This paper presents a new method of curvetting to a set of noisy samples. In the case of tting a curved line (or a curved surface) to given sample points, it seems natural the curve is decided so as to minimize the mean square of perpendicular distances from the sample points. However it is di cult to get the optimal curve in the sense of this criterion. In this paper, the perpendicular distanc...

Two dimensional parameterizations of meshes is a dynamic field of research. Most works focus on parameterizing complete surfaces, attempting to satisfy various constraints on distances and angles and produce a 2D map with minimal errors. Except for developable surfaces no single map can be devoid of errors, and a parametrization produced for one purpose usually doesn’t suit others. This work pr...

Colloidal particles embedded in the cytoplasm of living mammalian cells have been found to display remarkable heterogeneity in their amplitude of motion. However, consensus on the significance and origin of this phenomenon is still lacking. We conducted experiments on Hmec-1 cells loaded with about 100 particles, to reveal the intracellular particle dynamics as a function of both location and t...

We study the least squares estimator in the residual variance estimation context. We show that the mean squared differences of paired observations are asymptotically normally distributed. We further establish that, by regressing the mean squared differences of these paired observations on the squared distances between paired covariates via a simple least squares procedure, the resulting varianc...

We give a full and self contained account of the basic results in N-body scattering theory which emerged over the last ten years: The existence and completeness of scattering states for potentials decreasing like r−μ, μ > √ 3 − 1. Our approach is a synthesis of earlier work and of new ideas. Global conditions on the potentials are imposed only to define the dynamics. Asymptotic completeness is ...

We present the results of a study to exploit a multiple colour space model (CSM ) and variable kernels for object tracking in video sequences. The basis of our work is the mean shift algorithm; for a moving target, we develop a procedure to adaptively change the CSM throughout a video sequence. The optional CSM components are ranked using a similarity distance within an inner (representing the ...

Symmetric positive definite (spd) matrices pervade numerous scientific disciplines, including machine learning and optimization. We consider the key task of measuring distances between two spd matrices; a task that is often nontrivial whenever the distance function must respect the non-Euclidean geometry of spd matrices. Typical non-Euclidean distance measures such as the Riemannian metric δR(X...

An off-the-shelf low cost laser sensor was tested and evaluated both in laboratory and field conditions. The sensor identified the angular and straight edges of the laboratory test surface and replicated the straight edge profile with an error of 4%. In field conditions, the sensor identified three types of cut crop edges (wheat, alfalfa and corn) and replicated distinct shapes (triangle, curve...

Hooves preserve the isotopic information laid down during their growth and may be used for reconstruction of animal feeding history. To assign certain positions along hooves to corresponding times, growth rates are required. Hoof growth rates are known for domestic animals; however, they cannot be obtained easily in wild animals. We estimated the hoof growth rate of the European roe deer (Capre...

Our recent work (Arias-Castro et al., 2016) established the convergence of the mean shift algorithm under relatively general conditions. After the publication of this article, Prof. Jose E. Chacón — who has worked on the topic (Chacón and Monfort, 2013; Chacón and Duong, 2013) — alerted us of a mistake in the proof of the first part of our Theorem 1. The mistake is in the display following Eq. ...