arXiv subjects

Yunxin Zhang

Publications and source records attributed to Yunxin Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Gaussian-Restricted Barycenters for KL-Unbalanced Optimal Transport: Variational Theory and Fixed-Point Convergence

We study Gaussian-restricted barycenters for quadratic two-sided Kullback--Leibler unbalanced optimal transport with independent marginal penalties and no coupling entropy. Exact profiling of the barycenter mass reduces the problem to a smooth Gaussian shape functional with endogenous Gibbs weights. We establish global attainment, derive the stationary moment equations, and construct a reverse-KL majorization--minimization (MM) iteration whose full sequence converges from every nondegenerate Gaussian initialization to a stationary fixed point. The diagonal second variation induces a parallel-sum tensor coupling the Bures--Wasserstein and Fisher--Rao metrics; its finite-mass extension admits a radial cone representation. Under common penalty scaling, global minimizers converge to a Gaussian Wasserstein barycenter with effective weights; for sufficiently large penalties, the minimizer is unique and admits a first-order analytic expansion. In the small-penalty regime, the distance of every global minimizer to the compact maximizer set of a weighted Chernoff affinity functional vanishes with respect to the mean--covariance parameter distance. Numerical experiments illustrate MM descent, local contraction, and the two penalty limits.

math.OC↗

arXiv2026

High-Dimensional Spectral Limits for Gaussian KL-Unbalanced Optimal Transport

We study high-dimensional random-matrix limits of Gaussian Kullback--Leibler unbalanced optimal transport (KL-UOT). Under equal marginal penalties, the covariance action admits an exact log-determinant representation in terms of a nonlinear ridge product, together with a positive-semidefinite extension that remains finite at arbitrary aspect ratios. For independent real Wishart samples, strong asymptotic freeness gives the limiting free multiplicative convolution and almost-sure Hausdorff convergence of the ridge-product spectrum; independent Haar orientations yield the corresponding first-order limit for deformed populations. In the symmetric nonsingular identity-Wishart model, we derive an explicit $η$-transform and a low-degree algebraic equation that select the physical branch and determine the support interval, square-root edges, and extreme-eigenvalue limits. We further obtain all-aspect one-sample Marchenko--Pastur limits under finite fourth moments, real-Gaussian Bai--Silverstein fluctuations for $c<1$, and a joint random-matrix/penalty limit showing that sample-covariance noise produces the critical scale $τ_p\asymp p$.

math.PR↗

arXiv2026

General Divergence Regularized Optimal Transport: Sample Complexity and Central Limit Theorems

We study empirical divergence-regularized optimal transport on arbitrary Polish spaces. For bounded continuous costs and dual-regular conjugates $ψ\in C^1(\mathbb R)$, we establish a dimension-free $n^{-1/2}$ bound for the empirical transport value using dual interpolation, Hoeffding projection, and bounded-difference arguments. For the asymptotic theory, we isolate the population identifiability condition needed for stability and give sufficient conditions for population uniqueness. In particular, active-set identifiability implies uniqueness of the canonical population potentials, and connectedness of either population support is sufficient. This condition requires neither compactness nor Euclidean structure and covers quadratic regularization, whose conjugate is $C^1$ but not $C^2$. We also give finite-support and large-regularization criteria. Under a bounded Lipschitz cost, the empirical potentials are stable, the transport value is asymptotically linear, and one- and two-sample central limit theorems hold with population centering. This includes noncompact and infinite-dimensional Polish state spaces.

math.ST↗

arXiv2026

Minkowski-Type Wasserstein Metrics and Barycenters for Location-Scale Mixtures with Application to Domain Adaptation

Discrete optimal transport (OT) typically relies on pointwise matching between empirical measures, incurring computational costs that scale at least quadratically with the sample size. To circumvent this limitation, we introduce a mathematical framework for OT between finite location-scale mixture models. By defining a specific function class grounded in generalized Minkowski inequalities and characterizing OT maps between multivariate location-scale families, we extend Wasserstein-type metrics and barycenters to these mixture models under the assumption of identifiability. Furthermore, we prove that restricting joint couplings to a specific mixture structure reduces the continuous multimarginal OT problem to a discrete transport problem over mixture components. Computing transport plans between these components rather than individual samples reduces the computational complexity to linear scaling with respect to the sample size. Empirical evaluations on the VisDA-C benchmark confirm that this strategy achieves competitive accuracy compared to existing empirical OT approaches, while substantially reducing the computational cost and memory footprint.

math.OC↗

arXiv2026

Optimal transition in underdamped systems with memory

Optimal finite-time control is essential for energy-efficient operation of nanoscale devices. While existing work has largely focused on transitions between equilibrium states in overdamped systems, many settings of practical interest -- including nanomechanical resonators, biomolecular conformational dynamics, and quantum Brownian motion -- are governed by underdamped dynamics where both particle inertia and frequency-dependent friction (memory) play a non-negligible role. In this study, we analytically and computationally investigate optimal transitions between nonequilibrium steady states (NESS) for an underdamped particle in a moving harmonic trap with general memory kernels. We find that inertia qualitatively alters optimal control in the presence of memory. Compared to the overdamped case, underdamped dynamics break the time-reversal symmetry, making the forward and backward optimal protocols fundamentally distinct. Across the memory-kernel types examined, the asymmetry, rather than the detailed form of the kernel, governs the structure of the optimal strategy. These results offer a unified framework for optimal control in underdamped systems with memory.

physics.bio-ph↗

arXiv2026

Two-Sample Inference for Gaussian-Smoothed Wasserstein Costs with Finite Moments

Gaussian smoothing has emerged as an effective technique for reducing the sample complexity of optimal transport. In this paper, we study the two-sample plug-in estimator of the Gaussian-smoothed Wasserstein cost $T_p^{(σ)}(μ,ν)=W_p(μ*γ_σ,ν*γ_σ)^p$ on $\R^d$. For fixed smoothing and finite polynomial moments $M_{q_μ}(μ)<\infty$, $M_{q_ν}(ν)<\infty$, with $q_μ,q_ν>p$, we establish upper bounds in probability of order $ρ_{q_μ,p,d}(m)+ρ_{q_ν,p,d}(n)$. Here $ρ_{q,p,d}(N)=N^{-(q-p)/(q+d)}$ for $p d+2p$. This order also holds in expectation under $q_μ,q_ν\ge2p$. When the smoothed population distance is positive, the cost bound yields this rate for the distance itself. For $p>1$ and $q_μ,q_ν>d+2p$, we also derive a first-order expansion, a separated two-sample central limit theorem, and a sample-splitting variance estimator.

math.ST↗

arXiv2026

Asymptotics of Protein Number Distribution in Stochastic Gene Expression Models under Burst Approximation

The burst approximation is a widely used technique to simplify stochastic gene expression models. However, the dynamics and analytical properties of the protein number distribution in gene expression models under the burst approximation are barely studied. In this study, we propose and systematically analyze surrogate models with multiple gene states and arbitrary burst size distributions. An analytical time-dependent solution to the chemical master equation is derived and then exploited in two directions. Theoretically, several fine properties of the protein number distribution are established using functional analysis. For geometrically distributed burst sizes, the distribution is dominated by a scaled negative binomial distribution, and is light-tailed in certain parameter regimes. Computationally, we develop efficient algorithms in three settings, enabling fast calculation of the protein number distribution. Furthermore, the approximation error relative to full gene expression models is estimated in terms of low-order moments of the distribution, thereby clarifying the validity of the burst approximation.

physics.bio-ph↗

arXiv2026

Closed Forms for Gaussian Kullback--Leibler Unbalanced Optimal Transport without Coupling Entropy

We obtain an explicit solution for the static Kullback--Leibler (KL) unbalanced optimal transport problem between finite non-degenerate Gaussian measures with quadratic cost, two independent positive marginal relaxation parameters, and no entropy penalty on the coupling. The minimizer is a scaled Wasserstein coupling between two adjusted Gaussian marginals and is supported on an affine graph; in entropic Gaussian unbalanced transport, by contrast, the optimal plan is non-degenerate on the product space. The covariance map is the unique positive definite solution of a Riccati equation and admits a principal-square-root representation. Compared with the known equal-penalty Gaussian Hellinger--Kantorovich endpoint, the result treats the asymmetric two-sided Kullback--Leibler relaxation and gives the modified marginals, joint minimizer, value, and a direct quadratic KL-dual certificate. The large-relaxation limit recovers the Gaussian Wasserstein cost for equal masses.

math.OC↗

arXiv2026

Bures Geodesics and Restricted Barycenters for Kronecker Positive Definite Matrices

We study the extrinsic Bures--Wasserstein geometry of the determinant-normalized Kronecker model $\mcK_n=\{V\ot U:U,V\in\Sp^n,\ \det U=1\}\subset\Sp^{n^2}$, asking when the ambient Bures geodesic between two Kronecker positive definite matrices can remain in this lower-dimensional model. Local membership near an endpoint is shown to be equivalent to membership of the whole segment, and this happens exactly in the one-factor cases: either $U_1=U_0$ or $V_1$ is a positive scalar multiple of $V_0$. Consequently, any endpoint pair not confined to these one-factor alternatives leaves the model immediately. The criterion is expressed by a partial-trace residual. In fixed commuting charts it becomes an equivalent rank-one square-root profile and yields computable departure diagnostics. We also obtain exact formulas for two restricted barycenter problems: fixed commuting-coordinate slices, solved by Perron singular vectors, and one-factor subfamilies, reduced to standard Bures--Wasserstein barycenters on $\Sp^n$.

math.AG↗

arXiv2026

Approximation Error of the Burst Approximation for a Stochastic Gene Expression Model

Stochastic modeling of gene expression is a classic problem in theoretical biophysics, and the burst approximation is widely used to simplify gene expression models formulated via the chemical master equation. However, the approximation error has been investigated only for the simplest case. This article proposes and analyzes a general stochastic gene expression model with an arbitrary number of gene states, and quantifies the error introduced by the burst approximation. Using the standard binomial moment method, we derive recurrence relations for binomial moments in steady state. We develop an algorithm to numerically compute binomial moments in a hierarchical manner. In particular, explicit expressions for low-order moments are presented. Compared with surrogate models under the burst approximation, we conclude that the first-order moment of protein counts is preserved, whereas discrepancies generally arise in higher-order moments. By estimating the difference between two second-order moments using functional analysis, we evaluate the validity of the burst approximation.

physics.bio-ph↗

arXiv2025

Stochastic Kinetics of mRNA Molecules in a General Transcription Model

Stochastic modeling of transcription is a classic yet long-standing problem in theoretical biophysics. The lack of unified results and a computationally efficient approach for a general, fine-grained transcription model has confined relevant research to some over-simplified special cases like the Telegraph model. This article establishes a general, unified and computationally efficient framework for studying stochastic transcription kinetics. We consider a chemical reaction model of transcription and construct the time-dependent solution to the corresponding chemical master equation. A well-known matrix-form expression for steady-state binomial moments is recovered by calculating the temporal limit of the time-dependent dynamics. Two novel inequalities for binomial moments and the probability mass function are derived using techniques from functional analysis. It follows that the distribution of mRNA counts is upper-bounded by a constant multiple of Poisson distribution, thus mathematically proving the main statement of the Heavy-Tailed Law. Additionally, the standard binomial moment method is analyzed from a numerical perspective, where truncation error is estimated using our inequalities. Compared with some widely-used numerical methods, a key advantage of this result is the significantly lower computational complexity.

physics.bio-ph↗

arXiv2025

Optimal Transport and Wasserstein Barycenter for Radially Contoured Distributions

The optimal transport and Wasserstein barycenter of Gaussian distributions have been solved. In literature, the closed form formulas of the Monge map, the Wasserstein distance and the Wasserstein barycenter have been given. Moreover, when Gaussian distributions extend more generally to elliptically contoured distributions, similar results also hold true. In this case, Gaussian distributions are regarded as elliptically contoured distribution with generator function $e^{-x/2}$. However, there are few results about optimal transport for elliptically contoured distributions with different generator functions. In this paper, we degenerate elliptically contoured distributions to radially contoured distributions and study their optimal transport and prove their Wasserstein barycenter is still radially contoured. For general elliptically contoured distributions, we give two numerical counterexamples to show that the Wasserstein barycenter of elliptically contoured distributions does not have to be elliptically contoured.

math.OC↗

arXiv2025

A Relaxed Wasserstein Distance Formulation for Mixtures of Radially Contoured Distributions

Recently, a Wasserstein-type distance for Gaussian mixture models has been proposed. However, that framework can only be generalized to identifiable mixtures of general elliptically contoured distributions whose components come from the same family and satisfy marginal consistency. In this paper, we propose a simple relaxed Wasserstein distance for identifiable mixtures of radially contoured distributions whose components can come from different families. We show some properties of this distance and that its definition does not require marginal consistency. We apply this distance in color transfer tasks and compare its performance with the Wasserstein-type distance for Gaussian mixture models in an experiment. The error of our method is more stable and the color distribution of our output image is more desirable.

math.OC↗

arXiv2024

Factors influencing the stability of the motor-clutch model on compliant substrates under external load

Cellular migration is crucial for biological processes including embryonic development, immune response, and wound healing. The myosin-clutch model is a framework that describes how cells control migration through the interactions between myosin, the clutch mechanism, and the substrate. This model is related to how cells regulate adhesion, generate traction forces, and move on compliant substrates. In this study, we present a five-dimensional nonlinear autonomous system to investigate the influences of myosin, clutches, substrate, and external load on the system's stability. Moreover, we analyze the effects of various parameters on fixed points and explore the frequency and amplitude of the limit cycle associated with oscillations. We discovered that the system demonstrates oscillatory behavior when the velocity of the myosin motor is relatively low, or when the ratio of the motor attachment rate to motor detachment rate is relatively high. The external load shares a fraction of the force exerted by myosin motors, thereby diminishing the force endured by the clutches. Within a specific range, an increase in external load not only diminishes and eventually eliminates the region lacking fixed points but also decelerates clutch detachment, enhancing clutch protein adherence.

physics.bio-ph↗

arXiv2023

Cooperation of myosin II in muscle contraction through nonlinear elasticity

Myosin II plays a pivotal role in muscle contraction by generating force through the cooperative action of multiple motors on actin filaments. In this study, we integrate the nonlinear elasticity of the neck linker in individual myosin II and comprehensively investigate the evolution of cooperativity and dynamics at {\it microstate} and {\it mesostate} levels using a combined model of single and multiple motors. We find that a substantial proportion of actin-bound motors reside in the {\it mid-} and {\it post-power stroke} states, and our nonlinear model reveals their increased capacity for load sharing. Additionally, we systematically explore the impact of mechanical load and ATP concentration on myosin II motors. Notably, we observe that the average net distance of actin undergoes a transition from a weak load-sensitive regime at low ATP concentrations to a load-sensitive regime at higher ATP concentrations. Furthermore, increasing the load or raising the ATP concentration to saturation can enhance the efficiency and output power of myosin filament. Moreover, the efficiency of the myosin filament increases with the power stroke strength, reaching a maximum at a specific range, and subsequently declining beyond that threshold. Finally, we explore the mean run time/length and mean existence probability of myosin filament, shedding light on its overall behavior.

physics.bio-ph↗

arXiv2022

Existence and uniqueness of solution of the differential equation describing the TASEP-LK coupled transport process

In this paper, the existence and uniqueness of solution of a specific differential equation is studied. This equation originates from the description of a coupled process by totally asymmetric simple exclusion process (TASEP) and Langmuir kinetics (LK). In the fields of physics and biology, the properties of the TASEP-LK coupled process have been extensively studied by Monte Carlo simulations and numerical calculations, as well as detailed experiments. However, so far, no rigorous mathematical analysis has been given to the corresponding differential equations, especially their existence and uniqueness of solution. In this paper, using the upper and lower solution method, the existence of solution of the steady state equation is obtained. Then using a generalized maximum principle, we show that the solution constructed from the upper and lower solution method is actually the unique solution in Câˆž space. Moreover, the existence and uniqueness of solution of the time dependent differential equation are also obtained in one specific space X\b{eta}. Our results imply that the previous results obtained by numerical calculations and Monte Carlo simulations are theoretically correct, especially the most important phase diagram of particle density along the travel track under different model parameters. The study in this paper provides theoretical foundations for the analysis of TASEP-LK coupled process. At the same time, the methods used in this paper may be instructive for studies about the more general cases of the TASEP-LK process, such as the one with multiple travel tracks or the one with multiple particle species.

math.AP↗

arXiv2022

Existence and uniqueness of solution of the differential equation describing the TASEP-LK coupled transport process

We study the existence and uniqueness of solution of a evolutionary partial differential equation originating from the continuum limit of a coupled process of totally asymmetric simple exclusion process (TASEP) and Langmuir kinetics (LK). In the fields of physics and biology, the TASEP-LK coupled process has been extensively studied by Monte Carlo simulations, numerical computations, and detailed experiments. However, no rigorous mathematical analysis so far has been given for the corresponding differential equations, especially the existence and uniqueness of their solutions. In this paper, we prove the existence of the $C^\infty[0,1]$ steady-state solution by the method of upper and lower solution, and the uniqueness in both $W^{1,2}(0,1)$ and $L^\infty(0,1)$ by a generalized maximum principle. We further prove the global existence and uniqueness of the time-dependent solution in $C([0,1]\times [0,+\infty))\cap C^{2,1}([0,1]\times (0,+\infty))$, which, for any continuous initial value, converges to the steady-state solution in $C[0,1]$ (global attractivity). Our results support the numerical calculations and Monte Carlo simulations, and provide theoretical foundations for the TASEP-LK coupled process, especially the most important phase diagram of particle density along the travel track under different model parameters, which is difficult because the boundary layers (at one or both boundaries) and domain wall (separating high and low particle densities) may appear as the length of the travel track tends to infinity. The methods used in this paper may be instructive for studies of the more general cases of the TASEP-LK process, such as the one with multiple travel tracks and/or multiple particle species.

math.AP↗

arXiv2022

Dual-domain Attention-based Deep Network for Sparse-view CT Artifact Reduction

Due to the wide applications of X-ray computed tomography (CT) in medical imaging activities, radiation exposure has become a major concern for public health. Sparse-view CT is a promising approach to reduce the radiation dose by down-sampling the total number of acquired projections. However, the CT images reconstructed by this sparse-view imaging approach suffer from severe streaking artifacts and structural information loss. In this work, an end-to-end dual-domain attention-based deep network (DDANet) is proposed to solve such an ill-posed CT image reconstruction problem. The image-domain CT image and the projection-domain sinogram are put into the two parallel sub-networks of the DDANet to independently extract the distinct high-level feature maps. In addition, a specified attention module is introduced to fuse the aforementioned dual-domain feature maps to allow complementary optimizations of removing the streaking artifacts and mitigating the loss of structure. Numerical simulations, anthropomorphic thorax phantom and in vivo pre-clinical experiments are conducted to verify the sparse-view CT imaging performance of the DDANet. Results demonstrate that this newly developed approach is able to robustly remove the streaking artifacts while maintaining the fine structures. As a result, the DDANet provides a promising solution in achieving high quality sparse-view CT imaging.

physics.med-ph↗