The Shapley-Folkman Theorem and the Range of a Bounded Measure: An Elementary and Unified Treatment

We present proofs, based on the Shapley-Folkman theorem, of the convexity of the range of a strongly continuous, finitely additive measure, as well as that of an atomless, countably additive measure. We also present proofs, based on diagonalization and separation arguments respectively, of the closure of the range of a purely atomic or purely nonatomic countably additive measure. A combination of these results yields Lyapunov's celebrated theorem on the range of a countably additive measure. We also sketch, through a comprehensive bibliography, the pervasive diversity of the applications of the Shapley-Folkman theorem in mathematical economics.

Chemoenzymatic Synthesis of Cryptophycin Anticancer Agents by an Ester Bond-Forming Non-ribosomal Peptide Synthetase Module

Cryptophycins (Crp) are a group of cyanobacterial depsipeptides with activity against drug-resistant tumors. Although they have been shown to be promising, further efforts are required to return these highly potent compounds to the clinic through a new generation of analogues with improved medicinal properties. Herein, we report a chemosynthetic route relying on themultifunctional enzyme CrpD-M2 that incorporates a 2-hydroxy acid moiety (unit D) into Crp analogues. CrpD-M2 is a unique nonribosomal peptide synthetase (NRPS) module comprised of condensation-adenylation-ketoreduction-thiolation (C-A-KR-T) domains. We interrogated A-domain 2-keto and 2-hydroxy acid activation and loading, and KR domain activity in the presence of NADPH and NADH. The resulting 2-hydroxy acid was elongated with three synthetic Crp chain elongation intermediate analogues through ester bond formation catalyzed by CrpD-M2 C domain. Finally, the enzyme-bound seco-Crp products were macrolactonized by the Crp thioesterase. Analysis of these sequential steps was enabled through LC-FTICR-MS of enzyme-bound intermediates and products. This novel chemoenzymatic synthesis of Crp involves four sequential catalytic steps leading to the incorporation of a 2-hydroxy acid moiety in the final chain elongation intermediate. The presented work constitutes the first example where a NRPS-embedded KR domain is employed for assembly of a fully elaborated natural product, and serves as a proof-of-principle for chemoenzymatic synthesis of new Crp analogues

Exploiting the user interaction context for automatic task detection

Detecting the task a user is performing on her computer desktop is important for providing her with contextualized and personalized support. Some recent approaches propose to perform automatic user task detection by means of classifiers using captured user context data. In this paper we improve on that by using an ontology-based user interaction context model that can be automatically populated by (i) capturing simple user interaction events on the computer desktop and (ii) applying rule-based and information extraction mechanisms. We present evaluation results from a large user study we have carried out in a knowledge-intensive business environment, showing that our ontology-based approach provides new contextual features yielding good task detection performance. We also argue that good results can be achieved by training task classifiers `online' on user context data gathered in laboratory settings. Finally, we isolate a combination of contextual features that present a significantly better discriminative power than classical ones

El último Naturalista

El libro contiene catorce capítulos dedicados a diferentes facetas de la extensa actividad científica de este naturalista además de un prólogo escrito por Carlos Martín Escorza, del Museo Nacional de Ciencias Naturales, y una presentación por Emilio Cervantes (Coordinador de la Edición).Capítulo quinto en el libro dedicado al importante naturalista español Mariano de la Paz Graells y Agüera en el doscientos aniversario de su nacimiento.El libro se publicó por el Instituto de Estudios RiojanosPeer reviewe

How to improve drug dosing for patients with renal impairment in primary care - a cluster-randomized controlled trial

Background: Patients with chronic kidney disease (CKD) are at increased risk for inappropriate or potentially harmful prescribing. The aim of this study was to examine whether a multifaceted intervention including the use of a software programme for the estimation of creatinine clearance and recommendation of individual dosage requirements may improve correct dosage adjustment of relevant medications for patients with CKD in primary care. Methods: A cluster-randomized controlled trial was conducted between January and December 2007 in small primary care practices in Germany. Practices were randomly allocated to intervention or control groups. In each practice, we included patients with known CKD and elderly patients (>=70 years) suffering from hypertension. The practices in the intervention group received interactive training and were provided a software programme to assist with individual dose adjustment. The control group performed usual care. Data were collected at baseline and at 6 months. The outcome measures, analyzed across individual patients, included prescriptions exceeding recommended maximum daily doses, with the primary outcome being prescriptions exceeding recommended standard daily doses by 30% or more. Results: Data from 44 general practitioners and 404 patients are included. The intervention was effective in reducing prescriptions exceeding the maximum daily dose per patients, with a trend in reducing prescriptions exceeding the standard daily dose by more than 30%. Conclusions: A multifaceted intervention including the use of a software program effectively reduced inappropriately high doses of renally excreted medications in patients with CKD in the setting of small primary care practices

On Large Games with a Bio-Social Typology

We present a comprehensive theory of large non-anonymous games in which agents have a name and a determinate social-type and/or biological trait to resolve the dissonance of a (matching-pennies type) game with an exact pure-strategy Nash equilibrium with finite agents, but without one when modeled on the Lebesgue unit interval. We (i) establish saturated player spaces as both necessary and sufficient for an existence result for Nash equilibrium in pure strategies, (ii) clarify the relationship between pure, mixed and behavioral strategies via the exact law of large numbers in a framework of Fubini extension, (iii) illustrate corresponding asymptotic results.

Связь параметров электрического отклика на ударное воздействие с качеством контакта цементной матрицы и крупного заполнителя в бетоне

The work presents the research results of the parameters of the electric response to impact excitation of the heavy concrete samples with different quality of contact of the cement matrix and coarse aggregate. It is established that a change of the contact zone characteristics lead to the transformation of the spectra of the electric responses, shift of the spectrum towards lower frequencies and decrease in the attenuation coefficient of the energy of the electric responses