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Tingting Li

Tingting Li appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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math.RAphysics.app-phArtificial IntelligenceMachine Learningmath.APmath.CTmath.DSmath.NAmath.PRmath.STNumerical AnalysisStatistics Theory

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Published work

9 published item(s)

preprint2026arXiv

SciEval: A Benchmark for Automatic Evaluation of K-12 Science Instructional Materials

The need to evaluate instructional materials for K-12 science education has become increasingly important, as more educators use generative AI to create instructional materials. However, the review of instructional materials is time-consuming, expertise-intensive, and difficult to scale, motivating interest in automated evaluation approaches. While large language models (LLMs) have shown strong performance on general evaluation tasks, their performance and reliability on instructional materials remain unclear. To address this gap, we formulate Automatic Instructional Materials Evaluation (AIME) as a generative AI task that predicts scores and evidence using the rubric designed by the educator. We create a benchmark dataset and develop baseline models for AIME. First, we curate the first AIME dataset, SciEval, consisting of instructional materials annotated with pedagogy-aligned evaluation scores and evidence-based rationales. Expert annotations achieve high inter-rater reliability, resulting in a dataset of 273 lesson-level instructional materials evaluated across 13 criteria (N=3549) using the EQuIP rubric. Second, we test mainstream LLMs (GPT, Gemini, Llama, and Qwen) on SciEval and find that none achieve strong performance. Then we fine-tune Qwen3 on SciEval. Results on a held-out test set show that domain-aligned fine-tuning can achieve up to 11 percent performance gains, highlighting the importance of domain-specific fine-tuning for AIME and facilitating the use of LLMs in other educational tasks.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Optimal error estimates of multiphysics finite element method for a nonlinear poroelasticity model with nonlinear stress-strain relations

In this paper, we study the numerical algorithm for a nonlinear poroelasticity model with nonlinear stress-strain relations. By using variable substitution, the original problem can be reformulated to a new coupled fluid-fluid system, that is, a generalized nonlinear Stokes problem of displacement vector field related to pseudo pressure and a diffusion problem of other pseudo pressure fields. A new technique is used to get the existence and uniqueness of the solution of the reformulated model and a fully discrete nonlinear finite element method is proposed to solve the model numerically. The multiphysics finite element is used to get the discretization of the space variable and the backward Euler method is taken as the time-stepping method in the fully discrete case. Stability analysis and the error estimation are given for the fully discrete case and numerical test are taken to verify the theoretical results.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Experimental Extraction and Simulation of Charge Trapping during Endurance of FeFET with TiN/HfZrO/SiO2/Si (MFIS) Gate Structure

We investigate the charge trapping during endurance fatigue of FeFET with TiN/Hf0.5Zr0.5O2/SiO2/Si (MFIS) gate structure. We propose a method of experimentally extracting the number of trapped charges during the memory operation, by measuring the charges in the metal gate and Si substrate. We verify that the amount of trapped charges increases during the endurance fatigue process. This is the first time that the trapped charges are directly experimentally extracted and verified to increase during endurance fatigue. Moreover, we model the interplay between the trapped charges and ferroelectric polarization switching during endurance fatigue. Through the consistency of experimental results and simulated data, we demonstrate that as the memory window decreases: 1) The ferroelectric characteristic of Hf0.5Zr0.5O2 is not degraded. 2) The trap density in the upper bandgap of the gate stacks increases. 3) The reason for memory window decrease is increased trapped electrons after program operation but not related to hole trapping/de-trapping. Our work is helpful to study the charge trapping behavior of FeFET and the related endurance fatigue process.

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preprint2021arXiv

Impact of Interlayer and Ferroelectric Materials on Charge Trapping during Endurance Fatigue of FeFET with TiN/HfxZr1-xO2/interlayer/Si (MFIS) Gate Structure

We study the impact of different interlayers and ferroelectric materials on charge trapping during the endurance fatigue of Si FeFET with TiN/HfxZr1-xO2/interlayer/Si (MFIS) gate stack. We have fabricated FeFET devices with different interlayers (SiO2 or SiON) and HfxZr1-xO2 materials (x=0.75, 0.6, 0.5), and directly extracted the charge trapping during endurance fatigue. We find that: 1) The introduction of the N element in the interlayer suppresses charge trapping and defect generation, and improves the endurance characteristics. 2) As the spontaneous polarization (Ps) of the HfxZr1-xO2 decreases from 25.9 μC/cm2 (Hf0.5Zr0.5O2) to 20.3 μC/cm2 (Hf0.6Zr0.4O2), the charge trapping behavior decreases, resulting in the slow degradation rate of memory window (MW) during program/erase cycling; in addition, when the Ps further decreases to 8.1 μC/cm2 (Hf0.75Zr0.25O2), the initial MW nearly disappears (only ~0.02 V). Thus, the reduction of Ps could improve endurance characteristics. On the contract, it can also reduce the MW. Our work helps design the MFIS gate stack to improve endurance characteristics.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

MLPSVM:A new parallel support vector machine to multi-label learning

Multi-label learning has attracted the attention of the machine learning community. The problem conversion method Binary Relevance converts a familiar single label into a multi-label algorithm. The binary relevance method is widely used because of its simple structure and efficient algorithm. But binary relevance does not consider the links between labels, making it cumbersome to handle some tasks. This paper proposes a multi-label learning algorithm that can also be used for single-label classification. It is based on standard support vector machines and changes the original single decision hyperplane into two parallel decision hyper-planes, which call multi-label parallel support vector machine (MLPSVM). At the end of the article, MLPSVM is compared with other multi-label learning algorithms. The experimental results show that the algorithm performs well on data sets.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Numerical analysis and applications of Fokker-Planck equations for stochastic dynamical systems with multiplicative $α$-stable noises

The Fokker-Planck equations (FPEs) for stochastic systems driven by additive symmetric $α$-stable noises may not adequately describe the time evolution for the probability densities of solution paths in some practical applications, such as hydrodynamical systems, porous media, and composite materials. As a continuation of previous works on additive case, the FPEs for stochastic dynamical systems with multiplicative symmetric $α$-stable noises are derived by the adjoint operator method, which satisfy the nonlocal partial differential equations. A finite difference method for solving the nonlocal Fokker-Planck equation (FPE) is constructed, which is shown to satisfy the discrete maximum principle and to be convergent. Moreover, an example is given to illustrate this method. For asymmetric case, general finite difference schemes are proposed, and some analyses of the corresponding numerical schemes are given. Furthermore, the corresponding result is successfully applied to the nonlinear filtering problem.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Characterizations of core and dual core inverses in rings with involution

Let R be a unital ring with involution, we give the characterizations and representations of the core and dual core inverses of an element in R by Hermitian elements (or projections) and units. For example, let a in R and n is an integer greater than or equal to 1, then a is core invertible if and only if there exists a Hermitian element (or a projection) p such that pa=0, a^n+p is invertible. As a consequence, a is an EP element if and only if there exists a Hermitian element (or a projection) p such that pa=ap=0, a^n+p is invertible. We also get a new characterization for both core invertible and dual core invertible of a regular element by units, and their expressions are shown. In particular, we prove that for n is an integer greater than or equal to 2, a is both Moore-Penrose invertible and group invertible if and only if (a*)^n is invertible along a.

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preprint2016arXiv

Core and Dual Core Inverses of a Sum of Morphisms

Let $\mathscr{C}$ be an additive category with an involution $\ast$. Suppose that $φ: X \rightarrow X$ is a morphism of $\mathscr{C}$ with core inverse $φ^{\co} : X \rightarrow X$ and $η: X \rightarrow X$ is a morphism of $\mathscr{C}$ such that $1_X+φ^{\co}η$ is invertible. Let $α=(1_X+φ^{\co}η)^{-1},$ $β=(1_X+ηφ^{\co})^{-1},$ $\varepsilon=(1_X-φφ^{\co})ηα(1_X-φ^{\co}φ),$ $γ=α(1_X-φ^{\co}φ)β^{-1}φφ^{\co}β,$ $σ=αφ^{\co}φα^{-1}(1_X-φφ^{\co})β,$ $δ=β^{\ast}(φ^{\co})^{\ast}η^{\ast}(1_X-φφ^{\co})β.$ Then $f=φ+η-\varepsilon$ has a core inverse if and only if $1_X-γ$, $1_X-σ$ and $1_X-δ$ are invertible. Moreover, the expression of the core inverse of $f$ is presented. Let $R$ be a unital $\ast$-ring and $J(R)$ its Jacobson radical, if $a\in R^{\co}$ with core inverse $a^{\co}$ and $j\in J(R)$, then $a+j\in R^{\co}$ if and only if $(1-aa^{\co})j(1+a^{\co}j)^{-1}(1-a^{\co}a)=0$. We also give the similar results for the dual core inverse.

0 citations0 reviewsNo code linkedOpen access