Related papers: Sampling in the Euclidean Motion Group and a Probl…
This paper studies the asymptotic behavior of eigenvalues of random abelian G-circulant matrices, that is, matrices whose structure is related to a finite abelian group G in a way that naturally generalizes the relationship between…
In numerous applications data are observed at random times and an estimated graph of the spectral density may be relevant for characterizing and explaining phenomena. By using a wavelet analysis, one derives a nonparametric estimator of the…
In this paper we propose a wavelet-based methodology for estimation and variable selection in partially linear models. The inference is conducted in the wavelet domain, which provides a sparse and localized decomposition appropriate for…
Graph representation learning is a ubiquitous task in machine learning where the goal is to embed each vertex into a low-dimensional vector space. We consider the bipartite graph and formalize its representation learning problem as a…
We consider inverse problems in Hilbert spaces under correlated Gaussian noise and use a Bayesian approach to find their regularised solution. We focus on mildly ill-posed inverse problems with the noise being generalised derivative of…
We present a Machine Learning approach to solve electronic quantum transport equations of one-dimensional nanostructures. The transmission coefficients of disordered systems were computed to provide training and test datasets to the…
We study gravitational-wave production from bubble collisions in a cosmic first-order phase transition, focusing on the possibility of model separation by the bubble nucleation rate dependence of the resulting gravitational-wave spectrum.…
We present some applications of general harmonic/wavelet analysis approach (generalized coherent states, wavelet packets) to numerical/analytical calculations in (nonlinear) quasiclassical/quantum beam dynamics problems. (Naive) deformation…
Continuing from Part 1 (Hern\'andez \emph{et al.}, \emph{arXiv:2108.12395}, 2021), a generalized quasilinear (GQL) approximation is studied in turbulent channel flow using a flow decomposition defined with spanwise Fourier modes: the flow…
We construct the general permutation invariant Gaussian 2-matrix model for matrices of arbitrary size $D$. The parameters of the model are given in terms of variables defined using the representation theory of the symmetric group $S_D$. A…
We develop an alternative boson sampling model operating on single-photon states followed by linear interferometry and Gaussian measurements. The hardness proof for simulating such continuous-variable measurements is established in two main…
The brain is composed of billions of neurons with virtually endless morphologies and ion channel compositions, resulting in unique extracellular waveforms. Nevertheless, almost all neuronal morphologies can be reduced to a simple…
The kinematics of a robot manipulator are described in terms of the mapping connecting its joint space and the 6-dimensional Euclidean group of motions $SE(3)$. The associated Jacobian matrices map into its Lie algebra $\mathfrak{se}(3)$,…
Computer vision is hard because of a large variability in lighting, shape, and texture; in addition the image signal is non-additive due to occlusion. Generative models promised to account for this variability by accurately modelling the…
This paper gives an overview of a theory for modelling the interaction between geometric image transformations and receptive field responses for a visual observer that views objects and spatio-temporal events in the environment. This…
We suggest an adaptive sampling rule for obtaining information from noisy signals using wavelet methods. The technique involves increasing the sampling rate when relatively high-frequency terms are incorporated into the wavelet estimator,…
Bayesian estimation of Gaussian graphical models has proven to be challenging because the conjugate prior distribution on the Gaussian precision matrix, the G-Wishart distribution, has a doubly intractable partition function. Recent…
We develop Gaussian approximations for high-dimensional vectors formed by second-order $U$- and $V$-statistics whose kernels depend on sample size under independent but not identically distributed (i.n.i.d.) sampling. Our results hold…
Interpretability is a critical factor in applying complex deep learning models to advance the understanding of brain disorders in neuroimaging studies. To interpret the decision process of a trained classifier, existing techniques typically…
Here, we investigate the physical mechanisms that may enable squeezing a complex electromagnetic field distribution through a narrow and/or partially obstructed region with little amplitude and phase distortions. Following our recent works,…