arXiv subjects

Jianjun Liu

Publications and source records attributed to Jianjun Liu.

At least 19 recordsLinked to original sources

arXiv2026

Library Reachability in LSR-Synth: How Anti-Memorization Design Changes the Measurement of Symbolic Discovery

Existing benchmarks for scientific equation discovery are largely composed of well-known equations available in the public domain, making it difficult to determine whether a model is discovering laws from data or merely recalling answers from its training corpus. LSR-Synth mitigates this problem by introducing novel synthetic terms into established scientific mechanisms and filtering the resulting tasks for novelty, solvability, and scientific plausibility. This paper examines a narrower measurement question: can these tasks further distinguish scientific priors supplied by language models from conventional operator search that does not access task semantics? We construct a semantics-free baseline using a fixed vocabulary with publicly documented provenance, and assess the role of candidate coverage through semantic blinding, library weakening, and matched operator-family knockouts. Under the current task snapshot, search budget, and scoring protocol, the fixed vocabulary already covers most tasks, while language-model-generated candidates rarely expand the set of solvable instances. Their marginal contribution becomes substantial only when vocabulary coverage is selectively disrupted. Strict out-of-distribution evaluation lowers the absolute success rates of all methods but does not alter this relationship. These findings neither invalidate LSR-Synth's controls against memorization of complete formulas nor imply that language-model priors are generally unhelpful. Rather, they support a more limited conclusion: most current tasks remain suitable for evaluating the fitting and recombination of previously unseen expressions, but are insufficient on their own to identify contributions from priors beyond a fixed search space.

cs.AI↗

arXiv2026

A Sliding-Window-Based Reinforcement Learning for Dynamic Assembly Flow Shop Scheduling with Multi-Product Delivery

Multi-product kitting delivery imposes significant challenges for real-time scheduling in hybrid manufacturing systems that integrate processing and assembly, as dynamic order arrivals simultaneously alter supply dependencies and the set of feasible job-machine assignments. This paper proposes a sliding-window-based reinforcement learning (SWRL) framework for end-to-end online scheduling in the flexible assembly flow shop scheduling problem with complex kitting constraints. The problem is formulated as a heterogeneous graph-based Markov decision process that captures the dual-layer kitting structure and the tail-product bottleneck dynamics that produce a sparse reward landscape. To address the resulting challenges, SWRL integrates a sliding-window filtering mechanism that filters inactive nodes and prioritizes kitting-critical operations, a spatiotemporal graph encoding network that tracks bottleneck shifts across consecutive decision states, and a dynamic action mapping module with a constrained waiting strategy that adapts to the changing action space under variable topologies. Experiments on real-world instances from a home appliance manufacturer demonstrate that SWRL achieves consistent tardiness reductions over classical dispatching rules and existing deep reinforcement learning methods, and exhibits robust performance across varying resource configurations, order loads, and arrival concentrations.

cs.AI↗

arXiv2026

A Symmetry Method for Key Vanishing Lemmas and Optimal $2$-Jet Thresholds for Hyperbolicity

This manuscript reports on an ongoing project. The finite full-column-rank computations underlying the Key Vanishing Lemmas isolated below are currently undergoing exact computer-assisted verification. Conditional on successful completion of that verification, the arguments presented here would establish the two positivity endpoints of Demailly's invariant two-jet Riemann--Roch calculation: every very general surface in $\mathbb{P}^3$ of degree $15$ would be Kobayashi hyperbolic, and the complement of every general smooth plane curve of degree $11$ would be Kobayashi hyperbolic. At the logarithmic endpoint the same conditional argument would also give a Second Main Theorem with coefficient $1422$; the preceding work treated all degrees $d\geqslant12$. The argument separates an infinite geometric range from a finite algebraic obstruction.An $\mathcal{O}(3)$ slanted-vector-field package combines a quadratic acceleration with a classical matrix lift. Their incompatible actions on the invariant fibre ring, together with the common-twist, prime-ideal, and relative-family interfaces, exclude the dependence alternative for every weight $m\geqslant3$. This improves the differentiation range from $t\geqslant8$ to $t\geqslant4$ and leaves, beyond the twist-one ranges, only five compact and thirteen logarithmic systems. The residual systems are reduced by symmetry. A two-term Fermat perturbation carries an involution, so a hypothetical negatively twisted two-jet differential has an invariant or anti-invariant component. Imposing this eigencondition before elimination adds exact linear constraints without adding unknowns. The required full-column-rank statements are isolated in the Key Vanishing Lemmas as finite computational targets. This paper records their finite reduction and proof-to-certificate interface. Their exact computer-assisted verification is in progress.

math.AG↗

arXiv2026

MatMind: A Structure-Activity Knowledge-Driven Generative Foundation Model for Materials Science

Progress in AI-driven crystal materials science has so far been carried by narrow architectures purpose-built for individual tasks -- graph neural networks for property prediction, diffusion and flow-matching models for crystal generation -- each excelling within its niche yet unable to act as a shared backbone across the full spectrum of materials problems. Generative large language models offer a fundamentally different paradigm, in which structural representation, quantitative prediction, and structure-activity reasoning can be unified within one model, but the materials community has yet to see this paradigm realized at a level competitive with established narrow specialists. Here we present MatMind, a generative foundation model purpose-built for crystal materials science under this paradigm, developed through the coordinated activation of structure-activity knowledge and physics-informed feedback within a progressive training framework -- combining structure-activity knowledge injection, a dual-head architecture that jointly trains language reasoning and numerical regression in a shared representation space, and multi-objective physics-informed reinforcement learning over stability, novelty, and structural diversity. Across three task families, MatMind attains the lowest mean absolute error on energy above hull, bulk modulus, and band gap -- surpassing graph neural network predictors purpose-built for these tasks -- reaches an S.U.N. rate of 65.3% on unconditional crystal generation, and achieves a comparable multiplicative improvement on magnetization-density-conditioned generation, where only 21 positive samples exist within over 600000 training entries. By matching or surpassing narrow specialists on their own ground while operating within a single unified model, MatMind shows that the LLM-based paradigm can serve as a viable backbone for crystal materials science going forward.

cond-mat.mtrl-sci↗

arXiv2026

CT-Guided Spatially-varying Regularization for Voxel-Wise Deformable Whole-Body PET Registration

Whole-body Positron Emission Tomography (PET) registration is essential for multi-parametric tumor characterization and assessment of metastatic disease progression. In deep learning-based deformable registration, the dense displacement field (DDF) regularizer is crucial for stabilizing optimization and preventing unrealistic deformations in large 3D volumes. A key challenge in whole-body deformable registration is anatomical heterogeneity, rigid structures (e.g., bones) should undergo stronger regularization, whereas soft tissues require more flexible deformation and weaker constraints. In this work, we propose a simple yet effective CT-guided spatially-varying regularization strategy for whole-body cross-tracer deformable PET registration. The key idea is to use the paired CT volume from the PET/CT acquisition to construct a voxel-wise regularization map for the DDF, replacing the conventional single global regularization weight. This yields anatomy-adaptive regularization strength across rigid and soft tissues. The proposed method is evaluated on a real clinical cross-tracer PET/CT dataset of 296 patients involving 18F-PSMA and 18F-FDG, showing that the proposed method achieves statistically significant improvements over weakly-supervised registration baseline in both whole-body registration performance and organ-wise alignment.

eess.IV↗

arXiv2026

Interstellar Object 3I/ATLAS Observed from Mars by China's Tianwen-1 Spacecraft

China's Tianwen-1 Mars orbiter successfully imaged the third interstellar object, 3I/ATLAS, during its close encounter with Mars using the onboard HiRIC CMOS camera. This is China's first deep-space observation of an astronomical object. These observations constitute the first imaging of this object from a vantage point significantly out of its orbital plane, providing a unique constraint on dust dynamics. Three observing epochs between 2025 September 30 and October 3 reveal clear changes in coma and tail morphology driven by the rapidly evolving viewing geometry. Comparison with Finson-Probstein dust dynamical models indicates that the coma is dominated by large grains with solar radiation pressure parameter $\beta \approx 10^{-3} $ - $10^{-2}$, corresponding to grain sizes of a few 100s $\mu$m. The extent of the sunward coma implies dust ejection velocities of $3$ - $10$ m s$^{-1}$. Despite the morphological evolution, the azimuthally averaged surface brightness profile remains nearly unchanged through the three epochs, transitioning from a radial slope near -1 close to the nucleus to slightly steeper than -1.5 at larger cometocentric distances, consistent with steady-state dust outflow accelerated by solar radiation pressure. Photometry yields an average $Af\rho \sim (2.0\pm0.2)\times10^4$ cm and a corresponding dust mass loss rate of $\dot{M} \sim 10^3$ kg s$^{-1}$.

astro-ph.EP↗

arXiv2026

EvoDR: Evolving Dispatching Rules via Large Language Model for Dynamic Flexible Assembly Flow Shop Scheduling

Dynamic flexible assembly flow shop scheduling with multi-product delivery is a critical combinatorial problem, characterized by kitting supply and machine flexibility. Genetic programming is widely used to automatically generate dispatching rules, enabling responsive scheduling that reduces manual effort while meeting high responsiveness demands. However, these methods are dependent on fixed terminal sets and have weak interpretability. In this article, we develop an evolving dispatching rules framework (EvoDR) that leverages the semantic understanding and generation capabilities of large language models to achieve cross-domain integration of algorithm design and scheduling knowledge. Firstly, multi-stage assembly supply decisions are modeled as priority sorting of directed edges based on heterogeneous graphs. A dual-expert co-evolution mechanism is implemented, where LLM-A generates code while LLM-S conducts scheduling analysis and reflection. Guided by improvements in hybrid evaluation, adaptive rules that fit dynamic features are continuously evolved. Experimental results show that the EvoDR achieves lower average tardiness than state-of-the-art approaches. In 24 scenarios with different resource configurations and disturbance levels totaling 480 instances, it consistently outperforms expert-designed competitors, demonstrating superior robustness.

cs.NE↗

arXiv2025

Quantum Metrology via Adiabatic Control of Topological Edge States

Criticality-based quantum sensing exploits hypersensitive response to system parameters near phase transition points. This work uncovers two metrological advantages offered by topological phase transitions when the probe is prepared as topological edge states. Firstly, the order of topological band touching is found to determine how the metrology sensitivity scales with the system size. Engineering a topological phase transition with higher-order band touching is hence advocated, with the associated quantum Fisher information scaling as $ \mathcal{F}_Q \sim L^{2p}$, with $L$ the lattice size in one dimension, and $p$ the order of band touching. Secondly, with a topological lattice accommodating degenerate edge modes (such as multiple zero modes), preparing an $N$-particle entangled state at the edge and then adiabatically tuning the system to the phase transition point grows quantum entanglement to macroscopic sizes, yielding $\mathcal{F}_Q \sim N^2 L^{2p}$. This work hence paves a possible topological phase transition-based route to harness entanglement, large lattice size, and high-order band touching for quantum metrology.

quant-ph↗

arXiv2025

Material Synthesis 2025 (MatSyn25) Dataset for 2D Materials

Two-dimensional (2D) materials have shown broad application prospects in fields such as energy, environment, and aerospace owing to their unique electrical, mechanical, thermal and other properties. With the development of artificial intelligence (AI), the discovery and design of novel 2D materials have been significantly accelerated. However, due to the lack of basic theories of material synthesis, identifying reliable synthesis processes for theoretically designed materials is a challenge. The emergence of large language model offers new approaches for the reliability prediction of material synthesis processes. However, its development is limited by the lack of publicly available datasets of material synthesis processes. To address this, we present the Material Synthesis 2025 (MatSyn25), a large-scale open dataset of 2D material synthesis processes. MatSyn25 contains 163,240 pieces of synthesis process information extracted from 85,160 high-quality research articles, each including basic material information and detailed synthesis process steps. Based on MatSyn25, we developed MatSyn AI which specializes in material synthesis, and provided an interactive web platform that enables multifaceted exploration of the dataset (https://matsynai.stpaper.cn/). MatSyn25 is publicly available, allowing the research community to build upon our work and further advance AI-assisted materials science.

cond-mat.mtrl-sci↗

arXiv2025

S1-MatAgent: A planner driven multi-agent system for material discovery

The discovery of high-performance materials is crucial for technological advancement. Inverse design using multi-agent systems (MAS) shows great potential for new material discovery. However, current MAS for materials research rely on predefined configurations and tools, limiting their adaptability and scalability. To address these limitations, we developed a planner driven multi-agent system (S1-MatAgent) which adopts a Planner-Executor architecture. Planner automatically decomposes complex materials design tasks, dynamically configures various tools to generate dedicated Executor agents for each subtask, significantly reducing reliance on manual workflow construction and specialized configuration. Applied to high-entropy alloy catalysts for hydrogen evolution reactions in alkaline conditions, S1-MatAgent completed full-cycle closed-loop design from literature analysis and composition recommendation to performance optimization and experimental validation. To tackle the deviations between designed materials and target, as well as high experimental verification costs, S1-MatAgent employs a novel composition optimization algorithm based on gradients of machine learning interatomic potential, achieving 27.7 % improvement in material performance. S1-MatAgent designed 13 high-performance catalysts from 20 million candidates, with Ni4Co4Cu1Mo3Ru4 exhibiting an overpotential of 18.6 mV at 10 mA cm-2 and maintaining 97.5 % activity after 500 hours at 500 mA cm-2. The universal MAS framework offers a universal and scalable solution for material discovery, significantly improving design efficiency and adaptability.

cond-mat.mtrl-sci↗

arXiv2025

Almost Global Solutions of Kirchhoff Equation

This paper is concerned with the original Kirchhoff equation $$\left\{\begin{aligned} & \pa_{tt}u-\Big(1+\int_{0}^{\pi}|\pa_xu|^2 dx\Big)\pa_{xx}u=0, \\&u(t,0)=u(t,\pi)=0. \end{aligned}\right.$$ We obtain almost global existence and stability of solutions for almost any small initial data of size $\varepsilon$. In Sobolev spaces, the time of existence and stability is of order $\varepsilon^{-r}$ for arbitrary positive integer $r$. In Gevrey and analytic spaces, the time is of order $e^{\frac{|\ln\varepsilon|^2}{c\ln|\ln\varepsilon|}}$ with some positive constant $c$. To achieve these, we build rational normal form for infinite dimensional reversible vector fields without external parameters. We emphasize that for vector fields, the homological equation and the definition of rational normal form are significantly different from those for Hamiltonian functions.

math.AP↗

arXiv2024

A Birkhoff Normal Form Theorem for Partial Differential Equations on torus

We prove an abstract Birkhoff normal form theorem for Hamiltonian partial differential equations on torus. The normal form is complete up to arbitrary finite order. The proof is based on a valid non-resonant condition and a suitable norm of Hamiltonian function. Then as two examples, we apply this theorem to nonlinear wave equation in one dimension and nonlinear Schr\"{o}dinger equation in high dimension. Consequently, the polynomially long time stability is proved in Sobolev spaces $H^s$ with the index $s$ being much smaller than before. Further, by taking the iterative steps depending on the size of initial datum, we prove sub-exponentially long time stability for these two equations.

math.AP↗

arXiv2024

Superoscillation focusing of high-order cylindrical-vector beams

Traditional superoscillation focusing typically requires complex optimization of the incident light field. These complexities may limit the practical application of superoscillation. High-order radially polarized Laguerre-Gaussian beams inherently support superoscillation focusing due to their multi-ring amplitude distribution and 0 ~ \pi phase alternation, which align with the necessary destructive interference mechanisms. In this study, we demonstrate that by adjusting the beam mode order together with the incident beam size, we can easily control the full width at half maximum, field of view, and energy distribution of superoscillation focusing. Moreover, high-order azimuthally polarized vortex-phase Laguerre-Gaussian beams can also achieve superoscillation focusing, offering even better super-resolution effects. The distinct focusing behaviors of their circular components present unique opportunities for applications involving circular dichroism materials.

physics.optics↗

arXiv2024

KAM for high-dimensional nonlinear quantum harmonic oscillator

In this paper, we study high-dimensional nonlinear quantum harmonic oscillator equation. We show the equation admits many time quasi-periodic solutions by establishing an abstract infinite dimensional KAM theorem with multiple normal frequencies. The proof is based on the classical KAM scheme, and the key is a decaying structure of Hessian matrices of Hamiltonian functions.

math.AP↗

arXiv2024

HTD-Mamba: Efficient Hyperspectral Target Detection with Pyramid State Space Model

Hyperspectral target detection (HTD) identifies objects of interest from complex backgrounds at the pixel level, playing a vital role in Earth observation. However, HTD faces challenges due to limited prior knowledge and spectral variation, leading to underfitting models and unreliable performance. To address these challenges, this paper proposes an efficient self-supervised HTD method with a pyramid state space model (SSM), named HTD-Mamba, which employs spectrally contrastive learning to distinguish between target and background based on the similarity measurement of intrinsic features. Specifically, to obtain sufficient training samples and leverage spatial contextual information, we propose a spatial-encoded spectral augmentation technique that encodes all surrounding pixels within a patch into a transformed view of the center pixel. Additionally, to explore global band correlations, we divide pixels into continuous group-wise spectral embeddings and introduce Mamba to HTD for the first time to model long-range dependencies of the spectral sequence with linear complexity. Furthermore, to alleviate spectral variation and enhance robust representation, we propose a pyramid SSM as a backbone to capture and fuse multiresolution spectral-wise intrinsic features. Extensive experiments conducted on four public datasets demonstrate that the proposed method outperforms state-of-the-art methods in both quantitative and qualitative evaluations. Code is available at \url{https://github.com/shendb2022/HTD-Mamba}.

cs.CV↗

arXiv2024

A note on the $ \Pi $-property of some subgroups of finite groups

Let $ H $ be a subgroup of a finite group $ G $. We say that $ H $ satisfies the $ \Pi $-property in $ G $ if for any chief factor $ L / K $ of $ G $, $ |G/K : N_{G/K}(HK/K\cap L/K )| $ is a $ \pi (HK/K\cap L/K) $-number. In this paper, we obtain some criteria for the $ p $-supersolubility or $ p $-nilpotency of a finite group and extend some known results by concerning some subgroups that satisfy the $ \Pi $-property.

math.GR↗

arXiv2024

Hybrid skin-topological effect induced by eight-site cells and arbitrary adjustment of the localization of topological edge states

The hybrid skin-topological effect (HSTE) in non-Hermitian systems exhibits both the skin effect and topological protection, offering a novel mechanism for the localization of topological edge states (TESs) in electrons, circuits, and photons. However, it remains unclear whether the HSTE can be realized in quasicrystals, and the unique structure of quasicrystals with multi-site cells may provide novel localization phenomena for TESs induced by the HSTE. We propose an eight-site cell in two-dimensional quasicrystals and realize the HSTE with eight-site nonreciprocal intracell hoppings. Furthermore, we can arbitrarily adjust the eigenfield distributions of the TESs and discover domain walls associated with effective dissipation and their correlation with localization. We present a new scheme to precisely adjust the energy distribution in non-Hermitian quasicrystals with arbitrary polygonal outer boundaries.

cond-mat.mes-hall↗

arXiv2024

Aperiodic-quasiperiodic-periodic properties and topological transitions in twisted nested Moir\'e patterns

The Moir\'e patterns generated by altering the structural parameters in a two or more layers of periodic materials, including single-layer structure, interlayer stacking, and twisting parameters, exhibit prosperous topological physical properties. However, the intricate characteristics of twisted nested Moir\'e patterns and their relationship with topological transitions remain unclear. In this Letter, based on the proposed twisted nested photonic crystal (TNPC), we derive its spatial geometric functions (SGFs), aperiodic-quasiperiodic-periodic properties in twisted nested Moir\'e patterns, and the SSH{\phi} Hamiltonian. We reveal the intrinsic correlation between twisted nested Moir\'e patterns and topological transitions, obtaining higher-order topological states (HOTSs) with C2z symmetry. This work will provide theoretical references for the design and application of twisted topological PC and their devices.

cond-mat.mes-hall↗