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We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the…
This paper revisits the classical notion of sampling in the setting of real-time temporal logics for the modeling and analysis of systems. The relationship between the satisfiability of Metric Temporal Logic (MTL) formulas over…
Measurements are ordinarily described with respect to absolute "Newtonian" time. In reality however, the switching-on of the measuring device at the instance of the measurement requires a timing device. Hence the classical time $t$ must be…
We study for a composite quantum system with a quantum Turing architecture the temporal non-locality of quantum mechanics by using the temporal Bell inequality, which will be derived for a discretized network dynamics by identifying the…
This paper revisits a recently developed methodology based on the matrix Lambert W function for the stability analysis of linear time invariant, time delay systems. By studying a particular, yet common, second order system, we show that in…
The academic community has made outstanding achievements in researching the March algorithm. However, the current fault modeling method, which centers on fault primitives, cannot be directly applied to analyzing the March algorithm. This…
In this letter we briefly investigate the mathematical structure of space-time in the framework of discretization. It is shown that the discreteness of space-time may result in a new mechanical system which differ from the usual quantum…
The diagonal elements of the time correlation matrix are used to probe closed quantum systems that are measured at random times. This enables us to extract two distinct parts of the quantum evolution, a recurrent part and an exponentially…
In this paper, we consider the stability of discrete-time linear switched systems with a common non-strict Lyapunov matrix.
This short note gives a new framework for dealing with nonlinear sampled-data systems. We introduce a new idea of lifting, which is well known for linear systems, but not successfully generalized to nonlinear systems. This paper introduces…
In this work we are interested in general linear inverse problems where the corresponding forward problem is solved iteratively using fixed point methods. Then one-shot methods, which iterate at the same time on the forward problem solution…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
We study weaker variations of the property of flatness in matroid theory. We show that these variations form a chain of increasingly stronger properties all implying pseudomodularity on its lattice of flats. We show examples in the gammoid…
The density matrix yields probabilistic information about the outcome of measurements on a quantum system, but it does not distinguish between classical randomness in the preparation of the system and entanglement with its environment.…
We consider the numerical solution of time-dependent space tempered fractional diffusion equations. The use of Crank-Nicolson in time and of second-order accurate tempered weighted and shifted Gr\"unwald difference in space leads to dense…
In this paper, stability analysis of time delay systems is considered based on decomposition of the systems to subsystems. The decomposition process needs matrices of these systems to be simultaneously block triangularize. We show that a…
This paper concerns with the time-reversal characteristics of intrinsic normal diffusion in quantum systems. Time-reversible properties are quantified by the time-reversal test; the system evolved in the forward direction for a certain…
This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…
Recent advances in nonlinear dynamical systems theory provide a new insight into numerical properties of discrete algorithms developed to solve nonlinear initial value problems. Basic features like accuracy and stability are well pointed…
Modern statistical learning theory and deep learning characterize generalization primarily in terms of continuous capacity control (e.g., norm-based regularization, margin maximization, low-rank bias). While highly successful in continuous…