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The distributed system $\mathcal{S}_D$ described by the Dirac equation is investigated simply as a dynamic system, i.e. without usage of quantum principles. The Dirac equation is described in terms of hydrodynamic variables: 4-flux $j^{i}$,…
In this paper we combine the Alias method with the concept of systematic sampling, a method commonly used in particle filters for efficient low-variance resampling. The proposed method allows very fast sampling from a discrete distribution:…
Integrated sensing and communications (ISAC) has emerged as an intrinsic service of upcoming 6G wireless systems, enabling the reuse of communication signals for environmental sensing and supporting context-aware network functionalities.…
A simple framework for Dirac spinors is developed that parametrizes admissible quantum dynamics and also analytically constructs electromagnetic fields, obeying Maxwell's equations, which yield a desired evolution. In particular, we show…
A thesaurus is one, out of many, possible representations of term (or word) connectivity. The terms of a thesaurus are seen as the nodes and their relationship as the links of a directed graph. The directionality of the links retains all…
In 1945, Dirac attempted to develop a "formal probability" distribution to describe quantum operators in terms of two non-commuting variables, such as position x and momentum p [Rev. Mod. Phys. 17, 195 (1945)]. The resulting…
Using the example of a Dirac particle in external static fields, Dirac theory is reformulated as a one-particle quantum theory in the space of normalized two-component spinors. In this formulation, the Dirac operator ``splits'' into two…
Graphene as well as more generally Dirac solids constitute two dimensional materials where the electronic flow is ultra relativistic. When a Dirac solid is deposited on a different substrate surface with roughness, a local random potential…
We characterise the evolution of a dynamical system by combining two well-known complex systems' tools, namely, symbolic ordinal analysis and networks. From the ordinal representation of a time-series we construct a network in which every…
We propose a sampling theory for signals that are supported on either directed or undirected graphs. The theory follows the same paradigm as classical sampling theory. We show that perfect recovery is possible for graph signals bandlimited…
The Integrated Sensing and Communications (ISAC) paradigm is anticipated to be a cornerstone of the upcoming 6G networks. In order to optimize the use of wireless resources, 6G ISAC systems need to harness the communication data payload…
Stochastic models for collections of interacting populations have crucial roles in scientific fields such as epidemiology and ecology, yet the standard approach to extending an ordinary differential equation model to a Markov chain does not…
Signal scaling is a fundamental operation of practical importance in which a signal is enlarged or shrunk in the coordinate direction(s). Scaling or magnification is not trivial for signals of a discrete variable since the signal values may…
Using a sheaf-theoretic extension of conventional principal bundle theory, the Dirac monopole is formulated as a spherically symmetric model free of singularities outside the origin such that the charge may assume arbitrary real values. For…
In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…
In dynamical systems on networks, one assigns the dynamics to nodes, which are then coupled via links. This approach does not account for group interactions and dynamics on links and other higher dimensional structures. Higher-order network…
These lecture notes cover basic automata-theoretic concepts and logical formalisms for the modeling and verification of concurrent and distributed systems. Many of these concepts naturally extend the classical automata and logics over…
Distributed diffusion is a powerful algorithm for multi-task state estimation which enables networked agents to interact with neighbors to process input data and diffuse information across the network. Compared to a centralized approach,…
Diffusion models are state-of-the-art methods in generative modeling when samples from a target probability distribution are available, and can be efficiently sampled, using score matching to estimate score vectors guiding a Langevin…
Dynamical processes can be transformed into graphs through a family of mappings called visibility algorithms, enabling the possibility of (i) making empirical data analysis and signal processing and (ii) characterising classes of dynamical…