⎯It has been established that the class of bandpass sigma delta modulators (SDMs) with single bit quantizers could exhibit state space dynamics represented by elliptic or fractal patterns confined within trapezoidal regions. In this letter, we find that elliptical fractal patterns may also occur in bandpass SDMs with multi-bit quantizers, even for the case when the saturation regions of the mul...

Initial studies in five conscious dogs with their baroreceptors either intact or surgically isolated, demonstrate that deterministic chaos is likely to exist in both heart interval and mean arterial blood pressure. The nature of this chaotic activity is not qualitatively different between the intact and open loop preparations. To assess nonlinear dynamical behavior, we constructed phase space t...

Abstract— Fractal based CBIR is based on the self similarity fundamentals of fractals. Mathematical and natural fractals are the shapes whose roughness and fragmentation neither tend to vanish, nor fluctuate, but remain essentially unchanged as one zooms in continually and examination is refined. Since an image can be characterized by its fractal code, a fractal code can therefore be used as a ...

We study fluctuational transitions in discrete and continuous dynamical systems that have two coexisting attractors in phase space, separated by a fractal basin boundary which may be either locally disconnected or locally connected. Theoretical and numerical evidence is given to show that, in each case, the transition occurs via a unique accessible point on the boundary, both in discrete system...

BACKGROUND Knee osteoarthritis (OA) is largely attributable to chronic excessive and aberrant joint loading. The purpose of this pilot study was to quantify radiographic changes in subchondral bone after treatment with a minimally invasive joint unloading implant (KineSpring(®) Knee Implant System). METHODS Nine patients with unilateral medial knee OA resistant to nonsurgical therapy were tre...

The irregularity has been very attractive to the antenna and packaging engineers. More specifically, the self-similarity has inspired many researchers to use them for broadband designs, due to the fact that a fractal antenna is a repeated shape in different scales, which can be interpreted as a multiscale (“multi-wavelength”) radiator. In addition to this, the space filling property seems to be...

Accurate and robust image motion detection has been of substantial interest in the image processing and computer vision communities. Unfortunately, no single motion detection algorithm has been universally superior, yet biological vision systems are adept at motion detection. Recent research in neural signals have shown biological neural systems are highly responsive to signals which appear to ...

The theory of scale relativity extends Einstein's principle of relativity to scale transformations of resolutions. It is based on the giving up of the axiom of differentiability of the space-time continuum. Three consequences arise from this withdrawal: (i) The geometry of space-time must be fractal, i.e., explicitly resolutiondependent. (ii) The geodesics of the non-differentiable space-time a...

In this paper, we present a fractal (self-similar) model of acoustic propagation in porous material with rigid structure. The medium is modeled as continuous non-integer spatial dimension. basic equations acoustics are written. model, the fluid space considered while solid matrix non-fractal. fluid–structure interactions described by fractional operators time domain. resulting equation contains...

Curvature measures are an important tool in geometric measure theory and other fields of mathematics for describing the geometry of sets in Euclidean space. But the ‘classical’ concepts of curvature are not directly applicable to fractal sets. We try to bridge this gap between geometric measure theory and fractal geometry by introducing a notion of curvature for fractals. For compact sets F ⊆ R...