Estimating the Fractal Dimension, K_2-entropy, and the Predictability of the Atmosphere

The series of mean daily temperature of air recorded over a period of 215 years is used for analysing the dimensionality and the predictability of the atmospheric system. The total number of data points of the series is 78527. Other 37 versions of the original series are generated, including ``seasonally adjusted'' data, a smoothed series, series without annual course, etc. Modified methods of Grassberger and Procaccia are applied. A procedure for selection of the ``meaningful'' scaling region is proposed. Several scaling regions are revealed in the ln C(r) versus ln r diagram. The first one in the range of larger ln r has a gradual slope and the second one in the range of intermediate ln r has a fast slope. Other two regions are settled in the range of small ln r. The results lead us to claim that the series arises from the activity of at least two subsystems. The first subsystem is low-dimensional (d_f=1.6) and it possesses the potential predictability of several weeks. We suggest that this subsystem is connected with seasonal variability of weather. The second subsystem is high-dimensional (d_f>17) and its error-doubling time is about 4-7 days. It is found that the predictability differs in dependence on season. The predictability time for summer, winter and the entire year (T_2 approx. 4.7 days) is longer than for transition-seasons (T_2 approx. 4.0 days for spring, T_2 approx. 3.6 days for autumn). The role of random noise and the number of data points are discussed. It is shown that a 15-year-long daily temperature series is not sufficient for reliable estimations based on Grassberger and Procaccia algorithms.Comment: 27 pages (LaTex version 2.09) and 15 figures as .ps files, e-mail: [email protected]

Statistical Laws Governing Fluctuations in Word Use from Word Birth to Word Death

We analyze the dynamic properties of 10^7 words recorded in English, Spanish and Hebrew over the period 1800--2008 in order to gain insight into the coevolution of language and culture. We report language independent patterns useful as benchmarks for theoretical models of language evolution. A significantly decreasing (increasing) trend in the birth (death) rate of words indicates a recent shift in the selection laws governing word use. For new words, we observe a peak in the growth-rate fluctuations around 40 years after introduction, consistent with the typical entry time into standard dictionaries and the human generational timescale. Pronounced changes in the dynamics of language during periods of war shows that word correlations, occurring across time and between words, are largely influenced by coevolutionary social, technological, and political factors. We quantify cultural memory by analyzing the long-term correlations in the use of individual words using detrended fluctuation analysis.Comment: Version 1: 31 pages, 17 figures, 3 tables. Version 2 is streamlined, eliminates substantial material and incorporates referee comments: 19 pages, 14 figures, 3 table

Exact solutions to chaotic and stochastic systems

We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check, analytically, some recent results about the complexity of random dynamical systems. We confirm the result that a negative Lyapunov exponent does not imply predictability in random systems. We test the effectiveness of forecasting methods in distinguishing between chaotic and random time-series. Using the explicit random functions, we can give explicit analytical formulas for the output signal in some systems with stochastic resonance. We study the influence of chaos on the stochastic resonance. We show, theoretically, the existence of a new type of solitonic stochastic resonance, where the shape of the kink is crucial. Using our models we can predict specific patterns in the output signal of stochastic resonance systems.Comment: 31 pages, 18 figures (.eps). To appear in Chaos, March 200

Languages cool as they expand: Allometric scaling and the decreasing need for new words

We analyze the occurrence frequencies of over 15 million words recorded in millions of books published during the past two centuries in seven different languages. For all languages and chronological subsets of the data we confirm that two scaling regimes characterize the word frequency distributions, with only the more common words obeying the classic Zipf law. Using corpora of unprecedented size, we test the allometric scaling relation between the corpus size and the vocabulary size of growing languages to demonstrate a decreasing marginal need for new words, a feature that is likely related to the underlying correlations between words. We calculate the annual growth fluctuations of word use which has a decreasing trend as the corpus size increases, indicating a slowdown in linguistic evolution following language expansion. This ‘‘cooling pattern’’ forms the basis of a third statistical regularity, which unlike the Zipf and the Heaps law, is dynamical in nature

Local Difference Measures between Complex Networks for Dynamical System Model Evaluation

Acknowledgments We thank Reik V. Donner for inspiring suggestions that initialized the work presented herein. Jan H. Feldhoff is credited for providing us with the STARS simulation data and for his contributions to fruitful discussions. Comments by the anonymous reviewers are gratefully acknowledged as they led to substantial improvements of the manuscript.Peer reviewedPublisher PD

Complex networks for climate model evaluation with application to statistical versus dynamical modeling of South American climate

Acknowledgments: This paper was developed within the scope of the IRTG 1740/TRP 2011/50151-0, funded by the DFG/FAPESP. Furthermore, this work has been financially supported by the Leibniz Society (project ECONS), and the Stordalen Foundation (JFD). For certain calculations, the software packages pyunicorn (Donges et al. 2013a) and igraph (Csa´rdi and Nepusz 2006) were used. The authors would like to thank Manoel F. Cardoso, Niklas Boers, and the reviewers for helpful comments on the manuscript. Open Access: This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.Peer reviewedPostprin

miRNeye: a microRNA expression atlas of the mouse eye

<p>Abstract</p> <p>Background</p> <p>MicroRNAs (miRNAs) are key regulators of biological processes. To define miRNA function in the eye, it is essential to determine a high-resolution profile of their spatial and temporal distribution.</p> <p>Results</p> <p>In this report, we present the first comprehensive survey of miRNA expression in ocular tissues, using both microarray and RNA <it>in situ </it>hybridization (ISH) procedures. We initially determined the expression profiles of miRNAs in the retina, lens, cornea and retinal pigment epithelium of the adult mouse eye by microarray. Each tissue exhibited notably distinct miRNA enrichment patterns and cluster analysis identified groups of miRNAs that showed predominant expression in specific ocular tissues or combinations of them. Next, we performed RNA ISH for over 220 miRNAs, including those showing the highest expression levels by microarray, and generated a high-resolution expression atlas of miRNAs in the developing and adult wild-type mouse eye, which is accessible in the form of a publicly available web database. We found that 122 miRNAs displayed restricted expression domains in the eye at different developmental stages, with the majority of them expressed in one or more cell layers of the neural retina.</p> <p>Conclusions</p> <p>This analysis revealed miRNAs with differential expression in ocular tissues and provided a detailed atlas of their tissue-specific distribution during development of the murine eye. The combination of the two approaches offers a valuable resource to decipher the contributions of specific miRNAs and miRNA clusters to the development of distinct ocular structures.</p

Climate Change Impact on Neotropical Social Wasps

Establishing a direct link between climate change and fluctuations in animal populations through long-term monitoring is difficult given the paucity of baseline data. We hypothesized that social wasps are sensitive to climatic variations, and thus studied the impact of ENSO events on social wasp populations in French Guiana. We noted that during the 2000 La Niña year there was a 77.1% decrease in their nest abundance along ca. 5 km of forest edges, and that 70.5% of the species were no longer present. Two simultaneous 13-year surveys (1997–2009) confirmed the decrease in social wasps during La Niña years (2000 and 2006), while an increase occurred during the 2009 El Niño year. A 30-year weather survey showed that these phenomena corresponded to particularly high levels of rainfall, and that temperature, humidity and global solar radiation were correlated with rainfall. Using the Self-Organizing Map algorithm, we show that heavy rainfall during an entire rainy season has a negative impact on social wasps. Strong contrasts in rainfall between the dry season and the short rainy season exacerbate this effect. Social wasp populations never recovered to their pre-2000 levels. This is probably because these conditions occurred over four years; heavy rainfall during the major rainy seasons during four other years also had a detrimental effect. On the contrary, low levels of rainfall during the major rainy season in 2009 spurred an increase in social wasp populations. We conclude that recent climatic changes have likely resulted in fewer social wasp colonies because they have lowered the wasps' resistance to parasitoids and pathogens. These results imply that Neotropical social wasps can be regarded as bio-indicators because they highlight the impact of climatic changes not yet perceptible in plants and other animals

Self-organization of developing embryo using scale-invariant approach

<p>Abstract</p> <p>Background</p> <p>Self-organization is a fundamental feature of living organisms at all hierarchical levels from molecule to organ. It has also been documented in developing embryos.</p> <p>Methods</p> <p>In this study, a scale-invariant power law (SIPL) method has been used to study self-organization in developing embryos. The SIPL coefficient was calculated using a centro-axial skew symmetrical matrix (CSSM) generated by entering the components of the Cartesian coordinates; for each component, one CSSM was generated. A basic square matrix (BSM) was constructed and the determinant was calculated in order to estimate the SIPL coefficient. This was applied to developing <it>C. elegans </it>during early stages of embryogenesis. The power law property of the method was evaluated using the straight line and Koch curve and the results were consistent with fractal dimensions (fd). Diffusion-limited aggregation (DLA) was used to validate the SIPL method.</p> <p>Results and conclusion</p> <p>The fractal dimensions of both the straight line and Koch curve showed consistency with the SIPL coefficients, which indicated the power law behavior of the SIPL method. The results showed that the ABp sublineage had a higher SIPL coefficient than EMS, indicating that ABp is more organized than EMS. The fd determined using DLA was higher in ABp than in EMS and its value was consistent with type 1 cluster formation, while that in EMS was consistent with type 2.</p