Related papers: Time Evolution of Complexity: A Critique of Three …
A fundamental description of time can be consistent not only with the usual monotonic behavior but also with a periodic physical clock variable, coupled to the degrees of freedom of a system evolving in time. Generically, one would in fact…
Complexity is a signature quality of interest in artificial life systems. Alongside other dimensions of assessment, it is common to quantify genome sites that contribute to fitness as a complexity measure. However, limitations to the…
On account of a greater need for understanding the complexity of time series like physiological time series, financial time series, and many more that enter into picture for their inculpation with real-world problems, several complexity…
We consider the problem of detecting jumps in an otherwise smoothly evolving trend whilst the covariance and higher-order structures of the system can experience both smooth and abrupt changes over time. The number of jump points is allowed…
Our main goal in this paper is to extend to any system of coupled quadratic Hamiltonians some properties known for systems of quantum harmonic oscillators related with the Brownian Quantum Motion model. In a first part we get a rather…
Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…
A measure called Physical Complexity is established and calculated for a population of sequences, based on statistical physics, automata theory, and information theory. It is a measure of the quantity of information in an organism's genome.…
This paper describes a classifier pool generation method guided by the diversity estimated on the data complexity and classifier decisions. First, the behavior of complexity measures is assessed by considering several subsamples of the…
Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the…
We consider a two-level quantum system (qubit) which is continuously measured by a detector. The information provided by the detector is taken into account to describe the evolution during a particular realization of measurement process. We…
Time series are ubiquitous, and a measure to assess their similarity is a core part of many computational systems. In particular, the similarity measure is the most essential ingredient of time series clustering and classification systems.…
In this paper, we present a method for the Hamiltonian simulation in the context of eigenvalue estimation problems which improves earlier results dealing with Hamiltonian simulation through the truncated Taylor series. In particular, we…
Complexity is an important characteristic of any business process. The key assumption of much research in Business Process Management is that process complexity has a negative impact on process performance. So far, behavioral studies have…
Time series classification is an important problem in real world. Due to its non-stationary property that the distribution changes over time, it remains challenging to build models for generalization to unseen distributions. In this paper,…
Locality is a fundamental feature of many physical time evolutions. Assumptions on locality and related structural properties also underlie recently proposed procedures for learning an unknown Hamiltonian from access to the induced time…
The theory of computational complexity focuses on functions and, hence, studies programs whose interactive behavior is reduced to a simple question/answer pattern. We propose a broader theory whose ultimate goal is expressing and analyzing…
We address the time decay of the Loschmidt echo, measuring sensitivity of quantum dynamics to small Hamiltonian perturbations, in one-dimensional integrable systems. Using semiclassical analysis, we show that the Loschmidt echo may exhibit…
Echo dynamics and fidelity are often used to discuss stability in quantum information processing and quantum chaos. Yet fidelity yields no information about entanglement, the characteristic property of quantum mechanics. We study the…
This article develops mathematical formalisms and provides numerical methods for studying the evolution of measures in nonsmooth dynamical systems using the continuity equation. The nonsmooth dynamical system is described by an evolution…
We present a quantum algorithm for simulating the time evolution generated by any bounded, time-dependent operator $-A$ with non-positive logarithmic norm, thereby serving as a natural generalization of the Hamiltonian simulation problem.…