Geometric and Algebraic Aspects of 3D Affine and Projective Structures from Perspective 2D Views

We investigate the differences --- conceptually and algorithmically --- between affine and projective frameworks for the tasks of visual recognition and reconstruction from perspective views. It is shown that an affine invariant exists between any view and a fixed view chosen as a reference view. This implies that for tasks for which a reference view can be chosen, such as in alignment schemes for visual recognition, projective invariants are not really necessary. We then use the affine invariant to derive new algebraic connections between perspective views. It is shown that three perspective views of an object are connected by certain algebraic functions of image coordinates alone (no structure or camera geometry needs to be involved).

Dimension and coverage of multiple-models structures using clustering techniques

In this work a method for building multiple-model structures is presented. A clustering algorithm that uses data from the system is employed to define the architecture of the multiple-model, including the size of the region covered by each model, and the number of models. A heating ventilation and air conditioning system is used as a testbed of the proposed method.

An application of lattice basis reduction to polynomial identities for algebraic structures

The authors` recent classification of trilinear operations includes, among other cases, a fourth family of operations with parameter q epsilon Q boolean OR {infinity}, and weakly commutative and weakly anticommutative operations. These operations satisfy polynomial identities in degree 3 and further identities in degree 5. For each operation, using the row canonical form of the expansion matrix E to find the identities in degree 5 gives extremely complicated results. We use lattice basis reduction to simplify these identities: we compute the Hermite normal form H of E(t), obtain a basis of the nullspace lattice from the last rows of a matrix U for which UE(t) = H, and then use the LLL algorithm to reduce the basis. (C) 2008 Elsevier Inc. All rights reserved.

Integrability vs supersymmetry: Poisson structures of the pohlmeyer reduction

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Evaluation of 3-dimensional superimposition techniques on various skeletal structures of the head using surface models.

OBJECTIVES To test the applicability, accuracy, precision, and reproducibility of various 3D superimposition techniques for radiographic data, transformed to triangulated surface data. METHODS Five superimposition techniques (3P: three-point registration; AC: anterior cranial base; AC + F: anterior cranial base + foramen magnum; BZ: both zygomatic arches; 1Z: one zygomatic arch) were tested using eight pairs of pre-existing CT data (pre- and post-treatment). These were obtained from non-growing orthodontic patients treated with rapid maxillary expansion. All datasets were superimposed by three operators independently, who repeated the whole procedure one month later. Accuracy was assessed by the distance (D) between superimposed datasets on three form-stable anatomical areas, located on the anterior cranial base and the foramen magnum. Precision and reproducibility were assessed using the distances between models at four specific landmarks. Non parametric multivariate models and Bland-Altman difference plots were used for analyses. RESULTS There was no difference among operators or between time points on the accuracy of each superimposition technique (p>0.05). The AC + F technique was the most accurate (D<0.17 mm), as expected, followed by AC and BZ superimpositions that presented similar level of accuracy (D<0.5 mm). 3P and 1Z were the least accurate superimpositions (0.79of each superimposition technique (p>0.05), the detected structural changes differed significantly between different techniques (p<0.05). Bland-Altman difference plots showed that BZ superimposition was comparable to AC, though it presented slightly higher random error. CONCLUSIONS Superimposition of 3D datasets using surface models created from voxel data can provide accurate, precise, and reproducible results, offering also high efficiency and increased post-processing capabilities. In the present study population, the BZ superimposition was comparable to AC, with the added advantage of being applicable to scans with a smaller field of view.

A review of load models for the prediction of footfall-induced vibration in structures

Crowd induced dynamic loading in large structures, such as gymnasiums or stadium, is usually modelled as a series of harmonic loads which are defined in terms of their Fourier coefficients. Different values of these coefficients that were obtained from full scale measurements can be found in codes. Recently, an alternative has been proposed, based on random generation of load time histories that take into account phase lag among individuals inside the crowd. This paper presents the testing done on a structure designed to be a gymnasium. Two series of dynamic test were performed on the gym slab. For the first test an electrodynamic shaker was placed at several locations and during the second one people located inside a marked area bounced and jumped guided by different metronome rates. A finite element model (FEM) is presented and a comparison of numerically predicted and experimentally observed vibration modes and frequencies has been used to assess its validity. The second group of measurements will be compared with predictions made using the FEM model and three alternatives for crowd induced load modelling.

Analysis of dynamic models for structural insight and model reduction .2. A multi-stage compressor shutdown case-study

In this second paper, the three structural measures which have been developed are used in the modelling of a three stage centrifugal synthesis gas compressor. The goal of this case study is to determine the essential mathematical structure which must be incorporated into the compressor model to accurately model the shutdown of this system. A simple, accurate and functional model of the system is created via three structural measures. It was found that the model can be correctly reduced into its basic modes and that the order of the differential system can be reduced from 51(st) to 20(th). Of the 31 differential equational 21 reduce to algebraic relations, 8 become constants and 2 can be deleted thereby increasing the algebraic set from 70 to 91 equations. An interpretation is also obtained as to which physical phenomena are dominating the dynamics of the compressor add whether the compressor will enter surge during the shutdown. Comparisons of the reduced model performance against the full model are given, showing the accuracy and applicability of the approach. Copyright (C) 1996 Elsevier Science Ltd

Photoelastic Study of the Support Structures of Distal-Extension Removable Partial Dentures

Purpose: The double system of support, in which the distal-extension removable partial denture adapts, causes inadequate stress around abutment teeth, increasing the possibility of unequal bone resorption. Several ways to reduce or more adequately distribute the stress between abutment teeth and residual ridges have been reported; however, there are no definitive answers to the problem. The purpose of this study was to analyze, by means of photoelasticity, the most favorable stress distribution using three retainers: T bar, rest, proximal plate, I bar (RPI), and circumferential with mesialized rest. Materials and Methods: Three photoelastic models were made simulating a Kennedy Class II inferior arch. Fifteen dentures with long saddles, five of each design, were adjusted to the photoelastic patterns and submitted first to uniformly distributed load, and then to a load localized on the last artificial tooth. The saddles were then shortened and the tests repeated. The quantitative and qualitative analyses of stress intensity were done manually and by photography, respectively. For intragroup analyses the Wilcoxon test for paired samples was used, while for intergroup analyses Friedman and Wilcoxon tests were used to better identify the differences (p < 0.05). Results: The RPI retainer, followed by the T bar, demonstrated the best distribution of load between teeth and residual ridge. The circumferential retainer caused greater concentration of stress between dental apexes. Stress distribution was influenced by the type of retainer, the length of the saddle, and the manner of load application. Conclusions: The long saddles and the uniformly distributed loads demonstrated better distribution of stress on support structures.

Granular layer in the periplasmic space of gram-positive bacteria and fine structures of Enterococcus gallinarum and Streptococcus gordonii septa revealed by cryo-electron microscopy of vitreous sections.

High-resolution structural information on optimally preserved bacterial cells can be obtained with cryo-electron microscopy of vitreous sections. With the help of this technique, the existence of a periplasmic space between the plasma membrane and the thick peptidoglycan layer of the gram-positive bacteria Bacillus subtilis and Staphylococcus aureus was recently shown. This raises questions about the mode of polymerization of peptidoglycan. In the present study, we report the structure of the cell envelope of three gram-positive bacteria (B. subtilis, Streptococcus gordonii, and Enterococcus gallinarum). In the three cases, a previously undescribed granular layer adjacent to the plasma membrane is found in the periplasmic space. In order to better understand how nascent peptidoglycan is incorporated into the mature peptidoglycan, we investigated cellular regions known to represent the sites of cell wall production. Each of these sites possesses a specific structure. We propose a hypothetic model of peptidoglycan polymerization that accommodates these differences: peptidoglycan precursors could be exported from the cytoplasm to the periplasmic space, where they could diffuse until they would interact with the interface between the granular layer and the thick peptidoglycan layer. They could then polymerize with mature peptidoglycan. We report cytoplasmic structures at the E. gallinarum septum that could be interpreted as cytoskeletal elements driving cell division (FtsZ ring). Although immunoelectron microscopy and fluorescence microscopy studies have demonstrated the septal and cytoplasmic localization of FtsZ, direct visualization of in situ FtsZ filaments has not been obtained in any electron microscopy study of fixed and dehydrated bacteria.

Use of an in-house approach to study the three-dimensional structures of various outer membrane proteins: structure of the alcaligin outer membrane transporter FauA from Bordetella pertussis.

Bordetella pertussis is the bacterial agent of whooping cough in humans. Under iron-limiting conditions, it produces the siderophore alcaligin. Released to the extracellular environment, alcaligin chelates iron, which is then taken up as a ferric alcaligin complex via the FauA outer membrane transporter. FauA belongs to a family of TonB-dependent outer membrane transporters that function using energy derived from the proton motive force. Using an in-house protocol for membrane-protein expression, purification and crystallization, FauA was crystallized in its apo form together with three other TonB-dependent transporters from different organisms. Here, the protocol used to study FauA is described and its three-dimensional structure determined at 2.3 A resolution is discussed.

Crystal structures of two closely related but antigenically distinct HLA-A2/melanocyte-melanoma tumor-antigen peptide complexes.

We have determined high-resolution crystal structures of the complexes of HLA-A2 molecules with two modified immunodominant peptides from the melanoma tumor-associated protein Melan-A/Melanoma Ag recognized by T cells-1. The two peptides, a decamer and nonamer with overlapping sequences (ELAGIGILTV and ALGIGILTV), are modified in the second residue to increase their affinity for HLA-A2. The modified decamer is more immunogenic than the natural peptide and a candidate for peptide-based melanoma immunotherapy. The crystal structures at 1.8 and 2.15 A resolution define the differences in binding modes of the modified peptides, including different clusters of water molecules that appear to stabilize the peptide-HLA interaction. The structures suggest both how the wild-type peptides would bind and how three categories of cytotoxic T lymphocytes with differing fine specificity might recognize the two peptides.

A game theoretical approach to the algebraic counterpart of the Wagner hierarchy

La hiérarchie de Wagner constitue à ce jour la plus fine classification des langages ω-réguliers. Par ailleurs, l'approche algébrique de la théorie de langages formels montre que ces ensembles ω-réguliers correspondent précisément aux langages reconnaissables par des ω-semigroupes finis pointés. Ce travail s'inscrit dans ce contexte en fournissant une description complète de la contrepartie algébrique de la hiérarchie de Wagner, et ce par le biais de la théorie descriptive des jeux de Wadge. Plus précisément, nous montrons d'abord que le degré de Wagner d'un langage ω-régulier est effectivement un invariant syntaxique. Nous définissons ensuite une relation de réduction entre ω-semigroupes pointés par le biais d'un jeu infini de type Wadge. La collection de ces structures algébriques ordonnée par cette relation apparaît alors comme étant isomorphe à la hiérarchie de Wagner, soit un quasi bon ordre décidable de largeur 2 et de hauteur ω. Nous exposons par la suite une procédure de décidabilité de cette hiérarchie algébrique : on décrit une représentation graphique des ω-semigroupes finis pointés, puis un algorithme sur ces structures graphiques qui calcule le degré de Wagner de n'importe quel élément. Ainsi le degré de Wagner de tout langage ω-régulier peut être calculé de manière effective directement sur son image syntaxique. Nous montrons ensuite comment construire directement et inductivement une structure de n''importe quel degré. Nous terminons par une description détaillée des invariants algébriques qui caractérisent tous les degrés de cette hiérarchie. Abstract The Wagner hierarchy is known so far to be the most refined topological classification of ω-rational languages. Also, the algebraic study of formal languages shows that these ω-rational sets correspond precisely to the languages recognizable by finite pointed ω-semigroups. Within this framework, we provide a construction of the algebraic counterpart of the Wagner hierarchy. We adopt a hierarchical game approach, by translating the Wadge theory from the ω-rational language to the ω-semigroup context. More precisely, we first show that the Wagner degree is indeed a syntactic invariant. We then define a reduction relation on finite pointed ω-semigroups by means of a Wadge-like infinite two-player game. The collection of these algebraic structures ordered by this reduction is then proven to be isomorphic to the Wagner hierarchy, namely a well-founded and decidable partial ordering of width 2 and height $\omega^\omega$. We also describe a decidability procedure of this hierarchy: we introduce a graph representation of finite pointed ω-semigroups allowing to compute their precise Wagner degrees. The Wagner degree of every ω-rational language can therefore be computed directly on its syntactic image. We then show how to build a finite pointed ω-semigroup of any given Wagner degree. We finally describe the algebraic invariants characterizing every Wagner degree of this hierarchy.

Dynamics of integrable birational maps preserving genus 0 foliations

Pòster presentat al congrés NPDDS2014

Molecular structures of trimethylchlorogermane, (CH3)(3)GeCl, and trimethylbromogermane, (CH3)(3)GeBr, obtained by gas-phase electron diffraction and theoretical calculations

The structures of trimethylchlorogermane ((CH3)(3)GeCl) and trimethylbromogermane ((CH3)(3)GeBr) have been determined by gas-phase electron diffraction (GED), augmented by the results from ab initio calculations employing second-order Moller-Plesset (MP2) level of theory and the 6-311+G(d) basis set. All the electrons were included in the correlation calculation. The results from the ab initio calculations indicated that these molecules have C-3v symmetry, and models with this symmetry were used in the electron diffraction analysis. The results for the principal distances (r(g)) and angles (angle(alpha)) from the combined GED/ab initio study of trimethylchlorogermane (with estimated 2sigma uncertainties) are: r(Ge-C) = 1.950(4) Angstrom, r(Ge-Cl) = 2.173(4) Angstrom, r(C-H) = 1.090(9) Angstrom, angleCGeC = 112.7(7)degrees, angleCGeCl = 106.0(8)degrees, angleGeCH = 107.8(12)degrees. The results for the principal distances (r(g)) and angles (angle(alpha)) from the combined GED/ab initio study of trimethylbromogermane (with estimated 2sigma uncertainties) are: r(Ge-C) = 1.952(7) Angstrom, r(Ge-Br) = 2.325(4) Angstrom, r(C-H) = 1. 140(28) Angstrom, angleCGeC = 114.2(11)degrees, angleCGeBr = 104.2(13)degrees, angleGeCH 106.9(43)degrees. Local C-3v symmetry and staggered conformation were assumed for the methyl groups.

Molecular structures of 3-hydroxybenzoic acid and 4-hydroxybenzoic acid, obtained by gas-phase electron diffraction and theoretical calculations

The structures of 3-hydroxybenzoic acid and 4-hydroxybenzoic acid have been determined by gas-phase electron diffraction using results from quantum chemical calculations to inform the choice of restraints applied to some of the structural parameters. The results from the study presented here demonstrate that resonance hybrids are not as helpful in rationalizing the structures of 2-, 3-, and 4-hydroxybenzoic acids as are models based upon electrostatic effects.