Mathematical programs with complementarity constraints: convergence properties of a smoothing method

In this paper, optimization problems $P$ with complementarity constraints are considered. Characterizations for local minimizers $\bar{x}$ of $P$ of Orders 1 and 2 are presented. We analyze a parametric smoothing approach for solving these programs in which $P$ is replaced by a perturbed problem $P_{\tau}$ depending on a (small) parameter $\tau$. We are interested in the convergence behavior of the feasible set $\cal{F}_{\tau}$ and the convergence of the solutions $\bar{x}_{\tau}$ of $P_{\tau}$ for $\tau\to 0.$ In particular, it is shown that, under generic assumptions, the solutions $\bar{x}_{\tau}$ are unique and converge to a solution $\bar{x}$ of $P$ with a rate $\cal{O}(\sqrt{\tau})$. Moreover, the convergence for the Hausdorff distance $d(\cal{F}_{\tau}$, $\cal{F})$ between the feasible sets of $P_{\tau}$ and $P$ is of order $\cal{O}(\sqrt{\tau})$

Estimación bajo no-respuestas aleatorias al usar diseños de probabilidades desiguales

Sin resume

La correspondencia del hombre práctico. Los usos epistolares de la nobleza española del Siglo de Oro a través de seis años de cartas del tercer conde de Fernán Núñez (1679-1684)

Francisco Gutiérrez de los Ríos y Córdoba, 3rd Earl of Fernán Núñez, well known as an author (El hombre práctico. Seville?: 1686), also devoted his energies to letter-writing. He wrote almost six thousand letters from 1679 to 1684, setting up a varied correspondance which now can be studied thanks to a very single source, the daily six-year account of all his letters. This source provides a huge amount of information about the uses practised by early modern Hispanic and European nobles and it shows how the aristocratic letter-writing customs reveal a distinctive type of sociability based on manuscript correspondance

Introducción. Escritura en cartas

Sin resume

Consequences of Clostridium difficile infection: understanding the healthcare burden

AbstractClostridium difficile is the leading cause of infectious nosocomial diarrhoea in developed countries, with a measured incidence of approximately five episodes per 10 000 days of hospital stay in Europe. Accurate diagnosis of C. difficile infection (CDI) is a prerequisite for obtaining reliable epidemiological data, but in many European countries diagnosis is probably suboptimal. A significant percentage of CDI cases are missed because clinicians often fail to request tests for C. difficile toxins in cases of unexplained diarrhoea. In addition, some laboratories continue to use tests of low sensitivity or apply them inappropriately. In one study in Spain, failure to request CDI testing in more than two-thirds of patients with unexplained diarrhoea led to significant underdiagnosis of cases. A recent pan-European survey revealed huge discrepancies in the rate of CDI testing across Europe, which suggests that epidemiological reports underestimate the true incidence of CDI in many parts of Europe. This is important because, as this review of the clinical and economic burden of CDI illustrates, infection with C. difficile imposes a significant burden not only on patients, owing to increased morbidity and mortality, but also on healthcare systems and society in general. On the basis of current incidence rates, annual costs for management of CDI amount to approximately $800 million in the USA and €3000 million in Europe. Moreover, estimates suggest that costs associated with recurrent CDI can exceed those of primary CDI. Measures to more effectively prevent CDI and reduce CDI recurrence rates may help to reduce this burden

Novel Antimicrobials to Combat Gram Positive Bacteria

A novel class of antibacterial substances has been discovered in a collaborative project between the Chemistry and Biology Departments at Grand Valley State University (GVSU). These compounds do not rely on currently accepted antibiotic chemical structure but seemingly have a mechanism of action different from understood mechanistic pathways for treatment of infections and are readily synthesized, avoiding complex, stereoselective, multi-step synthesis. This new class of antibiotics is composed of chemical derivatives of the telomerase inhibitor BIBR1532 [US Patent 6362210]. Our compounds demonstrated significant antimicrobial activity against a group of Gram-Positive microorganisms. The antibiotic’s minimum inhibitory concentrations (MICs) against these bacteria are equivalent to existing antibiotics (2-78 ug/ml). In subsequent in-vitro tests these compounds showed activity against methicillin-resistant Staphylococcus aureus (MRSA), vancomycin resistant enterococci (VRE), Bacillus anthracis (anthrax), and Clostridium difficile (Cdiff). The antibacterial activity against MRSA, VRE, and Cdiff strains of bacteria is promising as it demonstrates the ability of BIBR 1532 to inhibit microbial growth in organisms with resistance to common antibiotics. In 2008, GVSU patented this antibiotic family. Since then, we determined that the frequency of bacterial resistance to this class of antibiotics is extremely low. Over 70 compounds were tested for antibacterial activity. Sixty demonstrated antibacterial activity and of these 18 were more thoroughly tested against 25 bacterial and fungal strains. We discovered that a number of compounds had low minimum inhibitory concentrations (MICs) against Staphylococcus aureus (including MRSA strains), Bacillus anthracis (anthrax), Clostridium difficile, and Streptococcus pneumonia. These results were encouraging as they demonstrate multiple bacterial targets with low drug concentrations (2-8 ug/ml). Additionally, we tested six compounds in acute in vitro toxicity screening in a rat hepatoma (H4IIE) cell line at 24 hour exposure. All compounds demonstrated minimal toxicity to the cell line. These toxicity results demonstrate that potential negative side-effects to patients appear to be minimal. Further testing of our antibiotics revealed significant binding to human serum protein. This is potentially problematic in clinical use as there is less available compound in the blood. There are conflicting opinions as to the significance of binding to serum protein. For example, nine of the top 10 best-selling small molecule, single agent prescription drugs of 2006 had 90% or greater binding to serum protein and seven of the top ten had 95% or greater [Rydzewski, R.M., 2008]. A potential problem exists and we continue to work towards lowering this binding to increase potential available drug concentrations in the blood. *This scholar and faculty mentor have requested that only an abstract be published