37,594 research outputs found
Mean-Field Pontryagin Maximum Principle
International audienceWe derive a Maximum Principle for optimal control problems with constraints given by the coupling of a system of ordinary differential equations and a partial differential equation of Vlasov-type with smooth interaction kernel. Such problems arise naturally as Gamma-limits of optimal control problems constrained by ordinary differential equations, modeling, for instance, external interventions on crowd dynamics by means of leaders. We obtain these first-order optimality conditions in the form of Hamiltonian flows in the Wasserstein space of probability measures with forward-backward boundary conditions with respect to the first and second marginals, respectively. In particular, we recover the equations and their solutions by means of a constructive procedure, which can be seen as the mean-field limit of the Pontryagin Maximum Principle applied to the optimal control problem for the discretized density, under a suitable scaling of the adjoint variables
Sparse Control of Alignment Models in High Dimension
For high dimensional particle systems, governed by smooth nonlinearities
depending on mutual distances between particles, one can construct
low-dimensional representations of the dynamical system, which allow the
learning of nearly optimal control strategies in high dimension with
overwhelming confidence. In this paper we present an instance of this general
statement tailored to the sparse control of models of consensus emergence in
high dimension, projected to lower dimensions by means of random linear maps.
We show that one can steer, nearly optimally and with high probability, a
high-dimensional alignment model to consensus by acting at each switching time
on one agent of the system only, with a control rule chosen essentially
exclusively according to information gathered from a randomly drawn
low-dimensional representation of the control system.Comment: 39 page
On the extraction of spectral quantities with open boundary conditions
We discuss methods to extract decay constants, meson masses and gluonic
observables in the presence of open boundary conditions. The ensembles have
been generated by the CLS effort and have 2+1 flavors of O(a)-improved Wilson
fermions with a small twisted-mass term as proposed by L\"uscher and Palombi.
We analyse the effect of the associated reweighting factors on the computation
of different observables.Comment: 7 pages, talk presented at the 32nd International Symposium on
Lattice Field Theory - Lattice 2014, Columbia University New Yor
Finite groups acting on 3-manifolds and cyclic branched coverings of knots
We are interested in finite groups acting orientation-preservingly on
3-manifolds (arbitrary actions, ie not necessarily free actions). In particular
we consider finite groups which contain an involution with nonempty connected
fixed point set. This condition is satisfied by the isometry group of any
hyperbolic cyclic branched covering of a strongly invertible knot as well as by
the isometry group of any hyperbolic 2-fold branched covering of a knot in the
3-sphere. In the paper we give a characterization of nonsolvable groups of this
type. Then we consider some possible applications to the study of cyclic
branched coverings of knots and of hyperelliptic diffeomorphisms of
3-manifolds. In particular we analyze the basic case of two distinct knots with
the same cyclic branched covering.Comment: This is the version published by Geometry & Topology Monographs on 29
April 200
Moduli of -covers of curves: geometry and singularities
In a recent paper Chiodo and Farkas described the singular locus and the
locus of non-canonical singularities of the moduli space of level curves. In
this work we generalize their results to the moduli space of curves with a -cover for any finite group . We show that
non-canonical singularities are of two types: -curves, that is singularities
lifted from the moduli space of stable curves, and
-curves, that is new singularities entirely characterized by the dual graph
of the cover. Finally, we prove that in the case , the -locus is
empty, which is the first fundamental step in evaluating the Kodaira dimension
of .Comment: 35 pages. arXiv admin note: text overlap with arXiv:1504.0056
The gradient flow coupling from numerical stochastic perturbation theory
Perturbative calculations of gradient flow observables are technically
challenging. Current results are limited to a few quantities and, in general,
to low perturbative orders. Numerical stochastic perturbation theory is a
potentially powerful tool that may be applied in this context. Precise results
using these techniques, however, require control over both statistical and
systematic uncertainties. In this contribution, we discuss some recent
algorithmic developments that lead to a substantial reduction of the cost of
the computations. The matching of the coupling with the
gradient flow coupling in a finite box with Schr\"odinger functional boundary
conditions is considered for illustration.Comment: Talk given at the 34th annual International Symposium on Lattice
Field Theory, 24-30 July 2016, University of Southampton, UK; LaTeX source, 7
pages, 2 figure
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