exponent ruling number-size distributions. (C) 2010 Elsevier Ltd. All rights reserved.