arXiv subjects

Ya-Nan Zhang

Publications and source records attributed to Ya-Nan Zhang.

12 recordsLinked to original sources

arXiv2026

Interpolation constrained rational minimax approximation with barycentric representation

In this paper, we propose a novel dual-based Lawson's method, termed {b-d-Lawson}, designed for addressing the rational minimax approximation under specific interpolation conditions. The {b-d-Lawson} approach incorporates two pivotal components that have been recently gained prominence in the realm of the rational approximations: the barycentric representation of the rational function and the dual framework for tackling minimax approximation challenges. The employment of barycentric formulae enables a streamlined parameterization of the rational function, ensuring natural satisfaction of interpolation conditions while mitigating numerical instability typically associated with Vandermonde basis matrices when monomial bases are utilized. This enhances both the accuracy and computational stability of the method. To address the bi-level min-max structure, the dual framework effectively transforms the challenge into a max-min dual problem, thereby facilitating the efficient application of Lawson's iteration. The integration of this dual perspective is crucial for optimizing the approximation process. We will discuss several applications of interpolation-constrained rational minimax approximation and illustrate numerical results to evaluate the performance of the {b-d-Lawson} method.

math.NA↗

arXiv2026

BiM-GeoAttn-Net: Linear-Time Depth Modeling with Geometry-Aware Attention for 3D Aortic Dissection CTA Segmentation

Accurate segmentation of aortic dissection (AD) lumens in CT angiography (CTA) is essential for quantitative morphological assessment and clinical decision-making. However, reliable 3D delineation remains challenging due to limited long-range context modeling, which compromises inter-slice coherence, and insufficient structural discrimination under low-contrast conditions. To address these limitations, we propose BiM-GeoAttn-Net, a lightweight framework that integrates linear-time depth-wise state-space modeling with geometry-aware vessel refinement. Our approach is featured by Bidirectional Depth Mamba (BiM) to efficiently capture cross-slice dependencies and Geometry-Aware Vessel Attention (GeoAttn) module that employs orientation-sensitive anisotropic filtering to refine tubular structures and sharpen ambiguous boundaries. Extensive experiments on a multi-source AD CTA dataset demonstrate that BiM-GeoAttn-Net achieves a Dice score of 93.35% and an HD95 of 12.36 mm, outperforming representative CNN-, Transformer-, and SSM-based baselines in overlap metrics while maintaining competitive boundary accuracy. These results suggest that coupling linear-time depth modeling with geometry-aware refinement provides an effective, computationally efficient solution for robust 3D AD segmentation.

eess.IV↗

arXiv2026

SpectralMamba-UNet: Frequency-Disentangled State Space Modeling for Texture-Structure Consistent Medical Image Segmentation

Accurate medical image segmentation requires effective modeling of both global anatomical structures and fine-grained boundary details. Recent state space models (e.g., Vision Mamba) offer efficient long-range dependency modeling. However, their one-dimensional serialization weakens local spatial continuity and high-frequency representation. To this end, we propose SpectralMamba-UNet, a novel frequency-disentangled framework to decouple the learning of structural and textural information in the spectral domain. Our Spectral Decomposition and Modeling (SDM) module applies discrete cosine transform to decompose low- and high-frequency features, where low frequency contributes to global contextual modeling via a frequency-domain Mamba and high frequency preserves boundary-sensitive details. To balance spectral contributions, we introduce a Spectral Channel Reweighting (SCR) mechanism to form channel-wise frequency-aware attention, and a Spectral-Guided Fusion (SGF) module to achieve adaptively multi-scale fusion in the decoder. Experiments on five public benchmarks demonstrate consistent improvements across diverse modalities and segmentation targets, validating the effectiveness and generalizability of our approach.

cs.CV↗

arXiv2026

VFGS-Net: Frequency-Guided State-Space Learning for Topology-Preserving Retinal Vessel Segmentation

Accurate retinal vessel segmentation is a critical prerequisite for quantitative analysis of retinal images and computer-aided diagnosis of vascular diseases such as diabetic retinopathy. However, the elongated morphology, wide scale variation, and low contrast of retinal vessels pose significant challenges for existing methods, making it difficult to simultaneously preserve fine capillaries and maintain global topological continuity. To address these challenges, we propose the Vessel-aware Frequency-domain and Global Spatial modeling Network (VFGS-Net), an end-to-end segmentation framework that seamlessly integrates frequency-aware feature enhancement, dual-path convolutional representation learning, and bidirectional asymmetric spatial state-space modeling within a unified architecture. Specifically, VFGS-Net employs a dual-path feature convolution module to jointly capture fine-grained local textures and multi-scale contextual semantics. A novel vessel-aware frequency-domain channel attention mechanism is introduced to adaptively reweight spectral components, thereby enhancing vessel-relevant responses in high-level features. Furthermore, at the network bottleneck, we propose a bidirectional asymmetric Mamba2-based spatial modeling block to efficiently capture long-range spatial dependencies and strengthen the global continuity of vascular structures. Extensive experiments on four publicly available retinal vessel datasets demonstrate that VFGS-Net achieves competitive or superior performance compared to state-of-the-art methods. Notably, our model consistently improves segmentation accuracy for fine vessels, complex branching patterns, and low-contrast regions, highlighting its robustness and clinical potential.

cs.CV↗

arXiv2026

Entropy stabilization and effect of A-site ionic size in bilayer nickelates

The discovery of high-temperature superconductivity in La$_3$Ni$_2$O$_7$ under high pressure has sparked a surge of research into Ruddlesden-Popper (RP) nickelates. Currently, stabilizing the bilayer RP phases with smaller $A$-site ions remains a significant challenge. In this work, we have successfully synthesized medium- and high-entropy bilayer nickelates, La$_{1.2}$Pr$_{0.6}$Nd$_{0.6}$Sm$_{0.6}$Ni$_2$O$_{7-δ}$ and La$_{0.67}$Pr$_{0.67}$Nd$_{0.67}$Sm$_{0.33}$Eu$_{0.33}$Gd$_{0.33}$Ni$_2$O$_{7-δ}$, by utilizing the concept of configuration entropy stabilization. The high-entropy nickelate exhibits the smallest unit-cell volume and the largest orthorhombic distortion reported to date. The chemical pressure induced by the smaller A-site ions significantly enhances the NiO$_6$ octahedral rotation/distortion and shortens the interlayer Ni-Ni interatomic spacing. Physical property measurements reveal bad electrical conductivity alongside a markedly elevated density-wave transition temperature. Notably, the superconducting transition temperature extrapolated from structural correlations is projected to exceed 100 K. Our work not only demonstrates entropy stabilization of bilayer nickelates, but also reveals the effect of $A$-site-ion size on the crystal structure and physical properties, opening a new pathway for developing nickelate superconductors and tuning their electronic properties.

cond-mat.supr-con↗

arXiv2025

Stabilization of Tetragonal Phase and Aluminum-Doping Effect in a Bilayer Nickelate

Recent studies suggest that the tetragonal phase of the Ruddlesden-Popper (RP) bilayer nickelate, La$_3$Ni$_2$O$_7$ or La$_2$PrNi$_2$O$_7$, which is stabilized under high pressures, is responsible for high-temperature superconductivity (HTSC). In this context, realization of the tetragonal phase at ambient pressure could be a rational step to achieve the goal of ambient-pressure HTSC in the nickelate system. By employing the concept of Goldschmidt tolerance factor, we succeed in stabilizing the tetragonal phase by aluminum doping together with post annealing under moderately high oxygen pressure. X-ray and neutron diffractions verify the tetragonal $I4/mmm$ structure for the post-annealed samples La$_3$Ni$_{2-x}$Al$_x$O$_{7-δ}$ (0.3 $\leq x \leq$ 0.5). The Al-doped samples, including the tetragonal ones, show semiconducting properties, carry localized magnetic moments, and exhibit spin-glass-like behaviors at low temperatures, all of which can be explained in terms of charge carrier localization. Furthermore, high-pressure resistance measurements on post-annealed samples reveal that even a low Al doping ($x$ = 0.05) suppresses superconductivity almost completely. This work gives information about the effect of nonmagnetic impurity on metallicity as well as superconductivity in bilayer nickelates, which would contribute to understanding the superconducting mechanism in RP nickelates.

cond-mat.supr-con↗

arXiv2025

Multivariate confluent Vandermonde with G-Arnoldi and applications

In the least-squares fitting framework, the Vandermonde with Arnoldi (V+A) method presented in [Brubeck, Nakatsukasa, and Trefethen, {SIAM Review}, 63 (2021), pp. 405-415] is an effective approach to compute a polynomial that approximates an underlying univariate function $f$. Extensions of V+A include its multivariate version and the univariate confluent V+A; the latter enables us to use the information of the derivative of $f$ in obtaining the approximation polynomial. In this paper, we shall extend V+A further to the multivariate confluent V+A. Besides the technical generalization of the univariate confluent V+A, we also introduce a general and application-dependent $G$-orthogonalization in the Arnoldi process. We shall demonstrate with several applications that, by specifying an application-related $G$-inner product, the desired approximate multivariate polynomial, as well as certain of its partial derivatives can be computed accurately from a well-conditioned least-squares problem whose coefficient matrix is orthonormal. The desired multivariate polynomial is represented in a discrete $G$-orthogonal polynomials basis which admits an explicit recurrence, and therefore, facilitates evaluating function values and certain partial derivatives at new nodes efficiently. We demonstrate its flexibility by applying it to solve the multivariate Hermite least-squares problem and PDEs with various boundary conditions in irregular domains.

math.NA↗

arXiv2025

Rational minimax approximation of matrix-valued functions

In this paper, we present a rigorous framework for rational minimax approximation of matrix-valued functions that generalizes classical scalar approximation theory. Given sampled data $\{(x_\ell, {F}(x_\ell))\}_{\ell=1}^m$ where ${F}:\mathbb{C} \to \mathbb{C}^{s \times t}$ is a matrix-valued function, we study the problem of finding a matrix-valued rational approximant ${R}(x) = {P}(x)/q(x)$ (with ${P}:\mathbb{C} \to \mathbb{C}^{s \times t}$ a matrix-valued polynomial and $q(x)$ a nonzero scalar polynomial of prescribed degrees) that minimizes the worst-case Frobenius norm error over the given nodes: $$ \inf_{{R}(x) = {P}(x)/q(x)} \max_{1 \leq \ell \leq m} \|{F}(x_\ell) - {R}(x_\ell)\|_{\rm F}. $$ By reformulating this min-max optimization problem through Lagrangian duality, we derive a maximization dual problem over the probability simplex. We analyze weak and strong duality properties and establish a sufficient condition ensuring that the solution of the dual problem yields the minimax approximant $R(x)$. For numerical implementation, we propose an efficient method (\textsf{m-d-Lawson}) to solve the dual problem, generalizing Lawson's iteration to matrix-valued functions. Convergence analysis of \textsf{m-d-Lawson} is established. Numerical experiments are conducted and compared to state-of-the-art approaches, demonstrating its efficiency as a novel computational framework for matrix-valued rational approximation.

math.NA↗

arXiv2025

Quantum Criticality by Interaction Frustration in a Square-Planar Lattice

We report experimental and theoretical investigations on ThCr$_2$Ge$_2$C, a metallic compound in which Cr$_2$C planes form a square-planar lattice. Neutron powder diffraction, magnetization, and specific heat measurements reveal no evidence of long-range magnetic order or short-range spin freezing down to 70~mK. Quantum critical behavior was indicated through logarithmic divergences in both the magnetic susceptibility and the specific heat divided by temperature. Resistivity measurements exhibit non-Fermi-liquid behavior, with a Fermi liquid recovered under magnetic fields or high pressures. First-principles calculations identify competing nearest-neighbor ($J_1$) and next-nearest-neighbor ($J_2$) exchange interactions, with $J_2/J_1 \sim -0.5$, pointing to strong magnetic frustration. The interaction frustration is reduced, and magnetically ordered phases are stabilized upon the application of negative or positive pressures. This work offers a rare example of zero-field, ambient pressure quantum criticality mainly driven by interaction frustration in a square lattice.

cond-mat.str-el↗

arXiv2024

A convex dual problem for the rational minimax approximation and Lawson's iteration

Computing the discrete rational minimax approximation in the complex plane is challenging. Apart from Ruttan's sufficient condition, there are few other sufficient conditions for global optimality. The state-of-the-art rational approximation algorithms, such as the adaptive Antoulas-Anderson (AAA), AAA-Lawson, and the rational Krylov fitting (RKFIT) method, perform highly efficiently, but the computed rational approximations may not be minimax solutions. In this paper, we propose a convex programming approach, the solution of which is guaranteed to be the rational minimax approximation under Ruttan's sufficient condition. Furthermore, we present a new version of Lawson's iteration for solving this convex programming problem. The computed solution can be easily verified as the rational minimax approximation. Our numerical experiments demonstrate that this updated version of Lawson's iteration generally converges monotonically with respect to the objective function of the convex optimization. It is an effective competitive approach for computing the rational minimax approximation, compared to the highly efficient AAA, AAA-Lawson, and the stabilized Sanathanan-Koerner iteration.

math.NA↗

arXiv2023

The $L_q$-weighted dual programming of the linear Chebyshev approximation and an interior-point method

Given samples of a real or complex-valued function on a set of distinct nodes, the traditional linear Chebyshev approximation is to compute the best minimax approximation on a prescribed linear functional space. Lawson's iteration is a classical and well-known method for that task. However, Lawson's iteration converges linearly and in many cases, the convergence is very slow. In this paper, by the duality theory of linear programming, we first provide an elementary and self-contained proof for the well-known Alternation Theorem in the real case. Also, relying upon the Lagrange duality, we further establish an $L_q$-weighted dual programming for the linear Chebyshev approximation. In this framework, we revisit the convergence of Lawson's iteration, and moreover, propose a Newton type iteration, the interior-point method, to solve the $L_2$-weighted dual programming. Numerical experiments are reported to demonstrate its fast convergence and its capability in finding the reference points that characterize the unique minimax approximation.

math.NA↗

arXiv2016

Holographic paramagnetism-ferromagnetism phase transition with the nonlinear electrodynamics

In the probe limit, we investigate the nonlinear electrodynamical effects of the both exponential form and the logarithmic form on the holographic paramagnetism-ferromagnetism phase transition in the background of a Schwarzschild-AdS black hole spacetime. Moreover, by comparing the exponential form of nonlinear electrodynamics with the logarithmic form of nonlinear electrodynamics and the Born-Infeld nonlinear electrodynamics which has been presented in Ref.~\cite{Wu:2016uyj}, we find that the higher nonlinear electrodynamics correction makes the critical temperature smaller and the magnetic moment harder form in the case without external field. Furthermore, the increase of nonlinear parameter b will result in extending the period of the external magnetic field. Especially, the effect of the exponential form of nonlinear electrodynamics on the periodicity of hysteresis loop is more noticeable.

hep-th↗