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Independent components in stimulus-related BOLD signals and estimation of the underlying neural responses
We measured blood oxygen level dependent (BOLD) responses to the onset of dynamic noise stimulation in defined regions of the primary retinotopic projection (V1) in visual cortex. The response waveforms showed a remarkable diversity across stimulus types, violating the basic assumption of a unitary general linear model of a uniform BOLD response function convolved with each stimulus sequence. We used independent component analysis (ICA) to analyze the component mechanisms contributing to these responses. The underlying neural responses for the components were estimated by nonlinear optimization through the Friston–Buxton hemodynamic model of the BOLD response. Our analysis suggests that one of the identified components reflected a sustained neural response to the stimulus and that another reflected an extremely slow neural response. A third component exhibited nonlinear change-specific transient responses. The first two components showed stable spatial structure in the V1 region of interest with respect to the eccentricity of the noise stimulus
Relative contributions of sustained and transient pathways to human stereoprocessing
AbstractIt has been proposed [Hubel & Livingstone (1987) Journal of Neuroscience, 7, 3378–3415] that stereopsis is mediated solely by magnocellular pathway in primates. This hypothesis was evaluated for humans in psychophysical experiments with dynamic random-noise stimuli, based on the sustained/transient relationship of behavior mediated by the two divisions of the LGN [Merigan & Maunsell (1993) Annual Review of Neuroscience, 16, 369–402]. The stereoscopic limits show that stereoscopic system is more sensitive to sustained random-dot stimuli than to transient ones. Quantitative modeling of the result implied a weak role for magnocellular input, suggests that human stereopsis is more strongly influenced by parvocellular input through the LGN
Endomorphisms of quantized Weyl algebras
Belov-Kanel and Kontsevich conjectured that the group of automorphisms of the
n'th Weyl algebra and the group of polynomial symplectomorphisms of C^2 are
canonically isomorphic. We discuss how this conjecture can be approached by
means of (second) quantized Weyl algebras at roots of unity
Violation of the phase space general covariance as a diffeomorphism anomaly in quantum mechanics
We consider a topological quantum mechanics described by a phase space path
integral and study the 1-dimensional analog for the path integral
representation of the Kontsevich formula. We see that the naive bosonic
integral possesses divergences, that it is even naively non-invariant and thus
is ill-defined. We then consider a super-extension of the theory which
eliminates the divergences and makes the theory naively invariant. This
super-extension is equivalent to the correct choice of measure and was
discussed in the literature. We then investigate the behavior of this extended
theory under diffeomorphisms of the extended phase space and despite of its
naive invariance find out that the theory possesses anomaly under nonlinear
diffeomorphisms. We localize the origin of the anomaly and calculate the lowest
nontrivial anomalous contribution.Comment: 36 page
The structure of 2D semi-simple field theories
I classify all cohomological 2D field theories based on a semi-simple complex
Frobenius algebra A. They are controlled by a linear combination of
kappa-classes and by an extension datum to the Deligne-Mumford boundary. Their
effect on the Gromov-Witten potential is described by Givental's Fock space
formulae. This leads to the reconstruction of Gromov-Witten invariants from the
quantum cup-product at a single semi-simple point and from the first Chern
class, confirming Givental's higher-genus reconstruction conjecture. The proof
uses the Mumford conjecture proved by Madsen and Weiss.Comment: Small errors corrected in v3. Agrees with published versio
Psi-floor diagrams and a Caporaso-Harris type recursion
Floor diagrams are combinatorial objects which organize the count of tropical
plane curves satisfying point conditions. In this paper we introduce Psi-floor
diagrams which count tropical curves satisfying not only point conditions but
also conditions given by Psi-classes (together with points). We then generalize
our definition to relative Psi-floor diagrams and prove a Caporaso-Harris type
formula for the corresponding numbers. This formula is shown to coincide with
the classical Caporaso-Harris formula for relative plane descendant
Gromov-Witten invariants. As a consequence, we can conclude that in our case
relative descendant Gromov-Witten invariants equal their tropical counterparts.Comment: minor changes to match the published versio
The Liouville-type theorem for integrable Hamiltonian systems with incomplete flows
For integrable Hamiltonian systems with two degrees of freedom whose
Hamiltonian vector fields have incomplete flows, an analogue of the Liouville
theorem is established. A canonical Liouville fibration is defined by means of
an "exact" 2-parameter family of flat polygons equipped with certain pairing of
sides. For the integrable Hamiltonian systems given by the vector field
on where
is a complex polynomial in 2 variables, geometric properties of
Liouville fibrations are described.Comment: 6 page
Projection on higher Landau levels and non-commutative geometry
The projection of a two dimensional planar system on the higher Landau levels
of an external magnetic field is formulated in the language of the non
commutative plane and leads to a new class of star products.Comment: 12 pages, latex, corrected versio
M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra
We show that the zeroth cohomology of M. Kontsevich's graph complex is
isomorphic to the Grothendieck-Teichmueller Lie algebra grt_1. The map is
explicitly described. This result has applications to deformation quantization
and Duflo theory. We also compute the homotopy derivations of the Gerstenhaber
operad. They are parameterized by grt_1, up to one class (or two, depending on
the definitions). More generally, the homotopy derivations of the (non-unital)
E_n operads may be expressed through the cohomology of a suitable graph
complex. Our methods also give a second proof of a result of H. Furusho,
stating that the pentagon equation for grt_1-elements implies the hexagon
equation
The Breakdown of Topology at Small Scales
We discuss how a topology (the Zariski topology) on a space can appear to
break down at small distances due to D-brane decay. The mechanism proposed
coincides perfectly with the phase picture of Calabi-Yau moduli spaces. The
topology breaks down as one approaches non-geometric phases. This picture is
not without its limitations, which are also discussed.Comment: 12 pages, 2 figure
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