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Yongqiang Liu

Publications and source records attributed to Yongqiang Liu.

At least 19 recordsLinked to original sources
arXiv2026

Accretion of a Plasma Vlasov Gas onto a Reissner-Nordström Black Hole

We develop a steady-state, spherically symmetric accretion model for a two-component plasma Vlasov gas in the background of a Reissner--Nordström black hole. Analytical expressions in parametric form for the critical angular momentum and impact parameter are derived for each species, leading to a rigorous partition of the absorption and scattering domains in phase space. For both monoenergetic and Jüttner distributions, electromagnetic attraction enhances, while repulsion suppresses, the particle number density, energy density, pressure and accretion rates of individual charged components relative to the neutral case. After proper normalization, the total physical quantities of the plasma (under non-extreme conditions) can be expressed exactly, or to high accuracy, as weighted averages of the two species. When the two components share identical distribution functions, accretion drives the Reissner--Nordström black hole naturally toward the Schwarzschild limit---a charge evolution that is absent in neutral-gas models. Numerical results further reveal that near the horizon the radial pressure is significantly smaller than the tangential pressure, sharply distinguishing the Vlasov gas from a perfect fluid.

gr-qc↗
arXiv2026

Twisted homology jump loci, twisted Alexander polynomials, and $Σ$-invariants

We introduce the twisted homology jump loci of a space $X$: the jump loci for homology with coefficients in rank-one local systems, twisted by a fixed finite-dimensional representation $σ$ of $π_1(X)$. These loci refine the classical characteristic varieties, and their defining equations in degree one are the twisted Alexander polynomials of knot theory. Our main theorem is that their tropicalizations bound from above the Bieri--Neumann--Strebel--Renz (BNSR) $Σ$-invariants of $X$. Twisting gains real ground. The resulting bound is strictly stronger than the untwisted tropical bounds obtained from the usual characteristic varieties: for a one-relator group whose $Σ^1$ was computed by Brown, the untwisted bound excludes only two directions in $H^1(G;\mathbb{R})$, whereas the twisted bound determines $Σ^1(G)$ exactly. For a compact orientable $3$-manifold $M$ with toroidal or empty boundary, the twisted bound is sharp: the union of the twisted tropical varieties over all finite-image integral representations of $π_1(M)$ computes $Σ^1(π_1(M))$, and hence recovers the fibered faces of the Thurston norm ball. Sharpness genuinely requires twisting: a non-fibered class enters the tropical variety through the vanishing of a twisted Alexander polynomial along it, and the untwisted polynomial need not vanish. For a compact Kähler manifold $X$, we prove that the first twisted Alexander polynomial $Δ^σ(X)$ is either $0$ or $1$, for every representation $σ$ over every field, and that $Σ^1(π_1(X))$ is controlled by the hyperbolic orbifold fibrations of $X$ for every $σ$. The obstruction to Kählerianity that comes out of this is strictly finer than its untwisted counterpart: we exhibit groups $G$ with $Δ(G)=1$ but $Δ^σ(G)\ne 1$, which the twisted test excludes from being Kähler and the classical one does not.

math.AG↗
arXiv2026

A discussion on the symmetry of relativistic Vlasov gas and its accretion in Kerr-Newman black hole

We investigate the kinetic properties of collisionless Vlasov gas in Kerr-Newman spacetime, analyzing how spacetime symmetries constrain the distribution functions. The distribution function is shown to depend on the constants of motion ($m, E, L_z, L$) and a configuration variable $Q^{3}$. Furthermore, we discuss in detail the different scenarios of charged particles being captured or scattered by the black hole in Kerr-Newman spacetime, and analytically derive the boundaries of the absorption and scattering domains in phase space. Within the Locally Non-Rotating Frame, we compute particle number density, energy density, principal pressures, and construct a set of diagnostic parameters to quantitatively measure the anisotropy information of the Vlasov gas (relative to a perfect fluid), and provide the analytic results of these physical quantities at spatial infinity. In addition, we discuss the accretion rates of the Kerr-Newman black hole and obtain their analytic expressions. Numerical results for the relative (normalized) mass and energy accretion rates reveal an identical parametric dependence: both are suppressed as the black hole's rotation $a$ and charge $Q$ increase. Conversely, the absolute value of the normalized angular momentum accretion rate (which is negative) increases with $a$, and $Q$ also moderately influences the angular momentum accretion rate through its effect on spacetime geometry. Accretion of weakly charged plasma drives charged black holes toward electrical neutrality while reducing angular momentum, ultimately favoring evolution toward Schwarzschild configurations. These findings provide new insights into kinetic accretion processes in spacetime geometries.

gr-qc↗
arXiv2026

MARDoc: A Memory-Aware Refinement Agent Framework for Multimodal Long Document QA

Iterative retrieval-reasoning agents have recently shown promise for multimodal long-document question answering. However, most existing systems maintain a single growing context that mixes retrieval traces, observations, and intermediate reasoning. As interactions accumulate, key evidence becomes scattered and diluted, making multi-hop reasoning noisy. We propose MARDoc, a Memory-Aware Refinement Agent framework that decouples long-document QA into three specialized agents: an Explorer for multi-granularity multimodal retrieval, a Refiner for distilling interaction traces into structured evidence and reasoning memories, and a Reflector for checking evidence sufficiency and providing targeted feedback. Across iterations, the agents rely on a dynamically updated structured memory rather than a full accumulated interaction history. This design reduces context noise while preserving answer-critical facts and their logical dependencies. Experiments on MMLongBench-Doc and DocBench show that MARDoc achieves strong results, outperforming same-backbone baselines and demonstrating the effectiveness of structured memory for agentic document QA.

cs.CL↗
arXiv2026

JoyAI-LLM Flash: Advancing Mid-Scale LLMs with Token Efficiency

We introduce JoyAI-LLM Flash, an efficient Mixture-of-Experts (MoE) language model designed to redefine the trade-off between strong performance and token efficiency in the sub-50B parameter regime. JoyAI-LLM Flash is pretrained on a massive corpus of 20 trillion tokens and further optimized through a rigorous post-training pipeline, including supervised fine-tuning (SFT), Direct Preference Optimization (DPO), and large-scale reinforcement learning (RL) across diverse environments. To improve token efficiency, JoyAI-LLM Flash strategically balances \emph{thinking} and \emph{non-thinking} cognitive modes and introduces FiberPO, a novel RL algorithm inspired by fibration theory that decomposes trust-region maintenance into global and local components, providing unified multi-scale stability control for LLM policy optimization. To enhance architectural sparsity, the model comprises 48B total parameters while activating only 2.7B parameters per forward pass, achieving a substantially higher sparsity ratio than contemporary industry leading models of comparable scale. To further improve inference throughput, we adopt a joint training-inference co-design that incorporates dense Multi-Token Prediction (MTP) and Quantization-Aware Training (QAT). We release the checkpoints for both JoyAI-LLM-48B-A3B Base and its post-trained variants on Hugging Face to support the open-source community.

cs.CL↗
arXiv2025

Spectral sequences, Massey products and homology of covering spaces

We revisit the equivariant spectral sequence considered by Papadima-Suciu, and show that all its differentials are computed by higher order Massey products. As a first application, we extend to arbitrary field coefficients results of Pajitnov relating the size of Jordan blocks for the eigenvalue 1 part of the Alexander modules to the length of nonvanishing Massey products in cohomology. We also give computable upper bounds for the mod p Betti numbers of prime power cyclic covers, and resp. for the ranks of the cohomology groups with coefficients in a prime order rank one local system. Under suitable conditions, these bounds are improvements of the ones obtained by Papadima-Suciu. We also specialize these results to the case of hyperplane arrangement complements, showing, e.g., that vanishing of higher-order Massey products implies that the mod p Betti numbers of prime p tower cyclic covers are combinatorially determined.

math.AT↗
arXiv2025

The homology groups of finite cyclic covering of line arrangement complement

In this paper, we study the first homology group of finite cyclic covering of complex line arrangement complement. We show that this first integral homology group is torsion-free under certain condition similar to the one used by Cohen-Dimca-Orlik. In particular, this includes the case of the Milnor fiber, which generalizes the previous results obtained by Williams for complexified line arrangement to any complex line arrangement.

math.AG↗
arXiv2025

$L^2$-type invariants and cohomology jump loci for complex smooth quasi-projective varieties

Let X be a complex smooth quasi-projective variety with a fixed epimorphism $ν\colonπ_1(X)\twoheadrightarrow \mathbb{Z}$. In this paper, we consider the asymptotic behaviour of invariants such as Betti numbers with all possible field coefficients and the order of the torsion part of singular integral homology associated to $ν$, known as the $L^2$-type invariants. At homological degree one, we give concrete formulas for these limits by the geometric information of $X$ when $ν$ is orbifold effective. The proof relies on a study about cohomological degree one jump loci of $X$. We extend part of Arapura's result for cohomological degree one jump loci of $X$ with complex field coefficients to the one with positive characteristic field coefficients. As an application, when $X$ is a hyperplane arrangement complement, a combinatoric upper bound is given for the number of parallel positive dimensional components in cohomological degree one jump loci with complex coefficients. Another application is that we give a positive answer to a question posed by Denham and Suciu for hyperplane arrangement.

math.AG↗
arXiv2025

Double star arrangement and the pointed multinet

Let $\mathcal{A}$ be a hyperplane arrangement in a complex projective space. It is an open question if the degree one cohomology jump loci (with complex coefficients) are determined by the combinatorics of $\mathcal{A}$. By the work of Falk and Yuzvinsky \cite{FY}, all the irreducible components passing through the origin are determined by the multinet structure, which are combinatorially determined. Denham and Suciu introduced the pointed multinet structure to obtain examples of arrangements with translated positive-dimensional components in the degree one cohomology jump loci \cite{DS}. Suciu asked the question if all translated positive-dimensional components appear in this manner \cite{Suc14}. In this paper, we show that the double star arrangement introduced by Ishibashi, Sugawara and Yoshinaga \cite[Example 3.2]{ISY22} gives a negative answer to this question.

math.AG↗
arXiv2025

Maximal Betti number for local system cohomology of hyperplane arrangement complements

Let $\mathcal{L}$ be a rank one local system with field coefficient on the complement $M(\mathcal{A})$ of an essential complex hyperplane arrangement $\mathcal{A}$ in $\mathbb{C}^\ell$. Dimca-Papadima and Randell independently showed that $M(\mathcal{A})$ is homotopy equivalent to a minimal CW-complex. It implies that $\dim H^k(M(\mathcal{A}),\mathcal{L}) \leq b_k(M(\mathcal{A}))$. In this paper, we show that if $\mathcal{A}$ is real, then the inequality holds as equality for some $0\leq k\leq \ell$ if and only if $\mathcal{L}$ is the constant sheaf. The proof is using the descriptions of local system cohomology of $M(\mathcal{A})$ in terms of chambers.

math.AG↗
arXiv2025

Bieri-Neumann-Strebel-Renz invariants and tropical varieties of integral homology jump loci

Papadima and Suciu studied the relationship between the Bieri-Neumann-Strebel-Renz (short as BNSR) invariants of spaces and the homology jump loci of rank one local systems. Recently, Suciu improved these results using the tropical variety associated to the homology jump loci of complex rank one local systems. In particular, the translated positive-dimensional component of homology jump loci can be detected by its tropical variety. In this paper, we generalize Suciu's results to integral coefficients and give a better upper bound for the BNSR invariants. Then we provide applications mainly to Kähler groups. Specifically, we classify the Kähler group contained in a large class of groups, which we call the weighted right-angled Artin groups. This class of groups comes from the edge-weighted finite simple graphs and is a natural generalization of the right-angled Artin groups.

math.GT↗
arXiv2024

$L^2$-type invariants for complex smooth quasi-projective varieties -- a survey

Let X be a complex smooth quasi-projective variety with an epimorphism $ν\colon π_1(X)\twoheadrightarrow \mathbb{Z}^n$. We survey recent developments about the asymptotic behaviour of Betti numbers with any field coefficients and the order of the torsion part of singular integral homology of finite abelian covers of $X$ associated to $ν$, known as the $L^2$-type invariants. We give relations between $L^2$-type invariants, Alexander invariants and cohomology jump loci. When $ν$ is orbifold effective, we give explicit formulas for $L^2$-invariants at homological degree one in terms of geometric information of $X$. We also propose several related open questions for hyperplane arrangement complement.

math.AG↗
arXiv2024

Orion-14B: Open-source Multilingual Large Language Models

In this study, we introduce Orion-14B, a collection of multilingual large language models with 14 billion parameters. We utilize a data scheduling approach to train a foundational model on a diverse corpus of 2.5 trillion tokens, sourced from texts in English, Chinese, Japanese, Korean, and other languages. Additionally, we fine-tuned a series of models tailored for conversational applications and other specific use cases. Our evaluation results demonstrate that Orion-14B achieves state-of-the-art performance across a broad spectrum of tasks. We make the Orion-14B model family and its associated code publicly accessible https://github.com/OrionStarAI/Orion, aiming to inspire future research and practical applications in the field.

cs.CL↗
arXiv2024

Generic Vanishing, 1-forms, and Topology of Albanese Maps

Given a bounded constructible complex of sheaves $\mathcal{F}$ on a complex Abelian variety, we prove an equality relating the cohomology jump loci of $\mathcal{F}$ and its singular support. As an application, we identify two subsets of the set of holomorphic 1-forms with zeros on a complex smooth projective irregular variety $X$; one from Green-Lazarsfeld's cohomology jump loci and one from the Kashiwara's estimates for singular supports. This result is related to Kotschick's conjecture about the equivalence between the existence of nowhere vanishing global holomorphic 1-forms and the existence of a fibre bundle structure over the circle. Our results give a conjecturally equivalent formulation using singular support, which is equivalent to a criterion involving cohomology jump loci proposed by Schreieder. As another application, we reprove a recent result proved by Schreieder and Yang; namely if $X$ has simple Albanese variety and admits a fibre bundle structure over the circle, then the Albanese morphism cohomologically behaves like a smooth morphism with respect to integer coefficients. In a related direction, we address the question whether the set of 1-forms that vanish somewhere is a finite union of linear subspaces of $H^0(X,Ω_X^1)$. We show that this is indeed the case for forms admitting zero locus of codimension 1.

math.AG↗
arXiv2023

The homology growth for finite abelian covers of smooth quasi-projective varieties

Let $X$ be a complex smooth quasi-projective variety with a fixed epimorphism $ν\colonπ_1(X)\twoheadrightarrow H$, where $H$ is a finitely generated abelian group with $\mathrm{rank}H\geq 1$. In this paper, we study the asymptotic behaviour of Betti numbers with all possible field coefficients and the order of the torsion subgroup of singular homology associated to $ν$, known as the $L^2$-type invariants. When $ν$ is orbifold effective, we give explicit formulas of these invariants at degree 1. This generalizes the authors' previous work for $H\cong \Z$.

math.AG↗