Complexity-Entropy Causality Plane as a Complexity Measure for Two-dimensional Patterns

Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less common. Here, we reduce this gap by applying the ideas of the permutation entropy combined with a relative entropic index. We build up a numerical procedure that can be easily implemented to evaluate the complexity of two or higher-dimensional patterns. We work out this method in different scenarios where numerical experiments and empirical data were taken into account. Specifically, we have applied the method to i) fractal landscapes generated numerically where we compare our measures with the Hurst exponent; ii) liquid crystal textures where nematic-isotropic-nematic phase transitions were properly identified; iii) 12 characteristic textures of liquid crystals where the different values show that the method can distinguish different phases; iv) and Ising surfaces where our method identified the critical temperature and also proved to be stable.Comment: Accepted for publication in PLoS On

A Solution to the Challenge of Optimization on ''Golf-Course''-Like Fitness Landscapes

Genetic algorithms (GAs) have been used to find efficient solutions to numerous fundamental and applied problems. While GAs are a robust and flexible approach to solve complex problems, there are some situations under which they perform poorly. Here, we introduce a genetic algorithm approach that is able to solve complex tasks plagued by so-called ''golf-course''-like fitness landscapes. Our approach, which we denote variable environment genetic algorithms (VEGAs), is able to find highly efficient solutions by inducing environmental changes that require more complex solutions and thus creating an evolutionary drive. Using the density classification task, a paradigmatic computer science problem, as a case study, we show that more complex rules that preserve information about the solution to simpler tasks can adapt to more challenging environments. Interestingly, we find that conservative strategies, which have a bias toward the current state, evolve naturally as a highly efficient solution to the density classification task under noisy conditions

Universal and non-universal properties of cross-correlations in financial time series

We use methods of random matrix theory to analyze the cross-correlation matrix C of price changes of the largest 1000 US stocks for the 2-year period 1994-95. We find that the statistics of most of the eigenvalues in the spectrum of C agree with the predictions of random matrix theory, but there are deviations for a few of the largest eigenvalues. We find that C has the universal properties of the Gaussian orthogonal ensemble of random matrices. Furthermore, we analyze the eigenvectors of C through their inverse participation ratio and find eigenvectors with large inverse participation ratios at both edges of the eigenvalue spectrum--a situation reminiscent of results in localization theory.Comment: 14 pages, 3 figures, Revte

Scaling of the distribution of fluctuations of financial market indices

We study the distribution of fluctuations over a time scale $\Delta t$ (i.e., the returns) of the S&P 500 index by analyzing three distinct databases. Database (i) contains approximately 1 million records sampled at 1 min intervals for the 13-year period 1984-1996, database (ii) contains 8686 daily records for the 35-year period 1962-1996, and database (iii) contains 852 monthly records for the 71-year period 1926-1996. We compute the probability distributions of returns over a time scale $\Delta t$, where $\Delta t$ varies approximately over a factor of 10^4 - from 1 min up to more than 1 month. We find that the distributions for $\Delta t \leq$ 4 days (1560 mins) are consistent with a power-law asymptotic behavior, characterized by an exponent $\alpha \approx 3$, well outside the stable L\'evy regime $0 < \alpha < 2$. To test the robustness of the S&P result, we perform a parallel analysis on two other financial market indices. Database (iv) contains 3560 daily records of the NIKKEI index for the 14-year period 1984-97, and database (v) contains 4649 daily records of the Hang-Seng index for the 18-year period 1980-97. We find estimates of $\alpha$ consistent with those describing the distribution of S&P 500 daily-returns. One possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility. For time scales longer than $(\Delta t)_{\times} \approx 4$ days, our results are consistent with slow convergence to Gaussian behavior.Comment: 12 pages in multicol LaTeX format with 27 postscript figures (Submitted to PRE May 20, 1999). See http://polymer.bu.edu/~amaral/Professional.html for more of our work on this are

Woodland Recovery after Suppression of Deer: Cascade effects for Small Mammals, Wood Mice (Apodemus sylvaticus) and Bank Voles (Myodes glareolus)

Over the past century, increases in both density and distribution of deer species in the Northern Hemisphere have resulted in major changes in ground flora and undergrowth vegetation of woodland habitats, and consequentially the animal communities that inhabit them. In this study, we tested whether recovery in the vegetative habitat of a woodland due to effective deer management (from a peak of 0.4–1.5 to <0.17 deer per ha) had translated to the small mammal community as an example of a higher order cascade effect. We compared deer-free exclosures with neighboring open woodland using capture-mark-recapture (CMR) methods to see if the significant difference in bank vole (Myodes glareolus) and wood mouse (Apodemus sylvaticus) numbers between these environments from 2001–2003 persisted in 2010. Using the multi-state Robust Design method in program MARK we found survival and abundance of both voles and mice to be equivalent between the open woodland and the experimental exclosures with no differences in various metrics of population structure (age structure, sex composition, reproductive activity) and individual fitness (weight), although the vole population showed variation both locally and temporally. This suggests that the vegetative habitat - having passed some threshold of complexity due to lowered deer density - has allowed recovery of the small mammal community, although patch dynamics associated with vegetation complexity still remain. We conclude that the response of small mammal communities to environmental disturbance such as intense browsing pressure can be rapidly reversed once the disturbing agent has been removed and the vegetative habitat is allowed to increase in density and complexity, although we encourage caution, as a source/sink dynamic may emerge between old growth patches and the recently disturbed habitat under harsh conditions

Who Eats Whom in a Pool? A Comparative Study of Prey Selectivity by Predatory Aquatic Insects

Predatory aquatic insects are a diverse group comprising top predators in small fishless water bodies. Knowledge of their diet composition is fragmentary, which hinders the understanding of mechanisms maintaining their high local diversity and of their impacts on local food web structure and dynamics. We conducted multiple-choice predation experiments using nine common species of predatory aquatic insects, including adult and larval Coleoptera, adult Heteroptera and larval Odonata, and complemented them with literature survey of similar experiments. All predators in our experiments fed selectively on the seven prey species offered, and vulnerability to predation varied strongly between the prey. The predators most often preferred dipteran larvae; previous studies further reported preferences for cladocerans. Diet overlaps between all predator pairs and predator overlaps between all prey pairs were non-zero. Modularity analysis separated all primarily nectonic predator and prey species from two groups of large and small benthic predators and their prey. These results, together with limited evidence from the literature, suggest a highly interconnected food web with several modules, in which similarly sized predators from the same microhabitat are likely to compete strongly for resources in the field (observed Pianka’s diet overlap indices >0.85). Our experiments further imply that ontogenetic diet shifts are common in predatory aquatic insects, although we observed higher diet overlaps than previously reported. Hence, individuals may or may not shift between food web modules during ontogeny

Photography-based taxonomy is inadequate, unnecessary, and potentially harmful for biological sciences

The question whether taxonomic descriptions naming new animal species without type specimen(s) deposited in collections should be accepted for publication by scientific journals and allowed by the Code has already been discussed in Zootaxa (Dubois & Nemésio 2007; Donegan 2008, 2009; Nemésio 2009a–b; Dubois 2009; Gentile & Snell 2009; Minelli 2009; Cianferoni & Bartolozzi 2016; Amorim et al. 2016). This question was again raised in a letter supported by 35 signatories published in the journal Nature (Pape et al. 2016) on 15 September 2016. On 25 September 2016, the following rebuttal (strictly limited to 300 words as per the editorial rules of Nature) was submitted to Nature, which on 18 October 2016 refused to publish it. As we think this problem is a very important one for zoological taxonomy, this text is published here exactly as submitted to Nature, followed by the list of the 493 taxonomists and collection-based researchers who signed it in the short time span from 20 September to 6 October 2016

The Variable Environment Genetic Algorithm dramatically speeds up the evolution of solutions to the density classification task.

<p>(A) Highest fitness in the population and (B) noise magnitude as a function generation number. We start simulations with 100 randomly selected populations of agents having genomes with 32 bits, that is, k = 5 and . When a genome reaches a fitness of , we increase the magnitude of the noise by . In the beginning of the process the most efficient rules are guessers, that have efficiency about 0.5. At some generation an innovative rule evolves that can classify both kinds of consensus, and in a few more generations the desired efficiency is achieved. The noise then increases rapidly until it reaches a critical level (about ). Then, no rule achieves the desired efficiency even after 50 generation. At this point, we promote the population of rules to include extra neighbors. The doted lines in the panels mark these moments. The promoted rules are essentially identical to the previous ones, with the extra neighbors acting as silent inputs, that is, the extra information does not affect the rule dynamics. The GA, by mutation and crossover, should make use of these new inputs to evolve more efficient rules. Eventually, members of the population will achieve the desired efficiency, noisy increases until it reaches another level that can not be surmounted by rules with this value of . The rules are promoted again, and the process continues with noise and complexity of the rules co-evolving until we obtain highly complex rules () that sustain high noise levels ().</p

Robustness of the evolved genomes again communication noise.

<p>(A) Comparison of the fitness of the genomes evolved using VEGA against the fitness of the majority rule for 5, 7 and 11. It is visually apparent that for the evolved genomes are more robust against communication noise than the majority rule. (B) Average updated state of an agent with a high fitness evolved genome with as a function of the number of neighbors in state one for . The red circles show the updated state of the agent when the initial state is one, and the red dashed line shows results for the majority rule for comparison. The empty circles show the updated state of the agent when the initial state is zero, and the black full line shows results for the majority rule. (C) Same as b, but for . It is visually apparent that the evolved genomes are more conservative than the majority rule — they require larger majorities of neighbors on the opposite state in order to change state.</p

Implementing variable environment genetic algorithms.

<p>(A) To promote a rule with to , we include extra neighbors keeping the same output with any combination of these two new neighbors. On the left we see a possible input and its respective output for a rule. On the right there are the respective possible outputs after generalization. Note that in the generalized rule the new inputs do not affect the rule's output. However, inter-generational mutation and crossover of the genetic material will yield changes in output that make the states of the new neighbors relevant. (B) Flowchart of the variable environment genetic algorithms. See the text for a more detailed description.</p