Related papers: Nonparametric statistics on manifolds with applica…
Let X be a geometrically irreducible smooth projective curve over a field k. We describe the algebra of endomorphisms of indecomposable unstable vector bundles over X of rank 2 and degree d. Fixing some numerical invariants, namely the…
We initiate the study of random iteration of automorphisms of real and complex projective surfaces, or more generally compact K{\"a}hler surfaces, focusing on the fundamental problem of classification of stationary measures. We show that,…
We describe a categorical framework for the classification of D-branes on noncommutative spaces using techniques from bivariant K-theory of C*-algebras. We present a new description of bivariant K-theory in terms of noncommutative…
Oriented circular cylinders in an opaque medium are used to represent certain microstructural objects in steel. The opaque medium is sliced parallel to the cylinder axes of symmetry and the cut-plane contains the observable rectangular…
One of the very few mathematically rigorous nonlinear model reduction methods is the restriction of a dynamical system to a low-dimensional, sufficiently smooth, attracting invariant manifold. Such manifolds are usually found using local…
Multi-type Markov point processes offer a flexible framework for modelling complex multi-type point patterns where it is pertinent to capture both interactions between points as well as large scale trends depending on observed covariates.…
In this paper, we consider a k-nearest neighbor kernel type estimator when the random variables belong in a Riemannian manifolds. We study asymptotic properties such as the consistency and the asymptotic distribution. A simulation study is…
We provide a survey of results on the statistics of random sections of holomorphic line bundles on K\"ahler manifolds, with an emphasis on the resulting asymptotics when a line bundle is raised to increasing tensor powers. We conclude with…
This is a brief review article of various applications of non-Archimedean geometry, p-adic numbers and adeles in modern mathematical physics.
Rapid progress in representation learning has led to a proliferation of embedding models, and to associated challenges of model selection and practical application. It is non-trivial to assess a model's generalizability to new, candidate…
We describe an extension of the axioms of quantization to the case of 2-plectic manifolds. We show how such quantum spaces can be obtained as stable classical solutions in a zero-dimensional 3-algebra reduced model obtained by dimensional…
The Kreck-Stolz s invariant is used to distinguish connected components of the moduli space of positive scalar curvature metrics. We use a formula of Kreck and Stolz to calculate the s invariant for metrics on S^n bundles with nonnegative…
This work deals with models described by a single real scalar field in two-dimensional spacetime. The aim is to propose potentials that support massless minima and investigate the presence of kinklike structures that engender polynomial…
Recent work has revealed the central role played by the Kirkwood-Dirac quasiprobability (KDQ) as a tool to properly account for non-classical features in the context of condensed matter physics (scrambling, dynamical phase transitions)…
A method of quantum tomography of arbitrary spin particle states is developed on the basis of the root approach. It is shown that the set of mutually complementary distributions of angular momentum projections can be naturally described by…
The purpose of this paper is to explore some mixtures of Kies distributions -- discrete and continuous. The last ones are also known as compound distributions. Some conditions for convergence are established. We study the probabilistic…
An attempt is made to extend some of the basic paradigms of dynamics, from the viewpoint of (continuous) flows, to non-metric manifolds.
The classification of shapes is of great interest in diverse areas ranging from medical imaging to computer vision and beyond. While many statistical frameworks have been developed for the classification problem, most are strongly tied to…
In the present survey we present some of the recent results concerning the geometry of nodal lines of random Gaussian eigenfunctions (in case of spectral degeneracies) or wavepackets and related issues. The most fundamental example, where…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…