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A wavelet transform spectrum analyzer operating in real time within the frequency range 3X10^(-5) - 1.3X10^5 Hz has been implemented on a low-cost Digital Signal Processing board operating at 150MHz. The wavelet decomposition of the signal…
We conjecture that chaotic resonance modes in scattering systems are a product of a conditionally invariant measure from classical dynamics and universal exponentially distributed fluctuations. The multifractal structure of the first factor…
Multivariate data sources with components of different information value seem to appear frequently in practice. Models in which the components change their homogeneity at different times are of significant importance. The fact whether any…
Characteristic scale is a notion that pervades the geophysical sciences, but it has no widely accepted precise definition. The wavelet transform decomposes a time series into coefficients that are associated with different scales. The…
This paper is concerned with an inverse wavenumber/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but…
In this work, we propose a new detector function based on wavelet transform to discriminate between turbulent and non-turbulent regions in an intermittent velocity signal. The derivative-based detector function, which is commonly used in…
Due to the vulnerability of the Caribbean islands to the climate change issue, it is important to investigate the behavior of rainfall. In addition, the soil of the French West Indies Islands has been contaminated by an insecticide…
We achieve the multifractal analysis of a class of complex valued statistically self-similar continuous functions. For we use multifractal formalisms associated with pointwise oscillation exponents of all orders. Our study exhibits new…
Identification of a transient gravitational-wave signal embedded into non-stationary noise requires the analysis of time-dependent spectral components in the resulting time series. The time-frequency distribution of the signal power can be…
Oscillatory processes are central for the understanding of the neural bases of cognition and behaviour. To analyse these processes, time-frequency (TF) decomposition methods are applied and non-parametric cluster-based statistical procedure…
Over the past three decades, describing the reality surrounding us using the language of complex networks has become very useful and therefore popular. One of the most important features, especially of real networks, is their complexity,…
Asymptotic homogenisation is considered for problems with integral constraints imposed on a slowly-varying microstructure; an insulator with an array of perfectly dielectric inclusions of slowly varying size serves as a paradigm. Although…
Multivariate time series forecasting plays a crucial role in various real-world applications. Significant efforts have been made to integrate advanced network architectures and training strategies that enhance the capture of temporal…
We review the time evolution of wavepackets at the metal-insulator transition in two- and three-dimensional disordered systems. The importance of scale invariance and multifractal eigenfunction fluctuations is stressed. The implications of…
Using graphs to model irregular information domains is an effective approach to deal with some of the intricacies of contemporary (network) data. A key aspect is how the data, represented as graph signals, depend on the topology of the…
Previous studies showed that hydro-climate processes are stochastic and complex systems, and it is difficult to discover the hidden patterns in the all non-stationary data and thoroughly understand the hydro-climate relationships. For the…
Detrended fluctuation analysis (DFA) is a scaling analysis method used to estimate long-range power-law correlation exponents in noisy signals. Many noisy signals in real systems display trends, so that the scaling results obtained from the…
Detecting oscillations in solar and stellar time series is complicated by non-stationary red noise and evolving background emission. Methods based on detrending and AR(1)-based wavelet analysis can introduce spurious periodicities and do…
Complex systems are usually represented as an intricate set of relations between their components forming a complex graph or network. The understanding of their functioning and emergent properties are strongly related to their structural…
Bayesian inference of gravitational wave signals is subject to systematic error due to modelling uncertainty in waveform signal models, coined approximants. A growing collection of approximants are available which use different approaches…