The estimation of the maximum expected magnitude is crucial for seismic hazard assessment. It is usually inferred via Bayesian analysis; alternatively, the size of the largest possible event can be roughly obtained from the extent of the seismogenic source and the depth of the brittle-ductile transition. However, the effectiveness of the first approach is strongly limited by catalog completeness and the intensity of recorded seismicity, so that it can be of practical use only for aftershocks, while the second is affected by extremely large uncertainties. In this article, we investigate whether it may be possible to assess the magnitude of the largest event using some statistical properties of seismic activity. Our analysis shows that, while local features are not appropriate for modeling the emergence of peaks of seismicity, some global properties (e.g., the global coefficient of variation of interevent times and the fractal dimension of epicenters) seem correlated with the largest magnitude. Unlike several scientific articles suggest, the b-value of the Gutenberg-Richter law is not observed to have a predictive power in this case, which can be explained in the light of heterogeneous tectonic settings hosting fault systems with different extension.

Fractal analysis can be properly applied to complex structures, like physical and chemical networks formed by particles or polymers, when they exhibit self-similarity over an extended range of length scales and, hence, can be profitably used not only for their morphological characterization but also for individuating possible relationships between morphology and mechanisms of aggregation and crosslinking, as well as between morphology and physical properties. Several experimental methods are available to determine the fractal dimension of gel networks, including various scattering techniques and microscopies, permeability measurements and rheology. The present study regards the self-assembly kinetics of High Methoxyl Pectin (HMP) solutions with different pectin and sucrose concentrations investigated by rheological measurements to highlight the effects of pectin and sucrose concentrations on the gel point and to evaluate the degree of compactness of the incipient gel networks through an interpretation of the viscoelastic response at the sol-gel transition

We study colloidal gels formed by competing electrostatic repulsion and short-range attraction by means of extensive numerical simulations under external shear. We show that, upon varying the repulsion strength, the gel structure and its viscoelastic properties can be largely tuned. In particular, the gel fractal dimension can be either increased or decreased with respect to mechanical equilibrium conditions. Unexpectedly, gels with stronger repulsion, despite being mechanically stiffer, are found to be less viscous with respect to purely attractive ones. We provide a microscopic explanation of these findings in terms of the influence of an underlying phase separation. Our results allow for the design of colloidal gels with desired structure and viscoelastic response by means of additional electrostatic interactions, easily controllable in experiments.

We characterize via small-angle neutron scattering the structural properties of a mixture of all-DNA particles with functionalities 4 (A) and 2 (B) constrained by design to reside close to the percolation threshold. DNA base sequences are selected such that A particles can only bind with B ones and that at the studied temperature (10 °C) all AB bonds are formed and long-lived, originating highly polydisperse persistent equilibrium clusters. The concentration dependence of the scattered intensity and its wavevector dependence is exploited to determine the fractal dimension and the size distribution of the clusters, which are found to be consistent with the critical exponents of the 3-D percolation universality class. The value of DNA nanoparticles as nanometric patchy colloids with well-defined functionality, bonding selectivity, and exquisite control of the interaction strength is demonstrated.

The fractal nature of graphs has traditionally been investigated by using the network's nodes as the basic units. Here, instead, we propose to concentrate on the graph's edges, and introduce a practical and computationally not demanding method for revealing changes in the fractal behavior of networks, and particularly for allowing distinction between mono-fractal, quasi mono-fractal, and multi-fractal structures. We show that degree homogeneity plays a crucial role in determining the fractal nature of the underlying network, and report on six different protein-protein interaction networks along with their corresponding random networks. Our analysis allows to identify varying levels of complexity in the species.

Background and purpose: During radiotherapy (RT) for head-and-neck cancer, parotid glands undergo significant anatomic, functional and structural changes which could characterize pre-clinical signs of an increased risk of xerostomia. Texture analysis is proposed to assess structural changes of parotids induced by RT, and to investigate whether early variations of textural parameters (such as mean intensity and fractal dimension) can predict parotid shrinkage at the end of treatment. Material and methods: Textural parameters and volumes of 42 parotids from 21 patients treated with intensity-modulated RT for nasopharyngeal cancer were extracted from CT images. To individuate which parameters changed during RT, a Wilcoxon signed-rank test between textural indices (first and second RT week; first and last RT week) was performed. Discriminant analysis was applied to variations of these parameters in the first two weeks of RT to assess their power in predicting parotid shrinkage at the end of RT.

BACKGROUND AND PURPOSE: During radiotherapy (RT) for head-and-neck cancer, parotid glands undergo significant anatomic, functional and structural changes which could characterize pre-clinical signs of an increased risk of xerostomia. Texture analysis is proposed to assess structural changes of parotids induced by RT, and to investigate whether early variations of textural parameters (such as mean intensity and fractal dimension) can predict parotid shrinkage at the end of treatment. MATERIAL AND METHODS: Textural parameters and volumes of 42 parotids from 21 patients treated with intensity-modulated RT for nasopharyngeal cancer were extracted from CT images. To individuate which parameters changed during RT, a Wilcoxon signed-rank test between textural indices (first and second RT week; first and last RT week) was performed. Discriminant analysis was applied to variations of these parameters in the first two weeks of RT to assess their power in predicting parotid shrinkage at the end of RT. RESULTS: A significant decrease in mean intensity (1.7HU and 3.8HU after the second and last weeks, respectively) and fractal dimension (0.016 and 0.021) was found. Discriminant analysis, based on volume and fractal dimension, was able to predict the final parotid shrinkage (accuracy of 71.4%). CONCLUSION: Textural features could be used in combination with volume to characterize structural modifications on parotid glands and to predict parotid shrinkage at the end of RT.

The paper presents an adaptive GP boosting ensemble method forthe classification of distributed homogeneous streaming data that comes from multiple locations. The approach is able to handle concept drift via change detection by employing a change detection strategy, based on self-similarity of the ensemble behavior, and measured by its fractal dimension. It is efficient since each nodeof the network works with its local streaming data, and communicate only the local model computed with the otherpeer-nodes. Furthermore, once the ensemble has been built, it isused to predict the class membership of new streams of data until concept drift is detected. Only in such a case the algorithm is executed to generate a new set of classifiers to update the current ensemble. Experimental results on a synthetic and reallife data set showed the validity of the approach in maintaining an accurate and up-to-date GP ensemble.

A well-suited approach to calculate the fractal dimension of digital images stems from the power spectrum of a fractional Brownian motion: the ratio between powers at different scales is related to the persistence parameter H and, thus, to the fractal dimension D=3-H. The signal-dependent nature of the speckle noise, however, prevents a correct estimation of fractal dimension from synthetic aperture radar (SAR) images. Here, we propose and assess a novel method to obtain D based on the multi-scale decomposition provided by the normalized Laplacian pyramid (LP), which is a bandpass representation obtained by dividing the layers of a LP by its expanded base band and is designed to force the noise to become signal independent. Extensive experiments on synthetic fractal textures, both noise free and noisy, corroborate the underlying assumptions and show the performances, in terms of both accuracy and confidence of estimation, of pyramid methods compared with the well-established method based on the wavelet transform. Preliminary results on true SAR images from ERS-1 look promising as well.

An analytical model is presented for the determination of the fractal dimensions of particles which are widely used as reinforcement in nanocomposites. The model is used to characterize the surface irregularity or roughness. It was found that fractal dimensions of both the contour and surface of particles depend only on the relative particles size ratio between secondary particles and subunits. It is proposed that, in practical applications, the fractal dimension of a certain reinforcement particle can be obtained by a combination of this model and a state-of-the-art instrument that can determine the sizes of primary and secondary particles by image analysis. It is possible to relate the fractal dimension with the adhesion and other physical and chemical properties at the interface between particles and matrix. © 1997 Kluwer Academic Publishers.