arXiv subjects

Yanxiang Zhao

Publications and source records attributed to Yanxiang Zhao.

At least 19 recordsLinked to original sources

arXiv2026

A Thermodynamically Consistent Model for Multicomponent Vesicles

We develop a thermodynamically consistent diffuse-interface model for multicomponent membranes. The proposed model is derived from a coupled free energy functional that incorporates protein-dependent bending elasticity, diffuse surface tension, a volume penalty, and a membrane-associated Ohta--Kawasaki energy. Applying the Onsager variational principle, we derive a coupled $L^2$ gradient flow system and its energy dissipation law. We then construct a stabilized alternating ETD1 scheme and a stabilized alternating ETDRK2 scheme with Strang-type composition (alternating Strang-ETDRK2). To the best of our knowledge, the proposed alternating Strang-ETDRK2 scheme has not previously been developed and analyzed for coupled phase field systems. We further prove the discrete energy dissipation for both schemes under some regularity assumptions on the numerical solutions. Numerical experiments in two and three dimensions validate the discrete energy dissipation law, and present the protein segregation and membrane deformation produced by the proposed model.

math.NA↗

arXiv2026

Exponential Time Differencing Schemes for a Phase-Field Model of Multicomponent Membranes

In this paper, we develop and analyze exponential time differencing (ETD) schemes for a phase-field model of multicomponent membranes proposed in our previous work \cite{luo2025ohta}, in which membrane deformation is governed by a force-balance phase-field equation and protein segregation is described by a membrane-associated Ohta-Kawasaki (OK) dynamics. For a fixed phase-field membrane, we introduce a geometry-adapted operator splitting method based on the localization function, which reformulates the surface OK dynamics into a form suitable for ETD integration. The resulting first- and second-order ETD schemes, combined with finite-difference spatial discretization, are rigorously proved to satisfy a discrete maximum-bound principle and unconditional energy stability. For the coupled system, we construct stabilized ETD schemes in an FFT-based spectral framework, treating stiff linear terms exactly and nonlinear mechanochemical couplings explicitly. A narrow-band implementation further reduces the computational cost by restricting surface calculations to the diffuse membrane region. Numerical experiments confirm the predicted temporal accuracy, maximum-bound preservation, and energy decay for the fixed-membrane OK problem, and demonstrate stable and efficient three-dimensional simulations of protein-driven pattern formation and membrane deformation.

math.NA↗

arXiv2026

RAFT-UP: Robust Alignment for Spatial Transcriptomics with Explicit Control of Spatial Distortion

Spatial transcriptomics (ST) profiles gene expression across a tissue section while preserving the spatial coordinates. Because current ST technologies typically profile two-dimensional tissue slices, integrating and aligning slices from different regions of the same three-dimensional tissue or from samples under different conditions enables analyses that reveal 3D organization and condition-associated spatial patterns. Two major challenges remain. First, interpretable and flexible control over spatial distortion is needed because rigid transformations can be overly restrictive, whereas highly deformable mappings may arbitrarily distort spatial proximity. Second, biologically plausible matching is also needed, especially when the slices overlap partially. Here, we introduce RAFT-UP, a tool for robust ST alignment that provides explicit control over spatial distance preservation through a fused supervised Gromov-Wasserstein (FsGW) optimal transport framework. FsGW combines expression and spatial information, incorporates spot-wise constraints to discourage biologically implausible matches, and enforces a pairwise distance-consistency constraint that prevents mapping two pairs of spots when their spatial distances differ beyond a specified tolerance. We demonstrate that RAFT-UP accurately aligns slices from different regions of the same tissue and slices from different samples. Benchmarking shows that RAFT-UP improves spatial distance preservation while achieving spot label matching accuracy comparable to state-of-the-art methods. Finally, we demonstrate RAFT-UP on two spatially constrained downstream applications, including spatiotemporal mapping of developing mouse midbrain and comparative cross-slice analysis of cell-cell communication. RAFT-UP is available as open-source software.

q-bio.QM↗

arXiv2026

Synchronization of Unbalanced Dynamical Optimal Transport across Multiple Spaces

Many biological systems are observed through heterogeneous modalities, requiring transport models that couple dynamics across spaces while allowing mass variation. To address this challenge, we introduce Unbalanced Synchronized Optimal Transport (UnSyncOT), a novel dynamical framework that synchronizes transport-reaction flows between spaces via either geometric embeddings (Monge type) or Markov kernels (Kantorovich type). For both cases we prove that UnSyncOT can be reduced to a single-space problem: the Monge model becomes a Benamou-Brenier problem with a metric-modified kinetic energy, and the Kantorovich model yields a nonlocal action induced by the synchronization operator, both of which fit within a dissipation-distance formulation. We also analyze the pure transport (Wasserstein) and pure reaction (Fisher-Rao) limits and derive structural properties. For the Kantorovich case we propose an approximate UnSyncOT by introducing a Hellinger-Kantorovich based trapezoidal time discretization of the secondary action for efficient computation. Finally we present staggered-grid discretizations and primal-dual solvers, validate the convergence, stability, and efficiency, and demonstrate coherent dynamics reconstructions across spaces.

math.OC↗

arXiv2025

Debiased Dual-Invariant Defense for Adversarially Robust Person Re-Identification

Person re-identification (ReID) is a fundamental task in many real-world applications such as pedestrian trajectory tracking. However, advanced deep learning-based ReID models are highly susceptible to adversarial attacks, where imperceptible perturbations to pedestrian images can cause entirely incorrect predictions, posing significant security threats. Although numerous adversarial defense strategies have been proposed for classification tasks, their extension to metric learning tasks such as person ReID remains relatively unexplored. Moreover, the several existing defenses for person ReID fail to address the inherent unique challenges of adversarially robust ReID. In this paper, we systematically identify the challenges of adversarial defense in person ReID into two key issues: model bias and composite generalization requirements. To address them, we propose a debiased dual-invariant defense framework composed of two main phases. In the data balancing phase, we mitigate model bias using a diffusion-model-based data resampling strategy that promotes fairness and diversity in training data. In the bi-adversarial self-meta defense phase, we introduce a novel metric adversarial training approach incorporating farthest negative extension softening to overcome the robustness degradation caused by the absence of classifier. Additionally, we introduce an adversarially-enhanced self-meta mechanism to achieve dual-generalization for both unseen identities and unseen attack types. Experiments demonstrate that our method significantly outperforms existing state-of-the-art defenses.

cs.CV↗

arXiv2025

Ohta-Kawasaki Model Reveals Patterns on Multicomponent Vesicles

We present a new mechanochemical modeling framework to explore the shape deformation and pattern formation in multicomponent vesicle membranes. In this framework, the shape of the membrane is described by an elastic bending model, while phase separation of membrane-bound activator proteins is determined by an Ohta-Kawasaki (OK) model. The coupled dynamics consist of an overdamped force-balanced equation for the membrane geometry and an OK-type advection-reaction-diffusion equation on the deformable membrane. We implement efficient spectral methods to simulate these dynamics in both two- and three-dimensions. Numerical experiments show that the model successfully reproduces a wide range of experimentally observed membrane morphologies \cite{baumgart2003imaging}. Taken together, the framework unifies curvature mechanics, microphase separation, and active forcing, providing new insight into membrane-bounded multicomponent vesicle dynamics and a practical platform for studying multicomponent biomembrane morphology.

math-ph↗

arXiv2025

OTMol: Robust Molecular Structure Comparison via Optimal Transport

Root-mean-square deviation (RMSD) is widely used to assess structural similarity in systems ranging from flexible ligand conformers to complex molecular cluster configurations. Despite its wide utility, RMSD calculation is often challenged by inconsistent atom ordering, indistinguishable configurations in molecular clusters, and potential chirality inversion during alignment. These issues highlight the necessity of accurate atom-to-atom correspondence as a prerequisite for meaningful alignment. Traditional approaches often rely on heuristic cost matrices combined with the Hungarian algorithm, yet these methods underutilize the rich intra-molecular structural information and may fail to generalize across chemically diverse systems. In this work, we introduce OTMol, a method that formulates the molecular alignment task as a fused supervised Gromov-Wasserstein (fsGW) optimal transport problem. By leveraging the intrinsic geometric and topological relationships within each molecule, OTMol eliminates the need for manually defined cost functions and enables a principled, data-driven matching strategy. Importantly, OTMol preserves key chemical features such as molecular chirality and bond connectivity consistency. We evaluate OTMol across a wide range of molecular systems, including Adenosine triphosphate, Imatinib, lipids, small peptides, and water clusters, and demonstrate that it consistently achieves low RMSD values while preserving computational efficiency. Importantly, OTMol maintains molecular integrity by enforcing one-to-one mappings between entire molecules, thereby avoiding erroneous many-to-one alignments that often arise in comparing molecular clusters. Our results underscore the utility of optimal transport theory for molecular alignment and offer a generalizable framework applicable to structural comparison tasks in cheminformatics, molecular modeling, and related disciplines.

q-bio.BM↗

arXiv2025

Double Fourier Sphere Methods with Low Rank Approximation for Block Copolymer Systems on Sphere

We introduce spectral methods for the Ohta-Kawasaki (OK) and Nakazawa-Ohta (NO) models on a spherical domain, examining their coarsening dynamics and equilibrium pattern formations. We employed the Double Fourier Sphere (DFS) method for spatial discretization and the second-order Backward Differentiation Formula (BDF2) scheme for time evolution, resulting in an efficient energy-stable scheme to simulate the OK and NO models on the unit sphere. Our numerical experiments reveal various self-assembled patterns, such as single-bubble assemblies in binary systems and double-bubble and mixed-bubble assemblies in ternary systems. These patterns closely resemble experimental biomembrane patterns, demonstrating the effectiveness of the OK model in real-world applications. Additionally, our study explores the relationship between repulsive strength and the number of bubbles in assemblies, confirming the two-thirds law in the OK model. This provides quantitative evidence of how self-assembled patterns depend on system parameters in copolymer systems.

math.NA↗

arXiv2024

Ultraspherical Spectral Method for Block Copolymer Systems on Unit Disk

In this paper, we investigate ultraspherical spectral method for the Ohta-Kawasaki (OK) and Nakazawa-Ohta (NO) models in the disk domain, representing diblock and triblock copolymer systems, respectively. We employ ultraspherical spectral discretization for spatial variables in the disk domain and apply the second-order backward differentiation formula (BDF) method for temporal discretization. To our best knowledge, this is the first study to develop a numerical method for diblock and triblock copolymer systems with long-range interactions in disk domains. We show the energy stability of the numerical method in both semi-discrete and fully-discrete discretizations. In our numerical experiments, we verify the second-order temporal convergence rate and the energy stability of the proposed methods. Our numerical results show that the coarsening dynamics in diblock copolymers lead to bubble assemblies both inside and on the boundary of the disk. Additionally, in the triblock copolymer system, we observe several novel pattern formations, including single and double bubble assemblies in the unit disk. These findings are detailed through extensive numerical experiments.

math.NA↗

arXiv2024

Synchronized Optimal Transport for Joint Modeling of Dynamics Across Multiple Spaces

Optimal transport has been an essential tool for reconstructing dynamics from complex data. With the increasingly available multifaceted data, a system can often be characterized across multiple spaces. Therefore, it is crucial to maintain coherence in the dynamics across these diverse spaces. To address this challenge, we introduce Synchronized Optimal Transport (SyncOT), a novel approach to jointly model dynamics that represent the same system through multiple spaces. With given correspondence between the spaces, SyncOT minimizes the aggregated cost of the dynamics induced across all considered spaces. The problem is discretized into a finite-dimensional convex problem using a staggered grid. Primal-dual algorithm-based approaches are then developed to solve the discretized problem. Various numerical experiments demonstrate the capabilities and properties of SyncOT and validate the effectiveness of the proposed algorithms.

math.OC↗

arXiv2024

Supervised Gromov-Wasserstein Optimal Transport

We introduce the supervised Gromov-Wasserstein (sGW) optimal transport, an extension of Gromov-Wasserstein by incorporating potential infinity patterns in the cost tensor. sGW enables the enforcement of application-induced constraints such as the preservation of pairwise distances by implementing the constraints as an infinity pattern. A numerical solver is proposed for the sGW problem and the effectiveness is demonstrated in various numerical experiments. The high-order constraints in sGW are transferred to constraints on the coupling matrix by solving a minimal vertex cover problem. The transformed problem is solved by the Mirror-C descent iteration coupled with the supervised optimal transport solver. In the numerical experiments, we first validate the proposed framework by applying it to matching synthetic datasets and investigating the impact of the model parameters. Additionally, we successfully apply sGW to real single-cell RNA sequencing data. Through comparisons with other Gromov-Wasserstein variants on real data, we demonstrate that sGW offers the novel utility of controlling distance preservation, leading to the automatic estimation of overlapping portions of datasets, which brings improved stability and flexibility in data-driven applications.

math.OC↗

arXiv2023

Asymptotically Compatible Schemes for Nonlocal Ohta Kawasaki Model

We study the asymptotical compatibility of the Fourier spectral method in multidimensional space for the Nonlocal Ohta-Kawasaka (NOK) model, which is proposed in our previous work. By introducing the Fourier collocation discretization for the spatial variable, we show that the asymptotical compatibility holds in 2D and 3D over a periodic domain. For the temporal discretization, we adopt the second-order backward differentiation formula (BDF) method. We prove that for certain nonlocal kernels, the proposed time discretization schemes inherit the energy dissipation law. In the numerical experiments, we verify the asymptotical compatibility, the second-order temporal convergence rate, and the energy stability of the proposed schemes. More importantly, we discover a novel square lattice pattern when certain nonlocal kernel are applied in the model. In addition, our numerical experiments confirm the existence of an upper bound for the optimal number of bubbles in 2D for some specific nonlocal kernels. Finally, we numerically explore the promotion/demotion effect induced by the nonlocal horizon, which is consistent with the theoretical studies presented in our earlier work.

math.NA↗

arXiv2023

Phase Field Modeling of Dictyostelium Discoideum Chemotaxis

A phase field approach is proposed to model the chemotaxis of Dictyostelium discoideum. In this framework, motion is controlled by active forces as determined by the Meinhardt model of chemical dynamics which is used to simulate directional sensing during chemotaxis. Then, the movement of the cell is achieved by the phase field dynamics, while the reaction-diffusion equations of the Meinhardt model are solved on an evolving cell boundary. This task requires the extension of the usual phase-field formulation to allow for components that are restricted to the membrane. The coupled system is numerically solved by an efficient spectral method under periodic boundary conditions. Numerical experiments show that our model system can successfully mimic the typically observed pseudopodia patterns during chemotaxis.

physics.bio-ph↗

arXiv2022

Bifurcation Analysis Reveals Solution Structures of Phase Field Models

Phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems. Here, we develop a new analytical approach based on bifurcation analysis to explore the mathematical solution structure of phase field models. Revealing such solution structures not only is of great mathematical interest but also may provide guidance to experimentally or computationally uncover new morphological evolution phenomena in materials undergoing electronic and structural phase transitions. To elucidate the idea, we apply this analytical approach to three representative phase field equations: Allen-Cahn equation, Cahn-Hilliard equation, and Allen-Cahn-Ohta-Kawasaki system. The solution structures of these three phase field equations are also verified numerically by the homotopy continuation method.

math.NA↗

arXiv2022

Numerical Approximations of the Allen-Cahn-Ohta-Kawasaki (ACOK) Equation with Modified Physics Informed Neural Networks (PINNs)

The physics informed neural networks (PINNs) has been widely utilized to numerically approximate PDE problems. While PINNs has achieved good results in producing solutions for many partial differential equations, studies have shown that it does not perform well on phase field models. In this paper, we partially address this issue by introducing a modified physics informed neural networks. In particular, they are used to numerically approximate Allen-Cahn-Ohta-Kawasaki (ACOK) equation with a volume constraint.

math.NA↗

arXiv2022

Noise and Edge Based Dual Branch Image Manipulation Detection

Unlike ordinary computer vision tasks that focus more on the semantic content of images, the image manipulation detection task pays more attention to the subtle information of image manipulation. In this paper, the noise image extracted by the improved constrained convolution is used as the input of the model instead of the original image to obtain more subtle traces of manipulation. Meanwhile, the dual-branch network, consisting of a high-resolution branch and a context branch, is used to capture the traces of artifacts as much as possible. In general, most manipulation leaves manipulation artifacts on the manipulation edge. A specially designed manipulation edge detection module is constructed based on the dual-branch network to identify these artifacts better. The correlation between pixels in an image is closely related to their distance. The farther the two pixels are, the weaker the correlation. We add a distance factor to the self-attention module to better describe the correlation between pixels. Experimental results on four publicly available image manipulation datasets demonstrate the effectiveness of our model.

cs.CV↗

arXiv2022

Supervised Optimal Transport

Optimal Transport, a theory for optimal allocation of resources, is widely used in various fields such as astrophysics, machine learning, and imaging science. However, many applications impose elementwise constraints on the transport plan which traditional optimal transport cannot enforce. Here we introduce Supervised Optimal Transport (sOT) that formulates a constrained optimal transport problem where couplings between certain elements are prohibited according to specific applications. sOT is proved to be equivalent to an $l^1$ penalized optimization problem, from which efficient algorithms are designed to solve its entropy regularized formulation. We demonstrate the capability of sOT by comparing it to other variants and extensions of traditional OT in color transfer problem. We also study the barycenter problem in sOT formulation, where we discover and prove a unique reverse and portion selection (control) mechanism. Supervised optimal transport is broadly applicable to applications in which constrained transport plan is involved and the original unit should be preserved by avoiding normalization.

math.OC↗

arXiv2022

Nonlocal Effect on a Generalized Ohta-Kawasaki Model

We propose a nonlocal Ohta-Kawasaki model to study the nonlocal effect on the pattern formation of some binary systems with general long-range interactions. While the nonlocal Ohta-Kawasaki model displays similar bubble patterns as the standard Ohta-Kawasaki model, by performing Fourier analysis, we find that the optimal number of bubbles for the nonlocal model may have an upper bound no matter how large the repulsive strength is. The existence of such an upper bound is characterized by the eigenvalues of the nonlocal kernels. Additionally we explore the conditions under which the nonlocal horizon parameter may promote or demote the bubble splitting, and apply the analysis framework to several case studies for various nonlocal operators.

math.NA↗