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Zhixin Liu

Publications and source records attributed to Zhixin Liu.

At least 19 recordsLinked to original sources
arXiv2026

Real-rootedness of the $τ$-polynomial under graph joins

For a simple graph $G$ with $n$ vertices, write its chromatic polynomial in the rising factorial basis as $$ χ_G(x)=\sum_{i=0}^{n}(-1)^{n-i}c_i(G)\langle x\rangle_i,$$ where $ \langle x\rangle_i=x(x+1)\cdots(x+i-1).$ The associated $τ$-polynomial $$ τ_G(x)=\sum_{i=0}^{n}c_i(G)x^i $$ was defined and systematically investigated by Brenti in 1992. In this paper, we prove that if the $τ$-polynomials of two vertex-disjoint simple graphs $G$ and $H$ have only real zeros, then the $τ$-polynomial of their join $G\vee H$ has only real zeros. This settles a conjecture posed by Brenti, Royle and Wagner since 1994.

math.CO↗
arXiv2026

Modeling Bond-Dependent Kitaev-like interaction in 2D Edge-Sharing Tetrahedral Magnets: FeX (X=Te, Se)

Bond-dependent magnetic interactions, exemplified by the Kitaev model, are known to arise from the interplay between spin-orbit coupling (SOC) and specific coordination geometries, but have so far been almost exclusively identified in edge-sharing octahedral systems. Whether such interactions persist in edge-sharing tetrahedral environments, characteristic of the parent compounds of iron-based superconductors, remains an open question. Here, we construct a Kitaev-like model for monolayer FeTe and FeSe and demonstrate the presence of a previously unrecognized bond-dependent Ising-type interaction, induced jointly by chalcogen-mediated SOC and the tetrahedral crystal-field geometry. A microscopic spin model for these bond-dependent interactions is derived via strong-coupling perturbation theory, and the strengths of the individual exchange terms are extracted by partitioning the magnetic anisotropy energy calculated using density functional theory across various collinear magnetic orders. We reveal that the Kitaev-like interaction dominates the magnetic anisotropy in FeTe, whereas in FeSe, it strongly competes with a single-ion anisotropy of opposite sign. The resulting noncollinear local anisotropy axes generate intrinsic single-site spin frustration, providing a microscopic mechanism for magnetic disorder that transcends isotropic exchange models. Our results establish edge-sharing tetrahedral magnets as a new platform for bond-dependent interactions and extend the scope of Kitaev physics beyond octahedral coordination.

physics.comp-ph↗
arXiv2026

Phase-slip residual-order spin state in FeSe

In unconventional superconductors, the microscopic form of magnetic correlations is crucial for identifying the origin of spin fluctuations and the associated pairing interaction. FeSe superconducts without chemical doping and shows no static long-range magnetic order, yet inelastic neutron scattering reveals a strong stripe response, finite linewidths, and reproducible Neel-side spectral weight. Here we propose a phase-slip residual-order spin state (ROSS). Stripe, Neel, pair-checkerboard, and staggered trimer antiferromagnetic states can be unified as symmetric phase-slip derivatives of a stripe background, while more general asymmetric phase slips form lower-energy configurations and reconstruct the spin structure factor S(q) within a finite coherence length. The ROSS therefore reconciles the absence of static magnetic order with strong spin excitations, provides a microscopic picture for the origin of spin fluctuations in FeSe, and establishes a magnetic basis for understanding pairing in unconventional superconducting systems with similar magnetic fingerprints.

cond-mat.supr-con↗
arXiv2026

Distributed adaptive estimation for stochastic large regression models

This paper studies the distributed adaptiveestimation problems for stochastic large regression modelswith an infinite number of parameters. By constructing a re-cursive local cost function, we propose a novel distributedrecursive least squares algorithm to estimate the unknownsystem parameters, where the growth rate of regressors'dimension is characterized by a non-decreasing positivefunction. The almost sure convergence of the proposedalgorithm is established under a cooperative excitationcondition, which incorporates the temporal information andthe spatial information to reflect the cooperative effectamong multiple agents. Moreover, we analyze the predic-tion error by establishing the asymptotic upper boundof the accumulated regret without any excitation condi-tions. The main difficulty of theoretical analysis lies in howto analyze properties of the product of non-independentand non-stationary random matrices, whose dimensionschange over time simultaneously. Some techniques, suchas stochastic Lyapunov function, double-array martingaletheory and algebraic graph theory, are employed to dealwith the above issue. Our theoretical results are derivedwithout imposing independence or stationarity assump-tions on the regression vectors, thereby not excluding thecorrelated feedback signals.

eess.SY↗
arXiv2026

Gradient-Based Adaptive Prediction and Control for Nonlinear Dynamical Systems

This paper investigates gradient-based adaptive prediction and control for nonlinear stochastic dynamical systems under a weak convexity condition on the prediction-based loss. This condition accommodates a broad range of nonlinear models in control and machine learning such as saturation functions, sigmoid, ReLU and tanh activation functions, and standard classification models. Without requiring any persistent excitation of the data, we establish global convergence of the proposed adaptive predictor and derive explicit rates for its asymptotic performance. Furthermore, under a classical nonlinear minimum-phase condition and with a linear growth bound on the nonlinearities, we establish the convergence rate of the resulting closed-loop control error. Finally, we demonstrate the effectiveness of the proposed adaptive prediction algorithm on a real-world judicial sentencing dataset. The adaptive control performance will also be evaluated via a numerical simulation.

eess.SY↗
arXiv2026

Broadband Second Harmonic Generation using Fixed-Period Periodically Poled Lithium Niobate

Periodically poled lithium niobate (PPLN) is a widely used nonlinear optical device for second harmonic generation (SHG). Despite its wide adoption in commercial systems, its bandwidth for SHG is fundamentally limited by the quasi-phase matching condition. This can be overcome by aperiodic or chirped PPLN structures; however, such devices are typically custom-fabricated and not readily available commercially. In this study, we investigate an alternative approach to achieving broadband SHG by using a standard PPLN crystal containing multiple fixed poling periods. Broadband operation is realized by angle tuning the crystal relative to input beam in free-space. The effect of angle tuning is examined over a range of incident angles, and an 1.6x enhancement in SHG bandwidth is demonstrated. These results suggest a practical and efficient strategy for broadband SHG using standard PPLN devices.

physics.optics↗
arXiv2026

A Comprehensive Evaluation of LLM Reasoning: From Single-Model to Multi-Agent Paradigms

Large Language Models (LLMs) are increasingly deployed as reasoning systems, where reasoning paradigms - such as Chain-of-Thought (CoT) and multi-agent systems (MAS) - play a critical role, yet their relative effectiveness and cost-accuracy trade-offs remain poorly understood. In this work, we conduct a comprehensive and unified evaluation of reasoning paradigms, spanning direct single-model generation, CoT-augmented single-model reasoning, and representative MAS workflows, characterizing their reasoning performance across a diverse suite of closed-form benchmarks. Beyond overall performance, we probe role-specific capability demands in MAS using targeted role isolation analyses, and analyze cost-accuracy trade-offs to identify which MAS workflows offer a favorable balance between cost and accuracy, and which incur prohibitive overhead for marginal gains. We further introduce MIMeBench, a new open-ended benchmark that targets two foundational yet underexplored semantic capabilities - semantic abstraction and contrastive discrimination - thereby providing an alternative evaluation axis beyond closed-form accuracy and enabling fine-grained assessment of semantic competence that is difficult to capture with existing benchmarks. Our results show that increased structural complexity does not consistently lead to improved reasoning performance, with its benefits being highly dependent on the properties and suitability of the reasoning paradigm itself. The codes are released at https://gitcode.com/HIT1920/OpenLLMBench.

cs.LG↗
arXiv2026

Convergence Analysis of Weighted Median Opinion Dynamics with Higher-Order Effects

The weighted median mechanism provides a robust alternative to weighted averaging in opinion dynamics. Existing models, however, are predominantly formulated on pairwise interaction graphs, which limits their ability to represent higher-order environmental effects. In this work, a generalized weighted median opinion dynamics model is proposed by incorporating high-order interactions through a simplicial complex representation. The resulting dynamics are formulated as a nonlinear discrete-time system with synchronous opinion updates, in which intrinsic agent interactions and external environmental influences are jointly modeled. Sufficient conditions for asymptotic consensus are established for heterogeneous systems composed of opinionated and unopinionated agents. For homogeneous opinionated systems, convergence and convergence rates are rigorously analyzed using the Banach fixed-point theorem. Theoretical results demonstrate the stability of the proposed dynamics under mild conditions, and numerical simulations are provided to corroborate the analysis. This work extends median-based opinion dynamics to high-order interaction settings and provides a system-level framework for stability and consensus analysis.

eess.SY↗
arXiv2026

Beyond Immediate Activation: Temporally Decoupled Backdoor Attacks on Time Series Forecasting

Existing backdoor attacks on multivariate time series (MTS) forecasting enforce strict temporal and dimensional coupling between triggers and target patterns, requiring synchronous activation at fixed positions across variables. However, realistic scenarios often demand delayed and variable-specific activation. We identify this critical unmet need and propose TDBA, a temporally decoupled backdoor attack framework for MTS forecasting. By injecting triggers that encode the expected location of the target pattern, TDBA enables the activation of the target pattern at any positions within the forecasted data, with the activation position flexibly varying across different variable dimensions. TDBA introduces two core modules: (1) a position-guided trigger generation mechanism that leverages smoothed Gaussian priors to generate triggers that are position-related to the predefined target pattern; and (2) a position-aware optimization module that assigns soft weights based on trigger completeness, pattern coverage, and temporal offset, facilitating targeted and stealthy attack optimization. Extensive experiments on real-world datasets show that TDBA consistently outperforms existing baselines in effectiveness while maintaining good stealthiness. Ablation studies confirm the controllability and robustness of its design.

cs.CR↗
arXiv2025

Adaptive Inverse Reinforcement Learning with Online Off-Policy Data Collection

In this paper, the inverse reinforcement learning (IRL) problem is addressed to reconstruct the unknown cost function underlying an observed optimal policy in a model-free manner, whose online adaptation with completely off-policy system data still remains unclear in the literature. Without prior knowledge of the system model parameters, an adaptive and direct learning rule for the cost parameter is proposed using online off-policy system data, which only needs to satisfy the mild persistently exciting condition in the general data-driven paradigm. The adaptive and online IRL algorithm is achieved by designing full Nesterov-Todd (NT)-step primal-dual interior-point iterations. Despite solving a nonlinear and time-varying semi-definite program (SDP), the influence of system noise is rigorously analyzed, and the proposed online algorithm is shown to achieve a sublinear convergence. The proposed method is further generalized to nonlinear IRL based on differential dynamic programming. The gradient of the loss function is directly obtained via a backward pass, which eliminates the need to repeatedly solve forward RL problems as in conventional bi-level IRL frameworks. Finally, the efficiency and effectiveness of the proposed algorithms are demonstrated by numerical examples.

math.OC↗
arXiv2025

FRAME: Feedback-Refined Agent Methodology for Enhancing Medical Research Insights

The automation of scientific research through large language models (LLMs) presents significant opportunities but faces critical challenges in knowledge synthesis and quality assurance. We introduce Feedback-Refined Agent Methodology (FRAME), a novel framework that enhances medical paper generation through iterative refinement and structured feedback. Our approach comprises three key innovations: (1) A structured dataset construction method that decomposes 4,287 medical papers into essential research components through iterative refinement; (2) A tripartite architecture integrating Generator, Evaluator, and Reflector agents that progressively improve content quality through metric-driven feedback; and (3) A comprehensive evaluation framework that combines statistical metrics with human-grounded benchmarks. Experimental results demonstrate FRAME's effectiveness, achieving significant improvements over conventional approaches across multiple models (9.91% average gain with DeepSeek V3, comparable improvements with GPT-4o Mini) and evaluation dimensions. Human evaluation confirms that FRAME-generated papers achieve quality comparable to human-authored works, with particular strength in synthesizing future research directions. The results demonstrated our work could efficiently assist medical research by building a robust foundation for automated medical research paper generation while maintaining rigorous academic standards.

cs.CL↗
arXiv2025

Impact of nonlinear spectral broadening on the phase noise properties of electro-optic frequency comb

Electro-optic modulation is an attractive approach for generating flat, stable, and low-noise optical frequency combs with relatively high power per comb line. However, a key limitation of electro-optic combs is the restricted number of comb lines imposed by the available RF source power. To overcome this limitation, a nonlinear spectral broadening stage is typically employed. The phase noise characteristics of an electro-optic comb are well described by the standard phase noise model, which depends on two parameters: the seed laser and the RF source phase noise. A fundamental question that arises is how nonlinear broadening processes affect the phase noise properties of the expanded comb. To address this, we employ coherent detection, digital signal processing, and subspace tracking. Our experimental results show that the nonlinearly broadened comb preserves the standard phase noise model of the input electro-optic comb. In other words, the nonlinear processes neither introduce additional phase noise terms nor amplify the existing contributions from the seed laser and RF source. Hence, nonlinear broadening can be viewed as equivalent to driving the electro-optic comb with a much higher RF modulation power.

physics.optics↗
arXiv2025

A Computationally Efficient Finite Element Method for Shape Reconstruction of Inverse Conductivity Problems

The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE constraints have been widely used to deal with this problem. However, such approaches typically require repeated iterations and solving the forward problem at each iteration, which leads to a heavy computational cost. To address this issue, we first reformulate the inverse conductivity problem as a minimization problem involving a regularized residual functional. We then transform this minimization problem into a variational problem and establish the equivalence between them. This reformulation enables the employment of the finite element method to reconstruct the shape of the object from finitely many measurements. Notably, the proposed approach allows us to identify the object directly without requiring any iterative procedure. {\it A prior} error estimates are rigorously established to demonstrate the theoretical soundness of the finite element method. Based on these estimates, we provide a criterion for selecting the regularization parameter. Additionally, several numerical examples are presented to verify the feasibility of the proposed approach in shape reconstruction.

math.NA↗
arXiv2025

Contest for system observability as an infinitely repeated game

This paper studies a system security problem in the context of observability based on a two-person noncooperative infinitely repeated game. Both the attacker and the defender have means to modify the dimension of the unobservable subspace, which is set as the value function. Utilizing tools from geometric control, we construct the best response sets considering one-step and two-step optimality respectively to maximize or minimize the value function. We establish a unified necessary-and-sufficient condition for Nash equilibrium that holds for both one-step and two-step optimizations. Our analysis further uncovers two evolutionary patterns, lock and loop modes, and shows an asymmetry between defense and attack. The defender can lock the game into equilibrium, whereas the attacker can disrupt it by sacrificing short-term utility for longer-term advantage. Six representative numerical examples corroborate the theoretical results and highlight the complexity of possible game outcomes.

math.OC↗
arXiv2025

Synchronous Clock and RF Carrier Transmission for Radio Access Network Fronthaul

We simultaneously achieve clock synchronisation, clock-synchronised data transmission and ultra-low noise RF carrier generation by combining clock phase caching and frequency comb transmission in radio access networks (RAN). We demonstrate <100fs jitter for 25GHz RF carrier and 2.5GHz clock, and 16-hour 6.6ps RMS wander.

eess.SY↗