We study the dynamics of the two-point statistics of the Kraichnan ensemble which describes the transport of a passive pollutant by a stochastic turbulent flow characterized by scale invariant structure functions. The fundamental equation of this problem consists in the Fokker-Planck equation for the two-point correlation function of the density of particles performing spatially correlated Brow...

Two approaches to the combination of robust variational deconvolution with positivity constraints are considered. The first approach modifies a standard robust variational deconvolution method by carrying out a gradient descent with respect to a multiplicative perturbation, which can also be considered as gradient descent in a hyperbolic metric. The second approach is based on the representatio...

Multiplicative cascades are often used to represent the structure of turbulence. Under the action of a multiplicative cascade, the relevant variables of the system can be understood as the result of a successive transfer of information in cascade from large to small scales. However, to make this cascade transfer explicit (i.e, being able to decompose each variable as the product of larger scale...

This paper proposes the use of self-organizing maps (SOMs) to the blind source separation (BSS) problem for nonlinearly mixed signals corrupted with multiplicative noise. After an overview of some signal denoising approaches, we introduce the generic independent component analysis (ICA) framework, followed by a survey of existing neural solutions on ICA and nonlinear ICA (NLICA). We then detail...

The purpose of this paper is to define and to analyze three new sets of logarithmic morphological operators and it is focused on theoretical and practical aspects concerning the enhancement of the transmitted images and the physical absorption/transmission laws expressed within LIP (Logarithmic Image Processing) mathematical framework. Using different logarithmic image representations, an appro...

We present a set of problem frames specialized to the area of geographic applications. Problem frames describe the elements of common problems, and help a specifier understand and decompose a complex problem into simpler subproblems for which a solution is often known. We provide an overview of the main issues in geographic applications, and present twelve frames that address many of the proble...

The present article argues for what is essentially a return to the functionalist approach to investigation of memory. Two experiments demonstrate that the effects of level of processing depend on scaled meaningfulness of the material and study time. Data from those experiments along with data currently in the literature are then reanalyzed to examine the effect of repetitions. Of particular int...