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The transmission poles of $N$ number of identical Dirac delta potentials placed periodically in one-dimension are examined in the complex-energy plane. The numerical results show that the imaginary part of the poles scales with 1/N. An…
Pump-probe techniques with high temporal resolution allow one to drive a system of interest out of equilibrium and at the same time, probe its properties. Recent advances in these techniques open the door to studying new, non-equilibrium…
We develop a discrete-time version of the blended dynamics theorem for the use of designing distributed computation algorithms. The blended dynamics theorem enables to predict the behavior of heterogeneous multi-agent systems. Therefore,…
Analog signals processed in digital hardware are quantized into a discrete bit-constrained representation. Quantization is typically carried out using analog-to-digital converters (ADCs), operating in a serial scalar manner. In some…
Opportunistic scheduling and routing can in principle greatly increase the throughput of decentralized wireless networks, but to be practical they must do so with small amounts of timely side information. In this paper, we propose three…
DIRAC is a freely distributed general-purpose program system for 1-, 2- and 4-component relativistic molecular calculations at the level of Hartree--Fock, Kohn--Sham (including range-separated theory), multiconfigurational…
Stream reasoning systems are designed for complex decision-making from possibly infinite, dynamic streams of data. Modern approaches to stream reasoning are usually performing their computations using stand-alone solvers, which…
The spectral problem of the Dirac equation in an external quadratic vector potential is considered using the methods of the perturbation theory. The problem is singular and the perturbation series is asymptotic, so that the methods for…
Data analysis is a powerful tool in all experimental sciences. Statistical methods, such as sampling theory, computer technologies necessary for handling large amounts of data, skill in analysing information contained in different types of…
Probing signal injection is a well-established technique to extract additional information from a weakly (or non) observable dynamical system. Using averaging theory, a framework to analyse such schemes for general nonlinear systems has…
For a wide variety of problems, creating detailed continuous models of (continuous) physical systems is, at the very least, impractical. Hybrid models can abstract away short transient behaviour (thus introducing discontinuities) in order…
Symbolic dynamics is a coarse-grained description of dynamics. By taking into account the ``geometry'' of the dynamics, it can be cast into a powerful tool for practitioners in nonlinear science. Detailed symbolic dynamics can be developed…
This technical note studies the distributed average tracking problem for multiple time-varying signals with general linear dynamics, whose reference inputs are nonzero and not available to any agent in the network. In distributed fashion, a…
We present a real-time path integral theory for the rate of electron transfer reactions. Using graph theoretic techniques, the dynamics is expressed in a formally exact way as a set of integral equations. With a simple approximation for the…
Aims To propose and analyze a general, dynamic, process-oriented theory of the area of distribution. Methods The area of distribution is modelled by combining (by multiplication) three matrices: one matrix represents movements, another…
A new definition of a fractional derivative has recently been developed, making use of a fractional Dirac delta function as its integral kernel. This derivative allows for the definition of a distributional fractional derivative, and as…
We propose Local Dirac Synchronization which uses the Dirac operator to capture the dynamics of coupled nodes and link signals on an arbitrary network. In Local Dirac Synchronization, the harmonic modes of the dynamics oscillate freely…
We consider topological dynamical systems over $\ZZ$ and, more generally, locally compact, $\sigma$-compact abelian groups. We relate spectral theory and diffraction theory. We first use a a recently developed general framework of…
Control theory of dynamical systems offers a powerful framework for tackling challenges in deep neural networks and other machine learning architectures. We show that concepts such as simultaneous and ensemble controllability offer new…
The system describing a single Dirac electron field coupled with classically moving point nuclei is presented and studied. The model is a semi-relativistic extension of corresponding time-dependent one-body Hartree-Fock equation coupled…