3,092 research outputs found
Maximal representations of uniform complex hyperbolic lattices in exceptional Hermitian Lie groups
We complete the classification of maximal representations of uniform complex
hyperbolic lattices in Hermitian Lie groups by dealing with the exceptional
groups and . We prove that if is a maximal
representation of a uniform complex hyperbolic lattice , , in an exceptional Hermitian group , then and , and we describe completely the representation . The case of
classical Hermitian target groups was treated by Vincent Koziarz and the second
named author (arxiv:1506.07274). However we do not focus immediately on the
exceptional cases and instead we provide a more unified perspective, as
independent as possible of the classification of the simple Hermitian Lie
groups. This relies on the study of the cominuscule representation of the
complexification of the target group. As a by-product of our methods, when the
target Hermitian group has tube type, we obtain an inequality on the Toledo
invariant of the representation which is stronger
than the Milnor-Wood inequality (thereby excluding maximal representations in
such groups).Comment: Comments are welcome
Bayesian subset simulation
We consider the problem of estimating a probability of failure ,
defined as the volume of the excursion set of a function above a given threshold, under a given
probability measure on . In this article, we combine the popular
subset simulation algorithm (Au and Beck, Probab. Eng. Mech. 2001) and our
sequential Bayesian approach for the estimation of a probability of failure
(Bect, Ginsbourger, Li, Picheny and Vazquez, Stat. Comput. 2012). This makes it
possible to estimate when the number of evaluations of is very
limited and is very small. The resulting algorithm is called Bayesian
subset simulation (BSS). A key idea, as in the subset simulation algorithm, is
to estimate the probabilities of a sequence of excursion sets of above
intermediate thresholds, using a sequential Monte Carlo (SMC) approach. A
Gaussian process prior on is used to define the sequence of densities
targeted by the SMC algorithm, and drive the selection of evaluation points of
to estimate the intermediate probabilities. Adaptive procedures are
proposed to determine the intermediate thresholds and the number of evaluations
to be carried out at each stage of the algorithm. Numerical experiments
illustrate that BSS achieves significant savings in the number of function
evaluations with respect to other Monte Carlo approaches
Bayesian Subset Simulation: a kriging-based subset simulation algorithm for the estimation of small probabilities of failure
The estimation of small probabilities of failure from computer simulations is
a classical problem in engineering, and the Subset Simulation algorithm
proposed by Au & Beck (Prob. Eng. Mech., 2001) has become one of the most
popular method to solve it. Subset simulation has been shown to provide
significant savings in the number of simulations to achieve a given accuracy of
estimation, with respect to many other Monte Carlo approaches. The number of
simulations remains still quite high however, and this method can be
impractical for applications where an expensive-to-evaluate computer model is
involved. We propose a new algorithm, called Bayesian Subset Simulation, that
takes the best from the Subset Simulation algorithm and from sequential
Bayesian methods based on kriging (also known as Gaussian process modeling).
The performance of this new algorithm is illustrated using a test case from the
literature. We are able to report promising results. In addition, we provide a
numerical study of the statistical properties of the estimator.Comment: 11th International Probabilistic Assessment and Management Conference
(PSAM11) and The Annual European Safety and Reliability Conference (ESREL
2012), Helsinki : Finland (2012
A Bayesian approach to constrained single- and multi-objective optimization
This article addresses the problem of derivative-free (single- or
multi-objective) optimization subject to multiple inequality constraints. Both
the objective and constraint functions are assumed to be smooth, non-linear and
expensive to evaluate. As a consequence, the number of evaluations that can be
used to carry out the optimization is very limited, as in complex industrial
design optimization problems. The method we propose to overcome this difficulty
has its roots in both the Bayesian and the multi-objective optimization
literatures. More specifically, an extended domination rule is used to handle
objectives and constraints in a unified way, and a corresponding expected
hyper-volume improvement sampling criterion is proposed. This new criterion is
naturally adapted to the search of a feasible point when none is available, and
reduces to existing Bayesian sampling criteria---the classical Expected
Improvement (EI) criterion and some of its constrained/multi-objective
extensions---as soon as at least one feasible point is available. The
calculation and optimization of the criterion are performed using Sequential
Monte Carlo techniques. In particular, an algorithm similar to the subset
simulation method, which is well known in the field of structural reliability,
is used to estimate the criterion. The method, which we call BMOO (for Bayesian
Multi-Objective Optimization), is compared to state-of-the-art algorithms for
single- and multi-objective constrained optimization
Stability of trajectories for N -particles dynamics with singular potential
We study the stability in finite times of the trajectories of interacting
particles. Our aim is to show that in average and uniformly in the number of
particles, two trajectories whose initial positions in phase space are close,
remain close enough at later times. For potential less singular than the
classical electrostatic kernel, we are able to prove such a result, for initial
positions/velocities distributed according to the Gibbs equilibrium of the
system
Bayesian robot Programming
We propose a new method to program robots based on Bayesian inference and learning. The capacities of this programming method are demonstrated through a succession of increasingly complex experiments. Starting from the learning of simple reactive behaviors, we present instances of behavior combinations, sensor fusion, hierarchical behavior composition, situation recognition and temporal sequencing. This series of experiments comprises the steps in the incremental development of a complex robot program. The advantages and drawbacks of this approach are discussed along with these different experiments and summed up as a conclusion. These different robotics programs may be seen as an illustration of probabilistic programming applicable whenever one must deal with problems based on uncertain or incomplete knowledge. The scope of possible applications is obviously much broader than robotics
Energy cascade and the four-fifths law in superfluid turbulence
The 4/5-law of turbulence, which characterizes the energy cascade from large
to small-sized eddies at high Reynolds numbers in classical fluids, is verified
experimentally in a superfluid 4He wind tunnel, operated down to 1.56 K and up
to R_lambda ~ 1640. The result is corroborated by high-resolution simulations
of Landau-Tisza's two-fluid model down to 1.15 K, corresponding to a residual
normal fluid concentration below 3 % but with a lower Reynolds number of order
R_lambda ~ 100. Although the K\'arm\'an-Howarth equation (including a viscous
term) is not valid \emph{a priori} in a superfluid, it is found that it
provides an empirical description of the deviation from the ideal 4/5-law at
small scales and allows us to identify an effective viscosity for the
superfluid, whose value matches the kinematic viscosity of the normal fluid
regardless of its concentration.Comment: 6 pages, 7 figure
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