On Some Methods to Derive Necessary and Sufficient Optimality Conditions in Vector Optimization

The aim of this paper is to address new approaches, in separate ways, to necessary and, respectively, sufficient optimality conditions in constrained vector optimization. In this respect, for the necessary optimality conditions that we derive, we use a kind of vectorial penalization technique, while for the sufficient optimality conditions we make use of an appropriate scalarization method. In both cases, the approaches couple a basic technique (of penalization or scalarization, respectively) with several results in variational analysis and optimization obtained by the authors in the last years. These combinations allow us to arrive to optimality conditions which are, in terms of assumptions made, new.     

A fluorescence anisotropy method for measuring protein concentration in complex cell culture media

The rapid, quantitative analysis of the complex cell culture media used in biopharmaceutical manufacturing is of critical importance. Requirements for cell culture media composition profiling, or changes in specific analyte concentrations (e.g. amino acids in the media or product protein in the bioprocess broth) often necessitate the use of complicated analytical methods and extensive sample handling. Rapid spectroscopic methods like multi-dimensional fluorescence (MDF) spectroscopy have been successfully applied for the routine determination of compositional changes in cell culture media and bioprocess broths. Quantifying macromolecules in cell culture media is a specific challenge as there is a need to implement measurements rapidly on the prepared media. However, the use of standard fluorescence spectroscopy is complicated by the emission overlap from many media components. Here, we demonstrate how combining anisotropy measurements with standard total synchronous fluorescence spectroscopy (TSFS) provides a rapid, accurate quantitation method for cell culture media. Anisotropy provides emission resolution between large and small fluorophores while TSFS provides a robust measurement space. Model cell culture media was prepared using yeastolate (2.5 mg mL^–1) spiked with bovine serum albumin (0 to 5 mg mL^–1). Using this method, protein emission is clearly discriminated from background yeastolate emission, allowing for accurate bovine serum albumin (BSA) quantification over a 0.1 to 4.0 mg mL^–1range with a limit of detection (LOD) of 13.8 μg mL^–1.     

On the convergence rate improvement of a primal-dual splitting algorithm for solving monotone inclusion problems

We present two modified versions of the primal-dual splitting algorithm relying on forward–backward splitting proposed in V\(\tilde{\mathrm{u}}\) (Adv Comput Math 38(3):667–681, 2013) for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators involved we obtain for the sequences of iterates that approach the solution orders of convergence of \(\mathcal{{O}}(\frac{1}{n})\) and \(\mathcal{{O}}(\omega ^n)\), for \(\omega \in (0,1)\), respectively. The investigated primal-dual algorithms are fully decomposable, in the sense that the operators are processed individually at each iteration. We also discuss the modified algorithms in the context of convex optimization problems and present numerical experiments in image processing and pattern recognition in cluster analysis.     

New Method for Theoretical Spinodals Corresponding to Ternary Solutions with an Amphiphile Component

A new method is presented to obtain a theoretical spinodal for ternary solutions with an amphiphile component. This method uses a generalized Wheeler-Widom model representing the ternary solution, and considers local fitting conditions with the experimental binodal, imposing that the theoretical binodal must pass through a point on the experimental binodal, and also that the slope of the theoretical binodal has to be as close as possible to the slope of the representative experimental binodal. Using the previously specified fitting conditions, the corresponding spinodal is derived. The results are in agreement with an older method of local fitting between the generalized Wheeler-Widom model and the experimental data, where the fitting condition implied the coincidence of the theoretical tie-line with the experimental tie-line.     

Green light radiation effects on free radicals inhibition in cellular and chemical systems

Free radicals generation is inhibited through green light (GL) irradiation in cellular systems and in chemical reactions. Standard melanocyte cultures were UV-irradiated and the induced cellular reactive oxygen species (ROS) were quantified by the fluorescence technique. The same cell cultures, previously protected by a 24h GL exposure, displayed a significantly lower ROS production. A simple chemical reaction is subsequently chosen, in which the production of free radicals is well defined. Paraffin wax and mineral oil were GL irradiated during thermal degradation and the oxidation products checked by chemiluminescence [CL] and Fourier transform infrared spectra [FT-IR]. The same clear inhibition of the radical oxidation of alkanes is recorded. A quantum chemistry modeling of these results is performed and a mechanism involving a new type of Rydberg macromolecular systems with implications for biology and medicine is suggested.     

A variational approach to stochastic nonlinear parabolic problems

This work is concerned with an optimal control approach to stochastic nonlinear parabolic diffusion equations with monotonically increasing nonlinearity. This approach leads to sharper existence and uniqueness results under minimal growth conditions on nonlinear diffusion coefficients.     

Two positive nontrivial solutions for a class of semilinear elliptic variational systems

We obtain existence and localization results of positive nontrivial solutions for a class of semilinear elliptic variational systems. The proof is based on variants of Schechter's localized critical point theorems for Hilbert spaces not identified to their duals and on the technique of inverse-positive matrices. The Leray-Schauder boundary condition is also involved.     

A note on meromorphic convexity

We give examples of Stein domains D in C ² such that C ² ? D is either completely pluripolar or union of germs of (principal) hypersurfaces not intersecting D such that D fails to be meromorphically convex in C ². © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

A compactness result for Landau state in thin-film micromagnetics

We deal with a nonconvex and nonlocal variational problem coming from thin-film micromagnetics. It consists in a free-energy functional depending on two small parameters ε and η and defined over vector fields m:Ω⊂R²→S² that are tangent at the boundary ∂Ω. We are interested in the behavior of minimizers as ε,η→0. They tend to be in-plane away from a region of length scale ε (generically, an interior vortex ball or two boundary vortex balls) and of vanishing divergence, so that S¹-transition layers of length scale η (Néel walls) are enforced by the boundary condition. We first prove an upper bound for the minimal energy that corresponds to the cost of a vortex and the configuration of Néel walls associated to the viscosity solution, so-called Landau state. Our main result concerns the compactness of vector fields {mε,η}_ε,η↓0 of energies close to the Landau state in the regime where a vortex is energetically more expensive than a Néel wall. Our method uses techniques developed for the Ginzburg-Landau type problems for the concentration of energy on vortex balls, together with an approximation argument of S²-vector fields by S¹-vector fields away from the vortex balls.     

Comparison of luminescence ADP production assay and radiometric scintillation proximity assay for Cdc7 kinase

Several assay technologies have been successfully adapted and used in HTS to screen for protein kinase inhibitors; however, emerging comparative analysis studies report very low hit overlap between the different technologies, which challenges the working assumption that hit identification is not dependent on the assay method of choice. To help address this issue, we performed two screens on the cancer target, Cdc7-Dbf4 heterodimeric protein kinase, using a direct assay detection method measuring [(33)P]-phosphate incorporation into the substrate and an indirect method measuring residual ADP production using luminescence. We conducted the two screens under similar conditions, where in one, we measured [(33)P]-phosphate incorporation using scintillation proximity assay (SPA), and in the other, we detected luminescence signal of the ATP-dependent luciferase after regenerating ATP from residual ADP (LUM). Surprisingly, little or no correlation were observed between the positives identified by the two methods; at a threshold of 30% inhibition, 25 positives were identified in the LUM screen whereas the SPA screen only identified two positives, Tannic acid and Gentian violet, with Tannic acid being common to both. We tested 20 out of the 25 positive compounds in secondary confirmatory study and confirmed 12 compounds including Tannic acid as Cdc7-Dbf4 kinase inhibitors. Gentian violet, which was only positive in the SPA screen, inhibited luminescence detection and categorized as a false positive. This report demonstrates the strong impact in detection format on the success of a screening campaign and the importance of carefully designed confirmatory assays to eliminate those compounds that target the detection part of the assay.