arXiv subjects

Shixin Xu

Publications and source records attributed to Shixin Xu.

At least 37 records · Page 2Linked to original sources

arXiv2025

TIME: TabPFN-Integrated Multimodal Engine for Robust Tabular-Image Learning

Tabular-image multimodal learning, which integrates structured tabular data with imaging data, holds great promise for a variety of tasks, especially in medical applications. Yet, two key challenges remain: (1) the lack of a standardized, pretrained representation for tabular data, as is commonly available in vision and language domains; and (2) the difficulty of handling missing values in the tabular modality, which are common in real-world medical datasets. To address these issues, we propose the TabPFN-Integrated Multimodal Engine (TIME), a novel multimodal framework that builds on the recently introduced tabular foundation model, TabPFN. TIME leverages TabPFN as a frozen tabular encoder to generate robust, strong embeddings that are naturally resilient to missing data, and combines them with image features from pretrained vision backbones. We explore a range of fusion strategies and tabular encoders, and evaluate our approach on both natural and medical datasets. Extensive experiments demonstrate that TIME consistently outperforms competitive baselines across both complete and incomplete tabular inputs, underscoring its practical value in real-world multimodal learning scenarios.

cs.CV↗

arXiv2025

Characterization of phospholipid-cholesterol bilayers as self-assembled amphiphile block polymers that contain headgroups

Cholesterol is known to modulate the structure and function of biological membranes. In this study, we use self-consistent field theory (SCFT) to investigate phospholipid/cholesterol bilayer membranes modeled with two types of diblock copolymers. These copolymer-based bilayers serve as biomimetic platforms with applications in areas such as drug delivery. Our simulations identify a minimum free energy configuration characterized by phospholipid tails tilted relative to the membrane normal. The model quantitatively captures the well-known area condensation effect as cholesterol concentration increases, along with membrane thickening and reduced tilt angle. Thermodynamically, we observe a linear dependence between cholesterol's chemical potential and its concentration within the 37-50% range, consistent with experimental results. Additionally, we analyze the effects of block copolymer length and headgroup interactions on bilayer structure. Interactions between phospholipid headgroups and the solvent emerge as the most influential. This work provides a theoretical framework for understanding cholesterol's regulatory role in membrane structure and mechanics.

cond-mat.soft↗

arXiv2025

A thermodynamically consistent phase-field model for mass transport with interfacial reaction and deformation

In this paper, a thermodynamically consistent phase-field model is proposed to describe the mass transport and reaction processes of multiple species in a fluid. A key feature of this model is that reactions between different species occur only at the interface, and may induce deformation of the interface. For the governing equations derived based on the energy variational method, we propose a structure-preserving numerical scheme that satisfies the mass conservation and energy dissipation laws at the discrete level. Furthermore, we carry out a rigorous error analysis of the time-discrete scheme for a simplified case. A series of numerical experiments are conducted to validate the effectiveness of the model as well as the accuracy and stability of the scheme. In particular, we simulate microvessels with straight and bifurcated structures to illustrate the risk of microaneurysm formation.

math.NA↗

arXiv2025

CLEP-GAN: An Innovative Approach to Subject-Independent ECG Reconstruction from PPG Signals

This study addresses the challenge of reconstructing unseen ECG signals from PPG signals, a critical task for non-invasive cardiac monitoring. While numerous public ECG-PPG datasets are available, they lack the diversity seen in image datasets, and data collection processes often introduce noise, complicating ECG reconstruction from PPG even with advanced machine learning models. To tackle these challenges, we first introduce a novel synthetic ECG-PPG data generation technique using an ODE model to enhance training diversity. Next, we develop a novel subject-independent PPG-to-ECG reconstruction model that integrates contrastive learning, adversarial learning, and attention gating, achieving results comparable to or even surpassing existing approaches for unseen ECG reconstruction. Finally, we examine factors such as sex and age that impact reconstruction accuracy, emphasizing the importance of considering demographic diversity during model training and dataset augmentation.

eess.SP↗

arXiv2025

An Imbalanced Learning-based Sampling Method for Physics-informed Neural Networks

This paper introduces Residual-based Smote (RSmote), an innovative local adaptive sampling technique tailored to improve the performance of Physics-Informed Neural Networks (PINNs) through imbalanced learning strategies. Traditional residual-based adaptive sampling methods, while effective in enhancing PINN accuracy, often struggle with efficiency and high memory consumption, particularly in high-dimensional problems. RSmote addresses these challenges by targeting regions with high residuals and employing oversampling techniques from imbalanced learning to refine the sampling process. Our approach is underpinned by a rigorous theoretical analysis that supports the effectiveness of RSmote in managing computational resources more efficiently. Through extensive evaluations, we benchmark RSmote against the state-of-the-art Residual-based Adaptive Distribution (RAD) method across a variety of dimensions and differential equations. The results demonstrate that RSmote not only achieves or exceeds the accuracy of RAD but also significantly reduces memory usage, making it particularly advantageous in high-dimensional scenarios. These contributions position RSmote as a robust and resource-efficient solution for solving complex partial differential equations, especially when computational constraints are a critical consideration.

cs.LG↗

arXiv2024

Multidomain Model for Optic Nerve Potassium Clearance: Roles of Glial Cells and Perivascular Spaces

The accumulation of potassium in the extracellular space surrounding nerve cells is a fundamental aspect of biophysics that has garnered significant attention in recent research. This phenomenon holds implications for various neurological conditions, including spreading depression, migraine, certain types of epilepsy, and potentially, learning processes. A quantitative analysis is essential for understanding the dynamics of potassium clearance following a series of action potentials. This clearance process involves multiple structures along the nerve, including glia, the extracellular space, axons, and the perivascular space, necessitating a spatially distributed systems approach akin to the cable equations of nerve physiology. In this study, we propose a multi-domain model for the optic nerve to investigate potassium accumulation and clearance dynamics. The model accounts for the convection, diffusion, and electrical migration of fluid and ions, revealing the significant roles of glia and the perivascular space in potassium buffering. Specifically, our findings suggest that potassium clearance primarily occurs through convective flow within the syncytia of glia, driven by osmotic pressure differences. Additionally, the perivascular space serves as a crucial pathway for potassium buffering and fluid circulation, further contributing to the overall clearance process. Importantly, our model's adaptability allows for its application to diverse structures with distinct channel and transporter distributions across the six compartments, extending its utility beyond the optic nerve.

physics.bio-ph↗

arXiv2024

Improving GBDT Performance on Imbalanced Datasets: An Empirical Study of Class-Balanced Loss Functions

Class imbalance remains a significant challenge in machine learning, particularly for tabular data classification tasks. While Gradient Boosting Decision Trees (GBDT) models have proven highly effective for such tasks, their performance can be compromised when dealing with imbalanced datasets. This paper presents the first comprehensive study on adapting class-balanced loss functions to three GBDT algorithms across various tabular classification tasks, including binary, multi-class, and multi-label classification. We conduct extensive experiments on multiple datasets to evaluate the impact of class-balanced losses on different GBDT models, establishing a valuable benchmark. Our results demonstrate the potential of class-balanced loss functions to enhance GBDT performance on imbalanced datasets, offering a robust approach for practitioners facing class imbalance challenges in real-world applications. Additionally, we introduce a Python package that facilitates the integration of class-balanced loss functions into GBDT workflows, making these advanced techniques accessible to a wider audience.

cs.LG↗

arXiv2024

Robust-GBDT: GBDT with Nonconvex Loss for Tabular Classification in the Presence of Label Noise and Class Imbalance

Dealing with label noise in tabular classification tasks poses a persistent challenge in machine learning. While robust boosting methods have shown promise in binary classification, their effectiveness in complex, multi-class scenarios is often limited. Additionally, issues like imbalanced datasets, missing values, and computational inefficiencies further complicate their practical utility. This study introduces Robust-GBDT, a groundbreaking approach that combines the power of Gradient Boosted Decision Trees (GBDT) with the resilience of nonconvex loss functions against label noise. By leveraging local convexity within specific regions, Robust-GBDT demonstrates unprecedented robustness, challenging conventional wisdom. Through seamless integration of advanced GBDT with a novel Robust Focal Loss tailored for class imbalance, Robust-GBDT significantly enhances generalization capabilities, particularly in noisy and imbalanced datasets. Notably, its user-friendly design facilitates integration with existing open-source code, enhancing computational efficiency and scalability. Extensive experiments validate Robust-GBDT's superiority over other noise-robust methods, establishing a new standard for accurate classification amidst label noise. This research heralds a paradigm shift in machine learning, paving the way for a new era of robust and precise classification across diverse real-world applications.

cs.LG↗

arXiv2024

NCART: Neural Classification and Regression Tree for Tabular Data

Deep learning models have become popular in the analysis of tabular data, as they address the limitations of decision trees and enable valuable applications like semi-supervised learning, online learning, and transfer learning. However, these deep-learning approaches often encounter a trade-off. On one hand, they can be computationally expensive when dealing with large-scale or high-dimensional datasets. On the other hand, they may lack interpretability and may not be suitable for small-scale datasets. In this study, we propose a novel interpretable neural network called Neural Classification and Regression Tree (NCART) to overcome these challenges. NCART is a modified version of Residual Networks that replaces fully-connected layers with multiple differentiable oblivious decision trees. By integrating decision trees into the architecture, NCART maintains its interpretability while benefiting from the end-to-end capabilities of neural networks. The simplicity of the NCART architecture makes it well-suited for datasets of varying sizes and reduces computational costs compared to state-of-the-art deep learning models. Extensive numerical experiments demonstrate the superior performance of NCART compared to existing deep learning models, establishing it as a strong competitor to tree-based models.

cs.LG↗

arXiv2024

A multi-domain model for microcirculation in optic nerve: blood flow and oxygen transport

Microcirculation of blood and oxygen transport play important roles in biological function of optic nerve and are directly affected by damages or pathologies. This work develops a multi-domain model for optic nerve, that includes important biological structures and various physical mechanisms in blood flow and oxygen delivery. The two sets of vasculature network are treated as five domains in the same geometric region, with various exchanges among them (such as Darcy's law for fluid flow) and with the tissue domain (such as water leak, diffusion). The numerical results of the coupled model for a uniform case of vasculature distribution show mechanisms and scales consistent with literature and intuition. The effects of various important model parameters (relevant to pathological conditions) are investigated to provide insights into the possible implications. The vasculature distribution (resting volume fractions here) has significant impacts on the blood circulation and could lead to insufficient blood supply in certain local region and in turn affect the oxygen delivery. The water leak across the capillary wall will have nontrivial effects after the leak coefficients pass a threshold. The periodic arterial pressure conditions lead to expected periodic patterns and stable spatial profiles, and the uniform case is almost the averaged version of periodic case. The effects of viscosity, the stiffness of blood vessel wall, oxygen demand, etc. have also been analyzed. The framework can be extended to include ionic transport or to study the retina when more biological structural information is available.

physics.bio-ph↗

arXiv2024

Local Discontinuous Galerkin Methods for Solving Convection-Diffusion and Cahn-Hilliard Equations on Surfaces

Local discontinuous Galerkin methods are developed for solving second order and fourth order time-dependent partial differential equations defined on static 2D manifolds. These schemes are second-order accurate with surfaces triangulized by planar triangles and careful design of numerical fluxes. The schemes are proven to be energy stable. Various numerical experiments are provided to validate the new schemes.

math.NA↗

arXiv2023

Coupled Chemical Reactions: Effects of Electric Field, Diffusion and Boundary Control

Chemical reactions involve the movement of charges, and this work presents a mathematical model for describing chemical reactions in electrolytes. The model is developed using an energy variational method that aligns with classical thermodynamics principles. It encompasses both electrostatics and chemical reactions within consistently defined energetic and dissipative functionals. Furthermore, the energy variation method is extended to account for open systems that involve the input and output of charge and mass. Such open systems have the capability to convert one form of input energy into another form of output energy. In particular, a two-domain model is developed to study a reaction system with self-regulation and internal switching, which plays a vital role in the electron transport chain of mitochondria responsible for ATP generation crucial process for sustaining life. Simulations are conducted to explore the influence of electric potential on reaction rates and switching dynamics within the two-domain system. It shows that the electric potential inhibits the oxidation reaction while accelerating the reduction reaction.

physics.chem-ph↗

arXiv2023

Micro-Macro Modeling of Polymeric Fluids and Shear-Induced Microscopic Behaviors

This article delves into the micro-macro modeling of polymeric fluids, considering various microscopic potential energies, including the classical Hookean potential, as well as newly proposed modified Morse and Elastic-plastic potentials. These proposed potentials encompass microscopic-scale bond-breaking processes. The development of a thermodynamically consistent micro-macro model is revisited, employing the energy variational method. To validate the model's predictions, we conduct numerical simulations utilizing a deterministic particle-FEM method. Our numerical findings shed light on the distinct behaviors exhibited by polymer chains at the micro-scale in comparison to the macro-scale velocity and induced shear stresses of fluids under shear flow. Notably, we observe that polymer elongation, rotation, and bond breaking contribute to the zero polymer-induced stress in the micro-macro model when employing Morse and Elastic-plastic potentials. Furthermore, at high shear rates, polymer rotation is found to induce shear-thinning behavior in the model employing the classical Hookean potential.

cond-mat.soft↗

arXiv2023

A phase field model for droplets suspended in viscous liquids under the influence of electric fields

In this paper, we propose a Poisson-Nernst-Planck-Navier-Stokes-Cahn-Hillard (PNP-NS-CH)model for an electrically charged droplet suspended in a viscous fluid subjected to an external electric field. Our model incorporates spatial variations of electric permittivity and diffusion constants, as well as interfacial capacitance. Based on a time scale analysis, we derive two approximations of the original model, namely a dynamic model for the net charge and a leaky-dielectric model. For the leaky-dielectric model, we conduct a detailed asymptotic analysis to demonstrate the convergence of the diffusive-interface leaky-dielectric model to the sharp interface model as the interface thickness approaches zero. Numerical computations are performed to validate the asymptotic analysis and demonstrate the model's effectiveness in handling topology changes, such as electrocoalescence. Our numerical results of these two approximation models reveal that the polarization force, which is induced by the spatial variation of electric permittivity in the direction perpendicular to the external electric field, consistently dominates the Lorentz force, which arises from the net charge. The equilibrium shape of droplets is determined by the interplay between these two forces along the direction of the electric field. Furthermore, in the presence of the interfacial capacitance, a local variation of effective permittivity leads to an accumulation of counter-ions near the interface, resulting in a reduction in droplet deformation. Our numerical solutions also confirm that the leaky dielectric model serves as a reasonable approximation of the original PNP-NS-CH model when the electric relaxation time is sufficiently short. The Lorentz force and droplet deformation both decrease when the diffusion of net charge is significant.

physics.flu-dyn↗

arXiv2023

TRBoost: A Generic Gradient Boosting Machine based on Trust-region Method

Gradient Boosting Machines (GBMs) have demonstrated remarkable success in solving diverse problems by utilizing Taylor expansions in functional space. However, achieving a balance between performance and generality has posed a challenge for GBMs. In particular, gradient descent-based GBMs employ the first-order Taylor expansion to ensure applicability to all loss functions, while Newton's method-based GBMs use positive Hessian information to achieve superior performance at the expense of generality. To address this issue, this study proposes a new generic Gradient Boosting Machine called Trust-region Boosting (TRBoost). In each iteration, TRBoost uses a constrained quadratic model to approximate the objective and applies the Trust-region algorithm to solve it and obtain a new learner. Unlike Newton's method-based GBMs, TRBoost does not require the Hessian to be positive definite, thereby allowing it to be applied to arbitrary loss functions while still maintaining competitive performance similar to second-order algorithms. The convergence analysis and numerical experiments conducted in this study confirm that TRBoost is as general as first-order GBMs and yields competitive results compared to second-order GBMs. Overall, TRBoost is a promising approach that balances performance and generality, making it a valuable addition to the toolkit of machine learning practitioners.

cs.LG↗

arXiv2022

Mathematical Model for Chemical Reactions in Electrolyte Applied to Cytochrome $c$ Oxidase: an Electro-osmotic Approach

A mathematical model for chemical reactions in electrolytes is developed using an Energy variational method consistent with classical thermodynamics. Electrostatics and chemical reactions are included in properly defined energetic and dissipative functionals. The energy variation method is generalized to deal with open systems with inputs of charge, mass, and energy. The open systems can transform input energy of one type into output energy of another type. The generalized method is used to analyze the conversion of electrical current into proton flow by cytochrome c oxidase, an important enzyme in mitochondria that helps generate the 'energetic currency of life' ATP. The structure of the oxidase guides flows of current and mass that interact according to the energetic and dissipative functionals of the generalized theory. Kirchhoff's current law provides important coupling when the enzyme is in its natural setting in the mitochondrial membrane. The natural function of the enzyme is the result. Electron flows are converted into proton flows and gradients.

physics.chem-ph↗

arXiv2022

Thermodynamically Consistent Diffuse Interface Model for Cell Adhesion and Aggregation

A thermodynamically consistent phase-field model is introduced for simulating multicellular deformation, and aggregation under flow conditions. In particular, a Lennard-Jones type potential is proposed under the phase-field framework for cell-cell, cell-wall interactions. A second-order accurate in both space and time $C^0$ finite element method is proposed to solve the model governing equations. Various numerical tests confirm the convergence, energy stability, and nonlinear mechanical properties of cells of the proposed scheme. Vesicles with different adhesion are also used to explain the pathological risk for patients with sickle cell disease.

math.NA↗

arXiv2022

A Bubble Model for the Gating of Kv Channels

Voltage-gated Kv channels play fundamental roles in many biological processes, such as the generation of the action potential. The gating mechanism of Kv channels is characterized experimentally by single-channel recordings and ensemble properties of the channel currents. In this work, we propose a bubble model coupled with a Poisson-Nernst-Planck (PNP) system to capture the key characteristics, particularly the delay in the opening of channels. The coupled PNP system is solved numerically by a finite-difference method and the solution is compared with an analytical approximation. We hypothesize that the stochastic behaviour of the gating phenomenon is due to randomness of the bubble and channel sizes. The predicted ensemble average of the currents under various applied voltages across the channels is consistent with experimental observations, and the Cole-Moore delay is captured by varying the holding potential.

physics.bio-ph↗