Front tracking with moving-least-squares surfaces

The representation of interfaces by means of the algebraic moving-least-squares (AMLS) technique is addressed. This technique, in which the interface is represented by an unconnected set of points, is interesting for evolving fluid interfaces since there is]to surface connectivity. The position of the surface points can thus be updated without concerns about the quality of any surface triangulation. We introduce a novel AMLS technique especially designed for evolving-interfaces applications that we denote RAMLS (for Robust AMLS). The main advantages with respect to previous AMLS techniques are: increased robustness, computational efficiency, and being free of user-tuned parameters. Further, we propose a new front-tracking method based on the Lagrangian advection of the unconnected point set that defines the RAMLS surface. We assume that a background Eulerian grid is defined with some grid spacing h. The advection of the point set makes the surface evolve in time. The point cloud can be regenerated at any time (in particular, we regenerate it each time step) by intersecting the gridlines with the evolved surface, which guarantees that the density of points on the surface is always well balanced. The intersection algorithm is essentially a ray-tracing algorithm, well-studied in computer graphics, in which a line (ray) is traced so as to detect all intersections with a surface. Also, the tracing of each gridline is independent and can thus be performed in parallel. Several tests are reported assessing first the accuracy of the proposed RAMLS technique, and then of the front-tracking method based on it. Comparison with previous Eulerian, Lagrangian and hybrid techniques encourage further development of the proposed method for fluid mechanics applications. (C) 2008 Elsevier Inc. All rights reserved.

p-iodophenol-enhanced luminol chemiluminescent assay applied to discrimination between acute lymphoblastic and minimally differentiated acute myeloid (FAB-M0) or acute megakaryoblastic (FAB-M7) leukemias

Introduction: In this report, we propose the application of the p-iodophenol-enhanced luminol chemiluminescent technique to the determination of peroxidase (myeloperoxidase and/or platelet peroxidase) activity in blasts of minimally differentiated acute myeloblastic leukemia (AML-M0) and acute megakaryoblastic leukemia (AML-M7).Methods: the frozen blast cells from 29 patients were thawed and submitted to the optimized protocol.Results: All cases of AML-M7 and AML-M0 exhibited integrated light emission greater than 73 (10(2) mV x s), which was the arbitrary cutoff point set for the discrimination between AML and acute lymphoblastic leukemia (ALL) (mean + 3 x s.d. of ALL samples, n = 10). In addition, five out of seven cases of AML-M0 showed results above the Cutoff point.Conclusion: This highly sensitive enhanced chemiluminescent technique may be applied to discriminate between ALL and AML-M7 or AML-M1 cases, and most AML-M0 cases. It is very simple, cheap and easy to perform compared to other procedures used to measure MPO activity in AML-leukemias including AML-M7 and AML-M0.

On the Betti number of the union of two generic map images

Let f: M --> N and g: K --> N be generic differentiable maps of compact manifolds without boundary into a manifold such that their intersection satisfies a certain transversality condition. We show, under a certain cohomological condition, that if the images f(M) and g(K) intersect, then the (upsilon + 1)th Betti number of their union is strictly greater than the sum of their (upsilon + 1)th Betti numbers, where upsilon = dim M + dim K - dim N. This result is applied to the study of coincidence sets and fixed point sets. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Friedrich Riesz' Beiträge zur Herausbildung des modernen mathematischen Konzepts abstrakter Räume

Der ungarische Mathematiker Friedrich Riesz studierte und forschte in den mathematischen Milieus von Budapest, Göttingen und Paris. Die vorliegende Arbeit möchte zeigen, daß die Beiträge von Riesz zur Herausbildung eines abstrakten Raumbegriffs durch eine Verknüpfung von Entwicklungen aus allen drei mathematischen Kulturen ermöglicht wurden, in denen er sich bewegt hat. Die Arbeit konzentriert sich dabei auf den von Riesz 1906 veröffentlichten Text „Die Genesis des Raumbegriffs". Sowohl für seine Fragestellungen als auch für seinen methodischen Zugang fand Riesz vor allem in Frankreich und Göttingen Anregungen: Henri Poincarés Beiträge zur Raumdiskussion, Maurice Fréchets Ansätze einer abstrakten Punktmengenlehre, David Hilberts Charakterisierung der Stetigkeit des geometrischen Raumes. Diese Impulse aufgreifend suchte Riesz ein Konzept zu schaffen, das die Forderungen von Poincaré, Hilbert und Fréchet gleichermaßen erfüllte. So schlug Riesz einen allgemeinen Begriff des mathematischen Kontinuums vor, dem sich Fréchets Konzept der L-Klasse, Hilberts Mannigfaltigkeitsbegriff und Poincarés erfahrungsgemäße Vorstellung der Stetigkeit des ‚wirklichen' Raumes unterordnen ließen. Für die Durchführung seines Projekts wandte Riesz mengentheoretische und axiomatische Methoden an, die er der Analysis in Frankreich und der Geometrie bei Hilbert entnommen hatte. Riesz' aufnahmebereite Haltung spielte dabei eine zentrale Rolle. Diese Haltung kann wiederum als ein Element der ungarischen mathematischen Kultur gedeutet werden, welche sich damals ihrerseits stark an den Entwicklungen in Frankreich und Deutschland orientierte. Darüber hinaus enthält Riesz’ Arbeit Ansätze einer konstruktiven Mengenlehre, die auf René Baire zurückzuführen sind. Aus diesen unerwarteten Ergebnissen ergibt sich die Aufgabe, den Bezug von Riesz’ und Baires Ideen zur späteren intuitionistischen Mengenlehre von L.E.J. Brouwer und Hermann Weyl weiter zu erforschen.

Improving shortest paths in the Delaunay triangulation

We study a problem about shortest paths in Delaunay triangulations. Given two nodes s; t in the Delaunay triangulation of a point set P, we look for a new point p that can be added, such that the shortest path from s to t in the Delaunay triangulation of P u{p} improves as much as possible. We study properties of the problem and give efficient algorithms to find such a point when the graph-distance used is Euclidean and for the link-distance. Several other variations of the problem are also discussed.

Multivariate orthogonal polynomials and integrable systems

Multivariate orthogonal polynomials in D real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formulae. The multivariate orthogonal polynomials, their second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants as well as Schur complements of bordered truncations of the moment matrix; quasi-tau functions are introduced. It is proven that the second kind functions are multivariate Cauchy transforms of the multivariate orthogonal polynomials. Discrete and continuous deformations of the measure lead to Toda type integrable hierarchy, being the corresponding flows described through Lax and Zakharov-Shabat equations; bilinear equations are found. Varying size matrix nonlinear partial difference and differential equations of the 2D Toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials. The discrete flows, which are shown to be connected with a Gauss-Borel factorization of the Jacobi type matrices and its quasi-determinants, lead to expressions for the multivariate orthogonal polynomials and their second kind functions in terms of shifted quasi-tau matrices, which generalize to the multidimensional realm, those that relate the Baker and adjoint Baker functions to ratios of Miwa shifted tau-functions in the 1D scenario. In this context, the multivariate extension of the elementary Darboux transformation is given in terms of quasi-determinants of matrices built up by the evaluation, at a poised set of nodes lying in an appropriate hyperplane in R^D, of the multivariate orthogonal polynomials. The multivariate Christoffel formula for the iteration of m elementary Darboux transformations is given as a quasi-determinant. It is shown, using congruences in the space of semi-infinite matrices, that the discrete and continuous flows are intimately connected and determine nonlinear partial difference-differential equations that involve only one site in the integrable lattice behaving as a Kadomstev-Petviashvili type system. Finally, a brief discussion of measures with a particular linear isometry invariance and some of its consequences for the corresponding multivariate polynomials is given. In particular, it is shown that the Toda times that preserve the invariance condition lay in a secant variety of the Veronese variety of the fixed point set of the linear isometry.

Metamorfose planar via métodos Level Set e Particle Level Set para a reconstrução de superfícies tridimensionais

Evolving interfaces were initially focused on solutions to scientific problems in Fluid Dynamics. With the advent of the more robust modeling provided by Level Set method, their original boundaries of applicability were extended. Specifically to the Geometric Modeling area, works published until then, relating Level Set to tridimensional surface reconstruction, centered themselves on reconstruction from a data cloud dispersed in space; the approach based on parallel planar slices transversal to the object to be reconstructed is still incipient. Based on this fact, the present work proposes to analyse the feasibility of Level Set to tridimensional reconstruction, offering a methodology that simultaneously integrates the proved efficient ideas already published about such approximation and the proposals to process the inherent limitations of the method not satisfactorily treated yet, in particular the excessive smoothing of fine characteristics of contours evolving under Level Set. In relation to this, the application of the variant Particle Level Set is suggested as a solution, for its intrinsic proved capability to preserve mass of dynamic fronts. At the end, synthetic and real data sets are used to evaluate the presented tridimensional surface reconstruction methodology qualitatively.

Metamorfose planar via métodos Level Set e Particle Level Set para a reconstrução de superfícies tridimensionais

Evolving interfaces were initially focused on solutions to scientific problems in Fluid Dynamics. With the advent of the more robust modeling provided by Level Set method, their original boundaries of applicability were extended. Specifically to the Geometric Modeling area, works published until then, relating Level Set to tridimensional surface reconstruction, centered themselves on reconstruction from a data cloud dispersed in space; the approach based on parallel planar slices transversal to the object to be reconstructed is still incipient. Based on this fact, the present work proposes to analyse the feasibility of Level Set to tridimensional reconstruction, offering a methodology that simultaneously integrates the proved efficient ideas already published about such approximation and the proposals to process the inherent limitations of the method not satisfactorily treated yet, in particular the excessive smoothing of fine characteristics of contours evolving under Level Set. In relation to this, the application of the variant Particle Level Set is suggested as a solution, for its intrinsic proved capability to preserve mass of dynamic fronts. At the end, synthetic and real data sets are used to evaluate the presented tridimensional surface reconstruction methodology qualitatively.

Logarithmically proportional objective function for planar surfaces recognition in 3D point cloud

3D laser scanning is becoming a standard technology to generate building models of a facility's as-is condition. Since most constructions are constructed upon planar surfaces, recognition of them paves the way for automation of generating building models. This paper introduces a new logarithmically proportional objective function that can be used in both heuristic and metaheuristic (MH) algorithms to discover planar surfaces in a point cloud without exploiting any prior knowledge about those surfaces. It can also adopt itself to the structural density of a scanned construction. In this paper, a metaheuristic method, genetic algorithm (GA), is used to test this introduced objective function on a synthetic point cloud. The results obtained show the proposed method is capable to find all plane configurations of planar surfaces (with a wide variety of sizes) in the point cloud with a minor distance to the actual configurations. © 2014 IEEE.

Testing of stair climbing point-of-choice prompts in Barcelona at an outdoor set of stairs and scalators on the Montjuïc site

Regular stair climbing has well-documented health dividends, such as increased fitness and strength, weight loss and reduced body fat, improved lipid profiles and reduced risk of osteoporosis. The general absence of barriers to participation makes stair climbing an ideal physical activity (PA) for health promotion. Studies in the US and the UK have consistently shown that interventions to increase the accumulation of lifestyle PA by climbing stairs rather than using the escalators are effective. However, there are no previous in Catalonia. This project tested one message for their ability to prompt travelers on the Montjuïc site to choose the stairs rather than the escalator when climbing up the Monjuïc hill. One standard message, " Take the stairs! 7 minutes of stair climbing a day protects your heart" provided a comparison with previous research done in the UK. Translated into Catalan and Spanish, it was presented on a poster positioned at the point of choice between the stairs and the escalator. The study used a quasi-experimental, interrupted time series design. Travelers, during several and specific hours on two days of the week, were coded for stair or escalator use, gender, age, ethnic status, presence of accompanying children or bags by one observer. Overall, the intervention resulted in a 81% increase in stair climbing. In the follow-up period without messages, stair climbing dropped out to baseline levels. This preliminary study showed a significant effect on stair use. However, caution is needed since results are based on a small sample and, only a low percentage of the sample took the stairs at baseline or the intervention phase . Future research on stair use in Catalonia should focus on using bigger samples, different sites (metro stations, airports, shopping centers, etc) , different messages and techniques to promote stair climbing.

Phylogenetic approach reveals that virus genotype largely determines HIV set-point viral load.

HIV virulence, i.e. the time of progression to AIDS, varies greatly among patients. As for other rapidly evolving pathogens of humans, it is difficult to know if this variance is controlled by the genotype of the host or that of the virus because the transmission chain is usually unknown. We apply the phylogenetic comparative approach (PCA) to estimate the heritability of a trait from one infection to the next, which indicates the control of the virus genotype over this trait. The idea is to use viral RNA sequences obtained from patients infected by HIV-1 subtype B to build a phylogeny, which approximately reflects the transmission chain. Heritability is measured statistically as the propensity for patients close in the phylogeny to exhibit similar infection trait values. The approach reveals that up to half of the variance in set-point viral load, a trait associated with virulence, can be heritable. Our estimate is significant and robust to noise in the phylogeny. We also check for the consistency of our approach by showing that a trait related to drug resistance is almost entirely heritable. Finally, we show the importance of taking into account the transmission chain when estimating correlations between infection traits. The fact that HIV virulence is, at least partially, heritable from one infection to the next has clinical and epidemiological implications. The difference between earlier studies and ours comes from the quality of our dataset and from the power of the PCA, which can be applied to large datasets and accounts for within-host evolution. The PCA opens new perspectives for approaches linking clinical data and evolutionary biology because it can be extended to study other traits or other infectious diseases.

Human immunodeficiency virus type 1 fitness is a determining factor in viral rebound and set point in chronic infection.

Human immunodeficiency virus type 1 (HIV-1) isolates from 20 chronically infected patients who participated in a structured treatment interruption (STI) trial were studied to determine whether viral fitness influences reestablishment of viremia. Viruses derived from individuals who spontaneously controlled viremia had significantly lower in vitro replication capacities than viruses derived from individuals that did not control viremia after interruption of antiretroviral therapy (ART), and replication capacities correlated with pre-ART and post-STI viral set points. Of note, no clinically relevant improvement of viral loads upon STI occurred. Virus isolates from controlling and noncontrolling patients were indistinguishable in terms of coreceptor usage, genetic subtype, and sensitivity to neutralizing antibodies. In contrast, viruses from controlling patients exhibited increased sensitivity to inhibition by chemokines. Sensitivity to inhibition by RANTES correlated strongly with slower replication kinetics of the virus isolates, suggesting a marked dependency of these virus isolates on high coreceptor densities on the target cells. In summary, our data indicate that viral fitness is a driving factor in determining the magnitude of viral rebound and viral set point in chronic HIV-1 infection, and thus fitness should be considered as a parameter influencing the outcome of therapeutic intervention in chronic infection.

Contact force transitions in regrasp tasks of planar objects

This paper presents a simple and fast solution to the problem of finding the time variations of the forces that keep the object equilibrium when a finger is removed from a three contact point grasp or a finger is added to a two contact point grasp, assuming the existence of an external perturbation force (that can be the object weight itself). The procedure returns force set points for the control system of a manipulator device in a regrasping action. The approach was implemented and a numerical example is included in the paper to illustrate how it works.

A new approach for the solution of the optimal set-point tracking problem for nonlinear systems

In this paper, a discrete time dynamic integrated system optimisation and parameter estimation algorithm is applied to the solution of the nonlinear tracking optimal control problem. A version of the algorithm with a linear-quadratic model-based problem is developed and implemented in software. The algorithm implemented is tested with simulation examples.

Reduced complexity set-point following in self-tuning control

An external input signal is incorporated into a self-tuning controller which, although it is based on a CARMA system model, employs a state-space framework for control law calculations. Steady-state set point following can then be accomplished even when only a recursive least squares parameter estimation scheme is used, despite the fact that the disturbance affecting the system may well be coloured.