29,620 research outputs found
The dynamical hierarchy for Roelcke precompact Polish groups
We study several distinguished function algebras on a Polish group , under
the assumption that is Roelcke precompact. We do this by means of the
model-theoretic translation initiated by Ben Yaacov and Tsankov: we investigate
the dynamics of -categorical metric structures under the action of
their automorphism group. We show that, in this context, every strongly
uniformly continuous function (in particular, every Asplund function) is weakly
almost periodic. We also point out the correspondence between tame functions
and NIP formulas, deducing that the isometry group of the Urysohn sphere is
\Tame\cap\UC-trivial.Comment: 25 page
Minimization via duality
We show how to use duality theory to construct minimized versions of a wide class of automata. We work out three cases in detail: (a variant of) ordinary automata, weighted automata and probabilistic automata. The basic idea is that instead of constructing a maximal quotient we go to the dual and look for a minimal subalgebra and then return to the original category. Duality ensures that the minimal subobject becomes the maximally quotiented object
Graded Lagrangians, exotic topological D-branes and enhanced triangulated categories
I point out that (BPS saturated) A-type D-branes in superstring
compactifications on Calabi-Yau threefolds correspond to {\em graded} special
Lagrangian submanifolds, a particular case of the graded Lagrangian
submanifolds considered by M. Kontsevich and P. Seidel. Combining this with the
categorical formulation of cubic string field theory in the presence of
D-branes, I consider a collection of {\em topological} D-branes wrapped over
the same Lagrangian cycle and {\em derive} its string field action from first
principles. The result is a {\em -graded} version of super-Chern-Simons
field theory living on the Lagrangian cycle, whose relevant string field is a
degree one superconnection in a -graded superbundle, in the sense
previously considered in mathematical work of J. M. Bismutt and J. Lott. This
gives a refined (and modified) version of a proposal previously made by C.
Vafa. I analyze the vacuum deformations of this theory and relate them to
topological D-brane composite formation, by using the general formalism
developed in a previous paper. This allows me to identify a large class of
topological D-brane composites (generalized, or `exotic' topological D-branes)
which do not admit a traditional description. Among these are objects which
correspond to the `covariantly constant sequences of flat bundles' considered
by Bismut and Lott, as well as more general structures, which are related to
the enhanced triangulated categories of Bondal and Kapranov. I also give a
rough sketch of the relation between this construction and the large radius
limit of a certain version of the `derived category of Fukaya's category'.Comment: 31 pages, 4 figures, minor typos corrected; v3: changed to JHEP styl
From Simple to Complex and Ultra-complex Systems:\ud A Paradigm Shift Towards Non-Abelian Systems Dynamics
Atoms, molecules, organisms distinguish layers of reality because of the causal links that govern their behavior, both horizontally (atom-atom, molecule-molecule, organism-organism) and vertically (atom-molecule-organism). This is the first intuition of the theory of levels. Even if the further development of the theory will require imposing a number of qualifications to this initial intuition, the idea of a series of entities organized on different levels of complexity will prove correct. Living systems as well as social systems and the human mind present features remarkably different from those characterizing non-living, simple physical and chemical systems. We propose that super-complexity requires at least four different categorical frameworks, provided by the theories of levels of reality, chronotopoids, (generalized) interactions, and anticipation
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