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Biao Ma

Publications and source records attributed to Biao Ma.

At least 19 recordsLinked to original sources
arXiv2026

Liouville Rigidity for Real and Complex Degenerate Hessian Equations

We prove Liouville rigidity theorems for translation-invariant real and complex Hessian equations in the viscosity sense, where the PDE is encoded by an admissible set $\mathcal{A}$. The main structural notion is Liouville admissibility, a recursive geometric condition requiring each quotient set to be either boundary compatible or to fall into a terminal class. Our main theorem states that every bounded, globally $C^{0,\alpha}$ entire viscosity solution of \[ \mathrm{Hess}_{\mathbb F}u\in\partial\mathcal{A} \] is constant if and only if $\mathcal{A}$ is Liouville admissible; thus the Liouville-type property is characterized as a geometric property of the admissible set. A central class of examples arises from polarizations of univariate G{\aa}rding polynomials satisfying the monotone root sequence condition, producing mixed elementary-symmetric admissible sets and recovering the standard $k$-Hessian equations as monomial cases. The framework also allows anisotropic constructions, including linear pullbacks and intersections of admissible sets.

math.AP↗
arXiv2026

Ideal G{\aa}rding polynomials

We introduce ideal G{\aa}rding polynomials, a convexity-enhanced subclass of G\aa{}rding polynomials whose G{\aa}rding components are recursively convex under partial differentiation. This class strictly contains real stable polynomials and, after translation and homogenization, lies in the Lorentzian class. Our main result is that ideal G{\aa}rding polynomials still admit a robust structure theory despite this additional convexity: they are preserved under polarization, satisfy natural closure properties, and support a linear preserver theory. A key contribution of this paper is a universal model for univariate G{\aa}rding polynomials, described by monotone root sequences and equivalently by volume polynomials of Pitman--Stanley polytopes. We establish quotient concavity, and Newton--Maclaurin type inequalities, which leads to the polarization theorem, and suggests further connections with convex geometry and Lorentzian polynomials.

math.CO↗
arXiv2026

Taut polynomials from finite quotients of fibered hyperbolic 3-manifold groups

We prove that the finite quotients of a fibered hyperbolic 3-manifold group detect the taut polynomials of fibered faces of the Thurston norm balls, whenever the monodromy map is fully-punctured. Toward this, we develop a general framework for the profinite invariance of twisted multivariable Alexander polynomials. We also identify specific hyperbolic one-cusped 3-manifolds that are profinitely rigid, by a strategy using normalized dilatations and the veering census.

math.GT↗
arXiv2026

G{\aa}rding Polynomials

We introduce G{\aa}rding polynomials, a class of real multivariate polynomials characterized by positivity regions that are invariant under translation by positive vectors and closed under strictly positive affine transformations. We prove that this geometric formulation is equivalent both to a reduction to the multi-affine setting via polarization and to a recursive criterion in terms of partial derivatives. The class of G{\aa}rding polynomials strictly extends that of real stable polynomials while preserving many of their structural properties. In particular, multi-affine G{\aa}rding polynomials with nonnegative coefficients satisfy the Rayleigh property, and their positive univariate specializations have ultra log-concave coefficient sequences. The G{\aa}rding property for several matroid generating functions is preserved under natural matroid operations. As applications, we derive new negative dependence results for generating functions associated with various classes of matroids and graphs, including examples previously beyond the scope of real stability and Lorentzian methods. We further obtain analogous results for characteristic polynomials arising from certain matrix classes.

math.CO↗
arXiv2026

Construction of Anosov flows on fibered hyperbolic 3-manifolds

We prove that fibered hyperbolic $3$-manifolds carrying transitive Anosov flows are abundant. More precisely, for every $g\geq 2$, there is a finite index subgroup~$\Gamma$ of $ \mathrm{Mod}(S_g)/\mathrm{Tor}(S_g) \simeq \mathrm{Sp}(2g,\mathbb{Z}) $ so that every element of $\Gamma$ has a representative $\varphi \in \operatorname{Mod}(S_g)$ such that the mapping torus $ M_\varphi := S_g \times [0,1]/(x,1) \sim (\varphi(x),0) $ carries a transitive Anosov flow. The manifold $M_\varphi$ is hyperbolic for almost every element of $\Gamma$. This shows in particular that, in the set of all fibered hyperbolic manifolds, the subset made of the manifolds carrying Anosov flows has positive density up to trivial linear monodromy. Moreover, the subgroup $\Gamma$ is defined by an explicit set of generators, and our construction yields many examples of simple fibered hyperbolic manifolds carrying Anosov flows.

math.DS↗
arXiv2025

Ancora: Accurate Intrusion Recovery for Web Applications

Modern web application recovery presents a critical dilemma. Coarse-grained snapshot rollbacks cause unacceptable data loss for legitimate users. Surgically removing an attack's impact is hindered by a fundamental challenge in high-concurrency environments: it is difficult to attribute resulting file and database modifications to a specific attack-related request. We present Ancora, a system for precise intrusion recovery in web applications without invasive instrumentation. Ancora first isolates the full sequence of syscalls triggered by a single malicious request. Based on this sequence, Ancora addresses file and database modifications separately. To trace file changes, it builds a provenance graph that reveals all modifications, including those by exploit-spawned processes. To attribute database operations, a more difficult challenge due to connection pooling, Ancora introduces a novel spatiotemporal anchor. This anchor uses the request's network connection tuple and active time window to pinpoint exact database operations. With all malicious file and database operations precisely identified, Ancora performs a unified rewind and selective replay recovery. It reverts the system to a clean snapshot taken before the attack, then selectively re-applies only legitimate operations to both the file system and database. This completely removes the attack's effects while preserving concurrent legitimate data. We evaluated Ancora on 10 web applications and 20 CVE-based attack scenarios with concurrency up to 150 connections. Experiments demonstrate Ancora achieves 99.9% recovery accuracy with manageable overhead: up to 19.8% response latency increase and 17.8% QPS decrease in worst cases, and recovery throughput of 110.7 database operations per second and 27.2 affected files per second, effectively preserving legitimate data.

cs.CR↗
arXiv2025

Cocycle superrigidity for median spaces of finite rank

We systematically investigate cocycle superrigidity in the setting of finite rank median spaces for product groups and Kazhdan groups. By employing a dynamical approach to superrigidity, we establish, for a median space X of finite rank, the superrigidity of Isom(X)-valued cocycles for a product of locally compact second countable groups. In the case of actions by irreducible lattices in such product groups, this approach yields a novel proof of the superrigidity of homomorphisms.

math.MG↗
arXiv2025

Constructing stable Hilbert bundles via Diophantine approximation

On any complex smooth projective curve with positive genus, we construct Hilbert bundles that admit Hermitian--Einstein metrics. Our main constructive step is by investigating the arithmetic property of the upper half plane in Bridgeland's definition of stability conditions and its homological countparts. The main analytic ingredient in our proof is a notion called a well-approximating sequence of stable bundles. This notion helps us to apply the Diophantine approximation to Donaldson's functional and bound the $L^\infty$ norm of Hermitian-Einstein metrics. We further study the continuous structures, smooth structures, and holomorphic structures on such Hilbert bundles. We hope that this construction can shed some new light on the geometric background of quantum field theory.

math.DG↗
arXiv2024

Impact of Stickers on Multimodal Sentiment and Intent in Social Media: A New Task, Dataset and Baseline

Stickers are increasingly used in social media to express sentiment and intent. Despite their significant impact on sentiment analysis and intent recognition, little research has been conducted in this area. To address this gap, we propose a new task: \textbf{M}ultimodal chat \textbf{S}entiment \textbf{A}nalysis and \textbf{I}ntent \textbf{R}ecognition involving \textbf{S}tickers (MSAIRS). Additionally, we introduce a novel multimodal dataset containing Chinese chat records and stickers excerpted from several mainstream social media platforms. Our dataset includes paired data with the same text but different stickers, the same sticker but different contexts, and various stickers consisting of the same images with different texts, allowing us to better understand the impact of stickers on chat sentiment and intent. We also propose an effective multimodal joint model, MMSAIR, featuring differential vector construction and cascaded attention mechanisms for enhanced multimodal fusion. Our experiments demonstrate the necessity and effectiveness of jointly modeling sentiment and intent, as they mutually reinforce each other's recognition accuracy. MMSAIR significantly outperforms traditional models and advanced MLLMs, demonstrating the challenge and uniqueness of sticker interpretation in social media. Our dataset and code are available on https://github.com/FakerBoom/MSAIRS-Dataset.

cs.CL↗
arXiv2023

Dynamics of subgroups of mapping class groups

Let $\rm{Mod(S)}$ be the mapping class group of a closed orientable surface $S$ of genus $g \geq 2$. Let $G$ be a non-elementary subgroup of $\rm{Mod(S)}$ so that the associated Bowen-Margulis measure is finite. In this paper, we give an asymptotic growth formula for $G$ with respect to the Teichmüller metric.

math.GT↗
arXiv2023

On a fully nonlinear elliptic equation with differential forms

We introduce a fully nonlinear PDE with a differential form $Λ$, which unifies several important equations in Kähler geometry including Monge-Ampère equations, J-equations, inverse $σ_{k}$ equations, and the deformed Hermitian Yang-Mills (dHYM) equation. We pose some natural positivity conditions on $Λ$, and prove analytical and algebraic criterions for the solvability of the equation. Our results generalize previous works of G.Chen, J.Song, Datar-Pingali and others. As an application, we prove a conjecture of Collins-Jacob-Yau for the dHYM equation with small global phase.

math.AP↗
arXiv2023

Semantic-aware Generation of Multi-view Portrait Drawings

Neural radiance fields (NeRF) based methods have shown amazing performance in synthesizing 3D-consistent photographic images, but fail to generate multi-view portrait drawings. The key is that the basic assumption of these methods -- a surface point is consistent when rendered from different views -- doesn't hold for drawings. In a portrait drawing, the appearance of a facial point may changes when viewed from different angles. Besides, portrait drawings usually present little 3D information and suffer from insufficient training data. To combat this challenge, in this paper, we propose a Semantic-Aware GEnerator (SAGE) for synthesizing multi-view portrait drawings. Our motivation is that facial semantic labels are view-consistent and correlate with drawing techniques. We therefore propose to collaboratively synthesize multi-view semantic maps and the corresponding portrait drawings. To facilitate training, we design a semantic-aware domain translator, which generates portrait drawings based on features of photographic faces. In addition, use data augmentation via synthesis to mitigate collapsed results. We apply SAGE to synthesize multi-view portrait drawings in diverse artistic styles. Experimental results show that SAGE achieves significantly superior or highly competitive performance, compared to existing 3D-aware image synthesis methods. The codes are available at https://github.com/AiArt-HDU/SAGE.

cs.CV↗
arXiv2023

Masked and Adaptive Transformer for Exemplar Based Image Translation

We present a novel framework for exemplar based image translation. Recent advanced methods for this task mainly focus on establishing cross-domain semantic correspondence, which sequentially dominates image generation in the manner of local style control. Unfortunately, cross-domain semantic matching is challenging; and matching errors ultimately degrade the quality of generated images. To overcome this challenge, we improve the accuracy of matching on the one hand, and diminish the role of matching in image generation on the other hand. To achieve the former, we propose a masked and adaptive transformer (MAT) for learning accurate cross-domain correspondence, and executing context-aware feature augmentation. To achieve the latter, we use source features of the input and global style codes of the exemplar, as supplementary information, for decoding an image. Besides, we devise a novel contrastive style learning method, for acquire quality-discriminative style representations, which in turn benefit high-quality image generation. Experimental results show that our method, dubbed MATEBIT, performs considerably better than state-of-the-art methods, in diverse image translation tasks. The codes are available at \url{https://github.com/AiArt-HDU/MATEBIT}.

cs.CV↗
arXiv2022

A Novel Speech Feature Fusion Algorithm for Text-Independent Speaker Recognition

A novel speech feature fusion algorithm with independent vector analysis (IVA) and parallel convolutional neural network (PCNN) is proposed for text-independent speaker recognition. Firstly, some different feature types, such as the time domain (TD) features and the frequency domain (FD) features, can be extracted from a speaker's speech, and the TD and the FD features can be considered as the linear mixtures of independent feature components (IFCs) with an unknown mixing system. To estimate the IFCs, the TD and the FD features of the speaker's speech are concatenated to build the TD and the FD feature matrix, respectively. Then, a feature tensor of the speaker's speech is obtained by paralleling the TD and the FD feature matrix. To enhance the dependence on different feature types and remove the redundancies of the same feature type, the independent vector analysis (IVA) can be used to estimate the IFC matrices of TD and FD features with the feature tensor. The IFC matrices are utilized as the input of the PCNN to extract the deep features of the TD and FD features, respectively. The deep features can be integrated to obtain the fusion feature of the speaker's speech. Finally, the fusion feature of the speaker's speech is employed as the input of a deep convolutional neural network (DCNN) classifier for speaker recognition. The experimental results show the effectiveness and performances of the proposed speaker recognition system.

eess.AS↗
arXiv2022

Boundary representations of mapping class groups

Let $S = S_g$ be a closed orientable surface of genus $g \geq 2$ and $Mod(S)$ be the mapping class group of $S$. In this paper, we show that the boundary representation of $Mod(S)$ is ergodic using statistical hyperbolicity, which generalizes the classical result of Masur on ergodicity of the action of $Mod(S)$ on the projective measured foliation space $\mathcal{PMF}(S).$ As a corollary, we show that the boundary representation of $Mod(S)$ is irreducible.

math.GT↗
arXiv2022

Curve shortening flow on Riemann surfaces with possible ambient conic singularities

In this paper, we study the curve shortening flow (CSF) on Riemann surfaces. We generalize Huisken's comparison function to Riemann surfaces and surfaces with conic singularities. We reprove the Gage-Hamilton-Grayson theorem on surfaces. We also prove that for embedded simple closed curves, CSF can not touch conic singularities with cone angles $\leq π$.

math.DG↗