20 papers · ranked by Valyu relevance
Lukas Hecker
Electroencephalography (EEG) source imaging remains difficult to compare systematically because inverse solvers are distributed across different software packages, programming languages, and evaluation protocols. We present a frozen four-scenario EEG benchmark of 106 solvers evaluated on a shared BioSemi-32 / ico3…
Hengfa Lu, Jewel Ashbrook, Andrew K. Dunn
Multi-exposure speckle imaging (MESI) estimates flow-related parameters by fitting a physics-based speckle contrast model to measurements acquired over multiple exposure times. In standard pipelines, parameters are recovered via nonlinear least-squares fitting at each pixel, which is computationally expensive and can…
K. Zhukovsky
We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal…
Ali Mohammad-Djafari, Wolfgang von der Linden, Sascha Ranftl
Classical methods for inverse problems are mainly based on regularization theory, in particular those, that are based on optimization of a criterion with two parts: a data-model matching and a regularization term. Different choices for these two terms and a great number of optimization algorithms have been proposed.…
S. ter Horst, M. A. Kaashoek, F. van Schagen
In this paper we consider a twofold Ellis-Gohberg type inverse problem in an abstract ∗-algebraic setting. Under natural assumptions, necessary and sufficient conditions for the existence of a solution are obtained, and it is shown that in case a solution exists, it is unique. The main result relies strongly on an…
K. V. Zhukovsky
We propose operational method with recourse to generalized forms of orthogonal polynomials for solution of a variety of differential equations of mathematical physics. Operational definitions of generalized families of orthogonal polynomials are used in this context. Integral transforms and the operational exponent…
Alexander Sakhnovich
We assume that s(x) ∈ L 2 (Ω), where e Ω = e {x : |x1| < ω1, |x2| < ω2}, and so the integrals in (1.1) are well-defined for f ∈ L 2 (Ω). Moreover, we assume that the right-hand side of (1.1) is well-defined and that S is bounded in L 2 (Ω).
Victor D. Didenko, Bernd Silbermann
In what follows, we often identify the spaces L p (R +) and L p (R −), 1 ≤ p ≤ ∞ with the subspaces χR+ L p (R) and χR− L p (R) of the space L p (R), which consist of the functions vanishing on R − and R +, respectively.
Authors not listed
Inverse problems, where we seek the values of inputs to a model that lead to a desired set of outputs, are a challenges subset of problems in science and engineering. In this work we demonstrate the use of two generative AI methods to solve inverse problems. We compare this approach to two more conventional approaches…
Guillermina Fongi, María Celeste González
In this article we explore several aspects concerning to the Moore-Penrose inverse of a bounded linear operator. On the one hand, we study monotonicity properties of the Moore-Penrose inverse with respect to the L¨owner, star, minus, sharp and diamond orders. On the other hand, we analyze the validity of the reverse…
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub
We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with respect to the PDE parameters. At the lower level, we train a neural network to…
Patricia M. Morillas
The theory of generalized inverses of matrices and operators is closely connected with projections, i.e., idempotent (bounded) linear transformations. We show that a similar situation occurs in any associative ring R with a unit 1 6= 0. We prove that generalized inverses in R are related to idempotent group…
Jan Schneider
This article is meant to give a lucid and widely accessible, self-contained account of a novel way of performing arithmetic operations on fuzzy intervals. Based on two formulae of generalized inversion (the first in close analogy to the inversion of cumulative distribution functions in probability and statistics, and…
Umashankara Kelathaya, Manjunatha Prasad Karantha
The reverse order law for outer inverses and the Moore-Penrose inverse is discussed in the context of associative rings. A class of pairs of outer inverses that satisfy reverse order law is determined. The notions of left-star and right-star orders have been extended to the case of arbitrary associative rings with…
Yongge Tian
Reverse order laws for generalized inverses of matrix products are a classic object of study in the theory of generalized inverses. One of the well-known reverse order laws for a matrix product AB is $(AB)(i,…,j)=B(s_{2},…,t_{2})A(s_{1},…,t_{1})$, where $(\cdot)(i,…,j)$ denotes a ${i,…,j}$-generalized inverse of…
Ratikanta Behera, Jajati Keshari Sahoo, R. N. Mohapatra, M. Zuhair Nashed
'M. Zuhair Nashed'] Generalized inverses of tensors play increasingly important roles in computational mathematics and numerical analysis. It is appropriate to develop the theory of generalized inverses of tensors within the algebraic structure of a ring. In this paper, we study different generalized inverses of…
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub
Uncertainty quantification in PDE inverse problems is essential in many applications. Scientific machine learning and AI enable data-driven learning of model components while preserving physical structure, and provide the scalability and adaptability needed for emerging imaging technologies and clinical insights. We…
Weian Mao, Muzhi Zhu, Hao Chen, Chunhua Shen
Proteins serve as the foundation of life. Most diseases and challenges in life sciences are intimately linked to protein structures. In this paper, we propose a novel vector field network (VFN) for modeling protein structure. Unlike previous methods that extract geometric information relying heavily on hand-crafted…
Authors not listed
Real-world datasets in chemical engineering and bioengineering processes--such as those from catalytic reactors, multiphase flows, polymerization reactors, bioreactors, and clinical trials--can often be unlabelled or disorganized, rendering the training of existing supervised learning models ineffective at learning the…
Sabine Willems, Romy Busch, Felix Nawa, Marco Ballarotto + 12 more
Nuclear receptor related 1 (Nurr1, NR4A2) is a ligand-sensing transcription factor with neuroprotective and anti-inflammatory roles widely distributed in the CNS. Pharmacological Nurr1 modulation is considered a promising experimental strategy in Parkinson's and Alzheimer's disease but target validation is incomplete.…