José M. Amigó

Bio: José M. Amigó is an academic researcher from Universidad Miguel Hernández de Elche. The author has contributed to research in topics: Dynamical systems theory & Topological entropy. The author has an hindex of 29, co-authored 128 publications receiving 2568 citations. Previous affiliations of José M. Amigó include Polish Academy of Sciences & University of Göttingen.

True and false forbidden patterns in deterministic and random dynamics

Abstract: In this letter we discuss some properties of order patterns both in deterministic and random orbit generation. As it turns out, the orbits of one-dimensional maps have always forbidden patterns, i.e., order patterns that cannot occur, in contrast with random time series, in which any order pattern appears with probability one. However, finite random sequences may exhibit "false" forbidden patterns with non-vanishing probability. In this case, forbidden patterns decay with the sequence length, thus unveiling the random nature of the sequence. Last but not least, true forbidden patterns are robust against noise and disintegrate with a rate that depends on the noise level. These properties can be embodied in a simple method to distinguish deterministic, finite time series with very high levels of observational noise, from random ones. We present numerical evidence for white noise.

Estimating the Entropy Rate of Spike Trains via Lempel-Ziv Complexity

Abstract: Normalized Lempel-Ziv complexity, which measures the generation rate of new patterns along a digital sequence, is closely related to such important source properties as entropy and compression ratio, but, in contrast to these, it is a property of individual sequences. In this article, we propose to exploit this concept to estimate (or, at least, to bound from below) the entropy of neural discharges (spike trains). The main advantages of this method include fast convergence of the estimator (as supported by numerical simulation) and the fact that there is no need to know the probability law of the process generating the signal. Furthermore, we present numerical and experimental comparisons of the new method against the standard method based on word frequencies, providing evidence that this new approach is an alternative entropy estimator for binned spike trains.

A Brief Review of Generalized Entropies

Abstract: Entropy appears in many contexts (thermodynamics, statistical mechanics, information theory, measure-preserving dynamical systems, topological dynamics, etc.) as a measure of different properties (energy that cannot produce work, disorder, uncertainty, randomness, complexity, etc.). In this review, we focus on the so-called generalized entropies, which from a mathematical point of view are nonnegative functions defined on probability distributions that satisfy the first three Shannon-Khinchin axioms: continuity, maximality and expansibility. While these three axioms are expected to be satisfied by all macroscopic physical systems, the fourth axiom (separability or strong additivity) is in general violated by non-ergodic systems with long range forces, this having been the main reason for exploring weaker axiomatic settings. Currently, non-additive generalized entropies are being used also to study new phenomena in complex dynamics (multifractality), quantum systems (entanglement), soft sciences, and more. Besides going through the axiomatic framework, we review the characterization of generalized entropies via two scaling exponents introduced by Hanel and Thurner. In turn, the first of these exponents is related to the diffusion scaling exponent of diffusion processes, as we also discuss. Applications are addressed as the description of the main generalized entropies advances.

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

Abstract: 抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

Some basic cryptographic requirements for chaos-based cryptosystems

Abstract: In recent years, a large amount of work on chaos-based cryptosystems have been published. However, many of the proposed schemes fail to explain or do not possess a number of features that are fundamentally important to all kind of cryptosystems. As a result, many proposed systems are difficult to implement in practice with a reasonable degree of security. Likewise, they are seldom accompanied by a thorough security analysis. Consequently, it is difficult for other researchers and end users to evaluate their security and performance. This work is intended to provide a common framework of basic guidelines that, if followed, could benefit every new cryptosystem. The suggested guidelines address three main issues: implementation, key management and security analysis, aiming at assisting designers of new cryptosystems to present their work in a more systematic and rigorous way to fulfill some basic cryptographic requirements. Meanwhile, several recommendations are made regarding some practical aspects of analog chaos-based secure communications, such as channel noise, limited bandwith and attenuation.

Nonlinear Time Series Analysis.

Abstract: : This thesis applies neural network feature selection techniques to multivariate time series data to improve prediction of a target time series. Two approaches to feature selection are used. First, a subset enumeration method is used to determine which financial indicators are most useful for aiding in prediction of the S&P 500 futures daily price. The candidate indicators evaluated include RSI, Stochastics and several moving averages. Results indicate that the Stochastics and RSI indicators result in better prediction results than the moving averages. The second approach to feature selection is calculation of individual saliency metrics. A new decision boundary-based individual saliency metric, and a classifier independent saliency metric are developed and tested. Ruck's saliency metric, the decision boundary based saliency metric, and the classifier independent saliency metric are compared for a data set consisting of the RSI and Stochastics indicators as well as delayed closing price values. The decision based metric and the Ruck metric results are similar, but the classifier independent metric agrees with neither of the other metrics. The nine most salient features, determined by the decision boundary based metric, are used to train a neural network and the results are presented and compared to other published results. (AN)

Estimation of entropy and mutual information

Abstract: We present some new results on the nonparametric estimation of entropy and mutual information. First, we use an exact local expansion of the entropy function to prove almost sure consistency and central limit theorems for three of the most commonly used discretized information estimators. The setup is related to Grenander's method of sieves and places no assumptions on the underlying probability measure generating the data. Second, we prove a converse to these consistency theorems, demonstrating that a misapplication of the most common estimation techniques leads to an arbitrarily poor estimate of the true information, even given unlimited data. This "inconsistency" theorem leads to an analytical approximation of the bias, valid in surprisingly small sample regimes and more accurate than the usual 1/N formula of Miller and Madow over a large region of parameter space. The two most practical implications of these results are negative: (1) information estimates in a certain data regime are likely contaminated by bias, even if "bias-corrected" estimators are used, and (2) confidence intervals calculated by standard techniques drastically underestimate the error of the most common estimation methods.Finally, we note a very useful connection between the bias of entropy estimators and a certain polynomial approximation problem. By casting bias calculation problems in this approximation theory framework, we obtain the best possible generalization of known asymptotic bias results. More interesting, this framework leads to an estimator with some nice properties: the estimator comes equipped with rigorous bounds on the maximum error over all possible underlying probability distributions, and this maximum error turns out to be surprisingly small. We demonstrate the application of this new estimator on both real and simulated data.