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A fundamental characteristic of computer networks is their topological structure. The question of the description of the structural characteristics of computer networks represents a problem that is not completely solved. Search methods for…
We translate a classification scheme for periodic CMC surfaces developed by J. Dorfmeister and the author to discrete CMC surfaces in the sense of A. Bobenko and U. Pinkall. The scheme uses the dressing action on discrete CMC surfaces to…
The interactions among the elementary components of many complex systems can be qualitatively different. Such systems are therefore naturally described in terms of multiplex or multi-layer networks, i.e. networks where each layer stands for…
While a generic smooth Ribaucour sphere congruence admits exactly two envelopes, a discrete R-congruence gives rise to a 2-parameter family of discrete enveloping surfaces. The main purpose of this paper is to gain geometric insights into…
The recent impressive results of deep learning-based methods on computer vision applications brought fresh air to the research and industrial community. This success is mainly due to the process that allows those methods to learn…
Real-world networks such as the Internet and WWW have many common traits. Until now, hundreds of models were proposed to characterize these traits for understanding the networks. Because different models used very different mechanisms, it…
$\partial\mathbb{B}$ nets are differentiable neural networks that learn discrete boolean-valued functions by gradient descent. $\partial\mathbb{B}$ nets have two semantically equivalent aspects: a differentiable soft-net, with real weights,…
In this paper we classify certain special ruled surfaces in $\R^3$ under the general theorem of characterization of constant angle surfaces. We study the tangent developable and conical surfaces from the point of view the constant angle…
We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another…
The concept of scale-free networks has been widely applied across natural and physical sciences. Many claims are made about the properties of these networks, even though the concept of scale-free is often vaguely defined. We present tools…
While studies of meso-scale structures in networks often focus on community structure, core--periphery structures can reveal new insights. This structure typically consists of a well-connected core and a periphery that is well connected to…
Complex networks have been characterised by their specific connectivity patterns (network motifs), but their building blocks can also be identified and described by node-motifs---a combination of local network features. One technique to…
Contour detection has been a fundamental component in many image segmentation and object detection systems. Most previous work utilizes low-level features such as texture or saliency to detect contours and then use them as cues for a…
Great part of the interest in complex networks has been motivated by the presence of structured, frequently non-uniform, connectivity. Because diverse connectivity patterns tend to result in distinct network dynamics, and also because they…
A theorem of Mumford states that, on complex surfaces, any normal isolated singularity whose link is diffeomorphic to a sphere is actually a smooth point. While this property fails in higher dimensions, McLean asks whether the contact…
We classify real families of minimal degree rational curves that cover an embedded rational surface. A corollary is that if the projective closure of a smooth surface is not biregular isomorphic to the projective closure of the unit-sphere,…
Although much of the focus of statistical works on networks has been on static networks, multiple networks are currently becoming more common among network data sets. Usually, a number of network data sets, which share some form of…
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant…
In this paper we present some properties for projective hypersurfaces, smooth and singular, to be criteria for identification. To make the decision with these criteria, we have included procedures written in Singular language.
Representing various networked data as multiplex networks, networks of networks and other multilayer networks can reveal completely new types of structures in these system. We introduce a general and principled graphlet framework for…