Diffusion properties of cortical and pericortical tissue: regional variations, reliability and methodological issues

Characterizing the diffusion properties of cortical tissue is complicated by intersubject variability in the relative locations of gyri and sulci. Here we extend methods of measuring the average diffusion properties of gyral and sulcal structures after they have been aligned to a common template of cortical surface anatomy. Diffusion tensor image (DTI) data were gathered from 82 young subjects and co-registered with high-resolution T1 images that had been inflated and co-registered to a hemispherically unified spherical coordinate system based on FreeSurfer. We analyzed fractional anisotropy (FA), mean diffusivity (MD) and the novel quantity of cortical primary diffusion direction (cPDD) at five surfaces parallel to the white/gray junction, spanning approximately 5 mm from the pial surface into white matter. FA increased with increasing depth, whereas MD and cPDD were reduced. There were highly significant and reliable regional differences in FA, MD and cPDD as well as systematic differences between cortical lobes and between the two hemispheres. The influence of nearby cortical spinal fluid (CSF), local cortical curvature and thickness, and sulcal depth was also investigated. We found that FA correlated significantly with cortical curvature and sulcal depth, while MD was strongly influenced by nearby CSF. The measurement of FA, MD and cPDD near the cortical surface clarifies the organization of fiber projections to and from the cortex.     

Magnetic properties of stable structures of small binary clusters

We have studied the optimum geometries and the magnetic behavior of small binary Fe_nGe_m (n+m≤4) clusters usingab initio spin-polarized density functional calculations. Our results reveal that the optimized clusters present high values in the HOMO–LUMO gap and generally prefer structures with high geometries, the local magnetic moments at Fe atoms present an enhancement with respect to Fe bulk magnetization, whereas the Ge atoms present local magnetic moments whose modulus take significative values. The magnetic coupling between Fe and Ge atoms is mainly antiferromagnetic-like. All the clusters studied here present a charge transference from Fe atoms to Ge atoms.     

Fractional motions

Brownian motion is the archetypal model for random transport processes in science and engineering. Brownian motion displays neither wild fluctuations (the “Noah effect”), nor long-range correlations (the “Joseph effect”). The quintessential model for processes displaying the Noah effect is Lévy motion, the quintessential model for processes displaying the Joseph effect is fractional Brownian motion, and the prototypical model for processes displaying both the Noah and Joseph effects is fractional Lévy motion. In this paper we review these four random-motion models–henceforth termed “fractional motions” –via a unified physical setting that is based on Langevin’s equation, the Einstein–Smoluchowski paradigm, and stochastic scaling limits. The unified setting explains the universal macroscopic emergence of fractional motions, and predicts–according to microscopic-level details–which of the four fractional motions will emerge on the macroscopic level. The statistical properties of fractional motions are classified and parametrized by two exponents—a “Noah exponent” governing their fluctuations, and a “Joseph exponent” governing their dispersions and correlations. This self-contained review provides a concise and cohesive introduction to fractional motions.     

Solvability of the fractional hyperbolic Keller–Segel system

We study a new nonlocal approach to the mathematical modelling of the chemotaxis problem, which describes the random motion of a certain population due to a substance concentration. Considering the initial–boundary value problem for the fractional hyperbolic Keller–Segel model, we prove the solvability of the problem. The solvability result relies mostly on fractional calculus and kinetic formulation of scalar conservation laws.     

S-wave baryons in an equally mixed scalar-vector square root potential model of independent quarks

A relativistic model of independent quarks based on Dirac equation with an equally mixed scalar-vector square root confining potential is used to compute the quark core contributions to the static properties like magnetic moments, charge radii and axial vector coupling constant ratios of the baryon octet. The results obtained with appropriate corrections due to centre-of-mass motion agree fairly well with experimental values. The model is also extended to the study of magnetic moments of the quark core of baryons in the charmed andb-flavoured sectors and the overall predictions so obtained compare well with other model predictions.     

Some Useful Integral Representations for Information-Theoretic Analyses

This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact formulas for quantities that involve expectations of the logarithm of a positive random variable. Here, in the same spirit, we derive an exact integral representation (in one or two dimensions) of the moment of a nonnegative random variable, or the sum of such independent random variables, where the moment order is a general positive non-integer real (also known as fractional moments). The proposed formula is applied to a variety of examples with an information-theoretic motivation, and it is shown how it facilitates their numerical evaluations. In particular, when applied to the calculation of a moment of the sum of a large number, n, of nonnegative random variables, it is clear that integration over one or two dimensions, as suggested by our proposed integral representation, is significantly easier than the alternative of integrating over n dimensions, as needed in the direct calculation of the desired moment.     

Magneto-thermoelasticity with thermoelectric properties and fractional derivative heat transfer

In this work, a new model of the magneto-thermoelasticity theory has been constructed in the context of a new consideration of heat conduction with fractional derivative. A one-dimensional application for a conducting half-space of thermoelectric elastic material, which is thermally shocked in the presence of a magnetic field, has been solved using Laplace transform and state-space techniques (Ezzat, 2008 [1]). According to the numerical results and its graphs, a conclusion about the new theory of magneto-thermoelasticity has been constructed. The theories of coupled magneto-thermoelasticity and of generalized magneto-thermoelasticity with one relaxation time follow as limited cases. The result provides a motivation to investigate conducting thermoelectric materials as a new class of applicable materials.     

Spectral- and Cepstral-Based Measures During Continuous Speech: Capacity to Distinguish Dysphonia and Consistency Within a Speaker

Spectral- and cepstral-based acoustic measures are preferable to time-based measures for accurately representing dysphonic voices during continuous speech. Although these measures show promising relationships to perceptual voice quality ratings, less is known regarding their ability to differentiate normal from dysphonic voice during continuous speech and the consistency of these measures across multiple utterances by the same speaker. The purpose of this study was to determine whether spectral moments of the long-term average spectrum (LTAS) (spectral mean, standard deviation, skewness, and kurtosis) and cepstral peak prominence measures were significantly different for speakers with and without voice disorders when assessed during continuous speech. The consistency of these measures within a speaker across utterances was also addressed. Continuous speech samples from 27 subjects without voice disorders and 27 subjects with mixed voice disorders were acoustically analyzed. In addition, voice samples were perceptually rated for overall severity. Acoustic analyses were performed on three continuous speech stimuli from a reading passage: two full sentences and one constituent phrase. Significant between-group differences were found for both cepstral measures and three LTAS measures (P < 0.001): spectral mean, skewness, and kurtosis. These five measures also showed moderate to strong correlations to overall voice severity. Furthermore, high degrees of within-speaker consistency (correlation coefficients ≥0.89) across utterances with varying length and phonemic content were evidenced for both subject groups.     

Numerical Analysis of Electromagnetic Fields in Multiscale Model

Modeling technique for electromagnetic fields excited by antennas is an important topic in computational electromagnetics, which is concerned with the numerical solution of Maxwell's equations. In this paper, a novel hybrid technique that combines method of moments(MoM) with finite-difference time-domain(FDTD) method is presented to handle the problem. This approach employed Huygen's principle to realize the hybridization of the two classical numerical algorithms. For wideband electromagnetic data, the interpolation scheme is used in the MoM based on the dyadic Green's function. On the other hand, with the help of equivalence principle, the scattered electric and magnetic fields on the Huygen's surface calculated by MoM are taken as the sources for FDTD. Therefore, the electromagnetic fields in the environment can be obtained by employing finite-difference time-domain method. Finally, numerical results show the validity of the proposed technique by analyzing two canonical samples.     

Some insights in superdiffusive transport

In a wide range of systems, the relaxation in response to an initial pulse has been experimentally found to follow a nonlinear relationship for the mean squared displacement, of the kind 〈x²(t)〉∝t^α$〈x^2(t)〉\propto t^{\alpha }$, where α$\alpha$ may be greater or smaller than 1. Such phenomena have been described under the generic term of anomalous diffusion. “Lévy flights” stochastic processes lead to superdiffusive behaviour (1<α<2)$(1<\alpha <2)$ and have been recently proposed to model—among the others—the subsurface contaminant spread in highly heterogeneous media under the effects of water flow. In this paper, within the continuous-time random walk (CTRW) approach to anomalous diffusion, we compare the analytical solution of the approximated fractional diffusion equation (FDE) with the Monte Carlo one, obtained by simulating the superdiffusive behaviour of an ensemble of particle in a medium. We show that the two are neatly different as the process approaches the standard diffusive behaviour. We argue that this is due to a truncation in the Fourier space expansion introduced by the FDE approach. We propose a second-order correction to this expansion and numerically solve the CTRW model under this hypothesis: the accuracy of the results thus obtained is validated through Monte Carlo simulation over all the superdiffusive range. The same kind of discrepancy is shown to occur also in the derivation of the fractional moments of the distribution: analogous corrections are proposed and validated through the Monte Carlo approach.