arXiv subjects

Qi Yan

Publications and source records attributed to Qi Yan.

At least 19 recordsLinked to original sources

arXiv2026

A Foundation Model for Large-Scale Wireless Network Planning , Operation and Optimization

Wireless cellular networks provide critical infrastructure for communication, transportation and industry, making reliable connectivity essential to modern society. Delivering this connectivity requires accurate models of the radio environment shaped jointly by network infrastructure and their surroundings. Such models underpin base-station deployment, network operation and parameter optimization, yet city-scale radio environments remain difficult to capture. Physics-based tools require detailed site descriptions and computation, whereas task-specific models need dedicated measurements and transfer poorly across deployments. Here we introduce ChaRT, a foundation model that learns transferable radio representations from measurement reports routinely generated by operational cellular networks. These reports provide abundant joint observations across multiple cells and beams without additional measurement campaigns. ChaRT incorporates beam-level angular structure, network hierarchy and propagation-regime diversity into its architecture, and is pretrained through context-aware masked beam modelling and self-distillation. We train ChaRT on more than one billion reports comprising 18.2 billion beam-level observations from 3,503 cells in one city. With a single set of weights, ChaRT reconstructs radio environments in unseen cities and transfers to new-site prediction, radio map construction and network parameter tuning. With only 1% of labelled data, it supports user localization, beam prediction, propagation scenario classification and estimation of the signal-to-interference-plus-noise ratio. The learned representation further enables beamspace clustering for reusable radio-grid construction. These results establish operational measurement reports as a scalable data foundation for transferable cellular-network intelligence.

eess.SP↗

arXiv2026

A Fano framework for binary delta-matroids

Dunshee and Ellingham recently showed that seven natural properties of a cellularly embedded graph form a Fano-plane framework. We establish an analogous framework for binary delta-matroids. For a binary delta-matroid $D$ and $\tau$, let $Z_3(D,\tau)$ denote its associated binary tight $3$-matroid. The six outer points are represented by evenness or bipartiteness of $D$ and its global vertex-flip transforms. For the seventh point, we call $D$ $Z_3$-bipartite when every circuit of $Z_3(D,\tau)$ has even cardinality. We show that the satisfied properties are precisely the nonzero vectors of a subspace of $\Ftwo^3$. For ribbon-graphic delta-matroids, $Z_3$-bipartiteness is equivalent to bipartiteness of the medial graph, so the construction recovers the Fano-plane framework for embedded graphs.

math.CO↗

arXiv2026

Monotone maximum partial-twuality widths of vf-safe delta-matroids

For a delta-matroid, the maximum twist width theorem states that the maximum width over all twists can be reached along a non-decreasing sequence of intermediate twist widths. In this paper we study analogous monotone maximum width sequences for partial twualities generated by twist and loop complementation. We prove that, for each non-twist partial-twuality operation on a vf-safe delta-matroid, there exists a subset attaining the corresponding maximum partial-twuality width whose elements can be ordered so that the successive intermediate widths are non-decreasing. Together with the known twist case, this gives a monotone maximum width theorem for all five nontrivial partial-twuality operations on vf-safe delta-matroids. We also prove feasible-set attainment results for the operations $\ast\times$ and $\ast\times\ast$. Finally, we translate these results to ribbon graphs, obtaining monotone sequences for maximum partial-twuality Euler genera and spanning quasi-tree attainment results for the corresponding ribbon graph operations.

math.CO↗

arXiv2026

Partial-twuality polynomial interpolation for binary delta-matroids

Gross, Mansour and Tucker introduced the partial-twuality polynomials for ribbon graphs and investigated the interpolation property of these polynomials. The ribbon group generated by $\delta$ and $\tau$ acts on set systems as twist $\ast$ and loop complementation $\times$, yielding five nontrivial twuality operators: $ \{\ast,\times,\ast\times ,\times\ast ,\ast\times\ast \}.$ Yan and Jin extended partial-twuality polynomials to set systems, yielding partial-$\bullet$ polynomials with $\bullet\in\{\ast,\times,\ast\times ,\times\ast ,\ast\times\ast\}.$ For partial-$\ast$ polynomials, Zhao and Yan proved that this polynomial is either even, odd, or both even-interpolating and odd-interpolating for every binary delta-matroid. In this paper, we extend this interpolation property to all the remaining nontrivial partial-twualities of binary delta-matroids. Consequently, for every binary delta-matroid and every $\bullet\in\{\ast,\times,\ast \times ,\times\ast ,\ast \times \ast \}$, the partial-$\bullet$ polynomial is either even, odd, or both even-interpolating and odd-interpolating. We also provide examples to show that the binary assumption is essential.

math.CO↗

arXiv2026

Point-Cloud-Assistant Localized Statistical Channel Prediction by Tangent Gaussian Splatting

Accurate, site-specific channel information is crucial for optimizing next-generation wireless networks. Among various approaches, localized statistical channel modeling (LSCM), which models the channel multipath angular power spectrum (APS) from the reference signal received power (RSRP) measurement, has emerged as a state-of-the-art method tailored for efficient network optimization. However, despite its effectiveness, LSCM cannot predict APS at the vast majority of locations where no measurements are available, which significantly restricts its applicability in large-scale, real-world scenarios. To address this challenge, we present point-cloud-assisted tangent Gaussian splatting (PC-TGS), the first framework to extrapolate APS to unmeasured outdoor grids by integrating sparse radio measurements with dense LiDAR-based geometry. PC-TGS represents environmental scatterers as anisotropic 3D Gaussians, initialized and refined through a relaxed-mean reparameterization of the raw point cloud. A tangent-plane projection accurately maps each Gaussian into the local angular domain, while a depth-aware electromagnetic splatting process aggregates their contributions. To ensure practical deployment, we derive a closed-form Gaussian-weighted average (GWA) for APS bin integration and provide a provable error bound. { Evaluations on a LiDAR-scanned city-scale dataset (5M points, 6,310 RSRP samples) demonstrate that PC-TGS achieves better APS and RSRP prediction performance compared to state-of-the-art baselines and faster inference time for APS extrapolation task. These results highlight the potential of PC-TGS to enable geometry-aware and data-efficient channel prediction in large-scale wireless digital twins.

eess.SP↗

arXiv2026

Recurrence and coefficient inequality for the partial Petrial polynomial of graphs

The partial Petrial polynomial of a ribbon graph, introduced by Gross, Mansour and Tucker, enumerates partial Petrials by Euler genus. Recently, Deng, Jin and Yan defined an analogue for grafts and showed that it can be expressed as a rank-generating function of an adjacency matrix. In this paper we first prove a recurrence relation that reduces the partial Petrial polynomial of a graph with respect to an arbitrary edge, expressing it as a sum of three terms involving graphs obtained by local complementation and edge pivoting. This recurrence extends the known leaf-reduction formula to vertices of any positive degree. Second, using this recurrence we compare the lowest and highest degree coefficients of the polynomial. We prove that the lowest coefficient is always at most the highest coefficient, and that equality holds if and only if the graph has no edges.

math.CO↗

arXiv2026

Twist polynomial interpolation for binary delta-matroids

Gross, Mansour and Tucker introduced the partial-dual polynomial of a ribbon graph and asked under what conditions such a polynomial is even-interpolating, odd-interpolating, or both. In this paper, we provide an answer to this open problem.Using the framework of delta-matroids, we prove that the twist polynomial of any binary delta-matroid is either an even polynomial, an odd polynomial, or both even-interpolating and odd-interpolating. Applying this to ribbon graphs, we deduce that the partial-dual polynomial of any ribbon graph satisfies the same conclusion.

math.CO↗

arXiv2026

The First Controllable Bokeh Rendering Challenge at NTIRE 2026

This study presents the outcomes of the first Controllable Bokeh Rendering Challenge at NTIRE and highlights the most effective submitted methodologies. In total, 44 participants registered for the competition, of which 8 teams submitted valid solutions after the conclusion of the final test phase. All submissions were evaluated on unseen images, focusing on portraits and intricate subjects with complex and visually appealing bokeh phenomena. In addition to the first track focusing on established quantitative fidelity metrics, we conducted a qualitative user study with a panel of experts for a second track focusing on perceptual assessment. As this was the inaugural challenge on this topic, most of the participants focused on refining and extending the Bokehlicious baseline method.

cs.CV↗

arXiv2026

Partial-twuality polynomials of matrices

The study of partial-twuality polynomials originates from the classical operations of geometric duality and Petrie duality on cellularly embedded graphs. These involutions generate the symmetric group $S_3$, and applying them to subsets of edges yields the notions of partial-(geometric) duality, partial-Petriality, and more generally, partial-twuality. In this paper, we generalize this theory of partial-twuality polynomials within the framework of matrix algebra. The key observation that the Euler genus of a bouquet under a partial-twuality can be expressed as a rank function of its adjacency matrix motivates and leads to the definition of a partial-twuality polynomial for an arbitrary square matrix over any field, thereby providing a universal algebraic counterpart to the topological polynomials. We then investigate basic properties of these polynomials, including product formulas, recursion relations, degrees, interpolation behaviors, and invariance and duality theorems under the matrix operations of pivoting and inversion. We conclude by posing some problems for further research.

math.CO↗

arXiv2026

On the maximum twist width of delta-matroids

For a ribbon graph $G$, let $\gamma(G)$ denote its Euler genus. Recently, Chen, Gross and Tucker [J. Algebraic Combin. 63 (2026) 13] derived a formula for the maximum partial-dual Euler-genus $\partial\gamma_M(G)$ of a ribbon graph $G$. Their key finding is that $\partial\gamma_M(G)$ can be achieved by a partial dual with respect to the edge set of a spanning quasi-tree. Moreover, they proposed the following problem: Given a ribbon graph $G$, is there a sequence of edges $e_1,e_2,\dots, e_k$ such that $\gamma(G^{\{e_1, e_2,\dots, e_k\}})=\partial\gamma_M(G)$ and such that the sequence $$\gamma(G), \gamma(G^{\{e_1\}}), \dots, \gamma(G^ {\{e_1, e_2,\dots, e_k\}})$$ rises monotonically (i.e., never decreasing) to $\partial\gamma_M(G)$? Delta-matroids are set systems that satisfy the symmetric exchange axiom and serve as a matroidal abstraction of ribbon graphs. In this paper, we first show that the maximum twist width of a set system can be attained by twisting one of its feasible sets, which extends the result of Chen, Gross and Tucker to set systems. Then we solve the delta-matroid version of their problem, thereby providing an affirmative answer to the original problem for ribbon graphs.

math.CO↗

arXiv2025

Multiscale Causal Geometric Deep Learning for Modeling Brain Structure

Multimodal MRI offers complementary multi-scale information to characterize the brain structure. However, it remains challenging to effectively integrate multimodal MRI while achieving neuroscience interpretability. Here we propose to use Laplacian harmonics and spectral graph theory for multimodal alignment and multiscale integration. Based on the cortical mesh and connectome matrix that offer multi-scale representations, we devise Laplacian operators and spectral graph attentions to construct a shared latent space for model alignment. Next, we employ a disentangled learning combined with Graph Variational Autoencoder architectures to separate scale-specific and shared features. Lastly, we design a mutual information-informed bilevel regularizer to separate causal and non-causal factors based on the disentangled features, achieving robust model performance with enhanced interpretability. Our model outperforms baselines and other state-of-the-art models. The ablation studies confirmed the effectiveness of the proposed modules. Our model promises to offer a robust and interpretable framework for multi-scale brain structure analysis.

q-bio.NC↗

arXiv2025

Matrix Quasi-tree Theorem

Building on prior work that established Matrix Quasi-tree Theorems for special embedded graphs, in this paper, we develop a comprehensive theory applicable to all embedded graphs. We introduce symbolic skew-adjacency matrices and reduction maps as key innovations, and prove that a specific polynomial derived from these matrices encodes all spanning quasi-trees of a bouquet. This result provides a complete analogue of the Matrix Tree Theorem for topological graph theory, with applications to quasi-tree enumeration in both orientable and non-orientable embedded graphs.

math.CO↗

arXiv2025

Monotonicity of Perelman $\mathcal{W}$-Entropy of Mean Curvature Flow

In this paper, we study Perelman' s $ \mathcal{W}$ entropy for mean curvature flow in $\mathbb{R}^{n+1}$. Analogously to Perelman's $\mathcal{W}$-entropy defined for Ricci flow, K. Ecker in \cite{Ecker07} defined a functional $\mathcal{W}$ for the mean curvature flow in $\mathbb{R}^{n+1}$ and the region it encloses, and made the conjecture that this functional is monotonically increasing in time. We modify K. Ecker's definition and, using Hamilton's Harnack inequality for mean curvature flow, prove that our redefined $\mathcal{W}$-entropy is monotonically decreasing in time. Additionally, we provide a rigidity theorem for this $\mathcal{W}$-entropy.

math.DG↗

arXiv2025

Harnack Inequality for $f$-Mean Curvature Flow

In this paper, we prove a Li-Yau-Hamilton type Harnack estimate for the $f$-mean curvature flow in Euclidean space, which can be viewed as a gradient flow of the weighed area functional with the measure density function $e^{-f}$.

math.DG↗

arXiv2025

Stochastic Curve Shortening Flow with Scale-Dependent Noise

In this paper, we study the motion by mean curvature of curves in the plane perturbed by scale-dependent noise. We first introduce a so-called scale-dependent noise from the physics background to the curve shortening flow. To be more precise, the scale-dependent noise defined on a curve is a noise whose intensity is proportional to the length of the curve. To get the well-posedness of stochastic curve shortening flow driven by scale-dependent noise, we equivalently formulate the stochastic curve shortening flow as a one-phase stochastic Stefan problem of its curvature parameterized by the arclength parameter and its length. After rewriting the one-phase stochastic Stefan problem as a quasilinear evolution equation, we apply the theory for quaslinear stochastic evolution equations developed by Agresti and Veraar in 2022 to get maximal unique local strong solution for the stochastic curve shortening flow up to a maximal stopping time which is characterized by a blow-up criterion.

math.PR↗

arXiv2025

Maximal Solutions and Stochastic Free Boundary Formulations for Stochastic Willmore and Surface Diffusion Flows on $\R^2$

We study the stochastic Willmore flow and the stochastic surface diffusion flow for closed or non-closed curves on $\mathbb{R}^2$ in this paper. We equivalently formulate them as a stochastic one-phase Stefan problem (or a stochastic free boundary problem) of the curvature, which is parameterized by the arc-length, and the length of the curves. After rewriting the stochastic Stefan problem as a quasilinear parabolic evolution equation, we apply the theory for quasilinear parabolic stochastic evolution equations developed by Agresti and Veraar in 2022 to get the existence and uniqueness of a local strong solution up to a maximal stopping time that is characterized by a blow-up alternative. When the solutions blow up, the corresponding stochastic curve flows either develop singularities or shrink to a point.

math.PR↗

arXiv2025

Proof of a conjecture of Fomichev and Karev

We prove a conjecture of Fomichev and Karev [{European J. Combin.} 127 (2025) 104160] by showing the equality of two graph invariants: $\varphi$, defined via graph colorings, and $\psi$, derived from the $\mathfrak{sl}(2)$-weight system of its 2-dimensional irreducible representation.

math.CO↗

arXiv2025

Orbits and self-twuality in set systems and delta-matroids

We introduce a new group action on set systems, constructed as a semidirect product of a permutation group and a group generated by twist and loop complementation operations on a single element. This action extends the ribbon group framework of Abrams and Ellis-Monaghan from ribbon graphs to set systems, facilitating a systematic investigation of self-twuality. We prove that different forms of self-twuality propagate through orbits under the group action and establish a characterization of the orbit of a vf-safe delta-matroid via multimatroids. As an application, we analyze orbits of ribbon-graphic delta-matroids. Our work answers a question posed by Abrams and Ellis-Monaghan and provides a unified algebraic framework for studying self-twuality in combinatorial structures.

math.CO↗