Related papers: Max filtering with reflection groups

A Coxeter polytope is a convex polytope in a real projective space equipped with linear reflections in its facets, such that the orbits of the polytope under the action of the group generated by the linear reflections tessellate a convex…

Biclustering techniques have been widely used to identify homogeneous subgroups within large data matrices, such as subsets of genes similarly expressed across subsets of patients. Mining a max-sum sub-matrix is a related but distinct…

A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…

Let $G$ be a locally compact group. Then for every $G$-space $X$ the maximal $G$-proximity $\beta_G$ can be characterized by the maximal topological proximity $\beta$ as follows: $$ A \ \overline{\beta_G} \ B \Leftrightarrow \exists V \in…

We derive and analyze an infinite-dimensional semidefinite program which computes least distortion embeddings of flat tori $\mathbb{R}^n/L$, where $L$ is an $n$-dimensional lattice, into Hilbert spaces. This enables us to provide a constant…

Covariant or invariant functions under a compact linear group can be expressed in terms of functions defined in the orbit space of the group. The semialgebraic relations defining the orbit spaces of all finite coregular real linear groups…

We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…

Zooplankton images, like many other real world data types, have intrinsic properties that make the design of effective classification systems difficult. For instance, the number of classes encountered in practical settings is potentially…

The analysis of manifold valued data using embedding based methods is linked to the problem of finding suitable embeddings. In this paper we are interested in embeddings of quotient manifolds $\mathrm{SO}(3)/\mathcal{S}$ of the rotation…

In this paper we prove a series of matching theorems for two sets of Coxeter generators of a finitely generated Coxeter group that identify common features of the two sets of generators. As an application, we describe an algorithm for…

We study the design of embeddings into Euclidean space with outliers. Given a metric space $(X,d)$ and an integer $k$, the goal is to embed all but $k$ points in $X$ (called the ``outliers") into $\ell_2$ with the smallest possible…

A tame filtration of an algebra is defined by the growth of its terms, which has to be majorated by an exponential function. A particular case is the degree filtration used in the definition of the growth of finitely generated algebras. The…

A Michael space is a Lindel\"of space which has a non-Lindel\"of product with the Baire space. In this work, we present the notion of Michael ultrafilter and we use it to construct a Michael space under the existence of a selective…

Let $n$ be a positive integer. We provide an explicit geometrically motivated $1$-Lipschitz map from the space of persistence diagrams on $n$ points (equipped with the Bottleneck distance) into the Hilbert space $\ell^2$. Such maps are a…

We show that for certain arithmetic groups, geometrically finite subgroups are the intersection of finite index subgroups containing them. Examples are the Bianchi groups and the Seifert-Weber dodecahedral space. In particular, for…

We observe that embeddings into random metrics can be fruitfully used to study the $L_1$-embeddability of lamplighter graphs or groups, and more generally lamplighter metric spaces. Once this connection has been established, several new…

In this paper we provide a framework for the study of isoperimetric problems in finitely generated group, through a combinatorial study of universal covers of compact simplicial complexes. We show that, when estimating filling functions,…

Let $X$ be a discrete metric space with bounded geometry. We show that if $X$ admits an "A-by-CE coarse fibration", then the canonical quotient map $\lambda: C^*_{\max}(X)\to C^*(X)$ from the maximal Roe algebra to the Roe algebra of $X$,…

For a discrete group $G$ and a discrete $G$-space $X$, we identify the Stone-\v{C}ech compactifications $\beta G$ and $\beta X$ with the sets of all ultrafilters on $G$ and $X$, and apply the natural action of $\beta G$ on $\beta X$ to…

Suppose a finite group acts on a scheme X and a finite-dimensional Lie algebra g. The corresponding equivariant map algebra is the Lie algebra M of equivariant regular maps from X to g. We classify the irreducible finite-dimensional…