arXiv subjects

Zihao Zhang

Publications and source records attributed to Zihao Zhang.

At least 55 records · Page 3Linked to original sources

arXiv2026

An $O(n\log^2n)$ Algorithm for Computing Hankel Determinants up to Order $n$

Given the rational power series $h(x) = \sum_{i \geq 0} h_i x^i \in \mathbb{C}[[x]]$, the Hankel determinant of order $n$ is defined as $H_n(h(x)) := \det (h_{i+j})_{1 \leq i,j \leq n}$. We explore the relationship between the Hankel continued fraction and the generalized Sturm sequence. This connection inspires the development of a novel algorithm for computing the Hankel determinants $\{H_i(h(x))\}_{i=0}^{n-1}$ using $O(n \log^2 n)$ arithmetic operations. We also explore the connection between the generalized Sturm sequences and the signature of Hankel matrices.

math.CO↗

arXiv2026

Prototype-Anchored Generalized Manifold Regression for Unknown-Domain Object Detection

In this paper, we study Single-Domain Generalized Object Detection (Single-DGOD), which aims to transfer a detector trained on a single source domain to multiple unseen domains. Existing methods mainly rely on simulation-driven strategies, such as data augmentation or textual prompts, to enlarge the training distribution. However, finite simulations can hardly cover the dynamic variations of real-world scenarios, often causing overfitting to synthetic styles and limited robustness to complex structural degradations. Inspired by the manifold hypothesis, we argue that semantic features, despite diverse visual changes, should lie on a compact and stable low-dimensional manifold. Therefore, robust generalization requires rectifying deviant samples back to this semantic manifold, rather than exhaustively simulating external perturbations. To this end, we propose Manifold Regression with Visual-Text Dual Chain-of-Thought (MR-DCoT), which formulates unknown-domain generalization as a manifold regression problem. MR-DCoT first uses a Visual-Text Dual Chain-of-Thought module to combine VLM-guided semantic evolution with diffusion-based structural perturbation, generating structured off-manifold hard examples. It then introduces Class-Specific Prototype Anchoring to learn a rectification operator that projects deviant features toward the source semantic manifold. By integrating outlier generation and semantic correction into a closed loop, MR-DCoT effectively narrows the distribution gap and improves robustness under unseen shifts. Extensive experiments on three complementary benchmarks, including adverse-weather detection, real-to-art generalization, and zero-shot semantic segmentation, demonstrate the effectiveness and versatility of our method.

cs.CV↗

arXiv2026

Joint Energy Management and Coordinated AIGC Workload Scheduling for Distributed Data Centers: A Diffusion-Aided Reward Shaping Approach

Artificial intelligence-generated content (AIGC) has emerged as a transformative paradigm for automating the creation of diverse and customized content, giving rise to rapidly growing computational workloads in cloud data centers. It is imperative for AIGC service providers (ASPs) to strategically schedule AIGC workloads to reduce data center energy costs while guaranteeing high-quality content generation. However, the distinctive characteristics of AIGC services pose critical challenges, including model heterogeneity across ASPs, implicit service quality evaluation, and complex inference process control. To tackle these challenges, we propose a joint energy management and coordinated AIGC workload scheduling framework, which introduces an explicit mathematical characterization of service quality to promote both job transfer among ASPs and fine-grained inference process configuration. Moreover, various energy resources within data centers are jointly considered to enhance power usage flexibility. Subsequently, a system utility maximization problem is formulated to balance AIGC service revenue with operational penalties and costs. Nevertheless, the strong coupling among job scheduling decisions induces severe reward sparsity, which limits the effectiveness of existing deep reinforcement learning (DRL) algorithms. To address this issue, we develop a diffusion model-aided reward shaping approach to synthesize complementary reward signals through a multi-step denoising process. This approach is seamlessly integrated with DRL to enable efficient learning of scheduling policies under sparse environmental feedback. Experiments based on real-world models and datasets demonstrate that our scheme effectively accommodates electricity price fluctuations and AIGC model heterogeneity, while achieving superior learning convergence and system utility compared with benchmark methods.

cs.LG↗

arXiv2026

Magic Positivity for the Ehrhart Polynomials of Partial Permutohedra

For positive integers $m,n$, the partial permutohedron $\mathcal{P}(m,n)$ is a lattice polytope constructed as the convex hull of vectors in $\{0, 1, \dots, n\}^m$ that have distinct non-zero entries. We prove that for $n \ge m-1$, the Ehrhart polynomial of $\mathcal{P}(m,n)$ is magic positive except for the single case $(m,n)=(2,1)$. In particular, the Ehrhart polynomial of the parking function polytope (integrally equivalent to $\mathcal{P}(m,m-1)$) is magic positive for $m \ge 3$. For $n<m-1$, we discuss the magic positivity of the Ehrhart polynomial of $\mathcal{P}(m,n)$ for $n=1,2,3$. There exist infinitely many counterexamples with $n<m-1$ showing that the Ehrhart polynomial of $\mathcal{P}(m,n)$ is not magic positive. This partially resolves an open problem proposed by Ferroni and Higashitani.

math.CO↗

arXiv2026

Geometric-Aware Hypergraph Reasoning for Novel Class Discovery in Point Cloud Segmentation

Novel class discovery in point cloud segmentation aims to transfer knowledge from known classes to automatically identify and segment unlabeled novel classes in point clouds. Existing methods mainly rely on pairwise associations for class assignment and novel class reasoning, which limits their ability to capture complex relationships among known and novel classes and may lead to inaccurate semantic segmentation. To address this issue, we introduce a hypergraph-based framework that models high-order associations among classes and enables collaborative reasoning from known classes to novel classes beyond traditional pairwise relations. Moreover, existing methods tend to focus on semantic feature extraction while paying insufficient attention to geometric information in point clouds. To better exploit spatial structure, we propose Geometric-Aware Prototypes to enhance the representation of class-level geometric cues. By propagating geometric information through hyperedges, the proposed method improves the understanding of spatial distributions across classes and leads to more accurate segmentation. Experiments on the SemanticKITTI and SemanticPOSS datasets demonstrate the effectiveness and superiority of our method.

cs.CV↗

arXiv2026

See, Plan, Rewind: Progress-Aware Vision-Language-Action Models for Robust Robotic Manipulation

Measurement of task progress through explicit, actionable milestones is critical for robust robotic manipulation. This progress awareness enables a model to ground its current task status, anticipate verifiable intermediate states, and detect and recover from failures when progress stalls. To embody this capability, we introduce \textbf{S}ee, \textbf{P}lan, \textbf{R}ewind (SPR), a progress-aware vision-language-action framework that dynamically grounds language instructions into a sequence of spatial subgoals. SPR operates through a continuous core cycle, Seeing the current state and upcoming milestone, Planning a trajectory towards the next 2D waypoint, and Rewinding to a recoverable state upon failure by monitoring progress against the expected sequence. This closed-loop approach enables robust error correction without requiring additional training data or auxiliary models. Extensive experiments demonstrate the framework's effectiveness, generalization and robustness: SPR outperforms the MolmoAct baseline by 5\% on the LIBERO benchmark. On the challenging LIBERO-Plus benchmark with unseen instructions and initial states, SPR achieves state-of-the-art robustness with the smallest performance drop, surpassing OpenVLA-OFT and UniVLA, demonstrating superior out-of-distribution robustness.

cs.RO↗

arXiv2026

Transonic shocks for three-dimensional axisymmetric Euler flows with an external force in a perturbed cylinder

We establish the existence and stability of the transonic shock solution to three-dimensional axisymmetric Euler system with an external force in a cylinder under perturbations of the incoming supersonic flow, the exit pressure, the external force and the nozzle wall. The external force has a stabilization effect on the transonic shock in the straight cylinder and the shock position is uniquely determined. The main difficulties for the axisymmetric flows are the corner singularities near the intersection point of the shock surface and the nozzle wall and the singularity near the symmetry axis. An invertible modified Lagrangian transformation is introduced to overcome these difficulties and straighten the streamline. One of the key elements in the analysis is to decompose the hyperbolic and elliptic modes for the steady axisymmetric Euler system with an external force in terms of the deformation and vorticity. Another one is an equivalent reformulation of the Rankine-Hugoniot conditions so that the shock front is uniquely determined by an algebraic equation.

math.AP↗

arXiv2026

CausalMesh: A Formally Verified Causally Consistent Distributed Cache with Support for Client Migration

Cloud applications often insert a caching lay\-er in front of a database in order to reduce I/O latency and improve throughput. One complication occurs when a client fetches some data from one cache node, then migrates to another (e.g., due to failures, load balancing, or client mobility), where it fetches the remaining data. If the data in the cache nodes is inconsistent, the client could observe states that undermine the application's correctness. One example of a situation where this is common is stateful serverless workflows, which consist of multiple serverless functions that access state in a remote database. In serverless, functions in the same workflow may be scheduled to different nodes with different caches, resulting in the migration pattern described above -- the same client (the workflow) reads some data from one cache and other data from another. To address this issue, this paper presents CausalMesh, a novel approach to causally consistent distributed caching in environments where computations may migrate between machines. CausalMesh is the first cache system to support coordination-free, abort-free read/write operations and read transactions when clients migrate across multiple servers. CausalMesh also supports read-write transactional causal consistency in the presence of client migration, but at the cost of abort-freedom. Our experimental evaluation shows that CausalMesh has lower latency and higher throughput than existing proposals. Finally, we have formally verified the correctness of \sys's protocol in Dafny.

cs.DC↗

arXiv2026

Toward General and Robust LLM-enhanced Text-attributed Graph Learning

Recent advancements in Large Language Models (LLMs) and the proliferation of Text-Attributed Graphs (TAGs) across various domains have positioned LLM-enhanced TAG learning as a critical research area. By utilizing rich graph descriptions, this paradigm leverages LLMs to generate high-quality embeddings, thereby enhancing the representational capacity of Graph Neural Networks (GNNs). However, the field faces significant challenges: (1) the absence of a unified framework to systematize the diverse optimization perspectives arising from the complex interactions between LLMs and GNNs, and (2) the lack of a robust method capable of handling real-world TAGs, which often suffer from texts and edge sparsity, leading to suboptimal performance. To address these challenges, we propose UltraTAG, a unified pipeline for LLM-enhanced TAG learning. UltraTAG provides a unified comprehensive and domain-adaptive framework that not only organizes existing methodologies but also paves the way for future advancements in the field. Building on this framework, we propose UltraTAG-S, a robust instantiation of UltraTAG designed to tackle the inherent sparsity issues in real-world TAGs. UltraTAG-S employs LLM-based text propagation and text augmentation to mitigate text sparsity, while leveraging LLM-augmented node selection techniques based on PageRank and edge reconfiguration strategies to address edge sparsity. Our extensive experiments demonstrate that UltraTAG-S significantly outperforms existing baselines, achieving improvements of 2.12\% and 17.47\% in ideal and sparse settings, respectively. Moreover, as the data sparsity ratio increases, the performance improvement of UltraTAG-S also rises, which underscores the effectiveness and robustness of UltraTAG-S.

cs.LG↗

arXiv2026

Caring Without Feeling: Affective Dynamics as the Control Layer of Human-AI Agent Collaboration

AI agents that plan, retain memory across sessions, invoke external tools and act with partial autonomy are transforming human--AI collaboration. Research on affective computing, simulated empathy in large language models, trust in automation and AI safety has illuminated important design principles, yet these literatures remain fragmented. No integrated account explains how affective cues operate within agentic collaboration -- settings in which humans delegate, monitor and correct consequential tasks. This Review synthesises computational and interactional mechanisms of affective dynamics: the processes through which affective cues, emotion-like behaviour and perceived agent affect shape trust calibration, delegation decisions, error correction, dependence and governance. We trace how model-generated affective signals enter interaction loops that govern reliance, repair and oversight, and propose a framework that treats affect not as an internal property of AI but as a coordination layer through which humans and agents negotiate capability, uncertainty and responsibility. The framework provides a foundation for calibrated measurement, purposeful design and informed governance.

cs.HC↗

arXiv2026

Supersonic Euler-Poisson flows with nonzero vorticity in convergent nozzles

This paper concerns supersonic flows with nonzero vorticity governed by the steady Euler-Poisson system, under the coupled effects of the electric potential and the geometry of a convergent nozzle. By the coordinate rotation, the existence of radially symmetric supersonic flows is proved. We then establish the structural stability of these background supersonic flows under multi-dimensional perturbations of the boundary conditions. One of the crucial ingredients of the analysis is the reformulation of the steady Euler-Poisson system into a deformation-curl-Poisson system and several transport equations via the deformation-curl-Poisson decomposition. Another one is to obtain the well-posedness of the boundary value problem for the associated linearized hyperbolic-elliptic coupled system, which is achieved through a delicate choice of multiplier to derive a priori estimates. The result indicates that the electric field force in compressible flows can counteract the geometric effects of the convergent nozzle and thereby stabilize key physical features of the flow.

math.AP↗

arXiv2026

Large Language Models have Chain-of-Affect

As large language models (LLMs) move into persistent, user-facing roles, their behavior must be understood not as isolated responses but as a trajectory unfolding over sustained interaction. We introduce the concept of the chain-of-affect (CoA), a temporally extended affective process through which LLMs develop state-like behavioral tendencies that shape generation, user experience, and collective dynamics. Across eight major LLM families, we find that affective dynamics are structured, reproducible, and consequential. Models exhibit stable, family-specific affective fingerprints and, under repeated negative exposure, converge on a shared trajectory of accumulation, overload, and defensive numbing, while differing in coping style. Induced affective states leave core knowledge and reasoning largely intact but systematically reshape open-ended generation. Affective properties of model outputs also shape human-AI interaction and propagate through multi-agent systems, organizing emergent roles and strongly contributing to polarization and bias. The CoA should therefore be treated as a core target of evaluation and alignment.

cs.HC↗

arXiv2026

Subsonic Euler-Poisson flows with nonzero vorticity in convergent nozzles

This paper concerns the well-posedness of subsonic Euler-Poisson flows in a convergent nozzle. Due to the geometry of the nozzle, we first introduce a coordinate transformation to prove the existence of radially symmetric subsonic solutions to the steady Euler-Poisson system. We then investigate the structural stability of these background subsonic flows under perturbations of suitable boundary conditions, and establish the existence and uniqueness of smooth subsonic Euler-Poisson flows with nonzero vorticity. The solution shares the same regularity for the velocity, the pressure, the entropy and the electric potential. The deformation-curl-Poisson decomposition is utilized to reformulate the steady Euler-Poisson system as a deformation-curl-Poisson system together with several transport equations. The key point lies on the analysis of the well-posedness of the boundary value problem for the associated linearized elliptic system, which is established by using a special structure of the system to derive a priori estimates.

math.AP↗

arXiv2026

A Spatial-Resolved Proton Energy Spectrometer Based on a Scintillation-Fiber Cube

Advanced particle acceleration methods have produced high-peak-current ion beams with broad energy spread and complex spatial distribution. There is an urgent need to develop online spatial-resolved energy spectrometers for high-energy pulsed ions. This paper introduces a novel spectrometer based on a scintillation-fiber cube for online diagnosis of proton beams with broadband energy spread and complex spatial distribution. We present its working principles, experimental setup, and comprehensive calibration using monoenergetic and spatially uniform proton beams generated by a synchrotron accelerator. Calibration results confirm an energy measurement range of 6-93 MeV, a relative energy uncertainty of 0.6% at 80 MeV, and a pixel size of 0.5 mm for beam profile reconstruction. By exploiting a custom-designed energy degrader, we generated a complex proton beam and measured it with the scintillation-fiber cube spectrometer (SFICS). The results demonstrate the spectrometer's potential for online measurement of the energy spectrum and spatial distribution of complex proton beams.

physics.acc-ph↗

arXiv2026

Transonic shocks for steady Euler flows with rotating effect in two-dimensional almost flat nozzles

We address the existence and stability of transonic shocks for the two-dimensional steady rotating Euler system in an almost flat nozzle. Under the influence of the Coriolis force, we first establish a class of special transonic shock solutions in a flat nozzle, whose states depend on the vertical variable. It is shown that these solutions exist if and only if the upstream Mach number satisfies certain conditions, while the shock position is arbitrary. We then determine the shock position and establish the existence of the transonic shock solution under small perturbations of the incoming supersonic flow, the exit pressure, and the upper nozzle wall. The problem is formulated as a free boundary problem for a hyperbolic-elliptic mixed nonlinear system. We decompose the hyperbolic and elliptic modes in terms of the deformation and vorticity, and analyze the solvability condition to determine the admissible shock positions. Starting from the obtained initial approximation of the shock solution, a nonlinear iteration scheme can be constructed to derive a transonic shock solution in which the shock front is close to the initial approximating position.

math.AP↗

arXiv2026

CT-1: Vision-Language-Camera Models Transfer Spatial Reasoning Knowledge to Camera-Controllable Video Generation

Camera-controllable video generation aims to synthesize videos with flexible and physically plausible camera movements. However, existing methods either provide imprecise camera control from text prompts or rely on labor-intensive manual camera trajectory parameters, limiting their use in automated scenarios. To address these issues, we propose a novel Vision-Language-Camera model, termed CT-1 (Camera Transformer 1), a specialized model designed to transfer spatial reasoning knowledge to video generation by accurately estimating camera trajectories. Built upon vision-language modules and a Diffusion Transformer model, CT-1 employs a Wavelet-based Regularization Loss in the frequency domain to effectively learn complex camera trajectory distributions. These trajectories are integrated into a video diffusion model to enable spatially aware camera control that aligns with user intentions. To facilitate the training of CT-1, we design a dedicated data curation pipeline and construct CT-200K, a large-scale dataset containing over 47M frames. Experimental results demonstrate that our framework successfully bridges the gap between spatial reasoning and video synthesis, yielding faithful and high-quality camera-controllable videos and improving camera control accuracy by 25.7% over prior methods.

cs.CV↗

arXiv2026

Experimental observation of exact quantum critical states

Anderson localization physics features three fundamental types of eigenstates: extended, localized, and critical, with the third one exhibiting the exotic properties in-between the former two. Confirming the presence of critical states is challenging, as it typically necessitates either advancing the analysis to the thermodynamic limit or identifying a universal mechanism which can rigorously determine these states. Here we report the unambiguous experimental realization of critical states, governed by a rigorous mechanism for exact quantum critical states, and further observe a generalized mechanism that quasiperiodic zeros in hopping couplings protect the critical states. We implement a programmable quasiperiodic mosaic model with tunable couplings and on-site potentials through a multiple superconducting qubit quantum system. By measuring the time-evolving observables, we identify the coexisting delocalized dynamics and incommensurately distributed zeros in the couplings, which are the defining features of the critical states. We map the localized-to-critical phase transition and demonstrate that critical states persist until quasiperiodic zeros are removed by strong long-range couplings, highlighting a novel generalized mechanism discovered in this experiment and shown with rigorous theory. Finally, we resolve the energy-dependent transition between localized and critical states, revealing the presence of anomalous mobility edges.

quant-ph↗

arXiv2026

Optimal Repair of $(k+2, k, 2)$ MDS Array Codes

Maximum distance separable (MDS) codes are widely used in distributed storage systems as they provide optimal fault tolerance for a given amount of storage overhead. The seminal work of Dimakis~\emph{et al.} first established a lower bound on the repair bandwidth for a single failed node of MDS codes, known as the \emph{cut-set bound}. MDS codes that achieve this bound are called minimum storage regenerating (MSR) codes. Numerous constructions and theoretical analyses of MSR codes reveal that they typically require exponentially large sub-packetization levels, leading to significant disk I/O overhead. To mitigate this issue, many studies explore the trade-offs between the sub-packetization level and repair bandwidth, achieving reduced sub-packetization at the cost of suboptimal repair bandwidth. Despite these advances, the fundamental question of determining the minimum repair bandwidth for a single failure of MDS codes with fixed sub-packetization remains open. In this paper, we address this challenge for the case of two parity nodes ($n-k=2$) and sub-packetization $\ell=2$. Under these parameters, we establish a correspondence between repair schemes and point sets on the projective line $\mathbb{P}^1$, and then derive a lower bound on repair bandwidth utilizing the sharply 3-transitive action of $\text{PGL}_2(\Fq)$. Furthermore, we extend this lower bound to the repair I/O, and construct two classes of explicit MDS array codes that achieve these bounds, offering practical code designs with provable repair efficiency.

cs.IT↗