Tatijana Stosic

Multifractal analysis of human retinal vessels

In this paper, it is shown that vascular structures of the human retina represent geometrical multifractals, characterized by a hierarchy of exponents rather then a single fractal dimension. A number of retinal images from the STARE database are analyzed, corresponding to both normal and pathological states of the retina. In all studied cases, a clearly multifractal behavior is observed, where capacity dimension is always found to be larger then the information dimension, which is in turn always larger then the correlation dimension, all the three being significantly lower then the diffusion limited aggregation (DLA) fractal dimension. We also observe a tendency of images corresponding to the pathological states of the retina to have lower generalized dimensions and a shifted spectrum range, in comparison with the normal cases

Anomalous behavior of the zero field susceptibility of the Ising model on the Cayley tree

It is found that the zero field susceptibility χ of the Ising model on the Cayley tree exhibits unusually weak divergence at the critical point TC. The susceptibility amplitude is found to diverge at TC proportionally to the tree generation level n, while the behavior of χ is otherwise analytic in the vicinity of TC,with the critical exponent γ=0.

RESIDUAL ENTROPY OF THE SQUARE ISING ANTIFERROMAGNET IN THE MAXIMUM CRITICAL FIELD : THE FIBONACCI MATRIX

We find the analytical expression for the residual entropy of the square Ising model with nearest-neighbour antiferromagnetic coupling J, in the maximum critical field , in terms of the Fibonacci matrix, which itself represents a self-similar, fractal object. The result coincides with the existing numerical data. By considering regular self-similar fractal objects rather than seemingly random transfer matrices, this approach opens the possibility of finding the corresponding solutions in more complicated cases, such as the antiferromagnets with longer than nearest-neighbour interactions and the three-dimensional antiferromagnets, as well as the possibility of unification of results pertinent to different lattices in two and three dimensions.

Power law correlations in time series of wild-land and forest fires in Brazil

We study temporal correlations in daily hot pixel time series detected in Brazil in the period 1998–2007, using detrended fluctuation analysis (DFA). We find that power law correlations decay following two distinct scaling regimes with exponents a 1 ≅ 0.8 and a 2 ≅ 1.3, with a crossover point at approximately 45 days. These results agree with previous studies of burned area time series of forest fires in other regions of the world and should be taken into account when modelling wild-land and forest fires in Brazil.

Ising model on the Sierpiński gasket: thermodynamic limit versus infinitesimal field

Owing to extremely slow decay of correlations, the limit H → 0 presents a poor approximation for the Ising model on the Sierpinski gasket. We present evidence of the competitive interplay between finite size scaling and thermodynamic scaling for this model, where both finite size and finite field induce an apparent phase transition. These observations may be relevant for the behavior of porous magnetic materials in real laboratory conditions.

Multifractal Properties of a Closed Contour: A Peek beyond the Shape Analysis

In recent decades multifractal analysis has been successfully applied to characterize the complex temporal and spatial organization of such diverse natural phenomena as heartbeat dynamics, the dendritic shape of neurons, retinal vessels, rock fractures, and intricately shaped volcanic ash particles. The characterization of multifractal properties of closed contours has remained elusive because applying traditional methods to their quasi-one-dimensional nature yields ambiguous answers. Here we show that multifractal analysis can reveal meaningful and sometimes unexpected information about natural structures with a perimeter well-defined by a closed contour. To this end, we demonstrate how to apply multifractal detrended fluctuation analysis, originally developed for the analysis of time series, to an arbitrary shape of a given study object. In particular, we show the application of the method to fish otoliths, calcareous concretions located in fishs inner ear. Frequently referred to as the fishs “black box, they contain a wealth of information about the fishs life history and thus have recently attracted increasing attention. As an illustrative example, we show that a multifractal approach can uncover unexpected relationships between otolith contours and size and age of fish at maturity.

An application of sample entropy to precipitation in Paraíba State, Brazil

A climate system is characterized to be a complex non-linear system. In order to describe the complex characteristics of precipitation series in Paraíba State, Brazil, we aim the use of sample entropy, a kind of entropy-based algorithm, to evaluate the complexity of precipitation series. Sixty-nine meteorological stations are distributed over four macroregions: Zona da Mata, Agreste, Borborema, and Sertão. The results of the analysis show that intricacies of monthly average precipitation have differences in the macroregions. Sample entropy is able to reflect the dynamic change of precipitation series providing a new way to investigate complexity of hydrological series. The complexity exhibits areal variation of local water resource systems which can influence the basis for utilizing and developing resources in dry areas.

Detrended fluctuation analysis and entropy-complexity causality analysis of temperatures in an urbanized mountain stream

We present the results of applying detrended fluctuation analysis (DFA) to study correlations in mountain stream temperatures over a 9-year period for impacted and unimpacted conditions. Permutation entropy and complexity are also computed for stream temperature time series at various locations characterized by varying degrees of human impact, and a graphical representation of the “complexity-entropy causality plane” is used to examine the degree of disturbance caused by human activities. Urban development such as canopy removal and urban infrastructure can lead to a higher degree of anti-persistent correlations indicated by lower values of DFA exponents. This effect is more pronounced downstream due to cumulative urbanization effects with downstream distance. Seasonal variations also influence stream temperature dynamics: less anti-persistent behavior is observed in winter months, and stronger anti-persistent correlations during summer. The position in the complexity-entropy plane, reflecting distribution of short term temperature patterns, is also affected, where most sites experience a shift towards higher entropy values afterxa0restoration, and only for one site entropy is reduced. Our results indicate the important role urbanization plays on stream evolution greatly influenced by human activities. This information may provide valuable insights for watershed management and water resources management.

Análise da variabilidade espaço temporal da chuva mensal no estado de Pernambuco utilizando o método entropia de permutação

In this work, we analyze spatial variability of rainfall dynamics on monthly scale, in the state of Pernambuco, Brazil, using Permutation Entropy. This method was introduced as a complexity measure for temporal series, considering time causality trough the symbolization technique based on comparison of neighboring values in a time series. The results show that the entropy values decrease with distance from the coast, indicating greater variability and less predictability of monthly rainfall in the regions Zona de Mata and Agreste, and smaller variability and higher predictability of monthly rainfall in the regions Sertão and Sao Francisco Valley.

Three‐dimensional multifractal analysis of trabecular bone under clinical computed tomography

Purpose: An adequate understanding of bone structural properties is critical for predicting fragility conditions caused by diseases such as osteoporosis, and in gauging the success of fracture prevention treatments. In this work we aim to develop multiresolution image analysis techniques to extrapolate high‐resolution images predictive power to images taken in clinical conditions. Methods: We performed multifractal analysis (MFA) on a set of 17 ex vivo human vertebrae clinical CT scans. The vertebræ failure loads (Symbol) were experimentally measured. We combined bone mineral density (BMD) with different multifractal dimensions, and BMD with multiresolution statistics (e.g., skewness, kurtosis) of MFA curves, to obtain linear models to predict Symbol. Furthermore we obtained short‐ and long‐term precisions from simulated in vivo scans, using a clinical CT scanner. Ground‐truth data — high‐resolution images — were obtained with a High‐Resolution Peripheral Quantitative Computed Tomography (HRpQCT) scanner. Symbol. No Caption available. Symbol. No Caption available. Results: At the same level of detail, BMD combined with traditional multifractal descriptors (Lipschitz–Hölder exponents), and BMD with monofractal features showed similar prediction powers in predicting Symbol (87%, adj. R2). However, at different levels of details, the prediction power of BMD with multifractal features raises to 92% (adj. Symbol) of Symbol. Our main finding is that a simpler but slightly less accurate model, combining BMD and the skewness of the resulting multifractal curves, predicts 90% (adj. Symbol) of Symbol. Symbol. No Caption available. Symbol. No Caption available. Symbol. No Caption available. Symbol. No Caption available. Symbol. No Caption available. Conclusions: Compared to monofractal and standard bone measures, multifractal analysis captured key insights in the conditions leading to Symbol. Instead of raw multifractal descriptors, the statistics of multifractal curves can be used in several other contexts, facilitating further research. Symbol. No Caption available.