Statistical Network Analysis for Functional MRI: Summary Networks and Group Comparisons

Comparing weighted networks in neuroscience is hard, because the topological properties of a given network are necessarily dependent on the number of edges of that network. This problem arises in the analysis of both weighted and unweighted networks. The term density is often used in this context, in order to refer to the mean edge weight of a weighted network, or to the number of edges in an unweighted one. Comparing families of networks is therefore statistically difficult because differences in topology are necessarily associated with differences in density. In this review paper, we consider this problem from two different perspectives, which include (i) the construction of summary networks, such as how to compute and visualize the mean network from a sample of network-valued data points; and (ii) how to test for topological differences, when two families of networks also exhibit significant differences in density. In the first instance, we show that the issue of summarizing a family of networks can be conducted by adopting a mass-univariate approach, which produces a statistical parametric network (SPN). In the second part of this review, we then highlight the inherent problems associated with the comparison of topological functions of families of networks that differ in density. In particular, we show that a wide range of topological summaries, such as global efficiency and network modularity are highly sensitive to differences in density. Moreover, these problems are not restricted to unweighted metrics, as we demonstrate that the same issues remain present when considering the weighted versions of these metrics. We conclude by encouraging caution, when reporting such statistical comparisons, and by emphasizing the importance of constructing summary networks.Comment: 16 pages, 5 figure

Weighted Frechet Means as Convex Combinations in Metric Spaces: Properties and Generalized Median Inequalities

In this short note, we study the properties of the weighted Frechet mean as a convex combination operator on an arbitrary metric space, (Y,d). We show that this binary operator is commutative, non-associative, idempotent, invariant to multiplication by a constant weight and possesses an identity element. We also treat the properties of the weighted cumulative Frechet mean. These tools allow us to derive several types of median inequalities for abstract metric spaces that hold for both negative and positive Alexandrov spaces. In particular, we show through an example that these bounds cannot be improved upon in general metric spaces. For weighted Frechet means, however, such inequalities can solely be derived for weights equal or greater than one. This latter limitation highlights the inherent difficulties associated with working with abstract-valued random variables.Comment: 7 pages, 1 figure. Submitted to Probability and Statistics Letter

Humain et Paysage dans l'oeuvre littéraire de Valère Bernard (1860-1936)

Joëlle Ginestet, Université Toulouse Jean Jaurès, Conférence, Journée Valère Bernard, Espace Culturel de Graveson, 22/09/2012. L'art de la fin du XIX e siècle met en question les approches réalistes qui visent à donner l'illusion du vrai et, naturalistes qui se livrent à l'exploration du monde contemporain. Valère Bernard, dont l'oeuvre se constitue entre 1883 et 1936 1 , se situe du côté d'une activité artistique qui ne cherche pas à imiter ou donner à voir une nature vraisemblable. Il veut en sonder les mystères. Ses choix linguistiques, soit la langue française, soit la langue d'oc dans ses variantes dialectales provençale maritime, provençale rhodanienne, languedocienne, soit l'espéranto, soit la langue de bohémiens d'origines diverses, soit celle d'immigrés italiens, tous sont intimement liés à sa recherche du « Beau » dans la laideur d'une ville, Marseille, qui s'industrialise de plus en plus ; et, il le craint, les arts aussi. Tout en maîtrisant la gravure, la peinture et l'écriture, tout en appréciant la musique, la céramique, la sculpture, la photographie…, il se positionne par rapport à des possibilités esthétiques en estimant dès le départ que l'oeuvre d'imitation est une rechute dans l'instinct et une démarche servile. Pour lui l'Art est aussi la nature vue « à travers la sensibilité humaine » et il obéit aux lois profondes de l'Être qui sont « l'ordre, le rythme et l'harmonie »

A CORAVEL radial-velocity monitoring of S stars: symbiotic activity vs. orbital separation

Orbital elements are presented for the Tc-poor S stars HR 363 (= HD 7351) and HD 191226. With an orbital period of 4592 d (=12.6 y), HR 363 has the longest period known among S stars, and yet it is a strong X-ray source. Its X-ray flux is similar to that of HD 35155, an S star with one of the shortest orbital periods (640 d). This surprising result is put in perspective with other diagnostics of binary interaction observed in binary S stars. They reveal that there is no correlation between the level of binary interaction and the orbital period. This situation may be accounted for if the wind mass-loss rate from the giant is the principal factor controlling the activity level in these (detached) systems, via a stream of matter funneled through the inner Lagragian point.Comment: Astronomy & Astrophysics Supplements, 6 pages, 2 figures, 4 tables (LaTeX A&A). Also available at: http://obswww.unige.ch/~udry/cine/barium/barium.htm

Binaries among Ap and Am stars

The results of long-term surveys of radial velocities of cool Ap and Am stars are presented. There are two samples, one of about 100 Ap stars and the other of 86 Am stars. Both have been observed with the CORAVEL scanner from Observatoire de Haute-Provence (CNRS), France. The conspicuous lack of short-period binaries among cool Ap stars seems confirmed, although this may be the result of an observational bias; one system has a period as short as 1.6 days. A dozen new orbits could be determined, including that of one SB2 system. Considering the mass functions of 68 binaries from the literature and from our work, we conclude that the distribution of the mass ratios is the same for the Bp-Ap stars than for normal G dwarfs. Among the Am stars, we found 52 binaries, i.e. 60%; an orbit could be computed for 29 of them. Among these 29, there are 7 SB2 systems, one triple and one quadruple system. The 21 stars with an apparently constant radial velocity may show up later as long-period binaries with a high eccentricity. The mass functions of the SB1 systems are compatible with cool main-sequence companions, also suggested by ongoing spectral observations.Comment: 5 pages, 2 figures, to appear in: Proc. of the 26th workshop of the European Working Group on CP stars, Contrib. Astr. Obs. Skalnate Pleso Vol. 27, No