Deformation quantization of gerbes

This is the first in a series of articles devoted to deformation quantization of gerbes. Here we give basic definitions and interpret deformations of a given gerbe as Maurer-Cartan elements of a differential graded Lie algebra (DGLA). We classify all deformations of a given gerbe on a symplectic manifold, as well as provide a deformation-theoretic interpretation of the first Rozansky-Witten class.Comment: Revised versio

A variant of the Mukai pairing via deformation quantization

We give a new method to prove a formula computing a variant of Caldararu's Mukai pairing \cite{Cal1}. Our method is based on some important results in the area of deformation quantization. In particular, part of the work of Kashiwara and Schapira in \cite{KS} as well as an algebraic index theorem of Bressler, Nest and Tsygan in \cite{BNT},\cite{BNT1} and \cite{BNT2} are used. It is hoped that our method is useful for generalization to settings involving certain singular varieties.Comment: 8 pages. Comments and suggestions welcom

Higher Descent Data as a Homotopy Limit

We define the 2-groupoid of descent data assigned to a cosimplicial 2-groupoid and present it as the homotopy limit of the cosimplicial space gotten after applying the 2-nerve in each cosimplicial degree. This can be applied also to the case of $n$-groupoids thus providing an analogous presentation of "descent data" in higher dimensions.Comment: Appeared in JHR

Task-Dependent Individual Differences in Prefrontal Connectivity

Recent advances in neuroimaging have permitted testing of hypotheses regarding the neural bases of individual differences, but this burgeoning literature has been characterized by inconsistent results. To test the hypothesis that differences in task demands could contribute to between-study variability in brain-behavior relationships, we had participants perform 2 tasks that varied in the extent of cognitive involvement. We examined connectivity between brain regions during a low-demand vigilance task and a higher-demand digit–symbol visual search task using Granger causality analysis (GCA). Our results showed 1) Significant differences in numbers of frontoparietal connections between low- and high-demand tasks 2) that GCA can detect activity changes that correspond with task-demand changes, and 3) faster participants showed more vigilance-related activity than slower participants, but less visual-search activity. These results suggest that relatively low-demand cognitive performance depends on spontaneous bidirectionally fluctuating network activity, whereas high-demand performance depends on a limited, unidirectional network. The nature of brain-behavior relationships may vary depending on the extent of cognitive demand. High-demand network activity may reflect the extent to which individuals require top-down executive guidance of behavior for successful task performance. Low-demand network activity may reflect task- and performance monitoring that minimizes executive requirements for guidance of behavior