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Source apportionment analysis, which aims to quantify the attribution of observed concentrations of multiple air pollutants to specific sources, can be formulated as a non-negative matrix factorization (NMF) problem. However, NMF is…

Statistics Theory · Mathematics 2025-10-08 Bora Jin , Abhirup Datta

The paper considers the wave equation, with constant or variable coefficients in $\R^n$, with odd $n\geq 3$. We study the asymptotics of the distribution $\mu_t$ of the random solution at time $t\in\R$ as $t\to\infty$. It is assumed that…

Mathematical Physics · Physics 2007-05-23 T. V. Dudnikova , A. I. Komech , N. E. Ratanov , Yu. M. Suhov

This study addresses the inverse source problem for the fractional diffusion-wave equation, characterized by a source comprising spatial and temporal components. The investigation is primarily concerned with practical scenarios where data…

Numerical Analysis · Mathematics 2025-04-22 Lingyun Qiu , Jiwoon Sim

In this paper, we investigate the inverse problem of determining an unknown time-dependent source term in a semilinear pseudo-parabolic equation with variable coefficients and a Dirichlet boundary condition. The unknown source term is…

Analysis of PDEs · Mathematics 2026-02-19 Karel Van Bockstal , Khonatbek Khompysh , Arshyn Altybay

This paper is concerned with the study of interaction of waves originating from the Riemann problem centred at two different points for a system of equations modelling propagation of elastic waves. The system consists of two equations for…

Analysis of PDEs · Mathematics 2024-08-20 Kayyunnapara Divya Joseph

This paper studies an inverse source problem for a viscoelastic membrane, where the material's memory effect is characterized by the Riemann-Liouville fractional derivative. The problem is to recover the unknown source term from the limited…

Numerical Analysis · Mathematics 2026-02-12 Zhiwei Yang , Yikan Liu

We consider point sources in hyperbolic equations discretized by finite differences. If the source is stationary, appropriate source discretization has been shown to preserve the accuracy of the finite difference method. Moving point…

Numerical Analysis · Mathematics 2022-01-24 Ylva Ljungberg Rydin , Martin Almquist

A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…

Numerical Analysis · Mathematics 2020-04-10 Zhaoxing Li , Yanfang Liu , Jiguang Sun , Liwei Xu

Nonlinear observers based on the well-known concept of minimum energy estimation are discussed. The approach relies on an output injection operator determined by a Hamilton-Jacobi-Bellman equation and is subsequently approximated by a…

Optimization and Control · Mathematics 2020-03-17 Tobias Breiten , Karl Kunisch

An inverse source problem for the heat equation is considered. Extraction formulae for information about the time and location when and where the unknown source of the equation firstly appeared are given from a single lateral boundary…

Analysis of PDEs · Mathematics 2010-02-16 Masaru Ikehata

We consider a system in which two nodes take correlated measurements of a random source with time-varying and unknown statistics. The observations of the source at the first node are to be losslessly replicated with a given probability of…

Information Theory · Computer Science 2016-10-27 Fangzhou Chen , Bin Li , Can Emre Koksal

An observer-based Hamiltonian identification algorithm for quantum systems is proposed. For the 2-level case an exponential convergence result based on averaging arguments and some relevant transformations is provided. The convergence for…

Mathematical Physics · Physics 2007-05-23 Mazyar Mirrahimi , Pierre Rouchon

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…

Systems and Control · Computer Science 2019-03-01 Ibrahim Ayed , Emmanuel de Bézenac , Arthur Pajot , Julien Brajard , Patrick Gallinari

We consider the problem of distributed state estimation of a linear time-invariant (LTI) system by a network of sensors. We develop a distributed observer that guarantees asymptotic reconstruction of the state for the most general class of…

Systems and Control · Computer Science 2017-04-27 Aritra Mitra , Shreyas Sundaram

The paper proposes an adaptive observer of the state vector of a nonlinear time varying system based on measurements of the output variable. The problem is solved under the assumption that the control matrix (vector) and the nonlinear…

Systems and Control · Electrical Eng. & Systems 2023-05-26 Olga Kozachek , Alexey Bobtsov , Nikolay Nikolaev

A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…

Analysis of PDEs · Mathematics 2007-05-23 Kenrick Bingham , Yaroslav Kurylev , Matti Lassas , Samuli Siltanen

We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced…

Probability · Mathematics 2017-11-28 Andrew Papanicolaou , Konstantinos Spiliopoulos

We study the problem of recovering the initial data (f, 0) of the standard wave equation from the Neumann trace (the normal derivative) of the solution on the boundary of convex domains in arbitrary spatial dimension. Among others, this…

Analysis of PDEs · Mathematics 2021-01-26 Florian Dreier , Markus Haltmeier

We present simulation friendly detectability conditions for 2D Navier-Stokes Equation (NSE) with periodic boundary conditions, and describe a generic class of ``detectable'' observation operators: it includes pointwise evaluation of NSE's…

Optimization and Control · Mathematics 2023-03-31 Sergiy Zhuk , Mykhaylo Zayats , Emilia Fridman

It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The…

Quantum Physics · Physics 2007-05-23 S. Dumitru