arXiv subjects

Xing Gao

Publications and source records attributed to Xing Gao.

At least 19 recordsLinked to original sources

arXiv2026

Extremely Low Mass Ratio Contact Binaries. III. Photometric and Spectroscopic Investigations of Eleven Systems

We present photometric and spectroscopic investigations of 11 totally eclipsing contact binaries with mass ratios below 0.15, classifying them as extremely low mass ratio contact binaries. The ground-based multiband light curves were modeled with PHysics Of Eclipsing BinariEs to derive the photometric parameters of these systems. The TESS light curves of J011323 and J002747 show pronounced asymmetries and continuous variations. Markov Chain Monte Carlo modeling suggests that these variations are related to longitudinal migration of spots on the primary components. Spectral subtraction of the LAMOST spectra reveals excess chromospheric emission in six systems, while no detectable excess emission is found in the other five. The O$-$C analysis indicates secular period increases in six systems and secular decreases in five systems. We estimated their orbital angular momenta and performed a dynamical analysis. {Within our adopted semi-analytical framework without energy transfer, the formation of these observed systems requires additional angular momentum loss beyond saturated magnetic braking and gravitational radiation, but this requirement could be modified by different assumptions on mass transfer or radius evolution.

astro-ph.SR↗

arXiv2026

Solution to an open problem on the computational complexity of immanant

Immanants are a class of generalized matrix functions associated with the irreducible characters of the symmetric group. B\"{u}rgisser [SIAM J. Comput., 30 (2000), pp. 1023--1040] proved that the computation of hook immanants and immanants corresponding to rectangular Young diagrams of polynomially growing width is VNP-complete under $p$-projections. And he posed an open problem: whether the family of immanants corresponding to rectangular Young diagrams of width $2$ is VNP-complete under $p$-projections. This paper gives a solution to this problem. We prove that, over any field of characteristic zero, the immanant families associated with rectangular Young diagrams of width $2$ and of length $2$ are both VNP-complete under $p$-projections.

math.CO↗

arXiv2026

Disuccessors, Gr\"obner-Shirshov bases and free L-dendriform algebras

In this paper, we prove respectively that the disuccessor operations on the associative operad $\as$, the Lie operad $\lie$, and the pre-Lie operad $\prelie$ preserve Gr\"obner-Shirshov bases. This structural preservation enables the transfer of known bases to more complex operads. As a consequence, we introduce new methods for constructing Gr\"obner-Shirshov bases for the $\dend$ and $\prelie$ operads, and explicitly construct a Gr\"obner-Shirshov basis for the free L-dendriform algebra. This provides a conceptual and computationally efficient resolution of Madariaga's problem and offers new insights into the combinatorial structure of L-dendriform algebras.

math.RA↗

arXiv2026

GAUGE: A Measurement-Grounded Benchmark for Physical Fidelity in Simulation Engines and Video World Models

Physics engines facilitate large-scale training and evaluation for embodied intelligence, while generative video world models are emerging as implicit simulators of future states and interactions. However, existing evaluations of physical fidelity are often conducted in isolation and rely heavily on perceptual similarity or human judgments, providing limited insight into which physical principles or parameters are violated. We introduce GAUGE, a real-world-grounded diagnostic benchmark for jointly evaluating how numerical simulators and generative video world models reproduce or deviate from real-world physics. It comprises 22 controlled task families covering rigid bodies, flexible cables, textiles, and volumetric deformable objects. Grounded in real-world trajectories and paired with calibrated physical metadata, uncertainty annotations, and task-specific observables, these tasks cover fundamental physical processes including collision, friction, momentum transfer, oscillation, self-contact, and deformation across diverse materials and conditions. We benchmark Isaac Sim, Genesis, and Newton on 14 task families using generalized trajectory errors, and evaluate 6 image-to-video models on 5 rigid-body tasks by testing physical-law consistency and the temporal stability of inferred parameters. Our results reveal no uniformly faithful physics engine, with the largest discrepancies arising in impulsive contact, rapid textile motion, and volumetric deformation. We further find that video world models can produce trajectories with the expected equation form while recovering incorrect accelerations, momentum transfer, and oscillation timing. GAUGE lays the groundwork for developing more physically faithful simulators and world models for embodied intelligence.

cs.AI↗

arXiv2026

From SQL Errors to Concept Gaps: An AI-Powered Knowledge Graph Analytics Platform for Personalized Feedback

This innovative practice full paper describes an AI-powered knowledge graph platform that connects SQL errors to conceptual gaps in undergraduate and graduate database systems courses. Students learning Structured Query Language (SQL) frequently struggle with semantic errors that reflect conceptual misunderstandings rather than syntax mistakes. A query may execute yet return incorrect results due to gaps spanning related concepts; misusing NATURAL JOIN in place of an explicit subquery reflects intertwined misunderstandings of JOIN, GROUP BY, and HAVING. Autograding systems detect correctness but provide surface-level feedback without connecting errors to the conceptual structure of the course. Educational knowledge graph research has shown the value of structured concept representations for curriculum analysis and adaptive learning, but these approaches have not been applied to diagnosing SQL misconceptions from student submissions. We present a platform that automatically extracts course concepts and relations from instructional materials, links them to student submission traces through a graph database, and classifies errors at the concept level. We evaluate the platform across two database systems courses at two universities, one using real student submissions and one using simulated submissions, through an expert study with five participants and an automated evaluation using an LLM as a judge. Results show that 95.7% of extracted nodes were rated as at least somewhat valid and 63.8% of triplets were rated fully correct. Expert feedback confirmed that the generated graphs align with instructor mental models and that mapping errors to course concepts provides actionable diagnostic insight; evaluating impact on student learning remains future work.

cs.CL↗

arXiv2026

Exploratory, Communicative, and Deployable: Vision-Driven Embodied Agents for Open-World Mobile Manipulation

Real-world deployment of embodied agents requires active exploration, visual grounding, and interactive intent disambiguation. However, existing frameworks often rely on privileged simulator states or assume complete instructions, bypassing realistic deployment challenges. To bridge this gap, we present REAL, an agentic framework for open-world mobile manipulation. REAL establishes sim-to-real-consistent environment APIs without oracle perception and integrates a simulated user to enable human-in-the-loop interaction. Within this environment, we design diverse task compositions to drive data collection, supervised fine-tuning, and online reinforcement learning, systematically optimizing agent performance. To comprehensively evaluate this approach, we introduce REAL-Bench, a benchmark spanning 241 tasks across active exploration, visual distraction, articulated manipulation, and interactive disambiguation. Experimental results demonstrate that our trained agent outperforms leading commercial closed-source VLMs on interactive tasks with a 56.9% success rate. Further empirical analysis reveals that our hierarchical training pipeline successfully aligns the model's tool-use capabilities while maintaining robust open-vocabulary reasoning under extended exploration horizons. Finally, we deploy and evaluate our framework on a physical dual-arm mobile robot, where it achieves a 78.3% end-to-end success rate over 60 real-world episodes. These physical trials demonstrate robust zero-shot transferability to unseen household scenarios, validating that our sim-to-real-consistent design successfully bridges the reality gap for long-horizon mobile manipulation. Code is available at https://github.com/InternRobotics/REAL.

cs.CV↗

arXiv2026

The planar Hopf algebra of noncommutative multi-indices

We construct the planar Linares--Otto--Tempelmayr Hopf algebra, thereby filling the missing planar noncommutative multi-index corner in the square relating the LOT, Butcher--Connes--Kreimer, and Munthe-Kaas--Wright Hopf algebras. Starting from the free associative algebra on a weighted alphabet $\mathbb Z_{\ge -1}\times A$, we define an insertion-type product yielding a post-Lie structure on the Lie algebra generated by the linear span $V(A)$ of weight $-1$ monomials whose proper left prefixes all have nonnegative weight, and the Guin--Oudom construction then produces the planar LOT Hopf algebra. We introduce a planar tree fertility map from decorated planar rooted trees to monomials in $V(A)$, prove that it is a linear isomorphism, and obtain a natural Hopf algebra isomorphism with the Munthe-Kaas--Wright Hopf algebra. We further derive an explicit coproduct formula in terms of left-admissible cuts, establish the extraction-contraction coproduct, and construct a word symmetrization operator compatible with the classical tree symmetrization operator.

math.CO↗

arXiv2026

InternVLA-A1.5: Unifying Understanding, Latent Foresight, and Action for Compositional Generalization

Unified models for robot manipulation aim to equip one policy with both the semantic priors of pretrained VLMs and the physical dynamics learned through future prediction. In practice, existing designs tend to erode the semantics of the pretrained backbone, suffer interference among heterogeneous objectives, and learn future prediction from scratch in pixel space, leaving the dynamics priors of pretrained video generators unexploited. We present InternVLA-A1.5, which builds the policy on a native VLM backbone that keeps training on VQA and subtask prediction, and attaches a lightweight unified expert for continuous action generation. Future prediction is recast as a latent-querying problem, where a small set of learnable foresight tokens condenses the task-relevant future into a compact latent code under the supervision of a frozen pretrained video generation model, so the policy inherits world-model dynamics priors without ever learning pixel-level generation. The video branch is discarded at inference, keeping real-time control. Pretrained on 1.2M robot episodes and 3M multimodal samples, InternVLA-A1.5 achieves the best overall results on all six simulation benchmarks. In the real world, the preserved semantics deliver the strongest compositional generalization on held-out instruction bindings, and the two designs together sustain long-horizon execution.

cs.RO↗

arXiv2026

Exact Signature Tail Asymptotics for Pure Rough Paths

We prove~\cite[Conjecture 2.12]{BGS20} on the signature tail asymptotics of pure rough paths and extend it to arbitrary reasonable tensor norms. In more details, let \[ \mathbf X_t=\exp(tl) \,\text{ with }\, l=l_1+\cdots+l_m\,\text{ and }\, l_r\in\mathcal L_r(V), \] be a pure $m$-rough path over a finite dimensional real or complex Banach space, and equip the tensor powers of $V$ with arbitrary reasonable tensor algebra norms. We prove that \[ \limsup_{n\to\infty}\left(\left(\frac{n}{m}\right)!\left\|\pi_n(\exp l)\right\|_n\right)^{m/n}=\|l_m\|_m . \] In particular, this identifies the signature tail with the local $m$-variation of the pure rough path. The upper bound was obtained in~\cite{BGS20}; the main contribution of the paper is the matching lower bound. Its proof is based on finite dimensional developments and a norming cyclic construction. For every top-level tensor $l_m$, we also build a contractive development in which $\|l_m\|_m$ appears as an eigenvalue at degree $m$.

math.PR↗

arXiv2026

EBench: Elemental Diagnosis of Generalist Mobile Manipulation Policies

We present EBench, a simulation benchmark that diagnoses generalist mobile manipulation policies beyond a single success-rate scalar. EBench comprises 26 diverse and challenging manipulation tasks annotated along 5 capability dimensions and 4 generalization dimensions. We evaluate state-of-the-art generalist manipulation models including $\pi_0$, $\pi_{0.5}$, XVLA, and InternVLA-A1, and reveal that the models exhibit strikingly different capability profiles: $\pi_{0.5}$ achieves the highest test success rate, the best train--test retention, and the strongest mobile manipulation performance; $\pi_0$ leads on dexterous fixed-base and high-precision tasks; XVLA and InternVLA-A1 exhibit complementary strengths across atomic skills and operating regimes. Beyond capability profiling, EBench analyzes the generalization ability from 4 representative perspectives, identifying the impact of different distribution shift factors. The results reveal strengths and weaknesses of models behind an overall score. We hope this benchmark offers a broad set of diagnostic signals to guide iteration on generalist manipulation models.

cs.RO↗

arXiv2026

A Low-Regularity Semigroup Sewing Lemma via Quotient Structures

We develop a low-regularity Sewing theory for the semigroup coboundary $\hat\delta=\delta-a$ associated with a strongly continuous semigroup $S$. Unlike the ordinary low-regularity Sewing problem, the semigroup setting has an intrinsic algebraic non-uniqueness below the threshold $1$, in the sense that solutions are canonical only modulo semigroup cocycles. Accordingly, the natural target is a quotient space rather than an increment space. We identify this quotient structure and construct the corresponding semigroup Sewing map. The construction uses a frozen terminal-time transform, which rewrites semigroup defects, for each terminal time, as ordinary low-regularity Sewing problems on a frozen simplex. This reduction, however, does not by itself produce a genuine semigroup increment; the main additional step is to prove that the frozen solution classes are compatible as the terminal time varies and hence assemble into a canonical quotient class for $\hat\delta$. This yields canonical classes for $0<\gamma<1$, and at $\gamma=1$ under logarithmic control. We further provide a scale-dependent criterion for selecting genuine representatives, verified for heat semigroups on Sobolev scales through a parabolic Littlewood--Paley tail condition.

math.PR↗

arXiv2026

Infinitesimal Bialgebra on Planar Binary Trees

We construct a weight-zero infinitesimal bialgebra structure on the $\bk$-module spanned by planar binary trees, using the under product $\backslash$ of Aguiar--Sottileand a root-recursive coproduct $\DeltaLR$. We prove that $\DeltaLR$ is coassociative and satisfies the infinitesimal derivation rule with respect to $\backslash$, hence gives a unitary infinitesimal bialgebra distinct from the usual Loday--Ronco Hopf structure. We also obtain an elementary vertex-cut formula, establish freeness properties for unitary $(\backslash,\vee)$-algebras and unitary infinitesimal $(\backslash,\vee)$-bialgebras, and identify the construction with the infinitesimal coproduct transported from planar rooted forests.

math.CO↗

arXiv2026

Stability of nontrivial graph pairs

A graph pair $(\Gamma, \Sigma)$ is called stable if every automorphism of the direct product $\Gamma\times\Sigma$ is induced componentwise by automorphisms of $\Gamma$ and $\Sigma$. A graph is twin-free if no two distinct vertices share the same neighbourhood in the graph. Two graphs $\Gamma$ and $\Sigma$ are coprime with respect to the direct product if there is no graph $\Delta$ of order greater than $1$ such that $\Gamma\cong\Gamma'\times\Delta$ and $\Sigma\cong\Sigma'\times\Delta$ for some graphs $\Gamma'$ and $\Sigma'$. A graph pair $(\Gamma,\Sigma)$ is nontrivial if $\Gamma$ and $\Sigma$ are coprime connected twin-free graphs and exactly one of them is bipartite. In this paper, we prove that if $\Gamma$ is non-bipartite, stable, and factor-loopless, then each nontrivial graph pair $(\Gamma,\Sigma)$ is stable. This gives a partial answer to [Question~19, Qin, Xia and Zhou, Discrete Math., 113856, (2024)] and proves the factor-loopless case of [Conjecture~1.3, Wang, Qin and Xia, arXiv:2509.26170]. We also give affirmative answers to [Questions~3.5, 3.6, Gan, Liu and Xia, J. Combin. Theory Ser. B, 140--164, (2025)] and a negative answer to [Question~3.7, Gan, Liu and Xia, J. Combin. Theory Ser. B, 140--164, (2025)].

math.CO↗

arXiv2026

Ni-O hybridization-driven electronic reconstruction across the superconducting dome in an infinite-layer nickelate

Superconductivity in infinite-layer nickelates has drawn wide interest as a cuprate analogue, yet how the electronic structure evolves with hole doping remains unsettled. Here we map the doping- and temperature-dependent unoccupied states of the La-based infinite-layer nickelate La1-xCaxNiO2 using O K-edge and Ni L-edge x-ray absorption spectroscopy. Superconductivity occurs for 0.18<=x<=0.27. Near x~0.20-0.23, low-energy spectral weight redistributes: Ni3d-dominated states decrease while O2p-hybridized states increase, indicating an orbital-selective crossover in Ni-O covalency. This crossover coincides with a sign reversal of the Hall coefficient and precedes the reduction of the superconducting critical temperature at higher doping. By directly linking transport anomalies and the superconducting dome to a measurable Ni-O orbital reorganization, our results provide a key step toward a unified, orbital-resolved phase diagram for infinite-layer nickelates and a practical route to engineer superconductivity via hybridization control.

cond-mat.supr-con↗

arXiv2026

Hole-doped superconductivity above 100 K in infinite-layer cuprate thin films

Since the discovery of superconductivity in (La,Ba)2CuO2 (Ref.~\cite{bednorz1986possible}), a broad family of structurally distinct cuprate superconductors has been proposed or engineered to elucidate the physics of high-temperature superconductivity~\cite{chu2015hole,plakida2010high}. Among them, the infinite-layer cuprate has the simplest structure, consisting only of the essential ingredients for superconductivity: CuO$_2$ square planes separated by spacer ions~\cite{siegrist1988parent}. Despite being proposed nearly 40 years ago, the hole-doped superconductivity via chemical substitution in this compound has not yet been achieved, a fundamental open question in the field. Here, we report the observation of superconductivity in the hole-doped infinite-layer cuprate thin film. Measurements of resistivity and magnetic-field response in Sr1-xRbxCuO2 single-crystal thin films show superconducting transitions with a high onset temperature of 100 K. Hole doping is achieved via the synergistic effect of rubidium substitution and apical oxygen incorporation, as evidenced by structural analysis and transport measurements. As the parent structure of the cuprate family~\cite{chu2015hole}, hole-doped infinite-layer cuprate provides a unique platform for revisiting key puzzles in cuprate superconductors~\cite{keimer2015quantum,tsuei2000pairing,armitage2010progress,dagotto1994correlated}, including strange metal~\cite{proust2019remarkable,taillefer2010scattering} and electron-hole symmetry~\cite{tohyama2004asymmetry,segawa2010zero,lee2014asymmetry}, while bridging to cuprate-nickelate symmetry~\cite{li2019superconductivity,zeng2022superconductivity,chow2025bulk,lechermann2020late}.

cond-mat.supr-con↗

arXiv2026

Fertility fibres and coproduct coefficients in the LOT Hopf algebra

We study fibres of the fertility map $\Phi$ from decorated rooted trees to decorated multi-index monomials. For a multi-index $\mathbf{k}$ of weight $-1$, the fibre $\mathcal F_{\mathbf{k}}=\{\,t:\Phi(t)=\xx^{\mathbf{k}}\,\}$ consists of all rooted trees with decoration--fertility profile $\mathbf{k}$. We consider its ordinary cardinality $F_{\mathbf{k}}$, its symmetry-weighted cardinality $W_{\mathbf{k}}$, and the coefficient mass $J_{\mathbf{k}}$ appearing in the tree expansion of the transposed embedding $\jmath$. We obtain an explicit formula and a functional equation for the weighted counts, and an exact multiset recursion together with a cycle-index functional equation for the ordinary counts. We also introduce coefficient generating functions for the lowering derivation $\bar\partial$, derive recursive and transport-array formulas for the corresponding coefficients, and use them to refine the admissible-cut formula for the coproduct in the LOT Hopf algebra.

math.CO↗

arXiv2026

Jump It\^o-type formula with arbitrary regularity

We establish an It\^o-type formula for finite $p$-variation paths with jumps for arbitrary $p\geq 1$. The formula is stated in a fully pathwise form and separates the reduced rough integral from explicit left- and right-jump correction terms. In the c\`adl\`ag case, only the left-jump correction remains, while in the continuous case, both jump correction terms vanish and the formula recovers the corresponding continuous arbitrary-regularity change-of-variable formula. The proof is based on the reduced rough path framework and a refinement Riemann-Stieltjes convergence criterion adapted to discontinuous paths. This approach allows us to handle the higher-order Taylor expansions required for large values of $p$ and to control the interaction between rough increments and discrete jumps. As applications, we derive It\^o-type formulas for stochastic processes whose sample paths have finite $p$-variation, including pure-jump models and mixed fractional Brownian-jump signals. The latter class includes cases with Hurst parameter $H\leq 1/3$, which fall outside the regime $2\leq p<3$. We also obtain chain-rule identities for nonlinear observables of c\`adl\`ag finite-$p$-variation solutions of random differential equations with jumps, together with a pathwise log-wealth decomposition.

math.PR↗

arXiv2026

A fast X-ray transient with chromatic flares: signatures of violent collisions induced by late-time central engine reactivation

Extragalactic Fast X-ray Transients (EFXTs) represent an emerging class of high-energy phenomena characterized by X-ray outbursts lasting from tens to hundreds of seconds. However, for more than half of the EFXTs, their physical origins remain elusive. In this Letter, we report the discovery of EP250302a, a luminous EFXT detected by the Einstein Probe (EP) at a redshift of $z = 1.131$. The multi-wavelength light curves of EP250302a reveal remarkable temporal features that distinguish it from the previously known EP-detected EFXT population, most notably a needle-like X-ray flare accompanied by smooth optical rebrightening during the afterglow phase. We suggest that the distinct X-ray and optical behaviors constitute the first observed instance of late-time violent collision of two relativistic shells in an EFXT. Drawing on insights from GRB studies, such a collision process strongly indicates the reactivation of a central engine, making EP250302a-like transients a unique laboratory for probing the late-time activity and jet physics of EFXT central engines.

astro-ph.HE↗