Discrete constant mean curvature nets in space forms: Steiner's formula and Christoffel duality

We show that the discrete principal nets in quadrics of constant curvature that have constant mixed area mean curvature can be characterized by the existence of a K\"onigs dual in a concentric quadric.Comment: 12 pages, 10 figures, pdfLaTeX (plain pdfTeX source included as bak file

Orthogonal nets and Clifford algebras

A Clifford algebra model for M"obius geometry is presented. The notion of Ribaucour pairs of orthogonal systems in arbitrary dimensions is introduced, and the structure equations for adapted frames are derived. These equations are discretized and the geometry of the occuring discrete nets and sphere congruences is discussed in a conformal setting. This way, the notions of ``discrete Ribaucour congruences'' and ``discrete Ribaucour pairs of orthogonal systems'' are obtained --- the latter as a generalization of discrete orthogonal systems in Euclidean space. The relation of a Cauchy problem for discrete orthogonal nets and a permutability theorem for the Ribaucour transformation of smooth orthogonal systems is discussed.Comment: Plain TeX, 16 pages, 4 picture

Periodic discrete conformal maps

A discrete conformal map (DCM) maps the square lattice to the Riemann sphere such that the image of every irreducible square has the same cross-ratio. This paper shows that every periodic DCM can be determined from spectral data (a hyperelliptic compact Riemann surface, called the spectral curve, equipped with some marked points). Each point of the map corresponds to a line bundle over the spectral curve so that the map corresponds to a discrete subgroup of the Jacobi variety. We derive an explicit formula for the generic maps using Riemann theta functions, describe the typical singularities and give a geometric interpretation of DCM's as a discrete version of the Schwarzian KdV equation. As such, the DCM equation is a discrete soliton equation and we describe the dressing action of a loop group on the set of DCM's. We also show that this action corresponds to a lattice of isospectral Darboux transforms for the finite gap solutions of the KdV equation.Comment: 41 pages, 10 figures, LaTeX2

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

Attentive Learning of Sequential Handwriting Movements: A Neural Network Model

Defense Advanced research Projects Agency and the Office of Naval Research (N00014-95-1-0409, N00014-92-J-1309); National Science Foundation (IRI-97-20333); National Institutes of Health (I-R29-DC02952-01)

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

Behavioural and neuroanatomical correlates of auditory speech analysis in primary progressive aphasias

Background Non-verbal auditory impairment is increasingly recognised in the primary progressive aphasias (PPAs) but its relationship to speech processing and brain substrates has not been defined. Here we addressed these issues in patients representing the non-fluent variant (nfvPPA) and semantic variant (svPPA) syndromes of PPA. Methods We studied 19 patients with PPA in relation to 19 healthy older individuals. We manipulated three key auditory parameters—temporal regularity, phonemic spectral structure and prosodic predictability (an index of fundamental information content, or entropy)—in sequences of spoken syllables. The ability of participants to process these parameters was assessed using two-alternative, forced-choice tasks and neuroanatomical associations of task performance were assessed using voxel-based morphometry of patients’ brain magnetic resonance images. Results Relative to healthy controls, both the nfvPPA and svPPA groups had impaired processing of phonemic spectral structure and signal predictability while the nfvPPA group additionally had impaired processing of temporal regularity in speech signals. Task performance correlated with standard disease severity and neurolinguistic measures. Across the patient cohort, performance on the temporal regularity task was associated with grey matter in the left supplementary motor area and right caudate, performance on the phoneme processing task was associated with grey matter in the left supramarginal gyrus, and performance on the prosodic predictability task was associated with grey matter in the right putamen. Conclusions Our findings suggest that PPA syndromes may be underpinned by more generic deficits of auditory signal analysis, with a distributed cortico-subcortical neuraoanatomical substrate extending beyond the canonical language network. This has implications for syndrome classification and biomarker development