We describe segmented multiresolution analyses of [0; 1]. Such multiresolution analyses lead to segmented wavelet bases which are adapted to discontinuities, cusps, etc., at a given location 2 [0; 1]. Our approach emphasizes the idea of average-interpolation { synthesizing a smooth function on the line having prescribed boxcar averages. This particular approach leads to methods with subpixel re...

The fast dynamo growth rate for a C k+l map or flow is bounded above by topological entropy plus a 1/k correction. The proof uses techniques of random maps combined with a result of Yomdin relating curve growth to topological entropy. This upper bound implies the following anti-dynamo theorem: in C ~ systems fast dynamo action is not possible without the presence of chaos. In addition topologic...

In this paper, the applicability of the entropy method for the trend towards equilibrium for reaction-diffusion systems arising from first order chemical reaction networks is studied. In particular, we present a suitable entropy structure for weakly reversible reaction networks without detail balance condition. We show by deriving an entropy-entropy dissipation estimate that for any weakly reve...

Contrast is an important factor affecting the image quality. In order to overcome the problems of local band-limited contrast, a novel image contrast assessment method based on the property of HVS is proposed. Firstly, the image by low-pass filter is performed fast wavelet decomposition. Secondly, all levels of band-pass filtered image and its corresponding low-pass filtered image are obtained ...

In this paper, we investigate a lossy source coding problem, where an upper limit on the permitted distortion is defined for every dataset element. It can be seen as an alternative approach to rate distortion theory where a bound on the allowed average error is specified. In order to find the entropy, which gives a statistical length of source code compatible with a fixed distortion bound, a co...

Information-theoretic measures such as the entropy, cross-entropy and the KullbackLeibler divergence between two mixture models is a core primitive in many signal processing tasks. Since the Kullback-Leibler divergence of mixtures provably does not admit a closed-form formula, it is in practice either estimated using costly Monte-Carlo stochastic integration, approximated, or bounded using vari...

the mechanical aspect of entropy-exergy relationship, together with the thermal aspect usually consid-ered, leads to an extended formulation of physical exergy based on both maximum useful work and maximum useful heat that are the outcome of available energy of a thermodynamic system. this approach suggests that a mechanical entropy can be studied, in addition to the already used thermal entrop...

[1] Geotail data were used to study the long‐term averaged spatial and flow speed dependencies of the ion entropy per unit volume and per unit flux tube and the average entropy per ion. It was concluded that some process associated with the production of fast flows substantially increased the entropy of an average ion. Entropy in the fastest flows exhibited little y dependence, showing that the...