Related papers: On the existence of hyperplane sequences, with qua…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
We study the $L_p$ discrepancy of digital NUT sequences which are an important sub-class of digital $(0,1)$-sequences in the sense of Niederreiter. The main result is a lower bound for certain sub-classes of digital NUT sequences.
A new global approach in the study of duality transformations is introduced. The geometrical structure of complex line bundles is generalized to higher order U(1) bundles which are classified by quantized charges and duality maps are…
Mostly acyclic directed networks, treated mathematically as directed graphs, arise in machine learning, biology, social science, physics, and other applications. Newman [1] has noted the mathematical challenges of such networks. In this…
Latent variable models for network data extract a summary of the relational structure underlying an observed network. The simplest possible models subdivide nodes of the network into clusters; the probability of a link between any two nodes…
Using group theoretic and topological concepts, together with tunneling phenomena, we geometrically design interfacial wave networks that contain splitters which partition energy in 2, 3, 4 or 5 directions. This enriches the valleytronics…
We discuss the intimate relationship between the filamentary features and the rare dense compact cluster nodes in this network, via the large scale tidal field going along with them, following the cosmic web theory developed Bond et al. The…
In recent years, networks with higher-order interactions have emerged as a powerful tool to model complex systems. Comparing these higher-order systems remains however a challenge. Traditional similarity measures designed for pairwise…
For every link $L$ we construct a complex algebraic plane curve that intersects $S^3$ transversally in a link $\tilde{L}$ that contains $L$ as a sublink. This construction proves that every link $L$ is the sublink of a quasipositive link…
Identifying networks with similar characteristics in a given ensemble, or detecting pattern discontinuities in a temporal sequence of networks, are two examples of tasks that require an effective metric capable of quantifying network…
We study the topology of the Megaparsec Cosmic Web in terms of the scale-dependent Betti numbers, which formalize the topological information content of the cosmic mass distribution. While the Betti numbers do not fully quantify topology,…
Generally speaking, `almost distance-regular' graphs share some, but not necessarily all, of the regularity properties that characterize distance-regular graphs. In this paper we propose two new dual concepts of almost distance-regularity,…
This work explores hypernetworks: an approach of using a one network, also known as a hypernetwork, to generate the weights for another network. Hypernetworks provide an abstraction that is similar to what is found in nature: the…
Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…
End-to-end Network has become increasingly important in multi-tasking. One prominent example of this is the growing significance of a driving perception system in autonomous driving. This paper systematically studies an end-to-end…
We introduce a new class of networks that grow by enhanced redirection. Nodes are introduced sequentially, and each either attaches to a randomly chosen target node with probability 1-r or to the ancestor of the target with probability r,…
The degree distribution is an important characteristic of complex networks. In many applications, quantification of degree distribution in the form of a fixed-length feature vector is a necessary step. On the other hand, we often need to…
Social media, e-commerce, streaming video, e-mail, cloud documents, web pages, traffic flows, and network packets fill vast digital lakes, rivers, and oceans that we each navigate daily. This digital hyperspace is an amorphous flow of data…
Subfactor theory provides a tool to analyze and construct extensions of Quantum Field Theories, once the latter are formulated as local nets of von Neumann algebras. We generalize some of the results of [LR95] to the case of extensions with…
Graphs are one of the most efficacious structures for representing datapoints and their relations, and they have been largely exploited for different applications. Previously, the higher-order relations between the nodes have been modeled…