Investigating directed influences between activated brain areas in a motor-response task using fMRI

Localization of cognitive processes is a strength of functional neuroimaging. However, information about functional interactions between brain areas is crucial for a deeper understanding of brain function. We applied vector autoregressive modeling in the context of Granger causality as a method to analyze directed connectivity in a standard event-related fMRI study using a simple auditory-motor paradigm. The basic idea is to use temporal information in stochastic time series of a brain region in order to predict signal time courses in other brain regions. Thus, we predicted that the method should demonstrate causal influence of the auditory cortex and the supplementary motor area (SMA) on primary motor cortex. Eleven right-handed healthy female subjects were instructed to press a ball with either their left or their right hand when hearing the command "left" or "right" in the scanner. Influence to the left motor cortex was found from bilateral auditory cortex as well as from the SMA in 9 of 11 subjects. Granger causality to the right motor cortex existed from bilateral auditory cortex in 5 and from SMA in 6 subjects. Granger causality to the SMA existed from right auditory cortex in 7 subjects and from left auditory cortex in 8 subjects. Our findings in a simple task show that even under suboptimal circumstances (a relatively long TR of 2440 ms), Granger causality can be a useful tool to explore effective connectivity. Temporally optimized scanning should increase that potential.     

An electrothermal instability: the influence of albedo boundary conditions on the stationary states of an exactly solvable model

In order to study the effect of partially reflective (albedo) boundary conditions on pattern formation and stability in reaction-diffusion systems, we have analyzed an exactly soluble model of an electrothermal instability: the Ballast resistor. The present results allow a continuous interpolation between the results corresponding to Neumann and Dirichlet boundary conditions, and they allow qualitative changes in the patterns to be followed.     

Analytical characterization of spectral anomalies in polychromatic apertured beams

The power spectrum of polychromatic apertured spherical waves changes strongly in the vicinity of phase singularities. A spectral shift effect is observed and, in some cases, a spectral switch occurs together with a broadening of the power spectrum. Low-order moments of the power spectrum are evaluated in points of the focal volume with spectral anomalies. First-order analytical expressions are proposed for the evaluation of the relative spectral shift and the relative spectral broadening in the transverse focal plane and along the optical axis. The influence of the fractional bandwidth and the selected singularity order is considered.     

Electrochemical impedance spectroscopy and linear polarization applied to evaluation of porosity of phosphate conversion coatings on electrogalvanized steels

In this work, electrochemical impedance spectroscopy and linear polarization are used in determining porosity of zinc phosphates, and of nickel and manganese modified zinc phosphates on electrogalvanized steel. The porosity of the phosphate layers ranges from 0.1% for the manganese-modified hopeite to 8% for hopeite, using the linear polarization and the electrochemical impedance spectroscopy techniques. The porosity values measured using the two techniques were in agreement. All impedance spectra of coated samples showed two steps, with two capacitive arcs and an inductive looping.     

Annealing effects on the magnetization of Co–Ni–B amorphous nanoparticles

Chemically prepared (Co_xNi_1−x)_1−yB_y (x=0.5, 0.75, 1; y≈0.4) amorphous fine particles were characterized by X-ray diffraction, DTA and TGA, and in situ magnetic measurement as a function of annealing temperature in an inert atmosphere. Magnetic measurement performed in as-prepared and 150°C annealed samples shows an increase of the saturation magnetization and magnetic moment after thermal treatment. Room temperature magnetization increases by factors of 3.5, 1.8, and 1.5, for x=0.5, 0.75, and 1, respectively. These measurements may indicate a local re-ordering of the amorphous phase at temperatures much lower than the full crystallization temperature.     

The embedding of General Relativity in five dimensions

We argue that General Relativistic solutions can always be locally embedded in Ricci-flat 5-dimensional spaces. This is a direct consequence of a theorem of Campbell (given here for both a timelike and spacelike extra dimension, together with a special case of this theorem) which guarantees that anyn-dimensional Riemannian manifold can be locally embedded in an (n+1)-dimensional Ricci-flat Riemannian manifold. This is of great importance in establishing local generality for a proposal recently put forward and developed by Wesson and others, whereby vacuum (4+1)-dimensional field equations give rise to (3+1)-dimensional equations with sources. An important feature of Campbell's procedure is that it automatically guarantees the compatibility of Gauss-Codazzi equations and therefore allows the construction of embeddings to be in principle always possible. We employ this procedure to construct such embeddings in a number of simple cases.     

Magnetic discontinuities in magnetohydrodynamic turbulence and in the solar wind

Recent measurements of solar wind turbulence report the presence of intermittent, exponentially distributed angular discontinuities in the magnetic field. In this Letter, we study whether such discontinuities can be produced by magnetohydrodynamic (MHD) turbulence. We detect the discontinuities by measuring the fluctuations of the magnetic field direction, Δθ, across fixed spatial increments Δx in direct numerical simulations of MHD turbulence with an imposed uniform guide field B(0). A large region of the probability density function (pdf) for Δθ is found to follow an exponential decay, proportional to exp(-Δθ/θ(*)), with characteristic angle θ(*)≈(14°)(b(rms)/B(0))(0.65) for a broad range of guide-field strengths. We find that discontinuities observed in the solar wind can be reproduced by MHD turbulence with reasonable ratios of b(rms)/B(0). We also observe an excess of small angular discontinuities when Δx becomes small, possibly indicating an increasing statistical significance of dissipation-scale structures. The structure of the pdf in this case closely resembles the two-population pdf seen in the solar wind. We thus propose that strong discontinuities are associated with inertial-range MHD turbulence, while weak discontinuities emerge from dissipation-range turbulence. In addition, we find that the structure functions of the magnetic field direction exhibit anomalous scaling exponents, which indicates the existence of intermittent structures.     

Carbon nanotubes as substrates for molecular spiropyran-based switches

We present a joint theory-experiment study investigating the excitonic absorption of spiropyran-functionalized carbon nanotubes. The functionalization is promising for engineering switches on a molecular level, since spiropyrans can be reversibly switched between two different conformations, inducing a distinguishable and measurable change of optical transition energies in the substrate nanotube. Here, we address the question of whether an optical read-out of such a molecular switch is possible. Combining density matrix and density functional theory, we first calculate the excitonic absorption of pristine and functionalized nanotubes. Depending on the switching state of the attached molecule, we observe a red-shift of transition energies by about 15?meV due to the coupling of excitons with the molecular dipole moment. Then we perform experiments measuring the absorption spectrum of functionalized carbon nanotubes for both conformations of the spiropyran molecule. We find good qualitative agreement between the theoretically predicted and experimentally measured red-shift, confirming the possibility for an optical read-out of the nanotube-based molecular switch.     

Quaternionic-valued Gravitation in 8D, Grand Unification and Finsler Geometry

A unification model of 4D gravity and SU(3)×SU(2)×U(1) Yang-Mills theory is presented. It is obtained from a Kaluza-Klein compactification of 8D quaternionic gravity on an internal CP ²=SU(3)/U(2) symmetric space. We proceed to explore the nonlinear connection formalism used in Finsler geometry to show how ordinary gravity in D=4+2 dimensions has enough degrees of freedom to encode a 4D gravitational and SU(5) Yang-Mills theory. This occurs when the internal two-dim space is a sphere S ². This is an appealing result because SU(5) is one of the candidate GUT groups. We conclude by discussing how the nonlinear connection formalism of Finsler geometry provides an infinite hierarchical extension of the Standard Model within a six dimensional gravitational theory due to the embedding of SU(3)×SU(2)×U(1)⊂SU(5)⊂SU(∞).