Modeling on triangulations with geodesic curves

This paper discusses the problem of modeling on triangulated surfaces with geodesic curves. In the first part of the paper we define a new class of curves, called geodesic Bézier curves, that are suitable for modeling on manifold triangulations. As a natural generalization of Bézier curves, the new curves are as smooth as possible. In the second part we discuss the construction of C ⁰ and C ¹ piecewise Bézier splines. We also describe how to perform editing operations, such as trimming, using these curves. Special care is taken to achieve interactive rates for modeling tasks. The third part is devoted to the definition and study of convex sets on triangulated surfaces. We derive the convex hull property of geodesic Bézier curves.

A review on the combination of binary classifiers in multiclass problems

Several real problems involve the classification of data into categories or classes. Given a data set containing data whose classes are known, Machine Learning algorithms can be employed for the induction of a classifier able to predict the class of new data from the same domain, performing the desired discrimination. Some learning techniques are originally conceived for the solution of problems with only two classes, also named binary classification problems. However, many problems require the discrimination of examples into more than two categories or classes. This paper presents a survey on the main strategies for the generalization of binary classifiers to problems with more than two classes, known as multiclass classification problems. The focus is on strategies that decompose the original multiclass problem into multiple binary subtasks, whose outputs are combined to obtain the final prediction.     

A prototype for cartographic human body analysis

A cartographic-oriented model uses algebraic map operations to perform spatial analysis of medical data relative to the human body. A prototype system uses 3D visualization techniques to deliver analysis results. A prototype implementation suggests the model might provide the basis for a medical application tool that introduces new information insight.     

Dynamic Clustering of Interval-Valued Data Based on Adaptive Quadratic Distances

This paper presents partitioning dynamic clustering methods for interval-valued data based on suitable adaptive quadratic distances. These methods furnish a partition and a prototype for each cluster by optimizing an adequacy criterion that measures the fitting between the clusters and their representatives. These adaptive quadratic distances change at each algorithm iteration and can either be the same for all clusters or different from one cluster to another. Moreover, various tools for the partition and cluster interpretation of interval-valued data are also presented. Experiments with real and synthetic interval-valued data sets show the usefulness of these adaptive clustering methods and the merit of the partition and cluster interpretation tools.     

Slow-flow measurements and fluid dynamics analysis using the Fresnel drag effect

We have employed a Sagnac interferometer to measure small optical phase shifts induced by the Fresnel drag effect on moving media. The system detects volumetric flow rates of water as slow as 43 μL/min while maintaining a small pressure drop across the measuring pipe. Velocity profiles and turbulence measurements of flowing water are also demonstrated and discussed.     

Range of validity of the Rayleigh-Debye-Gans theory for optics of fractal aggregates

The range of validity of the Rayleigh-Debye-Gans approximation for the optical cross sections of fractal aggregates (RDG-FA) that are formed by uniform small particles was evaluated in comparison with the integral equation formulation for scattering (IEFS), which accounts for the effects of multiple scattering and self-interaction. Numerical simulations were performed to create aggregates that exhibit mass fractallike characteristics with a wide range of particle and aggregate sizes and morphologies, including x(p) = 0.01-1.0, ‖m - 1‖ = 0.1-2.0, N = 16-256, and D(f) = 1.0-3.0. The percent differences between both scattering theories were presented as error contour charts in the ‖m - 1‖x(p) domains for various size aggregates, emphasizing fractal properties representative of diffusion-limited cluster-cluster aggregation. These charts conveniently identified the regions in which the differences were less than 10%, between 10% and 30%, and more than 30% for easy to use general guidelines for suitability of the RDG-FA theory in any scattering applications of interest, such as laser-based particulate diagnostics. Various types of aggregate geometry ranging from straight chains (D(f) ≈ 1.0) to compact clusters (D(f) ≈ 3.0) were also considered for generalization of the findings. For the present computational conditions, the RDG-FA theory yielded accurate predictions to within 10% for ‖m - 1‖ to approximately 1 or more as long as the primary particles in aggregates were within the Rayleigh scattering limit (x(p) ≤ 0.3). Additionally, the effect of fractal dimension on the performance of the RDG-FA was generally found to be insignificant. The results suggested that the RDG-FA theory is a reasonable approximation for optics of a wide range of fractal aggregates, considerably extending its domain of applicability.     

Parameter identification in dynamic systems using the homotopy optimization approach

Identifying the parameters in a mathematical model governed by a system of ordinary differential equations is considered in this work. It is assumed that only partial state measurement is available from experiments, and that the parameters appear nonlinearly in the system equations. The problem of parameter identification is often posed as an optimization problem, and when deterministic methods are used for optimization, one often converges to a local minimum rather than the global minimum. To mitigate the problem of converging to local minima, a new approach is proposed for applying the homotopy technique to the problem of parameter identification. Several examples are used to demonstrate the effectiveness of the homotopy method for obtaining global minima, thereby successfully identifying the system parameters.     

Constrained linear regression models for symbolic interval-valued variables

This paper introduces an approach to fitting a constrained linear regression model to interval-valued data. Each example of the learning set is described by a feature vector for which each feature value is an interval. The new approach fits a constrained linear regression model on the midpoints and range of the interval values assumed by the variables in the learning set. The prediction of the lower and upper boundaries of the interval value of the dependent variable is accomplished from its midpoint and range, which are estimated from the fitted linear regression models applied to the midpoint and range of each interval value of the independent variables. This new method shows the importance of range information in prediction performance as well as the use of inequality constraints to ensure mathematical coherence between the predicted values of the lower () and upper () boundaries of the interval. The authors also propose an expression for the goodness-of-fit measure denominated determination coefficient. The assessment of the proposed prediction method is based on the estimation of the average behavior of the root-mean-square error and square of the correlation coefficient in the framework of a Monte Carlo experiment with different data set configurations. Among other aspects, the synthetic data sets take into account the dependence, or lack thereof, between the midpoint and range of the intervals. The bias produced by the use of inequality constraints over the vector of parameters is also examined in terms of the mean-square error of the parameter estimates. Finally, the approaches proposed in this paper are applied to a real data set and performances are compared.     

Segmentation of the carotid intima-media region in B-mode ultrasound images

This paper proposes a new approach for the segmentation of both near-end and far-end intima-media regions of the common carotid artery in ultrasound images. The method requires minimal user interaction and is able to segment the near-end wall in arteries with large, hypoechogenic and irregular plaques, issues usually not considered previously due to the increased segmentation difficulty.