516 research outputs found
Hyper-symplectic structures on integrable systems
We prove that an integrable system over a symplectic manifold, whose
symplectic form is covariantly constant w.r.t. the Gauss-Manin connection,
carries a natural hyper-symplectic structure. Moreover, a special Kaehler
structure is induced on the base manifold.Comment: LaTeX file, 7 pages; to be published in Journal of Geometry and
Physic
Categorial mirror symmetry for K3 surfaces
We study the structure of a modified Fukaya category
associated with a K3 surface , and prove that whenever is an elliptic K3
surface with a section, the derived category of \fF(X) is equivalent to a
subcategory of the derived category of coherent sheaves on
the mirror K3 surface .Comment: 11 pages, AmsLatex. Exposition (hopefully) improved, one argument
simplifie
A Fourier-Mukai Transform for Stable Bundles on K3 Surfaces
We define a Fourier-Mukai transform for sheaves on K3 surfaces over \C, and
show that it maps polystable bundles to polystable ones. The role of ``dual''
variety to the given K3 surface is here played by a suitable component
of the moduli space of stable sheaves on . For a wide class of K3
surfaces can be chosen to be isomorphic to ; then the Fourier-Mukai
transform is invertible, and the image of a zero-degree stable bundle is
stable and has the same Euler characteristic as .Comment: Revised version, 15 pages AMSTeX with AMSppt.sty v. 2.1
Preface of the special issue on Model Checking of Software
Software Model Checking consists of a broad collection of techniques to tackle the complexity and the diversity in the use of software in safety-critical systems. The contributions in this special issue address some of the core problems in software model checking. The articles are based on papers selected from the 2013 SPIN Symposium on Model Checking of Software, an annual forum for practitioners and researchers interested in symbolic and state space-based techniques for the validation and analysis of software systems.The final publication is available at Springer via https://doi.org/10.1007/s10009-016-0414-5.(VLID)138711
Robust Online Monitoring of Signal Temporal Logic
Signal Temporal Logic (STL) is a formalism used to rigorously specify
requirements of cyberphysical systems (CPS), i.e., systems mixing digital or
discrete components in interaction with a continuous environment or analog com-
ponents. STL is naturally equipped with a quantitative semantics which can be
used for various purposes: from assessing the robustness of a specification to
guiding searches over the input and parameter space with the goal of falsifying
the given property over system behaviors. Algorithms have been proposed and
implemented for offline computation of such quantitative semantics, but only
few methods exist for an online setting, where one would want to monitor the
satisfaction of a formula during simulation. In this paper, we formalize a
semantics for robust online monitoring of partial traces, i.e., traces for
which there might not be enough data to decide the Boolean satisfaction (and to
compute its quantitative counterpart). We propose an efficient algorithm to
compute it and demonstrate its usage on two large scale real-world case studies
coming from the automotive domain and from CPS education in a Massively Open
Online Course (MOOC) setting. We show that savings in computationally expensive
simulations far outweigh any overheads incurred by an online approach
On the irreducibility of some quiver varieties
We prove that certain quiver varieties are irreducible and therefore are isomor-phic to Hilbert schemes of points of the total spaces of the bundles OP1( 12n) for n 65 1
Poisson Structures of Calogero-Moser and Ruijsenaars-Schneider Models
We examine the Hamiltonian structures of some Calogero-Moser and
Ruijsenaars-Schneider N-body integrable models. We propose explicit
formulations of the bihamiltonian structures for the discrete models, and
field-theoretical realizations of these structures. We discuss the relevance of
these realizations as collective-field theory for the discrete models.Comment: 15 pages, no figures; v2 references added, typos correcte
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