arXiv subjects

Yixiao Zhang

Publications and source records attributed to Yixiao Zhang.

At least 19 recordsLinked to original sources

arXiv2026

A Higher-Order Clique Density Theorem

Reiher's clique density theorem determines the sharp lower envelope for the density of $K_r$ at fixed edge density. We prove a higher-order version in which the prescribed quantity is itself a clique density. For every $3\le s<r$, we determine the minimum possible $K_r$-density among graphons with prescribed $K_s$-density. For $s\ge3$ the constraint is genuinely nonlinear and leaves the edge density undetermined; nevertheless, on the positive range the sharp lower boundary is the classical multipartite edge-to-clique profile, reparametrised by $K_s$-density. We also prove stability on the positive branches of this profile: at every interior point, near extremality forces cut-distance closeness to the corresponding extremal family at the induced edge density.

math.CO↗

arXiv2026

Turán numbers of $4$-uniform tight even cycles minus one edge

For every integer $k \ge 1$ and sufficiently large $n$, we show that the extremal construction for the Turán number of the $4$-uniform tight cycle of length $4k+2$ minus one edge is a complete odd-bipartite $4$-graph. In particular, since $C_{6}^{4-}$ contains the $4$-uniform expanded triangle as a subgraph, our result extends that of Frankl and Keevash--Sudakov on the Turán density and the Turán number of the $4$-uniform expanded triangle. We also show that the Turán density of $C_{4k+2}^{4}$ is $1/2$ for all integers $k \ge 2$, and establish the corresponding stability result. This strengthens the result of Sankar on the Turán density of $C_{4k+2}^{4}$ which holds only for all sufficiently large $k$.

math.CO↗

arXiv2026

On a hypergraph Turán problem of Balogh-Bohman-Bollobás-Zhao

Let $S$ and $T$ be disjoint sets with $|S|=i$ and $|T|=r-1$ for $2\le i\le r-1$, and let $B_i^{(r)}$ be the $r$-graph on $S\cup T$ whose edges are the $r$-subsets containing $S$ or $T$. We study the deficit $q_{r,i}:=1-π(B_i^{(r)})$ in its Turán density. Balogh, Bohman, Bollobás, and Zhao previously obtained bounds for these deficits with logarithmic gaps near both ends of the sequence $B_i^{(r)}$, namely, when $i=O(1)$ or $i=r-O(1)$. We close these gaps by showing that, as $r\to\infty$, for every fixed integer $a\ge1$, $q_{r,a+1}=Θ_a(r^{-a})$, and for every fixed integer $b\ge2$, $q_{r,r-b}=Θ_b(r^{-b}\log r)$.

math.CO↗

arXiv2026

Hybrid-Field 6D Movable Antenna for Terahertz Communications: Channel Modeling and Estimation

In this work, we study a six-dimensional movable antenna (6DMA)-enhanced Terahertz (THz) network that supports a large number of users with a few antennas by controlling the three-dimensional (3D) positions and 3D rotations of antenna surfaces/subarrays at the base station (BS). However, the short wavelength of THz signals combined with a large 6DMA movement range extends the near-field region. As a result, a user can be in the far-field region relative to the antennas on one 6DMA surface, while simultaneously residing in the near-field region relative to other 6DMA surfaces. Moreover, 6DMA THz channel estimation suffers from increased computational complexity and pilot overhead due to uneven power distribution across the large number of candidate position-rotation pairs, as well as the limited number of radio frequency (RF) chains in THz bands. To address these issues, we propose an efficient hybrid-field generalized 6DMA THz channel model, which accounts for planar wave propagation within individual 6DMA surfaces and spherical waves among different 6DMA surfaces. Furthermore, we propose a low-overhead channel estimation algorithm that leverages directional sparsity to construct a complete channel map for all potential antenna position-rotation pairs. Numerical results show that the proposed hybrid-field channel model achieves a sum rate close to that of the ground-truth near-field channel model and confirm that the channel estimation method yields accurate results with low complexity.

cs.IT↗

arXiv2026

Vertex-colored Turán theorems with applications in extremal hypergraph problems

Balogh, Clemen, and Lidický proved that the $\ell_{2}$-norm Turán problem for $K_{5}^{3}$ is asymptotically solved by the balanced bipartite construction, and they further conjectured that this construction is uniquely extremal for all sufficiently large $n$. We confirm this conjecture. We also determine exactly the maximum number of cliques in an $n$-vertex $K_{5}^{3}$-free $3$-uniform hypergraph for all sufficiently large $n$, thereby verifying the corresponding case of a conjecture of Frankl, Gryaznov, and Talebanfard. The main ingredients are Turán-type theorems for vertex-colored graphs forbidding balanced cliques, including an edge bound, an $\ell_{2}$-norm bound, and a sharp crossing-triangle theorem in the two-colored balanced $K_{4}$-free case. We also use a local modification procedure within the stability method. This reduces the exact hypergraph problems to proving that the relevant objective function increases under suitable local changes near the bipartite construction.

math.CO↗

arXiv2026

Physics-Informed Digital Twins for Channel Estimation and Traffic Prediction of Non-Terrestrial Networks

In non-terrestrial networks (NTN), high-speed satellite orbital motion, limited pilot signaling resources, and spatiotemporally heterogeneous traffic make accurate channel and traffic state characterization particularly challenging. In this paper, we propose a physics-informed digital twin (DT) framework for channel estimation and traffic prediction. Particularly, it formulates channel state information (CSI) reconstruction as a controllable generative process guided by physical-prior tensors. Through a physics-aware attention mechanism, it effectively reconstructs the real-time full-resolution CSI from highly sparse and outdated pilots. Then, we develop an orbit-adaptive spatiotemporal graph neural network for traffic prediction. By leveraging a dual-stream attention mechanism to capture intra- and inter-plane spatial dependencies and a gated recurrent unit to model temporal evolution, the neural network effectively predicts stochastic traffic residuals, which are integrated with the deterministic physical traffic baseline to form the complete traffic state. To evaluate the proposed DT framework, we establish a high-fidelity NTN DT simulation platform based on real-world Starlink ephemeris, global population, and ERA5 weather data. Experimental results demonstrate that our framework significantly outperforms state-of-the-art baselines in both CSI reconstruction and traffic prediction accuracy.

eess.SP↗

arXiv2026

A note on the $t$-partite link problem of Füredi

Motivated by the Erdős--Sós bipartite link conjecture, Füredi (Oberwolfach, 2004) asked for the asymptotic maximum edge density $π_{\mathrm{link}}(t)$ of $3$-graphs in which the link graph of every vertex is $t$-partite. Goldwasser's recursive blow-up construction based on projective planes gives the lower bound $π_{\mathrm{link}}(t)\ge 1-t^{-1}-(2+o_t(1))t^{-2}$ whenever $t-1$ is a prime power. In this note, we prove the upper bound $π_{\mathrm{link}}(t)\le 1-t^{-1}-t^{-2}/12$ for every $t \ge 2$. Together with Goldwasser's construction, this determines, up to a constant factor, the correct order of the gap between $π_{\mathrm{link}}(t)$ and the trivial averaging upper bound $1-t^{-1}$ for all prime-power values of $t-1$. In fact, our argument applies in the more general setting of $3$-graphs with no generalized daisies, equivalently, $3$-graphs in which the link graph of every vertex is $K_{t+1}$-free. We also establish an analogous upper bound for the positive $(r-1)$-codegree Turán density of generalized daisies.

math.CO↗

arXiv2026

Reachability Analysis of the State Transition and State Covariance Matrices for an LTV System

In this paper, we study the reachability of two closely related matrices appearing in the analysis of linear time-varying (LTV) systems over a finite time interval, namely, its closed-loop state transition matrix via a state feedback control and its state covariance matrix starting from some given initial state covariance matrix. Under a mild assumption, we first characterize the set of closed-loop terminal state transition matrices reachable from the identity matrix using controls of the state feedback form. Then, we provide the set of terminal state covariance matrices reachable from any given positive definite initial state covariance matrix when the LTV system is not necessarily controllable. Both results are based on the solutions of corresponding matrix Riccati differential equations (RDE).

eess.SY↗

arXiv2026

From Inpainting to Layer Decomposition: Repurposing Generative Inpainting Models for Image Layer Decomposition

Images can be viewed as layered compositions, foreground objects over background, with potential occlusions. This layered representation enables independent editing of elements, offering greater flexibility for content creation. Despite the progress in large generative models, decomposing a single image into layers remains challenging due to limited methods and data. We observe a strong connection between layer decomposition and in/outpainting tasks, and propose adapting a diffusion-based inpainting model for layer decomposition using lightweight finetuning. To further preserve detail in the latent space, we introduce a novel multi-modal context fusion module with linear attention complexity. Our model is trained purely on a synthetic dataset constructed from open-source assets and achieves superior performance in object removal and occlusion recovery, unlocking new possibilities in downstream editing and creative applications.

cs.CV↗

arXiv2026

Subsurface ocean salinity and dissipation rate inferred from Enceladus ice shell morphology

The habitability of Enceladus' subsurface ocean and the detectability of potential biosignatures depend on efficient ocean circulation and suitable ocean conditions. Directly probing the ocean is challenging because it lies beneath a thick ice shell; however, the ice thickness distribution is relatively well constrained and provides indirect insight into the underlying ocean dynamics. This study investigates how ocean circulation and the associated heat transport depend on ocean salinity and tide-induced vertical mixing using scaling analysis, supported by numerical simulations. We find that ocean circulation and equatorward heat convergence are stronger under extremely high or low salinity conditions than under intermediate salinity, and both increase with tidal mixing rates. Because the poleward thinning of Enceladus' ice shell cannot be maintained in the presence of strong equatorward ocean heat transport, these results place constraints on the ocean salinity, diffusivity, circulation timescale, and ocean dissipation rate. Energetic analysis further shows that Enceladus' ocean behaves like an extremely efficient heat pump (inefficient heat engine), potentially transporting up to 1000 times more heat across latitudes than the energy dissipated within the ocean itself, thereby placing strong constraints on the ocean's energy dissipation rate.

astro-ph.EP↗

arXiv2026

Flexible Coupler Array with Reconfigurable Pattern: Mechanical Beamforming and Digital Agent

Flexible coupler is a promising solution for enhancing wireless network capacity by moving passive couplers around a fixed-position active antenna to reshape the induced currents on passive elements. Motivated by this, this paper proposes a novel flexible coupler array that incorporates additional degrees of freedom (DoF) in radiation pattern reconfiguration and enhanced communication coverage with low hardware cost. Specifically, a new form of mechanical beamforming can be obtained by moving only the passive coupling elements while keeping the active antenna stationary. In addition, the flexible coupler antenna can slide along a rail toward users, thereby enhancing communication coverage. To fully exploit the potential of the flexible coupler array, we formulate a two-timescale sum-rate maximization problem with statistical channel state information (CSI). The antenna position is optimized based on scattering cluster-core statistics in the slow timescale, while mechanical beamforming is optimized based on multipath channel statistics in the fast timescale, subject to movement and energy constraints. To address the coupling between timescales and the high cost of extensive channel sampling, we develop a digital agent framework that leverages an electromagnetic (EM) map to generate statistical channel information for different user and antenna positions. Then, a deep neural network is trained to learn a slow-fast performance (SFP) surrogate. Mechanical beamforming at the fast timescale is obtained by selecting per-antenna radiation patterns from a predefined dictionary via a convex relaxation. Simulation results verify the performance gains achieved by the proposed flexible coupler array and the digital-agent-assisted algorithm.

cs.IT↗

arXiv2026

On a refinement of the Ahlswede--Katona Theorem

A classical theorem of Ahlswede and Katona determines the maximum density of the $2$-edge star in a graph with a given edge density. Motivated by its application in hypergraph Turán problems, we establish a refinement of their result under the additional assumption that the graph contains a large independent set in which every vertex has high degree.

math.CO↗

arXiv2025

Tetrahedron Conjecture in the $\ell_2$-norm

The famous Tetrahedron Conjecture of Turán from the 1940s asserts that the number of edges in an $n$-vertex $3$-graph without the tetrahedron, the complete $3$-graph on four vertices, cannot exceed that of the balanced complete cyclic $3$-partite $3$-graph, whose edges are of types $V_1 V_2 V_3$, $V_1 V_1 V_2$, $V_2 V_2 V_3$, and $V_3 V_3 V_1$. A recent surprising result of Balogh-Clemen-Lidický [J. Lond. Math. Soc. (2) 106 (2022)] shows that this conjecture is asymptotically true in the $\ell_2$-norm, where the number of edges is replaced by the sum of squared codegrees. They further conjectured that, in this $\ell_2$-norm setting, the $3$-partite construction is uniquely extremal for large $n$. We confirm this conjecture. Two key ingredients in our proofs include establishing a Mantel theorem for vertex-colored graphs that forbid certain types of triangles, and introducing a novel procedure integrated into Simonovits' stability method, which essentially reduces the task to verifying that the $\ell_2$-norm of certain near-extremal constructions increases under suitable local modifications. The strategy in the latter may be of independent interest and potentially applicable to other extremal problems.

math.CO↗

arXiv2025

How does ice shell geometry shape ocean dynamics on icy moons?

A poleward-thinning ice shell can drive circulation in the subsurface oceans of icy moons by imposing a meridional temperature gradient--colder at the equator than the pole--through the freezing point suppression due to pressure. This temperature gradient sets a buoyancy gradient, whose sign depends on the thermal expansion coefficient determined by ocean salinity. Together with vertical mixing, this buoyancy forcing shapes key oceanic features, including zonal currents in thermal wind balance, baroclinic instability of those currents, meridional heat transport by eddies, and vertical stratification. We use high-resolution numerical simulations to explore how variations in ice shell thickness affect these processes. Our simulations span a wide range of topographic slopes, pole-to-equator temperature differences, and vertical mixing strengths, for both fresh and salty oceans. We find that baroclinic eddies dominate large-scale circulation and meridional heat transport, consistent with studies assuming a flat ice-ocean interface. However, sloped topography introduces new effects: when lighter water overlies denser water along the slope, circulation weakens as a stratified layer thickens beneath the poles. Conversely, when denser water lies beneath the poles, circulation strengthens as topography increases the available potential energy. We develop a scaling framework that predicts heat transport and stratification across all simulations. Applying this framework to Enceladus, Europa, and Titan, we infer ocean heat fluxes, stratification, and tidal energy dissipation and showing large-scale circulation constrains tidal heating and links future observations of ice thickness and rotation to subsurface ocean dynamics.

astro-ph.EP↗

arXiv2025

Odd hypergraph Mantel theorems

A classical result of Sidorenko (1989) shows that the Turán density of every $r$-uniform hypergraph with three edges is bounded from above by $1/2$. For even $r$, this bound is tight, as demonstrated by Mantel's theorem on triangles and Frankl's theorem on expanded triangles. In this note, we prove that for odd $r$, the bound $1/2$ is never attained, thereby answering a question of Keevash and revealing a fundamental difference between hypergraphs of odd and even uniformity. Moreover, our result implies that the expanded triangles form the unique class of three-edge hypergraphs whose Turán density attains $1/2$.

math.CO↗

arXiv2025

STASE: A spatialized text-to-audio synthesis engine for music generation

While many text-to-audio systems produce monophonic or fixed-stereo outputs, generating audio with user-defined spatial properties remains a challenge. Existing deep learning-based spatialization methods often rely on latent-space manipulations, which can limit direct control over psychoacoustic parameters critical to spatial perception. To address this, we introduce STASE, a system that leverages a Large Language Model (LLM) as an agent to interpret spatial cues from text. A key feature of STASE is the decoupling of semantic interpretation from a separate, physics-based spatial rendering engine, which facilitates interpretable and user-controllable spatial reasoning. The LLM processes prompts through two main pathways: (i) Description Prompts, for direct mapping of explicit spatial information (e.g., "place the lead guitar at 45° azimuth, 10 m distance"), and (ii) Abstract Prompts, where a Retrieval-Augmented Generation (RAG) module retrieves relevant spatial templates to inform the rendering. This paper details the STASE workflow, discusses implementation considerations, and highlights current challenges in evaluating generative spatial audio.

cs.SD↗

arXiv2025

Instruct-MusicGen: Unlocking Text-to-Music Editing for Music Language Models via Instruction Tuning

Recent advances in text-to-music editing, which employ text queries to modify music (e.g.\ by changing its style or adjusting instrumental components), present unique challenges and opportunities for AI-assisted music creation. Previous approaches in this domain have been constrained by the necessity to train specific editing models from scratch, which is both resource-intensive and inefficient; other research uses large language models to predict edited music, resulting in imprecise audio reconstruction. To Combine the strengths and address these limitations, we introduce Instruct-MusicGen, a novel approach that finetunes a pretrained MusicGen model to efficiently follow editing instructions such as adding, removing, or separating stems. Our approach involves a modification of the original MusicGen architecture by incorporating a text fusion module and an audio fusion module, which allow the model to process instruction texts and audio inputs concurrently and yield the desired edited music. Remarkably, Instruct-MusicGen only introduces 8% new parameters to the original MusicGen model and only trains for 5K steps, yet it achieves superior performance across all tasks compared to existing baselines, and demonstrates performance comparable to the models trained for specific tasks. This advancement not only enhances the efficiency of text-to-music editing but also broadens the applicability of music language models in dynamic music production environments.

cs.SD↗

arXiv2025

Temporal Adaptation of Pre-trained Foundation Models for Music Structure Analysis

Audio-based music structure analysis (MSA) is an essential task in Music Information Retrieval that remains challenging due to the complexity and variability of musical form. Recent advances highlight the potential of fine-tuning pre-trained music foundation models for MSA tasks. However, these models are typically trained with high temporal feature resolution and short audio windows, which limits their efficiency and introduces bias when applied to long-form audio. This paper presents a temporal adaptation approach for fine-tuning music foundation models tailored to MSA. Our method enables efficient analysis of full-length songs in a single forward pass by incorporating two key strategies: (1) audio window extension and (2) low-resolution adaptation. Experiments on the Harmonix Set and RWC-Pop datasets show that our method significantly improves both boundary detection and structural function prediction, while maintaining comparable memory usage and inference speed.

cs.SD↗