A Reduced-Order Gauss-Newton Method for Nonlinear Problems Based on Compressed Sensing for PDE Applications

A global regularized Gauss-Newton (GN) method is proposed to obtain a zero residual for square nonlinear problems on an affine subspace built by wavelets, which allows reducing systems that arise from the discretization of nonlinear elliptic partial differential equations (PDEs) without performing a priori simulations. This chapter introduces a Petrov-Galerkin (PG) GN approach together with its standard assumptions that ensure retaining the q-quadratic rate of convergence. It also proposes a regularization strategy, which maintains the fast pace of convergence, to avoid singularities and high nonlinearities. It also includes a line-search method for achieving global convergence. The numerical results manifest the capability of the algorithm for reproducing the full-order model (FOM) essential features while decreasing the runtime by a significant magnitude. This chapter refers to a wavelet-based reduced-order model (ROM) as WROM, while PROM is the proper orthogonal decomposition (POD)-based counterpart. The authors also implemented the combination of WROM and PROM as a hybrid method referred herein as (HROM). Preliminary results with Bratu?s problem show that if the WROM could correctly reproduce the FOM behavior, then HROM can also reproduce that FOM accurately

A prospective cohort study to evaluate peridomestic infection as a determinant of dengue transmission: Protocol

<p>Abstract</p> <p>Background</p> <p>Vector control programs, which have focused mainly on the patient house and peridomestic areas around dengue cases, have not produced the expected impact on transmission. This project will evaluate the assumption that the endemic/epidemic transmission of dengue begins around peridomestic vicinities of the primary cases. Its objective is to assess the relationship between symptomatic dengue case exposure and peridomestic infection incidence.</p> <p>Methods/Design</p> <p>A prospective cohort study will be conducted (in Tepalcingo and Axochiapan, in the state of Morelos, Mexico), using the state surveillance system for the detection of incident cases. Paired blood specimens will be collected from both the individuals who live with the incident cases and a sample of subjects residing within a 25-meter radius of such cases (exposed cohort), in order to measure dengue-specific antibodies. Other subjects will be selected from areas which have not presented any incident cases within 200 meters, during the two months preceding the sampling (non-exposed cohort). Symptomatic/asymptomatic incident infection will be considered as the dependent variable, exposure to confirmed dengue cases, as the principal variable, and the socio-demographic, environmental and socio-cultural conditions of the subjects, as additional explanatory variables.</p> <p>Discussion</p> <p>Results indicating a high infection rate among the exposed subjects would justify the application of peridomestic control measures and call for an evaluation of alternate causes for insufficient program impact. On the other hand, a low incidence of peridomestic-infected subjects would support the hypothesis that infection occurs outside the domicile, and would thus explain why the vector control measures applied in the past have exerted such a limited impact on cases incidence rates. The results of the present study may therefore serve to reassess site selection for interventions of this type.</p

Lipoproteomics: Methodologies and Analysis of Lipoprotein-Associated Proteins along with the Drug Intervention

Lipoproteins are specialized particles involved in the transport and distribution of hydrophobic lipids, as cholesterol and triglycerides, throughout the body. The lipoproteins exhibit a basic spherical shape as complexes of lipids and proteins, and these latter are known as apolipoproteins. Initially, the proteins associated with lipoproteins were recognized as integral or peripheral proteins that only maintain the dynamics and metabolism of lipoproteins. However, there exist many studies on different lipoproteins evidencing that the quantity and type of apolipoproteins and lipoprotein-associated proteins are diverse and could be associated with different lipoprotein function outcomes. Here, we summarized recent processes in the determination of apolipoproteins and lipoprotein-associated proteins profiles through a proteomic approach, analyzing the major methods available and are used to achieve this. We also discuss the relevance of these lipoproteomic analyses on the human disease outcomes

An Interior-Point Krylov-Orthogonal Projection Method for Nonlinear Programming

In this work we consider an inexact Newton's method implementation of the primal-dual interior-point algorithm for solving general nonlinear programming problems recently introduced by Argáez and Tapia. This inexact method is designed to solve large scale problems. The iterative solution technique uses an orthogonal projection - Krylov subspace scheme to solve the highly indefinite and nonsymmetric linear systems associated with nonlinear programming. Our iterative method is a projection method that maintains linearized feasibility with respect to both the equality constraints and the complementarity conditions. This guarantees that in each iteration the linear solver generates a descent direction, so that the iterative solver is not required to find a Newton step but rather cheaply provides a way to march toward an optimal solution of the problem. This makes the use of a preconditioner inconsequential except near the solution of the problem, where the Newton step is effective. Moreover, we limit the problem to finding a good preconditioner only for the Hessian of the Lagrangian function associated with the problem plus a positive diagonal matrix. We report numerical experimentation for several large scale problems to illustrate the viability of the method

The report to Congress by the Board of Directors - March 2003

El Informe que se presenta al Honorable Congreso de la República analiza el comportamiento de la economía colombiana y la política macroeconómica adelantada en el año 2002. La economía colombiana se desenvolvió en un entorno internacional particularmente desfavorable, caracterizado por la coincidencia de dos choques negativos: la caída de la demanda externa y el menor acceso a los mercados internacionales de crédito. Estas mismas condiciones afectaron a otros países de América Latina, cuyo producto global solamente creció 0,5% en 2002.The following report, presented to the Congress of the Republic of Colombia, offers an analysis of the country's economic performance in 2002 and the macroeconomic policy implemented during that period. The Colombian economy faced in a particularly unfavorable international environment characterized by a combination of two negative shocks: a drop in external demand and less access to international markets for credit. Other Latin American countries were affected by these conditions as well, and their overall product rose by only 0.5% in 2002

The report to Congress by the Board of Directors - July 2002

El Informe que se presenta al Honorable Congreso de la República analiza el comportamiento de la economía colombiana y la política macroeconómica ejecutada durante 2002. La actividad económica continuó exhibiendo un bajo dinamismo en los primeros meses si bien se vio un repunte en el segundo trimestre del año. El desempleo, aunque se ha venido reduciendo y la ocupación ha aumentado, se mantuvo en niveles elevados. La cuenta corriente de la balanza de pagos registró un déficit menor que el del primer trimestre del año anterior, como consecuencia de la mayor caída de las importaciones con respecto a las exportaciones. La inflación anual descendió en los primeros cuatro meses del año en curso en respuesta al exceso de capacidad que aún registra la economía, la estabilidad cambiaria y la credibilidad de la política monetaria y de sus metas. En los meses de mayo y junio, se evidenció un aumento de la inflación, como consecuencia de un alza de los precios de los alimentos.The following report, presented to the Colombian Congress, offers an analysis of Colombia’s economic performance and the macroeconomic policy implemented in 2002. Economic activity continued to be slow during the early months of the year, although the second quarter saw a rebound. Unemployment remained high, although it has declined and occupation has increased. The current account in the balance of payments registered less of a deficit than in the first quarter of the previous year, thanks to more of a decline in imports as opposed to exports. Annual inflation dropped during the first four months of 2002 in response to continued excess capacity in the economy, exchange stability, and the credibility of the monetary policy and its goals. May and June saw evidence of a rise in inflation due to an increase in food prices

Modificaciones y mejoras al método de Karmarkar

IP 1106-05-307-93ARTICULO(S) EN REVISTA: On the characterization of q-superlinearconvergence of quasi-newton interior-point;methods for nonlinear programming / Hector J. Martinez, Z.Parada, R. A. Tapia - En: Boletin de la sociedad;matematica mexicana vol. 1 No 3 (1995); p. 137-148