Related papers: On the existence of hyperplane sequences, with qua…

In this paper we devise a generative random network model with core-periphery properties whose core nodes act as sublinear dominators, that is, if the network has $n$ nodes, the core has size $o(n)$ and dominates the entire network. We show…

A new and extensive formalism is developed for monads and galaxies in non-standard enlargements. It is shown that monads and galaxies can be manipulated using order-preserving and order-reversing set-to-set maps, and that set properties…

Core-periphery structure is a common property of complex networks, which is a composition of tightly connected groups of core vertices and sparsely connected periphery vertices. This structure frequently emerges in traffic systems, biology,…

Based on the well-established theory of discrete conjugate nets in discrete differential geometry, we propose and examine discrete analogues of important objects and notions in the theory of semi-Hamiltonian systems of hydrodynamic type. In…

We introduce a new family of models for growing networks. In these networks new edges are attached preferentially to vertices with higher number of connections, and new vertices are created by already existing ones, inheriting part of their…

Scale-free percolation is a percolation model on $\mathbb{Z}^d$ which can be used to model real-world networks. We prove bounds for the graph distance in the regime where vertices have infinite degrees. We fully characterize transience vs.…

The class of $(0,m,s)$-nets in base $b$ has been introduced by Niederreiter as examples of point sets in the $s$-dimensional unit cube with excellent uniform distribution properties. In particular such nets have been proved to have very low…

Previous hypergraph expansions are solely carried out on either vertex level or hyperedge level, thereby missing the symmetric nature of data co-occurrence, and resulting in information loss. To address the problem, this paper treats…

This paper deals with properties of the algebraic variety defined as the set of zeros of a "deficient" sequence of multivariate polynomials. We consider two types of varieties: ideal-theoretic complete intersections and absolutely…

Supercyclides are surfaces with a characteristic conjugate parametrization consisting of two families of conics. Patches of supercyclides can be adapted to a Q-net (a discrete quadrilateral net with planar faces) such that neighboring…

In this work, we use the theory of spatial networks to analyze galaxy distributions. The aim is to develop new approaches to study the spatial galaxy environment properties by means of the network parameters. We investigate how each of the…

Networks in the real world do not exist as isolated entities, but they are often part of more complicated structures composed of many interconnected network layers. Recent studies have shown that such mutual dependence makes real networked…

Context. Filaments are ubiquitous in the Galaxy, and they host star formation. Detecting them in a reliable way is therefore key towards our understanding of the star formation process. Aims. We explore whether supervised machine learning…

We consider a heterogeneous cellular network (HetNet) where a macrocell tier with a large antenna array base station (BS) is overlaid with a dense tier of small cells (SCs). We investigate the potential benefits of incorporating a massive…

The combination of persistent homology and discrete Morse theory has proven very effective in visualizing and analyzing big and heterogeneous data. Indeed, topology provides computable and coarse summaries of data independently from…

We compute the cohomology with group ring coefficients of the complement of a finite collection of affine hyperplanes in a finite dimensional complex vector space. It is nonzero in exactly one degree, namely the degree equal to the rank of…

High resolution surveys reveal that the interstellar medium in the Milky Way and nearby galaxies consists of interlinked hierarchies of filamentary structure and superbubbles extending from galactic to subpc scales. The characterization of…

The degree distribution, referred to as the delta-sequence of a network is studied. Using the non-normalized Lorenz curve, we apply a generalized form of the classical majorization partial order. Next, we introduce a new class of small…

In this paper, we construct a category of short exact sequences of vector bundles and prove that it is equivalent to the category of double vector bundles. Moreover, operations on double vector bundles can be transferred to operations on…

As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra,…