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Researcher profile

Zhijian Yang

Zhijian Yang contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine Learningeess.IVComputer Visionmath.APmath.FAQuantitative MethodsArtificial IntelligenceInformation Theorymath.ITmath.NANeurons and CognitionNumerical Analysis

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Published work

11 published item(s)

preprint2026arXiv

Dynamics for a viscoelastic beam equation with past history and nonlocal boundary dissipation

This article aims to study the long-time dynamics of the linear viscoelastic plate equation $\displaystyle{u_{tt}+Δ^2 u-\int_τ^tg(t-s)Δ^2u(s)ds=0}$ subject to nonlinear and nonlocal boundary conditions. This model, with $τ=0$, was first considered by Cavalcanti (Discrete Contin. Dyn. Syst., 8(3), 675-695, 2002), where results of global existence and uniform decay rates of energy have been established. In this work, by taking $τ=-\infty$, and considering the autonomous equivalent problem we prove that the dynamical system $(\mathcal{H},S_t)$ generated by the weak solutions has a compact global attractor $\mathfrak{A}$ (in the topology of the weak phase space $\mathcal{H}$), which in subcritical case has finite dimension and smoothness. Furthermore, when the force follows the {\it Hook Law}, we prove that $(\mathcal{H},S_t)$ possesses a (generalized) fractal exponential attractor $\mathfrak{A}_{\exp}$ with finite dimension in a space $\widetilde{\mathcal{H}}\supset\mathcal{H}$.

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preprint2026arXiv

WavesFM: Hierarchical Representation Learning for Longitudinal Wearable Sensor Waveforms

Wearable sensors enable the continuous acquisition of high-resolution physiological waveforms, such as photoplethysmography and accelerometry, under free-living conditions. However, inferring health-related phenotypes from these signals presents significant challenges due to high sampling frequencies, multimodal dependencies, and extreme sequence lengths (e.g., weeks of recordings), compounded by a scarcity of ground-truth labels. To address these challenges, existing self-supervised learning (SSL) methodologies typically follow two paradigms: (1) learning rich morphological representations from short waveform segments while collapsing longitudinal dynamics through simple aggregation, or (2) modeling behavioral patterns from coarse, hand-crafted features (e.g. heart rate, step counts) spanning longer horizons but foregoing subtle, predictive signatures in raw waveforms. To bridge this gap, we propose WavesFM, a foundation model utilizing a two-stage SSL framework for longitudinal physiological data. Specifically, we decompose the learning problem into two stages: first, a segment-level encoder is pretrained to extract local embeddings from short waveforms; subsequently, a temporal encoder is trained to model the sequence of these embeddings across a multi-day horizon. This hierarchical approach overcomes the computational complexity of high-resolution, long-sequence data, allowing the overall model to capture both local signal semantics and the complex circadian and inter-day variations governing physiological dynamics. Pretrained on over 6.8M hours (N=324k individuals) of recordings for the first stage and 5.3M hours (N=10k) for the second stage, WavesFM demonstrates superior performance across 58 diverse tasks spanning demographics, lifestyle, health conditions, and medications.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Continuity of the attractors in time-dependent spaces and applications

In this paper, we investigate the continuity of the attractors in time-dependent phase spaces. (i) We establish two abstract criteria on the upper semicontinuity and the residual continuity of the pullback $\mathscr D$-attractor with respect to the perturbations, and an equivalence criterion between their continuity and the pullback equi-attraction, which generalize the continuity theory of attractors developed recently in [27,28] to that in time-dependent spaces. (ii) We propose the notion of pullback $\mathscr D$-exponential attractor, which includes the notion of time-dependent exponential attractor [33] as its spacial case, and establish its existence and Hölder continuity criterion via quasi-stability method introduced originally by Chueshov and Lasiecka [12,13]. (iii) We apply above-mentioned criteria to the semilinear damped wave equations with perturbed time-dependent speed of propagation: $\eρ(t) u_{tt}+αu_t -Δu+f(u)=g$, with perturbation parameter $\e\in(0, 1]$, to realize above mentioned continuity of pullback $\mathscr D$ and $\mathscr D$-exponential attractors in time-dependent phase spaces, and the method developed here allows to overcome the difficulty of the hyperbolicity of the model. These results deepen and extend recent theory of attractors in time-dependent spaces in literatures [15,20,19].

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preprint2022arXiv

New Geometric Constant Related to the P-angle Function in Banach Spaces

In this paper, combined with the P-angle function of Banach spaces and the geometric constants that can characterize Hilbert spaces, the new angular geometric constant is defined. Firstly, this paper explores the basic properties of the new constant and obtains some inequalities with significant geometric constants. Then according to the derived inequalities, this paper studies the relationship between the new constant and the geometric properties of Banach spaces. Furthermore, the necessary and sufficient condition for uniform non-squareness, and the sufficient conditions for uniform convexity, the normal structure and the fixed point property will be established.

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preprint2022arXiv

New geometric constants of isosceles orthogonal type

Based on the parallelogram law and isosceles orthogonality, we define a new orthogonal geometric constant. We first discuss some basic properties of this new constant. Next, we consider the relation between the constant and the uniformly non-square property. Moreover, a generalized constant is also introduced and some basic properties are presented. It is shown that, for a normed space, the constant value is equal to 1 if and only if the norm can be induced by the inner product. Finally, we verify that this constant is closely related to the well-known geometric constants through some inequalities.

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preprint2022arXiv

Subtyping brain diseases from imaging data

The imaging community has increasingly adopted machine learning (ML) methods to provide individualized imaging signatures related to disease diagnosis, prognosis, and response to treatment. Clinical neuroscience and cancer imaging have been two areas in which ML has offered particular promise. However, many neurologic and neuropsychiatric diseases, as well as cancer, are often heterogeneous in terms of their clinical manifestations, neuroanatomical patterns or genetic underpinnings. Therefore, in such cases, seeking a single disease signature might be ineffectual in delivering individualized precision diagnostics. The current chapter focuses on ML methods, especially semi-supervised clustering, that seek disease subtypes using imaging data. Work from Alzheimer Disease and its prodromal stages, psychosis, depression, autism, and brain cancer are discussed. Our goal is to provide the readers with a broad overview in terms of methodology and clinical applications.

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preprint2022arXiv

Surreal-GAN:Semi-Supervised Representation Learning via GAN for uncovering heterogeneous disease-related imaging patterns

A plethora of machine learning methods have been applied to imaging data, enabling the construction of clinically relevant imaging signatures of neurological and neuropsychiatric diseases. Oftentimes, such methods don't explicitly model the heterogeneity of disease effects, or approach it via nonlinear models that are not interpretable. Moreover, unsupervised methods may parse heterogeneity that is driven by nuisance confounding factors that affect brain structure or function, rather than heterogeneity relevant to a pathology of interest. On the other hand, semi-supervised clustering methods seek to derive a dichotomous subtype membership, ignoring the truth that disease heterogeneity spatially and temporally extends along a continuum. To address the aforementioned limitations, herein, we propose a novel method, termed Surreal-GAN (Semi-SUpeRvised ReprEsentAtion Learning via GAN). Using cross-sectional imaging data, Surreal-GAN dissects underlying disease-related heterogeneity under the principle of semi-supervised clustering (cluster mappings from normal control to patient), proposes a continuously dimensional representation, and infers the disease severity of patients at individual level along each dimension. The model first learns a transformation function from normal control (CN) domain to the patient (PT) domain with latent variables controlling transformation directions. An inverse mapping function together with regularization on function continuity, pattern orthogonality and monotonicity was also imposed to make sure that the transformation function captures necessarily meaningful imaging patterns with clinical significance. We first validated the model through extensive semi-synthetic experiments, and then demonstrate its potential in capturing biologically plausible imaging patterns in Alzheimer's disease (AD).

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preprint2021arXiv

Convergence Rate Analysis for Deep Ritz Method

Using deep neural networks to solve PDEs has attracted a lot of attentions recently. However, why the deep learning method works is falling far behind its empirical success. In this paper, we provide a rigorous numerical analysis on deep Ritz method (DRM) \cite{wan11} for second order elliptic equations with Neumann boundary conditions. We establish the first nonasymptotic convergence rate in $H^1$ norm for DRM using deep networks with $\mathrm{ReLU}^2$ activation functions. In addition to providing a theoretical justification of DRM, our study also shed light on how to set the hyper-parameter of depth and width to achieve the desired convergence rate in terms of number of training samples. Technically, we derive bounds on the approximation error of deep $\mathrm{ReLU}^2$ network in $H^1$ norm and on the Rademacher complexity of the non-Lipschitz composition of gradient norm and $\mathrm{ReLU}^2$ network, both of which are of independent interest.

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preprint2021arXiv

Disentangling brain heterogeneity via semi-supervised deep-learning and MRI: dimensional representations of Alzheimer's Disease

Heterogeneity of brain diseases is a challenge for precision diagnosis/prognosis. We describe and validate Smile-GAN (SeMI-supervised cLustEring-Generative Adversarial Network), a novel semi-supervised deep-clustering method, which dissects neuroanatomical heterogeneity, enabling identification of disease subtypes via their imaging signatures relative to controls. When applied to MRIs (2 studies; 2,832 participants; 8,146 scans) including cognitively normal individuals and those with cognitive impairment and dementia, Smile-GAN identified 4 neurodegenerative patterns/axes: P1, normal anatomy and highest cognitive performance; P2, mild/diffuse atrophy and more prominent executive dysfunction; P3, focal medial temporal atrophy and relatively greater memory impairment; P4, advanced neurodegeneration. Further application to longitudinal data revealed two distinct progression pathways: P1$\rightarrow$P2$\rightarrow$P4 and P1$\rightarrow$P3$\rightarrow$P4. Baseline expression of these patterns predicted the pathway and rate of future neurodegeneration. Pattern expression offered better yet complementary performance in predicting clinical progression, compared to amyloid/tau. These deep-learning derived biomarkers offer promise for precision diagnostics and targeted clinical trial recruitment.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Robust Decoding from Binary Measurements with Cardinality Constraint Least Squares

The main goal of 1-bit compressive sampling is to decode $n$ dimensional signals with sparsity level $s$ from $m$ binary measurements. This is a challenging task due to the presence of nonlinearity, noises and sign flips. In this paper, the cardinality constraint least square is proposed as a desired decoder. We prove that, up to a constant $c$, with high probability, the proposed decoder achieves a minimax estimation error as long as $m \geq \mathcal{O}( s\log n)$. Computationally, we utilize a generalized Newton algorithm (GNA) to solve the cardinality constraint minimization problem with the cost of solving a least squares problem with small size at each iteration. We prove that, with high probability, the $\ell_{\infty}$ norm of the estimation error between the output of GNA and the underlying target decays to $\mathcal{O}(\sqrt{\frac{\log n }{m}}) $ after at most $\mathcal{O}(\log s)$ iterations. Moreover, the underlying support can be recovered with high probability in $\mathcal{O}(\log s)$ steps provided that the target signal is detectable. Extensive numerical simulations and comparisons with state-of-the-art methods are presented to illustrate the robustness of our proposed decoder and the efficiency of the GNA algorithm.

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preprint2020arXiv

Smile-GANs: Semi-supervised clustering via GANs for dissecting brain disease heterogeneity from medical images

Machine learning methods applied to complex biomedical data has enabled the construction of disease signatures of diagnostic/prognostic value. However, less attention has been given to understanding disease heterogeneity. Semi-supervised clustering methods can address this problem by estimating multiple transformations from a (e.g. healthy) control (CN) group to a patient (PT) group, seeking to capture the heterogeneity of underlying pathlogic processes. Herein, we propose a novel method, Smile-GANs (SeMi-supervIsed cLustEring via GANs), for semi-supervised clustering, and apply it to brain MRI scans. Smile-GANs first learns multiple distinct mappings by generating PT from CN, with each mapping characterizing one relatively distinct pathological pattern. Moreover, a clustering model is trained interactively with mapping functions to assign PT into corresponding subtype memberships. Using relaxed assumptions on PT/CN data distribution and imposing mapping non-linearity, Smile-GANs captures heterogeneous differences in distribution between the CN and PT domains. We first validate Smile-GANs using simulated data, subsequently on real data, by demonstrating its potential in characterizing heterogeneity in Alzheimer's Disease (AD) and its prodromal phases. The model was first trained using baseline MRIs from the ADNI2 database and then applied to longitudinal data from ADNI1 and BLSA. Four robust subtypes with distinct neuroanatomical patterns were discovered: 1) normal brain, 2) diffuse atrophy atypical of AD, 3) focal medial temporal lobe atrophy, 4) typical-AD. Further longitudinal analyses discover two distinct progressive pathways from prodromal to full AD: i) subtypes 1 - 2 - 4, and ii) subtypes 1 - 3 - 4. Although demonstrated on an important biomedical problem, Smile-GANs is general and can find application in many biomedical and other domains.

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