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Published work

10 published item(s)

preprint2026arXiv

Triple Spectral Fusion for Sensor-based Human Activity Recognition

The field of sensor-based human activity recognition (HAR) mainly uses posture, motion and context data of Inertial Measurement Units (IMUs) to identify daily activities. Despite the advancements in learning-based methods, it is challenging to perform information fusion from the temporal perspective due to the complexities in fusing heterogeneous sensor data and establishing long-term context correlations. This paper proposes a novel triple spectral fusion framework tailored for HAR. First, we develop an adaptive complementary filtering technique for noise suppression and organize each IMU's sensors into posture and motion modality nodes. Given that IMU nodes form a dynamic heterogeneous graph, we then apply adaptive filtering within the graph Fourier domain to merge both homogeneous and heterogeneous node information. Furthermore, an adaptive wavelet frequency selection approach is implemented to suppress context redundancy and shorten the length of features. This approach enhances both timestamp-based graph aggregation and the correlation of long-term contexts. Our framework uses adaptive filtering in the Fourier, graph Fourier, and wavelet domains, enabling effective multi-sensor fusion and context correlation. Extensive experiments on ten benchmark datasets demonstrate the superior performance of our framework. Project page: https://github.com/crocodilegogogo/TSF-TPAMI2026.

preprint2022arXiv

Discrimination in the Venture Capital Industry: Evidence from Field Experiments

This paper examines discrimination by early-stage investors based on startup founders' gender and race using two complementary field experiments with real U.S. venture capitalists. Results show the following. (i) Discrimination varies depending on the context. Investors implicitly discriminate against female and Asian founders when evaluating attractive startups, but they favor female and Asian founders when evaluating struggling startups. This helps to reconcile the contradictory results in the extant literature and confirms the theoretical predictions of "discrimination reversion" and "pro-cyclical discrimination" phenomena. (ii) Among multiple coexisting sources of discrimination identified, statistical discrimination and implicit discrimination are important reasons for investors' "anti-minority" behaviors. A consistent estimator is developed to measure the polarization of investors' discrimination behaviors and their separate driving forces. (iii) Homophily exists when investors provide anonymous encouragement to startups in a non-investment setting. (iv) There was temporary, stronger discrimination against Asian founders during the COVID-19 outbreak.

preprint2022arXiv

N-Grammer: Augmenting Transformers with latent n-grams

Transformer models have recently emerged as one of the foundational models in natural language processing, and as a byproduct, there is significant recent interest and investment in scaling these models. However, the training and inference costs of these large Transformer language models are prohibitive, thus necessitating more research in identifying more efficient variants. In this work, we propose a simple yet effective modification to the Transformer architecture inspired by the literature in statistical language modeling, by augmenting the model with n-grams that are constructed from a discrete latent representation of the text sequence. We evaluate our model, the N-Grammer on language modeling on the C4 data-set as well as text classification on the SuperGLUE data-set, and find that it outperforms several strong baselines such as the Transformer and the Primer. We open-source our model for reproducibility purposes in Jax.

preprint2022arXiv

Proxy ensemble geometric phase and proxy index of time-reversal invariant topological insulators at finite temperatures

The ensemble geometric phase (EGP) has been proposed as a topological indicator for finite-temperatures systems. The ensemble Wilson loop, or the transfer matrix, contains the crucial information in the EGP construction. We propose a proxy index and a proxy EGP directly from the transfer matrix and apply them to time-reversal invariant topological insulators exemplified by the Bernevig-Hughes-Zhang (BHZ) and Kane-Mele (KM) models. The quantized proxy index and proxy EGP smoothly generalize the ground-state topological index to finite temperatures. For the BHZ model, a comparison with another topological indicator, the Uhlmann phase, shows different transition behavior with temperature. For the KM model, the EGP have been generalized to the time-reversal EGP previously, but the proxy EGP does not require any splitting of the contributions. The proxy index and proxy EGP thus offer an efficient means for characterizing finite-temperature topological properties.

preprint2021arXiv

Estimating Adsorption Isotherm Parameters in Chromatography via a Virtual Injection Promoting Feed-forward Neural Network

The means to obtain the adsorption isotherms is a fundamental open problem in competitive chromatography. A modern technique of estimating adsorption isotherms is to solve an inverse problem so that the simulated batch separation coincides with actual experimental results. However, this identification process is usually ill-posed in the sense that the small noise in the measured response can lead to a large fluctuation in the estimated quantity of adsorption isotherms. The conventional mathematical method of solving this problem is the variational regularization, which is formulated as a non-convex minimization problem with a regularized objective functional. However, in this method, the choice of regularization parameter and the design of a convergent solution algorithm are quite difficult in practice. Moreover, due to the restricted number of injection profiles in experiments, the types of measured data are extremely limited, which may lead to a biased estimation. In order to overcome these difficulties, in this paper, we develop a new inversion method -- the Virtual Injection Promoting Feed-forward Neural Network (VIP-FNN). In this approach, the training data contain various types of artificial injections and synthetic noisy measurement at outlet, generated by a conventional physics model -- a time-dependent convection-diffusion system. Numerical experiments with both artificial and real data from laboratory experiments show that the proposed VIP-FNN is an efficient and robust algorithm.

preprint2021arXiv

Further studies on numerical instabilities of Godunov-type schemes for strong shocks

In this paper, continuous research is undertaken to explore the underlying mechanism of numerical shock instabilities of Godunov-type schemes for strong shocks. By conducting dissipation analysis of Godunov-type schemes and a sequence of numerical experiments, we are able to clarify that the instability may be attributed to insufficient entropy production inside the numerical shock structure. As a result, a general entropy-control technique for improving the robustness of various Godunov-type schemes at strong shocks is developed. It plays a part in guaranteeing that enough entropy is produced inside the numerical shock structure. Furthermore, such a modified approach does not introduce any additional numerical dissipation on linear degenerate waves to suppress the shock instability. Numerical results that are obtained for various test cases indicate that the proposed methods have a good performance in terms of accuracy and robustness.

preprint2021arXiv

Sub-Riemannian geometry on some step-two Carnot groups

This paper is a continuation of the previous work of the first author. We characterize a class of step-two groups introduced in \cite{Li19}, saying GM-groups, via some basic sub-Riemannian geometric properties, including the squared Carnot-Carathéodory distance, the cut locus, the classical cut locus, the optimal synthesis, etc. Also, the shortest abnormal set can be exhibited easily in such situation. Some examples of such groups are step-two groups of corank $2$, of Kolmogorov type, or those associated to quadratic CR manifolds. As a byproduct, the main goal in \cite{BBG12} is achieved from the setting of step-two groups of corank $2$ to all possible step-two groups, via a completely different method. A partial answer to the open questions \cite[(29)-(30)]{BR19} is provided in this paper as well. Moreover, we provide a entirely different proof, based yet on \cite{Li19}, for the Gaveau-Brockett optimal control problem on the free step-two Carnot group with three generators. As a byproduct, we provide a new and independent proof for the main results obtained in \cite{MM17}, namely, the exact expression of $d(g)^2$ for $g$ belonging to the classical cut locus of the identity element $o$, as well as the determination of all shortest geodesics joining $o$ to such $g$.

preprint2020arXiv

A new class of accelerated regularization methods, with application to bioluminescence tomography

In this paper we propose a new class of iterative regularization methods for solving ill-posed linear operator equations. The prototype of these iterative regularization methods is in the form of second order evolution equation with a linear vanishing damping term, which can be viewed not only as an extension of the asymptotical regularization, but also as a continuous analog of the Nesterov's acceleration scheme. New iterative regularization methods are derived from this continuous model in combination with damped symplectic numerical schemes. The regularization property as well as convergence rates and acceleration effects under the Hölder-type source conditions of both continuous and discretized methods are proven. The second part of this paper is concerned with the application of the newly developed accelerated iterative regularization methods to the diffusion-based bioluminescence tomography, which is modeled as an inverse source problem in elliptic partial differential equations with both Dirichlet and Neumann boundary data. A relaxed mathematical formulation is proposed so that the discrepancy principle can be applied to the iterative scheme without the usage of Sobolev embedding constants. Several numerical examples, as well as a comparison with the state-of-the-art methods, are given to show the accuracy and the acceleration effect of the new methods.

preprint2020arXiv

Angle-Resolved Thermal Emission Spectroscopy Characterization of Non-Hermitian Meta-Crystals

We establish the angle-resolved thermal emission spectroscopy (ARTES) as a new platform to characterize the intrinsic eigenmode properties of non-Hermitian systems. This method can directly map the dispersion of meta-crystals within the light cone with a high angular resolution. To illustrate its usefulness, we demonstrate the existence of bound states in the continuum (BICs) and non-Hermitian Fermi arcs in a planar corrugated meta-crystal by measuring its angle-resolved thermal emission spectra. We show that change in the thickness of the meta-crystal can induce a band inversion between a BIC and a radiative state, and a pair of exceptional points emerge when the band inversion occurs. With this approach, the band mapping of non-Hermitian photonic systems can become a relatively straightforward task.

preprint2020arXiv

Two new non-negativity preserving iterative regularization methods for ill-posed inverse problems

Many inverse problems are concerned with the estimation of non-negative parameter functions. In this paper, in order to obtain non-negative stable approximate solutions to ill-posed linear operator equations in a Hilbert space setting, we develop two novel non-negativity preserving iterative regularization methods. They are based on fixed point iterations in combination with preconditioning ideas. In contrast to the projected Landweber iteration, for which only weak convergence can be shown for the regularized solution when the noise level tends to zero, the introduced regularization methods exhibit strong convergence. There are presented convergence results, even for a combination of noisy right-hand side and imperfect forward operators, and for one of the approaches there are also convergence rates results. Specifically adapted discrepancy principles are used as a posteriori stopping rules of the established iterative regularization algorithms. For an application of the suggested new approaches, we consider a biosensor problem, which is modelled as a two dimensional linear Fredholm integral equation of the first kind. Several numerical examples, as well as a comparison with the projected Landweber method, are presented to show the accuracy and the acceleration effect of the novel methods. Case studies of a real data problem indicate that the developed methods can produce meaningful featured regularized solutions.