Fundamental domains for proper affine actions of Coxeter groups in three dimensions

We study proper actions of groups $G \cong \Z/2\Z \ast \Z/2\Z \ast \Z/2\Z$ on affine space of three real dimensions. Since $G$ is nonsolvable, work of Fried and Goldman implies that it preserves a Lorentzian metric. A subgroup $\Gamma < G$ of index two acts freely, and $\R^3/\Gamma$ is a Margulis spacetime associated to a hyperbolic surface $\Sigma$. When $\Sigma$ is convex cocompact, work of Danciger, Gu{\'e}ritaud, and Kassel shows that the action of $\Gamma$ admits a polyhedral fundamental domain bounded by crooked planes. We consider under what circumstances the action of $G$ also admits a crooked fundamental domain. We show that it is possible to construct actions of $G$ that fail to admit crooked fundamental domains exactly when the extended mapping class group of $\Sigma$ fails to act transitively on the top-dimensional simplices of the arc complex of $\Sigma$. We also provide explicit descriptions of the moduli space of $G$ actions that admit crooked fundamental domains.

Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions

We develop the energy norm a-posteriori error estimation for hp-version discontinuous Galerkin (DG) discretizations of elliptic boundary-value problems on 1-irregularly, isotropically refined affine hexahedral meshes in three dimensions. We derive a reliable and efficient indicator for the errors measured in terms of the natural energy norm. The ratio of the efficiency and reliability constants is independent of the local mesh sizes and weakly depending on the polynomial degrees. In our analysis we make use of an hp-version averaging operator in three dimensions, which we explicitly construct and analyze. We use our error indicator in an hp-adaptive refinement algorithm and illustrate its practical performance in a series of numerical examples. Our numerical results indicate that exponential rates of convergence are achieved for problems with smooth solutions, as well as for problems with isotropic corner singularities.

Three-dimensional finite element thermal analysis of dental tissues irradiated with Er,Cr:YSGG laser

In the present study, a finite element model of a half-sectioned molar tooth was developed in order to understand the thermal behavior of dental hard tissues (both enamel and dentin) under laser irradiation. The model was validated by comparing it with an in vitro experiment where a sound molar tooth was irradiated by an Er,Cr:YSGG pulsed laser. The numerical tooth model was conceived to simulate the in vitro experiment, reproducing the dimensions and physical conditions of the typical molar sound tooth, considering laser energy absorption and calculating the heat transfer through the dental tissues in three dimensions. The numerical assay considered the same three laser energy densities at the same wavelength (2.79 mu m) used in the experiment. A thermographic camera was used to perform the in vitro experiment, in which an Er, Cr: YSGG laser (2.79 mu m) was used to irradiate tooth samples and the infrared images obtained were stored and analyzed. The temperature increments in both the finite element model and the in vitro experiment were compared. The distribution of temperature inside the tooth versus time plotted for two critical points showed a relatively good agreement between the results of the experiment and model. The three dimensional model allows one to understand how the heat propagates through the dentin and enamel and to relate the amount of energy applied, width of the laser pulses, and temperature inside the tooth. (C) 2008 American Institute of Physics. [DOI: 10.1063/1.2953526]

Three-point vertices in Landau-gauge Yang-Mills theory

Vertices are of central importance for constructing QCD bound states out of the individual constituents of the theory, i.e. quarks and gluons. In particular, the determination of three-point vertices is crucial in nonperturbative investigations of QCD. We use numerical simulations of lattice gauge theory to obtain results for the 3-point vertices in Landau-gauge SU(2) Yang-Mills theory in three and four space-time dimensions for various kinematic configurations. In all cases considered, the ghost-gluon vertex is found to be essentially tree-level-like, while the three-gluon vertex is suppressed at intermediate momenta. For the smallest physical momenta, reachable only in three dimensions, we find that some of the three-gluon-vertex tensor structures change sign.

Three-dimensional quantum solitons with parametric coupling

We consider the quantum field theory of two bosonic fields interacting via both parametric (cubic) and quartic couplings. In the case of photonic fields in a nonlinear optical medium, this corresponds to the process of second-harmonic generation (via chi((2)) nonlinearity) modified by the chi((3)) nonlinearity. The quantum solitons or energy eigenstates (bound-state solutions) are obtained exactly in the simplest case of two-particle binding, in one, two, and three space dimensions. We also investigate three-particle binding in one space dimension. The results indicate that the exact quantum solitons of this field theory have a singular, pointlike structure in two and three dimensions-even though the corresponding classical theory is nonsingular. To estimate the physically accessible radii and binding energies of the bound states, we impose a momentum cutoff on the nonlinear couplings. In the case of nonlinear optical interactions, the resulting radii and binding energies of these photonic particlelike excitations in highly nonlinear parametric media appear to be close to physically observable values.

Three dimensional preparatory trunk motion precedes asymmetrical upper limb movement

Three-dimensional trunk motion. trunk muscle electromyography and intra-abdominal pressure were evaluated to investigate the preparatory control of the trunk associated with voluntary unilateral upper limb movement. The directions of angular motion produced by moments reactive to limb movement in each direction were predicted using a three-dimensional model of the body. Preparatory motion of the trunk occurred in three dimensions in the directions opposite to the reactive moments. Electromyographic recordings from the superficial trunk muscles were consistent with preparatory trunk motion. However, activation of transversus abdominis was inconsistent with control of direction-specific moments acting on the trunk. The results provide evidence that anticipatory postural adjustments result in movements and not simple rigidification of the trunk. (C) 2000 Elsevier Science B.V. All rights reserved.

Three-dimensional orthotropic viscoelastic finite element model of a human ligament

Ligaments undergo finite strain displaying hyperelastic behaviour as the initially tangled fibrils present straighten out, combined with viscoelastic behaviour (strain rate sensitivity). In the present study the anterior cruciate ligament of the human knee joint is modelled in three dimensions to gain an understanding of the stress distribution over the ligament due to motion imposed on the ends, determined from experimental studies. A three dimensional, finite strain material model of ligaments has recently been proposed by Pioletti in Ref. [2]. It is attractive as it separates out elastic stress from that due to the present strain rate and that due to the past history of deformation. However, it treats the ligament as isotropic and incompressible. While the second assumption is reasonable, the first is clearly untrue. In the present study an alternative model of the elastic behaviour due to Bonet and Burton (Ref. [4]) is generalized. Bonet and Burton consider finite strain with constant modulii for the fibres and for the matrix of a transversely isotropic composite. In the present work, the fibre modulus is first made to increase exponentially from zero with an invariant that provides a measure of the stretch in the fibre direction. At 12% strain in the fibre direction, a new reference state is then adopted, after which the material modulus is made constant, as in Bonet and Burton's model. The strain rate dependence can be added, either using Pioletti's isotropic approximation, or by making the effect depend on the strain rate in the fibre direction only. A solid model of a ligament is constructed, based on experimentally measured sections, and the deformation predicted using explicit integration in time. This approach simplifies the coding of the material model, but has a limitation due to the detrimental effect on stability of integration of the substantial damping implied by the nonlinear dependence of stress on strain rate. At present, an artificially high density is being used to provide stability, while the dynamics are being removed from the solution using artificial viscosity. The result is a quasi-static solution incorporating the effect of strain rate. Alternate approaches to material modelling and integration are discussed, that may result in a better model.

Three-dimensional magnetic resonance myocardial motion tracking from a single image plane.

Three-dimensional imaging for the quantification of myocardial motion is a key step in the evaluation of cardiac disease. A tagged magnetic resonance imaging method that automatically tracks myocardial displacement in three dimensions is presented. Unlike other techniques, this method tracks both in-plane and through-plane motion from a single image plane without affecting the duration of image acquisition. A small z-encoding gradient is subsequently added to the refocusing lobe of the slice-selection gradient pulse in a slice following CSPAMM acquisition. An opposite polarity z-encoding gradient is added to the orthogonal tag direction. The additional z-gradients encode the instantaneous through plane position of the slice. The vertical and horizontal tags are used to resolve in-plane motion, while the added z-gradients is used to resolve through-plane motion. Postprocessing automatically decodes the acquired data and tracks the three-dimensional displacement of every material point within the image plane for each cine frame. Experiments include both a phantom and in vivo human validation. These studies demonstrate that the simultaneous extraction of both in-plane and through-plane displacements and pathlines from tagged images is achievable. This capability should open up new avenues for the automatic quantification of cardiac motion and strain for scientific and clinical purposes.

ZHARP: three-dimensional motion tracking from a single image plane.

Three-dimensional imaging and quantification of myocardial function are essential steps in the evaluation of cardiac disease. We propose a tagged magnetic resonance imaging methodology called zHARP that encodes and automatically tracks myocardial displacement in three dimensions. Unlike other motion encoding techniques, zHARP encodes both in-plane and through-plane motion in a single image plane without affecting the acquisition speed. Postprocessing unravels this encoding in order to directly track the 3-D displacement of every point within the image plane throughout an entire image sequence. Experimental results include a phantom validation experiment, which compares zHARP to phase contrast imaging, and an in vivo study of a normal human volunteer. Results demonstrate that the simultaneous extraction of in-plane and through-plane displacements from tagged images is feasible.

Facing the broader dimensions of biological invasions

Invasive species are an excellent opportunity to think about the nature society desires, particularly in the face of global changes. Nature and human views of nature are rapidly evolving; our approach to bio- logical invasions through biosecurity institutions and land management policies must evolve in tandem with these changes. We review three dimensions that are insufficiently addressed. First, biological inva- sions are culturally shaped and interpreted. Humans play a major role in the movement and nurturing of alien life, and esthetics, perception, and emotion are deeply implicated in the management of invasive species. What people fear or regret with invasive species are not their effects on nature per se, but their effects on a particular desired nature, and policymaking must reflect this. Second, biological invasions are not restricted to negative impacts. Invasions take place in landscapes where many natural condi- tions have been altered, so policy tools must recognize that invasive species are a functional, structural, and compositional part of transformed ecosystems. In some cases, native species benefit from changes in resource availability caused by invasions or from protections provided by an invasive plant. Finally, invasive species can help ecosystems and people to adapt to global change by maintaining ecosystem processes such as productivity, carbon storage, and nutrient cycling in a context of climate change or land cover transformations. While recognition is growing among ecologists that novel, invaded ecosystems have value, and while the on-the-ground application of biosecurity policies has of necessity adjusted to local contexts and other agendas, invasion biology could aid policymaking by better addressing the three complexities inherent in the three dimensions highlighted above.

Radiographic volume analysis as a novel tool to determine nasopalatine duct cyst dimensions and its association with presenting symptoms and postoperative complications.

OBJECTIVES: The aims of the study were to use cone beam computed tomography (CBCT) images of nasopalatine duct cysts (NPDC) and to calculate the diameter, surface area, and 3D-volume using a custom-made software program. Furthermore, any associations of dimensions of NPDC with age, gender, presence/absence of maxillary incisors/canines (MI/MC), endodontic treatment of MI/MC, presenting symptoms, and postoperative complications were evaluated. MATERIAL AND METHODS: The study comprised 40 patients with a histopathologically confirmed NPDC. On preoperative CBCT scans, curves delineating the cystic borders were drawn in all planes and the widest diameter (in millimeter), surface area (in square millimeter), and volume (in cubic millimeter) were calculated. RESULTS: The overall mean cyst diameter was 15 mm (range 7-47 mm), the mean cyst surface area 566 mm(2) (84-4,516 mm(2)), and the mean cyst volume 1,735 mm(3) (65-25,350 mm(3)). For 22 randomly allocated cases, a second measurement resulted in a mean absolute aberration of ±4.2 % for the volume, ±2.8 % for the surface, and ±4.9 % for the diameter. A statistically significant association was found for the CBCT determined cyst measurements and the need for preoperative endodontic treatment to MI/MC and for postoperative complications. CONCLUSION: In the hands of a single experienced operator, the novel software exhibited high repeatability for measurements of cyst dimensions. Further studies are needed to assess the application of this tool for dimensional analysis of different jaw cysts and lesions including treatment planning. CLINICAL RELEVANCE: Accurate radiographic information of the bone volume lost (osteolysis) due to expansion of a cystic lesion in three dimensions could help in personalized treatment planning.

A Farewell to Flat Biology. Three-dimensional Cell Culture Models in Cancer Drug Target Identification and Validation

Cells of epithelial origin, e.g. from breast and prostate cancers, effectively differentiate into complex multicellular structures when cultured in three-dimensions (3D) instead of conventional two-dimensional (2D) adherent surfaces. The spectrum of different organotypic morphologies is highly dependent on the culture environment that can be either non-adherent or scaffold-based. When embedded in physiological extracellular matrices (ECMs), such as laminin-rich basement membrane extracts, normal epithelial cells differentiate into acinar spheroids reminiscent of glandular ductal structures. Transformed cancer cells, in contrast, typically fail to undergo acinar morphogenic patterns, forming poorly differentiated or invasive multicellular structures. The 3D cancer spheroids are widely accepted to better recapitulate various tumorigenic processes and drug responses. So far, however, 3D models have been employed predominantly in the Academia, whereas the pharmaceutical industry has yet to adopt a more widely and routine use. This is mainly due to poor characterisation of cell models, lack of standardised workflows and high throughput cell culture platforms, and the availability of proper readout and quantification tools. In this thesis, a complete workflow has been established entailing well-characterised 3D cell culture models for prostate cancer, a standardised 3D cell culture routine based on high-throughput-ready platform, automated image acquisition with concomitant morphometric image analysis, and data visualisation, in order to enable large-scale high-content screens. Our integrated suite of software and statistical analysis tools were optimised and validated using a comprehensive panel of prostate cancer cell lines and 3D models. The tools quantify multiple key cancer-relevant morphological features, ranging from cancer cell invasion through multicellular differentiation to growth, and detect dynamic changes both in morphology and function, such as cell death and apoptosis, in response to experimental perturbations including RNA interference and small molecule inhibitors. Our panel of cell lines included many non-transformed and most currently available classic prostate cancer cell lines, which were characterised for their morphogenetic properties in 3D laminin-rich ECM. The phenotypes and gene expression profiles were evaluated concerning their relevance for pre-clinical drug discovery, disease modelling and basic research. In addition, a spontaneous model for invasive transformation was discovered, displaying a highdegree of epithelial plasticity. This plasticity is mediated by an abundant bioactive serum lipid, lysophosphatidic acid (LPA), and its receptor LPAR1. The invasive transformation was caused by abrupt cytoskeletal rearrangement through impaired G protein alpha 12/13 and RhoA/ROCK, and mediated by upregulated adenylyl cyclase/cyclic AMP (cAMP)/protein kinase A, and Rac/ PAK pathways. The spontaneous invasion model tangibly exemplifies the biological relevance of organotypic cell culture models. Overall, this thesis work underlines the power of novel morphometric screening tools in drug discovery.

Les déterminants organisationnels et sociaux des trois dimensions de l'épuisement professionnel

Réalisée à partir d’un échantillon de 410 travailleurs civils et policiers du Service de Police de la Ville de Montréal (SPVM) atteint en février 2009, cette recherche vise à approfondir les connaissances relatives à l’influence de l’utilisation des compétences, de l’autorité décisionnelle, du soutien social au travail, de la supervision abusive et du soutien social hors travail sur les trois dimensions du syndrome d’épuisement professionnel (épuisement émotionnel, cynisme, efficacité professionnelle). Cette recherche vise également à déterminer si les relations qui unissent ces facteurs organisationnels et sociaux aux trois dimensions d’épuisement professionnel varient selon que les travailleurs appartiennent à la main-d’œuvre policière ou civile. Les résultats des analyses multivariées témoignent de l’influence distinctive des variables explicatives sur les trois dimensions d’épuisement professionnel et supportent la conceptualisation tridimensionnelle du syndrome d’épuisement professionnel. Les résultats appuient également la distinction des concepts d’utilisation des compétences et d’autorité décisionnelle et permettent d’approfondir les connaissances relatives à l’influence de la supervision abusive, du soutien social hors travail et du rôle modérateur de la profession sur les trois dimensions du syndrome d’épuisement professionnel.