Related papers: Peel neighborhoods

We review and improve a recently introduced method for the detection of communities in complex networks. This method combines spectral properties of some matrices encoding the network topology, with well known hierarchical clustering…

We study the topology of metric spaces which are definable in o-minimal expansions of ordered fields. We show that a definable metric space either contains an infinite definable discrete set or is definably homeomorphic to a definable set…

Spherical Designs are finite sets of points on the sphere $\mathbb{S}^{d}$ with the property that the average of certain (low-degree) polynomials in these points coincides with the global average of the polynomial on $\mathbb{S}^{d}$. They…

Let $X$ be the prime spectrum of a ring. In [arXiv:0707.1525] the authors define a topology on $X$ by using ultrafilters and they show that this topology is precisely the constructible topology. In this paper we generalize the construction…

From descent theory to higher geometry, the idea of gluing has been embedded in many elegant and powerful techniques, proving instrumental for the solution of many problems. In this paper, we introduce a framework that allows to link…

Community detection is a powerful tool from complex networks analysis that finds applications in various research areas. Several image segmentation methods rely for instance on community detection algorithms as a black box in order to…

We study computable topological spaces and semicomputable and computable sets in these spaces. In particular, we investigate conditions under which semicomputable sets are computable. We prove that a semicomputable compact manifold $M$ is…

Sampling from distributions of implicitly defined shapes enables analysis of various energy functionals used for image segmentation. Recent work describes a computationally efficient Metropolis-Hastings method for accomplishing this task.…

We propose a novel perspective on varied-density clustering for high-dimensional data by framing it as a label propagation process in neighborhood graphs that adapt to local density variations. Our method formally connects density-based…

We study generalized density-based clustering in which sharply defined clusters such as clusters on lower-dimensional manifolds are allowed. We show that accurate clustering is possible even in high dimensions. We propose two data-based…

We derive optimal estimates for the Bergman kernel and the Bergman metric for certain model domains in $\mathbb{C}^2$ near boundary points that are of infinite type. Being unbounded models, these domains obey certain geometric constraints…

We show that the theory of varifolds can be suitably enriched to open the way to applications in the field of discrete and computational geometry. Using appropriate regularizations of the mass and of the first variation of a varifold we…

Kernel methods are an incredibly popular technique for extending linear models to non-linear problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature…

Topologies on algebraic and equational theories are used to define germ determined, near-point determined, and point determined rings of smooth functions, without requiring them to be finitely generated. It is proved, that any commutative…

Yiannis Sakellaridis and Akshay Venkathesh have determined, when the group $G$ is split and the field $\F$ is of characteristic zero, the Plancherel formula for any spherical space $X$ for $G$ modulo the knowledge of the discrete spectrum.…

A topological space $X$ is defined to have a neighborhood $P$-base at any $x\in X$ from some poset $P$ if there exists a neighborhood base $(U_p[x])_{p\in P}$ at $x$ such that $U_p[x]\subseteq U_{p'}[x]$ for all $p\geq p'$ in $P$. We prove…

This paper presents a new algorithm based on interval methods for rigorously constructing inner estimates of feasible parameter regions together with enclosures of the solution set for parameter-dependent systems of nonlinear equations in…

We consider smoothed versions of geometric range spaces, so an element of the ground set (e.g. a point) can be contained in a range with a non-binary value in $[0,1]$. Similar notions have been considered for kernels; we extend them to more…

On arithmetic surfaces over local rings of integers we examine whether any geometric point has a basis of \'etale neighborhoods whose $\mathfrak{c}$-completed \'etale homotopy types are of type $K(\pi,1)$ for a given full…

Neighborhood gentrification plays a significant role in shaping the social and economic well-being of both individuals and communities at large. While some efforts have been made to detect gentrification in cities, existing approaches rely…