Related papers: Time series, correlation matrices and random matri…
We present a brief overview of random matrix theory (RMT) with the objectives of highlighting the computational results and applications in financial markets as complex systems. An oft-encountered problem in computational finance is the…
We review elementary properties of random matrices and discuss widely used mathematical methods for both hermitian and nonhermitian random matrix ensembles. Applications to a wide range of physics problems are summarized. This paper…
This paper presents a new approach for analysing structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
It is shown that a choice of degrees of freedom of a bipartite continuous variable system determines amount of non-classical correlations (quantified by discord) in the system's state. Non-classical correlations (that include entanglement…
The eigenvalues of quantum chaotic systems have been conjectured to follow, in the large energy limit, the statistical distribution of eigenvalues of random ensembles of matrices of size $N\rightarrow\infty$. Here we provide semiclassical…
From the climate system to the effect of the internet on society, chaotic systems appear to have a significant role in our future. Here a method of statistical learning for a class of chaotic systems is described along with underlying…
The error model of a quantum computer is essential for optimizing quantum algorithms to minimize the impact of errors using quantum error correction or error mitigation. Noise with temporal correlations, e.g. low-frequency noise and…
We investigate the correlations of initially separable probability distributions in a globally pure bipartite system with two degrees of freedom for classical and quantum systems. A classical version of the quantum linear mutual information…
In this document, some general results in approximation theory and matrix analysis with applications to sparse identification of time series models and nonlinear discrete-time dynamical systems are presented. The aforementioned theoretical…
For finite random systems, it is possible to define two types of variances (noises). It is demonstrated that their ratio is useful in calculating the correlation length of an infinite and rather general random system, as a function of…
Continuously measured quantum systems are characterized by an output current, in the form of a stochastic and correlated time series which conveys crucial information about the underlying quantum system. The many tools used to describe…
Correlations obtained from sequences of measurements have been employed to distinguish among different physical theories or to witness the dimension of a system. In this work we show that they can also be used to establish semi-device…
Beneficial to advanced computing devices, models with massive parameters are increasingly employed to extract more information to enhance the precision in describing and predicting the patterns of objective systems. This phenomenon is…
Generalizing the quantifiers used to classify correlations in bipartite systems, we define genuine total, quantum, and classical correlations in multipartite systems. The measure we give is based on the use of relative entropy to quantify…
We provide an overview of a canonical formalism that describes mixed quantum-classical systems in terms of statistical ensembles on configuration space, and discuss applications to measurement theory. It is shown that the formalism allows a…
We deal here with the issue of determinism versus randomness in time series. One wishes to identify their relative importance in a given time series. To this end we extend i) the use of ordinal patterns-based probability distribution…
A possibility to detect correlations between two quantum mechanical systems only from the information of a subsystem is investigated. For generic cases, we prove that there exist correlations between two quantum systems if the…
Quantum circuits -- built from local unitary gates and local measurements -- are a new playground for quantum many-body physics and a tractable setting to explore universal collective phenomena far-from-equilibrium. These models have shed…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…