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The Internet is constantly changing, and its hierarchy was recently shown to become flatter. Recent studies of inter-domain traffic showed that large content providers drive this change by bypassing tier-1 networks and reaching closer to…
A method for embedding graphs in Euclidean space is suggested. The method connects nodes to their geographically closest neighbors and economizes on the total physical length of links. The topological and geometrical properties of…
Crystalline symmetries play an important role in the classification of band structures, and the rich variety of spatial symmetries in solids leads to various topological crystalline phases (TCPs). However, compared with topological…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
For a regular coupled cell network, synchrony subspaces are the polydiagonal subspaces that are invariant under the network adjacency matrix. The complete lattice of synchrony subspaces of an $n$-cell regular network can be seen as an…
It is known that the folded sum of two contact mapping tori whose fibers are compact exact symplectic manifolds having a common convex boundary (called the ``fold'') admits a cooriented contact structure compatible with the obvious…
Networks provide a popular representation of complex data. Often, different types of relational measurements are taken on the same subjects. Such data can be represented as a \textit{multislice network}, a collection of networks on the same…
The duality between a class of the Davey-Stewartson type coupled systems and a class of two-dimensional Toda type lattices is discussed. For the recently found integrable lattice the hierarchy of symmetries is described. Second and third…
This paper constructs (with challenging obstacles) on the three torus with its cubical decomposition: Firstly, a combinatorial graded intersection algebra (graded by the codimension) which is commutative and associative defined by…
The problem of connectivity assessment in an asymmetric network represented by a weighted directed graph is investigated in this article. A power iteration algorithm in a centralized implementation is developed first to compute the…
Increasingly large AI workloads are calling for hyper-scale infrastructure; however, traditional interconnection network architecture is neither scalable nor cost-effective enough. Tree-based topologies such as the \textit{Rail-optimized}…
Turing patterns, arising from the interplay between competing species of diffusive particles, has long been an important concept for describing non-equilibrium self-organization in nature, and has been extensively investigated in many…
Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…
Datacenter network design plays a critical role in AI training by supporting scaling to thousands of accelerators. An open problem, designing a near-optimal throughput oriented network-topology, routing, and collectives-has not been…
Topological insulators (TIs) are an emerging class of materials that host highly robust in-gap surface/interface states while maintaining an insulating bulk. While most notable scientific advancements in this field have been focused on TIs…
Graphs are used in almost every scientific discipline to express relations among a set of objects. Algorithms that compare graphs, and output a closeness score, or a correspondence among their nodes, are thus extremely important. Despite…
We currently witness the emergence of interesting new network topologies optimized towards the traffic matrices they serve, such as demand-aware datacenter interconnects (e.g., ProjecToR) and demand-aware overlay networks (e.g., SplayNets).…
Data centers are becoming increasingly popular for their flexibility and processing capabilities in the modern computing environment. They are managed by a single entity (administrator) and allow dynamic resource provisioning, performance…
Despite prevailing concerns that the current Internet interdomain routing system will not scale to meet the needs of the 21st century global Internet, networking research has not yet led to the construction of a new routing architecture…
Efficient communication between qubits relies on robust networks which allow for fast and coherent transfer of quantum information. It seems natural to harvest the remarkable properties of systems characterized by topological invariants to…