相关论文: Random Wavelet Series: Theory and Applications
Random shapes arise naturally in many contexts. The topological and geometric structure of such objects is interesting for its own sake, and also for applications. In physics, for example, such objects arise naturally in quantum gravity, in…
Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…
Three recently suggested random matrix ensembles (RME) are linked together by an exact mapping and plausible conjections. Since it is known that in one of these ensembles the eigenvector statistics is multifractal, we argue that all three…
All random wave fields possess a network of phase singularities. We show that while the phase statistics within speckle patterns is generic, the statistics of the motion of phase singularities differs substantially for diffusive and…
Random matrix theory (RMT) provides a framework to study the spectral fluctuations in physical systems. RMT is capable of making predictions for the fluctuations only after the removal of the secular properties of the spectrum. Spectral…
The goal of this tutorial is to promote interest in the study of random Boolean networks (RBNs). These can be very interesting models, since one does not have to assume any functionality or particular connectivity of the networks to study…
We report results of sumulation of wave turbulence. Both inverse and direct cascades are observed. The definition of "mesoscopic turbulence" is given. This is a regime when the number of modes in a system involved in turbulence is high…
The phenomenology of the scaling behavior of higher order structure functions of velocity differences across a scale $R$ in turbulence should be built around the irreducible representations of the rotation symmetry group. Every irreducible…
We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The…
Wavelet sets that are finite unions of convex sets are constructed in $\mathbb R^n$, $n\geq 2$, for dilation by any expansive matrix that has a power equal to a scalar times the identity and also has all singular values greater than $\sqrt…
Analytical methods for finding moments of random Vandermonde matrices with entries on the unit circle are developed. Vandermonde Matrices play an important role in signal processing and wireless applications such as direction of arrival…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…
In this paper high resolution wave probe records are examined using wavelet techniques with a view to determining the sources and relative contributions of capillary wave energy along representative wind wave forms. Wavelets enable…
Multiscale correlation functions in high Reynolds number experimental turbulence, numerical simulations and synthetic signals are investigated. Fusion Rules predictions as they arise from multiplicative, almost uncorrelated, random…
We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
It is shown that a random binary process with impulse-like autocorrelation can be generated by randomizing the length of symbols occurring in a random Bernoulli process. Such randomization is achieved by random (or judiciously designed…
Time-series classification is essential across diverse domains, including medical diagnosis, industrial monitoring, financial forecasting, and human activity recognition. The Rocket algorithm has emerged as a simple yet powerful method,…
Wavelets are known to be closely related to atomic orbital. A new approach of 2D, 3D and multidimensional wavelet system is proposed from a paralell with anti-symmetric systems of several isolated particles. The theory of fermionic states…
We study radial waves in (2+1)-dimensional noncommutative scalar field theory, using operatorial methods. The waves propagate along a discrete radial coordinate and are described by finite series deformations of Bessel-type functions. At…