On Bohr-Sommerfeld bases

This paper combines algebraic and Lagrangian geometry to construct a special basis in every space of conformal blocks, the Bohr-Sommerfeld (BS) basis. We use the method of [D. Borthwick, T. Paul and A. Uribe, Legendrian distributions with applications to the non-vanishing of Poincar\'e series of large weight, Invent. math, 122 (1995), 359-402, preprint hep-th/9406036], whereby every vector of a BS basis is defined by some half-weighted Legendrian distribution coming from a Bohr-Sommerfeld fibre of a real polarization of the underlying symplectic manifold. The advantage of BS bases (compared to bases of theta functions in [A. Tyurin, Quantization and ``theta functions'', Jussieu preprint 216 (Apr 1999), e-print math.AG/9904046, 32pp.]) is that we can use information from the skillful analysis of the asymptotics of quantum states. This gives that Bohr-Sommerfeld bases are unitary quasi-classically. Thus we can apply these bases to compare the Hitchin connection with the KZ connection defined by the monodromy of the Knizhnik-Zamolodchikov equation in combinatorial theory (see, for example, [T. Kohno, Topological invariants for 3-manifolds using representations of mapping class group I, Topology 31 (1992), 203-230; II, Contemp. math 175} (1994), 193-217]).Comment: 43 pages, uses: latex2e with amsmath,amsfonts,theore

Long Lasting Egocentric Disorientation Induced by Normal Sensori-Motor Spatial Interaction

Perception of the cardinal directions of the body, right-left, up-down, ahead-behind, which appears so absolute and fundamental to the organisation of behaviour can in fact, be modified. Perhaps unsurprisingly, it has been shown that prolonged distorted perception of the orientation of body axes can be a consequence of disordered sensori-motor signals, including long-term prismatic adaptation and lesions of the central nervous system. We report the novel and surprising finding that a long-lasting distortion of perception of personal space can also be induced by an ecological pointing task without the artifice of distorting normal sensori-motor relationships.Twelve right-handed healthy adults performed the task of pointing with their arms, without vision, to indicate their subjective 'straight ahead', a task often used to assess the Egocentric Reference. This was performed before, immediately, and one day after a second task intended to 'modulate' perception of spatial direction. The 'modulating' task lasted 5 minutes and consisted of asking participants to point with the right finger to targets that appeared only in one (right or left) half of a computer screen. Estimates of the 'straight-ahead' during pre-test were accurate (inferior to 0.3 degrees deviation). Significantly, up to one day after performing the modulating task, the subjective 'straight-ahead' was deviated (by approximately 3.2 degrees) to the same side to which subjects had pointed to targets.These results reveal that the perception of directional axes for behaviour is readily influenced by interactions with the environment that involve no artificial distortion of normal sensori-motor-spatial relationships and does not necessarily conform to the cardinal directions as defined by the anatomy of orthostatic posture. We thus suggest that perceived space is a dynamic construction directly dependent upon our past experience about the direction and/or the localisation of our sensori-motor spatial interaction with environment

Trigonal curves and Galois Spin(8)-bundles

this paper we study the moduli of principal holomorphic Spin(8)-bundles over an algebraic curve. However, in order to exploit triality, and to obtain a moduli space with particularly nice properties, we impose some additional constraints on our bundles. We suppose that X is an algebraic curve with an S 3 -action. The group S 3 then acts in two ways on Spin(8)-bundles over a curve: by pull-back under the action on X, and by the triality action on the structure group. We call a Spin(8)-bundle Galois if these two actions coincide, that is, if it is a fixed point of the group actio

Quantitative fMRI assessment of the differences in lateralization of language-related brain activation in patients with temporal lobe epilepsy

Defining language lateralization is important to minimize morbidity in patients treated surgically for temporal lobe epilepsy (TLE). Functional magnetic resonance imaging (fMRI) offers a promising, noninvasive, alternative strategy to the Wada test. Here we have used fMRI to study healthy controls and patients with TLE in order to (i) define language-related activation patterns and their reproducibility; (ii) compare lateralization determined by fMRI with those from of the Wada test; and (iii) contrast different methods of assessing fMRI lateralization. Twelve healthy right-handed controls and 19 right-handed preoperative patients with TLE (12 left- and seven right-TLE) were studied at 3T using fMRI and a verbal fluency paradigm. A Wada test also was performed on each of the patients. Greater activation was found in several areas in the right hemisphere for the left-TLE group relative to controls or right-TLE patients. Relative hemispheric activations calculated based on either the extent or the mean signal change gave consistent results showing a more bihemispheric language representation in the left-TLE patients. There was good agreement between the Wada and fMRI results, although the latter were more sensitive to involvement of the nondominant right hemisphere. The reproducibility of the fMRI values was lowest for the more bihemispherically represented left-TLE patients. Overall, our results further demonstrate that noninvasive fMRI measures of language-related lateralization may provide a practical and reliable alternative to invasive testing for presurgical language lateralization in patients with TLE. The high proportion (33%) of left-TLE patients showing bilateral or right hemispheric language-related lateralization suggests that there is considerable plasticity of language representation in the brains of patients with intractable TLE