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In this paper, we develop interval estimation methods for means of bounded random variables based on a sequential procedure such that the sampling is continued until the sample sum is no less than a prescribed threshold.
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…
Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…
An integrable theory is developed for the perturbation equations engendered from small disturbances of solutions. It includes various integrable properties of the perturbation equations: hereditary recursion operators, master symmetries,…
Instrumental variable methods are among the most commonly used causal inference approaches to deal with unmeasured confounders in observational studies. The presence of invalid instruments is the primary concern for practical applications,…
Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in…
We provide a theory to establish the existence of nonzero solutions of perturbed Hammerstein integral equations with deviated arguments, being our main ingredient the theory of fixed point index. Our approach is fairly general and covers a…
By means of topological methods, we provide new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of perturbed Hammerstein integral equations. In order to illustrate our theoretical…
We address functional uncertainty quantification for ill-posed inverse problems where it is possible to evaluate a possibly rank-deficient forward model, the observation noise distribution is known, and there are known parameter…
In this paper, we present algorithms for reconstructing an unknown compact scatterer embedded in a random noisy background medium, given measurements of the scattered field and information about the background medium and the sound profile.…
Inverse spectral problems are studied for first-order integro-differential operators on a finite interval. These problems consist in recovering some components of the kernel from one or multiple spectra. Uniqueness theorems are proved for…
In this paper, we study the inverse acoustic medium scattering problem to reconstruct the unknown inhomogeneous medium from far field patterns of scattered waves. We propose the reconstruction scheme based on the Kalman filter, which…
We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and…
Some iterative techniques are defined to solve reversible inverse problems and a common formulation is explained. Numerical improvements are suggested and tests validate the methods.
We propose to solve inverse problems involving the temporal evolution of physics systems by leveraging recent advances from diffusion models. Our method moves the system's current state backward in time step by step by combining an…
The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
This papers deals with a construction and convergence analysis of a finite difference scheme for solving time-fractional porous medium equation. The governing equation exhibits both nonlocal and nonlinear behaviour making the numerical…
It is well known that many problems in interval computation are intractable, which restricts our attempts to solve large problems in reasonable time. This does not mean, however, that all problems are computationally hard. Identifying…
An integral equation is a way to encapsulate the relationships between a function and its integrals. We develop a systematic way of describing Volterra integral equations -- specifically an algorithm that reduces any separable Volterra…
We analyze the convergence and approximation error of the inverse Born series, obtaining results that hold under qualitatively weaker conditions than previously known. Our approach makes use of tools from geometric function theory in Banach…