Jinqiao Duan
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View article: A clinical case report on transcranial low-intensity focused ultrasound neuromodulation for central post-stroke pain
A clinical case report on transcranial low-intensity focused ultrasound neuromodulation for central post-stroke pain Open
Central post-stroke pain (CPSP) manifests as persistent or intermittent pain following cerebral infarction or hemorrhage and is described as “one of the most agonizing, disabling, and refractory pain syndromes.” Its treatment represents a …
View article: Artificial intelligence as a surrogate brain: Bridging neural dynamical models and data
Artificial intelligence as a surrogate brain: Bridging neural dynamical models and data Open
Recent breakthroughs in artificial intelligence (AI) are reshaping the way we construct computational counterparts of the brain, giving rise to a new class of “surrogate brains”. In contrast to conventional hypothesis-driven biophysical mo…
View article: Artificial intelligence as a surrogate brain: Bridging neural dynamical models and data
Artificial intelligence as a surrogate brain: Bridging neural dynamical models and data Open
Recent breakthroughs in artificial intelligence (AI) are reshaping the way we construct computational counterparts of the brain, giving rise to a new class of ``surrogate brains''. In contrast to conventional hypothesis-driven biophysical …
View article: Passive wake flow control of vertical axis wind turbines in array configurations
Passive wake flow control of vertical axis wind turbines in array configurations Open
This study introduces a passive wake control strategy for vertical axis wind turbine (VAWT) arrays using arc-shaped deflectors. Unlike prior works focusing solely on layout or blade optimization, this research systematically explores the e…
View article: Influence of extreme events modeled by Lévy flight on Atlantic meridional overturning circulation stability
Influence of extreme events modeled by Lévy flight on Atlantic meridional overturning circulation stability Open
View article: Adaptive control for multi-scale stochastic dynamical systems with stochastic next generation reservoir computing
Adaptive control for multi-scale stochastic dynamical systems with stochastic next generation reservoir computing Open
The rapid advancement of neuroscience and machine learning has established data-driven stochastic dynamical system modeling as a powerful tool for understanding and controlling high-dimensional, spatio-temporal processes. We introduce the …
View article: The stochastic Hamilton-Jacobi-Bellman equation on Jacobi structures
The stochastic Hamilton-Jacobi-Bellman equation on Jacobi structures Open
Jacobi structures are known to generalize Poisson structures, encompassing symplectic, cosymplectic, and Lie-Poisson manifolds. Notably, other intriguing geometric structures -- such as contact and locally conformal symplectic manifolds --…
View article: Action functional as an early warning indicator in the space of probability measures via Schrödinger bridge
Action functional as an early warning indicator in the space of probability measures via Schrödinger bridge Open
Critical transitions and tipping phenomena between two meta‐stable states in stochastic dynamical systems are a scientific issue. In this work, we expand the methodology of identifying the most probable transition pathway between two meta‐…
View article: Homogenization and corrector results for the stochastic non-homogeneous incompressible Navier-Stokes equations
Homogenization and corrector results for the stochastic non-homogeneous incompressible Navier-Stokes equations Open
In this paper we are concerned with the homogenization property of stochastic non-homogeneous incompressible Navier-Stokes equations with rapid oscillation in a smooth bounded domain of $\mathbb{R}^d$, $d=2,3$, and driven by multiplicative…
View article: Influence of Extreme Events Modeled by Lévy Flight on Atlantic Meridional Overturning Circulation Stability
Influence of Extreme Events Modeled by Lévy Flight on Atlantic Meridional Overturning Circulation Stability Open
View article: A new maximal regularity for parabolic equations and an application
A new maximal regularity for parabolic equations and an application Open
We introduce the Lebesgue--Hölder--Dini and Lebesgue--Hölder spaces $L^p(\mathbb{R};{\mathcal C}_{\vartheta,ς}^{α,ρ}({\mathbb R}^n))$ ($\vartheta\in \{l,b\}, \, ς\in \{d,s,c,w\}$, $p\in (1,+\infty]$ and $α\in [0,1)$), and then use a vector…
View article: Numerical integrations of stochastic contact Hamiltonian systems via stochastic contact Hamilton-Jacobi equation
Numerical integrations of stochastic contact Hamiltonian systems via stochastic contact Hamilton-Jacobi equation Open
Stochastic contact Hamiltonian systems are a class of important mathematical models, which can describe the dissipative properties with odd dimensions in the stochastic environment. In this article, we investigate the numerical dynamics of…
View article: An evolutionary approach for discovering non-Gaussian stochastic dynamical systems based on nonlocal Kramers-Moyal formulas
An evolutionary approach for discovering non-Gaussian stochastic dynamical systems based on nonlocal Kramers-Moyal formulas Open
Discovering explicit governing equations of stochastic dynamical systems with both (Gaussian) Brownian noise and (non-Gaussian) Lévy noise from data is chanllenging due to possible intricate functional forms and the inherent complexity of …
View article: Probability Flow Approach to the Onsager--Machlup Functional for Jump-Diffusion Processes
Probability Flow Approach to the Onsager--Machlup Functional for Jump-Diffusion Processes Open
The Onsager--Machlup action functional is an important concept in statistical mechanics and thermodynamics to describe the probability of fluctuations in nonequilibrium systems. It provides a powerful tool for analyzing and predicting the …
View article: Strichartz estimates for orthonormal functions and probabilistic convergence of density functions of compact operators on manifolds
Strichartz estimates for orthonormal functions and probabilistic convergence of density functions of compact operators on manifolds Open
In this paper, we establish some Strichartz estimates for orthonormal functions and probabilistic convergence of density functions related to compact operators on manifolds. Firstly, we present the suitable bound of $\int_{a\leq|s|\leq b}e…
View article: Stochastic parameter reduced-order model based on hybrid machine learning approaches
Stochastic parameter reduced-order model based on hybrid machine learning approaches Open
Establishing appropriate mathematical models for complex systems in natural phenomena not only helps deepen our understanding of nature but can also be used for state estimation and prediction. However, the extreme complexity of natural ph…
View article: Action Functional as an Early Warning Indicator in the Space of Probability Measures via Schrödinger Bridge
Action Functional as an Early Warning Indicator in the Space of Probability Measures via Schrödinger Bridge Open
Critical transitions and tipping phenomena between two meta-stable states in stochastic dynamical systems are a significant scientific issue. In this work, we expand the methodology of identifying the most probable transition pathway betwe…
View article: Early warning indicators via latent stochastic dynamical systems
Early warning indicators via latent stochastic dynamical systems Open
Detecting early warning indicators for abrupt dynamical transitions in complex systems or high-dimensional observation data are essential in many real-world applications, such as brain diseases, natural disasters, and engineering reliabili…
View article: Small mass limit for stochastic interacting particle systems with Lévy noise and linear alignment force
Small mass limit for stochastic interacting particle systems with Lévy noise and linear alignment force Open
We study the small mass limit in mean field theory for an interacting particle system with non-Gaussian Lévy noise. When the Lévy noise has a finite second moment, we obtain the limit equation with convergence rate ε+1/εN, by taking first …
View article: The stochastic fractional nonlinear Schrödinger equations in $H^α$ and structure-preserving algorithm
The stochastic fractional nonlinear Schrödinger equations in $H^α$ and structure-preserving algorithm Open
In this paper, we first investigate the global existence of a solution for the stochastic fractional nonlinear Schrödinger equation with radially symmetric initial data in a suitable energy space $H^α$. We then show that the stochastic fra…
View article: Diffusion Model Conditioning on Gaussian Mixture Model and Negative Gaussian Mixture Gradient
Diffusion Model Conditioning on Gaussian Mixture Model and Negative Gaussian Mixture Gradient Open
Diffusion models (DMs) are a type of generative model that has a huge impact on image synthesis and beyond. They achieve state-of-the-art generation results in various generative tasks. A great diversity of conditioning inputs, such as tex…
View article: Fourier neural operator based fluid-structure interaction for predicting the vesicle dynamics
Fourier neural operator based fluid-structure interaction for predicting the vesicle dynamics Open
Solving complex fluid-structure interaction (FSI) problems, characterized by nonlinear partial differential equations, is crucial in various scientific and engineering applications. Traditional computational fluid dynamics (CFD) solvers ar…
View article: Fourier Neural Operator Based Fluid-Structure Interaction for Predicting the Vesicle Dynamics
Fourier Neural Operator Based Fluid-Structure Interaction for Predicting the Vesicle Dynamics Open
View article: Stochastic dynamics of human papillomavirus delineates cervical cancer progression
Stochastic dynamics of human papillomavirus delineates cervical cancer progression Open
View article: Early Warning Prediction with Automatic Labeling in Epilepsy Patients
Early Warning Prediction with Automatic Labeling in Epilepsy Patients Open
Early warning for epilepsy patients is crucial for their safety and well-being, in particular to prevent or minimize the severity of seizures. Through the patients' EEG data, we propose a meta learning framework to improve the prediction o…
View article: Planar Bistable Structures Detection via the Conley Index and Applications to Biological Systems
Planar Bistable Structures Detection via the Conley Index and Applications to Biological Systems Open
Bistability is a ubiquitous phenomenon in life sciences. In this paper, two kinds of bistable structures in two-dimensional dynamical systems are studied: one is two one-point attractors, another is a one-point attractor accompanied by a c…
View article: Reservoir computing with error correction: Long-term behaviors of stochastic dynamical systems
Reservoir computing with error correction: Long-term behaviors of stochastic dynamical systems Open
View article: Efficient Privacy-Preserving Convolutional Spiking Neural Networks with FHE
Efficient Privacy-Preserving Convolutional Spiking Neural Networks with FHE Open
With the rapid development of AI technology, we have witnessed numerous innovations and conveniences. However, along with these advancements come privacy threats and risks. Fully Homomorphic Encryption (FHE) emerges as a key technology for…
View article: Early warning indicators via latent stochastic dynamical systems
Early warning indicators via latent stochastic dynamical systems Open
Detecting early warning indicators for abrupt dynamical transitions in complex systems or high-dimensional observation data is essential in many real-world applications, such as brain diseases, natural disasters, and engineering reliabilit…
View article: Well-posedness and averaging principle for Lévy-type McKean-Vlasov stochastic differential equations under local Lipschitz conditions
Well-posedness and averaging principle for Lévy-type McKean-Vlasov stochastic differential equations under local Lipschitz conditions Open
In this paper, we investigate a class of McKean-Vlasov stochastic differential equations under Lévy-type perturbations. We first establish the existence and uniqueness theorem for solutions of the McKean-Vlasov stochastic differential equa…