Optimal strategies for mitigating the HIV/AIDS epidemic in the Philippines

The human immunodeficiency virus (HIV) impairs a person's immune system against many infections and some types of cancer, leading to acquired immunodeficiency syndrome (AIDS), which is characterized by severe illnesses. The number of HIV infections in the Philippines has increased, more than doubled, within the last decade. This alarming HIV crisis in the country requires urgent actions. In this study, a mathematical model is developed to describe the disease transmission in the Philippines. Disease-free and endemic equilibria are obtained, stability analysis is performed, and the basic reproduction number is computed. Sensitivity analyses and subset selection are performed to identify influential parameters and to determine an identifiable parameter set given measurements, respectively. Available data on the number of asymptomatic aware infectious, those who are in the AIDS stage, and those under treatment are utilized to estimate key epidemiological parameters such as transmission, treatment, and screening rates. Uncertainty of these parameter estimates is quantified through bootstrapping method. Furthermore, intervention strategies are investigated in the framework of optimal control theory. Control measures include precaution, HIV screening, antiretroviral treatment, and pre-exposure prophylaxis (PrEP) treatment. These various control efforts are compared with regard to cost efficiency and effectiveness in reducing the number of infected individuals. Given limited available control measures, the PrEP-only scenario is shown to be the most cost-effective, followed by other scenarios that combine PrEP with other controls.     

Interior point methods specialized to optimal pump operation costs of water distribution networks

In the water distribution problem the loss is important and the objective function must consider it combined with pump costs. The problem becomes complex because the loss in each branch is as a nonlinear function of water outflow. The objective of this work consists in solving the water distribution problem using interior point methods and to exploit the particular structure of the problem and the specific matrix sparse pattern of the of the resulting linear systems. The interior point methods show to be robust, achieving fast convergence in all instances tested. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A robust and efficient proposal for solving linear systems arising in interior-point methods for linear programming

We introduce an efficient and robust proposal for solving linear systems arising at each iteration of primal-dual interior-point methods for linear programming. Our proposal is based on the stable system presented by Gonzalez-Lima et al. (Comput. Opt. Appl. 44:213–247, 2009). Using similar techniques as those employed in the splitting preconditioner introduced by Oliveira and Sorensen (Linear Algebra Appl. 394:1–24, 2005) we are able to express the stable system matrix in block form such that the diagonal blocks are nonsingular diagonal matrices and the off-diagonal blocks are matrices close to zero when the iterates are close to the solution set of the linear programming problem. For degenerate problems a perturbation of the diagonal is added. We use a low-cost fixed iterative method to solve this system. Numerical experiments have shown that our approach leads to very accurate solutions for the linear programming problem.     

Bicategories of spans and relations

A new kind of bicategorical limit is used to characterize bicategories of the form Spant($\text{E}$) and Rel($\text{E}$) where in the former case $\text{E}$ is a category with pullbacks and in the latter $\text{E}$ is a regular category. The characterization of Rel($\text{E}$) differs from those in the literature which require involutions on the bicategories.     

Diastereoselective synthesis and estimation of the conformational flexibility of 6-oxoperhydropyridazine-3-carboxylic acid derivatives

alpha,beta-Didehydroglutamates have been diastereoselectively transformed into 6-oxoperhydropyridazine-3-carboxylic acid derivatives (OPCAs), which constitute a new class of cyclic amino acid derivatives. Acylation at N-1 renders dipeptides which show considerable conformational rigidity. Semiempirical calculations suggest that OPCAs might force peptide turns with different amplitudes depending on the substitution pattern and relative stereochemistry of the substituents of the pyridazinone ring.     

A novel synthesis of N-methyl asparagine,arginine, histidine,and tryptophan

[reaction: see text] N-Methyl amino acid residues in peptides modify several pharmacologically useful parameters, but synthesis of alkylated peptides is hampered by unavailability of N-methylated monomers. The syntheses of four N-methyl amino acids with basic side chains are presented. The side chains of these basic amino acids needed to be specially protected or constructed. This completes the set of 20 common L-amino acid N-methyl derivatives prepared via 5-oxazolidinone intermediates by our group.     

Improving photocurrent generation: supramolecularly and covalently functionalized single-wall carbon nanotubes-polymer/porphyrin donor-acceptor nanohybrids

Novel nanohybrids based on covalently and noncovalently functionalized single-wall carbon nanotubes (SWNTs) have been prepared and assembled for the construction of photoactive electrodes. Polymer-grafted SWNTs were synthesized by free-radical polymerization of (vinylbenzyl)trimethylammonium chloride. Poly[(vinylbenzyl)trimethylammonium chloride] (PVBTAn+) was also noncovalently wrapped around SWNTs to form stable, positively charged SWNT/PVBTAn+ suspensions in water. Versatile donor-acceptor nanohybrids were prepared by using the electrostatic/van der Waals interactions between covalent SWNT-PVBTAn+ and/or noncovalent SWNT/PVBTAn+ and porphyrins (H2P8- and/or ZnP8-). Several spectroscopic, microscopic, transient, and photoelectrochemical measurements were taken to characterize the resulting supramolecular complexes. Photoexcitation of the nanohybrids afforded long-lived radical ion pairs with lifetimes as long as 2.2 micros. In the final part, photoactive electrodes were constructed by using a layer-by-layer technique on an indium tin oxide covered glass support. Photocurrent measurements gave remarkable internal photon-to-current efficiencies of 3.81 and 9.90 % for the covalent ZnP8-/SWNT-PVBTAn+ and noncovalent ZnP8-/SWNT/PVBTAn+ complex, respectively, when a potential of 0.5 V was applied.     

Effect of carbon nanofiber functionalization on the adsorption properties of volatile organic compounds

The effect of the chemical activation, using HNO3, of a commercial carbon nanofiber (CNF) on its surface chemistry and adsorption properties is studied in this work. The adsorption of different alkanes (linear and cyclic), aromatic compounds and chlorohydrocarbons on both the parent and the oxidized CNF were compared. Temperature-programmed desorption results, in agreement with X-ray photoelectron spectroscopy experiments, reveal the existence of oxygen groups on the surface of the treated CNF. Capacity of adsorption was derived from the adsorption isotherms, whereas thermodynamic properties (enthalpy of adsorption, surface free energy characteristics) have been determined from chromatographic retention data. Both the capacity and the strength of adsorption decrease after the oxidant treatment of the carbon nanofibers, although in the case of chlorinated compounds the specific component of the surface energy shows an important increase. For n-alkanes and cyclic compounds, it was demonstrated that the presence of oxygen surface groups does not affect their interaction, the morphology of the surface being the key parameter. The oxidation of the nanofiber leads to steric limitations of the adsorption. In the adsorption of aromatic compounds, these limitations are compensated by the nucleophilic interactions between the aromatic ring and surface oxygenated groups, leading to similar performances of both materials. The absence of nucleophilic groups in the chlorinated compounds hinders their adsorption on the activated nanofibers.     

A new approach for finding a basis for the splitting preconditioner for linear systems from interior point methods

The class of splitting preconditioners for the iterative solution of linear systems arising from Mehrotra’s predictor-corrector method for large scale linear programming problems needs to find a basis through a sophisticated process based on the application of a rectangular LU factorization. This class of splitting preconditioners works better near a solution of the linear programming problem when the matrices are highly ill-conditioned. In this study, we develop and implement a new approach to find a basis for the splitting preconditioner, based on standard rectangular LU factorization with partial permutation of the scaled transpose linear programming constraint matrix. In most cases, this basis is better conditioned than the existing one. In addition, we include a penalty parameter in Mehrotra’s predictor-corrector method in order to reduce ill-conditioning of the normal equations matrix. Computational experiments show a reduction in the average number of iterations of the preconditioned conjugate gradient method. Also, the increased efficiency and robustness of the new approach become evident by the performance profile.