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See detailLe géomètre et le SIG
Billen, Roland ULg

Article for general public (2010)

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See detailGéomètre: les enjeux de l'enseignement
Billen, Roland ULg

Article for general public (2013)

Detailed reference viewed: 30 (2 ULg)
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See detailGeometric and healing laws in simple stochastic models of fracture in a sputtering process
Dhulst, R.; Vandewalle, Nicolas ULg; Ausloos, Marcel ULg

in Physical Review. E : Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics (1997), 55(1), 189-193

We investigated two simple models of two-dimensional square lattice fracture under sputtering process conditions extending a previously studied model by Ausloos and Kowalski [Phys. Rev. B 45, 12 830 (1992 ... [more ▼]

We investigated two simple models of two-dimensional square lattice fracture under sputtering process conditions extending a previously studied model by Ausloos and Kowalski [Phys. Rev. B 45, 12 830 (1992)]. The models differ by the particle displacement rules during the fracture. Healing of the medium is observed in both models. This effect implies the formation of several thresholds during sputtering process fracture. They are distributed as a size-dependent power law. An avalanche like exponent is also obtained. We study this phenomenology within scaling arguments of classical percolation theory and mean-field arguments. [less ▲]

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See detailGeometric control of a pyridoxal-catalyzed aldol condensation
Koh, John T.; Delaude, Lionel ULg; Breslow, Ronald

in Journal of the American Chemical Society (1994), 116(25), 11234-11240

A chiral cyclophane derivative of pyridoxal has been synthesized that has amino groups oriented specifically over one face of the cofactor. The compound catalyzes the formation of threonine and allo ... [more ▼]

A chiral cyclophane derivative of pyridoxal has been synthesized that has amino groups oriented specifically over one face of the cofactor. The compound catalyzes the formation of threonine and allo-threonine from glycine and acetaldehyde with enantioinductions that are a function of pH, reversing the optical selectivity between low pH and high pH. The stereochemical results are compared with those of structurally related pyridoxal cyclophanes that lack titratable catalytic groups. Explanations are advanced for this stereochemical reversal and for the otherwise surprising preference of most of these compounds to react on the more hindered face of the pyridoxal. Models indicate that the transamination intermediate is distorted by the transannular chain, and stereoelectronic arguments predict that this distortion should lead to reaction on the face that carries the chain, as observed. The stereochemical reversal with the attached (dimethylamino)alkyl group, as a function of pH, may reflect catalysis by the protonated form, but metal coordination by the basic form cannot be excluded. [less ▲]

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See detailGeometric Design of Scroll Expanders Optimized for Small Organic Rankine Cycles
Orosz, M.S.; Muller, A.V.; Dechesne, Bertrand ULg et al

in Journal of Engineering for Gas Turbines & Power (2013)

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See detailGeometric ferroelectricity in fluoroperovskites
Garcia Castro, Andrés Camilo ULg; Spaldin, Nicola A.; Romero, A. H. et al

in Physical Review. B, Condensed Matter and Materials Physics (2014), 89

We used first-principles calculations to investigate the existence and origin of the ferroelectric instability in the ABF3 fluoroperovskites. While the ground states of most ABF3 compounds are ... [more ▼]

We used first-principles calculations to investigate the existence and origin of the ferroelectric instability in the ABF3 fluoroperovskites. While the ground states of most ABF3 compounds are paraelectric (Pnma phase), we find that many fluoroperovskites have a ferroelectric instability in their high-symmetry cubic structure that is of similar amplitude to that commonly found in oxide perovskites. In contrast to the oxides, however, the fluorides have nominal Born effective charges, indicating a different mechanism for the instability.We show that the instability originates from ionic size effects, and is therefore in most cases largely insensitive to pressure and strain, again in contrast to the oxide perovskites. An exception is NaMnF3, where coherent epitaxial strain matching to a substrate with equal in-plane lattice constants destabilizes the bulk Pnma structure, leading to a ferroelectric, and indeed multiferroic, ground state with an unusual polarization/strain response. [less ▲]

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See detailGeometric framework for coordination on Lie groups
Sarlette, Alain ULg; Bonnabel, Silvère ULg; Sepulchre, Rodolphe ULg

Conference (2008, March)

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See detailGeometric interpretation of a non-linear beam finite element on the Lie group SE(3)
Sonneville, Valentin ULg; Cardona, Alberto; Bruls, Olivier ULg

in Archive of Mechanical Engineering (2014), 61(2), 305-329

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See detailA geometric local frame approach for flexible multibody systems
Sonneville, Valentin ULg

Doctoral thesis (2015)

The notion of frame is ubiquitous in the kinematic description of flexible multibody models. In this work, a differential-geometric framework is selected to describe frame operations in a rigorous and ... [more ▼]

The notion of frame is ubiquitous in the kinematic description of flexible multibody models. In this work, a differential-geometric framework is selected to describe frame operations in a rigorous and systematic way. A frame transformation is thus seen as an element of the special Euclidean group $SE(3)$, which is represented by a four by four transformation matrix, and frame operations, such as spatial interpolation or time integration, rely on non-linear but analytical expressions in which translation and rotation contributions are inherently coupled. Based on this formalism, this thesis develops geometrically exact formulations of many classical components used in flexible multibody system modelling, which includes the formulation of a rigid body, several kinematic joints, a flexible beam, a flexible shell and a superelement. As opposed to most popular techniques in the literature, a local frame representation of the equations of motion is adopted in this work. This means that the unknown kinematic variables such as the motion increments, the velocities and the accelerations, as well as the generalized forces are all expressed in a local frame attached to the body. After spatial semi-discretization, the equations of motion of a multibody system take the form of differential-algebraic equations on a Lie group which can be conveniently solved in a global parametrization-free approach using a Lie group integration scheme. This thesis presents numerous arguments to recommend this framework for the development of efficient codes for the numerical simulation of flexible multibody systems. On the one hand, the proposed framework leads to novel and interesting theoretical aspects. For instance, it features a naturally singularity-free description of large rotations and it leads to inherently shear-locking free beam and shell finite elements. On the other hand, the formulation leads to unprecedented computational properties. The geometric non-linearities are naturally filtered out of the equilibrium equations such that non-linearities are significantly reduced, as compared to classical formulations. In particular, the iteration matrix, which is used in implicit integration schemes, is insensitive to overall large amplitude motions and is only affected by local relative transformations, such as deformations in flexible elements and relative motions in kinematic joints. This property can be exploited to strongly reduce computational costs, as compared to classical formulations. [less ▲]

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See detailGeometric minimization of highly symmetric potentials
Degée, Audrey ULg; Ivanov, Igor ULg; Keus, Venus ULg

in Journal of High Energy Physics [=JHEP] (2013), 2013

In non-minimal Higgs mechanisms, one often needs to minimize highly symmetric Higgs potentials. Here we propose a geometric way of doing it, which, surprisingly, is often much more efficient than the ... [more ▼]

In non-minimal Higgs mechanisms, one often needs to minimize highly symmetric Higgs potentials. Here we propose a geometric way of doing it, which, surprisingly, is often much more efficient than the usual method. By construction, it gives the global minimum for any set of free parameters of the potential, thus offering an intuitive understanding of how they affect the vacuum expectation values. For illustration, we apply this method to the S_4 and A_4-symmetric three-Higgs-doublet models. We find that at least three recent phenomenological analyses of the A_4-symmetric model used a local, not the global minimum. We discuss coexistence of minima of different types, and comment on the mathematical origin of geometrical CP-violation and on a new symmetry linking different minima. [less ▲]

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See detailGeometric optimization algorithms for linear regression on fixed-rank matrices
Meyer, Gilles ULg

Doctoral thesis (2011)

Nowadays, large and rapidly evolving data sets are commonly encountered in many modern applications. Efficiently mining and exploiting these data sets generally results in the extraction of valuable ... [more ▼]

Nowadays, large and rapidly evolving data sets are commonly encountered in many modern applications. Efficiently mining and exploiting these data sets generally results in the extraction of valuable information and therefore appears as an important challenge in various domains including network security, computer vision, internet search engines, bioinformatics, marketing systems, online advertisement, social networks, just to name a few. The rapid development of these modern computer science applications sustains an ever-increasing demand for efficient machine learning algorithms that can cope with large-scale problems, characterized by a large number of samples and a large number of variables. The research reported in the present thesis is devoted to the design of efficient machine learning algorithms for large-scale problems. Specifically, we adopt a geometric optimization viewpoint to address the problem of linear regression in nonlinear and high-dimensional matrix search spaces. Our purpose is to efficiently exploit the geometric structure of the search space in the design of scalable linear regression algorithms. Our search space of main interest will be the set of low-rank matrices. Learning a low-rank matrix is a typical approach to cope with high-dimensional problems. The low-rank constraint is expected to force the learning algorithm to capture a limited number of dominant factors that mostly influence the sought solution. We consider both the learning of a fixed-rank symmetric positive semidefinite matrix and of a fixed-rank non-symmetric matrix. A first contribution of the thesis is to show that many modern machine learning problems can be formulated as linear regression problems on the set of fixed-rank matrices. For example, the learning of a low-rank distance, low-rank matrix completion and the learning on data pairs are cast into the considered linear regression framework. For these problems, the low-rank constraint is either part of the original problem formulation or is a sound approximation that significantly reduces the original problem size and complexity, resulting in a dramatic decrease in the computational complexity of algorithms. Our main contribution is the development of novel efficient algorithms for learning a linear regression model parameterized by a fixed-rank matrix. The resulting algorithms preserve the underlying geometric structure of the problem, scale to high-dimensional problems, enjoy local convergence properties and confer a geometric basis to recent contributions on learning fixed-rank matrices. We thereby show that the considered geometric optimization framework offers a solid and versatile framework for the design of rank-constrained machine learning algorithms. The efficiency of the proposed algorithms is illustrated on several machine learning applications. Numerical experiments suggest that the proposed algorithms compete favorably with the state-of-the-art in terms of achieved performance and required computational time. [less ▲]

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See detailGeometric optimization methods for independent component analysis applied on gene expression data
Journee, Michel ULg; Teschendorff, A. E.; Absil, P.-A. et al

in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2007) (2007)

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See detailGeometric optimization methods for the analysis of gene expression data
Journee, Michel ULg; Teschendorff, A. E.; Absil, P.-A. et al

Part of book (2007)

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See detailGeometric parameters influence on Piano Key Weir hydraulic performances
Erpicum, Sébastien ULg; Archambeau, Pierre ULg; Pirotton, Michel ULg et al

in Chanson, Hubert; Toombes, Luke (Eds.) Hydraulic Structures and Society – Engineering Challenges (2014, June)

The Piano Key Weir is a recent evolution of the traditional labyrinth weir. Thanks to a reduced foot print, this nonlinear weir can be placed on the top of gravity dams. The Piano Key Weir geometry ... [more ▼]

The Piano Key Weir is a recent evolution of the traditional labyrinth weir. Thanks to a reduced foot print, this nonlinear weir can be placed on the top of gravity dams. The Piano Key Weir geometry involves a large number of geometric parameters. Several experimental studies have been carried out to investigate the main geometric parameters influencing the weir hydraulic efficiency and to define their optimal value. In this paper, the experimental data gathered at the University of Liege are re-examined to show how the weir height, the keys widths and the overhangs positions influence, for a given crest length magnification ratio, the weir discharge capacity. The theoretical rating curve of a standard linear weir is considered for comparison. The analysis highlights that the keys widths and overhangs lengths ratios influence significantly the Piano Key Weir efficiency, but less than the weir height. Considering the above mentioned results, a cost efficient design proposed in the literature is also proved to be close to the hydraulic optimum. [less ▲]

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See detailGeometric properties of mechanical forward motion compensation system controlled by a piezoelectric drive
Collette, François; Gline, Simon; Losseau, Julien et al

in International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences (2012), XXXIX(B5), 321-325

Forward Motion Compensation (FMC) systems have been designed to ensure the radiometric quality of motion acquisition in airborne cameras. If the radiometric benefits of FMC have been acknowledged, what ... [more ▼]

Forward Motion Compensation (FMC) systems have been designed to ensure the radiometric quality of motion acquisition in airborne cameras. If the radiometric benefits of FMC have been acknowledged, what are its effects on the geometrical properties of the camera? This paper demonstrates that FMC significantly improves geometrical properties of a camera. Aspects of FMC theory are discussed, with a focus on the near-lossless implementation of this technology into digital aerial camera systems. Among mechanical FMC technologies, the piezoelectric drive is proving to excel in dynamic positioning in both accuracy and repeatability. The patented piezoelectric drive integrated into Optech aerial camera systems allows for continuous and precise sensor motion to ensure exact compensation of the aircraft's forward motion. This paper presents findings that demonstrate the validity of this assertion. The paper also discusses the physical principles involved in motion acquisition. Equations are included that define the motion effect at image level and illustrate how FMC acts to prevent motion effects. The residual motion effect or compensation error is formulated and a practical computation applied to the more restrictive camera case. The assessment concludes that, in the range of airborne camera utilization, the mechanical FMC technique is free of "visible" error at both human eye and computer assessment level. Lastly, the paper proceeds to a detailed technical discussion of piezoelectric drives and why they have proven to be so effective as nanopositioning devices for optical applications. The effectiveness of the patented piezoelectric drives used to achieve FMC in Optech cameras is conclusively demonstrated. [less ▲]

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See detailGeometric quantities associated to differential operators
Mathonet, Pierre ULg

in Communications in Algebra (2000), 28(2), 699-718

Denote by F_lambda the space of fields of tensor densities of weight -lambda over a manifold M. The space D^p_{lambda,mu} of differential operators of order at most p that map F_lambda onto F_mu are ... [more ▼]

Denote by F_lambda the space of fields of tensor densities of weight -lambda over a manifold M. The space D^p_{lambda,mu} of differential operators of order at most p that map F_lambda onto F_mu are modules over the Lie algebra of vector fields Vect(M). We compute all the Vect(M)-invariant mappings from D^p_{lambda,mu} onto F_nu. [less ▲]

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See detailGeometric statistical processing of brain diffusion tensor images
Collard, Anne ULg

Doctoral thesis (2013)

Nowadays, the functioning of the human brain is still one of the biggest mysteries of humanity. The multiple holes in the understanding of the human brain explain why an intensification of brain-oriented ... [more ▼]

Nowadays, the functioning of the human brain is still one of the biggest mysteries of humanity. The multiple holes in the understanding of the human brain explain why an intensification of brain-oriented research can be observed since a few years. One of the most recent techniques to better understand the brain is Diffusion Tensor Imaging (DTI), a noninvasive imaging modality that provides information about orientation of nervous fibers, and their spatial density, with a high resolution. The particular nature of DTI images makes them multi-valued. Their processing therefore requires to adapt state-of-the-art techniques, which are fundamentally tailored to scalar-valued images. The objective of this PhD thesis is to develop a novel framework for the processing of tensor diffusion images. The focus is threefold: first, we adopt a Riemannian geometric framework to generalize image processing from linear to nonlinear spaces. Second, we aim at developing a processing framework that retains the physical information of measurement data. Thirdly, the proposed algorithm must be computationally efficient in order to scale with the data size of clinical applications. The main contribution of this thesis is the development of a novel processing method, which has the particularity to preserve the important features of diffusion tensors, while being computationally affordable. This technique is based on the decoupling between the two types of information conveyed by tensors: the diffusion intensity on one hand, and the orientation of diffusion on the other hand. Moreover, the computational cost is limited thanks to the use of unit quaternions to represent tensors orientation. Another contribution of the thesis lies in the development of a statistical method for group comparison. This method uses the notion of similarity measure between the values, a notion that can be defined for multi-valued images, and which enables to reduce the computational cost. The use, for the statistical tests, of the similarity measure associated to our framework turns out to be efficient and informative. The study of geometric methods for multi-valued images together with the study of potential applications of diffusion tensor images have enabled the introduction of a novel framework, which is particularly appropriate for those images. The basic operations developed in the thesis open the way to more sophisticated processing algorithms, while ensuring the preservation of the main information associated to the tensors. [less ▲]

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See detailGeometric Study of Mixed-integer Sets from Two Rows of Two Adjacent Simplex Bases
Louveaux, Quentin ULg

Conference (2009, August)

We generalize the study of sets arising from two rows of a simplex tableau by considering bounds on the nonbasic variables. We show that new classes of facets arise that cannot be obtained from triangles ... [more ▼]

We generalize the study of sets arising from two rows of a simplex tableau by considering bounds on the nonbasic variables. We show that new classes of facets arise that cannot be obtained from triangles and quadrilaterals. Specifically, when exactly one upper bound on a non-basic variable is introduced, inequalities that can be derived from pentagons involving up to six variables also appear. [less ▲]

Detailed reference viewed: 17 (0 ULg)