Related papers: Random Delaunay triangulations and metric uniformi…
The boundary of the Siegel disk of a quadratic polynomial with an irrationally indifferent fixed point with the golden mean rotation number has been observed to be self-similar. The geometry of this self-similarity is universal for a large…
Given a compact connected set $E$ in the unit disk $\mathbb{B}^{2}$, we give a new upper bound for the conformal capacity of the condenser $(\mathbb{B}^{2}, E)$ in terms of the hyperbolic diameter $t$ of $E$. Moreover, for $t>0$, we…
We develop a universal distributional calculus for regulated volumes of metrics that are singular along hypersurfaces. When the hypersurface is a conformal infinity we give simple integrated distribution expressions for the divergences and…
Random projection is often used to project higher-dimensional vectors onto a lower-dimensional space, while approximately preserving their pairwise distances. It has emerged as a powerful tool in various data processing tasks and has…
The paper is devoted to discretization of integral norms of functions from a given finite dimensional subspace. We use recent general results on sampling discretization to derive a new Marcinkiewicz type discretization theorem for the…
This paper is motivated by the classical theorem due to Hardy and Littlewood which concerns analytic mappings on the unit disk and relates the growth of the derivative with the H\"{o}lder continuity. We obtain a version of this result in a…
The computational complexity of some depths that satisfy the projection property, such as the halfspace depth or the projection depth, is known to be high, especially for data of higher dimensionality. In such scenarios, the exact depth is…
In this paper, we propose a novel parameterization method for genus-one and multiply connected genus-zero surfaces, called periodic conformal flattening. The conformal energy minimization technique is utilized to compute the desired…
In this paper, we consider the decentralized optimization problems with generalized orthogonality constraints, where both the objective function and the constraint exhibit a distributed structure. Such optimization problems, albeit…
A decoration of a hyperbolic surface of finite type is a choice of circle, horocycle or hypercycle about each cone-point, cusp or flare of the surface, respectively. In this article we show that a decoration induces a unique canonical…
In the author's PhD thesis (2019) universal envelopes were introduced as a tool for studying the continuously obtainable information on discontinuous functions. To any function $f \colon X \to Y$ between $\operatorname{qcb}_0$-spaces one…
We typically construct optimal designs based on a single objective function. To better capture the breadth of an experiment's goals, we could instead construct a multiple objective optimal design based on multiple objective functions. While…
The notion of discrete conformality proposed by Luo and Bobenko-Pinkall-Springborn on triangle meshes has rich mathematical theories and wide applications. Gu et al. proved that the discrete uniformizations approximate the continuous…
Many geometric optimization problems can be reduced to finding points in space (centers) minimizing an objective function which continuously depends on the distances from the centers to given input points. Examples are $k$-Means, Geometric…
Over recent years, numerous attempts were taken to provide efficient methods of directivity representation, either regarding sound sources or head-related transfer functions. Because of the wide variety of programming tools and scripts used…
Object detection and identification is surely a fundamental topic in the computer vision field; it plays a crucial role in many applications such as object tracking, industrial robots control, image retrieval, etc. We propose a…
We derive the asymptotic distribution of the domination number of a new family of random digraph called proximity catch digraph (PCD), which has application to statistical testing of spatial point patterns and to pattern recognition. The…
Large models and enormous data are essential driving forces of the unprecedented successes achieved by modern algorithms, especially in scientific computing and machine learning. Nevertheless, the growing dimensionality and model…
We consider constellations of disks which are unions of disjoint hyperbolic disks in the unit disk with fixed radii and unfixed centers. We study the problem of maximizing the conformal capacity of a constellation with a fixed number of…
This paper proposes a novel paradigm for machine learning that moves beyond traditional parameter optimization. Unlike conventional approaches that search for optimal parameters within a fixed geometric space, our core idea is to treat the…