Effect of slice orientation on reproducibility of fMRI motor activation at 3 Tesla

The effect of slice orientation on reproducibility and sensitivity of 3T fMRI activation using a motor task has been investigated in six normal volunteers. Four slice orientations were used; axial, oblique axial, coronal and sagittal. We applied analysis of variance (ANOVA) to suprathreshold voxel statistics to quantify variability in activation between orientations and between subjects. We also assessed signal detection accuracy in voxels across the whole brain by using a finite mixture model to fit receiver operating characteristic (ROC) curves to the data. Preliminary findings suggest that suprathreshold cluster characteristics demonstrate high motor reproducibility across subjects and orientations, although a significant difference between slice orientations in number of activated voxels was demonstrated in left motor cortex but not cerebellum. Subtle inter-orientation differences are highlighted in the ROC analyses, which are not obvious by ANOVA; the oblique axial slice orientation offers the highest signal detection accuracy, whereas coronal slices give the lowest.     

Photorefractive solitons and light-induced resonance control in semiconductor CdZnTe

We demonstrate the formation of (1+1) - and (2+1) -dimensional solitons in photorefractive CdZnTe:V, exploiting the intensity-resonant behavior of the space-charge field. We control the resonance optically, facilitating a 10-mus soliton formation times with very low optical power.     

Optimized light-matter interaction and defect hole placement in photonic crystal cavity sensors

Photonic crystal slab cavities were investigated for increased light-matter interaction based on selective placement of sublattice hole sized defect holes inside L3 cavities. A multiple-hole defect (MHD) consisting of three defect holes placed in the regions of highest cavity mode field intensity were demonstrated through finite-difference time-domain simulations and experiments to exhibit the strongest light-matter interaction without introducing significant scattering losses. Compared to an L3 cavity without defect holes, these strategically designed three-hole MHD cavities presented higher quality factor and more than double the resonance wavelength shift upon exposure to a thin oxide and two small chemical molecules.     

Bivariate interpolation based on univariate subdivision schemes

The paper presents a bivariate subdivision scheme interpolating data consisting of univariate functions along equidistant parallel lines by repeated refinements. This method can be applied to the construction of a surface passing through a given set of parametric curves. Following the methodology of polysplines and tension surfaces, we define a local interpolator of four consecutive univariate functions, from which we sample a univariate function at the mid-point. This refinement step is the basis to an extension of the 4-point subdivision scheme to our setting. The bivariate subdivision scheme can be reduced to a countable number of univariate, interpolatory, non-stationary subdivision schemes. Properties of the generated interpolant are derived, such as continuity, smoothness and approximation order.     

Students Talk About Prime: What We Heard About Definitions

This study examines data from college students who worked in pairs to make decisions about a list of potential definitions of prime number. Analysis focused on the evidence each student pair cited when they decided whether or not a statement could be used as a definition for prime number. The purpose of this paper is to describe patterns in the ways students used the evidence they cited. Findings suggest that students attend to important features of mathematical definitions, with some students giving preference to usability and others giving preference to definitions that are unambiguous.     

On the decomposition theorem for meromorphic Fredholm resolvents

In this note results of B. Gramsch and W. Kaballo [8] on the decomposition of meromorphic (semi-) Fredholm resolvents are sharpened. A condition on an Orlicz function is given, under which the singular part in this decomposition can be chosen meromorphic inN , the ideal of -nuclear operators. Then the necessity of this condition is studied. Moreover, it is shown that for the rather steep Orlicz functions relevant to this question,N equalsS , the ideal of -approximable operators.Dedicated to Professor Albert Schneider on the occasion of his 60 ^th birthdayresearch supported by a grant from DAAD