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Evidence of deterministic components in the apparent randomness of GRBs: clues of a chaotic dynamic.

ABSTRACT: Prompt ?-ray emissions from gamma-ray bursts (GRBs) exhibit a vast range of extremely complex temporal structures with a typical variability time-scale significantly short - as fast as milliseconds. This work aims to investigate the apparent randomness of the GRB time profiles making extensive use of nonlinear techniques combining the advanced spectral method of the Singular Spectrum Analysis (SSA) with the classical tools provided by the Chaos Theory. Despite their morphological complexity, we detect evidence of a non stochastic short-term variability during the overall burst duration - seemingly consistent with a chaotic behavior. The phase space portrait of such variability shows the existence of a well-defined strange attractor underlying the erratic prompt emission structures. This scenario can shed new light on the ultra-relativistic processes believed to take place in GRB explosions and usually associated with the birth of a fast-spinning magnetar or accretion of matter onto a newly formed black hole.

SUBMITTER: Greco G

PROVIDER: S-EPMC3216577 | biostudies-literature | 2011

REPOSITORIES: biostudies-literature

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Evidence of deterministic components in the apparent randomness of GRBs: clues of a chaotic dynamic.

Greco G G Rosa R R Beskin G G Karpov S S Romano L L Guarnieri A A Bartolini C C Bedogni R R

Scientific reports 20110914

Prompt γ-ray emissions from gamma-ray bursts (GRBs) exhibit a vast range of extremely complex temporal structures with a typical variability time-scale significantly short - as fast as milliseconds. This work aims to investigate the apparent randomness of the GRB time profiles making extensive use of nonlinear techniques combining the advanced spectral method of the Singular Spectrum Analysis (SSA) with the classical tools provided by the Chaos Theory. Despite their morphological complexity, we ...[more]

PMID: 22355609

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Project description:BackgroundWhen assessing connectivity, it is crucial to rely on accurate modeling frameworks that consider species movement preferences and patterns. One important aspect is the level of randomness or unpredictability in the route selection. In this respect, traditional approaches (based on least-cost path or circuit theory) consider species movements unrealistically as totally deterministic or as totally random. A recent approach (randomized shortest path) advocates for choosing intermediate levels of randomness through a single parameter. This parameter may be optimized by validating connectivity surfaces developed from different levels of randomness against observed movement data. However, connectivity models are seldom validated, and it is still unclear how to approach this task. To address this knowledge gap, this paper aims at comparing different validation methods to infer the optimal randomness level in connectivity studies. Additionally, we aimed to disentangle the practical consequences of applying traditional connectivity approaches versus using an optimized level of movement randomness when delineating corridors.MethodsThese objectives were accomplished through the study case of the Iberian lynx, an endangered species whose maintenance and recovery depend on the current connectivity among its population nuclei. We firstly determined a conductance surface based on point selection functions accounting for the behavioral state (territorial or exploratory) of individuals. Secondly, we identified the level of randomness that better fits lynxes' movements with independent GPS locations and different validation techniques. Lastly, we delineated corridors between lynx population nuclei through a) the randomized shortest path approach and the extreme and optimal levels of randomness of each validation method, and b) the traditional connectivity approaches.ResultsAccording to all used validation methodologies, models with intermediate levels of randomness outperformed those with extreme randomness levels representing totally deterministic or random movements. We found differences in the optimal randomness level among validation methods but similar results in the delineation of corridors. Our results also revealed that models with extreme randomness levels (deterministic and random walk) of the randomized path approach provided equivalent corridor networks to those from traditional approaches. Moreover, these corridor networks calculated with traditional approaches showed notable differences in patterns from the corridor network calculated with an optimized randomness level.ConclusionsHere we presented a connectivity model with a solid biological basis that calibrates the level of movement randomness and is supported by comprehensive validation methods. It is thus a step forward in the search and evaluation of connectivity approaches that lead to improved, efficient, and successful management actions.

Project description:AbstractThe correlated random walk paradigm is the dominant conceptual framework for modeling animal movement patterns. Nonetheless, we do not know whether the randomness is apparent or actual. Apparent randomness could result from individuals reacting to environmental cues and their internal states in accordance with some set of behavioral rules. Here, we show how apparent randomness can result from one simple kind of algorithmic response to environmental cues. This results in an exponential step-length distribution in homogeneous environments and in generalized stretched exponential step-length distributions in more complex fractal environments. We find support for these predictions in the movement patterns of the Australian bull ant Myrmecia midas searching on natural surfaces and on artificial uniform and quasi-fractal surfaces. The bull ants spread their search significantly farther on the quasi-fractal surface than on the uniform surface, showing that search characteristics differed as a function of the substrate on which ants are searching. Further tentative support comes from a re-analysis of Australian desert ants Melophorus bagoti moving on smoothed-over sand and on a more strongly textured surface. Our findings call for more experimental studies on different surfaces to test the surprising predicted linkage between fractal dimension and the exponent in the step-length distribution.Significance statementAnimal search patterns often appear to be irregular and erratic. This behavior is captured by random walk models. Despite their considerable successes, extrapolation and prediction beyond observations remain questionable because the true nature and interpretation of the randomness in these models have until now been elusive. Here, we show how apparent randomness can result from simple algorithmic responses to environmental cues. Distinctive predictions from our theory find support in analyses of the search patterns of two species of Australian ants.

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Evidence of deterministic components in the apparent randomness of GRBs: clues of a chaotic dynamic.

Publications

Evidence of deterministic components in the apparent randomness of GRBs: clues of a chaotic dynamic.

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