ANOMALIES OF COMPLEX VARIATIONAL PHASE-SHIFTS

It is argued, contrary to various claims and expectations, that the phase shifts calculated via variational principles for the t matrix involving complex algebra may exhibit anomalous behavior. These anomalies are numerically demonstrated in the case of the complex Kohn and the Newton variational principles for the t matrix and are expected to appear for other similar variational principles for the t matrix, such as the Takatsuka-McKoy variational principle.

Comparison between Two Methods to Calculate the Transition Matrix of Orbit Motion

Two methods to evaluate the state transition matrix are implemented and analyzed to verify the computational cost and the accuracy of both methods. This evaluation represents one of the highest computational costs on the artificial satellite orbit determination task. The first method is an approximation of the Keplerian motion, providing an analytical solution which is then calculated numerically by solving Kepler's equation. The second one is a local numerical approximation that includes the effect of J(2). The analysis is performed comparing these two methods with a reference generated by a numerical integrator. For small intervals of time (1 to 10s) and when one needs more accuracy, it is recommended to use the second method, since the CPU time does not excessively overload the computer during the orbit determination procedure. For larger intervals of time and when one expects more stability on the calculation, it is recommended to use the first method.

A control chart based on sample ranges for monitoring the covariance matrix of the multivariate processes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A new chart based on sample variances for monitoring the covariance matrix of multivariate processes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A new chart for monitoring the covariance matrix of bivariate processes

In this article we consider a control chart based on the sample variances of two quality characteristics. The points plotted on the chart correspond to the maximum value of these two statistics. The main reason to consider the proposed chart instead of the generalized variance |S| chart is its better diagnostic feature, that is, with the new chart it is easier to relate an out-of-control signal to the variables whose parameters have moved away from their in-control values. We study the control chart efficiency considering different shifts in the covariance matrix. In this way, we obtain the average run length (ARL) that measures the effectiveness of a control chart in detecting process shifts. The proposed chart always detects process disturbances faster than the generalized variance |S| chart. The same is observed when the size of the samples is variable, except in a few cases in which the size of the samples switches between small size and very large size.

Control charts for monitoring the mean vector and the covariance matrix of bivariate processes

In this article, we propose new control charts for monitoring the mean vector and the covariance matrix of bivariate processes. The traditional tools used for this purpose are the T (2) and the |S| charts. However, these charts have two drawbacks: (1) the T (2) and the |S| statistics are not easy to compute, and (2) after a signal, they do not distinguish the variable affected by the assignable cause. As an alternative to (1), we propose the MVMAX chart, which only requires the computation of sample means and sample variances. As an alternative to (2), we propose the joint use of two charts based on the non-central chi-square statistic (NCS statistic), named as the NCS charts. Once the NCS charts signal, the user can immediately identify the out-of-control variable. In general, the synthetic MVMAX chart is faster than the NCS charts and the joint T (2) and |S| charts in signaling processes disturbances.

Monitoring the mean vector and the covariance ­matrix of multivariate processes with sample means and sample ranges

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Formation and maintenance of complex systems

A complex system is often identified by the absence of a characteristic length, e.g. as in a fractal. A very large system subject to a fragmentation and/or aggregation dynamics passes through such complex configurations. We study statistically creation and maintenance of such configurations in space dimensions d = 1 to 5 and find that they are easily created (maintained) for small (large) d. An intermediate d such as d = 3 seems to be ideal for the creation and maintenance of complex systems. This has consequences in a statistical description of the universe.

Extracellular matrix of porcine pericardium: Biochemistry and collagen architecture

Pericardial tissue has been used to construct bioprostheses employed in the repair of different kinds of injuries, mostly cardiac. However, calcification and mechanical failure have been the main causes of the limited durability of cardiac bioprostheses constructed with bovine pericardium. In the course of this work, a study was conducted on porcine fibrous pericardium, its microscopic structure and biochemical nature. The general morphology and architecture of collagen were studied under conventional light and polarized light microscopy. The biochemical study of the pericardial matrix was conducted according to the following procedures: swelling test, hydroxyproline and collagen dosage, quantification of amino acids in soluble collagen, component extraction of the extracellular matrix of the right and left ventral regions of pericardium with different molarities of guanidine chloride, protein and glycosaminoglycan (GAG) dosage, sodium dodecyl sulfate-polyacrylamide gel electrophoresis and total GAG analysis. Microscopic analysis showed collagen fibers arranged in multidirectionally oriented layers forming a closely knit web, with a larger number of fibers obliquely oriented, initiating at the lower central region toward the upper left lateral relative to the heart. No qualitative differences were found between proteins extracted from the right and left regions. Likewise, no differences were found between fresh and frozen material. Protein dosages from left frontal and right frontal pericardium regions showed no significant differences. The quantities of extracted GAGs were too small for detection by the method used. Enzymatic digestion and electrophoretic analysis showed that the GAG found is possibly dermatan sulfate. The proteoglycan showed a running standard very similar to the small proteoglycan decorin.

A single statistic for monitoring the covariance matrix of bivariate processes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Studies on the formation of complex coacervates between chitosan and alginate during microparticles preparation

The formation of complex coacervates between chitosan and alginate was evaluated during microparticles formation. Mass ratio between polyelectrolytes and calcium chloride concentration were determinated by conductimetric analysis and by calcium ions quantification, respectively. Inert microparticles were prepared using a complex coacervation method in W/O emulsion and morphological analyses of microparticles were carried out. This method enabled the production of spherical particles, with slightly rough surface and narrow size distribution with maximal diameter of 10 μm.

Analysis of numeric conditioning of Hessian matrix of Lagrangian via singular values

This paper presents an analyze of numeric conditioning of the Hessian matrix of Lagrangian of modified barrier function Lagrangian method (MBFL) and primal-dual logarithmic barrier method (PDLB), which are obtained in the process of solution of an optimal power flow problem (OPF). This analyze is done by a comparative study through the singular values decomposition (SVD) of those matrixes. In the MBLF method the inequality constraints are treated by the modified barrier and PDLB methods. The inequality constraints are transformed into equalities by introducing positive auxiliary variables and are perturbed by the barrier parameter. The first-order necessary conditions of the Lagrangian function are solved by Newton's method. The perturbation of the auxiliary variables results in an expansion of the feasible set of the original problem, allowing the limits of the inequality constraints to be reached. The electric systems IEEE 14, 162 and 300 buses were used in the comparative analysis. ©2007 IEEE.

A single chart with supplementary runs rules for monitoring the mean vector and the covariance matrix of multivariate processes

The MRMAX chart is a single chart based on the standardized sample means and sample ranges for monitoring the mean vector and the covariance matrix of multivariate processes. User's familiarity with the computation of these statistics is a point in favor of the MRMAX chart. As a single chart, the recently proposed MRMAX chart is very appropriate for supplementary runs rules. In this article, we compare the supplemented MRMAX chart and the synthetic MRMAX chart with the standard MRMAX chart. The supplementary and the synthetic runs rules enhance the performance of the MRMAX chart. © 2013 Elsevier Ltd.