Li Zhang

Enrique Mallada, Xiaoqiao Meng, Michel Hack et al.

This paper examines synchronization of computer clocks connected via a data network and proposes a skewless algorithm to synchronize them. Unlike existing solutions, which either estimate and compensate the frequency difference (skew) among clocks or introduce offset corrections that can generate jitter and possibly even backward jumps, our solution achieves synchronization without these problems. We first analyze the convergence property of the algorithm and provide explicit necessary and sufficient conditions on the parameters to guarantee synchronization. We then study the effect of noisy measurements (jitter) and frequency drift (wander) on the offsets and synchronization frequency, and further optimize the parameter values to minimize their variance. Our study reveals a few insights, for example, we show that our algorithm can converge even in the presence of timing loops and noise, provided that there is a well defined leader. This marks a clear contrast with current standards such as NTP and PTP, where timing loops are specifically avoided. Furthermore, timing loops can even be beneficial in our scheme as it is demonstrated that highly connected subnetworks can collectively outperform individual clients when the time source has large jitter. The results are supported by experiments running on a cluster of IBM BladeCenter servers with Linux.

Enrique Mallada, Xiaoqiao Meng, Michel Hack et al.

This paper examines synchronization of computer clocks connected via a data network and proposes a skewless algorithm to synchronize them. Unlike existing solutions, which either estimate and compensate the frequency difference (skew) among clocks or introduce offset corrections that can generate jitter and possibly even backward jumps, our algorithm achieves synchronization without these problems. We first analyze the convergence property of the algorithm and provide necessary and sufficient conditions on the parameters to guarantee synchronization. We then implement our solution on a cluster of IBM BladeCenter servers running Linux and study its performance. In particular, both analytically and experimentally, we show that our algorithm can converge in the presence of timing loops. This marks a clear contrast with current standards such as NTP and PTP, where timing loops are specifically avoided. Furthermore, timing loops can even be beneficial in our scheme. For example, it is demonstrated that highly connected subnetworks can collectively outperform individual clients when the time source has large jitter. It is also experimentally demonstrated that our algorithm outperforms other well-established software-based solutions such as the NTPv4 and IBM Coordinated Cluster Time (IBM CCT).

Zhipeng Yang, Xiaoming He, Li Zhang et al.

In this article we develop a multi-grid multi-level Monte Carlo (MGMLMC) method for the stochastic Stokes-Darcy interface model with random hydraulic conductivity both in the porous media domain and on the interface. Because the randomness through the interface affects the flow in the Stokes domain, we investigate the coupled stochastic Stokes-Darcy model to improve the fidelity as this model also considers the second and third porosity of the free flow. Then we prove the existence and uniqueness of the weak solution of the variational form. For the numerical solution, we adopt the Monte Carlo (MC) method and finite element method (FEM), for the discrete form in the probability space and physical space, respectively. In the traditional single-level Monte Carlo (SLMC) method, more accurate numerical approximate requires both larger number of samples in probability space and smaller mesh size in the physical space. Then the computational cost increase significantly as the mesh size becomes smaller for the more accurate numerical approximate. Therefore we adopt the multi-level Monte Carlo (MLMC) method to dramatically reduce the computational cost in the probability space, because the number of samples decays fast while the mesh size decreases. We also develop a strategy to calculate the number of samples needed in MLMC method for the stochastic Stokes-Darcy model. Furthermore MLMC naturally provides the hierarchial grids and sufficient information on these grids for multi-grid (MG) method, which can in turn improve the efficiency of MLMC. In order to fully make use of the dynamical interaction between this two methods, we propose the multi-grid multi-level Monte Carlo method for more efficiently solving the stochastic model. Numerical examples are provided to verify and illustrate the proposed method and the theoretical conclusions.

Yuang Wang, Pengfei Jin, Li Zhang et al.

Diffusion bridge models have demonstrated promising performance in conditional image generation tasks, such as image restoration and translation, by initializing the generative process from corrupted images instead of pure Gaussian noise. However, existing diffusion bridge models often rely on Stochastic Differential Equation (SDE) samplers, which result in slower inference speed compared to diffusion models that employ high-order Ordinary Differential Equation (ODE) solvers for acceleration. To mitigate this gap, we propose a high-order ODE sampler with a stochastic start for diffusion bridge models. To overcome the singular behavior of the probability flow ODE (PF-ODE) at the beginning of the reverse process, a posterior sampling approach was introduced at the first reverse step. The sampling was designed to ensure a smooth transition from corrupted images to the generative trajectory while reducing discretization errors. Following this stochastic start, Heun's second-order solver is applied to solve the PF-ODE, achieving high perceptual quality with significantly reduced neural function evaluations (NFEs). Our method is fully compatible with pretrained diffusion bridge models and requires no additional training. Extensive experiments on image restoration and translation tasks, including super-resolution, JPEG restoration, Edges-to-Handbags, and DIODE-Outdoor, demonstrated that our sampler outperforms state-of-the-art methods in both visual quality and Frechet Inception Distance (FID).