We extend the group-theoretic notion of conditional flatness for a localization functor to any pointed category, and investigate it in the context of homological categories and of semi-abelian categories. In the presence of functorial fiberwise localizatio ...
When learning from data, leveraging the symmetries of the domain the data lies on is a principled way to combat the curse of dimensionality: it constrains the set of functions to learn from. It is more data efficient than augmentation and gives a generaliz ...
It is known that the pitchfork bifurcation of Kelvin-Helmholtz instability occurring at minimum gradient Richardson number Ri(m) similar or equal to 1/4 in viscous stratified shear flows can be subcritical or supercritical depending on the value of the Pra ...
Extensive amenability is a property of group actions which has recently been used as a tool to prove amenability of groups. We study this property and prove that it is preserved under a very general construction of semidirect products. As an application, w ...
We show that the Flaschka map, originally introduced to analyze the dynamics of the integrable Toda lattice system, is the inverse of a momentum map. We discuss the geometrical setting of the map and apply it to the generalized Toda lattice systems on semi ...
Let R be a unital commutative ring, and let M be an R-module that is generated by k elements but not less. Let be the subgroup of generated by the elementary matrices. In this paper we study the action of by matrix multiplication on the set of unimodular r ...
Reduction and abstraction techniques have been proposed to address the state space explosion problem in verification. In this paper, we present reduction and abstraction techniques for component-based systems modeled in BIP (Behavior, Interaction and Prior ...
Let G be a finite group with a Sylow 2-subgroup P which is either quaternion or semi-dihedral. Let k be an algebraically closed field of characteristic 2. We prove the existence of exotic endotrivial kG-modules, whose restrictions to P are isomorphic to th ...
Supramenability of groups is characterised in terms of invariant measures on locally compact spaces. This opens the door to constructing interesting crossed product C*-algebras for non-supramenable groups. In particular, stable Kirchberg algebras in the UC ...
Let G be a finite group and let k be a field. Our purpose is to investigate the simple modules for the double Burnside ring kB(G,G). It turns out that they are evaluations at G of simple biset functors. For a fixed finite group H, we introduce a suitable b ...
In the framework of large deformation diffeomorphic metric mapping (LDDMM), a multiscale theory for the diffeomorphism group is developed based on previous works of the authors. The purpose of this paper is (1) to develop in detail a variational approach f ...
For linear models, compressed sensing theory and methods enable recovery of sparse signals of interest from few measurements-in the order of the number of nonzero entries as opposed to the length of the signal of interest. Results of similar flavor have mo ...
IEEE Institute of Electrical and Electronics Engineers2012
This paper discusses the mathematical framework for designing methods of Large Deformation Diffeomorphic Matching (LDM) for image registration in computational anatomy. After reviewing the geometrical framework of LDM image registration methods, we prove a ...
The EPDiff equation (or dispersionless Camassa-Holm equation in 1D) is a well known example of geodesic motion on the Diff group of smooth invertible maps (diffeomorphisms). Its recent two-component extension governs geodesic motion on the semidirect produ ...
We analyse volume-preserving actions of product groups on Riemannian manifolds. Under a natural spectral irreducibility assumption, we prove the following dichotomy: Either the action is measurably isometric, in which case there are at most two factors; or ...
Let T-1, ... , T-d be homogeneous trees with degrees q(1) + 1, ... , q(d) + 1 >= 3; respectively. For each tree, let h : Tj -> Z be the Busemann function with respect to a fixed boundary point ( end). Its level sets are the horocycles. The horocyclic produ ...
This thesis deals with applications of Lie symmetries in differential geometry and dynamical systems. The first chapter of the thesis studies the singular reduction of symmetries of cosphere bundles, the conservation properties of contact systems and their ...
We introduce a three-dimensional (3-D) parametric active contour algorithm for the shape estimation of DNA molecules from stereo cryo-electron micrographs. We estimate the shape by matching the projections of a 3-D global shape model with the micrographs; ...
The main purpose of this paper is to show that, if G is a finite p-group which is not cyclic, quaternion or semi-dihedral, then the group of endo-trivial G-modules is detected on restriction to elementary abelian p-subgroups of rank 2. Consequently, the to ...
