Jiaming Chen
We introduce a class of L\'evy-driven graph Ornstein-Uhlenbeck (grOU) models for edge-indexed network time series. The proposed framework extends generalized network autoregressive (GNAR) processes for edge-indexed network time series to…
The Vision Transformer (ViT) has achieved notable success in computer vision, with its variants widely validated across various downstream tasks, including semantic segmentation. However, as general-purpose visual encoders, ViT backbones…
This paper describes the stochastic Levy--Lorentz gas driven by general long-range reference random walk on correlated and entangled random medium. Further consideration has been laid on the stochastic reinforcement of the underlying random…
We consider the stochastic heat equation on a compact smooth Riemannian manifold without boundary satisfying \begin{equation*} \partial_tu(t,x)=\frac{1}{2}\Delta_Mu(t,x)+\sigma(t,x,u)\dot{W}(t,x),\quad (t,x)\in\mathbb{R}_+\times M,…
Robust generalization in robotic manipulation is crucial for robots to adapt flexibly to diverse environments. Existing methods usually improve generalization by scaling data and networks, but model tasks independently and overlook…
Neural rendering, particularly 3D Gaussian Splatting (3DGS), has evolved rapidly and become a key component for building world models. However, existing viewer solutions remain fragmented, heavy, or constrained by legacy pipelines,…
Dual-arm cooperative manipulation holds great promise for tackling complex real-world tasks that demand seamless coordination and adaptive dynamics. Despite substantial progress in learning-based motion planning, most approaches struggle to…
The dissipation phenomena of relative entropy from an It\^o--Langevin dynamical system is a classic topic from stochastic analysis. Relying on the time-reversal of diffusions, a novel trajectorial approach investigates the pathwise behavior…
We present a discrete space-time stochastic partial differential equation (SPDE) model to describe the dynamics of a weakly self-avoiding polymer with intrinsic length $J$. By introducing a penalty factor tailored to the discrete setting,…
Vibration energy harvesting is a promising solution for powering battery-free IoT systems; however, the instability of ambient vibrations presents significant challenges, such as limited harvested energy, intermittent power supply, and poor…
Recent advances in Schramm-Loewner evolution have driven increasing interest in non-standard Loewner flows. In this work, we propose a novel splitting algorithm to simulate random Loewner curves with rigorous convergence analysis in…
In this work, we establish the existence of large deviation principles of random walk in strongly mixing environments. The quenched and annealed rate functions have the same zero set whose shape is either a singleton point or a line…
The quenched and annealed large deviations of the random walk in random environment are shown to conform on any compact set whenever the level of disorder is sufficiently low. In this work, we show that these two large deviations always…
Model Predictive Control (MPC) is a widely adopted control paradigm that leverages predictive models to estimate future system states and optimize control inputs accordingly. However, while MPC excels in planning and control, it lacks the…
We consider the fractional stochastic heat equation on the $d$-dimensional torus $\mathbb{T}^d:=\left[-\frac{1}{2},\frac{1}{2}\right]^d$, $d\geq 1$, with periodic boundary conditions: \[ \partial_t u(t,\textbf{x})=…
This paper describes directed polymer on general time-correlated random field. Law of large numbers, existence and smoothness of limiting free energies are proved at all temperature. We also display the delocalized-localized transition, via…
In the first part of the paper we propose and study the approximation of the $SLE_\kappa$ trace via the Ninomiya-Victoir splitting algorithm. We prove the uniform convergence in probability with respect to the sup-norm to the distance…
We consider the stochastic heat equation on the 1-dimensional torus $\mathbb{T}:=\left[-1,1\right]$ with periodic boundary conditions: $$ \partial_t u(t,x)=\partial^2_x u(t,x)+\sigma(t,x,u)\dot{F}(t,x),\quad x\in…
Although Model Predictive Control (MPC) can effectively predict the future states of a system and thus is widely used in robotic manipulation tasks, it does not have the capability of environmental perception, leading to the failure in some…
We study effective global generation of adjoint line bundles on smooth projective varieties. To measure the effectivity we introduce the concept of the convex Fujita number of a smooth projective variety and compute its value for a class of…