arXiv subjects

Xiaomei Yang

Publications and source records attributed to Xiaomei Yang.

32 records · Page 2Linked to original sources

arXiv2026

A Bayesian approach with persistent homology prior for Robin coefficient identification in a parabolic problem

The reconstruction of time-dependent Robin coefficients is a challenging inverse heat transfer problem due to its inherent ill-posedness. This paper introduces a hierarchical Bayesian approach integrated with a persistent homology (PH) prior for robust coefficient estimation. By quantifying the birth and death of topological features, the PH-based prior provides a global structural constraint that transcends local derivative based penalties. Numerical experiments show that this topological perspective allows for the preservation of complex temporal profiles without the typical staircase distortions of total variation (TV) priors or the excessive blurring of Gaussian models. A key feature of our framework is the hierarchical implementation, which yields an automated, data-driven selection of hyperparameters. The results demonstrate that while PH-based inference yields competitive accuracy compared to TV regularization, it offers superior performance in preserving the multiscale characteristics of the Robin coefficient, providing a robust alternative for convective heat transfer diagnostics

stat.CO↗

arXiv2025

A novel viewpoint for Bayesian inversion based on the Poisson point process

We present a novel Bayesian framework for inverse problems in which the pos terior distribution is interpreted as the intensity measure of a Poisson point process (PPP). The posterior density is approximated using kernel density estimation, and the superposition property of PPPs is then exploited to enable efficient sampling from each kernel component. This methodology offers a new means of exploring the posterior distribution and facilitates the generation of independent and identically distributed samples, thereby enhancing the analysis of inverse problem solutions.

math.NA↗

arXiv2025

A persistent-homology-based Bayesian prior for potential coefficient reconstruction in an elliptic PDE

We address the reconstruction of a potential coefficient in an elliptic partial differential equation from distributed observations within the Bayesian framework. The choice of prior distribution is crucial in such inverse problems, particularly when the target function exhibits sharp discontinuities that conventional Gaussian priors fail to capture effectively. To overcome this limitation, we introduce a novel prior based on persistent homology (PH), which quantifies and encodes the topological features of candidate functions through their persistent pairs. To ensure a well-defined distribution in infinite-dimensional spaces, the prior is constructed with respect to a Gaussian reference measure. A significant advantage over classical approaches is that the PH prior only requires the unknown functions to belong to a suitable topological space, which substantially enhances its applicability. Numerical results demonstrate that the proposed PH prior outperforms the Gaussian prior and achieves a modest yet consistent improvement over the classical total variation (TV) prior.

math.NA↗

arXiv2025

A Bayesian thinning algorithm for the point source identification of heat equation

In this work, we propose a Bayesian thinning algorithm for recovering weighted point source functions in the heat equation from boundary flux observations. The major challenge in the classical Bayesian framework lies in constructing suitable priors for such highly structured unknowns. To address this, we introduce a level set representation on a discretized mesh for the unknown, which enables the infinite-dimensional Bayesian framework to the reconstruction. From another perspective, the point source configuration can be modeled as a marked Poisson point process (PPP), then a thinning mechanism is employed to selectively retain points. These two proposals are complementary with the Bayesian level set sampling generating candidate point sources and the thinning process acting as a filter to refine them. This combined framework is validated through numerical experiments, which demonstrate its accuracy in reconstructing point sources.

stat.CO↗

arXiv2024

Symmetric properties and two variants of shuffle-cubes

Li et al. in [Inf. Process. Lett. 77 (2001) 35--41] proposed the shuffle cube $SQ_{n}$ as an attractive interconnection network topology for massive parallel and distributed systems. By far, symmetric properties of the shuffle cube remains unknown. In this paper, we show that $SQ_{n}$ is not vertex-transitive for all $n>2$, which is not an appealing property in interconnection networks. To overcome this limitation, two novel vertex-transitive variants of the shuffle-cube, namely simplified shuffle-cube $SSQ_{n}$ and balanced shuffle cube $BSQ_{n}$ are introduced. Then, routing algorithms of $SSQ_{n}$ and $BSQ_{n}$ for all $n>2$ are given respectively. Furthermore, we show that both $SSQ_{n}$ and $BSQ_{n}$ possess Hamiltonian cycle embedding for all $n>2$. Finally, as a by-product, we mend a flaw in the Property 3 in [IEEE Trans. Comput. 46 (1997) 484--490].

math.CO↗

arXiv2022

Multiplicative maps on matrix algebras

In this paper, we use elementary method to give a classification of the multiplicative maps on matrix algebra $M_{n}(\mF)$ over a field $\mF$ of characteristic $0$. All the multiplicative maps are classified into three classes: the trivial ones, the degenerate ones and the non-degenerate ones.

math.RT↗

arXiv2022

Flat Lie groups, Frobenius Lie algebras and étale prehomogeneous vector spaces for reductive Lie groups

In this paper, we established the relationship among left-invariant flat connections on Lie groups, left-symmetric algebras, Frobenius Lie algebras and étale prehomogeneous vector spaces, gave a one-to-one correspondence between the left-symmetric Lie algebras with a right identity and the étale prehomogeneous vector spaces for a Lie group, and proved that, in essence, any left-symmetric structure on a reductive Lie algebra has a right identity, which implies that the classification of flat connections on a reductive Lie group $G$ amounts to that of étale prehomogeneous vector spaces for $G$. We classified the étale prehomogeneous vector spaces for $G$ with simple Levi factors.

math.RT↗

arXiv2019

Scalar Quantization as Sparse Least Square Optimization

Quantization can be used to form new vectors/matrices with shared values close to the original. In recent years, the popularity of scalar quantization for value-sharing applications has been soaring as it has been found huge utilities in reducing the complexity of neural networks. Existing clustering-based quantization techniques, while being well-developed, have multiple drawbacks including the dependency of the random seed, empty or out-of-the-range clusters, and high time complexity for a large number of clusters. To overcome these problems, in this paper, the problem of scalar quantization is examined from a new perspective, namely sparse least square optimization. Specifically, inspired by the property of sparse least square regression, several quantization algorithms based on $l_1$ least square are proposed. In addition, similar schemes with $l_1 + l_2$ and $l_0$ regularization are proposed. Furthermore, to compute quantization results with a given amount of values/clusters, this paper designed an iterative method and a clustering-based method, and both of them are built on sparse least square. The paper shows that the latter method is mathematically equivalent to an improved version of k-means clustering-based quantization algorithm, although the two algorithms originated from different intuitions. The algorithms proposed were tested with three types of data and their computational performances, including information loss, time consumption, and the distribution of the values of the sparse vectors, were compared and analyzed. The paper offers a new perspective to probe the area of quantization, and the algorithms proposed can outperform existing methods especially under some bit-width reduction scenarios, when the required post-quantization resolution (number of values) is not significantly lower than the original number.

cs.LG↗

arXiv2019

An ensemble Kalman filter approach based on level set parameterization for acoustic source identification using multiple frequency information

The spatial dependent unknown acoustic source is reconstructed according noisy multiple frequency data on a remote closed surface. Assume that the unknown function is supported on a bounded domain. To determine the support, we present a statistical inversion algorithm, which combines the ensemble Kalman filter approach with level set technique. Several numerical examples show that the proposed method give good numerical reconstruction.

math.NA↗

arXiv2019

A parametric Bayesian level set approach for acoustic source identification using multiple frequency information

The reconstruction of the unknown acoustic source is studied using the noisy multiple frequency data on a remote closed surface. Assume that the unknown source is coded in a spatial dependent piecewise constant function, whose support set is the target to be determined. In this setting, the unknown source can be formalized by a level set function. The function is explored with Bayesian level set approach. To reduce the infinite dimensional problem to finite dimension, we parameterize the level set function by the radial basis expansion. The well-posedness of the posterior distribution is proven. The posterior samples are generated according to the Metropolis-Hastings algorithm and the sample mean is used to approximate the unknown. Several shapes are tested to verify the effectiveness of the proposed algorithm. These numerical results show that the proposed algorithm is feasible and competitive with the Matérn random field for the acoustic source problem.

math.NA↗

arXiv2019

Multi-layer Attention Mechanism for Speech Keyword Recognition

As an important part of speech recognition technology, automatic speech keyword recognition has been intensively studied in recent years. Such technology becomes especially pivotal under situations with limited infrastructures and computational resources, such as voice command recognition in vehicles and robot interaction. At present, the mainstream methods in automatic speech keyword recognition are based on long short-term memory (LSTM) networks with attention mechanism. However, due to inevitable information losses for the LSTM layer caused during feature extraction, the calculated attention weights are biased. In this paper, a novel approach, namely Multi-layer Attention Mechanism, is proposed to handle the inaccurate attention weights problem. The key idea is that, in addition to the conventional attention mechanism, information of layers prior to feature extraction and LSTM are introduced into attention weights calculations. Therefore, the attention weights are more accurate because the overall model can have more precise and focused areas. We conduct a comprehensive comparison and analysis on the keyword spotting performances on convolution neural network, bi-directional LSTM cyclic neural network, and cyclic neural network with the proposed attention mechanism on Google Speech Command datasets V2 datasets. Experimental results indicate favorable results for the proposed method and demonstrate the validity of the proposed method. The proposed multi-layer attention methods can be useful for other researches related to object spotting.

cs.LG↗

arXiv2019

Bayesian approach for inverse obstacle scattering with Poisson data

We consider an acoustic obstacle reconstruction problem with Poisson data. Due to the stochastic nature of the data, we tackle this problem in the framework of Bayesian inversion. The unknown obstacle is parameterized in its angular form. The prior for the parameterized unknown plays key role in the Bayes reconstruction algorithm. The most popular used prior is the Gaussian. Under the Gaussian prior assumption, we further suppose that the unknown satisfies the total variation prior. With the hybrid prior, the well-posedness of the posterior distribution is discussed. The numerical examples verify the effectiveness of the proposed algorithm.

math.NA↗

arXiv2018

Q-Hermite polynomials chaos approximation of likelihood function based on q-Gaussian prior in Bayesian inversion

In real applications, the construction of prior and acceleration of sampling for posterior are usually two key points of Bayesian inversion algorithm for engineers. In this paper, q-analogy of Gaussian distribution, q-Gaussian distribution, is introduced as the prior of inverse problems. And an acceleration algorithm based on spectral likelihood approximation is discussed. We mainly focus on the convergence of the posterior distribution in the sense of Kullback-Leibler divergence when approximated likelihood function and truncated prior distribution are used. Moreover, the convergence in the sense of total variation and Hellinger metric is obtained. In the end two numerical examples are displayed.

math.NA↗

arXiv2013

Spin-enhanced organic bulk heterojunction photovoltaic solar cells

Recently, much effort has been devoted to improve the efficiency of organic photovoltaic solar cells based on blends of donors and acceptors molecules in bulk heterojunction architecture. One of the major losses in organic photovoltaic devices has been recombination of polaron pairs at the donor/acceptor domain interfaces. Here, we present a novel method to suppress polaron pair recombination at the donor/acceptor domain interfaces and thus improve the organic photovoltaic solar cell efficiency, by doping the device active layer with spin 1/2 radical galvinoxyl. At an optimal doping level of 3 wt%, the efficiency of a standard poly(3-hexylthiophene)/1-(3-(methoxycarbonyl)propyl)-1-1-phenyl)(6,6)C61 solar cell improves by 18%. A spin-flip mechanism is proposed and supported by magneto-photocurrent measurements, as well as by density functional theory calculations in which polaron pair recombination rate is suppressed by resonant exchange interaction between the spin 1/2 radicals and charged acceptors, which convert the polaron pair spin state from singlet to triplet.

cond-mat.mtrl-sci↗