3,701 research outputs found
Some Definability Results in Abstract Kummer Theory
Let be a semiabelian variety over an algebraically closed field, and let
be an irreducible subvariety not contained in a coset of a proper algebraic
subgroup of . We show that the number of irreducible components of
is bounded uniformly in , and moreover that the bound is
uniform in families .
We prove this by purely Galois-theoretic methods. This proof applies in the
more general context of divisible abelian groups of finite Morley rank. In this
latter context, we deduce a definability result under the assumption of the
Definable Multiplicity Property (DMP). We give sufficient conditions for finite
Morley rank groups to have the DMP, and hence give examples where our
definability result holds.Comment: 21 pages; minor notational fixe
Generic Automorphisms and Green Fields
We show that the generic automorphism is axiomatisable in the green field of
Poizat (once Morleyised) as well as in the bad fields which are obtained by
collapsing this green field to finite Morley rank. As a corollary, we obtain
"bad pseudofinite fields" in characteristic 0. In both cases, we give geometric
axioms. In fact, a general framework is presented allowing this kind of
axiomatisation. We deduce from various constructibility results for algebraic
varieties in characteristic 0 that the green and bad fields fall into this
framework. Finally, we give similar results for other theories obtained by
Hrushovski amalgamation, e.g. the free fusion of two strongly minimal theories
having the definable multiplicity property. We also close a gap in the
construction of the bad field, showing that the codes may be chosen to be
families of strongly minimal sets.Comment: Some minor changes; new: a result of the paper (Cor 4.8) closes a gap
in the construction of the bad fiel
Fields and Fusions: Hrushovski constructions and their definable groups
An overview is given of the various expansions of fields and fusions of
strongly minimal sets obtained by means of Hrushovski's amalgamation method, as
well as a characterization of the groups definable in these structures
Equidistribution towards the Green current for holomorphic maps
Let f be a non-invertible holomorphic endomorphism of a projective space and
f^n its iterate of order n. We prove that the pull-back by f^n of a generic (in
the Zariski sense) hypersurface, properly normalized, converge to the Green
current associated to f when n tends to infinity. We also give an analogous
result for the pull-back of positive closed (1,1)-currents.Comment: 34 pages, added theorem, propositions, references, to appear in Ann.
Sci. EN
A simple analytical description of the non-stationary dynamics in Ising spin systems
The analytical description of the dynamics in models with discrete variables (e.g. Isingspins) is a notoriously difficult problem, that can be tackled only undersome approximation.Recently a novel variational approach to solve the stationary dynamical regime has beenintroduced by Pelizzola [Eur. Phys. J. B, 86 (2013) 120], where simpleclosed equations arederived under mean-field approximations based on the cluster variational method. Here wepropose to use the same approximation based on the cluster variational method also for thenon-stationary regime, which has not been considered up to now within this framework. Wecheck the validity of this approximation in describing the non-stationary dynamical regime ofseveral Ising models defined on Erdos-R Ìenyi random graphs: westudy ferromagnetic modelswith symmetric and partially asymmetric couplings, models with randomfields and also spinglass models. A comparison with the actual Glauber dynamics, solvednumerically, showsthat one of the two studied approximations (the so-called âdiamondâapproximation) providesvery accurate results in all the systems studied. Only for the spin glass models we find somesmall discrepancies in the very low temperature phase, probably due to the existence of alarge number of metastable states. Given the simplicity of the equations to be solved, webelieve the diamond approximation should be considered as the âminimalstandardâ in thedescription of the non-stationary regime of Ising-like models: any new method pretending toprovide a better approximate description to the dynamics of Ising-like models should performat least as good as the diamond approximation
Rational physical agent reasoning beyond logic
The paper addresses the problem of defining a theoretical physical agent framework that satisfies practical requirements of programmability by non-programmer engineers and at the same time permitting fast realtime operation of agents on digital computer networks. The objective of the new framework is to enable the satisfaction of performance requirements on autonomous vehicles and robots in space exploration, deep underwater exploration, defense reconnaissance, automated manufacturing and household automation
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