Related papers: Weighted Birkhoff Averages and the Parameterizatio…
Quantifying and reducing uncertainty in Earth system model parameterizations is essential to improving their reliability in decision-making. Forward uncertainty propagation is used to derive parameter sensitivity but requires physically…
Nonlinearity parameter tomography leads to the problem of identifying a coefficient in a nonlinear wave equation (such as the Westervelt equation) modeling ultrasound propagation. In this paper we transfer this into frequency domain, where…
We analyse and compare several algorithms to compute numerically periodic solutions of high-dimensional dynamical systems and investigate their Floquet stability without building the monodromy matrix. The solution and its perturbation are…
Classical Fisher-information asymptotics describe the covariance of regular efficient estimators through the local quadratic approximation of the log-likelihood, and thus capture first-order geometry only. In curved models, including…
Harmonic inversion is introduced as a powerful tool for both the analysis of quantum spectra and semiclassical periodic orbit quantization. The method allows to circumvent the uncertainty principle of the conventional Fourier transform and…
We propose a two stage procedure for the estimation of the parameters of a fairly general, continuous-time stochastic volatility. An important ingredient of the proposed method is the Cuchiero-Teichmann volatility estimator, which is based…
The parametrized black hole quasinormal ringdown formalism is useful to compute quasinormal mode (QNM) frequencies if a master equation for the gravitational perturbation around a black hole has a small deviation from the Regge-Wheeler or…
We consider an undamped nonlinear hinged-hinged beam with stretching nonlinearity as an infinite dimensional hamiltonian system. We obtain analytically a quantitative Birkhoff Normal Form, via a nonlinear coordinate transformation that…
Searching recurrent patterns in complex systems with high-dimensional phase spaces is an important task in diverse fields. In the current work, an improved scheme is proposed to accelerate the recently designed variational approach for…
Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…
We propose a stochastic variance-reduced cubic regularized Newton algorithm to optimize the finite-sum problem over a Riemannian submanifold of the Euclidean space. The proposed algorithm requires a full gradient and Hessian update at the…
In this paper we present a frequentist-Bayesian hybrid method for estimating covariances of unfolded distributions using pseudo-experiments. The method is compared with other covariance estimation methods using the unbiased Rao-Cramer bound…
While General Fractional Calculus has successfully expanded the scope of memory operators beyond power-laws, standard formulations remain predominantly restricted to the half-line via Riemann-Liouville or Caputo definitions. This constraint…
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…
A set of semi-analytical techniques based on Fourier analysis is used to solve wave scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are newly developed conformal mapping…
In this paper, we consider the problem of recovering a compactly supported multivariate function from a collection of pointwise samples of its Fourier transform taken nonuniformly. We do this by using the concept of weighted Fourier frames.…
The phase-amplitude framework extends the classical phase reduction method by incorporating amplitude coordinates (or isostables) to describe transient dynamics transverse to the limit cycle in a simplified form. While the full set of…
A trajectory $u_n := F^n(u_0), n = 0,1,2, \dots $ is quasiperiodic if the trajectory lies on and is dense in some $d$-dimensional torus, and there is a choice of coordinates on the torus $\mathbb{T}$ for which $F$ has the form $F(\theta) =…
We present a novel family of continuous, linear time-frequency transforms adaptable to a multitude of (nonlinear) frequency scales. Similar to classical time-frequency or time-scale representations, the representation coefficients are…
This paper introduces a weighted generalized inverse framework for Fourier extensions, designed to suppress spurious oscillations in the extended region while maintaining high approximation accuracy on the original interval. By formulating…