Related papers: Shirac: A linear algebra for event-based system mo…

The study of reaction-diffusion systems on networks is of paramount relevance for the understanding of nonlinear processes in systems where the topology is intrinsically discrete, such as the brain. Until now reaction-diffusion systems have…

We demonstrate that the Dirac representation theory can be effectively adjusted and applied to signal theory. The main emphasis is on orthogonality as the principal physical requirement. The particular role of the identity and projection…

Topological signals defined on nodes, links and higher dimensional simplices define the dynamical state of a network or of a simplicial complex. As such, topological signals are attracting increasing attention in network theory, dynamical…

Topological signals are variables or features associated with both nodes and edges of a network. Recently, in the context of Topological Machine Learning, great attention has been devoted to signal processing of such topological signals.…

Distributed estimation and processing in networks modeled by graphs have received a great deal of interest recently, due to the benefits of decentralised processing in terms of performance and robustness to communications link failure…

Acyclic digraphs arise in many natural and artificial processes. Among the broader set, dynamic citation networks represent a substantively important form of acyclic digraphs. For example, the study of such networks includes the spread of…

We generalize previous results and demonstrate that the Dirac representation theory can be effectively adjusted and applied to continuous or discrete signals of infinite time duration. The role of the identity and projection operators is…

Network systems have become a ubiquitous modeling tool in many areas of science where nodes in a graph represent distributed processes and edges between nodes represent a form of dynamic coupling. When a network topology is already known…

Topological signals are dynamical variables not only defined on nodes but also on links of a network that are gaining significant attention in non-linear dynamics and topology and have important applications in brain dynamics. Here we show…

This paper introduces the distributed and intelligent integrated sensing and communications (DISAC) concept, a transformative approach for 6G wireless networks that extends the emerging concept of integrated sensing and communications…

We derive new all-purpose methods that involve the Dirac Delta distribution. Some of the new methods use derivatives in the argument of the Dirac Delta. We highlight potential avenues for applications to quantum field theory and we also…

Node clustering is a powerful tool in the analysis of networks. We introduce a graph neural network framework, named DIGRAC, to obtain node embeddings for directed networks in a self-supervised manner, including a novel probabilistic…

Various coarse-grained models have been proposed to study the spreading dynamics in the network. A microscopic theory is needed to connect the spreading dynamics with the individual behaviors. In this letter, we unify the description of…

The core concept of quantum simulation is the mapping of an inaccessible quantum system onto a controllable one by identifying analogous dynamics. We map the Dirac equation of relativistic quantum mechanics in 3+1 dimensions onto a…

Stochastic point processes relevant to the theory of long-range aperiodic order are considered that display diffraction spectra of mixed type, with special emphasis on explicitly computable cases together with a unified approach of…

The Dirac exchange interaction is derived from recent quantum kinetic theory for collisionless plasmas. For this purpose, the kinetic equation is written in the semiclassical and long wavelength approximations. The validity of the model for…

We define the topological Dirac equation describing the evolution of a topological wave function on networks or on simplicial complexes. On networks, the topological wave function describes the dynamics of topological signals or cochains,…

Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. They amount to a generalization of series expansions from 2-point to point-link-point interactions. We outline…

Traffic dynamics is universally crucial in analyzing and designing almost any network. This article introduces a novel theoretical approach to analyzing network traffic dynamics. This theory's machinery is based on the notion of traffic…

Dirac particle dynamics is encoded as a unitary path summation rule and implemented on a qubit array, where the qubit array represents both spacetime and the fermions contained therein. The unitary path summation rule gives a quantum…