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We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where…

Numerical Analysis · Mathematics 2014-11-21 Liliana Borcea , Vladimir Druskin , Alexander V. Mamonov , Mikhail Zaslavsky

This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…

Numerical Analysis · Mathematics 2025-01-31 Zhiyuan Li , Chunlong Sun , Xiangcheng Zheng

In this paper, we propose a framework for efficient Source-Free Domain Adaptation (SFDA) in the context of time-series, focusing on enhancing both parameter efficiency and data-sample utilization. Our approach introduces an improved…

Machine Learning · Computer Science 2025-02-04 Gaurav Patel , Christopher Sandino , Behrooz Mahasseni , Ellen L Zippi , Erdrin Azemi , Ali Moin , Juri Minxha

This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for solving inverse electromagnetic source scattering problems with multi-frequency sparse phased or phaseless far field data. With the phased data,…

Analysis of PDEs · Mathematics 2019-06-07 Xia Ji , Xiaodong Liu

This paper investigates a joint source-channel secrecy problem for the Shannon cipher broadcast system. We suppose list secrecy is applied, i.e., a wiretapper is allowed to produce a list of reconstruction sequences and the secrecy is…

Information Theory · Computer Science 2017-07-25 Lei Yu , Houqiang Li , Weiping Li

The modeling and prediction of multivariate spatio-temporal data involve numerous challenges. Dimension reduction methods can significantly simplify this process, provided that they account for the complex dependencies between variables and…

Machine Learning · Statistics 2025-12-18 Mika Sipilä , Klaus Nordhausen , Sara Taskinen

Differentiable programming is a new programming paradigm which enables large scale optimization through automatic calculation of gradients also known as auto-differentiation. This concept emerges from deep learning, and has also been…

Quantum Physics · Physics 2022-02-01 Chenhua Geng , Hong-Ye Hu , Yijian Zou

While local basis function (LBF) estimation algorithms, commonly used for identifying/tracking systems with time-varying parameters, demonstrate good performance under the assumption of normally distributed measurement noise, the estimation…

Signal Processing · Electrical Eng. & Systems 2025-04-01 Maciej Niedźwiecki , Artur Gańcza , Wojciech Żuławiński , Agnieszka Wyłomańska

This article addresses the modeling of reverberant recording environments in the context of under-determined convolutive blind source separation. We model the contribution of each source to all mixture channels in the time-frequency domain…

Machine Learning · Statistics 2009-12-14 Ngoc Duong , Emmanuel Vincent , Remi Gribonval

We develop a fast method for optimally designing experiments in the context of statistical seismic source inversion. In particular, we efficiently compute the optimal number and locations of the receivers or seismographs. The seismic source…

Computation · Statistics 2023-07-19 Quan Long , Mohammad Motamed , Raul Tempone

There are several solutions to code the signal arising from optical long baseline multi-aperture interferometers. In this paper,we focus on the {\bf non homothetic spatial coding scheme} (multiaxial) with the fringe pattern coded along one…

Astrophysics · Physics 2009-11-11 E. Tatulli , J. -B. LeBouquin

In many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the sparsifying dictionary is usually characterized by a set of unknown parameters in a continuous domain. To apply the conventional…

Information Theory · Computer Science 2015-06-18 Jun Fang , Jing Li , Yanning Shen , Hongbin Li , Shaoqian Li

The problem of reconstructing the spatial support of an extended radiating electric current source density in a lossy dielectric medium from transient boundary measurements of the electric fields is studied. A time reversal algorithm is…

Mathematical Physics · Physics 2014-09-19 Abdul Wahab , Amer Rasheed , Tasawar Hayat , Rab Nawaz

Supervised deep learning approaches to underdetermined audio source separation achieve state-of-the-art performance but require a dataset of mixtures along with their corresponding isolated source signals. Such datasets can be extremely…

A simple inverse problem for the wave equation requires determination of both the wave velocity in a homogenous acoustic material and the transient waveform of an isotropic point radiator, given the time history of the wavefield at a remote…

Optimization and Control · Mathematics 2022-09-28 William W. Symes

We propose a new sequential monitoring scheme for changes in the parameters of a multivariate time series. In contrast to procedures proposed in the literature which compare an estimator from the training sample with an estimator calculated…

Statistics Theory · Mathematics 2020-07-28 Josua Gösmann , Tobias Kley , Holger Dette

We consider the problem of decentralized estimation using wireless sensor networks. Specifically, we propose a novel framework based on level-triggered sampling, a non-uniform sampling strategy, and sequential estimation. The proposed…

Applications · Statistics 2013-09-24 Yasin Yilmaz , Xiaodong Wang

We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…

Numerical Analysis · Mathematics 2026-04-20 Erik Burman , Mats G. Larson , Karl Larsson , Jonatan Vallin

We experimentally demonstrate the simultaneous estimation of the three parameters characterizing a pair of incoherent optical sources in the sub-Rayleigh regime, enabling super-resolved scene characterization. Using spatial-mode…

We address the nonlinear inverse source problem of identifying a time-dependent source occurring in one node of a network governed by a wave equation. We prove that time records of the associated state taken at a strategic set of two nodes…

Optimization and Control · Mathematics 2019-05-22 J. G. Caputo , A. Hamdi , A. Knippel