We show that, in general, a spacetime having a quantum group symmetry has also a scale-dependent fractal dimension which deviates from its classical value at short scales, a phenomenon that resembles what is observed in some approaches to quantum gravity. In particular, we analyze the cases of a quantum sphere and of kappa-Minkowski spacetime, the latter being relevant in the context of quantum...

A hierarchical framework is proposed to address the issues of modeling different type of words in keyword spotting (KWS). Keyword models are built at various levels according to the availability of training set resources for each individual word. The proposed approach improves the performance of KWS even when no training speech is available for the keywords. It also suggests an easier way to co...

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Fractal behavior has been observed in both ion-channel gating and neuronal spiking patterns, but a causal relationship between the two has not yet been established. Here, we examine the effects of fractal ion-channel activity in modifications of two classical neuronal models: Fitzhugh-Nagumo (FHN) and Hodgkin-Huxley (HH). For the modified FHN model, the recovery variable was represented as a po...

Moran’s Theorem is one of the milestones in Fractal Geometry. It allows the calculation of the similarity dimension of any (strict) self-similar set lying under the open set condition. Throughout a new fractal dimension we provide in the context of fractal structures, we generalize such a classical result for attractors which are required to satisfy no separation properties.

The ideas of Benôıt Mandelbrot, about the geometrical properties of sets which he called fractal, was published as late as 1975. Since then, there have for fractals, and most commonly the estimation of the fractal dimension, been found uses in the most diverse applications. Fractal geometry has been used in information theory, economics, flow dynamics and image analysis, among many different ar...

We describe an approach focussing on hierarchical composition of components during both design and development levels. We present an overview of our UML composition model which is based on well-defined composition properties. Thus we present how we have implemented a control mechanism of theses properties into Julia, an implementation of the Fractal component model. MOTS-CLÉS : UML, composition...

Fractals are self-similar and scale-invariant patterns found ubiquitously in nature. A lot of evidences implying fractal properties such as 1/f power spectrums have been also observed in resting state fMRI time series. While the traditional model of fractal behavior in resting state fMRI has been a fractional Gaussian noise, it is limited to describe the physical implication of fractal behavior...