Permutation entropy and its main biomedical and econophysics applications: a review

Entropy is a powerful tool for the analysis of time series, as it allows describing the probability distributions of the possible state of a system, and therefore the information encoded in it. Nevertheless, important information may be codified also in the temporal dynamics, an aspect which is not usually taken into account. The idea of calculating entropy based on permutation patterns (that is, permutations defined by the order relations among values of a time series) has received a lot of attention in the last years, especially for the understanding of complex and chaotic systems. Permutation entropy directly accounts for the temporal information contained in the time series; furthermore, it has the quality of simplicity, robustness and very low computational cost. To celebrate the tenth anniversary of the original work, here we analyze the theoretical foundations of the permutation entropy, as well as the main recent applications to the analysis of economical markets and to the understanding of biomedical systems.Facultad de Ingenierí

Resolution-scale relativistic formulation of non-differentiable mechanics

This article motivates and presents the scale relativistic approach to non-differentiability in mechanics and its relation to quantum mechanics. It stems from the scale relativity proposal to extend the principle of relativity to resolution-scale transformations, which leads to considering non-differentiable dynamical paths. We first define a complex scale-covariant time-differential operator and show that mechanics of non-differentiable paths is implemented in the same way as classical mechanics but with the replacement of the time derivative and velocity with the time-differential operator and associated complex velocity. With this, the generalized form of Newton's fundamental relation of dynamics is shown to take the form of a Langevin equation in the case of stationary motion characterized by a null average classical velocity. The numerical integration of the Langevin equation in the case of a harmonic oscillator taken as an example reveals the same statistics as the stationary solutions of the Schrodinger equation for the same problem. This motivates the rest of the paper, which shows Schrodinger's equation to be a reformulation of Newton's fundamental relation of dynamics as generalized to non-differentiable geometries and leads to an alternative interpretation of the other axioms of standard quantum mechanics in a coherent picture. This exercise validates the scale relativistic approach and, at the same time, it allows to envision macroscopic chaotic systems observed at resolution time-scales exceeding their horizon of predictability as candidates in which to search for quantum-like dynamics and structures.Comment: 30 pages, 4 figure

A way to synchronize models with seismic faults for earthquake forecasting: Insights from a simple stochastic model

Numerical models are starting to be used for determining the future behaviour of seismic faults and fault networks. Their final goal would be to forecast future large earthquakes. In order to use them for this task, it is necessary to synchronize each model with the current status of the actual fault or fault network it simulates (just as, for example, meteorologists synchronize their models with the atmosphere by incorporating current atmospheric data in them). However, lithospheric dynamics is largely unobservable: important parameters cannot (or can rarely) be measured in Nature. Earthquakes, though, provide indirect but measurable clues of the stress and strain status in the lithosphere, which should be helpful for the synchronization of the models. The rupture area is one of the measurable parameters of earthquakes. Here we explore how it can be used to at least synchronize fault models between themselves and forecast synthetic earthquakes. Our purpose here is to forecast synthetic earthquakes in a simple but stochastic (random) fault model. By imposing the rupture area of the synthetic earthquakes of this model on other models, the latter become partially synchronized with the first one. We use these partially synchronized models to successfully forecast most of the largest earthquakes generated by the first model. This forecasting strategy outperforms others that only take into account the earthquake series. Our results suggest that probably a good way to synchronize more detailed models with real faults is to force them to reproduce the sequence of previous earthquake ruptures on the faults. This hypothesis could be tested in the future with more detailed models and actual seismic data.Comment: Revised version. Recommended for publication in Tectonophysic

Making Sense of Public Policy in a Fragmented World: the Search for Solutions and the Limits of Learning

This paper explores innovation, learning and change in an environment where the historical moment of ‘New Public Management’ (NPM) has given way to unprecedented fluidity in public policy and decision making. To begin, we examine key elements of the post-NPM environment, where foundational approaches (in theory and practice) can be challenged either by innovation or by default to previous positions: both trends are evident in the incoherence of policy responses to the global economic crisis. We then consider the search for meaning and sense-making by policy actors who seek new solutions to cope with intractable problems. This can generate innovative responses, including the growth of Third Sector (voluntary organisation) involvement in public policy and public services, or the rediscovery of a public service ethic amidst the banking crisis, including citizen withdrawal from multi-national banks in favour of ethical or mutual providers. We will then suggest that although there is a certain inevitability to the process of change in an era which has moved beyond modernist and foundationalist solutions, this does not necessarily generate positive and desirable innovation. Change may instead involve a retreat to failed responses of a previous era. It is as though a familiar script is still recited by policy actors even though the overall storyline has fundamentally changed. In this sense, entrenched learning may produce negative results even though ‘reverse organisational learning’ (ie organisational amnesia) may accord a superficial appearance of novelty. This may be readily illustrated by examples from recent European public policy. Finally, in an era where the modernist conception of gradual mastery (of the world, and of theory) has fallen away, the discussion considers the kind of analytical tools that may assist in the theoretical understanding of a changed public policy environment

Information-theoretic approach to lead-lag effect on financial markets

Recently the interest of researchers has shifted from the analysis of synchronous relationships of financial instruments to the analysis of more meaningful asynchronous relationships. Both of those analyses are concentrated only on Pearson's correlation coefficient and thus intraday lead-lag relationships associated with such. Under Efficient Market Hypothesis such relationships are not possible as all information is embedded in the prices. In this paper we analyse lead-lag relationships of financial instruments and extend known methodology by using mutual information instead of Pearson's correlation coefficient, which not only is a more general measure, sensitive to non-linear dependencies, but also can lead to a simpler procedure of statistical validation of links between financial instruments. We analyse lagged relationships using NYSE 100 data not only on intraday level but also for daily stock returns, which has usually been ignored.Comment: 9 pages, 19 figure

Playing Smart - Artificial Intelligence in Computer Games

Abstract: With this document we will present an overview of artificial intelligence in general and artificial intelligence in the context of its use in modern computer games in particular. To this end we will firstly provide an introduction to the terminology of artificial intelligence, followed by a brief history of this field of computer science and finally we will discuss the impact which this science has had on the development of computer games. This will be further illustrated by a number of case studies, looking at how artificially intelligent behaviour has been achieved in selected games

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