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We introduce a wide family of stochastic processes that are obtained as sums of self-similar localized "waveforms" with multiplicative intensity in the spirit of the Richardson cascade picture of turbulence. We establish the convergence and…
A study of correlations in tractable multiparticle cascade models in terms of wavelets reveals many promising features. The selfsimilar construction of the wavelet basis functions and their multiscale localization properties provide a new…
Humans naturally obtain intuition about the interactions between and the stability of rigid objects by observing and interacting with the world. It is this intuition that governs the way in which we regularly configure objects in our…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
We develop a statistical theory of waveform shaping of incident waves that aim to efficiently deliver energy at weakly lossy targets which are embedded inside chaotic enclosures. Our approach utilizes the universal features of chaotic…
Localized rain events have been found to follow power-law distributions over several decades, suggesting parallels between precipitation and seismic activity [O. Peters et al., PRL 88, 018701 (2002)]. Similar power laws can be generated by…
Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and…
Most time series observed in practice exhibit time-varying trend (first-order) and autocovariance (second-order) behaviour. Differencing is a commonly-used technique to remove the trend in such series, in order to estimate the time-varying…
Wavelets provide the flexibility to analyse stochastic processes at different scales. Here, we apply them to multivariate point processes as a means of detecting and analysing unknown non-stationarity, both within and across data streams.…
The topic of this paper is the presentation of a new network model designed for networks consisting of spatial objects. This model allows the development of more advance representations of systems of networked objects and the study of…
We propose a simple method to visualize spatio-temporal correlation between scales using wavelets, and apply it to two typical spatio-temporally chaotic systems, namely to coupled complex Ginzburg-Landau oscillators with diffusive…
Continuous time branching models are used to create random fractals in a Euclidean space, whose Hausdorff dimension is controlled by an input parameter. Finite realizations are applied in modelling the set of sites visited in models of…
We develop a mesoscopic modeling framework for diffusion in a crowded environment, particularly targeting applications in the modeling of living cells. Through homogenization techniques we effectively coarse-grain a detailed microscopic…
A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
Dynamic modulation of material properties in space and time enables powerful control over wave propagation, yet existing theories largely rely on idealized, nondispersive models. In realistic media, frequency dispersion can strongly reshape…
This chapter is dedicated to recent developments in the field of wavelet analysis for scattered data. We introduce the concept of samplets, which are signed measures of wavelet type and may be defined on sets of arbitrarily distributed data…
We introduce a mean-field framework for the study of systems of interacting particles sharing a conserved quantity. The work generalises and unites the existing fields of asset-exchange models, often applied to socio-economic systems, and…
The incorporation of particle inertia into the usual mean field theory for particle aggregation and fragmentation in fluid flows is still an unsolved problem. We therefore suggest an alternative approach that is based on the dynamics of…
We propose a generative model for the spatio-temporal distribution of high dimensional categorical observations. These are commonly produced by robots equipped with an imaging sensor such as a camera, paired with an image classifier,…
This is a brief introduction to fractals, multifractals and wavelets in an accessible way, in order that the founding ideas of those strange and intriguing newcomers to science as fractals may be communicated to a wider public. Fractals are…