Multiscaling and information content of natural color images

Naive scale invariance is not a true property of natural images. Natural monochrome images possess a much richer geometrical structure, which is particularly well described in terms of multiscaling relations. This means that the pixels of a given image can be decomposed into sets, the fractal components of the image, with well-defined scaling exponents [Turiel and Parga, Neural Comput. 12, 763 (2000)]. Here it is shown that hyperspectral representations of natural scenes also exhibit multiscaling properties, observing the same kind of behavior. A precise measure of the informational relevance of the fractal components is also given, and it is shown that there are important differences between the intrinsically redundant red-green-blue system and the decorrelated one defined in Ruderman, Cronin, and Chiao [J. Opt. Soc. Am. A 15, 2036 (1998)].

Scaling and Multiscaling Exponents in Networks and Flows

The main focus of this paper is on mathematical theory and methods which have a direct bearing on problems involving multiscale phenomena. Modern technology is refining measurement and data collection to spatio-temporal scales on which observed geophysical phenomena are displayed as intrinsically highly variable and intermittant heirarchical structures,e.g. rainfall, turbulence, etc. The heirarchical structure is reflected in the occurence of a natural separation of scales which collectively manifest at some basic unit scale. Thus proper data analysis and inference require a mathematical framework which couples the variability over multiple decades of scale in which basic theoretical benchmarks can be identified and calculated. This continues the main theme of the research in this area of applied probability over the past twenty years.

Multifractal wavelet filter of natural images

Natural images are characterized by the multiscaling properties of their contrast gradient, in addition to their power spectrum. In this Letter we show that those properties uniquely define an intrinsic wavelet and present a suitable technique to obtain it from an ensemble of images. Once this wavelet is known, images can be represented as expansions in the associated wavelet basis. The resulting code has the remarkable properties that it separates independent features at different resolution level, reducing the redundancy, and remains essentially unchanged under changes in the power spectrum. The possible generalization of this representation to other systems is discussed.

Coexisting spatio-temporal scales in neuroscience

In this study I propose an epistemological discussion of multiple spatio-temporal scales in neuroscience. Are such scales merely convenient levels of description of structure and function, or do they correspond to irreducible levels of brain organization? What criteria should we employ in order to reduce one level to another, or to identify levels that are not reducible to others? Should we think of these criteria as based on empirical and/or theoretical reasons? Beginning with an empirical criterion - the necessity of different experimental methodologies for the measurement of different phenomena in the same system - I summarize spatial and temporal scales currently used in neuroscience and discuss the possibility of a more general theoretical criterion. I conclude that multiscaling should be recognized as a central concept in the epistemology of neuroscience.

Spatial and temporal precipitation patterns of the Ebro River Basin, Spain

The Ebro River Basin, with around 85 000 km2 and located in NE Spain, is characterized by the high spatial heterogeneity of its geology, topography, climatology and land use. Rainfall is one of the most important climatic variables studied owing to its non-homogenous behaviour in event and intensity, which creates drought, water runoff and soil erosion with negative environmental and social consequences. In this work we characterized the rainfall variability pattern in the Ebro River Basin using universal multifractal (UM) analysis, which estimates the concentration of the data around the precipitation average (C1, codimension average), the degree of multiscaling behaviour in time (? index) and the maximum probable singularity in the rainfall distribution ( s). A spatial and temporal analysis of the UM parameters is applied to study the possible changes. With this porpoise, 60 daily rainfall series were selected from 132 synthetic series generated by Luna and Balairón (AEMet). These daily rainfall series present a length of 60 years, from 1950 to 2009. Each one of them was subdivided (1950?1970 and 1980?2009) to analyse the difference between the two periods. The range of variation of precipitation amounts and the frequency of dry events between both periods are discussed, as well as the evolution of the UM parameters through the years.

Community Structurein Soil Porous System.

Soil is well recognized as a highly complex system. The interaction and coupled physical, chemical, and biological processes and phenomena occurring in the soil environment at different spatial and temporal scales are the main reasons for such complexity. There is a need for appropriate methodologies to characterize soil porous systems with an interdisciplinary character. Four different real soil samples, presenting different textures, have been modeled as heterogeneous complex networks, applying a model known as the heterogeneous preferential attachment. An analytical study of the degree distributions in the soil model shows a multiscaling behavior in the connectivity degrees, leaving an empirically testable signature of heterogeneity in the topology of soil pore networks. We also show that the power-law scaling in the degree distribution is a robust trait of the soil model. Last, the detection of spatial pore communities, as densely connected groups with only sparser connections between them, has been studied for the first time in these soil networks. Our results show that the presence of these communities depends on the parameter values used to construct the network. These findings could contribute to understanding the mechanisms of the diffusion phenomena in soils, such as gas and water diffusion, development and dynamics of microorganisms, among others.