Related papers: Reparametrizations with given stop data
We demonstrate the reparametrization invariance of perturbatively defined one-dimensional functional integrals up to the three-loop level for a path integral of a quantum-mechanical point particle in a box. We exhibit the origin of the…
We give a new proof for the self-improvement of uniform p-fatness in the setting of general metric spaces. Our proof is based on rather standard methods of geometric analysis, and in particular the proof avoids the use of deep results from…
This paper employs techniques from metric geometry and optimal transport theory to address questions related to the analysis of functional data on metric or metric-measure spaces, which we refer to as fields. Formally, fields are viewed as…
Reparametrization-invariant theories of point relativistic particle interaction with fields of arbitrary tensor dimension are considered. It has been shown that the equations of motion obtained by Kalman [G. Kalman, Phys. Rev. vol.123,…
We extend the validity of a Gromov's dimension comparison estimate for topological hypersurfaces to sufficiently large classes of rectifiable sets, arising from Sobolev mappings. Our tools are a suitably weak exterior differentiation for…
Within the Kardar-Parisi-Zhang universality class, the space-time Airy sheet is conjectured to be the canonical scaling limit for last passage percolation models. In recent work arXiv:1812.00309 of Dauvergne, Ortmann, and Vir\'ag, this…
In this paper we consider adaptive sampling's local-feature size, used in surface reconstruction and geometric inference, with respect to an arbitrary landmark set rather than the medial axis and relate it to a path-based adaptive metric on…
Optimal transport is widely used in pure and applied mathematics to find probabilistic solutions to hard combinatorial matching problems. We extend the Wasserstein metric and other elements of optimal transport from the matching of sets to…
Continuous mappings between compact Hausdorff spaces can be studied using homomorphisms between algebraic structures (lattices, Boolean algebras) associated with the spaces. This gives us more tools with which to tackle problems about these…
In topological data analysis, we want to discern topological and geometric structure of data, and to understand whether or not certain features of data are significant as opposed to simply random noise. While progress has been made on…
We study deformations of the geodesic distances on a domain of R N induced by a function called conformal factor. We show that under a positive reach assumption on the domain (not necessarily a submanifold) and mild assumptions on the…
Transit agencies have been removing a large number of bus stops, but discussions around the bus stop spacings exhibit a lack of clarity and data for comparison. This paper proposes new terminology and concepts for statistical consideration…
In this paper we study the continuous dependence with respect to obstacles for obstacle problems with measure data. This is deeply investigated introducing a suitable type of convergence, which gives stability under very general hypotheses.…
We give rigorous foundations for parametrized homotopy theory in this monograph. After preliminaries on point-set topology, base change functors, and proper actions of non-compact Lie groups, we develop the homotopy theory of equivariant…
Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…
We prove some extension theorems involving uniformly continuous maps of the universal Urysohn space. We also prove reconstruction theorems for certain groups of autohomeomorphisms of this space and of its open subsets.
Let Y be a locally convex Hausdorff space, K \subset E a cone and \leq_K the partial order defined by K. Let (X, p) be a TV S- cone metric space, {\phi} : K \rightarrow K a vectorial comparison function and f : X \rightarrow X such that…
In this paper we study reconstruction of a function $f$ from its discrete Radon transform data in $\mathbb R^3$ when $f$ has jump discontinuities. Consider a conventional parametrization of the Radon data in terms of the affine and angular…
Statistical data by their very nature are indeterminate in the sense that if one repeats the process of collecting the data the new data set will be different from the original. But two data sets generated in the same way should ``tell the…
Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the…