Ergodicity for the GI/G/1GI/G/1-type Markov Chain

Ergodicity is a fundamental issue for a stochastic process. In this paper, we refine results on ergodicity for a general type of Markov chain to a specific type or the $GI/G/1$-type Markov chain, which has many interesting and important applications in various areas. It is of interest to obtain conditions in terms of system parameters or the given information about the process, under which the chain has various ergodic properties. Specifically, we provide necessary and sufficient conditions for geometric, strong and polynomial ergodicity, respectively.Comment: 16 page

Modeling of two-phase flow in heterogeneous wet porous media

The characterization of two-phase flow has been commonly based on homogeneous wet capillary models, which are limited to heterogeneous wet porous media. In this work, capillary pressure and relative permeability models for three heterogeneous wet systems are derived, which enable the analysis of the effect of oil-wet ratio on the two-phase flow mechanism. The capillary pressures, relative permeabilities and water cut curves of three systems are simulated at the primary drainage stage. The results show that water-wet and oil-wet systems exhibit drainage and imbibition characteristics, respectively, while heterogeneous wet systems show both of these characteristics, and a large oil- wet ratio is favourable to oil imbibition. Mixed-wet large and mixed-wet small systems have water-wet and oil-wet characteristics, respectively, at the end and the beginning of oil displacement. At the drainage stage, the oil-wet ratio can significantly decrease oil conductivity, while water conductivity is enhanced. The conductivity difference between oil and water firstly decreases and then increases with rising water saturation, and the difference diminishes with the increase in oil-wet ratio. The oil-wet ratio can reduce water displacement efficiency, and its effects on the water cut curves vary between the three systems due to wettability distribution and pore-size mutation. The mixed-wet small system has the strongest oil imbibition ability caused by the largest capillary pressure in oil-wet pores and the smallest drainage pressure in water-wet pores, and high water conductivity causes the greatest water cut. The trend of variations in the mixed-wet large system is opposite to that in the mixed-wet small system, and the fractional-wet system is located between the other two systems.Cited as: Xiao, Y., He, Y., Zheng, J., Zhao, J. Modeling of two-phase flow in heterogeneous wet porous media. Capillarity, 2022, 5(3): 41-50. https://doi.org/10.46690/capi.2022.03.0

Machine Learning-Enhanced Aircraft Landing Scheduling under Uncertainties

This paper addresses aircraft delays, emphasizing their impact on safety and financial losses. To mitigate these issues, an innovative machine learning (ML)-enhanced landing scheduling methodology is proposed, aiming to improve automation and safety. Analyzing flight arrival delay scenarios reveals strong multimodal distributions and clusters in arrival flight time durations. A multi-stage conditional ML predictor enhances separation time prediction based on flight events. ML predictions are then integrated as safety constraints in a time-constrained traveling salesman problem formulation, solved using mixed-integer linear programming (MILP). Historical flight recordings and model predictions address uncertainties between successive flights, ensuring reliability. The proposed method is validated using real-world data from the Atlanta Air Route Traffic Control Center (ARTCC ZTL). Case studies demonstrate an average 17.2% reduction in total landing time compared to the First-Come-First-Served (FCFS) rule. Unlike FCFS, the proposed methodology considers uncertainties, instilling confidence in scheduling. The study concludes with remarks and outlines future research directions

Extended Finite Element Method for Predicting Productivity of Multifractured Horizontal Wells

Based on the theory of the extended finite element method (XFEM), which was first proposed by Moës for dealing with the problem characterized by discontinuities, an extended finite element model for predicting productivity of multifractured horizontal well has been established. The model couples four main porous flow regimes, including fluid flow in the away-from-wellbore region of reservoir matrix, radial flow in the near-wellbore region of reservoir matrix, linear flow in the away-from-wellbore region of fracture, and radial flow in the near-wellbore region of fracture by considering mass transfer between fracture and matrix. The method to introduce the interior well boundary condition into the XFEM is proposed, and therefore the model can be highly adaptable to the complex and asymmetrical physical conditions. Case studies indicate that this kind of multiflow problems can be solved with high accuracy by the use of the XFEM

UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models

Diffusion probabilistic models (DPMs) have demonstrated a very promising ability in high-resolution image synthesis. However, sampling from a pre-trained DPM is time-consuming due to the multiple evaluations of the denoising network, making it more and more important to accelerate the sampling of DPMs. Despite recent progress in designing fast samplers, existing methods still cannot generate satisfying images in many applications where fewer steps (e.g., $<$10) are favored. In this paper, we develop a unified corrector (UniC) that can be applied after any existing DPM sampler to increase the order of accuracy without extra model evaluations, and derive a unified predictor (UniP) that supports arbitrary order as a byproduct. Combining UniP and UniC, we propose a unified predictor-corrector framework called UniPC for the fast sampling of DPMs, which has a unified analytical form for any order and can significantly improve the sampling quality over previous methods, especially in extremely few steps. We evaluate our methods through extensive experiments including both unconditional and conditional sampling using pixel-space and latent-space DPMs. Our UniPC can achieve 3.87 FID on CIFAR10 (unconditional) and 7.51 FID on ImageNet 256$\times$256 (conditional) with only 10 function evaluations. Code is available at https://github.com/wl-zhao/UniPC.Comment: Accepted by NeurIPS 2023. Project page: https://unipc.ivg-research.xy

Dynamic Spatial Sparsification for Efficient Vision Transformers and Convolutional Neural Networks

In this paper, we present a new approach for model acceleration by exploiting spatial sparsity in visual data. We observe that the final prediction in vision Transformers is only based on a subset of the most informative tokens, which is sufficient for accurate image recognition. Based on this observation, we propose a dynamic token sparsification framework to prune redundant tokens progressively and dynamically based on the input to accelerate vision Transformers. Specifically, we devise a lightweight prediction module to estimate the importance score of each token given the current features. The module is added to different layers to prune redundant tokens hierarchically. While the framework is inspired by our observation of the sparse attention in vision Transformers, we find the idea of adaptive and asymmetric computation can be a general solution for accelerating various architectures. We extend our method to hierarchical models including CNNs and hierarchical vision Transformers as well as more complex dense prediction tasks that require structured feature maps by formulating a more generic dynamic spatial sparsification framework with progressive sparsification and asymmetric computation for different spatial locations. By applying lightweight fast paths to less informative features and using more expressive slow paths to more important locations, we can maintain the structure of feature maps while significantly reducing the overall computations. Extensive experiments demonstrate the effectiveness of our framework on various modern architectures and different visual recognition tasks. Our results clearly demonstrate that dynamic spatial sparsification offers a new and more effective dimension for model acceleration. Code is available at https://github.com/raoyongming/DynamicViTComment: Accepted to T-PAMI. Journal version of our NeurIPS 2021 work: arXiv:2106.02034. Code is available at https://github.com/raoyongming/DynamicVi

Research on the structure of a new type of multi party bicycle system

at present, many people’s gathering bicycles suitable for scenic spots, parks and pedestrian streets are popular abroad, but they have not been introduced in China. Based on the analysis of foreign multi person bicycles, this paper improves the suspension device, steering device, transmission device, braking device and parking device of bicycle vehicles, so as to improve the ability of multi person gathering bicycles to adapt to diff erent road conditions and the safety, reliability and comfort in the process of riding. The research results are expected to provide reference for the development of multi-party bicycles in China

RPN: A Word Vector Level Data Augmentation Algorithm in Deep Learning for Language Understanding

This paper presents a new data augmentation algorithm for natural understanding tasks, called RPN:Random Position Noise algorithm.Due to the relative paucity of current text augmentation methods. Few of the extant methods apply to natural language understanding tasks for all sentence-level tasks.RPN applies the traditional augmentation on the original text to the word vector level. The RPN algorithm makes a substitution in one or several dimensions of some word vectors. As a result, the RPN can introduce a certain degree of perturbation to the sample and can adjust the range of perturbation on different tasks. The augmented samples are then used to give the model training.This makes the model more robust. In subsequent experiments, we found that adding RPN to the training or fine-tuning model resulted in a stable boost on all 8 natural language processing tasks, including TweetEval, CoLA, and SST-2 datasets, and more significant improvements than other data augmentation algorithms.The RPN algorithm applies to all sentence-level tasks for language understanding and is used in any deep learning model with a word embedding layer.Comment: 10 pages, 4 figure