Parallel Computation of 2D Morse-Smale Complexes

The Morse-Smale complex is a useful topological data structure for the analysis and visualization of scalar data. This paper describes an algorithm that processes all mesh elements of the domain in parallel to compute the Morse-Smale complex of large two-dimensional data sets at interactive speeds. We employ a reformulation of the Morse-Smale complex using Forman's Discrete Morse Theory and achieve scalability by computing the discrete gradient using local accesses only. We also introduce a novel approach to merge gradient paths that ensures accurate geometry of the computed complex. We demonstrate that our algorithm performs well on both multicore environments and on massively parallel architectures such as the GPU.

Parallel Computation of 3D Morse-Smale Complexes

The Morse-Smale complex is a topological structure that captures the behavior of the gradient of a scalar function on a manifold. This paper discusses scalable techniques to compute the Morse-Smale complex of scalar functions defined on large three-dimensional structured grids. Computing the Morse-Smale complex of three-dimensional domains is challenging as compared to two-dimensional domains because of the non-trivial structure introduced by the two types of saddle criticalities. We present a parallel shared-memory algorithm to compute the Morse-Smale complex based on Forman's discrete Morse theory. The algorithm achieves scalability via synergistic use of the CPU and the GPU. We first prove that the discrete gradient on the domain can be computed independently for each cell and hence can be implemented on the GPU. Second, we describe a two-step graph traversal algorithm to compute the 1-saddle-2-saddle connections efficiently and in parallel on the CPU. Simultaneously, the extremasaddle connections are computed using a tree traversal algorithm on the GPU.

GAUSSIAN PULSE SCATTERING BY NONLINEAR THUE-MORSE QUASIPERIODIC MULTILAYERS

The pulse mixing and scattering by finite nonlinear Thue-Morse quasi-periodic dielectric multilayered structure illuminated by two Gaussian pulses with different centre frequencies and lengths are investigated. The three-wave mixing technique is applied to study the nonlinear processes. The properties of the scattered waveforms and the effects of the structure and the incident pulses' parameters on the mixing process are discussed.

Pulse mixing by Fibonacci and Thue-Morse ordered semiconductor layers

The properties of combinatorial frequency generation by two-tone Gaussian pulses incident at oblique angles on quasiperiodic (Fibonacci and Thue-Morse) stacks of binary semiconductor layers are discussed. The analysis has been performed using the self-consistent model taking into account the nonlinear dynamics of mobile charges in the layers. The effects of the stack arrangements and constituent layer parameters on the combinatorial frequency waveforms are presented for the specific structures of both types

Morse Island Creek S094

The South Carolina Department of Natural Resources provides maps to recreational and state shellfish grounds, available to the public for recreational harvesting or to commercial harvest. This map shows the location of Morse Island Creek S094 Recreational Shellfish Ground in Beaufort County.

Homologie de morse et théorème de la signature

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

États cohérents et comprimés du potentiel de Morse et intrication créée par un miroir semi-transparent

Pour décrire les vibrations à l'intérieur des molécules diatomiques, le potentiel de Morse est une meilleure approximation que le système de l'oscillateur harmonique. Ainsi, en se basant sur la définition des états cohérents et comprimés donnée dans le cadre du problème de l'oscillateur harmonique, la première partie de ce travail suggère une construction des états cohérents et comprimés pour le potentiel de Morse. Deux types d’états seront construits et leurs différentes propriétés seront étudiées en portant une attention particulière aux trajectoires et aux dispersions afin de confirmer la quasi-classicité de ces états. La deuxième partie de ce travail propose d'insérer ces deux types d’états cohérents et comprimés de Morse dans un miroir semi-transparent afin d'introduire un nouveau moyen de créer de l'intrication. Cette intrication sera mesurée à l’aide de l’entropie linéaire et nous étudierons la dépendance par rapport aux paramètres de cohérence et de compression.

Complexe de Morse et bifurcations

Soit une famille de couples (ft,Xt)t∈J , où J est un intervalle, ft est une fonction lisse à valeurs réelles définie sur une variété lisse et compacte V , et Xt est un pseudo-gradient associé à la fonction ft. L’objet de ce mémoire est l’étude des bifurcations subies par les complexes de Morse associés à ces couples. Deux approches sont utilisées : l’étude directe des bifurcations et l’approche par homotopie. On montre que finalement ces deux approches permettent d’obtenir les mêmes résultats d’un point de vue fonctoriel.

Construcción de un telégrafo morse.

Ejemplar mecanografiado

Bone Remodeling Adjacent to Morse Cone-Connection Implants with Platform Switch: A Fluorescence Study in the Dog Mandible

Purpose: The aim of this study was to evaluate, through fluorescence analysis, the effect that different interimplant distances, after prosthetic restoration, will have on bone remodeling in submerged and nonsubmerged implants restored with a ""platform switch."" Materials and Methods: Fifty-six Ankylos implants were placed 1.5 mm subcrestally in seven dogs. The implants were placed so that two fixed prostheses, with three interimplant contacts separated by 1-mm, 2-mm, and 3-mm distances, could be fabricated for each side of the mandible. The sides and the positions of the groups were selected randomly. To better evaluate bone remodeling, calcein green was injected 3 days before placement of the prostheses at 12 weeks postimplantation. At 3 days before sacrifice (8 weeks postloading), alizarin red was injected. The amounts of remodeled bone within the different interimplant areas were compared statistically before and after loading in submerged and nonsubmerged implants. Results: Statistically significant differences existed in the percentage of remodeled bone seen in the different regions. Mean percentages of remodeled bone in the submerged and nonsubmerged groups, respectively, were as follows: for the 1-mm distance, 23.0% +/- 0.05% and 23.1% +/- 0.03% preloading and 27.0% +/- 0.03% and 25.2% +/- 0.04% postloading, for the 2-mm distance, 18.2% +/- 0.05% and 18.1% +/- 0.04% preloading and 21.3% +/- 0.07% and 19.9% +/- 0.03% postloading, for the 3-mm distance, 18.3% +/- 0.03% and 18.3% +/- 0.03% preloading and 18.8% +/- 0.04% and 19.8% +/- 0.04% postloading, for distal-extension regions, 16.6% +/- 0.02% and 17.4% +/- 0.04% preloading and 17.0% +/- 0.04% and 18.4% +/- 0.04% postloading. Conclusions: Based upon this animal study, loading increases bone formation for submerged or nonsubmerged implants, and the interimplant distance of 1 mm appears to result in more pronounced bone remodeling than the 2-mm or 3-mm distances in implants with a ""platform switch."" INT J ORAL MAXILLOFAC IMPLANTS 2009;24:257-266

The curve selection lemma and the Morse-Sard theorem

We use an inequality due to Bochnak and Lojasiewicz, which follows from the Curve Selection Lemma of real algebraic geometry in order to prove that, given a C(r) function f : U subset of R(m) -> R, we have lim(y -> xy is an element of crit(f)) vertical bar f(y) - f(x)vertical bar/vertical bar y - x vertical bar(r) = 0, for all x is an element of crit(f)` boolean AND U, where crit( f) = {x is an element of U vertical bar df ( x) = 0}. This shows that the so-called Morse decomposition of the critical set, used in the classical proof of the Morse-Sard theorem, is not necessary: the conclusion of the Morse decomposition lemma holds for the whole critical set. We use this result to give a simple proof of the classical Morse-Sard theorem ( with sharp differentiability assumptions).

On the variations of the Betti numbers of regular levels of Morse flows

We generalize results in Cruz and de Rezende (1999) [7] by completely describing how the Beth numbers of the boundary of an orientable manifold vary after attaching a handle, when the homology coefficients are in Z, Q, R or Z/pZ with p prime. First we apply this result to the Conley index theory of Lyapunov graphs. Next we consider the Ogasa invariant associated with handle decompositions of manifolds. We make use of the above results in order to obtain upper bounds for the Ogasa invariant of product manifolds. (C) 2011 Elsevier B.V. All rights reserved.

Genericity of Nondegenerate Critical Points and Morse Geodesic Functionals

We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Using classical techniques, we prove an abstract genericity result that employs the infinite dimensional Sard-Smale theorem, along the lines of an analogous result of B. White [29]. Applications are given by proving the genericity of metrics without degenerate geodesics between fixed endpoints in general (non compact) semi-Riemannian manifolds, in orthogonally split semi-Riemannian manifolds and in globally hyperbolic Lorentzian manifolds. We discuss the genericity property also in stationary Lorentzian manifolds.