Related papers: Peel neighborhoods
We classify all possible automorphism groups of smooth cubic surfaces over an algebraically closed field of arbitrary characteristic. As an intermediate step we also classify automorphism groups of quartic del Pezzo surfaces. We show that…
Image segmentation is a popular area of research in computer vision that has many applications in automated image processing. A recent technique called piecewise flat embeddings (PFE) has been proposed for use in image segmentation; PFE…
Piecewise constant image approximations of sequential number of segments or clusters of disconnected pixels are treated. The method of majorizing of optimal approximation sequence by hierarchical sequence of image approximations is…
This survey describes some useful properties of the local homology of abstract simplicial complexes. Although the existing literature on local homology is somewhat dispersed, it is largely dedicated to the study of manifolds, submanifolds,…
Recent work on background subtraction has shown developments on two major fronts. In one, there has been increasing sophistication of probabilistic models, from mixtures of Gaussians at each pixel [7], to kernel density estimates at each…
Consider the set of solutions to a system of polynomial equations in many variables. An algebraic manifold is an open submanifold of such a set. We introduce a new method for computing integrals and sampling from distributions on algebraic…
We focus on spectral clustering of unlabeled graphs and review some results on clustering methods which achieve weak or strong consistent identification in data generated by such models. We also present a new algorithm which appears to…
We present an axiomatic approach to finite- and infinite-dimensional differential calculus over arbitrary infinite fields (and, more generally, suitable rings). The corresponding basic theory of manifolds and Lie groups is developed.…
Community detection is one of the fundamental problems in the study of network data. Most existing community detection approaches only consider edge information as inputs, and the output could be suboptimal when nodal information is…
We survey some recent results concerning the so called Categorical Torelli problem. This is to say how one can reconstruct a smooth projective variety up to isomorphism, by using the homological properties of special admissible…
We present a method that allows for the discovery of communities within graphs of arbitrary size in times that scale linearly with their size. This method avoids edge cutting and is based on notions of voltage drops across networks that are…
Pellet's theorem determines when the zeros of a polynomial can be separated into two regions, according to their moduli. We refine one of those regions and replace it with the closed interior of a lemniscate that provides more precise…
Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data…
Many complex networks in the real world have community structures -- groups of well-connected nodes with important functional roles. It has been well recognized that the identification of communities bears numerous practical applications.…
We revisit the definition of effective local compactness, and propose an approach that works for arbitrary countably-based spaces extending the previous work on computable metric spaces. We use this to show that effective local compactness…
We study the large-scale geometry of mapping class groups of surfaces of infinite type, using the framework of Rosendal for coarse geometry of non locally compact groups. We give a complete classification of those surfaces whose mapping…
Unsupervised node clustering (or community detection) is a classical graph learning task. In this paper, we study algorithms, which exploit the geometry of the graph to identify densely connected substructures, which form clusters or…
In this paper a relative number density parameter, called the neighborhood function, is introduced so that the crowded nature of the neighborhood of individual sources can be described. With this parameter one can determine the probability…
We consider a community finding problem called Co-located Community Detection (CCD) over geo-social networks, which retrieves communities that satisfy both high structural tightness and spatial closeness constraints. To provide a solution…
A novel method for segmenting bright objects from dark background for grayscale image is proposed. The concept of this method can be stated simply as: to pick out the local-thinnest bands on the grayscale grade-map. It turns out to be a…