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.

Localization of handwritten text in documents using moment invariants and Delaunay triangulation

This paper describes an approach based on Zernike moments and Delaunay triangulation for localization of hand-written text in machine printed text documents. The Zernike moments of the image are first evaluated and we classify the text as hand-written using the nearest neighbor classifier. These features are independent of size, slant, orientation, translation and other variations in handwritten text. We then use Delaunay triangulation to reclassify the misclassified text regions. When imposing Delaunay triangulation on the centroid points of the connected components, we extract features based on the triangles and reclassify the text. We remove the noise components in the document as part of the preprocessing step so this method works well on noisy documents. The success rate of the method is found to be 86%. Also for specific hand-written elements such as signatures or similar text the accuracy is found to be even higher at 93%.

Rapid localization of damage using a circular sensor array and Lamb wave based triangulation

A damage detection and imaging methodology based on symmetry of neighborhood sensor path and similarity of signal patterns with respect to radial paths in a circular array of sensors has been developed It uses information regarding Limb wave propagation along with a triangulation scheme to rapidly locate and quantify the severity of damage without using all of the sensor data. In a plate like structure, such a scheme can be effectively employed besides full field imaging of wave scattering pattern from the damage, if present in the plate. This new scheme is validated experimentally. Hole and corrosion type damages have been detected and quantified using the proposed scheme successfully. A wavelet based cumulative damage index has been studied which shows monotonic sensitivity against the severity of the damage. which is most desired in a Structural Health Monitoring system. (C) 2010 Elsevier Ltd. All rights reserved.

A geodesic-based triangulation technique for damage location in metallic and composite plates

Lamb-wave-based damage detection methods using the triangulation technique are not suitable for handling structures with complex shapes and discontinuities as the parametric/analytical representation of these structures is very difficult. The geodesic concept is used along with the triangulation technique to overcome the above problem. The present work is based on the fundamental fact that a wave takes the minimum energy path to travel between two points on any multiply connected surface and this reduces to the shortest distance path or geodesic. The geodesics are computed on the meshed surface of the structure using the fast marching method. The wave response matrix of the given sensor configuration for the healthy and the damaged structure is obtained experimentally. The healthy and damage response matrices are compared and their difference gives the time information about the reflection of waves from the damage. A wavelet transform is used to extract the arrival time information of the wave scattered by the damage from the acquired Lamb wave signals. The computed geodesics and time information are used in the ellipse algorithm of triangulation formulation to locate the loci of possible damage location points for each actuator-sensor pair. The results obtained for all actuator-sensor pairs are combined and the intersection of multiple loci gives the damage location result. Experiments were conducted in aluminum and composite plate specimens to validate this method.

On Walkup's class K (d) and a minimal triangulation of (S-3 (sic) S-1)(#3)

For d >= 2, Walkup's class K (d) consists of the d-dimensional simplicial complexes all whose vertex-links are stacked (d - 1)-spheres. Kalai showed that for d >= 4, all connected members of K (d) are obtained from stacked d-spheres by finitely many elementary handle additions. According to a result of Walkup, the face vector of any triangulated 4-manifold X with Euler characteristic chi satisfies f(1) >= 5f(0) - 15/2 chi, with equality only for X is an element of K(4). Kuhnel observed that this implies f(0)(f(0) - 11) >= -15 chi, with equality only for 2-neighborly members of K(4). Kuhnel also asked if there is a triangulated 4-manifold with f(0) = 15, chi = -4 (attaining equality in his lower bound). In this paper, guided by Kalai's theorem, we show that indeed there is such a triangulation. It triangulates the connected sum of three copies of the twisted sphere product S-3 (sic) S-1. Because of Kuhnel's inequality, the given triangulation of this manifold is a vertex-minimal triangulation. By a recent result of Effenberger, the triangulation constructed here is tight. Apart from the neighborly 2-manifolds and the infinite family of (2d + 3)-vertex sphere products Sd-1 X S-1 (twisted for d odd), only fourteen tight triangulated manifolds were known so far. The present construction yields a new member of this sporadic family. We also present a self-contained proof of Kalai's result. (C) 2011 Elsevier B.V. All rights reserved.

Minimal triangulation, complementarity and projective planes

Brehm and Kuhnel proved that if M-d is a combinatorial d-manifold with 3d/2 + 3 vertices and \ M-d \ is not homeomorphic to Sd then the combinatorial Morse number of M-d is three and hence d is an element of {0, 2, 4, 8, 16} and \ M-d \ is a manifold like a projective plane in the sense of Eells and Kuiper. We discuss the existence and uniqueness of such combinatorial manifolds. We also present the following result: ''Let M-n(d) be a combinatorial d-manifold with n vertices. M-n(d) satisfies complementarity if and only if d is an element of {0, 2, 4, 8, 16} with n = 3d/2 + 3 and \ M-n(d) \ is a manifold like a projective plane''.

A Triangulation of CP3 as Symmetric Cube of S-2

The symmetric group acts on the Cartesian product (S (2)) (d) by coordinate permutation, and the quotient space is homeomorphic to the complex projective space a'',P (d) . We used the case d=2 of this fact to construct a 10-vertex triangulation of a'',P (2) earlier. In this paper, we have constructed a 124-vertex simplicial subdivision of the 64-vertex standard cellulation of (S (2))(3), such that the -action on this cellulation naturally extends to an action on . Further, the -action on is ``good'', so that the quotient simplicial complex is a 30-vertex triangulation of a'',P (3). In other words, we have constructed a simplicial realization of the branched covering (S (2))(3)-> a'',P (3).

Linear Chromatic Adaptation Transform Based on Delaunay Triangulation

Computer vision algorithms that use color information require color constant images to operate correctly. Color constancy of the images is usually achieved in two steps: first the illuminant is detected and then image is transformed with the chromatic adaptation transform ( CAT). Existing CAT methods use a single transformation matrix for all the colors of the input image. The method proposed in this paper requires multiple corresponding color pairs between source and target illuminants given by patches of the Macbeth color checker. It uses Delaunay triangulation to divide the color gamut of the input image into small triangles. Each color of the input image is associated with the triangle containing the color point and transformed with a full linear model associated with the triangle. Full linear model is used because diagonal models are known to be inaccurate if channel color matching functions do not have narrow peaks. Objective evaluation showed that the proposed method outperforms existing CAT methods by more than 21%; that is, it performs statistically significantly better than other existing methods.

Linear Chromatic Adaptation Transform Based on Delaunay Triangulation

Computer vision algorithms that use color information require color constant images to operate correctly. Color constancy of the images is usually achieved in two steps: first the illuminant is detected and then image is transformed with the chromatic adaptation transform ( CAT). Existing CAT methods use a single transformation matrix for all the colors of the input image. The method proposed in this paper requires multiple corresponding color pairs between source and target illuminants given by patches of the Macbeth color checker. It uses Delaunay triangulation to divide the color gamut of the input image into small triangles. Each color of the input image is associated with the triangle containing the color point and transformed with a full linear model associated with the triangle. Full linear model is used because diagonal models are known to be inaccurate if channel color matching functions do not have narrow peaks. Objective evaluation showed that the proposed method outperforms existing CAT methods by more than 21%; that is, it performs statistically significantly better than other existing methods.

The Housing Triangulation: A discourse on Quality, Affordability and Lifestyles in India

Since 1991 with the advent of globalization and economic liberalisation, basic conceptual and discursive changes are taking place in housing sector in India. The new changes suggest how housing affordability, quality and lifestyles reality is shifting for various segments of the population. Such shift not only reflects structural patterns but also stimulates an ongoing transition process. The paper highlights a twin impetus that continue to shape the ongoing transition: expanding middle class and their wealth - a category with distinctive lifestyles, desires and habits and corresponding ‘market defining’ of affordable housing standards - to articulate function of housing as a conceptualization of social reality in modern India. The paper highlights the contradictions and paradoxes, and the manner in which the concept of affordability, quality and lifestyles are embedded in both discourse and practice in India. The housing ‘dream’ currently being packaged and fed through to the middle class population has an upper middle class bias and is set to alienate those at the lower end of the middle-and low-income population. In the context of growing agreement and inevitability of market provision of ‘affordable housing’, the unbridled ‘market-defining’ of housing quality and lifestyles must be checked.

Decentralized Target Tracking based on Multi-Robot Cooperative Triangulation

Target tracking with bearing-only sensors is a challenging problem when the target moves dynamically in complex scenarios. Besides the partial observability of such sensors, they have limited field of views, occlusions can occur, etc. In those cases, cooperative approaches with multiple tracking robots are interesting, but the different sources of uncertain information need to be considered appropriately in order to achieve better estimates. Even though there exist probabilistic filters that can estimate the position of a target dealing with incertainties, bearing-only measurements bring usually additional problems with initialization and data association. In this paper, we propose a multi-robot triangulation method with a dynamic baseline that can triangulate bearing-only measurements in a probabilistic manner to produce 3D observations. This method is combined with a decentralized stochastic filter and used to tackle those initialization and data association issues. The approach is validated with simulations and field experiments where a team of aerial and ground robots with cameras track a dynamic target.

Special report of New York State Survey on the preservation of the scenery of Niagara Falls ; and fourth annual report on the triangulation of State. For the Year 1879 /

Notes by F. L. Olmsted.

Triangulation of rights, balancing of interests : exploring the tensions between freedom of conscience and freedom of religion in comparative constitutional law

La liberté de religion, souvent reconnue comme étant la « première liberté » dans de nombreuses traditions juridiques, reflète également les différentes conceptions de la place de l’individu et de la communauté dans la société. Notre étude analysera les modèles constitutionnels canadien, américain et européen de liberté de religion et conscience. Dans un premier chapitre, nous examinerons les conceptions théoriques de la religion dans les sciences sociales ainsi les approches juridiques afin de mieux cerner comment la religion est conçue et de plus, comprendre les diverses influences sur sa conceptualisation. Dans un second et troisième chapitre, nous tenterons d’une part, de qualifier la relation entre la liberté de conscience et la liberté de religion au Canada en nous livrant à une analyse approfondie des deux libertés et d’autre part, d’identifier les questions qui demeurent irrésolues. Dans le chapitre final, nous observerons comment la liberté de conscience a été interprétée dans les contextes américain et dans l’Union Européenne, par le biais de la Cour Européenne des droits de l’Homme. Notre hypothèse est que l’on peut arriver à une meilleure compréhension de la relation entre les libertés de conscience et religion en clarifiant les conceptions théoriques de la religion et de la conscience en droit constitutionnel comparé.

Du père psychanalytique au père développemental : vision systémique de la fonction de triangulation: aplication à l'évaluation de la parentalité psychique

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal