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The computation of coefficients of amplitude systems for Turing bifurcations is a straightforward but sometimes elaborate task, in particular for 2D or 3D wave vector lattices. The Matlab tool ampsys automates such computations for two…
In this paper we focus on the linear functionals defining an approximate version of the gradient of a function. These functionals are often used when dealing with optimization problems where the computation of the gradient of the objective…
Compared with the traditional spherical harmonics, the spherical needlets are a new generation of spherical wavelets that possess several attractive properties. Their double localization in both spatial and frequency domains empowers them…
Reflection of particles from a disordered or chaotic medium is characterized by a scattering matrix that can be represented as a superposition of resonances. Each resonance corresponds to an eigenstate inside the medium and has a width…
Reverberant sound fields are often modeled as isotropic. However, it has been observed that spatial properties change during the decay of the sound field energy, due to non-isotropic attenuation in non-ideal rooms. In this letter, a model…
In multichannel signal processing with distributed sensors, choosing the optimal subset of observed sensor signals to be exploited is crucial in order to maximize algorithmic performance and reduce computational load, ideally both at the…
We present a method for numerical computation of conformal mappings from simply or doubly connected domains onto so-called canonical domains, which in our case are rectangles or annuli. The method is based on conjugate harmonic functions…
We prove a quantum version of the Sabine law from acoustics describing the location of resonances in transmission problems. This work extends the author's previous work to a broader class of systems. Our main applications are to scattering…
We derive the $\mathcal{T}$-matrix formalism tailored for numerical analysis of second-harmonic (SH) generation from arbitrarily shaped particles made of centrosymmetric optical materials. First, the transfer matrix of a single particle is…
Embedding acoustic information into fixed length representations is of interest for a whole range of applications in speech and audio technology. Two novel unsupervised approaches to generate acoustic embeddings by modelling of acoustic…
In sound field control applications, it is commonly assumed that one has access to an accurate representation of the sound field in the region of interest. This is a problematic assumption since the reconstruction of a sound field from…
Stochastic gradient descent (SGD) is a well known method for regression and classification tasks. However, it is an inherently sequential algorithm at each step, the processing of the current example depends on the parameters learned from…
This paper considers the estimation of quantiles via a smoothed version of the stochastic gradient descent (SGD) algorithm. By smoothing the score function in the conventional SGD quantile algorithm, we achieve monotonicity in the quantile…
Deep neural networks have shown promise for music audio signal processing applications, often surpassing prior approaches, particularly as end-to-end models in the waveform domain. Yet results to date have tended to be constrained by low…
Matrix elements of spinor and principal series representations of the Lorentz group are studied in the basis of complex angular momentum (helicity basis). It is shown that matrix elements are expressed via hyperspherical functions…
We develop a compositional approach for automatic and symbolic differentiation based on categorical constructions in functional analysis where derivatives are linear functions on abstract vectors rather than being limited to scalars,…
In the harmonic oscillator representation, the Schrodinger equation has a form of a set of infinite number of algebraical equations which are labeled by the radial quantum number "n". It is shown that at n>>1 these equations are…
Several recent works have demonstrated the powerful algebraic simplifications that can be achieved for scattering amplitudes through a systematic grading of transcendental quantities. We develop these concepts to construct a minimal basis…
A stochastic conjugate gradient method for approximation of a function is proposed. The proposed method avoids computing and storing the covariance matrix in the normal equations for the least squares solution. In addition, the method…
The application of Compressive sensing approach to the speech and musical signals is considered in this paper. Compressive sensing (CS) is a new approach to the signal sampling that allows signal reconstruction from a small set of randomly…