On computation of the greatest common divisor of several polynomials over a finite field

We propose a probabilistic algorithm to reduce computing the greatest common divisor of m polynomials over a finite field (which requires computing m−1 pairwise greatest common divisors) to computing the greatest common divisor of two polynomials over the same field.     

Approximate Entropy of Brain Network in the Study of Hemispheric Differences

Human brain, a dynamic complex system, can be studied with different approaches, including linear and nonlinear ones. One of the nonlinear approaches widely used in electroencephalographic (EEG) analyses is the entropy, the measurement of disorder in a system. The present study investigates brain networks applying approximate entropy (ApEn) measure for assessing the hemispheric EEG differences; reproducibility and stability of ApEn data across separate recording sessions were evaluated. Twenty healthy adult volunteers were submitted to eyes-closed resting EEG recordings, for 80 recordings. Significant differences in the occipital region, with higher values of entropy in the left hemisphere than in the right one, show that the hemispheres become active with different intensities according to the performed function. Besides, the present methodology proved to be reproducible and stable, when carried out on relatively brief EEG epochs but also at a 1-week distance in a group of 36 subjects. Nonlinear approaches represent an interesting probe to study the dynamics of brain networks. ApEn technique might provide more insight into the pathophysiological processes underlying age-related brain disconnection as well as for monitoring the impact of pharmacological and rehabilitation treatments.     

Multichannel transceiver dual-tuned RF coil for proton/sodium MR imaging of knee cartilage at 3 T

Sodium magnetic resonance (MR) imaging is a promising technique for detecting changes of proteoglycan (PG) content in cartilage associated with knee osteoarthritis. Despite its potential clinical benefit, sodium MR imaging in vivo is challenging because of intrinsically low sodium concentration and low MR signal sensitivity. Some of the challenges in sodium MR imaging may be eliminated by the use of a high-sensitivity radiofrequency (RF) coil, specifically, a dual-tuned (DT) proton/sodium RF coil which facilitates the co-registration of sodium and proton MR images and the evaluation of both physiochemical and structural properties of knee cartilage. Nevertheless, implementation of a DT proton/sodium RF coil is technically difficult because of the coupling effect between the coil elements (particularly at high field) and the required compact design with improved coil sensitivity. In this study, we applied a multitransceiver RF coil design to develop a DT proton/sodium coil for knee cartilage imaging at 3 T. With the new design, the size of the coil was minimized, and a high signal-to-noise ratio (SNR) was achieved. DT coil exhibited high levels of reflection S11 (～-21 dB) and transmission coefficient S12 (～-19 dB) for both the proton and sodium coils. High SNR (range 27-38) and contrast-to-noise ratio (CNR) (range 15-21) were achieved in sodium MR imaging of knee cartilage in vivo at 3-mm(3) isotropic resolution. This DT coil performance was comparable to that measured using a sodium-only birdcage coil (SNR of 28 and CNR of 20). Clinical evaluation of the DT coil on four normal subjects demonstrated a consistent acquisition of high-resolution proton images and measurement of relative sodium concentrations of knee cartilages without repositioning of the subjects during the same MR scanning session.     

Photorefractive solitons embedded in gratings in centrosymmetric crystals

We investigate (1+1D) spatial optical solitons embedded in a fixed-volume grating in centrosymmetric photorefractive crystals. We numerically identify a two-parameter soliton family and deduce both its existence surface and soliton profiles. For shallow gratings, the soliton Fourier spectrum exhibits three lobes located at the reciprocal lattice points -K, 0, and K. Soliton trapping is a consequence of both the self-induced nonlinear waveguide and the grating reflectivity, which prevents the breakaway of the lateral components. To provide a preliminary evaluation of soliton stability, we also investigate the propagation of slightly perturbed soliton profiles.     

Fast Drift and Diffusion in a Class of Isochronous Systems with the Windows Method

The aim of the paper is to deal with some peculiar difficulties arising from the use of the geometrical tool known as windows method in the context of the well known problem of Arnold’s diffusion for isochronous nearly-integrable Hamiltonian systems. Despite the simple features of the class of systems at hand, it is possible to show how the absence of an anisochrony term leads to several substantial differences in the application of the method, requiring some additional devices, such as non-equally spaced transition chains and variable windows. As a consequence, we show the existence of a set of unstable orbits, whose drifting time matches, up to a constant, the one obtained via variational methods.     

First glances at the transversity parton distribution through dihadron fragmentation functions

We present first observations of the transversity parton distribution based on an analysis of pion-pair production in deep-inelastic scattering off transversely polarized targets. The extraction of transversity relies on the knowledge of dihadron fragmentation functions, which we take from electron-positron annihilation measurements. This is the first attempt to determine the transversity distribution in the framework of collinear factorization.     

Phase-shifted Bragg microstructured optical fiber gratings utilizing infiltrated ferrofluids

Results are presented on the efficient spectral manipulation of uniform and chirped Bragg reflectors inscribed in microstructured optical fibers utilizing short lengths of ferrofluids infiltrated in their capillaries. The infiltrated ferrofluidic defects can generate either parasitic reflection notch features in uniform Bragg reflectors of up to 80% visibility and ~0.1 nm spectral shift or tunability of the bandwidth and strength reflection up to 100% when introduced into chirped gratings. Spectra are presented for different spatial positions and optical characteristics of the ferrofluidic section.     

Hardy's paradox and violation of a state-independent Bell inequality in time

Tests such as Bell's inequality and Hardy's paradox show that joint probabilities and correlations between distant particles in quantum mechanics are inconsistent with local realistic theories. Here we experimentally demonstrate these concepts in the time domain, using a photonic entangling gate to perform nondestructive measurements on a single photon at different times. We show that Hardy's paradox is much stronger in time and demonstrate the violation of a temporal Bell inequality independent of the quantum state, including for fully mixed states.