Related papers: A Large Scale Approach to Decomposition Spaces
The decomposition into interaction subspaces is an important result for graphical models and plays a central role for results on the linearized marginal problem; similarly the Chaos decomposition plays an important role in statistical…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
The paper introduces the class of O-metric spaces, a novel generalization of metric-type spaces, classifying almost all possible metric types into upward and downward O-metrics. We list some topologies arising from O-metrics and discuss…
Understanding the interplay between ordered structures and substrate curvature is an interesting problem with versatile applications, including functionalization of charged supramolecular surfaces and modern microfluidic technologies. In…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
In this article, we introduce and study a natural notion of coarse separation for metric spaces, with an emphasis on coarse separation by subspaces of polynomial or subexponential growth. For instance, we show that symmetric spaces of…
The objective of this paper is to learn dense 3D shape correspondence for topology-varying generic objects in an unsupervised manner. Conventional implicit functions estimate the occupancy of a 3D point given a shape latent code. Instead,…
A powerful and flexible approach to structured prediction consists in embedding the structured objects to be predicted into a feature space of possibly infinite dimension by means of output kernels, and then, solving a regression problem in…
L^p spaces of mappings taking values in arbitrary metric spaces, which we call nonlinear Lebesgue spaces, play an important role in several fields of mathematics. For instance, membership in these spaces is typically required for transport…
It is well-known that point-set topology (without additional structure) lacks the capacity to generalize the analytic concepts of completeness, boundedness, and other typically-metric properties. The ability of metric spaces to capture this…
One common task in image forensics is to detect spliced images, where multiple source images are composed to one output image. Most of the currently best performing splicing detectors leverage high-frequency artifacts. However, after an…
Intermediate feature representations represent the backbone for the expressivity and adaptability of deep neural networks. However, their geometric structure remains poorly understood. In this submission, we provide indirect insights into…
A micromorphic computational homogenization framework has recently been developed to deal with materials showing long-range correlated interactions, i.e. displaying patterning modes. Typical examples of such materials are elastomeric…
There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…
Developable surfaces are commonly observed in various applications such as architecture, product design, manufacturing, mechanical materials, and data physicalization as well as in the development of tangible interaction and deformable…
Vertical decomposition is a widely used general technique for decomposing the cells of arrangements of semi-algebraic sets in ${{\mathbb R}}^d$ into constant-complexity subcells. In this paper, we settle in the affirmative a few…
Sobolev embeddings, of arbitrary order, are considered into function spaces on domains of $\mathbb R^n$ endowed with measures whose decay on balls is dominated by a power $d$ of their radius. Norms in arbitrary rearrangement-invariant…
We study deformation spaces using multi-centered dilatations. Interpolating Fulton simple deformation space and Rost asymmetric double deformation space, we introduce (asymmetric) deformation spaces attached to chains of immersions of…
A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only…