Related papers: Laplace Transform Integration of a Baroclinic Mode…
The Laplace transform is an algebraic method that is widely used for analyzing physical systems by either solving the differential equations modeling their dynamics or by evaluating their transfer function. The dynamics of the given system…
Linear time-translation-invariant (LTI) models offer simple, yet powerful, abstractions of complex classical dynamical systems. Quantum versions of such models have so far relied on assumptions of Markovianity or an internal state-space…
This paper investigates the numerical modeling of a time-dependent heat transmission problem by the convolution quadrature boundary element method. It introduces the latest theoretical development into the error analysis of the numerical…
This paper studies computationally and theoretically attractive estimators called the Laplace type estimators (LTE), which include means and quantiles of Quasi-posterior distributions defined as transformations of general…
We propose a numerical method to spline-interpolate discrete signals and then apply the integral transforms to the corresponding analytical spline functions. This represents a robust and computationally efficient technique for estimating…
We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in…
We extend our previous work [F. Henr'iquez and J. S. Hesthaven, arXiv:2403.02847 (2024)] to the linear, second-order wave equation in bounded domains. This technique uses two widely known mathematical tools to construct a fast and efficient…
The classical Talbot method for the computation of the inverse Laplace transform is improved for the case where the transform is analytic in the complex plane except for the negative real axis. First, by using a truncated Talbot contour…
We further develop a thermal LB model for multiphase flows. In the improved model, we propose to use the FFT scheme to calculate both the convection term and external force term. The usage of FFT scheme is detailed and analyzed. By using…
We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…
Consistent initialization of the Laplace transform has been a fundamental and long-standing issue. The consistency of the L- approach has been questioned, yet it is a popular approach since the L+ approach requires a priori computation of…
Time series classification (TSC) is fundamental in numerous domains, including finance, healthcare, and environmental monitoring. However, traditional TSC methods often struggle with the inherent complexity and variability of time series…
Lattice reduction algorithms have numerous applications in number theory, algebra, as well as in cryptanalysis. The most famous algorithm for lattice reduction is the LLL algorithm. In polynomial time it computes a reduced basis with…
An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function,…
Laplace transform method has proved to be very efficient and easy to parallelize for the solution of time-dependent problems. However, the synchronization delay among processors implies an upper bound on the expectable acceleration factor,…
While many classical algorithms rely on Laplace transforms, it has remained an open question whether these operations could be implemented efficiently on quantum computers. In this work, we introduce the Quantum Laplace Transform (QLT),…
Incremental processing allows interactive systems to respond based on partial inputs, which is a desirable property e.g. in dialogue agents. The currently popular Transformer architecture inherently processes sequences as a whole,…
Over the past few decades, tremendous progress has been made in the development of particle-based discrete simulation methods versus the conventional continuum-based methods. In particular, the lattice Boltzmann (LB) method has evolved from…
Continuous time (CT) and discrete time (DT) linear time invariant (LTI) systems are commonly introduced through distinct mathematical formalisms, which can obscure their underlying dynamical equivalence. This tutorial presents a unified…
Bayesian inference tasks continue to pose a computational challenge. This especially holds for spatial-temporal modeling where high-dimensional latent parameter spaces are ubiquitous. The methodology of integrated nested Laplace…