An informational approach to the global optimization of expensive-to-evaluate functions

In many global optimization problems motivated by engineering applications, the number of function evaluations is severely limited by time or cost. To ensure that each evaluation contributes to the localization of good candidates for the role of global minimizer, a sequential choice of evaluation points is usually carried out. In particular, when Kriging is used to interpolate past evaluations, the uncertainty associated with the lack of information on the function can be expressed and used to compute a number of criteria accounting for the interest of an additional evaluation at any given point. This paper introduces minimizer entropy as a new Kriging-based criterion for the sequential choice of points at which the function should be evaluated. Based on \emph{stepwise uncertainty reduction}, it accounts for the informational gain on the minimizer expected from a new evaluation. The criterion is approximated using conditional simulations of the Gaussian process model behind Kriging, and then inserted into an algorithm similar in spirit to the \emph{Efficient Global Optimization} (EGO) algorithm. An empirical comparison is carried out between our criterion and \emph{expected improvement}, one of the reference criteria in the literature. Experimental results indicate major evaluation savings over EGO. Finally, the method, which we call IAGO (for Informational Approach to Global Optimization) is extended to robust optimization problems, where both the factors to be tuned and the function evaluations are corrupted by noise.Comment: Accepted for publication in the Journal of Global Optimization (This is the revised version, with additional details on computational problems, and some grammatical changes

Magnitude bias of microlensed sources towards the Large Magellanic Cloud

There are lines of evidence suggesting that some of the observed microlensing events in the direction of the Large Magellanic Cloud (LMC) are caused by ordinary star lenses as opposed to dark Machos in the Galactic halo. Efficient lensing by ordinary stars generally requires the presence of one or more additional concentrations of stars along the line of sight to the LMC disk. If such a population behind the LMC disk exists, then the source stars (for lensing by LMC disk objects) will be drawn preferentially from the background population and will show systematic differences from LMC field stars. One such difference is that the (lensed) source stars will be farther away than the average LMC field stars, and this should be reflected in their apparent baseline magnitudes. We focus on red clump stars: these should appear in the color-magnitude diagram at a few tenths of a magnitude fainter than the field red clump. Suggestively, one of the two near-clump confirmed events, MACHO-LMC-1, is a few tenths of magnitude fainter than the clump.Comment: To appear in ApJ Letters. Shortened to match the accepted version, 8 pages plus 1 ps figur

Black Hole Relics in String Gravity: Last Stages of Hawking Evaporation

One of the most intriguing problem of modern physics is the question of the endpoint of black hole evaporation. Based on Einstein-dilaton-Gauss-Bonnet four dimensional string gravity model we show that black holes do not disappear and that the end of the evaporation process leaves some relic. The possibility of experimental detection of the remnant black holes is investigated. If they really exist, such objects could be a considerable part of the non baryonic dark matter in our Universe.Comment: 15 pages, accepted to Class. Quant. Gra

Inverse semigroup actions as groupoid actions

To an inverse semigroup, we associate an \'etale groupoid such that its actions on topological spaces are equivalent to actions of the inverse semigroup. Both the object and the arrow space of this groupoid are non-Hausdorff. We show that this construction provides an adjoint functor to the functor that maps a groupoid to its inverse semigroup of bisections, where we turn \'etale groupoids into a category using algebraic morphisms. We also discuss how to recover a groupoid from this inverse semigroup.Comment: Corrected a typo in Lemma 2.14 in the published versio

An insight into polarization states of solid-state organic lasers

The polarization states of lasers are crucial issues both for practical applications and fundamental research. In general, they depend in a combined manner on the properties of the gain material and on the structure of the electromagnetic modes. In this paper, we address this issue in the case of solid-state organic lasers, a technology which enables to vary independently gain and mode properties. Different kinds of resonators are investigated: in-plane micro-resonators with Fabry-Perot, square, pentagon, stadium, disk, and kite shapes, and external vertical resonators. The degree of polarization P is measured in each case. It is shown that although TE modes prevail generally (P>0), kite-shaped micro-laser generates negative values for P, i.e. a flip of the dominant polarization which becomes mostly TM polarized. We at last investigated two degrees of freedom that are available to tailor the polarization of organic lasers, in addition to the pump polarization and the resonator geometry: upon using resonant energy transfer (RET) or upon pumping the laser dye to an higher excited state. We then demonstrate that significantly lower P factors can be obtained.Comment: 12 pages, 12 figure

Constrained Dynamics of Universally Coupled Massive Spin 2-spin 0 Gravities

The 2-parameter family of massive variants of Einstein's gravity (on a Minkowski background) found by Ogievetsky and Polubarinov by excluding lower spins can also be derived using universal coupling. A Dirac-Bergmann constrained dynamics analysis seems not to have been presented for these theories, the Freund-Maheshwari-Schonberg special case, or any other massive gravity beyond the linear level treated by Marzban, Whiting and van Dam. Here the Dirac-Bergmann apparatus is applied to these theories. A few remarks are made on the question of positive energy. Being bimetric, massive gravities have a causality puzzle, but it appears soluble by the introduction and judicious use of gauge freedom.Comment: 6 pages; Talk given at QG05, Cala Gonone (Italy), September 200

First Astronomical Use of Multiplexed Transition Edge Bolometers

We present performance results based on the first astronomical use of multiplexed superconducting bolometers. The Fabry-Perot Interferometer Bolometer Research Experiment (FIBRE) is a broadband submillimeter spectrometer that achieved first light in June 2001 at the Caltech Submillimeter Observatory (CSO). FIBRE'S detectors are superconducting transition edge sensor (TES) bolometers read out by a SQUID multiplexer. The Fabry-Perot uses a low resolution grating to order sort the incoming light. A linear bolometer array consisting of 16 elements detects this dispersed light, capturing 5 orders simultaneously from one position on the sky. With tuning of the Fabry-Perot over one free spectral range, a spectrum covering Δλ/λ= 1/7 at a resolution of δλ/λ ≈ 1/1200 can be acquired. This spectral resolution is sufficient to resolve Doppler-broadened line emission from external galaxies. FIBRE operates in the 350 µm and 450 µm bands. These bands cover line emission from the important star formation tracers neutral carbon [Cl] and carbon monoxide (CO). We have verified that the multiplexed bolometers are photon noise limited even with the low power present in moderate resolution spectrometry

Cartan subalgebras and the UCT problem, II

We show that outer approximately represenbtable actions of a finite cyclic group on UCT Kirchberg algebras satisfy a certain quasi-freeness type property if the corresponding crossed products satisfy the UCT and absorb a suitable UHF algebra tensorially. More concretely, we prove that for such an action there exists an inverse semigroup of homogeneous partial isometries that generates the ambient C*-algebra and whose idempotent semilattice generates a Cartan subalgebra. We prove a similar result for actions of finite cyclic groups with the Rokhlin property on UCT Kirchberg algebras absorbing a suitable UHF algebra. These results rely on a new construction of Cartan subalgebras in certain inductive limits of Cartan pairs. We also provide a characterisation of the UCT problem in terms of finite order automorphisms, Cartan subalgebras and inverse semigroups of partial isometries of the Cuntz algebra $\mathcal{O}_2$. This generalizes earlier work of the authors.Comment: minor revisions; final version, accepted for publication in Math. Ann.; 26 page