MATHEMATICAL MODELS AND POLYHEDRAL STUDIES FOR INTEGRAL SHEET METAL DESIGN

We deal with the optimization of the production of branched sheet metal products. New forming techniques for sheet metal give rise to a wide variety of possible profiles and possible ways of production. In particular, we show how the problem of producing a given profile geometry can be modeled as a discrete optimization problem. We provide a theoretical analysis of the model in order to improve its solution time. In this context we give the complete convex hull description of some substructures of the underlying polyhedron. Moreover, we introduce a new class of facet-defining inequalities that represent connectivity constraints for the profile and show how these inequalities can be separated in polynomial time. Finally, we present numerical results for various test instances, both real-world and academic examples.

Predictive models for mutations in mismatch repair genes: implication for genetic counseling in developing countries

Background: Lynch syndrome (LS) is the most common form of inherited predisposition to colorectal cancer (CRC), accounting for 2-5% of all CRC. LS is an autosomal dominant disease characterized by mutations in the mismatch repair genes mutL homolog 1 (MLH1), mutS homolog 2 (MSH2), postmeiotic segregation increased 1 (PMS1), post-meiotic segregation increased 2 (PMS2) and mutS homolog 6 (MSH6). Mutation risk prediction models can be incorporated into clinical practice, facilitating the decision-making process and identifying individuals for molecular investigation. This is extremely important in countries with limited economic resources. This study aims to evaluate sensitivity and specificity of five predictive models for germline mutations in repair genes in a sample of individuals with suspected Lynch syndrome. Methods: Blood samples from 88 patients were analyzed through sequencing MLH1, MSH2 and MSH6 genes. The probability of detecting a mutation was calculated using the PREMM, Barnetson, MMRpro, Wijnen and Myriad models. To evaluate the sensitivity and specificity of the models, receiver operating characteristic curves were constructed. Results: Of the 88 patients included in this analysis, 31 mutations were identified: 16 were found in the MSH2 gene, 15 in the MLH1 gene and no pathogenic mutations were identified in the MSH6 gene. It was observed that the AUC for the PREMM (0.846), Barnetson (0.850), MMRpro (0.821) and Wijnen (0.807) models did not present significant statistical difference. The Myriad model presented lower AUC (0.704) than the four other models evaluated. Considering thresholds of >= 5%, the models sensitivity varied between 1 (Myriad) and 0.87 (Wijnen) and specificity ranged from 0 (Myriad) to 0.38 (Barnetson). Conclusions: The Barnetson, PREMM, MMRpro and Wijnen models present similar AUC. The AUC of the Myriad model is statistically inferior to the four other models.

An in-depth analysis of the HIV-1/AIDS dynamics by comprehensive mathematical modeling

This work presents major results from a novel dynamic model intended to deterministically represent the complex relation between HIV-1 and the human immune system. The novel structure of the model extends previous work by representing different host anatomic compartments under a more in-depth cellular and molecular immunological phenomenology. Recently identified mechanisms related to HIV-1 infection as well as other well known relevant mechanisms typically ignored in mathematical models of HIV-1 pathogenesis and immunology, such as cell-cell transmission, are also addressed. (C) 2011 Elsevier Ltd. All rights reserved.