Predicting the connectivity of primate cortical networks from topological and spatial node properties

The organization of the connectivity between mammalian cortical areas has become a major subject of study, because of its important role in scaffolding the macroscopic aspects of animal behavior and intelligence. In this study we present a computational reconstruction approach to the problem of network organization, by considering the topological and spatial features of each area in the primate cerebral cortex as subsidy for the reconstruction of the global cortical network connectivity. Starting with all areas being disconnected, pairs of areas with similar sets of features are linked together, in an attempt to recover the original network structure. Inferring primate cortical connectivity from the properties of the nodes, remarkably good reconstructions of the global network organization could be obtained, with the topological features allowing slightly superior accuracy to the spatial ones. Analogous reconstruction attempts for the C. elegans neuronal network resulted in substantially poorer recovery, indicating that cortical area interconnections are relatively stronger related to the considered topological and spatial properties than neuronal projections in the nematode. The close relationship between area-based features and global connectivity may hint on developmental rules and constraints for cortical networks. Particularly, differences between the predictions from topological and spatial properties, together with the poorer recovery resulting from spatial properties, indicate that the organization of cortical networks is not entirely determined by spatial constraints

Equality of symmetrized tensors and the coordinate ring of the flag variety

In this note we give a transparent proof of a result of da Cruz and Dias da Silva on the equality of symmetrized decomposable tensors. This will be done by explaining that their result follows from the fact that the coordinate ring of a flag variety is a unique factorization domain.Comment: 5 page

Practical characterization of quantum devices without tomography

Quantum tomography is the main method used to assess the quality of quantum information processing devices, but its complexity presents a major obstacle for the characterization of even moderately large systems. The number of experimental settings required to extract complete information about a device grows exponentially with its size, and so does the running time for processing the data generated by these experiments. Part of the problem is that tomography generates much more information than is usually sought. Taking a more targeted approach, we develop schemes that enable (i) estimating the fidelity of an experiment to a theoretical ideal description, (ii) learning which description within a reduced subset best matches the experimental data. Both these approaches yield a significant reduction in resources compared to tomography. In particular, we demonstrate that fidelity can be estimated from a number of simple experimental settings that is independent of the system size, removing an important roadblock for the experimental study of larger quantum information processing units.Comment: (v1) 11 pages, 1 table, 4 figures. (v2) See also the closely related work: arXiv:1104.4695 (v3) method extended to continuous variable systems (v4) updated to published versio

DEA investment strategy in the Brazilian stock market

This paper presents a multi-period investment strategy using Data Envelopment Analysis (DEA) in the Brazilian stock market. Results show that the returns based on the DEA strategy were superior to the returns of a Brazilian stock index in most of the 22 quarters analyzed, presenting a significant Jensen's alpha.