Quantifying uncertainty with ensembles of surrogates for blackbox optimization

Blackbox optimization tackles problems where the functions are expensive to evaluate and where no analytical information is available. In this context, a tried and tested technique is to build surrogates of the objective and the constraints in order to conduct the optimization at a cheaper computational cost. This work introduces an extension to a specific type of surrogates: ensembles of surrogates, enabling them to quantify the uncertainty on the predictions they produce. The resulting extended ensembles of surrogates behave as stochastic models and allow the use of efficient Bayesian optimization tools. The method is incorporated in the search step of the mesh adaptive direct search (MADS) algorithm to improve the exploration of the search space. Computational experiments are conducted on seven analytical problems, two multi-disciplinary optimization problems and two simulation problems. The results show that the proposed approach solves expensive simulation-based problems at a greater precision and with a lower computational effort than stochastic models.

     

Magnetic penetration depth in V3Si and LiTi2O4 measured by μSR

Muon spin relaxation (SR) studies have been performed in the normal spinel LiTi₂O₄ and the A-15 superconductor V₃Si to measure the magnetic penetration depth . The relaxation rate(T) 1/² in field-cooled measurements shows a sharp increase belowT _c followed by saturation at low temperatures in both systems. This feature implies an isotropic energy gap without anomalous zeros, and most likelys-wave pairing. The low temperature penetration depth (T 0) is determined to be 2100Å for LiTi₂O₄ and 1300Å for V₃Si respectively. Assuming a clean limit relation ^–2 n _s /m ^*, we derive the Fermi temperatureT _F n _s/ ^2/3 m ^* from the relaxation rate and the Sommerfeld constant asT _F ^3/4–1/4. Unlike conventional superconductors, both LiTi₂O₄ and V₃Si have a large ratio ofT _c /T _F 0.01, only slightly smaller than those ratios in more exotic superconductors.We thank C. Ballard and K. Hoyle for technical assistance. Work at Columbia University is supported by NSF Grant No. DMR-89-13784 and Packard Foundation (YJU). Ames Laboratory is operated for the U. S. Department of Energy by Iowa State University under Contract No. W-7405-Eng-82. Work at Ames was supported by the Director for Energy Research, Office of Basic Energy Sciences.     

Amperometric detection of pyridine nucleotides via immobilized viologen-accepting pyridine nucleotide oxidoreductase or immobilized diaphorase

The immobilization and electrical connection of a viologen-accepting pyridine nucleotide oxidoreductase (VAPOR) on an electrode surface by coadsorption with an amphiphilic pyrrole viologen and electropolymerization of this pyrrole monomer are described. The immobilized VAPOR catalyzes the reduction of NAD(P)(+) to NAD(P)H by the viologen redox couple (V(2+2+)). The sensitivity of this biosensor is 1.4 and 2.5 mA M(-1) cm(-2) for NAD(+) and NADP(+) respectively. The immobilization of diaphorase within a laponite gel adsorbed on an electrode surface is described. The incorporation and electropolymerization of Methylene Blue in the biolayer allows an electron transfer communication between diaphorase molecules and the electrode surface. The diaphorase electrode thus obtained responds to NADH at 0 V. The sensitivity and detection limit of this biosensor are 11.2 mA M(-1) cm(-2) and 1 muM respectively.     

Mortality of iterated Gallai graphs

For a finite or infinite graphG, theGallai graph (G) ofG is defined as the graph whose vertex set is the edge setE(G) ofG; two distinct edges ofG are adjacent in (G) if they are incident but do not span a triangle inG. For any positive integert, thetth iterated Gallai graph ^t (G) ofG is defined by ( ^t–1(G)), where ⁰(G):=G. A graph is said to beGallai-mortal if some of its iterated Gallai graphs finally equals the empty graph. In this paper we characterize Gallai-mortal graphs in several ways.     

Non-linear parabolic problem associated with the penetration of a magnetic field into a substance

We study the following initial and boundary value problem: In section 1, with u₀ in L²(Ω), f continuous such that f(u) + ? non-decreasing for ? positive, we prove the existence of a unique solution on (0,T), for each T > 0. In section 2 it is proved that the unique soluition u belongs to L²(0, T; H ∩ H²) ∩ L^∞(0, T; H) if we assume u₀ in H and f in C¹(?,?). Numerical results are given for these two cases.