arXiv subjects

Xiaoyan Zhang

Publications and source records attributed to Xiaoyan Zhang.

At least 19 recordsLinked to original sources

arXiv2026

The high dimensional monostable reaction-diffusion equation with free boundary and radial symmetry

We consider the radially symmetric version of the reaction-diffusion equation $u_t-dΔu=f(u)$ with a monostable nonlinearity $f$, viewed as a model for the spreading of a species with population range $r 0$ and $h'(t)=-d u_r(t,h(t))/δ$. For the one-dimensional case ($N=1$), Du \cite{DN} proved that when $δ\in(0,1)$, spreading occurs: $u\to1$ locally uniformly in $\mathbb{R}$, $h(t)\to\infty$, and $\lim_{t\to\infty}[h(t)-c_*t]=\tilde{h}\in\mathbb{R}$ with no logarithmic shift. In the present paper we consider $N\ge2$ and establish a complete trichotomy: spreading for $δ\in(0,1)$; transition for $δ=1$, where $u\to1$ uniformly on $[0,h(t)]$ and $h(t)\to h_\infty\in(0,\infty)$; and vanishing for $δ>1$, where $h(t)\to0$ and $u\toδ$ uniformly on $[0,h(t)]$. For the spreading regime, by constructing sharp upper and lower solutions, we prove that the solution converges globally to the semi-wave profile and reveal a logarithmic shift of the form $ \lim_{t\to\infty}\big[h(t)-c_*t+c_N(δ)\log t\big]=\hat{h}\in\mathbb{R}$, with the coefficient $c_N(δ)>0$ satisfying $ \lim_{δ\to0}c_N(δ)=d(N-1)/c_0$, where $d(N-1)/c_0$ is the shift coefficient for the high-dimensional radial pushed-case Cauchy problem. These results reveal the connection to the spreading behavior modeled by the corresponding Cauchy problem.

math.AP↗

arXiv2026

Constructing edge-disjoint Steiner trees in Cartesian product networks

Cartesian product networks are always regarded as a tool for ``combining'' two given networks with established properties to obtain a new one that inherits properties from both. For a graph $F=(V,E)$ and a set $S\subseteq V(F)$ of at least two vertices, \emph{an $S$-Steiner tree} or \emph{a Steiner tree connecting $S$} (or simply, \emph{an $S$-tree}) is a subgraph $T=(V',E')$ of $F$ that is a tree with $S\subseteq V'$. For $S\subseteq V(F)$ and $|S|\geq 2$, the {\it generalized local edge-connectivity} $λ(S)$ is the maximum number of edge-disjoint Steiner trees connecting $S$ in $F$. For an integer $k$ with $2\leq k\leq n$, the {\it generalized $k$-edge-connectivity} $λ_k(F)$ of a graph $F$ is defined as $λ_k(F)=\min\{λ(S)\,|\,S\subseteq V(F) \ and \ |S|=k\}$.In this paper, we give sharp upper and lower bounds for $λ_k(G\Box H)$, where $\Box$ is the Cartesian product operation, and $G,H$ are two graphs.

math.CO↗

arXiv2026

Chains and Antichains inside Many-One Degrees and Variants

The relations between many-one degrees and one-one degrees have been studied since the beginning of recursion theory; early results from the 1960s include that many-one degrees always have a largest one-one degree and either that one-one degree is the only one-one degree inside the many-one degree or every countable linear order is noneffectively embeddable into the structure of one-one degrees inside the given many-one degree. Furthermore, the greatest recursive many-one degree is a special case, as it allows to embed ascending infinite chains but not descending infinite chains, all other many-one degrees fall into the two cases mentioned above. It remained open whether infinite antichains can always be embedded when the many-one degree is nonrecursive and nonirreducible; Odifreddi stated in a survey 1981 and in his book Classical Recursion Theory in the year 1989 this question explicitly as an open problem. Dëgtev had already in 1976 constructed antichains of one-one degrees inside all nonrecursive and nonirreducible recursively enumerable many-one degrees and Batyrshin generalised the result to all nonrecursive and nonirreducible limit-recursive many-one degrees. In 2026, Cintioli showed that there is a measure $1$ class of sets whose many-one degrees contain infinite antichains of one-one degrees. This class contains all rigid many-one degrees. The present work generalises Batyrshin's result to all nonrecursive and nonirreducible many-one degrees and solves therefore Odifreddi's open problem. The present work also proposes to deepen the study of reducibilities between one-one and many-one in recursion theory in order to get a more complete and detailed picture for the structures inside many-one degrees. In particular it studies finite-one and bounded finite-one reducibilities where the first was introduced by Maslova in the 1970ies.

math.LO↗

arXiv2026

Risk Assessment and Security Analysis of Large Language Models

As large language models (LLMs) expose systemic security challenges in high risk applications, including privacy leaks, bias amplification, and malicious abuse, there is an urgent need for a dynamic risk assessment and collaborative defence framework that covers their entire life cycle. This paper focuses on the security problems of large language models (LLMs) in critical application scenarios, such as the possibility of disclosure of user data, the deliberate input of harmful instructions, or the models bias. To solve these problems, we describe the design of a system for dynamic risk assessment and a hierarchical defence system that allows different levels of protection to cooperate. This paper presents a risk assessment system capable of evaluating both static and dynamic indicators simultaneously. It uses entropy weighting to calculate essential data, such as the frequency of sensitive words, whether the API call is typical, the realtime risk entropy value is significant, and the degree of context deviation. The experimental results show that the system is capable of identifying concealed attacks, such as role escape, and can perform rapid risk evaluation. The paper uses a hybrid model called BERT-CRF (Bidirectional Encoder Representation from Transformers) at the input layer to identify and filter malicious commands. The model layer uses dynamic adversarial training and differential privacy noise injection technology together. The output layer also has a neural watermarking system that can track the source of the content. In practice, the quality of this method, especially important in terms of customer service in the financial industry.

cs.CR↗

arXiv2026

Securing High-Concurrency Ticket Sales: A Framework Based on Microservice

The railway ticketing system is one of the most important public service infrastructure. In peak periods such as holidays, it is often faced with the challenge of high concurrency scenarios because of a large number of users accessing at the same time. The traditional aggregation architecture can not meet the peak user requirements because of its insufficient fault tolerance and low ability. Therefore, the system needs to use microservice architecture for development, and add multiple security methods to ensure that the system can have good stability and data consistency under high concurrency scenarios, and can respond quickly to user requests. This paper introduces the use of B/S architecture and Spring Cloud to design and develop a railway ticket purchase system that can maintain stability and reliability under high concurrency scenarios, and formulate multiple security design methods for the system. This system integrates a range of functions, such as real-time train inquiries, dynamic seat updates, online seat selection, and ticket purchasing, effectively addressing common problems associated with offline ticket purchasing, such as long queues and delayed information. It enables a complete online process from inquiry and booking to payment and refunds. Furthermore, the "add passenger" function allows users to purchase tickets for others, extending the convenience of online ticketing to people with limited internet access. The system design prioritizes security and stability, while also focusing on high performance, and achieves these goals through a carefully designed architecture and the integration of multiple middleware components. After the completion of the system development, the core interface of the system is tested, and then the results are analyzed. The test data proves that the system has good ability and stability under high concurrency.

cs.SE↗

arXiv2026

Normalized solutions of quasilinear Schrödinger equations in the general $L^2$-supercritical case

This paper is devoted to studying the existence of normalized solutions for the following quasilinear Schrödinger equation \begin{equation*} \begin{aligned} -Δu-uΔu^2 +λu=h(u) \quad\mathrm{in}\ \mathbb{R}^{3}, \end{aligned} \end{equation*} where $λ$ appears as a Lagrange multiplier, $h$ is a $L^2$-supercritical and Sobolev subcritical nonlinearity. The solutions correspond to critical points of the energy functional subject to the $L^2$-norm constraint $\int_{\mathbb{R}^3}|u|^2dx=a^2>0$. Taking into account the Pohozaev manifold and perturbation method, we obtain the existence of ground state normalized solutions and infinitely many normalized solutions. Moreover, our results cover several relevant existing results in \cite{LZ2023}. And in the end, we get the asymptotic properties of energy as $a$ tends to $+\infty$ and $a$ tends to $0^+$.

math.AP↗

arXiv2026

Trichotomy dynamics of a free boundary model for biological invasion

It is well known that the reaction-diffusion equation $u_t=du_{xx}+f(u)$ with compactly supported nonnegative initial functions exhibits trichotomy dynamics for bistable and combustion type $f(u)$ \cite{DM, zlatos}. The same is true for the corresponding Stefan type free boundary problem \cite{DL}. In this paper, we reveal a rather different type of trichotomy for this reaction-diffusion equation under a new set of (free) boundary conditions, arising as a model for biological invasion with $u(t,x)$ representing the density of an invading species over the one dimensional spatial regin $[0, h(t)]$. The evolution of the invading front $x=h(t)$ is governed by $h'(t)=-\frac dδu_x(t, h(t))$ and $u(t, h(t))=δ\in (\hatθ_f, 1)$, with $\hatθ_f \in [0, 1)$ uniquely determined by $f$; they allow $h(t)$ to advance as well as to retreat when time increases. At the fixed boundary $x=0$, the density is controlled by $u(t,0)=δ_0\geq 0$. We completely classify the long-time dynamics of the model when $f(u)$ is a monostable, or bistable, or combustion type nonlinear function. In the biologically interesting case that $δ_0<δ$, we show that there are exactly three scenarios: (i) successful spreading, (ii) finite-time vanishing, (iii) a transition state characterized by $h(t)\to l_*\in (0, \infty)$ and $u(t,x)\to w_*(x)$ as $t\to\infty$, where $(u(t,x), h(t))\equiv (w_*(x), l_*)$ is the unique stationary solution of the free boundary problem. The model here does not have the usual order-preserving property enjoyed by those considered in \cite{DM, zlatos, DL} and elsewhere (i.e., $u(0,x)\leq v(0,x)$ implies $u(t,x)\leq v(t,x)$ for all $t>0$ if $u$ and $v$ are two solutions of the problem), which is intrinsically linked to the many novel features of the model.

math.AP↗

arXiv2026

See What I See, Know What I Think: Dense Latent Communication Across Heterogeneous Agents

Multi-agent systems communicate mostly through text, paying a lossy and expensive decode and re-encode cost. KV-cache communication is a promising alternative, yet most prior work is homogeneous, using duplicate copies of the same model, and avoids the central challenge of cross-model latent alignment; existing heterogeneous methods are also restrictive, typically assuming shared input and using transferred caches mainly for steering. We study a more fundamental question: can heterogeneous agents be aligned well enough to perform real "mind reading" and transfer both what one agent sees and how it thinks? Our information-structure analysis reveals a duality: context-aware transfer is driven by sparse reasoning signals, while context-unaware transfer, where the receiver sees no input, requires dense contextual knowledge preservation. Motivated by this, we propose dense alignment for heterogeneous KV-cache communication via a lightweight cross-model cache transformation and two-phase training: reconstruction followed by generation. Across all six directions of {Qwen3-4B, 8B, 14B} and six in-domain and out-of-domain benchmarks, our method outperforms prior heterogeneous baselines, matches or exceeds text communication in context-aware settings at roughly 2 to 3 times lower compute, and remains effective in context-unaware transfer where prior methods collapse.

cs.MA↗

arXiv2026

Multimodal sampling via Schrödinger-Föllmer samplers with temperatures

Generating samples from complex and high-dimensional distributions is ubiquitous in various scientific fields of statistical physics, Bayesian inference, scientific computing and machine learning. Very recently, Huang et al. (IEEE Trans. Inform. Theory, 2025) proposed new Schrödinger-Föllmer samplers (SFS), based on the Euler discretization of the Schrödinger-Föllmer diffusion evolving on the unit interval $[0, 1]$. There, a convergence rate of order $\mathcal{O}(\sqrt{h})$ in the $L^2$-Wasserstein distance was obtained for the Euler discretization with a uniform time step-size $h>0$. By introducing a temperature parameter, different samplers are proposed in this paper, based on the Euler discretization of the Schrödinger-Föllmer process with temperatures. As revealed by numerical experiments, high temperatures are vital, particularly in sampling from multimodal distributions. Further, a novel approach of error analysis is developed for the time discretization and an enhanced convergence rate of order $\mathcal{O}(h)$ is obtained in the $L^2$-Wasserstein distance, under certain smoothness conditions on the drift. This significantly improves the existing order-half convergence in the aforementioned paper. Unlike Langevin samplers, SFS is gradient-free, works in a unit interval $[0, 1]$ and does not require any ergodicity. Numerical experiments confirm the convergence rate and show that, the SFS substantially outperforms vanilla Langevin samplers, particularly in sampling from multimodal distributions.

math.NA↗

arXiv2026

Accelerated Schrödinger-Föllmer samplers

Sampling is a fundamental algorithmic task in wide-ranging applications across multiple disciplines such as scientific computing, statistics and machine learning. In this paper, an efficient stochastic Runge-Kutta scheme is proposed to accelerate the Schrödinger-Föllmer sampler, designed for sampling from complex and high-dimensional multimodal distributions. The resulting stochastic Runge-Kutta Schrödinger-Föllmer sampler (SRKSFS) is proved to achieve a convergence rate of order $\mathcal{O} ( h^{3/2} |\ln h|)$ in the $L^2$-Wasserstein distance, considerably improving the order $\mathcal{O}(h)$ of the existing Euler type sampler. Obtaining the enhanced convergence rate is, however, not trivial, by noting that the drift of the diffusion process is not differentiable but only $\frac{1}{2}$-Hölder continuity with respect to the time variable. To address the difficulty, we rely on delicate error estimates to overcome the singularity due to time derivatives of the drift, at the expense of the logarithmic factor. Furthermore, the framework is extended to data-driven Schrödinger-Föllmer generation with empirical measures, enabling data-driven sampling without known density. A variety of numerical experiments are reported to validate the effectiveness of the proposed sampling algorithms.

math.ST↗

arXiv2026

Dual-Imbalance Continual Learning for Real-World Food Recognition

Visual food recognition in real-world dietary logging scenarios naturally exhibits severe data imbalance, where a small number of food categories appear frequently while many others occur rarely, resulting in long-tailed class distributions. In practice, food recognition systems often operate in a continual learning setting, where new categories are introduced sequentially over time. However, existing studies typically assume that each incremental step introduces a similar number of new food classes, which rarely happens in real world where the number of newly observed categories can vary significantly across steps, leading to highly uneven learning dynamics. As a result, continual food recognition exhibits a dual imbalance: imbalanced samples within each food class and imbalanced numbers of new food classes to learn at each incremental learning step. In this work, we introduce DIME, a Dual-Imbalance-aware Adapter Merging framework for continual food recognition. DIME learns lightweight adapters for each task using parameter-efficient fine-tuning and progressively integrates them through a class-count guided spectral merging strategy. A rank-wise threshold modulation mechanism further stabilizes the merging process by preserving dominant knowledge while allowing adaptive updates. The resulting model maintains a single merged adapter for inference, enabling efficient deployment without accumulating task-specific modules. Experiments on realistic long-tailed food benchmarks under our step-imbalanced setup show that the proposed method consistently improves by more than 3% over the strongest existing continual learning baselines. Code is available at https://github.com/xiaoyanzhang1/DIME.

cs.CV↗

arXiv2026

One Adapter for All: Towards Unified Representation in Step-Imbalanced Class-Incremental Learning

Class-incremental learning (CIL) aims to acquire new classes over time while retaining prior knowledge, yet most setups and methods assume balanced task streams. In practice, the number of classes per task often varies significantly. We refer to this as step imbalance, where large tasks that contain more classes dominate learning and small tasks inject unstable updates. Existing CIL methods assume balanced tasks and therefore treat all tasks uniformly, producing imbalanced updates that degrade overall learning performance. To address this challenge, we propose One-A, a unified and imbalance-aware framework that incrementally merges task updates into a single adapter, maintaining constant inference cost. One-A performs asymmetric subspace alignment to preserve dominant subspaces learned from large tasks while constraining low-information updates within them. An information-adaptive weighting balances the contribution between base and new adapters, and a directional gating mechanism selectively fuses updates along each singular direction, maintaining stability in head directions and plasticity in tail ones. Across multiple benchmarks and step-imbalanced streams, One-A achieves competitive accuracy with significantly low inference overhead, showing that a single, asymmetrically fused adapter can remain both adaptive to dynamic task sizes and efficient at deployment.

cs.CV↗

arXiv2026

A Variant Of Chaitin's Omega function

We investigate the continuous function $f$ defined by $$x\mapsto \sum_{σ\le_L x }2^{-K(σ)}$$ as a variant of Chaitin's Omega from the perspective of analysis, computability, and algorithmic randomness. Among other results, we obtain that: (i) $f$ is differentiable precisely at density random points; (ii) $f(x)$ is $x$-random if and only if $x$ is weakly low for $K$ (low for $Ω$); (iii) the range of $f$ is a null, nowhere dense, perfect $Π^0_1(\emptyset')$ class with Hausdorff dimension $1$; (iv) $f(x)\oplus x\ge_T\emptyset'$ for all $x$; (v) there are $2^{\aleph_0}$ many $x$ such that $f(x)$ is not 1-random; (vi) $f$ is not Turing invariant but is Turing invariant on the ideal of $K$-trivial reals. We also discuss the connection between $f$ and other variants of Omega.

math.LO↗

arXiv2026

MFP3D: Monocular Food Portion Estimation Leveraging 3D Point Clouds

Food portion estimation is crucial for monitoring health and tracking dietary intake. Image-based dietary assessment, which involves analyzing eating occasion images using computer vision techniques, is increasingly replacing traditional methods such as 24-hour recalls. However, accurately estimating the nutritional content from images remains challenging due to the loss of 3D information when projecting to the 2D image plane. Existing portion estimation methods are challenging to deploy in real-world scenarios due to their reliance on specific requirements, such as physical reference objects, high-quality depth information, or multi-view images and videos. In this paper, we introduce MFP3D, a new framework for accurate food portion estimation using only a single monocular image. Specifically, MFP3D consists of three key modules: (1) a 3D Reconstruction Module that generates a 3D point cloud representation of the food from the 2D image, (2) a Feature Extraction Module that extracts and concatenates features from both the 3D point cloud and the 2D RGB image, and (3) a Portion Regression Module that employs a deep regression model to estimate the food's volume and energy content based on the extracted features. Our MFP3D is evaluated on MetaFood3D dataset, demonstrating its significant improvement in accurate portion estimation over existing methods.

cs.CV↗

arXiv2026

SpatiaLQA: A Benchmark for Evaluating Spatial Logical Reasoning in Vision-Language Models

Vision-Language Models (VLMs) have been increasingly applied in real-world scenarios due to their outstanding understanding and reasoning capabilities. Although VLMs have already demonstrated impressive capabilities in common visual question answering and logical reasoning, they still lack the ability to make reasonable decisions in complex real-world environments. We define this ability as spatial logical reasoning, which not only requires understanding the spatial relationships among objects in complex scenes, but also the logical dependencies between steps in multi-step tasks. To bridge this gap, we introduce Spatial Logical Question Answering (SpatiaLQA), a benchmark designed to evaluate the spatial logical reasoning capabilities of VLMs. SpatiaLQA consists of 9,605 question answer pairs derived from 241 real-world indoor scenes. We conduct extensive experiments on 41 mainstream VLMs, and the results show that even the most advanced models still struggle with spatial logical reasoning. To address this issue, we propose a method called recursive scene graph assisted reasoning, which leverages visual foundation models to progressively decompose complex scenes into task-relevant scene graphs, thereby enhancing the spatial logical reasoning ability of VLMs, outperforming all previous methods. Code and dataset are available at https://github.com/xieyc99/SpatiaLQA.

cs.CV↗

arXiv2026

Dimensionality and randomness

Arranging the bits of a random string or real into k columns of a two-dimensional array or higher dimensional structure is typically accompanied with loss in the Kolmogorov complexity of the columns, which depends on k. We quantify and characterize this phenomenon for arrays and trees and its relationship to negligible classes.

math.LO↗

arXiv2026

SIGMA: Selective-Interleaved Generation with Multi-Attribute Tokens

Recent unified models such as Bagel demonstrate that paired image-edit data can effectively align multiple visual tasks within a single diffusion transformer. However, these models remain limited to single-condition inputs and lack the flexibility needed to synthesize results from multiple heterogeneous sources. We present SIGMA (Selective-Interleaved Generation with Multi-Attribute Tokens), a unified post-training framework that enables interleaved multi-condition generation within diffusion transformers. SIGMA introduces selective multi-attribute tokens, including style, content, subject, and identity tokens, which allow the model to interpret and compose multiple visual conditions in an interleaved text-image sequence. Through post-training on the Bagel unified backbone with 700K interleaved examples, SIGMA supports compositional editing, selective attribute transfer, and fine-grained multimodal alignment. Extensive experiments show that SIGMA improves controllability, cross-condition consistency, and visual quality across diverse editing and generation tasks, with substantial gains over Bagel on compositional tasks.

cs.CV↗

arXiv2025

Beyond the Hype: A Large-Scale Empirical Analysis of On-Chain Transactions in NFT Scams

Non-fungible tokens (NFTs) serve as a representative form of digital asset ownership and have attracted numerous investors, creators, and tech enthusiasts in recent years. However, related fraud activities, especially phishing scams, have caused significant property losses. There are many graph analysis methods to detect malicious scam incidents, but no research on the transaction patterns of the NFT scams. Therefore, to fill this gap, we are the first to systematically explore NFT phishing frauds through graph analysis, aiming to comprehensively investigate the characteristics and patterns of NFT phishing frauds on the transaction graph. During the research process, we collect transaction records, log data, and security reports related to NFT phishing incidents published on multiple platforms. After collecting, sanitizing, and unifying the data, we construct a transaction graph and analyze the distribution, transaction features, and interaction patterns of NFT phishing scams. We find that normal transactions on the blockchain accounted for 96.71% of all transactions. Although phishing-related accounts accounted for only 0.94% of the total accounts, they appeared in 8.36% of the transaction scenarios, and their interaction probability with normal accounts is significantly higher in large-scale transaction networks. Moreover, NFT phishing scammers often carry out fraud in a collective manner, targeting specific accounts, tend to interact with victims through multiple token standards, have shorter transaction cycles than normal transactions, and involve more multi-party transactions. This study reveals the core behavioral features of NFT phishing scams, providing important references for the detection and prevention of NFT phishing scams in the future.

cs.CR↗