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In recent years, there is a growing need for processing methods aimed at extracting useful information from large datasets. In many cases the challenge is to discover a low-dimensional structure in the data, often concealed by the existence…
The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be…
In this paper, a novel decomposition method for non-stationary and nonlinear signals is proposed. This method is inspired by the adaptive wavelet filter bank of the empirical wavelet transform (EWT) and Fourier intrinsic band functions…
We propose a feature-extraction procedure based on the statistical characterization of waveforms, applied as a fast pre-processing stage in a pattern recognition task using simple artificial neural network models. This procedure involves…
This paper introduces the novel class of modulated cyclostationary processes, a class of non-stationary processes exhibiting frequency coupling, and proposes a method of their estimation from repeated trials. Cyclostationary processes also…
Clustering high-dimensional data is a critical challenge in machine learning due to the curse of dimensionality and the presence of noise. Traditional clustering algorithms often fail to capture the intrinsic structures in such data. This…
Multivariate oscillatory signals from complex systems often exhibit non-stationary dynamics and metastable regime structure, making dynamical interpretation challenging. We introduce a ``dynamical microscope'' framework that converts…
We present recent results on noise-induced transitions in a nonlinear oscillator with randomly modulated frequency. The presence of stochastic perturbations drastically alters the dynamical behaviour of the oscillator: noise can wash out a…
Clusters of wave-scattering oscillators offer the ability to passively control wave energy in elastic continua. However, designing such clusters to achieve a desired wave energy pattern is a highly nontrivial task. While the forward…
Whisking is a rhythmic and adaptive behavior that rodents use to probe and interact with their environment, and the frequency of movement reflects both sensorimotor processing and internal brain states. A robust and traditional method of…
Nonstationary spatial processes can often be represented as stationary processes on a warped spatial domain. Selecting an appropriate spatial warping function for a given application is often difficult and, as a result of this, warping…
In this paper, we consider signals with intra-wave frequency modulation. To handle this kind of signals effectively, we generalize our data-driven time-frequency analysis by using a shape function to describe the intra-wave frequency…
We consider the problem of decentralized estimation using wireless sensor networks. Specifically, we propose a novel framework based on level-triggered sampling, a non-uniform sampling strategy, and sequential estimation. The proposed…
This method solves the dual problem of blind deconvolution and estimation of the time waveform of noisy second-order cyclo-stationary (CS2) signals that traverse a Transfer Function (TF) en route to a sensor. We have proven that the…
We consider the problem of spectral clustering under group fairness constraints, where samples from each sensitive group are approximately proportionally represented in each cluster. Traditional fair spectral clustering (FSC) methods…
Technological advancements have enabled the recording of spiking activities from large neuron ensembles, presenting an exciting yet challenging opportunity for statistical analysis. This project considers the challenges from a common type…
We study here the spontaneous clustering of a submonolayer of grains under horizontal circular shaking. The clustering of grains occurs when increasing the oscillation amplitude beyond a threshold. The dense area travels in a circular…
In this paper, we present a first attempt to incorporate in the GNU Radio ecosystem a tool called CycloDSP, devoted to the analysis of complex-valued cyclostationary signals. Such signals are ubiquitous in communication and signal…
We show that the time-resolved dynamics of an underdamped harmonic oscillator can be used to do multifunctional computation, performing distinct computations at distinct times within a single dynamical trajectory. We consider the amplitude…
Variable-amplitude oscillatory shear tests are emerging as powerful tools to investigate and quantify the nonlinear rheology of amorphous solids, complex fluids and biological materials. Quite a few recent experimental and atomistic…