相关论文: Non-equilibrium allele frequency spectra via spect…

Semilinear, $N-$dimensional stochastic differential equations (SDEs) driven by additive L\'evy noise are investigated. Specifically, given $\alpha\in\left(\frac{1}{2},1\right)$, the interest is on SDEs driven by $2\alpha-$stable,…

Spectral methods provide an elegant and efficient way of numerically solving differential equations of all kinds. For smooth problems, truncation error for spectral methods vanishes exponentially in the infinity norm and $L_2$-norm.…

The site frequency spectrum (SFS) is a widely used summary statistic of genomic data. Motivated by recent evidence for the role of neutral evolution in cancer, we investigate the SFS of neutral mutations in an exponentially growing…

Efficient and accurate spectral solvers for nonlocal models in any spatial dimension are presented. The approach we pursue is based on the Fourier multipliers of nonlocal Laplace operators introduced in a previous work. It is demonstrated…

We introduce a new numerical method for solving time-harmonic acoustic scattering problems. The main focus is on plane waves scattered by smoothly varying material inhomogeneities. The proposed method works for any frequency $\omega$, but…

A new type of ensemble Kalman filter is developed, which is based on replacing the sample covariance in the analysis step by its diagonal in a spectral basis. It is proved that this technique improves the aproximation of the covariance when…

Fleming-Viot diffusions are widely used stochastic models for population dynamics which extend the celebrated Wright-Fisher diffusions. They describe the temporal evolution of the relative frequencies of the allelic types in an ideally…

The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational…

A novel approach towards the spectral analysis of stationary random bivariate signals is proposed. Using the Quaternion Fourier Transform, we introduce a quaternion-valued spectral representation of random bivariate signals seen as…

Physics-informed neural networks (PINNs) have great potential for flexibility and effectiveness in forward modeling and inversion of seismic waves. However, coordinate-based neural networks (NNs) commonly suffer from the "spectral bias"…

A numerical study of the Einstein field equations, based on the 3+1 foliation of the spacetime, is presented. A pseudo-spectral technique has been employed for simulations in vacuum, within two different formalisms, namely the…

We consider a population model where individuals behave independently from each other and whose genealogy is described by a chronological tree called splitting tree. The individuals have i.i.d. (non-exponential) lifetime durations and give…

Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…

Spectral sampling is associated with the group of unitary transformations acting on matrices in much the same way that simple random sampling is associated with the symmetric group acting on vectors. This parallel extends to symmetric…

Aims. The main goal of this paper is to present an accurate and efficient numerical strategy for solving the radiative transfer problem for polarised radiation in strong resonance lines forming out of local thermodynamic equilibrium, taking…

The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models, is a method for solving integrable partial differential equations governing wave propagation in certain nonlinear media. The NFT…

We consider the inverse problem of determining the fragmentation rate from noisy measurements in the growth-fragmentation equation. We use Fourier transform theory on locally compact groups to treat this problem for general fragmentation…

We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite…

We introduce a novel spectral element method based on the ultraspherical spectral method and the hierarchical Poincar\'{e}-Steklov scheme for solving second-order linear partial differential equations on polygonal domains with unstructured…

A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse problems aim at solving an elliptic partial differential…