Symmetry of Quantum Torus with Crossed Product Algebra

In this paper, we study the symmetry of quantum torus with the concept of crossed product algebra. As a classical counterpart, we consider the orbifold of classical torus with complex structure and investigate the transformation property of classical theta function. An invariant function under the group action is constructed as a variant of the classical theta function. Then our main issue, the crossed product algebra representation of quantum torus with complex structure under the symplectic group is analyzed as a quantum version of orbifolding. We perform this analysis with Manin's so-called model II quantum theta function approach. The symplectic group Sp(2n,Z) satisfies the consistency condition of crossed product algebra representation. However, only a subgroup of Sp(2n,Z) satisfies the consistency condition for orbifolding of quantum torus.Comment: LaTeX 17pages, changes in section 3 on crossed product algebr

Hilbert Series for Flavor Invariants of the Standard Model

The Hilbert series is computed for the lepton flavor invariants of the Standard Model with three generations including the right-handed neutrino sector needed to generate light neutrino masses via the see-saw mechanism. We also compute the Hilbert series of the quark flavor invariants for the case of four generations.Comment: 6 page

Is there an interaction between perceived direction and perceived aspect ratio in stereoscopic vision?

In monocular vision, the horizontal/vertical aspect ratio (shape) of a fronto-parallel rectangle can be based upon the comparison of the perceived directions of the rectangle's edges. In binocular vision of a typical three-dimensional scene (when occlusions are present) this is not the case: fronto-parallel rectangles would be perceived in a distorted fashion if an observer were to base perceived aspect ratio on the perceived directions of the rectangle's edges. We psychophysically investigated stereoscopically perceived aspect ratios of fronto-parallel occluding and occluded rectangles for various distances and fixation depths. We found that observers did not perceive the distortions as predicted on the basis of the above-mentioned comparison of the perceived visual direction of the edges of the rectangle. Our results strongly suggest that the mechanism that determines perceived aspect ratio is dissociated from the mechanism that determines perceived direction. The consequences of the findings for the Kanizsa, Poggendorff, and horizontal/vertical illusions are discussed

Removal of monocular interactions equates rivalry behavior for monocular, binocular, and stimulus rivalries

When the two eyes are presented with conflicting stimuli, perception starts to fluctuate over time (i.e., binocular rivalry). A similar fluctuation occurs when two patterns are presented to a single eye (i.e., monocular rivalry), or when they are swapped rapidly and repeatedly between the eyes (i.e., stimulus rivalry). Although all these cases lead to rivalry, in quantitative terms these modes of rivalry are generally found to differ significantly. We studied these different modes of rivalry with identical intermittently shown stimuli while varying the temporal layout of stimulation. We show that the quantitative differences between the modes of rivalry are caused by the presence of monocular interactions between the rivaling patterns; the introduction of a blank period just before a stimulus swap changed the number of rivalry reports to the extent that monocular and stimulus rivalries were inducible over ranges of spatial frequency content and contrast values that were nearly identical to binocular rivalry. Moreover when monocular interactions did not occur the perceptual dynamics of monocular, binocular, and stimulus rivalries were statistically indistinguishable. This range of identical behavior exhibited a monocular (∼50 ms) and a binocular (∼350 ms) limit. We argue that a common binocular, or pattern-based, mechanism determines the temporal constraints for these modes of rivalry

Morita Equivalence of Noncommutative Supertori

In this paper we study the extension of Morita equivalence of noncommutative tori to the supersymmetric case. The structure of the symmetry group yielding Morita equivalence appears to be intact but its parameter field becomes supersymmetrized having both body and soul parts. Our result is mainly in the two dimensional case in which noncommutative supertori have been constructed recently: The group $SO(2,2,V_{\Z}^0)$, where $V_{\Z}^0$ denotes Grassmann even number whose body part belongs to ${\Z}$, yields Morita equivalent noncommutative supertori in two dimensions.Comment: LaTeX 18 pages, the version appeared in JM

Multisensory Congruency as a Mechanism for Attentional Control over Perceptual Selection

The neural mechanisms underlying attentional selection of competing neural signals for awareness remains an unresolved issue. We studied attentional selection, using perceptually ambiguous stimuli in a novel multisensory paradigm that combined competing auditory and competing visual stimuli. We demonstrate that the ability to select, and attentively hold, one of the competing alternatives in either sensory modality is greatly enhanced when there is a matching cross-modal stimulus. Intriguingly, this multimodal enhancement of attentional selection seems to require a conscious act of attention, as passively experiencing the multisensory stimuli did not enhance control over the stimulus. We also demonstrate that congruent auditory or tactile information, and combined auditory–tactile information, aids attentional control over competing visual stimuli and visa versa. Our data suggest a functional role for recently found neurons that combine voluntarily initiated attentional functions across sensory modalities. We argue that these units provide a mechanism for structuring multisensory inputs that are then used to selectively modulate early (unimodal) cortical processing, boosting the gain of task-relevant features for willful control over perceptual awareness

Electromagnetic form factor via Minkowski and Euclidean Bethe-Salpeter amplitudes

The electromagnetic form factors calculated through Euclidean Bethe-Salpeter amplitude and through the light-front wave function are compared with the one found using the Bethe-Salpeter amplitude in Minkowski space. The form factor expressed through the Euclidean Bethe-Salpeter amplitude (both within and without static approximation) considerably differs from the Minkowski one, whereas form factor found in the light-front approach is almost indistinguishable from it.Comment: 3 pages, 2 figures. Contribution to the proceedings of the 20th International Conference on Few-Body Problems in Physics (FB20), Pisa, Italy, September 10-14, 2007. To be published in "Few-Body Systems

A categorical foundation for Bayesian probability

Given two measurable spaces $H$ and $D$ with countably generated $\sigma$-algebras, a perfect prior probability measure $P_H$ on $H$ and a sampling distribution $S: H \rightarrow D$, there is a corresponding inference map $I: D \rightarrow H$ which is unique up to a set of measure zero. Thus, given a data measurement $\mu: 1 \rightarrow D$, a posterior probability $\widehat{P_H}= I \circ \mu$ can be computed. This procedure is iterative: with each updated probability $P_H$, we obtain a new joint distribution which in turn yields a new inference map $I$ and the process repeats with each additional measurement. The main result uses an existence theorem for regular conditional probabilities by Faden, which holds in more generality than the setting of Polish spaces. This less stringent setting then allows for non-trivial decision rules (Eilenberg--Moore algebras) on finite (as well as non finite) spaces, and also provides for a common framework for decision theory and Bayesian probability.Comment: 15 pages; revised setting to more clearly explain how to incorporate perfect measures and the Giry monad; to appear in Applied Categorical Structure