arXiv subjects

Ting Lin

Publications and source records attributed to Ting Lin.

At least 19 recordsLinked to original sources

arXiv2026

Symmetric Taylor--Hood elements for the linear stress gradient problem

We develop mixed finite element methods for the linear stress-gradient elasticity problem based on symmetric Taylor--Hood elements. We establish the stability of the symmetric Taylor--Hood pair on simplicial meshes in both two and three dimensions, thereby resolving the stability left open by Brezzi, Fortin, and Marini in 1993. Combing the Nitsche's method, we further construct finite element schemes for linear stress problem in general boundary condition. Numerical experiments confirm the theoretical results.

math.NA↗

arXiv2026

Hyperon-Nucleon Spectrometer

Chirality lies at the heart of low-energy QCD, governing the symmetry structure that shapes hadron masses and strong interaction dynamics. Among the most compelling open questions tied to chiral dynamics and spontaneous chiral symmetry breaking is the longstanding $\Lambda$ polarization puzzle, in which $\Lambda$ hyperons produced in unpolarized hadronic collisions exhibit a surprisingly large transverse polarization that remains theoretically unexplained. This whitepaper presents the proposal for the Hyperon-Nucleon Spectrometer (H-NS) at the High-Intensity heavy-ion Accelerator Facility (HIAF). Leveraging the high energy and high intensity of HIAF's proton and heavy-ion beams, the H-NS experiment will perform systematic studies of hyperon polarization phenomena and their underlying mechanisms in proton-proton ($pp$), proton-nucleus ($pA$), and nucleus-nucleus ($AA$) collisions in the fixed target mode. A wide-range beam energy scan, including proton beams from 3 GeV up to 9.3 GeV (HIAF) and up to 32 GeV (upgraded HIAF), will be conducted to examine the dependence of polarization on collision energy. The spectrometer is designed with specialized detectors capable of high-precision reconstruction of final-state baryon polarizations. Among its many interesting and important measurements, H-NS will simultaneously measure hyperon and proton spin observables to explore the polarization mechanism in hadronic interactions and the spin structure of baryons. Furthermore, the use of $pA$ and $AA$ collisions will enable detailed investigations of cold and hot nuclear matter effects on spin polarization. Its physics program and detector development will significantly benefit the future Electron-ion Collider in China.

physics.ins-det↗

arXiv2026

Leakage Suppression in Quantum Control via Static Parameter Offsets

High-fidelity quantum operations require the system dynamics to be strictly confined to the computational subspace. In practice, however, control fields inevitably couple to leakage levels, giving rise to quantum state leakage that significantly reduces the fidelity of the operation. To address this challenge, we propose a general strategy for actively suppressing leakage errors by applying small, static offsets to tunable system parameters. This approach systematically mitigates leakage's detrimental impact on quantum control, without modifying the original control framework or incurring additional time overhead. By avoiding the need for extra suppression pulses or complex optimization procedures altogether, it offers a streamlined solution for leakage compensation while remaining fully compatible with subsequent optimal control techniques. Numerical validation conducted on superconducting quantum circuits demonstrates effective leakage suppression, enabling high-fidelity single-qubit gates, precise control of two-qubit interactions, and perfect state transfer in multi-level systems. Moreover, when integrated with optimal control techniques, our approach also allows for the cooperative suppression of both leakage errors and residual crosstalk. Therefore, this work provides a feasible technical pathway toward the low error thresholds required for fault-tolerant quantum computation.

quant-ph↗

arXiv2026

A Construction of $C^{r}$ Conforming Finite Elements on the Alfeld Split in Any Dimension

Constructing $C^r$ conforming finite element spaces in any dimension is a long-standing problem. For general triangulations, this problem was recently addressed by Hu-Lin-Wu (2024), under certain conditions on supersmoothness and polynomial degree. In this paper, a first unified construction on the Alfeld split in any dimension is given, where the supersmoothness conditions and the polynomial degree requirement are relaxed.

math.NA↗

arXiv2026

Deep learning and the rate of approximation by flows

We investigate the dependence of the approximation capacity of deep residual networks on its depth in a continuous dynamical systems setting. This can be formulated as the general problem of quantifying the minimal time-horizon required to approximate a diffeomorphism by flows driven by a given family $\mathcal F$ of vector fields. We show that this minimal time can be identified as a geodesic distance on a sub-Finsler manifold of diffeomorphisms, where the local geometry is characterised by a variational principle involving $\mathcal F$. This connects the learning efficiency of target relationships to their compatibility with the learning architectural choice. Further, the results suggest that the key approximation mechanism in deep learning, namely the approximation of functions by composition or dynamics, differs in a fundamental way from linear approximation theory, where linear spaces and norm-based rate estimates are replaced by manifolds and geodesic distances.

cs.LG↗

arXiv2026

Regge metrics with enhanced trace

We introduce variants of Regge finite element metrics with enhanced properties of the trace. In particular the trace operator is surjective to a finite element space of continuous functions. Multiplying these scalar functions by the identity tensor brings one back to the finite element space of metrics. The metrics can be based on high order polynomials and be constructed on refinements, such as the Clough-Tocher or Worsey-Farin splits. Potential applications to general relativity, incompressible elasticity and conformal geometry are sketched.

math.NA↗

arXiv2026

Machine learning-aided direct estimation of coherence and entanglement for unknown states

Quantum coherence and entanglement are fundamental resources in quantum technologies, yet their efficient estimation for unknown states by employing minimal resources in experimental settings remains challenging, particularly in high-dimensional systems. We present a machine learning approach based on support vector regression (SVR) that directly estimates the coherence measures and the geometric measure of quantum entanglement using minimal experimental resources. Our method requires only the diagonal entries of the density matrix, along with the traces of the squared and cubed density matrices for quantum coherence, and additionally along with the traces of the squared and cubed reduced density matrix for estimating quantum entanglement. These quantities can be obtained through random measurements or a hybrid quantum-classical framework. This approach significantly reduces the resource overhead compared to quantum state tomography while maintaining high accuracy. {Furthermore, the support vector quantile regression (SVQR) with pinball loss is employed to prevent SVR overestimation. This model not only ensures that over 95\% of predictions are conservative lower bounds in most cases, but also maintains this lower-bound reliability for over 93\% of predictions, despite 2\% perturbations in the input features.} The proposed technique provides a practical and scalable tool for characterizing quantum resources across computation, communication, and metrology applications.

quant-ph↗

arXiv2025

Feasibility Study of Pion and Kaon Structure via the Sullivan Process at EicC

The Electron--Ion Collider in China (EicC) provides an excellent opportunity to explore the internal structure of pions and kaons via the Sullivan process in deep-inelastic scattering (DIS). In this study, we present detailed projections for the pion and kaon structure functions, $F_2^\pi$ and $F_2^K$, at EicC, with a focus on both statistical and systematic uncertainties. Leveraging EicC's high luminosity and broad kinematic coverage, the accessible kinematic region is extended beyond previous measurements. The projected statistical uncertainties for $F_2^\pi$ and $F_2^K$ are below 5\% and 8\%, respectively, across most kinematic bins. Systematic uncertainties arising from detector effects have been carefully evaluated. These results significantly enhance the precision of meson structure function measurements and provide important constraints on theoretical models of meson parton distributions. Moreover, this study bridges the gap between fixed-target and collider-era measurements, highlighting the pivotal role of EicC in advancing our understanding of hadronic structure.

hep-ex↗

arXiv2025

In-plane polar domains enhanced energy storage

Relaxor ferroelectric thin films are recognized for their ultrahigh power density, rendering them highly promising for energy storage applications in electrical and electronic systems. However, achieving high energy storage performance with chemically homogeneous, environmentally friendly and compositionally stable materials remains challenging. In this work, we present a design of dielectrics with high energy storage performance via an in-plane polar domains incorporating polar nanoregions mechanism. Guided by phase-field simulations, we synthesized La/Si co-doping BaTiO3 solid-solution thin films with high chemical homogeneity to realize high energy storage performance. Given that, we achieve a high energy density of 203.7J/cm3 and an energy efficiency of approximately 80% at an electric field of 6.15MV/cm. This mechanism holds significant promise for the design of next-generation high-performance dielectric materials for energy storage and other advanced functional materials.

cond-mat.mtrl-sci↗

arXiv2025

Finite Element Complexes with Traces Structures: A unified framework for cohomology and bounded interpolation

This paper considers the cohomology and bounded interpolation of nonstandard finite element complexes, e.g. Stokes, Hessian, Elasticity, divdiv. Compared to the standard finite element exterior calculus, the main challenge is the existence of extra smoothness. This paper provides a unified framework for finite element complexes with extra smoothness. The trace structure is introduced to derive the bubble complexes in different dimensions (vertices, edges, faces). It is shown that if the bubble complexes in different dimensions are all exact, then the finite element has the correct cohomology. Moreover, the $L^2$ bounded interpolation can be constructed.

math.NA↗

arXiv2025

Shift-Left Techniques in Electronic Design Automation: A Survey

The chip design process involves numerous steps, beginning with defining product requirements and progressing through architectural planning, system-level design, and the physical layout of individual circuit blocks. As the enablers of large-scale chip development, Electronic Design Automation (EDA) tools play a vital role in helping designers achieve high-quality results. The Shift-Left methodology introduces a pathway toward creating digital twins and fusing multiple design steps, thereby transitioning traditionally sequential, physically-aware processes into virtual design environments. This shift allows designers to establish stronger correlations earlier and optimize designs more effectively. However, challenges remain, especially in accurately replicating downstream behaviors and determining the right scope and timing for adoption. These challenges, in turn, have revealed new opportunities for EDA vendors, physical designers, and logic designers alike. As the industry advances toward intelligent EDA tools and techniques, it is timely to reflect on Shift-Left progress made and the challenges that remain. The rise of AI techniques and the momentum of open-source design flows have significantly strengthened prediction and modeling capabilities, making data-driven methods increasingly relevant to the EDA community. This, in turn, enhances the ''Shift-Left'' features embedded in current tools. In this paper, we present a comprehensive survey of existing and emerging paradigms in Shift-Left research within EDA and the broader design ecosystem. Our goal is to provide a unique perspective on the state of the field and its future directions. Relevant papers mentioned are organized in https://github.com/iCAS-SJTU/Shift-Left-EDA-Papers.

cs.AR↗

arXiv2025

Discretizing linearized Einstein-Bianchi system by symmetric and traceless tensors

The Einstein-Bianchi system uses symmetric and traceless tensors to reformulate Einstein's original field equations. However, preserving these algebraic constraints simultaneously remains a challenge for numerical methods. This paper proposes a new formulation that treats the linearized Einstein-Bianchi system (near the trivial Minkowski metric) as the Hodge wave equation associated with the conformal Hessian complex. To discretize this equation, a conforming finite element conformal Hessian complex that preserves symmetry and traceless-ness simultaneously is constructed on general three-dimensional tetrahedral grids, and its exactness is proven.

math.NA↗

arXiv2025

A unified framework for establishing the universal approximation of transformer-type architectures

We investigate the universal approximation property (UAP) of transformer-type architectures, providing a unified theoretical framework that extends prior results on residual networks to models incorporating attention mechanisms. Our work identifies token distinguishability as a fundamental requirement for UAP and introduces a general sufficient condition that applies to a broad class of architectures. Leveraging an analyticity assumption on the attention layer, we can significantly simplify the verification of this condition, providing a non-constructive approach in establishing UAP for such architectures. We demonstrate the applicability of our framework by proving UAP for transformers with various attention mechanisms, including kernel-based and sparse attention mechanisms. The corollaries of our results either generalize prior works or establish UAP for architectures not previously covered. Furthermore, our framework offers a principled foundation for designing novel transformer architectures with inherent UAP guarantees, including those with specific functional symmetries. We propose examples to illustrate these insights.

cs.LG↗

arXiv2025

Mixed Finite element method for stress gradient elasticity

This paper develops stable finite element pairs for the linear stress gradient elasticity model, overcoming classical elasticity's limitations in capturing size effects. We analyze mesh conditions to establish parameter-robust error estimates for the proposed pairs, achieving unconditional stability for finite elements with higher vertex continuity and conditional stability for Continuous Galerkin-Discontinuous Galerkin (CG-DG) pairs when no interior vertex has edges lying on three or fewer lines. Numerical experiments validate the theoretical results, demonstrating optimal convergence rates.

math.NA↗

arXiv2025

Electric-field independent spin-orbit coupling gap in hBN-encapsulated bilayer graphene

The weak spin-orbit coupling (SOC) in bilayer graphene (BLG) is essential for encoding spin qubits while bringing technical challenges for extracting the opened small SOC gap {\Delta}_SO in experiments. Moreover, in addition to the intrinsic Kane-Mele term, extrinsic mechanisms also contribute to SOC in BLG, especially under experimental conditions including encapsulation of BLG with hexagonal boron nitride (hBN) and applying an external out-of-plane electric displacement field D. Although measurements of {\Delta}_SO in hBN-encapsulated BLG have been reported, the relatively large experimental variations and existing experimental controversy make it difficult to fully understand the physical origin of {\Delta}_SO. Here, we report a combined experimental and theoretical study on {\Delta}_SO in hBN-encapsulated BLG. We use an averaging method to extract {\Delta}_SO in gate-defined single quantum dot devices. Under D fields as large as 0.57-0.90 V/nm, {\Delta}_SO=53.4-61.8 {\mu}eV is obtained from two devices. Benchmarked with values reported at lower D field regime, our results support a D field-independent {\Delta}_SO. This behavior is confirmed by our first-principle calculations, based on which {\Delta}_SO is found to be independent of D field, regardless of different hBN/BLG/hBN stacking configurations. Our calculations also suggest a weak proximity effect from hBN, indicating that SOC in hBN-encapsulated BLG is dominated by the intrinsic Kane-Mele mechanism. Our results offer insightful understandings of SOC in BLG, which benefit SOC engineering and spin manipulations in BLG.

cond-mat.mes-hall↗

arXiv2025

Cool-3D: An End-to-End Thermal-Aware Framework for Early-Phase Design Space Exploration of Microfluidic-Cooled 3DICs

The rapid advancement of three-dimensional integrated circuits (3DICs) has heightened the need for early-phase design space exploration (DSE) to minimize design iterations and unexpected challenges. Emphasizing the pre-register-transfer level (Pre-RTL) design phase is crucial for reducing trial-and-error costs. However, 3DIC design introduces additional complexities due to thermal constraints and an expanded design space resulting from vertical stacking and various cooling strategies. Despite this need, existing Pre-RTL DSE tools for 3DICs remain scarce, with available solutions often lacking comprehensive design options and full customization support. To bridge this gap, we present Cool-3D, an end-to-end, thermal-aware framework for 3DIC design that integrates mainstream architectural-level simulators, including gem5, McPAT, and HotSpot 7.0, with advanced cooling models. Cool-3D enables broad and fine-grained design space exploration, built-in microfluidic cooling support for thermal analysis, and an extension interface for non-parameterizable customization, allowing designers to model and optimize 3DIC architectures with greater flexibility and accuracy. To validate the Cool-3D framework, we conduct three case studies demonstrating its ability to model various hardware design options and accurately capture thermal behaviors. Cool-3D serves as a foundational framework that not only facilitates comprehensive 3DIC design space exploration but also enables future innovations in 3DIC architecture, cooling strategies, and optimization techniques. The entire framework, along with the experimental data, is in the process of being released on GitHub.

cs.AR↗

arXiv2025

Finite element form-valued forms: Construction

We provide a finite element discretization of $\ell$-form-valued $k$-forms on triangulation in $\mathbb{R}^{n}$ for general $k$, $\ell$ and $n$ and any polynomial degree. The construction generalizes finite element Whitney forms for the de~Rham complex and their higher-order and distributional versions, the Regge finite elements and the Christiansen--Regge elasticity complex, the TDNNS element for symmetric stress tensors, the MCS element for traceless matrix fields, the Hellan--Herrmann--Johnson (HHJ) elements for biharmonic equations, and discrete divdiv and Hessian complexes in [Hu, Lin, and Zhang, 2025]. The construction discretizes the Bernstein--Gelfand--Gelfand (BGG) diagrams. Applications of the construction include discretization of strain and stress tensors in continuum mechanics and metric and curvature tensors in differential geometry in any dimension.

math.NA↗

arXiv2024

Confined Magnetization at the Sublattice-Matched Ruthenium Oxide Heterointerface

Creating a heterostructure by combining two magnetically and structurally distinct ruthenium oxides is a crucial approach for investigating their emergent magnetic states and interactions. Previously, research has predominantly concentrated on the intrinsic properties of the ferromagnet SrRuO3 and recently discovered altermagnet RuO2 solely. Here, we engineered an ultrasharp sublattice-matched heterointerface using pseudo-cubic SrRuO3 and rutile RuO2, conducting an in-depth analysis of their spin interactions. Structurally, to accommodate the lattice symmetry mismatch, the inverted RuO2 layer undergoes an in-plane rotation of 18 degrees during epitaxial growth on SrRuO3 layer, resulting in an interesting and rotational interface with perfect crystallinity and negligible chemical intermixing. Performance-wise, the interfacial layer of 6 nm in RuO2 adjacent to SrRuO3 exhibits a nonzero magnetic moment, contributing to an enhanced anomalous Hall effect (AHE) at low temperatures. Furthermore, our observations indicate that, in contrast to SrRuO3 single layers, the AHE of [(RuO2)15/(SrRuO3)n] heterostructures shows nonlinear behavior and reaches its maximum when the SrRuO3 thickness reaches tens of nm. These results suggest that the interfacial magnetic interaction surpasses that of all-perovskite oxides (~5-unit cells). This study underscores the significance and potential applications of magnetic interactions based on the crystallographic asymmetric interfaces in the design of spintronic devices.

cond-mat.mtrl-sci↗