Related papers: Special points of the Brownian net

It is known that determining the observability and reconstructibility of Boolean control networks (BCNs) are both NP-hard in the number of nodes of BCNs. In this paper, we use the aggregation method to overcome the challenging complexity…

Deep neural networks are state of the art methods for many learning tasks due to their ability to extract increasingly better features at each network layer. However, the improved performance of additional layers in a deep network comes at…

Network theory has unveiled the underlying structure of complex systems such as the Internet or the biological networks in the cell. It has identified universal properties of complex networks, and the interplay between their structure and…

Consider the $d$ dimensional lattice $\mathbb{Z}^d$ where each vertex is open or closed with probability $p$ or $1-p$ respectively. An open vertex $\mathbb{u} := (\mathbb{u}(1), \mathbb{u}(2),...,\mathbb{u}(d))$ is connected by an edge to…

Real-world networks exhibit prominent hierarchical and modular structures, with various subgraphs as building blocks. Most existing studies simply consider distinct subgraphs as motifs and use only their numbers to characterize the…

A complete understanding of the widely used over-parameterized deep networks is a key step for AI. In this work we try to give a geometric picture of over-parameterized deep networks using our geometrization scheme. We show that the…

In this paper, we explore complex network properties of word collocation networks (Ferret, 2002) from four different genres. Each document of a particular genre was converted into a network of words with word collocations as edges. We…

Webs are a kind of planar, directed, edge-labeled graph that encode invariant vectors for quantum representations of $\mathfrak{sl}_n$. The theory of webs developed organically for $\mathfrak{sl}_2$, where they are also known as noncrossing…

The goal of this tutorial is to promote interest in the study of random Boolean networks (RBNs). These can be very interesting models, since one does not have to assume any functionality or particular connectivity of the networks to study…

Benjamini, Burdzy and Chen (2007) introduced the notion of a shy coupling: a coupling of a Markov process such that, for suitable starting points, there is a positive chance of the two component processes of the coupling staying a positive…

We study the law of the minimum of a Brownian bridge, conditioned to take specific values at specific points, and the law of the location of the minimum. They are used to compare some non-adaptive optimisation algorithms for black-box…

Since the point cloud data is inherently irregular and unstructured, point cloud semantic segmentation has always been a challenging task. The graph-based method attempts to model the irregular point cloud by representing it as a graph;…

Networks describe a variety of interacting complex systems in social science, biology and information technology. Usually the nodes of real networks are identified not only by their connections but also by some other characteristics.…

We prove a conjecture by Kreiman and Lakshmibai on a combinatorial description of multiplicities of points on Schubert varieties in Graszmannians in terms of certain sets of reflections in the corresponding Weyl group. The proof is…

Network detection is an important capability in many areas of applied research in which data can be represented as a graph of entities and relationships. Oftentimes the object of interest is a relatively small subgraph in an enormous,…

Pruning large neural networks while maintaining their performance is often desirable due to the reduced space and time complexity. In existing methods, pruning is done within an iterative optimization procedure with either heuristically…

The classes of $(u,m,{\bf e},s)$-nets and $(u,{\bf e},s)$-sequences were recently introduced by Tezuka, and in a slightly more restrictive form by Hofer and Niederreiter. We study propagation rules for these point sets, which state how one…

The increasing interest in complex networks research has been a consequence of several intrinsic features of this area, such as the generality of the approach to represent and model virtually any discrete system, and the incorporation of…

Network classification aims to group networks (or graphs) into distinct categories based on their structure. We study the connection between classification of a network and of its constituent nodes, and whether nodes from networks in…

The coalescing Brownian flow on $\mathbb{R}$ is a process which was introduced by Arratia [Coalescing Brownian motions on the line (1979) Univ. Wisconsin, Madison] and T\'{o}th and Werner [Probab. Theory Related Fields 111 (1998) 375-452],…