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Jie Shen

Publications and source records attributed to Jie Shen.

At least 37 records · Page 2Linked to original sources
arXiv2026

A high-order nodally bound-preserving and mass-conservative method for linear fourth-order elliptic problems and its applications to nonlinear parabolic equations

We propose a high-order finite element method for linear fourth-order elliptic problems that is both nodally bound-preserving and mass-conservative, based on a variational inequality formulation. The method admits an equivalent strictly convex minimization structure, which ensures well-posedness and enables an optimal error estimate in the $H^1$-seminorm, under suitable regularity assumptions. This framework is further extended to nonlinear fourth-order parabolic problems through space--time high-order discretizations that combine variational inequalities, BDF schemes, and scalar auxiliary variable (SAV) techniques. The fully discrete schemes preserve nodal bounds and mass, and a modified energy stability result is established for the first-order temporal scheme. We also apply the same framework to nonlinear second-order parabolic problems by introducing a consistent fourth-order regularization, leading to space--time high-order schemes with the same bound-preserving and mass-conservative properties. Extensive numerical results, including challenging tests with singularities and low regularity, demonstrate the stability, efficiency, and high-order accuracy of the proposed methods.

math.NA↗
arXiv2026

Chern number reversal and emergent superconductivity in rhombohedral graphene induced by in-plane magnetic fields

Rhombohedral graphene with topological flat bands offers an ideal platform for realizing correlated and topological quantum phases. Here we investigate hBN aligned eight-layer rhombohedral graphene moire superlattices, which host a robust quantum anomalous Hall (QAH) state alongside three unconventional superconducting phases. For electron-doped carriers away from the moire potential, we observe QAH Chern number reversal driven by the displacement fields and in plane magnetic fields. For hole-doped carriers near the moire superlattice, the three superconducting phases exhibit distinctively different in plane magnetic field responses: one is weakly enhanced, the second is strongly suppressed, and the third exclusively induced by in plane magnetic field. The isotropic in plane magnetic field response in the QAH regime points to interplay between orbital magnetism and spin-orbit coupling, and the field-emergent superconductivity provides compelling evidence for spin-triplet pairing. Our work demonstrates a highly versatile platform for coexisting topological and superconducting states, and highlights in plane magnetic field as a powerful in-situ control knob for engineering novel quantum devices.

cond-mat.str-el↗
arXiv2026

Predicting Trajectories of Long COVID in Adult Women: The Critical Role of Causal Disentanglement

Early prediction of Post-Acute Sequelae of SARS-CoV-2 severity is a critical challenge for women's health, particularly given the diagnostic overlap between PASC and common hormonal transitions such as menopause. Identifying and accounting for these confounding factors is essential for accurate long-term trajectory prediction. We conducted a retrospective study of 1,155 women (mean age 61) from the NIH RECOVER dataset. By integrating static clinical profiles with four weeks of longitudinal wearable data (monitoring cardiac activity and sleep), we developed a causal network based on a Large Language Model to predict future PASC scores. Our framework achieved a precision of 86.7\% in clinical severity prediction. Our causal attribution analysis demonstrate the model's ability to differentiate between active pathology and baseline noise: direct indicators such as breathlessness and malaise reached maximum saliency (1.00), while confounding factors like menopause and diabetes were successfully suppressed with saliency scores below 0.27.

cs.LG↗
arXiv2026

LLM-Augmented Computational Phenotyping of Long Covid

Phenotypic characterization is essential for understanding heterogeneity in chronic diseases and for guiding personalized interventions. Long COVID, a complex and persistent condition, yet its clinical subphenotypes remain poorly understood. In this work, we propose an LLM-augmented computational phenotyping framework ``Grace Cycle'' that iteratively integrates hypothesis generation, evidence extraction, and feature refinement to discover clinically meaningful subgroups from longitudinal patient data. The framework identifies three distinct clinical phenotypes, Protected, Responder, and Refractory, based on 13,511 Long Covid participants. These phenotypes exhibit pronounced separation in peak symptom severity, baseline disease burden, and longitudinal dose-response patterns, with strong statistical support across multiple independent dimensions. This study illustrates how large language models can be integrated into a principled, statistically grounded pipeline for phenotypic screening from complex longitudinal data. Note that the proposed framework is disease-agnostic and offers a general approach for discovering clinically interpretable subphenotypes.

cs.LG↗
arXiv2026

A scalar auxiliary variable-based semi-implicit scheme for stochastic Cahn--Hilliard equation

In this paper, we present a novel semi-implicit numerical scheme for the stochastic Cahn--Hilliard equation driven by multiplicative noise. By reformulating the original equation into an equivalent stochastic scalar auxiliary variable (SSAV) system, our method enables an efficient and stable treatment of polynomial nonlinearities in a semi-implicit fashion. In order to accurately capture the impact of stochastic perturbations, we carefully incorporate Itô correction terms into the SSAV approximation. Leveraging the smoothing properties of the underlying semigroup and the $H^{-1}$-dissipative structure of the nonlinear term, we establish the optimal strong convergence order of one-half for the proposed scheme in the trace-class noise case. Moreover, we show that the modified SAV energy asymptotically preserves the energy evolution law. Finally, numerical experiments are provided to validate the theoretical results and to explore the influence of noise near the sharp-interface limit.

math.NA↗
arXiv2026

Double-Carrier Fitting of Hall Resistance Assisted by Gate-Induced Shubnikov-de Haas Oscillations in Possible Excitonic Insulator Ta2Pd3Te5

Hall effect is an important phenomenon when a magnetic field is applied to materials. From the curve depicting the Hall resistance versus the magnetic field, crucial information such as carrier concentration can be extracted. If the curve exhibits a linear dependence up to rather high magnetic fields, it indicates that charge transport involves only a single type of carrier, and if a non-linear curve is measured, then the double-carrier model should be considered for fitting. However, this model involves four unknown parameters, including the concentration and mobility of the two carriers, resulting in that such fitting is usually non-unique, which significantly reduces the reliability and accuracy. In this work, a double-carrier platform was constructed on a probable excitonic insulator Ta2Pd3Te5, and the four-parameter fitting based on the double-carrier model was simplified to a single-parameter fitting by employing methods such as analyzing the shape of the Hall resistance curve and generating gate-induced Shubnikov-de Haas oscillations. Thus, we provide a reliable method for double-carrier fitting of Hall resistance and a new evidence for the existence of excitonic-insulator state in Ta2Pd3Te5.

cond-mat.mes-hall↗
arXiv2026

Linking the pressure dependence of the structure and thermal stability to α- and \b{eta}-relaxations in metallic glasses

Glasses derive their functional properties from complex relaxation dynamics that remain enigmatic under extreme conditions. While the temperature dependence of these relaxation processes is well-established, their behavior under high-pressure conditions remains poorly understood due to significant experimental difficulties. In this study, we employ cutting-edge experimental techniques to probe the pressure evolution of the relaxation spectrum in a Zr46.8Ti8.2Cu7.5Ni10Be27.5 metallic glass across gigapascal pressure ranges. Our findings reveal two distinct relaxation mechanisms under high pressure: In the \b{eta}-relaxation regime, compression drives the system with reduced atomic mobility and enhanced structural disorder, without significant density changes. Conversely, α-relaxation under pressure promotes density-driven structural ordering that improves thermal stability. Notably, the transition between these regimes occurs at a constant T/Tg,P ratio, independent of applied pressure. These results provide crucial insights for decoupling the competing structural and relaxation contributions to glass stability, establishing a systematic framework for tailoring glass properties through controlled thermo-mechanical processing.

cond-mat.mtrl-sci↗
arXiv2026

High-pressure X-ray photon correlation spectroscopy at fourth-generation synchrotron sources

A new experimental setup combining X-Ray Photon Correlation Spectroscopy (XPCS) in the hard x-ray regime and a high-pressure sample environment is developed to monitor the pressure dependence of the internal motion of complex systems down to the atomic scale in the multi-gigapascal range, from room temperature to 600K. The high flux of coherent high energy x-rays at 4th generation synchrotron source solves the problems caused by the absorption of the Diamond Anvil Cells used to generate the high pressure, enabling the measurement of the intermediate scattering function over 6 orders of magnitude in time, from $10^{-3}$ s to $10^{3}$s. The constraints posed by the high-pressure generation such as the preservation of X-ray coherence, as well as the sample, pressure and temperature stability, are discussed, and the feasibility of high-pressure XPCS is demonstrated through results obtained on metallic glasses.

physics.app-ph↗
arXiv2026

Break-down of the relationship between α-relaxation and equilibration in hydrostatically compressed metallic glasses

Glasses encode the memory of any thermo-mechanical treatment applied to them. This ability is associated to the existence of a myriad of metastable amorphous states which can be probed through different experimental pathways. It is usually assumed that this memory can be erased in the supercooled liquid, and that this process occurs on a time scale controlled by the α-relaxation. We find that this assumption does not apply for hydrostatically compressed glasses. Annealing under pressure a prototypical metallic glass can irreversibly modify its dynamics, thermodynamics and structure, reduce the atomic mobility and lead to structural modifications of the first coordination shells which reduce the thermal stability with respect to a glass annealed in absence of pressure. When heated above their glass transition temperature, these compressed glasses do not convert into the pristine supercooled liquid, implying the existence of an additional process, beyond the α-relaxation, contributing to the equilibrium recovery of the material. These results establish pressure as a powerful tool for engineering non-equilibrium glassy materials with tailored properties, while deepening our understanding of relaxation dynamics in disordered systems under extreme conditions.

cond-mat.mtrl-sci↗
arXiv2026

Fast Jacobi Spectral Methods and Closure Approximations for the Homogeneous FENE Model of Complex Fluids

The Finitely Extensible Nonlinear Elastic (FENE) dumbbell model is a widely used mathematical model for complex fluids. Direct simulation of the FENE Fokker--Planck equation is computationally challenging due to high dimensionality and singularity of its potential. In this paper, we develop two fast Jacobi-Spherical Harmonic spectral methods for the spatially homogeneous FENE Fokker--Planck equation. These methods effectively resolve the singularity near the boundary by combining properly designed Jacobi polynomials with a weighted variational formulation. A semi-implicit backward differentiation formula of second-order (BDF2) is employed for time marching, and its energy stability is rigorously proved. The resulting linear algebraic system possesses a sparse structure and can be efficiently solved. Numerical results verify the spectral convergence and efficiency of the direct spectral solvers, establishing them as a reliable tool for generating reference solutions for challenging benchmark problems. Furthermore, to achieve an optimal trade-off between accuracy and efficiency, we compare several closure approximation models, including the industry workhorse Peterlin approximation (FENE-P), the quasi-equilibrium approximation (FENE-QE), and a novel neural network implementation for FENE-QE proposed in this paper (FENE-QE-NN). Numerical experiments in extensional and shear flows demonstrate the superior accuracy and efficiency of the proposed methods compared to traditional approaches.

math.NA↗
arXiv2026

C-kNN-LSH: A Nearest-Neighbor Algorithm for Sequential Counterfactual Inference

Estimating causal effects from longitudinal trajectories is central to understanding the progression of complex conditions and optimizing clinical decision-making, such as comorbidities and long COVID recovery. We introduce \emph{C-kNN--LSH}, a nearest-neighbor framework for sequential causal inference designed to handle such high-dimensional, confounded situations. By utilizing locality-sensitive hashing, we efficiently identify ``clinical twins'' with similar covariate histories, enabling local estimation of conditional treatment effects across evolving disease states. To mitigate bias from irregular sampling and shifting patient recovery profiles, we integrate neighborhood estimator with a doubly-robust correction. Theoretical analysis guarantees our estimator is consistent and second-order robust to nuisance error. Evaluated on a real-world Long COVID cohort with 13,511 participants, \emph{C-kNN-LSH} demonstrates superior performance in capturing recovery heterogeneity and estimating policy values compared to existing baselines.

cs.LG↗
arXiv2026

Optimal Budgeted Adaptation of Large Language Models

The trade-off between labeled data availability and downstream accuracy remains a central challenge in fine-tuning large language models (LLMs). We propose a principled framework for \emph{budget-aware supervised fine-tuning} by casting LLM adaptation as a contextual Stackelberg game. In our formulation, the learner (leader) commits to a scoring policy and a label-querying strategy, while an adaptive environment (follower) selects challenging supervised alternatives in response. To explicitly address label efficiency, we incorporate a finite supervision budget directly into the learning objective. Our algorithm operates in the full-feedback regime and achieves $\tilde{O}(d\sqrt{T})$ regret under standard linear contextual assumptions. We extend the framework with a Largest-Latency-First (LLF) confidence gate that selectively queries labels, achieving a budget-aware regret bound of $\tilde{O}(\sqrt{dB} + c\sqrt{B})$ with $B=βT$.

cs.LG↗
arXiv2026

Novel linear, decoupled, and energy dissipative schemes for the Navier-Stokes-Darcy model and extension to related two-phase flow

We construct efficient original-energy-dissipative schemes for the Navier-Stokes-Darcy model and related two-phase flows using a prediction-correction framework. A new relaxation technique is incorporated in the correction step to guarantee dissipation of the original energy, thereby ensuring unconditional boundedness of the numerical solutions for velocity and hydraulic head in the $l^{\infty}(L^2)$ and $l^2(H^1)$ norms. At each time step, the schemes require solving only a sequence of linear equations with constant coefficients. We rigorously prove that the schemes dissipate the original energy and, as an example, carry out a rigorous error analysis of the first-order scheme for the Navier-Stokes-Darcy model. Finally, a series of benchmark numerical experiments are conducted to demonstrate the accuracy, stability, and effectiveness of the proposed methods.

math.NA↗
arXiv2026

Deterministic non-local parity control and supercurrent-based detection in an Andreev molecule

The ability to manipulate and detect the parity of quantum states in superconductor-semiconductor hybrid systems is pivotal to realizing the promise of topological quantum computation. However, as these architectures scale toward artificial Kitaev chains with phase-control loops, local accessibility becomes restricted, constraining conventional local parity control and detection. While Andreev molecules offer a platform for non-local intervention, deterministic protocols for parity manipulation have yet to be experimentally established. Here, we demonstrate deterministic non-local control over the parity configuration of a quantum dot (QD) by electrically modulating the coherent hybridization with a spatially adjacent QD within an Andreev molecule. By systematically investigating three distinct joint parity configuration regimes in the elastic co-tunneling limit, we experimentally uncover the operational conditions for this non-local control. In conjunction with theoretical simulations establishing a global phase diagram, we identify a set of universal selection rules governing parity transitions, dictated by the symmetry-imposed interplay between the joint parity configuration and the dominant inter-dot coupling mechanism (elastic co-tunneling vs. crossed Andreev reflection). Furthermore, we establish the supercurrent, directly signaled by zero-bias conductance peaks, as an intrinsic, sensor-free probe of the parity configuration, obviating the need for auxiliary charge sensors. Our results provide a validated physical framework for parity engineering, offering a key building block for scalable, multi-QD superconducting architectures.

cond-mat.mes-hall↗
arXiv2026

Immunological Density Shapes Recovery Trajectories in Long COVID

Post-acute sequelae of SARS-CoV-2 infection (Long COVID) frequently persists for months, yet drivers of clinical remission remain incompletely defined. Here we analyzed 97,564 longitudinal PASC assessments from 13,511 participants with linked vaccination histories to disentangle passive temporal progression from vaccine-associated change. Using a clinically validated threshold (PASC $\geq 12$), trajectories separated into three phenotypes: Protected (persistently sub-threshold), Refractory (persistently symptomatic), and Responders (transitioning from symptomatic to recovered). Across the full cohort, symptom severity increased modestly with elapsed time ($r=0.0521$, $P=1.26\times10^{-59}$), whereas cumulative vaccination showed an inverse association with severity ($r=-0.0434$, $P=5.95\times10^{-42}$). In summary, baseline Long COVID severity appears clinically deterministic. In the absence of intervention, symptoms typically persist without spontaneous resolution. Recovery is primarily associated with repeated immunization.

q-bio.OT↗
arXiv2026

X-ray photo-induced atomic motion in Phase Change Materials and conventional covalent chalcogenide glasses

X-ray Photon Correlation Spectroscopy (XPCS) enables direct access to atomic-scale dynamics in disordered materials, revealing both spontaneous and X-ray-induced relaxation processes. Here, we study two compositionally similar alloy glasses near their glass transition temperatures: the phase change material (PCM) Ge15Sb85 and the non-PCM alloy Ge15Te85. Both exhibit X-ray induced atomic motion, yet with markedly different responses. Ge15Sb85 undergoes an immediate transition to a photo-induced yielding state, characterised by stationary dynamics governed solely by the absorbed dose. In contrast, Ge15Te85 shows a progressive slowing-down of the relaxation process, accompanied by a crossover from compressed to stretched exponential decay in the density autocorrelation functions. This behaviour is consistent with the emergence of liquid-like collective motion as supported by de Gennes narrowing in the wave-vector dependence of the dynamics at length scales comparable with the first sharp diffraction peak. Unlike Ge15Sb85, this alloy does not reach a stationary regime within experimental timescales, implying that the yielding transition occurs only after thousands of seconds with the available dose rate. Its response is also temperature dependent: at lower temperatures, the dynamics reflects intrinsic stress relaxation processes, whereas at higher temperatures becomes dose-controlled. These findings demonstrate that the dynamical response to X-ray excitation is not determined solely by chemical composition or bonding character, but results from the interplay between irradiation effects and structural relaxation pathways.

cond-mat.mtrl-sci↗
arXiv2026

A general formula for walk determinants of rooted products with applications to DGS-graph constructions

For an $n$-vertex graph $G$, and a rooted graph $H^{(v)}$ with $v$ as the root, the rooted product graph $G\circ H^{(v)}$ is obtained from $G$ and $n$ copies of $H$ by identifying the root of the $i$th copy of $H$ with the $i$th vertex of $G$ for each $i$. As a refinement of the controllability criterion of $G\circ H^{(v)}$ obtained recently by Shan and Liu (2025), we obtain an explicit formula for the determinant of the walk matrix of $G\circ H^{(v)}$. Furthermore, for an important family of graphs $\mathcal{F}$ that are determined by their generalized spectrum (DGS), we introduce the concept of $\mathcal{F}$-preservers and provide a sufficient condition for a rooted graph to be an $\mathcal{F}$-preserver. A list of $\mathcal{F}$-preservers of small order is provided, which leads to many new infinite families of DGS-graphs using rooted products.

math.CO↗
arXiv2025

Metric-Fair Prompting: Treating Similar Samples Similarly

We introduce \emph{Metric-Fair Prompting}, a fairness-aware prompting framework that guides large language models (LLMs) to make decisions under metric-fairness constraints. In the application of multiple-choice medical question answering, each {(question, option)} pair is treated as a binary instance with label $+1$ (correct) or $-1$ (incorrect). To promote {individual fairness}~--~treating similar instances similarly~--~we compute question similarity using NLP embeddings and solve items in \emph{joint pairs of similar questions} rather than in isolation. The prompt enforces a global decision protocol: extract decisive clinical features, map each \((\text{question}, \text{option})\) to a score $f(x)$ that acts as confidence, and impose a Lipschitz-style constraint so that similar inputs receive similar scores and, hence, consistent outputs. Evaluated on the {MedQA (US)} benchmark, Metric-Fair Prompting is shown to improve performance over standard single-item prompting, demonstrating that fairness-guided, confidence-oriented reasoning can enhance LLM accuracy on high-stakes clinical multiple-choice questions.

cs.CL↗