On the Continuity of the Optimal Value in Parametric Linear Optimization: Stable Discretization of the Lagrangian Dual of Nonlinear Problems

This paper is focused on the stability of the optimal value, and its immediate repercussion on the stability of the optimal set, for a general parametric family of linear optimization problems in ⁿ. In our approach, the parameter ranges over an arbitrary metric space, and each parameter determines directly a set of coefficient vectors describing the linear system of constraints. Thus, systems associated with different parameters are not required to have the same number (cardinality) of inequalities. In this way, discretization techniques for solving a nominal linear semi-infinite optimization problem may be modeled in terms of suitable parametrized problems. The stability results given in the paper are applied to the stability analysis of the Lagrangian dual associated with a parametric family of nonlinear programming problems. This dual problem is translated into a linear (semi-infinite) programming problem and, then, we prove that the lower semicontinuity of the corresponding feasible set mapping, the continuity of the optimal value function, and the upper semicontinuity of the optimal set mapping are satisfied. Then, the paper shows how these stability properties for the dual problem entail a nice behavior of parametric approximation and discretization strategies (in which an ordinary linear programming problem may be considered in each step). This approximation–discretization process is formalized by means of considering a double parameter: the original one and the finite subset of indices (grid) itself. Finally, the convex case is analyzed, showing that the referred process also allows us to approach the primal problem.Mathematics Subject Classifications (2000) Primary 90C34, 90C31; secondary 90C25, 90C05.     

Assignment of relative configurations to acyclic diastereomeric carbinols with the lanthanide shift reagent Eu (fod)3 by 1H and 13C NMR

An assignment of relative configurations has been achieved for the diastereomeric racemates (1R2R,1S2S) and (1R2S,1S2R) of 3,3-dimethyl-1,2-diphenylbutan-1-ol through the comparative analysis of the respective chemical shifts induced by Eu(fod)₃ in the ¹H and ¹³C NMR spectra, and the corresponding conformational distribution.     

Illusory percepts from auditory adaptation

Phenomena resembling tinnitus and Zwicker phantom tone are seen to result from an auditory gain adaptation mechanism that attempts to make full use of a fixed-capacity channel. In the case of tinnitus, the gain adaptation enhances internal noise of a frequency band otherwise silent due to damage. This generates a percept of a phantom sound as a consequence of hearing loss. In the case of Zwicker tone, a frequency band is temporarily silent during the presentation of a notched broadband sound, resulting in a percept of a tone at the notched frequency. The model suggests a link between tinnitus and the Zwicker tone percept, in that it predicts different results for normal and tinnitus subjects due to a loss of instantaneous nonlinear compression. Listening experiments on 44 subjects show that tinnitus subjects (11 of 44) are significantly more likely to hear the Zwicker tone. This psychoacoustic experiment establishes the first empirical link between the Zwicker tone percept and tinnitus. Together with the modeling results, this supports the hypothesis that the phantom percept is a consequence of a central adaptation mechanism confronted with a degraded sensory apparatus.     

Homogeneous nucleation: classical formulas as asymptotic limits of the Cahn-Hilliard approach

Classical expressions for the critical cluster work of formation approximate the nonclassical expressions based in the density functional theory of capillarity for the limit of low supersaturation degrees. However, the ratio between classical and nonclassical expressions for nucleation rates grows as the supersaturation degree decreases. Here, with the aim to obtain simple and more accurate expressions that approximate the modern nucleation rate formulas, an asymptotic expansion of the Cahn-Hilliard expression of the critical work of formation is developed within the limit of low supersaturation. In such asymptotic expansion, terms up to third order are retained. The ratios between the corrected classical expressions and the nonclassical ones are now decreasing for supersaturation degrees tending to zero. However, the corrected approximate formulas are as difficult to handle as the exact Cahn-Hilliard expressions. When only the two first low-order terms of the asymptotic expansion are retained, a simpler corrected classical expression is obtained but it can only approximate nonclassical expressions up to order unity. Finally, using a Becker-Doring model of nucleation, the kinetic prefactor of the critical nuclei rate of formation is modeled consistently with the Cahn-Hilliard approach to the critical work of formation.     

Sampling of states for estimating the folding funnel entropy and energy landscape of a model alpha-helical hairpin peptide

Protein folding times are many orders of magnitude shorter than would occur if the peptide chain randomly sampled possible configurations, which implies that protein folding is a directed process. The detailed shape of protein's energy landscape determines the rate and reliability of folding to the native state, but the large number of structural degrees of freedom generates an energy landscape that is hard to visualize because of its high dimensionality. A commonly used picture is that of an energy funnel leading from high energy random coil state down to the low energy native state. As lattice computer models of protein dynamics become more realistic, the number of possible configurations becomes too large to count directly. Statistical mechanic and thermodynamic approaches allow us to count states in an approximate manner to quantify the entropy and energy of the energy landscape within a folding funnel for an alpha-helical protein. We also discuss the problems that arise in attempting to count the huge number of individual states of the random coil at the top of the funnel.     

New hybrid films based on cellulose and hydroxygallium phthalocyanine. Synergetic effects in the structure and properties

Hydroxygallium phthalocyanine (HOGaPc) and cellulose (from a trimethylsilyl derivative) have been used as native elements for the preparation of a novel family of hybrid films. By spin-coating, both components allow the building of films with different configurations on various substrates in a controlled way. The particularities of these hybrid films have been characterized by a range of techniques such as Fourier transform infrared spectroscopy (FTIRS) in attenuated total reflection using multiple internal reflections (ATR/MIR), absorption ultraviolet and visible spectroscopy (UV-vis), X-ray photoelectron spectroscopy (XPS), atomic force microscopy (AFM), and surface potential measurements using the Kelvin-Zisman vibrating capacitor probe (KP). This enabled determination of the influence of cellulose on the arrangement of HOGaPc and, consequently, control of the relation between the structure and the properties of the films. Finally, gas sensor tests were performed to check the potentialities of these hybrid films. In particular, the synergetic behavior between the film-forming materials allows a fast and sensible change in surface potential after cyclic exposures to ozone (O3, 100 ppb) and nitrogen. Overall, we present the advantages of combining phthalocyanine with cellulose in enhancing the properties of the final product. Introduction of cellulose as a host material opens up a new area of hybrid films.     

Thermotropic behavior of ceramides and their isolation from wool

The composition of internal wool lipids (IWL) resembles that of lipids present in other keratinic tissues such as human hair or the stratum corneum. Advances in the isolation of ceramides from wool and in the characterization of their thermotropic properties could facilitate their application in human skin care treatments. IWL are solvents extracted from wool fibers. Ceramide isolation is carried out by medium-pressure liquid chromatography. The different fractions obtained were analyzed quantitatively by thin layer chromatography coupled to an automated flame ionization detector and by high-performance thin layer chromatography using a densitometric detector. Two important fractions were isolated: one was a mixture of different ceramides and the other was exclusively made of ceramide 2 (nonhydroxy acid sphingosine [NS]). The thermotropic behavior of IWL and their isolated fractions were studied by thermogravimetric analysis, differential scanning calorimetry (DSC), and by attenuated total reflection Fourier-transform infrared spectroscopy (ATR-FTIR) methodologies. The transition temperature (Tm) obtained was compared with the results of the IWL extract, stratum corneum lipids, and the values found in the bibliography for isolated ceramides. The Tm obtained for IWL (48 degrees C) was lower than that achieved for SCL (65 degrees C). This discrepancy could be due to the different ceramide pattern and to the larger amounts of free fatty acids present in the IWL extract. Although the isolated ceramides had higher Tm values, they resembled the values reported in the bibliography. The suitability of the fraction composed exclusively of ceramide 2 [NS] for skin applications was confirmed by ATR-FTIR and DSC.     

Determination of total As in onion plants growing in contaminated substrates by total reflection X-ray fluorescence

The onion (Allium cepa L.) is one of the most important cultivars in the world and its production level occupies the second place in Venezuela. It becomes important to develop analytical procedures for arsenic determination and to study the effect of this element on the cultures, as well the absorption, transport and translocation processes. A TXRF method for As determination in onions was developed. Two treatments were applied to the onion plants, As contaminated and control. The contaminant was added to the plants to an amount of 100 μg, in a single time 3 weeks after the transplant of plantlets. The green leaves bulbs, and roots together with the stems were separated 45 days after transplant and analyzed by TXRF and HG-AAS for total Arsenic determination. A good agreement was found between these two techniques, demonstrating the accuracy of the TXRF procedure. It was found that the highest concentration corresponded to the root and stems (37 ± 31 μg g⁻¹), followed by the bulbs (11 ± 7 μg g⁻¹), being the smallest level found in the green leaves (4 ± 3 μg g⁻¹). At low As contamination levels of 0.25 μg g⁻¹, a risk for translocation of the toxic element to the edible parts of the onion plants exists. At this level the normal development of the plant is not affected, being the only exception the root length, which is significantly higher in the contaminated treatment.     

Targeting norovirus infection-multivalent entry inhibitor design based on NMR experiments

Noroviruses attach to their host cells through histo blood group antigens (HBGAs), and compounds that interfere with this interaction are likely to be of therapeutic or diagnostic interest. It is shown that NMR binding studies can simultaneously identify and differentiate the site for binding HBGA ligands and complementary ligands from a large compound library, thereby facilitating the design of potent heterobifunctional ligands. Saturation transfer difference (STD) NMR experiments, spin-lock filtered NMR experiments, and interligand NOE (ILOE) experiments in the presence of virus-like particles (VLPs), identified compounds that bind to the HBGA binding site of human norovirus. Based on these data two multivalent prototype entry-inhibitors against norovirus infection were synthesized. A surface plasmon resonance based inhibition assay showed avidity gains of 1000 and one million fold over a millimolar univalent ligand. This suggests that further rational design of multivalent inhibitors based on our strategy will identify potent entry-inhibitors against norovirus infections.