A review of statistical models for global optimization

A review of statistical models for global optimization is presented. Rationality of the search for a global minimum is formulated axiomatically and the features of the corresponding algorithm are derived from the axioms. Furthermore the results of some applications of the proposed algorithm are presented and the perspectives of the approach are discussed.     

Nucleation and growth of Cu onto polycrystalline Pt electrode from acidic CuSO4 solution in the presence of H2SeO3

The early stages of Cu electrodeposition onto Pt(poly) have been investigated in 0.5 M H₂SO₄ + 0.01 M CuSO₄ solution without or with H₂SeO₃ when a molar concentration ratio [Cu(II)]/[Se(IV)] ≥ 2×10² using electrochemical and ex situ AFM techniques. The overpotential deposition of Cu has been performed onto a Pt surface precovered independently with Cu in amount close to an equivalent monolayer. Chronoamperometric results have been shown to follow an instantaneous 3D nucleation and diffusion-controlled growth model. The values of diffusion coefficient D for Cu²⁺, number of nuclei N and average nuclei radius r _av have been calculated. In the local regions of the surface, the separate large agglomerates composed of the different diameter clusters have been revealed in both cases, but, in the presence of the H₂SeO₃, they attained a distinct chain-like configuration. Some morphological characteristics have been reported.     

Zinc-phosphate nanoparticles with reversibly attached TNF-α analogs: an interesting concept for potential use in active immunotherapy

The authors’ intention was to prepare nanometer-sized zinc-phosphate nanoparticles that would be capable of binding histidine-rich TNF-α analogs onto their surface via a coordinative bond. Zinc-phosphate nanoparticles with a size of around 60 nm were prepared by a wet precipitation method and characterized using SEM, EDX, XRD, and DLS. First, BSA was bound as a testing protein, afterward two TNF-α analogs with decreased activity were bound to the described nanoparticles. The efficiency of binding and the existence of coordinative bond were confirmed with SDS-PAGE analysis. During binding, particle storage, and release experiments, the prepared TNF-α analogs retained their biological activity—hence the epitopes necessary for formation of antibodies stayed intact. The particle size did not change within a period of 2 weeks. No significant agglomeration was observed, the particles could be quickly dispersed in ultrasound. The present nanoparticles and the general approach of coordinative binding are widely applicable for natural and engineered histidine-rich proteins. The nanoparticles bearing appropriate TNF-α analogs could also be potentially used for active immunotherapy to tackle the chronic inflammatory diseases associated with pathogenically elevated levels of TNF-α.     

Limit theorems in the space of analytic functions for the Hurwitz zeta-function with an algebraic irrational parameter

We prove a limit theorem in the space of analytic functions for the Hurwitz zeta-function with algebraic irrational parameter.     

Limit theorems for the Mellin transform of the fourth power of the Riemann zeta-function

We prove limit theorems in the sense of weak convergence of probability measures on the complex plane as well as in the space of analytic functions for the Mellin transform of {ie88-01}     

A hybrid method for multidimensional scaling using city-block distances

The problem of multidimensional scaling with city-block distances in the embedding space is reduced to a two level optimization problem consisting of a combinatorial problem at the upper level and a quadratic programming problem at the lower level. A hybrid method is proposed combining randomized search for the upper level problem with a standard quadratic programming algorithm for the lower level problem. Several algorithms for the combinatorial problem have been tested and an evolutionary global search algorithm has been proved most suitable. An experimental code of the proposed hybrid multidimensional scaling algorithm is developed and tested using several test problems of two- and three-dimensional scaling.     

Cyclodextrin modified gold nanoparticles-based open-tubular capillary electrochromatographic separations of polyaromatic hydrocarbons

In this study, spherical gold nanoparticles (GNPs) of 14.7 nm diameter, prepared by citrate reduction of a gold(III) salt and characterized by UV–Vis absorption spectrometry and transmission electron microscopy, were modified by a covalent attachment of 6^I-O-(3-mercaptopropyl)β-cyclodextrin (β-CD-SH) or per-6-deoxy-per-6-mercapto-β-cyclodextrin (β-CD-SH7). Subsequently, via three alternative approaches, β-CD-modified GNPs were immobilized onto the inner wall of the fused-silica (FS) capillaries and applied as special stationary phases for open-tubular capillary electrochromatography (OT-CEC). The first immobilization procedure was based on pre-derivatization of a FS capillary with (3-mercaptopropyl)trimethoxysilane (MPTMS) followed by subsequent reactions with GNPs and β-CD-SH or β-CD-SH7. The other two preparation protocols took advantage of sol–gel approach gaining a significant increase in the interaction surface for solutes. In both instances, the sol–gel created 3D structure was further covalently modified with GNPs. Serving that purpose, either β-CD-SH7 modified GNPs were used for the immobilization into the sol–gel matrix (“one-step sol–gel technique”) or native GNPs were immobilized first into the sol–gel matrix and subsequently modified with β-CD-SH7 (“two-step sol–gel technique”). The separation performance of CD-GNPs modified FS capillaries was tested by OT-CEC in reversed-phase mode applied to separation of a model mixture of five polyaromatic hydrocarbons. The highest separation efficiencies were obtained with the capillaries prepared by two-step sol–gel technique. However, with respect to the relatively low reproducibility of this method, the first of the above preparation procedures, i.e., a simple pre-derivatization of the FS capillary with MPTMS ensued with β-CD-SH7-GNPs immobilization seems to be more feasible approach providing decent separation efficiency.