Related papers: Special points of the Brownian net

In this paper, we classify the possible group structures on the set of $R$-valued points of an abelian variety, where $R$ is any real closed field. We make use of a family of abelian varieties that, in effect, allows one to quantify over…

In this paper, we extend the notions of $\lambda$-cent-dian and generalized-center from Facility Location Theory to the more intricate domain of Network Design. Our focus is on the task of designing a sub-network within a given underlying…

Though commonly found in the real world, directed networks have received relatively less attention from the literature in which concerns their topological and dynamical characteristics. In this work, we develop a magnetic Laplacian-based…

We present a lightweight network that infers grouping and boundaries, including curves, corners and junctions. It operates in a bottom-up fashion, analogous to classical methods for sub-pixel edge localization and edge-linking, but with a…

Motivated by the Double Gyroid nanowire network we develop methods to detect Dirac points and classify level crossings, aka. singularities in the spectrum of a family of Hamiltonians. The approach we use is singularity theory. Using this…

In this paper it is shown that for any network there is a uniquely determined network based on a structure tree that provides a convenient way of determining a minimal cut separating a pair $s, t$ where each of $s, t$ is either a vertex or…

Various approaches and measures from network analysis have been applied to granular and particulate networks to gain insights into their structural, transport, failure-propagation and other systems-level properties. In this article, we…

We introduce Forman-Ricci curvature and its corresponding flow as characteristics for complex networks attempting to extend the common approach of node-based network analysis by edge-based characteristics. Following a theoretical…

Fine-grained classification is challenging due to the difficulty of finding discriminative features. Finding those subtle traits that fully characterize the object is not straightforward. To handle this circumstance, we propose a novel…

Networks are useful descriptions of the structure of many complex systems. Unsurprisingly, it is thus important to analyze the robustness of networks in many scientific disciplines. In applications in communication, logistics, finance,…

Webs are sets of Feynman diagrams that contribute to the exponents of scattering amplitudes, in the kinematic limit in which emitted radiation is soft. As such, they have a number of phenomenological and formal applications, and offer…

We provide a new construction of Brownian disks in terms of forests of continuous random trees equipped with nonnegative labels corresponding to distances from a distinguished point uniformly distributed on the boundary of the disk. This…

Every knot has a plat projection, obtained by closing up a braid with bridges. The plat projection is determined by the number of strands and the number of rows of twist regions in the braid, and an integer number of crossings in each twist…

Frequently, knots are enumerated by their crossing number. However, the number of knots with crossing number $c$ grows exponentially with $c$, and to date computer-assisted proofs can only classify diagrams up to around twenty crossings.…

We discuss subordination of random compact R-trees. We focus on the case of the Brownian tree, where the subordination function is given by the past maximum process of Brownian motion indexed by the tree. In that particular case, the…

Prevalence of deeper networks driven by self-attention is in stark contrast to underexplored point-based methods. In this paper, we propose groupwise self-attention as the basic block to construct our network: SepNet. Our proposed module…

Few prior works study deep learning on point sets. PointNet by Qi et al. is a pioneer in this direction. However, by design PointNet does not capture local structures induced by the metric space points live in, limiting its ability to…

Branch points of a real 2-surface S in a 4-manifold M generalize the branch points of complex curves in complex surfaces: for example, they can occur as singularities of minimal surfaces. We investigate such a branch point p when S is…

We study the sensitivity of directed complex networks to the addition and pruning of edges and vertices and introduce the susceptibility, which quantifies this sensitivity. We show that topologically different parts of a directed network…

More and more scientific research shows that there is a close correlation between the Internet and brain science. This paper presents the idea of establishing the Internet neurology, which means to make a cross-contrast between the two in…