Distortion in transformation groups

We exhibit rigid rotations of spheres as distortion elements in groups of diffeomorphisms, thereby answering a question of J Franks and M Handel. We also show that every homeomorphism of a sphere is, in a suitable sense, as distorted as possible in the group Homeo(Sn), thought of as a discrete group. An appendix by Y de Cornulier shows that Homeo(Sn) has the strong boundedness property, recently introduced by G Bergman. This means that every action of the discrete group Homeo(Sn) on a metric space by isometries has bounded orbits

On the beliefs off the path: equilibrium refinement due to quantal response and level-k

This paper studies the relevance of equilibrium and nonequilibrium explanations of behavior, with respects to equilibrium refinement, as players gain experience. We investigate this experimentally using an incomplete information sequential move game with heterogeneous preferences and multiple perfect equilibria. Only the limit point of quantal response (the limiting logit equilibrium), and alternatively that of level-k reasoning (extensive form rationalizability), restricts beliefs off the equilibrium path. Both concepts converge to the same unique equilibrium, but the predictions differ prior to convergence. We show that with experience of repeated play in relatively constant environments, subjects approach equilibrium via the quantal response learning path. With experience spanning also across relatively novel environments, though, level-k reasoning tends to dominate

The performance of modularity maximization in practical contexts

Although widely used in practice, the behavior and accuracy of the popular module identification technique called modularity maximization is not well understood in practical contexts. Here, we present a broad characterization of its performance in such situations. First, we revisit and clarify the resolution limit phenomenon for modularity maximization. Second, we show that the modularity function Q exhibits extreme degeneracies: it typically admits an exponential number of distinct high-scoring solutions and typically lacks a clear global maximum. Third, we derive the limiting behavior of the maximum modularity Q_max for one model of infinitely modular networks, showing that it depends strongly both on the size of the network and on the number of modules it contains. Finally, using three real-world metabolic networks as examples, we show that the degenerate solutions can fundamentally disagree on many, but not all, partition properties such as the composition of the largest modules and the distribution of module sizes. These results imply that the output of any modularity maximization procedure should be interpreted cautiously in scientific contexts. They also explain why many heuristics are often successful at finding high-scoring partitions in practice and why different heuristics can disagree on the modular structure of the same network. We conclude by discussing avenues for mitigating some of these behaviors, such as combining information from many degenerate solutions or using generative models.Comment: 20 pages, 14 figures, 6 appendices; code available at http://www.santafe.edu/~aaronc/modularity

Electrically charged black branes in N=4^+, D=5 gauged supergravity

We analyze the properties of asymptotically AdS electrically charged black brane solutions in a consistent truncation of the N=4^+, D=5 Romans' gauged supergravity which contains gravity, SU(2) and U(1) gauge fields, and a dilaton possessing a nontrivial potential approaching a constant negative value at infinity. We find that the U(1)\times U(1) solutions become unstable to forming non-Abelian hair. These configurations emerge as zero modes of the Abelian solutions at critical temperature and a critical (nonvanishing) ratio of the electric charges and can be viewed as holographic p-wave superfluids.Comment: 12 pages, 4 figure

Decomposition of Bivariate Inequality Indicesby Attributes

We provide, for the class of relative bidimensional inequality indices, adecomposition of inequality into two univariate Atkinson-Kolm-Senindices and a third statistic which depends on the joint distribution ofresources.multidimensional inequality, relative indices, correlationincreasing transfers, copulas.

Decomposition of bivariate inequality indices by attributes

We provide, for the class of relative bidimensional inequality indices, a decomposition of inequality into two univariate Atkinson- Kolm-Sen indices and a third statistic which depends on the joint distribution of resources.multidimensional inequality ; relative indices ; correlation increasing transfers ; copulas

The mechanics of shuffle products and their siblings

We carry on the investigation initiated in [15] : we describe new shuffle products coming from some special functions and group them, along with other products encountered in the literature, in a class of products, which we name $\varphi$-shuffle products. Our paper is dedicated to a study of the latter class, from a combinatorial standpoint. We consider first how to extend Radford's theorem to the products in that class, then how to construct their bi-algebras. As some conditions are necessary do carry that out, we study them closely and simplify them so that they can be seen directly from the definition of the product. We eventually test these conditions on the products mentioned above

Larval description and phylogenetic placement of the Australian endemic genus Barretthydrus Lea, 1927 (Coleoptera: Dytiscidae: Hydroporinae: Hydroporini: Sternopriscina)

The larvae of the Australian endemic species Barretthydrus tibialis Lea, 1927 and Barretthydrus geminatus Lea, 1927 are described and illustrated for the first time, with detailed morphometric and chaetotaxic analyses of the cephalic capsule, head appendages, legs, last abdominal segment, and urogomphi. A parsimony analysis based on 118 informative larval characteristics of 34 species in all 10 tribes of the subfamily Hydroporinae was conducted using the program TNT. No clear larval morphological synapomorphies support the monophyletic origin of the tribe Hydroporini. Compared to other known larvae of Hydroporini, Barretthydrus Lea is postulated to share a closer phylogenetic relationship with Antiporus Sharp, which reinforces their inclusion in the subtribe Sternopriscina.Fil: Alarie, Yves. Laurentian University. Department of Biology; CanadáFil: Michat, Mariano Cruz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Biodiversidad y Biología Experimental y Aplicada. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Biodiversidad y Biología Experimental y Aplicada; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Biodiversidad y Biología Experimental. Laboratorio de Entomología; ArgentinaFil: Hendrich, L.. Zoologische Staatssammlung Munchen; AlemaniaFil: Watts, Chris H. S.. South Australian Museum; Australi