Related papers: Statistical Complexity of Sampled Chaotic Attracto…
We consider the concept of statistical complexity to write the quasiperiodical damped systems applying the snapshot attractors. This allows us to understand the behaviour of these dynamical systems by the probability distribution of the…
The stochastic simulation algorithm (SSA) and the corresponding Monte Carlo (MC) method are among the most common approaches for studying stochastic processes. They rely on knowledge of interevent probability density functions (PDFs) and on…
Compressed Counting (CC), based on maximally skewed stable random projections, was recently proposed for estimating the p-th frequency moments of data streams. The case p->1 is extremely useful for estimating Shannon entropy of data…
A powerful tool is developed for the characterization of chaotic signals. The approach is based on the symbolic encoding of time series (according to their ordinal patterns) combined with the ensuing characterization of the corresponding…
Hamiltonian Monte Carlo (HMC) algorithms which combine numerical approximation of Hamiltonian dynamics on finite intervals with stochastic refreshment and Metropolis correction are popular sampling schemes, but it is known that they may…
Compressed Counting (CC)} was recently proposed for approximating the $\alpha$th frequency moments of data streams, for $0<\alpha \leq 2$. Under the relaxed strict-Turnstile model, CC dramatically improves the standard algorithm based on…
Recurrence entropy $(\cal S)$ is a novel time series complexity quantifier based on recurrence microstates. Here we show that $\mathsf{max}(\cal S)$ is a \textit{parameter-free} quantifier of time correlation of stochastic and chaotic…
The definition of complexity through Statistical Complexity Measures (SCM) has recently seen major improvements. Mostly, effort is concentrated in measures on time series. We propose a SCM definition for spatial dynamical systems. Our…
Sequential Monte Carlo (SMC) methods are a class of techniques to sample approximately from any sequence of probability distributions using a combination of importance sampling and resampling steps. This paper is concerned with the…
The aim of this paper is to introduce the Lempel-Ziv permutation complexity vs permutation entropy plane as a tool to analyze time series of different nature. This two quantities make use of the Bandt and Pompe representation to quantify…
Electromagnetic (EM) wave scattering in electrically large, irregularly shaped, environments is a common phenomenon. The deterministic, or first principles, study of this process is usually computationally expensive and the results exhibit…
Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process' intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical…
The most common state space reconstruction method in the analysis of chaotic time series is the Method of Delays (MOD). Many techniques have been suggested to estimate the parameters of MOD, i.e. the time delay $\tau$ and the embedding…
In this paper we present the concept of description of random processes in complex systems with the discrete time. It involves the description of kinetics of discrete processes by means of the chain of finite-difference non-Markov equations…
Particle density fluctuations in the scrape-off layer of magnetically confined plasmas, as measured by gas-puff imaging or Langmuir probes, are modeled as the realization of a stochastic process in which a superposition of pulses with a…
Sampling the parameters of high-dimensional Continuous Time Markov Chains (CTMC) is a challenging problem with important applications in many fields of applied statistics. In this work a recently proposed type of non-reversible…
We propose to examine the predictability and the complexity characteristics of the Standard&Poor500 dynamics behaviors in a coarse-grained way using the symbolic dynamics method and under the prism of the Information theory through the…
The evolution of a quantum system, appropriate to describe nano-magnets, can be mapped on a Markov process, continuous in $\beta$. The mapping implies a probability assignment that can be used to study the probability density (PDF) of the…
We consider the stochastic linear contextual bandit problem with high-dimensional features. We analyze the Thompson sampling algorithm using special classes of sparsity-inducing priors (e.g., spike-and-slab) to model the unknown parameter…
A succesful method to describe the asymptotic behavior of a discrete time stochastic process governed by some recursive formula is to relate it to the limit sets of a well chosen mean differential equation. Under an attainability condition,…