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The semiring of discrete dynamical systems is a simple algebraic model for modularity in deterministic systems. The objects of the semiring are finite transformations (viewed as directed graphs and regarded up to isomorphism), the sum of…
We consider the Dirac equation on periodic networks (quantum graphs). The self-adjoint quasi periodic boundary conditions are derived. The secular equation allowing us to find the energy spectrum of the Dirac particles on periodic quantum…
Distributed statistical learning has become a popular technique for large-scale data analysis. Most existing work in this area focuses on dividing the observations, but we propose a new algorithm, DDAC-SpAM, which divides the features under…
Spreading phenomena on networks are essential for the collective dynamics of various natural and technological systems, from information spreading in gene regulatory networks to neural circuits or from epidemics to supply networks…
We revisit the method of cumulants for analysing dynamic light scattering data in particle sizing applications. Here the data, in the form of the time correlation function of scattered light, is written as a series involving the first few…
The present work attempts both a review of previous methods for transferring digital and symbolic computations in an analog or optical substrate and also to offer certain alternatives not yet fully explored. The essential difference from…
Multivariate problems are typically governed by anisotropic features such as edges in images. A common bracket of most of the various directional representation systems which have been proposed to deliver sparse approximations of such…
The system decomposition theory has recently been developed for the dynamic analysis of nonlinear compartmental systems. The application of this theory to the ecosystem analysis has also been introduced in a separate article. Based on this…
Investigating properties of two-dimensional Dirac operators coupled to an electric and a magnetic field (perpendicular to the plane) requires in general unbounded (vector-) potentials. If the system has a certain symmetry, the fields can be…
This study is devoted to the profound implications of tilted Dirac cones on the quantum transport properties of two-dimensional (2D) Dirac materials. These materials, characterized by their linear conic energy dispersions in the vicinity of…
The Dirac equation, usually obtained by `quantizing' a classical stochastic model is here obtained directly within classical statistical mechanics. The special underlying space-time geometry of the random walk replaces the missing analytic…
In this paper we propose and analyze a distributed algorithm for achieving globally optimal decisions, either estimation or detection, through a self-synchronization mechanism among linearly coupled integrators initialized with local…
Due to the importance of the lower bounding distances and the attractiveness of symbolic representations, the family of symbolic aggregate approximations (SAX) has been used extensively for encoding time series data. However, typical…
Dynamic sampling mechanisms in deep learning architectures have demonstrated utility across many computer vision models, though the theoretical analysis of these structures has not yet been unified. In this paper we connect the various…
This article develops a new mathematical method for holistic analysis of nonlinear dynamic compartmental systems through the system decomposition theory. The method is based on the novel dynamic system and subsystem partitioning…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
Advantageous numerical methods for solving the Dirac equations are derived. They are based on different stochastic optimization techniques, namely the Genetic algorithms, the Particle Swarm Optimization and the Simulated Annealing method,…
The problem of predicting links in large networks is an important task in a variety of practical applications, including social sciences, biology and computer security. In this paper, statistical techniques for link prediction based on the…
We develop a comprehensive analysis of the Kirkwood-Dirac distributions in classical optics, revealing their deep connection with optical coherence as fundamental concept in optics. From their very definition, the Kirkwood-Dirac…
In directed graphs, a cycle can be seen as a structure that allows its vertices to loop back to themselves, or as a structure that allows pairs of vertices to reach each other through distinct paths. We extend these concepts to temporal…