Harmonic deformation of Delaunay triangulations

We construct harmonic functions on random graphs given by Delaunay triangulations of ergodic point processes as the limit of the zero-temperature harness process. (C) 2012 Elsevier B.V All rights reserved.

Phase Transition for the Ising Model on the Critical Lorentzian Triangulation

The ferromagnetic Ising model without external field on an infinite Lorentzian triangulation sampled from the uniform distribution is considered. We prove uniqueness of the Gibbs measure in the high temperature region and coexistence of at least two Gibbs measures at low temperature. The proofs are based on the disagreement percolation method and on a variant of the Peierls contour method. The critical temperature is shown to be constant a.s.

The meccano method for automatic 3-d triangulation and volume parametrization of complex solids

[EN]In this paper we review the novel meccano method. We summarize the main stages (subdivision, mapping, optimization) of this automatic tetrahedral mesh generation technique and we concentrate the study to complex genus-zero solids. In this case, our procedure only requires a surface triangulation of the solid. A crucial consequence of our method is the volume parametrization of the solid to a cube. We construct volume T-meshes for isogeometric analysis by using this result. The efficiency of the proposed technique is shown with several examples. A comparison between the meccano method and standard mesh generation techniques is introduced.-1…

Perhaps Triangulation Isn’t Enough: a Call for Crystallization as a Methodological Referent in NOS Research

This research compares the methodological tools employed in NOS research, with analysis of what the comparison implies about the structure of nature of science knowledge. Descriptions of practicing teachers’ nature of science conceptions were compared based on data collected from forced choice responses, responses to a qualitative survey, and course writing samples. Participants’ understandings were scored differently on the Views of Nature of Science Questionnaire (VNOS) than the forced-choice measure, Scientific Thinking and Internet Learning Technologies (STILT). In addition, analysis of the writing samples and observations combined with interviews portrayed more sophisticated, but more variable, understandings of the nature of science than was evidenced by either the survey or the forced-choice measure. The differences between data collection measures included the degree to which they drew upon context bound or context general reasoning, the degree to which they required students to move beyond the simple intelligibility of their responses and allowed students to explore the fruitfulness of the constructs, as well as the degree to which they revealed the interconnection of participants NOS conceptions. In light of the different portrayals of a participants NOS conceptions yielded by these different measures, we call for the use of crystallization as a methodological referent in research.

Approximations on minimum weight pseudo-triangulation problem using ant colony optimization

In this work, we consider the Minimum Weight Pseudo-Triangulation (MWPT) problem of a given set of n points in the plane. Globally optimal pseudo-triangulations with respect to the weight, as optimization criteria, are difficult to be found by deterministic methods, since no polynomial algorithm is known. We show how the Ant Colony Optimization (ACO) metaheuristic can be used to find high quality pseudo-triangulations of minimum weight. We present the experimental and statistical study based on our own set of instances since no reference to benchmarks for these problems were found in the literature. Throughout the experimental evaluation, we appraise the ACO metaheuristic performance for MWPT problem.

Statistical analysis of shape through triangulation of landmarks: A study of sexual dimorphism in hominids

Two objects with homologous landmarks are said to be of the same shape if the configuration of landmarks of one object can be exactly matched with that of the other by translation, rotation/reflection, and scaling. In an earlier paper, the authors proposed statistical analysis of shape by considering logarithmic differences of all possible Euclidean distances between landmarks. Tests of significance for differences in the shape of objects and methods of discrimination between populations were developed with such data. In the present paper, the corresponding statistical methodology is developed by triangulation of the landmarks and by considering the angles as natural measurements of shape. This method is applied to the study of sexual dimorphism in hominids.

The new metal worker pattern book; a complete course of instruction in the modern methods of developing and cutting the patterns for sheet metal work, giving the principles underlying practically every problem that is likely to come up in practice and explaining the selection and use of drawing tools and linear and geometrical drawing so clearly that one, who has had no previous knowledge of arithmetic or drawing, may understand these essentials and apply them in using the 253 problems in the development of patterns by the parallel line, conical or flaring, and triangulation systems.

Mode of access: Internet.

Triangulation du Roayume de Belgique : exécutée par MM. les officiers de la section géodésique du dépot de la guerre.

Libros II: Mesure des bases; Libro III: Observations astronomiques.

Curso elemental de mecánica teórica y aplicada: escrito en francés por M. Ch. Delaunay /

Mode of access: Internet.

Account of the observations and calculations, of the principal triangulation;

Mode of access: Internet.

Cantilever extension of ground control in strips of convergent photographs by analytical triangulation.

"Contract no. DA-44-009 Eng-2986, Department of the Army Project no. 8-35-11-106."

Mémoires de Mme. de Staal Delaunay, de M. le Marquis d'Argenson et de Madame Mère du Régent. Suivis d'éclaircissements extraits des mémoires du Duc de Saint-Simon, avec avant-propos et notices,

Mode of access: Internet.

Single-molecule dynamic triangulation

A proposal for using single molecules as nanoprobes capable of detecting the trajectory of an elementary charge is discussed in detail. Presented numerical simulations prove that this singlemolecule technique allows determination of a three-dimensional single-electron displacement within a few seconds with an accurocy better than 0.006 nm. Surprisingly, this significantly exceeds the accuracy with which the probe;, molecule itself can be localized (given the same measuring time by means of single-molecule microscopy. It is also shown that the optimal concentration of probe molecules in the vicinity of:the electron (i.e. the concentration which provides the best accuracy of the inferred electron displacement) is of the order of 10(-5) m.

Triangulation mobility of auto-theft offenders

This research paper presents an examination of the journey to and from crime for autotheft offenders in the UK. For 852 offences, ‘wheel’ distances are calculated for triangles formed by offenders’ home location, theft location, and vehicle disposal location. The study demonstrates typical isosceles mobility triangles; distances travelled to and from home locations are roughly equal, whereas distances between theft and disposal points were shorter. Distances travelled by offenders under 17 years old and offences involving drug and drink were shown to be shorter than comparison groups. Prolifi c offenders tend to travel further, although there is signifi cant variation in this subgroup. Explanations and implications are discussed.