A reversal coarse-grained analysis with application to an altered functional circuit in depression

Introduction: When studying brain function using functional magnetic resonance imaging (fMRI) data containing tens of thousands of voxels, a coarse-grained approach – dividing the whole brain into regions of interest – is applied frequently to investigate the organization of the functional network on a relatively coarse scale. However, a coarse-grained scheme may average out the fine details over small spatial scales, thus rendering it difficult to identify the exact locations of functional abnormalities. Methods: A novel and general approach to reverse the coarse-grained approach by locating the exact sources of the functional abnormalities is proposed. Results: Thirty-nine patients with major depressive disorder (MDD) and 37 matched healthy controls are studied. A circuit comprising the left superior frontal gyrus (SFGdor), right insula (INS), and right putamen (PUT) exhibit the greatest changes between the patients with MDD and controls. A reversal coarse-grained analysis is applied to this circuit to determine the exact location of functional abnormalities. Conclusions: The voxel-wise time series extracted from the reversal coarse-grained analysis (source) had several advantages over the original coarse-grained approach: (1) presence of a larger and detectable amplitude of fluctuations, which indicates that neuronal activities in the source are more synchronized; (2) identification of more significant differences between patients and controls in terms of the functional connectivity associated with the sources; and (3) marked improvement in performing discrimination tasks. A software package for pattern classification between controls and patients is available in Supporting Information

Demonstration of Deutsch's Algorithm on a Stable Linear-Optical Quantum Computer

We report an experimental demonstration of quantum Deutsch's algorithm by using linear-optical system. By employing photon's polarization and spatial modes, we implement all balanced and constant functions for quantum computer. The experimental system is very stable and the experimental data are excellent in accordance with the theoretical results.Comment: 7 pages, 4 figure

Higher theta series for unitary groups over function fields

In previous work, we defined certain virtual fundamental classes for special cycles on the moduli stack of Hermitian shtukas, and related them to the higher derivatives of non-singular Fourier coefficients of Siegel-Eisenstein series. In the present article, we construct virtual fundamental classes in greater generality, including those expected to relate to the higher derivatives of singular Fourier coefficients. We assemble these classes into "higher" theta series, which we conjecture to be modular. Two types of evidence are presented: structural properties affirming that the cycle classes behave as conjectured under certain natural operations such as intersection products, and verification of modularity in several special situations. One innovation underlying these results is a new approach to special cycles in terms of derived algebraic geometry.Comment: Comments welcome