arXiv subjects

José M. Amigó

Publications and source records attributed to José M. Amigó.

22 records · Page 2Linked to original sources

arXiv2020

A generalized permutation entropy for random processes

Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in time series analysis include that (i) it converges to the Kolmogorov-Sinai entropy of the underlying dynamics in the limit of ever longer permutations, and (ii) its computation dispenses with generating and ad hoc partitions. However, permutation entropy diverges when the number of allowed permutations grows super-exponentially with their length, as is usually the case when time series are output by random processes. In this Letter we propose a generalized permutation entropy that is finite for random processes, including discrete-time dynamical systems with observational or dynamical noise.

physics.data-an↗

arXiv2020

Internet congestion control: from stochastic to dynamical models

Since its inception, control of data congestion on the Internet has been based on stochastic models. One of the first such models was Random Early Detection. Later, this model was reformulated as a dynamical system, with the average queue sizes at a router's buffer being the states. Recently, the dynamical model has been generalized to improve global stability. In this paper we review the original stochastic model and both nonlinear models of Random Early Detection with a two-fold objective: (i) illustrate how a random model can be "smoothed out" to a deterministic one through data aggregation, and (ii) how this translation can shed light into complex processes such as the Internet data traffic. Furthermore, this paper contains new materials concerning the occurrence of chaos, bifurcation diagrams, Lyapunov exponents and global stability robustness with respect to control parameters. The results reviewed and reported here are expected to help design an active queue management algorithm in real conditions, that is, when system parameters such as the number of users and the round-trip time of the data packets change over time. The topic also illustrates the much-needed synergy of a theoretical approach, practical intuition and numerical simulations in engineering.

math.DS↗

arXiv2017

General Algorithmic Search

In this paper we present a metaheuristic for global optimization called General Algorithmic Search (GAS). Specifically, GAS is a stochastic, single-objective method that evolves a swarm of agents in search of a global extremum. Numerical simulations with a sample of 31 test functions show that GAS outperforms Basin Hopping, Cuckoo Search, and Differential Evolution, especially in concurrent optimization, i.e., when several runs with different initial settings are executed and the first best wins. Python codes of all algorithms and complementary information are available online.

math.OC↗

arXiv2007

Forbidden patterns and shift systems

The scope of this paper is two-fold. First, to present to the researchers in combinatorics an interesting implementation of permutations avoiding generalized patterns in the framework of discrete-time dynamical systems. Indeed, the orbits generated by piecewise monotone maps on one-dimensional intervals have forbidden order patterns, i.e., order patterns that do not occur in any orbit. The allowed patterns are then those patterns avoiding the so-called forbidden root patterns and their shifted patterns. The second scope is to study forbidden patterns in shift systems, which are universal models in information theory, dynamical systems and stochastic processes. Due to its simple structure, shift systems are accessible to a more detailed analysis and, at the same time, exhibit all important properties of low-dimensional chaotic dynamical systems (e.g., sensitivity to initial conditions, strong mixing and a dense set of periodic points), allowing to export the results to other dynamical systems via order-isomorphisms.

math.DS↗