The multi-fractal structure of contrast changes in natural images: from sharp edges to textures

We present a formalism that leads very naturally to a hierarchical description of the different contrast structures in images, providing precise definitions of sharp edges and other texture components. Within this formalism, we achieve a decomposition of pixels of the image in sets, the fractal components of the image, such that each set only contains points characterized by a fixed stregth of the singularity of the contrast gradient in its neighborhood. A crucial role in this description of images is played by the behavior of contrast differences under changes in scale. Contrary to naive scaling ideas where the image is thought to have uniform transformation properties \cite{Fie87}, each of these fractal components has its own transformation law and scaling exponents. A conjecture on their biological relevance is also given.Comment: 41 pages, 8 figures, LaTe

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 work we show that those properties uniquely define an {\em 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.Comment: 4 pages, 4 figures, RevTe

Preface "Nonlinear processes in oceanic and atmospheric flows"

Nonlinear phenomena are essential ingredients in many oceanic and atmospheric processes, and successful understanding of them benefits from multidisciplinary collaboration between oceanographers, meteorologists, physicists and mathematicians. The present Special Issue on ``Nonlinear Processes in Oceanic and Atmospheric Flows'' contains selected contributions from attendants to the workshop which, in the above spirit, was held in Castro Urdiales, Spain, in July 2008. Here we summarize the Special Issue contributions, which include papers on the characterization of ocean transport in the Lagrangian and in the Eulerian frameworks, generation and variability of jets and waves, interactions of fluid flow with plankton dynamics or heavy drops, scaling in meteorological fields, and statistical properties of El Ni\~no Southern Oscillation.Comment: This is the introductory article to a Special Issue on "Nonlinear Processes in Oceanic and Atmospheric Flows'', published in the journal Nonlinear Processes in Geophysics, where the different contributions are summarized. The Special Issue itself is freely available from http://www.nonlin-processes-geophys.net/special_issue103.htm

Numerical simulation of a binary communication channel: Comparison between a replica calculation and an exact solution

The mutual information of a single-layer perceptron with $N$ Gaussian inputs and $P$ deterministic binary outputs is studied by numerical simulations. The relevant parameters of the problem are the ratio between the number of output and input units, $\alpha = P/N$, and those describing the two-point correlations between inputs. The main motivation of this work refers to the comparison between the replica computation of the mutual information and an analytical solution valid up to $\alpha \sim O(1)$. The most relevant results are: (1) the simulation supports the validity of the analytical prediction, and (2) it also verifies a previously proposed conjecture that the replica solution interpolates well between large and small values of $\alpha$.Comment: 6 pages, 8 figures, LaTeX fil

Smooth actions of connected compact Lie groups with a free point are determined by two vector fields

Consider a smooth action $\mathbf G\times M \rightarrow M$ of a compact connected Lie group $\mathbf G$ on a connected manifold $M$. Assume the existence of a point of $M$ whose isotropy group has a single element (free point). Then we prove that there exist two complete vector field $X,X_1$ such that their group of automorphisms equals $\mathbf G$ regarded as a group of diffeomorphisms of $M$ (the existence of a free point implies that the action of $\mathbf G$ is effective). Moreover, some examples of effective actions with no free point where this result fails are exhibited.Comment: 30 pages, no figures. V2: Major revision. Exposition improved and added a new section presenting some open question

Using empirical mode decomposition to correlate paleoclimatic time-series

International audienceDetermination of the timing and duration of paleoclimatic events is a challenging task. Classical techniques for time-series analysis rely too strongly on having a constant sampling rate, which poorly adapts to the uneven time recording of paleoclimatic variables; new, more flexible methods issued from Non-Linear Physics are hence required. In this paper, we have used Huang's Empirical Mode Decomposition (EMD) for the analysis of paleoclimatic series. We have studied three different time series of temperature proxies, characterizing oscillation patterns by using EMD. To measure the degree of temporal correlation of two variables, we have developed a method that relates couples of modes from different series by calculating the instantaneous phase differences among the associated modes. We observed that when two modes exhibited a constant phase difference, their frequencies were nearly equal to that of Milankovich cycles. Our results show that EMD is a good methodology not only for synchronization of different records but also for determination of the different local frequencies in each time series. Some of the obtained modes may be interpreted as the result of global forcing mechanisms

An optimized algorithm for the evaluation of local singularity exponents in digital signals

International audienceRecent works show that the determination of singularity exponents in images can be useful to assess their information content, and in some cases they can cast additional information about underlying physical processes. However, the concept of singularity exponent is associated to differential calculus and thus cannot be easily translated to a digital context, even using wavelets. In this work we show that a recently patented algorithm allows obtaining precise, meaningful values of singularity exponents at every point in the image by the use of a discretized combinatorial mask, which is an extension of a particular wavelet basis. This mask is defined under the hypothesis that singularity exponents are a measure not only of the degree of regularity of the image, but also of the reconstructibility of a signal from their points

Ventajas y desventajas de la aplicación de la técnica de HR-ICP-MS al análisis inorgánico de aguas en terrenos volcánicos

La técnica de ICP-MS ha supuesto un gran avance en el análisis de aguas en los últimos decenios tal y como recogen las normativas al respecto en Europa, Estados Unidos, etc., habiéndose convertido en una técnica de referencia particularmente en el tema de calidad del agua. La alta resolución aplicada a la ICP-MS reduce considerablemente las interferencias y su combinación con detectores aptos para concentraciones mayoritarias hace que se disponga de una herramienta analítica muy competitiva que permite determinar simultáneamente elementos mayoritarios y trazas, incluidos halógenos (Cl, Br, I), y además relaciones isotópicas (ej., Li y B). Estos aproximadamente 60 parámetros geoquímicos permiten una caracterización exhaustiva de las aguas para temas de calidad y también ayudan a discernir más fácilmente el origen y el tránsito de las aguas a través de diferentes terrenos volcánicos. Por otra parte, la HR-ICP-MS es de gran aplicación a la determinación de los aportes geoquímicos volcanogénicos a los balances biogeoquímicos regionales, como por ejemplo de los materiales piroclásticos, a través del análisis de lixiviados procedentes de la simulación de la interacción del agua con estos productos eruptivos. En este trabajo se exponen los pros y contras de la aplicación de la HR-ICP-MS a aguas en problemáticas volcanogénicas a través de diferentes ejemplos (Islandia, Argentina, Chile, etc.). Agradecemos la asistencia del Servicio labGEOTOP (infraestructura cofinanciada por FEDER-UE, Ref. CSIC08-4E-001) del ICTJA-CSIC. La financiación fue proporcionada por QUECA (MINECO, CGL2011-23307). Este estudio se llevó a cabo en el marco del Grupo Reconocido GEOPAM (2014 SGR 869).La financiación fue proporcionada por QUECA (MINECO, CGL2011-23307). Este estudio se llevó a cabo en el marco del Grupo Reconocido GEOPAM (2014 SGR 869).Peer Reviewe