Robust optimization of noisy blackbox problems using the Mesh Adaptive Direct Search algorithm

Blackbox optimization problems are often contaminated with numerical noise, and direct search methods such as the Mesh Adaptive Direct Search (MADS) algorithm may get stuck at solutions artificially created by the noise. We propose a way to smooth out the objective function of an unconstrained problem using previously evaluated function evaluations, rather than resampling points. The new algorithm, called Robust-MADS is applied to a collection of noisy analytical problems from the literature and on an optimization problem to tune the parameters of a trust-region method.     

Preconditioners for pseudodifferential equations on the sphere with radial basis functions

In a previous paper a preconditioning strategy based on overlapping domain decomposition was applied to the Galerkin approximation of elliptic partial differential equations on the sphere. In this paper the methods are extended to more general pseudodifferential equations on the sphere, using as before spherical radial basis functions for the approximation space, and again preconditioning the ill-conditioned linear systems of the Galerkin approximation by the additive Schwarz method. Numerical results are presented for the case of hypersingular and weakly singular integral operators on the sphere \mathbbS²{\mathbb{S}^2} .     

Thresholding methods to estimate copula density

This paper deals with the problem of multivariate copula density estimation. Using wavelet methods we provide two shrinkage procedures based on thresholding rules for which knowledge of the regularity of the copula density to be estimated is not necessary. These methods, said to be adaptive, have proved to be very effective when adopting the minimax and the maxiset approaches. Moreover we show that these procedures can be discriminated in the maxiset sense. We provide an estimation algorithm and evaluate its properties using simulation. Finally, we propose a real life application for financial data.     

Upper semicontinuity result for the solution mapping of a mixed parametric generalized vector quasiequilibrium problem with moving cones

In this paper, we give sufficient conditions for the upper semicontinuity property of the solution mapping of a parametric generalized vector quasiequilibrium problem with mixed relations and moving cones. The main result is proven under the assumption that moving cones have local openness/local closedness properties and set-valued maps are cone-semicontinuous in a sense weaker than the usual sense of semicontinuity. The nonemptiness and the compactness of the solution set are also investigated.     

Étude numérique du couplage de la convection naturelle avec le rayonnement de surfaces en cavité carrée remplie d'airNumerical study of natural convection-surface radiation coupling in air-filled square cavities

A numerical tool is developed for coupling natural convection in cavities with surface radiation and computations are performed for an air-filled square cavity whose four walls have the same emissivity. Compared to the adiabatic case without radiation, the top wall is cooled, the bottom wall is heated, air flow along the horizontal walls are reinforced and thermal stratification in cavity core is reduced. Detailed analysis shows that net radiative heat flux is linear with ΔT if $\mathrm{\Delta }T?T_0$, which is the case at low Rayleigh number, and that radiative Nusselt number is a linear function of the cavity height. Surface radiation induces an early transition to time-dependent flows: for $?=0.2$ and a cavity height of 0.335 m the critical Rayleigh number is equal to $9.3\times {10}^6$ and the corresponding Hopf bifurcation is supercritical. Furthermore, multiple periodic solutions are observed between $\mathit{Ra}=1.2\times {10}^7$ and $1.3\times {10}^7$. To cite this article: H. Wang et al., C. R. Mecanique 334 (2006).     

Enhanced core polarization in (70)Ni and (74)Zn

The reduced transition probabilities B(E2;0(+) --> 2(+)(1)) of the neutron-rich (74)Zn and (70)Ni nuclei have been measured by Coulomb excitation in a (208)Pb target at intermediate energy. These nuclei have been produced at Grand Accélérateur National d'Ions Lourds via interactions of a 60A MeV (76)Ge beam with a Be target. The B(E2) value for (70)Ni(42) is unexpectedly large, which indicates that neutrons added above N=40 strongly polarize the Z=28 proton core. In the Zn isotopic chain, the steep rise of B(E2) values beyond N=40 continues up to (74)Zn(44). The enhanced proton core polarization in (70)Ni is attributed to the monopole interaction between the neutron in the g(9/2) and protons in the f(7/2) and f(5/2) spin-orbit partner orbitals. This interaction could result in a weakening of magicity in (78)Ni(50).     

Transient development of backward stimulated Raman and Brillouin scattering on a picosecond time scale measured by subpicosecond thomson diagnostic

The excitation and the relaxation of the plasma waves and ion acoustic waves (IAW), respectively, driven by stimulated Raman (SRS) and Brillouin (SBS) backscatterings have been experimentally investigated with short-pulse lasers. The spectra have been obtained with a 0.3 ps time resolution. It is shown that SRS develops before SBS and suddenly decays around the peak of the pump, as the IAW reaches saturation. On this short time scale, electron kinetic effects play a major role for SRS saturation, contrary to ion dynamics. These results are supported by particle-in-cell simulations.     

Dynamic compressibility and aging in Wigner crystals and quantum glasses

We study the nonequilibrium linear response of quantum elastic systems pinned by quenched disorder with Schwinger-Keldysh real-time techniques complemented by a mean-field variational approach. We find (i) a quasiequilibrium regime in which the analytic continuation from the imaginary-time replica results holds provided the marginality condition is enforced, and (ii) an aging regime. The conductivity and compressibility are computed. The latter is found to cross over from its dynamic to static value on a scale set by the waiting time after a quench, an effect which can be probed in experiments in, e.g., Wigner glasses.     

Model storage,exchange and integration

The field of Computational Systems Neurobiology is maturing quickly. If one wants it to fulfil its central role in the new Integrative Neurobiology, the reuse of quantitative models needs to be facilitated. The community has to develop standards and guidelines in order to maximise the diffusion of its scientific production, but also to render it more trustworthy. In the recent years, various projects tackled the problems of the syntax and semantics of quantitative models. More recently the international initiative BioModels.net launched three projects: (1) MIRIAM is a standard to curate and annotate models, in order to facilitate their reuse. (2) The Systems Biology Ontology is a set of controlled vocabularies aimed to be used in conjunction with models, in order to characterise their components. (3) BioModels Database is a resource that allows biologists to store, search and retrieve published mathematical models of biological interests. We expect that those resources, together with the use of formal languages such as SBML, will support the fruitful exchange and reuse of quantitative models.     

Reachability analysis of linear systems using support functions

This work is concerned with the algorithmic reachability analysis of continuous-time linear systems with constrained initial states and inputs. We propose an approach for computing an over-approximation of the set of states reachable on a bounded time interval. The main contribution over previous works is that it allows us to consider systems whose sets of initial states and inputs are given by arbitrary compact convex sets represented by their support functions. We actually compute two over-approximations of the reachable set. The first one is given by the union of convex sets with computable support functions. As the representation of convex sets by their support function is not suitable for some tasks, we derive from this first over-approximation a second one given by the union of polyhedrons. The overall computational complexity of our approach is comparable to the complexity of the most competitive available specialized algorithms for reachability analysis of linear systems using zonotopes or ellipsoids. The effectiveness of our approach is demonstrated on several examples.