A class of test functions for global optimization

We suggest weighted least squares scaling, a basic method in multidimensional scaling, as a class of test functions for global optimization. The functions are easy to code, cheap to calculate, and have important applications in data analysis. For certain data these functions have many local minima. Some characteristic features of the test functions are investigated.This paper was written while the second author was a visiting Professor at Aachen University of Technology, funded by the Deutsche Forschungsgemeinschaft.     

EXCITON ANNIHILATION IN THE ISOLATED PHYCOBILIPROTEINS FROM THE BLUE-GREEN ALGA NOSTOC SP. USING PICOSECOND ABSORPTION SPECTROSCOPY

Abstract— Phycobilisomes from the blue-green alga Nostoc sp. contain the phycobiliproteins: c -phycoerythrin ( c -PE), c -phycocyanin ( c -PC) and allophycocyanin (APC). The depletion and the recovery of the ground states for the individual phycobiliproteins were measured using picosecond (ps) absorption spectroscopy. In all cases the depletion time was Glops. The recovery was found to be non-exponenzial which could be fitted to a single exponential ('fast' component) and a second component with a relaxation time of > 300ps. The recovery times of the fast component were found to be intensity dependent and for c -PE, c -PC and APC were measured to be 19, 27 and 35ps, respectively, at intensity ( I ) ∼ 7 × 10²⁰ photons/m² and increased to 54, 55 and 67 ps, respectively, at I ∼ 8 × 10¹⁹ photons/m2. The ps absorption data support the assignment of the'fast' component to singlet-singlet exciton annihilation.     

On a Global Optimization Algorithm for Bivariate Smooth Functions

The problem of approximating the global minimum of a function of two variables is considered. A method is proposed rooted in the statistical approach to global optimization. The proposed algorithm partitions the feasible region using a Delaunay triangulation. Only the objective function values are required by the optimization algorithm. The asymptotic convergence rate is analyzed for a class of smooth functions. Numerical examples are provided.     

Pulsed-laser generation of gold nanoparticles with on-line surface plasmon resonance detection

Size of nanoparticles is an important parameter for their applications. The real-time monitoring is required for reliable and reproducible production of nanoparticles with controllable size. We present results of our research on development of the system for the online nanoparticle characterization during their production by a laser. The laser ablation chamber which allows measurements of surface plasmon resonance spectra during the nanoparticle generation process has been designed and fabricated. The online characterization system was tested by producing and modification of gold nanoparticles. Nanoparticles were generated by nanosecond-laser (wavelength 1064 nm) ablation of gold target in deionized water, and optimal conditions for the highest nanoparticle productivity were estimated. The mean diameter of nanoparticles was determined using their absorption spectra measured in the real-time during the ablation experiments and from the TEM images analysis, and it varied from 20 to 45 nm. The mismatch between nanoparticle diameters, estimated using these two methods, is due to the polydispersity of the generated nanoparticles. The further experiments of laser-induced modification of colloidal gold nanoparticles were carried out using second harmonic (wavelength 532 nm) of nanosecond Nd:YAG laser and alteration in nanoparticle size were acquired by the online measurement system.     

Axiomatic characterization of a global optimization algorithm and investigation of its search strategy

A new axiomatic characterization of a rational algorithm for global minimization based on a statistical model of the objective function is suggested. The globality of the search strategy of such an algorithm is investigated as well as the convergence of the algorithm.     

Fluorescence kinetics of emission from a small finite volume of a biological system

The fluorescence decay, apparent quantum yield and transmission from chromophores constrained to a microscopic volume using a single picosecond laser excitation were measured as a function of incident intensity. The β subunit of phycoeryhthrin aggregate isolated from the photosynthetic antenna system of Nostoc sp. was selected since it contains only four chromophores in a volume of less than 5.6×10⁴ ų. The non-exponential fluorescence decay profiles were intensity independent for the intensity range studied (5 × 10¹³ - 2 × 10¹⁵ photon cm^?2 per pulse). The apparent decrease in the relative fluorescence quantum yield and increase of the relative transmission with increasing excitation intensity is attributed to the combined effects of ground state depletion and upper excited state absorption. Evidence suggests that exciton annihilation is absent within isolated β subunits.     

Effect of H<Subscript>2</Subscript>SeO<Subscript>3</Subscript> on the early stages of nucleation and growth during Cu electrocrystallization in acidic medium on glassy carbon electrode

The early stages of Cu electrodeposition onto a GC electrode were investigated in 0.5 M H₂SO₄ + 0.01 M CuSO₄ solution without or with H₂SeO₃ when a molar concentration ratio [Cu(II)]/[Se(IV)] was 1.10⁴ to 2.10². The H₂SeO₃ solution in 0.5 M H₂SO₄ was also used. The electrochemical techniques such as cyclic voltammetry and chronoamperometry and structural investigation using ex situ AFM were applied to study the nucleation and growth of Cu onto a GC electrode. Chronoamperometric results were shown to follow an instantaneous 3D nucleation and diffusion-controlled growth model by Scharifker and Hills. The values of number of Cu nuclei N and average nuclei radius r _av were calculated. It was shown that, in the presence of H₂SeO₃ in amounts of 0.001 to 0.005 mM, N increases and r _av decreases. At higher concentrations of the additive, the changes of these parameters with the deposition potential E _dep were shown to be somewhat more complex. The dependences of N and r _av on the concentration of H₂SeO₃ in different regions of Cu overpotentials were also revealed.     

On Convergence of a P-Algorithm Based on a Statistical Model of Continuously Differentiable Functions

This paper is a study of the one-dimensional global optimization problem for continuously differentiable functions. We propose a variant of the so-called P-algorithm, originally proposed for a Wiener process model of an unknown objective function. The original algorithm has proven to be quite effective for global search, though it is not efficient for the local component of the optimization search if the objective function is smooth near the global minimizer. In this paper we construct a P-algorithm for a stochastic model of continuously differentiable functions, namely the once-integrated Wiener process. This process is continuously differentiable, but nowhere does it have a second derivative. We prove convergence properties of the algorithm.     

Performance of global random search algorithms for large dimensions

We investigate the rate of convergence of general global random search (GRS) algorithms. We show that if the dimension of the feasible domain is large then it is impossible to give any guarantee that the global minimizer is found by a general GRS algorithm with reasonable accuracy. We then study precision of statistical estimates of the global minimum in the case of large dimensions. We show that these estimates also suffer the curse of dimensionality. Finally, we demonstrate that the use of quasi-random points in place of the random ones does not give any visible advantage in large dimensions.