A globally convergent primal—dual interior point algorithm for convex programming

In this paper, we study the global convergence of a large class of primal—dual interior point algorithms for solving the linearly constrained convex programming problem. The algorithms in this class decrease the value of a primal—dual potential function and hence belong to the class of so-called potential reduction algorithms. An inexact line search based on Armijo stepsize rule is used to compute the stepsize. The directions used by the algorithms are the same as the ones used in primal—dual path following and potential reduction algorithms and a very mild condition on the choice of the centering parameter is assumed. The algorithms always keep primal and dual feasibility and, in contrast to the polynomial potential reduction algorithms, they do not need to drive the value of the potential function towards — in order to converge. One of the techniques used in the convergence analysis of these algorithms has its root in nonlinear unconstrained optimization theory.Research supported in part by NSF Grant DDM-9109404.     

A modified nearly exact method for solving low-rank trust region subproblem

In this paper, we first discuss how the nearly exact (NE) method proposed by Moré and Sorensen [14] for solving trust region (TR) subproblems can be modified to solve large-scale “low-rank” TR subproblems efficiently. Our modified algorithm completely avoids computation of Cholesky factorizations by instead relying primarily on the Sherman–Morrison–Woodbury formula for computing inverses of “diagonal plus low-rank” type matrices. We also implement a specific version of the modified log-barrier (MLB) algorithm proposed by Polyak [17] where the generated log-barrier subproblems are solved by a trust region method. The corresponding direction finding TR subproblems are of the low-rank type and are then solved by our modified NE method. We finally discuss the computational results of our implementation of the MLB method and its comparison with a version of LANCELOT [5] based on a collection extracted from CUTEr [12] of nonlinear programming problems with simple bound constraints.      

Improving the spectrophotometric determination of the alkylating activity of anticancer agents: A new insight into the mechanism of the NBP method

In this paper, the mechanism of the nitrobenzylpyridine (NBP) method to measure the alkylating activity of drugs originally described by Epstein et al. [J. Epstein, R.W. Rosenthal, R.J. Ess, Anal. Chem. 27 (1955) 1435-1439] and modified later by others was revisited using melphalan, m-sarcolysin, chlorambucil, cyclophosphamide and ifosfamide. Its direct application to determine the activity of these drugs in human serum and aqueous media is described and discussed.This method, based on the formation of a chromophore due to the reaction between the alkylating agent and NBP, was significantly improved by extracting as quickly as possible the reaction product(s) into chloroform before adding alkali to develop the color. This significantly limited the degradation by hydrolysis of the products and enhanced the yield of the end chromophore in the organic phase. The reaction time was optimized by monitoring each compound color development.The best reaction time for each compound was selected and a higher stability of the extracted color over at least 1 h was obtained (compared to a couple of minutes in previous studies). Most interestingly, water evaporation due to heating had little or no effect on the linearity of standard curves evaluated in the micromolar concentration range. Both the sensitivity and reproducibility of the method were therefore significantly improved.There appears to be a direct correlation between compound hydrolysis and alkylation activity; the relative reactivity is different among the compounds owing to the rate of (i) production, (ii) the relative proportions and (iii) the hydrolysis of the intermediates. A general mechanism for the nucleophilic competitive substitution is proposed.     

Optimization and validation of a high-performance liquid chromatography method for the analysis of cardiac glycosides in Digitalis lanata

In this study, a simple and reliable HPLC method for the qualitative and quantitative analysis of cardiac glycosides in Digitalis lanata Ehrh. raw material was developed and applied to healthy and phytoplasma-infected plants. The target analytes cover a broad range of secondary metabolites, including primary, secondary and tertiary glycosides and the corresponding aglycones. The sample preparation was carried out by sonication of the plant material with 70% (v/v) aqueous methanol at room temperature, followed by reversed-phase solid-phase extraction purification from interfering pigments. The HPLC analyses were performed on a Symmetry C₁₈ column (75 mm × 4.6 mm I.D., 3.5 μm), with a gradient elution composed of water and acetonitrile, at a flow rate of 1.0 mL/min. The column temperature was set at 20 °C and the photodiode array detector monitored the eluent at 220 nm. The method was validated with respect to ICH guidelines and the validation parameters were found to be highly satisfactory. The application of the method to the analysis of D. lanata leaves indicated that air-drying was the optimum method for raw material processing when compared with freeze-drying. The analysis of healthy and phytoplasma-infected plants demonstrated that the secondary metabolite mainly affected by the pathogen presence was lanatoside C (153.2 μg/100 mg versus 76.1 μg/100 mg). Considering the importance of D. lanata plant material as source of cardiac glycosides, the developed method can be considered suitable for the phytochemical analysis and for the quality assurance of D. lanata used for pharmaceutical purpose.     

Cluster identification and characterization in the riser of a circulating fluidized bed from numerical simulation results

A methodology of identification and characterization of coherent structures mostly known as clusters is applied to hydrodynamic results of numerical simulation generated for the riser of a circulating fluidized bed. The numerical simulation is performed using the MICEFLOW code, which includes the two-fluids IIT’s hydrodynamic model B. The methodology for cluster characterization that is used is based in the determination of four characteristics, related to average life time, average volumetric fraction of solid, existing time fraction and frequency of occurrence. The identification of clusters is performed by applying a criterion related to the time average value of the volumetric solid fraction. A qualitative rather than quantitative analysis is performed mainly owing to the unavailability of operational data used in the considered experiments. Concerning qualitative analysis, the simulation results are in good agreement with literature. Some quantitative comparisons between predictions and experiment were also presented to emphasize the capability of the modeling procedure regarding the analysis of macroscopic scale coherent structures.     

Local Minima and Convergence in Low-Rank Semidefinite Programming

The low-rank semidefinite programming problem LRSDP_r is a restriction of the semidefinite programming problem SDP in which a bound r is imposed on the rank of X, and it is well known that LRSDP_r is equivalent to SDP if r is not too small. In this paper, we classify the local minima of LRSDP_r and prove the optimal convergence of a slight variant of the successful, yet experimental, algorithm of Burer and Monteiro [5], which handles LRSDP_r via the nonconvex change of variables X=RR^T. In addition, for particular problem classes, we describe a practical technique for obtaining lower bounds on the optimal solution value during the execution of the algorithm. Computational results are presented on a set of combinatorial optimization relaxations, including some of the largest quadratic assignment SDPs solved to date.This author was supported in part by NSF Grant CCR-0203426.This author was supported in part by NSF Grants CCR-0203113 and INT-9910084 and ONR grant N00014-03-1-0401.     

Light parameters influence cell viability in antifungal photodynamic therapy in a fluence and rate fluence-dependent manner

The aim of this study was to investigate the influence of light parameters on yeast cells. It has been proposed for many years that photodynamic therapy (PDT) can inactivate microbial cells. A number of photosensitizer and light sources were reported in different light parameters and in a range of dye concentrations. However, much more knowledge concerning the importance of fluence, fluence rate and exposure time are required for a better understanding of the photodynamic efficiency. Suspensions (10⁶ CFU/mL) of Candida albicans, Candida krusei, and Cryptococcus neoformans var. grubii were used. Two fluence rates, 100 and 300 mW/cm² were compared at 3, 6, and 9 min of irradiation, resulting fluences from 18 to 162 J/cm². The light source was a laser emitting at λ = 660 nm with output power adjusted at 30 and 90 mW. As photosensitizer, one hundred-μM methylene blue was used. Temperature was monitored to verify possible heat effect and reactive oxygen species (ROS) formation was evaluated. The same fluence in different fluence rates showed dissimilar levels of inactivation on yeast cells as well as in ROS formation. In addition, the increase of the fluence rate showed an improvement on cell photoinactivation. PDT was efficient against yeast cells (6 log reduction), and no significant temperature increase was observed. Fluence per se should not be used as an isolate parameter to compare photoinactivation effects on yeast cells. The higher fluence rate was more effective than the lower one. Furthermore, an adequate duration of light exposure cannot be discarded.     

The 2-Methoxyethanol + 1,2-Dimethoxyethane + Water Ternary System. Static Relative Permittivities from −10 To +80°C

Static relative permittivities of the 2-methoxyethanol + 1,2-dimethoxyethane + water ternary solvent system were measured as a function of temperature (-10 = t/°C = 80) and of composition, over the whole molar fractions range 0 = x₂, x₂, x₃ = 1. The experimental values have been used to test some empirical relationships accounting for the dependence of e on T, x_i, and on T, x_i couples of values. A comparison between calculated and experimental data shows that these relationships can be profitably employed to predict e values in correspondence to experimental data gaps. The excess dielectric permittivity, e^E, assumes, in the most cases, negative values for any compositions of the mixtures, while the values of the excess molar polarization, P^E, are positive. The large values of the excess quantities are indicative of the strong specific interactions among similar, as well as different molecules in the mixtures. Discussion of the data in terms of Kirkwood correlation factor also gives information on the short-range intermolecular interactions among the components, suggesting the formation of two-components adducts rather than of than more complex moieties involving all three molecular species.