207,012 research outputs found
Solving the G-problems in less than 500 iterations: Improved efficient constrained optimization by surrogate modeling and adaptive parameter control
Constrained optimization of high-dimensional numerical problems plays an
important role in many scientific and industrial applications. Function
evaluations in many industrial applications are severely limited and no
analytical information about objective function and constraint functions is
available. For such expensive black-box optimization tasks, the constraint
optimization algorithm COBRA was proposed, making use of RBF surrogate modeling
for both the objective and the constraint functions. COBRA has shown remarkable
success in solving reliably complex benchmark problems in less than 500
function evaluations. Unfortunately, COBRA requires careful adjustment of
parameters in order to do so.
In this work we present a new self-adjusting algorithm SACOBRA, which is
based on COBRA and capable to achieve high-quality results with very few
function evaluations and no parameter tuning. It is shown with the help of
performance profiles on a set of benchmark problems (G-problems, MOPTA08) that
SACOBRA consistently outperforms any COBRA algorithm with fixed parameter
setting. We analyze the importance of the several new elements in SACOBRA and
find that each element of SACOBRA plays a role to boost up the overall
optimization performance. We discuss the reasons behind and get in this way a
better understanding of high-quality RBF surrogate modeling
Hanany-Witten effect and SL(2,Z) dualities in matrix models
We provide tests of dualities for three-dimensional N=4 quiver SCFTs with
brane realizations in IIB string theory, by matching their exact partition
functions on . The dualities are generated by SL(2,Z) transformations and
Hanany-Witten 5-brane moves. These contain mirror symmetry as well as dualities
identifiying fixed points of Yang-Mills quivers and Chern-Simons theories. The
partition function is given by a matrix model, that can be nicely rearranged
into a sequence of factors mimicking the brane realization. Identities obeyed
by these elementary factors can be used to match the partition functions of
dual theories, providing tests for the full web of dualities. In particular we
are able to check mirror symmetry for linear and circular quivers with gauge
nodes of arbitrary ranks. Our analysis also leads to a proof of a conjectured
formula evaluating the matrix models of linear quiver theories.Comment: 65 pages, 23 figures, v2, minor clarifications added, version
published on JHE
Conformally maximal metrics for Laplace eigenvalues on surfaces
The paper is concerned with the maximization of Laplace eigenvalues on
surfaces of given volume with a Riemannian metric in a fixed conformal class. A
significant progress on this problem has been recently achieved by
Nadirashvili-Sire and Petrides using related, though different methods. In
particular, it was shown that for a given , the maximum of the -th
Laplace eigenvalue in a conformal class on a surface is either attained on a
metric which is smooth except possibly at a finite number of conical
singularities, or it is attained in the limit while a "bubble tree" is formed
on a surface. Geometrically, the bubble tree appearing in this setting can be
viewed as a union of touching identical round spheres. We present another proof
of this statement, developing the approach proposed by the second author and Y.
Sire. As a side result, we provide explicit upper bounds on the topological
spectrum of surfaces.Comment: 52 pages, 3 figures, added a section on explicit constant in
Korevaar's inequality, minor correction
Lukasiewicz mu-Calculus
We consider state-based systems modelled as coalgebras whose type incorporates branching, and show that by suitably adapting the definition of coalgebraic bisimulation, one obtains a general and uniform account of the linear-time behaviour of a state in such a coalgebra. By moving away from a boolean universe of truth values, our approach can measure the extent to which a state in a system with branching is able to exhibit a particular linear-time behaviour. This instantiates to measuring the probability of a specific behaviour occurring in a probabilistic system, or measuring the minimal cost of exhibiting a specific behaviour in the case of weighted computations
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