On the extremality of Hofer's metric on the group of Hamiltonian diffeomorphisms

Let M be a closed symplectic manifold, and let | | be a norm on the space of all smooth functions on M, which are zero-mean normalized with respect to the canonical volume form. We show that if | | is dominated from above by the L-Infinity-norm, and | | is invariant under the action of Hamiltonian diffeomorphisms, then it is also invariant under all volume preserving diffeomorphisms. We also prove that if | | is, additionally, not equivalent to the L-Infinity-norm, then the induced Finsler metric on the group of Hamiltonian diffeomorphisms on M vanishes identically.Comment: Latex, 17 page

Cognitive stories and the image of mathematics

This paper considers two models of embodied mathematical cognition (a modular model and a dynamic model), and analyses the image of mathematics that they support.; Este artículo considera dos modelos de cognición matemática corporizada (un modelo modular y un modelo dinámico), y analiza la imagen de las matemáticas que apoya

Cognitive stories and the image of mathematics

This paper considers two models of embodied mathematical cognition (a modular model and a dynamic model), and analyses the image of mathematics that they support.; Este artículo considera dos modelos de cognición matemática corporizada (un modelo modular y un modelo dinámico), y analiza la imagen de las matemáticas que apoya

The Logic of Invention

In this long-awaited sequel to The Invention of Culture, Roy Wagner tackles the logic and motives that underlie cultural invention. Could there be a single, logical factor that makes the invention of the distinction between self and other possible, much as specific human genes allow for language? Wagner explores what he calls “the reciprocity of perspectives” through a journey between Euro-American bodies of knowledge and his in-depth knowledge of Melanesian modes of thought. This logic grounds variants of the subject/object transformation, as Wagner works through examples such as the figure-ground reversal in Gestalt psychology, Lacan’s theory of the mirror-stage formation of the Ego, and even the self-recursive structure of the aphorism and the joke. Juxtaposing Wittgenstein’s and Leibniz’s philosophy with Melanesian social logic, Wagner explores the cosmological dimensions of the ways in which different societies develop models of self and the subject/object distinction

Utilizing Performance Records in Commercial Beef Herds.

4 p

Utilizing Performance Records in Commercial Beef Herds.

4 p

Proximity to ℓ1and Distortion in Asymptotic L1Spaces

AbstractFor an asymptotic ℓ1spaceXwith a basis (xi) certain asymptotic ℓ1constants,δα(X) are defined forα<ω1.δα(X) measures the equivalence between all normalized block bases (yi)ki=1of (xi) which areSα-admissible with respect to (xi) (Sαis theαth-Schreier class of sets) and the unit vector basis of ℓk1. This leads to the concept of the delta spectrum ofX,Δ(X), which reflects the behavior of stabilized limits ofδα(X). The analogues of these constants under all renormings ofXare also defined and studied. We investigateΔ(X) both in general and for spaces of bounded distortion. We also prove several results on distorting the classical Tsirelson's spaceTand its relatives

Evidence for Trait-Based Dominance in Occupancy among Fossil Taxa and the Decoupling of Macroecological and Macroevolutionary Success

Biological systems provide examples of differential success among taxa, from ecosystems with a few dominant species (ecological success) to clades that possess far more species than sister clades (macroevolutionary success). Macroecological success, the occupation by a species or clade of an unusually high number of areas, has received less attention. If macroecological success reflects heritable traits, then successful species should be related. Genera composed of species possessing those traits should occupy more areas than genera with comparable species richness that lack such traits. Alternatively, if macroecological success reflects autapomorphic traits, then generic occupancy should be a by-product of species richness among genera and occupancy of constituent species. We test this using Phanerozoic marine invertebrates. Although temporal patterns of species and generic occupancy are strongly correlated, inequality in generic occupancy typically is greater than expected. Genus-level patterns cannot be explained solely with species-level patterns. Within individual intervals, deviations between the observed and expected generic occupancy correlate with the number of lithological units (stratigraphic formations), particularly after controlling for geographic range and species richness. However, elevated generic occupancy is unrelated to or negatively associated with either generic geographic ranges or within-genus species richness. Our results suggest that shared traits among congeneric species encourage shortterm macroecological success without generating short-term macroevolutionary success. A broad niche may confer high occupancy but does not necessarily promote speciation. Supplemental files attached below (.zip