On Guichard's nets and Cyclic systems

In the first part, we give a self contained introduction to the theory of cyclic systems in n-dimensional space which can be considered as immersions into certain Grassmannians. We show how the (metric) geometries on spaces of constant curvature arise as subgeometries of Moebius geometry which provides a slightly new viewpoint. In the second part we characterize Guichard nets which are given by cyclic systems as being Moebius equivalent to 1-parameter families of linear Weingarten surfaces. This provides a new method to study families of parallel Weingarten surfaces in space forms. In particular, analogs of Bonnet's theorem on parallel constant mean curvature surfaces can be easily obtained in this setting.Comment: 25 pages, plain Te

Generalized isothermic lattices

We study multidimensional quadrilateral lattices satisfying simultaneously two integrable constraints: a quadratic constraint and the projective Moutard constraint. When the lattice is two dimensional and the quadric under consideration is the Moebius sphere one obtains, after the stereographic projection, the discrete isothermic surfaces defined by Bobenko and Pinkall by an algebraic constraint imposed on the (complex) cross-ratio of the circular lattice. We derive the analogous condition for our generalized isthermic lattices using Steiner's projective structure of conics and we present basic geometric constructions which encode integrability of the lattice. In particular, we introduce the Darboux transformation of the generalized isothermic lattice and we derive the corresponding Bianchi permutability principle. Finally, we study two dimensional generalized isothermic lattices, in particular geometry of their initial boundary value problem.Comment: 19 pages, 11 figures; v2. some typos corrected; v3. new references added, higlighted similarities and differences with recent papers on the subjec

Willmore Surfaces of Constant Moebius Curvature

We study Willmore surfaces of constant Moebius curvature $K$ in $S^4$. It is proved that such a surface in $S^3$ must be part of a minimal surface in $R^3$ or the Clifford torus. Another result in this paper is that an isotropic surface (hence also Willmore) in $S^4$ of constant $K$ could only be part of a complex curve in $C^2\cong R^4$ or the Veronese 2-sphere in $S^4$. It is conjectured that they are the only examples possible. The main ingredients of the proofs are over-determined systems and isoparametric functions.Comment: 16 pages. Mistakes occured in the proof to the main theorem (Thm 3.6) has been correcte

The PT-symmetric brachistochrone problem, Lorentz boosts and non-unitary operator equivalence classes

The PT-symmetric (PTS) quantum brachistochrone problem is reanalyzed as quantum system consisting of a non-Hermitian PTS component and a purely Hermitian component simultaneously. Interpreting this specific setup as subsystem of a larger Hermitian system, we find non-unitary operator equivalence classes (conjugacy classes) as natural ingredient which contain at least one Dirac-Hermitian representative. With the help of a geometric analysis the compatibility of the vanishing passage time solution of a PTS brachistochrone with the Anandan-Aharonov lower bound for passage times of Hermitian brachistochrones is demonstrated.Comment: 12 pages, 2 figures, strongly extended versio

Modulated structures in electroconvection in nematic liquid crystals

Motivated by experiments in electroconvection in nematic liquid crystals with homeotropic alignment we study the coupled amplitude equations describing the formation of a stationary roll pattern in the presence of a weakly-damped mode that breaks isotropy. The equations can be generalized to describe the planarly aligned case if the orienting effect of the boundaries is small, which can be achieved by a destabilizing magnetic field. The slow mode represents the in-plane director at the center of the cell. The simplest uniform states are normal rolls which may undergo a pitchfork bifurcation to abnormal rolls with a misaligned in-plane director.We present a new class of defect-free solutions with spatial modulations perpendicular to the rolls. In a parameter range where the zig-zag instability is not relevant these solutions are stable attractors, as observed in experiments. We also present two-dimensionally modulated states with and without defects which result from the destabilization of the one-dimensionally modulated structures. Finally, for no (or very small) damping, and away from the rotationally symmetric case, we find static chevrons made up of a periodic arrangement of defect chains (or bands of defects) separating homogeneous regions of oblique rolls with very small amplitude. These states may provide a model for a class of poorly understood stationary structures observed in various highly-conducting materials ("prechevrons" or "broad domains").Comment: 13 pages, 13 figure

Discrimination of Timbre in Early Auditory Responses of the Human Brain

The issue of how differences in timbre are represented in the neural response still has not been well addressed, particularly with regard to the relevant brain mechanisms. Here we employ phasing and clipping of tones to produce auditory stimuli differing to describe the multidimensional nature of timbre. We investigated the auditory response and sensory gating as well, using by magnetoencephalography (MEG).Thirty-five healthy subjects without hearing deficit participated in the experiments. Two different or same tones in timbre were presented through conditioning (S1) – testing (S2) paradigm as a pair with an interval of 500 ms. As a result, the magnitudes of auditory M50 and M100 responses were different with timbre in both hemispheres. This result might support that timbre, at least by phasing and clipping, is discriminated in the auditory early processing. The second response in a pair affected by S1 in the consecutive stimuli occurred in M100 of the left hemisphere, whereas both M50 and M100 responses to S2 only in the right hemisphere reflected whether two stimuli in a pair were the same or not. Both M50 and M100 magnitudes were different with the presenting order (S1 vs. S2) for both same and different conditions in the both hemispheres.Our results demonstrate that the auditory response depends on timbre characteristics. Moreover, it was revealed that the auditory sensory gating is determined not by the stimulus that directly evokes the response, but rather by whether or not the two stimuli are identical in timbre

New results on solar neutrino fluxes from 192 days of Borexino data

We report the direct measurement of the ^7Be solar neutrino signal rate performed with the Borexino detector at the Laboratori Nazionali del Gran Sasso. The interaction rate of the 0.862 MeV ^7Be neutrinos is 49+-3(stat)+-4(syst) counts/(day * 100ton). The hypothesis of no oscillation for ^7Be solar neutrinos is inconsistent with our measurement at the 4sigma level. Our result is the first direct measurement of the survival probability for solar nu_e in the transition region between matter-enhanced and vacuum-driven oscillations. The measurement improves the experimental determination of the flux of ^7Be, pp, and CNO solar nu_e, and the limit on the magnetic moment of neutrinos

The Borexino detector at the Laboratori Nazionali del Gran Sasso

Borexino, a large volume detector for low energy neutrino spectroscopy, is currently running underground at the Laboratori Nazionali del Gran Sasso, Italy. The main goal of the experiment is the real-time measurement of sub MeV solar neutrinos, and particularly of the mono energetic (862 keV) Be7 electron capture neutrinos, via neutrino-electron scattering in an ultra-pure liquid scintillator. This paper is mostly devoted to the description of the detector structure, the photomultipliers, the electronics, and the trigger and calibration systems. The real performance of the detector, which always meets, and sometimes exceeds, design expectations, is also shown. Some important aspects of the Borexino project, i.e. the fluid handling plants, the purification techniques and the filling procedures, are not covered in this paper and are, or will be, published elsewhere (see Introduction and Bibliography).Comment: 37 pages, 43 figures, to be submitted to NI

Mood Modulates Auditory Laterality of Hemodynamic Mismatch Responses during Dichotic Listening

Hemodynamic mismatch responses can be elicited by deviant stimuli in a sequence of standard stimuli even during cognitive demanding tasks. Emotional context is known to modulate lateralized processing. Right-hemispheric negative emotion processing may bias attention to the right and enhance processing of right-ear stimuli. The present study examined the influence of induced mood on lateralized pre-attentive auditory processing of dichotic stimuli using functional magnetic resonance imaging (fMRI). Faces expressing emotions (sad/happy/neutral) were presented in a blocked design while a dichotic oddball sequence with consonant-vowel (CV) syllables in an event-related design was simultaneously administered. Twenty healthy participants were instructed to feel the emotion perceived on the images and to ignore the syllables. Deviant sounds reliably activated bilateral auditory cortices and confirmed attention effects by modulation of visual activity. Sad mood induction activated visual, limbic and right prefrontal areas. A lateralization effect of emotion-attention interaction was reflected in a stronger response to right-ear deviants in the right auditory cortex during sad mood. This imbalance of resources may be a neurophysiological correlate of laterality in sad mood and depression. Conceivably, the compensatory right-hemispheric enhancement of resources elicits increased ipsilateral processing

Less is more: neural mechanisms underlying anomia treatment in chronic aphasic patients.

Previous research with aphasic patients has shown that picture naming can be facilitated by concurrent phonemic cueing [e.g.initial phoneme(s) of the word that the patient is trying to retrieve], both as an immediate word retrieval technique, and when practiced repeatedly over time as a long-term anomia treatment. Here, to investigate the neural mechanisms supporting word retrieval, we adopted—for the first time—a functional magnetic resonance imaging task using the same naming procedure as it occurs during the anomia treatment process. Before and directly after a 6-week anomia treatment programme, 18 chronic aphasic stroke patients completed our functional magnetic resonance imaging protocol—a picture naming task aided by three different types of phonemic cues (whole words, initial phonemes, final phonemes) and a noise-control condition. Patients completed a naming task based on the training materials, and a more general comprehensive battery of language tests both before and after the anomia treatment, to determine the effectiveness and specificity of the therapy. Our results demonstrate that the anomia treatment was effective and specific to speech production, significantly improving both patients’ naming accuracy and reaction time immediately post-treatment (unstandardized effect size: 29% and 17%, respectively; Cohen’s d: 3.45 and 1.83). Longer term gains in naming were maintained 3 months later. Functional imaging results showed that both immediate and long-term facilitation of naming involved a largely overlapping bilateral frontal network including the right anterior insula, inferior frontal and dorsal anterior cingulate cortices, and the left premotor cortex. These areas were associated with a neural priming effect (i.e. reduced blood oxygen level-dependent signal) during both immediate (phonemically-cued versus control-cue conditions), and long-term facilitation of naming (i.e. treated versus untreated items). Of note is that different brain regions were sensitive to different phonemic cue types. Processing of whole word cues was associated with increased activity in the right angular gyrus; whereas partial word cues (initial and final phonemes) recruited the left supplementary motor area, and right anterior insula, inferior frontal cortex, and basal ganglia. The recruitment of multiple and bilateral areas may help explain why phonemic cueing is such a successful behavioural facilitation tool for anomia treatment. Our results have important implications for optimizing current anomia treatment approaches, developing new treatments, and improving speech outcome for aphasic patient