Partition Points Research Articles

Input-to-state stability of switched systems with counter-dependent multiple discontinuous Lyapunov function

This paper investigates the input-to-state stability (ISS) of switched systems under the mode-dependent average dwell time (MDADT) switching. A new non-equidistant partitioning (NEP) method for maximum and actual dwell time intervals is proposed, enhancing the flexibility in constructing the Lyapunov function. Building upon the proposed NEP method, a novel counter-dependent multiple discontinuous Lyapunov function (CDMDLF) is constructed by incorporating a counter, where the value of the counter is the partitioning number of the current mode-running time interval. Furthermore, the evolution of Lyapunov functions at adjacent partitioning points dynamically depends on the previous partitioning point rather than a fixed constant, which is more flexible and practical. Utilizing the developed CDMDLF, some less conservative stability criteria are established for nonlinear and linear switched systems. It is revealed that our proposed method covers the multiple discontinuous Lyapunov function (MDLF) and the switching-signal-based MDLF (SMDLF) methods as exceptional cases while providing tighter bounds on the MDADT. In the end, two numerical examples are given to illustrate the advantages and effectiveness of the presented approach.

Transformer-Based Visual Segmentation: A Survey.

Visual segmentation seeks to partition images, video frames, or point clouds into multiple segments or groups. This technique has numerous real-world applications, such as autonomous driving, image editing, robot sensing, and medical analysis. Over the past decade, deep learning-based methods have made remarkable strides in this area. Recently, transformers, a type of neural network based on self-attention originally designed for natural language processing, have considerably surpassed previous convolutional or recurrent approaches in various vision processing tasks. Specifically, vision transformers offer robust, unified, and even simpler solutions for various segmentation tasks. This survey provides a thorough overview of transformer-based visual segmentation, summarizing recent advancements. We first review the background, encompassing problem definitions, datasets, and prior convolutional methods. Next, we summarize a meta-architecture that unifies all recent transformer-based approaches. Based on this meta-architecture, we examine various method designs, including modifications to the meta-architecture and associated applications. We also present several specific subfields, including 3D point cloud segmentation, foundation model tuning, domain-aware segmentation, efficient segmentation, and medical segmentation. Additionally, we compile and re-evaluate the reviewed methods on several well-established datasets. Finally, we identify open challenges in this field and propose directions for future research.

Numerical Simulation Based on Interpolation Technique for Multi-Term Time-Fractional Convection–Diffusion Equations

This paper introduces a novel approach for solving multi-term time-fractional convection–diffusion equations with the fractional derivatives in the Caputo sense. The proposed highly accurate numerical algorithm is based on the barycentric rational interpolation collocation method (BRICM) in conjunction with the Gauss–Legendre quadrature rule. The discrete scheme constructed in this paper can achieve high computational accuracy with very few interval partitioning points. To verify the effectiveness of the present discrete scheme, some numerical examples are presented and are compared with the other existing method. Numerical results demonstrate the effectiveness of the method and the correctness of the theoretical analysis.

Using PySpark to accelerate batch data point rotation for paleogeographic reconstruction

ABSTRACT Batch paleogeographic point rotation (BPPR) is a PySpark-based extensible batch data point rotation method that accelerates rotation during paleogeographic reconstruction. Data point rotation is an important part of paleogeographic reconstruction and a significant tool for exploring the co-evolution of Earth and life. However, current point rotation techniques have challenges with processing speeds when handling extensive paleogeographic data. Therefore, this study introduced a parallel-computing framework to construct a BPPR. This method combines PySpark and PyGPlates, which can partition points and compute them simultaneously in multiple threads. The rotation of 232,277 fossil occurrences from the Cretaceous Period in the Paleobiology Database (PBDB) was completed within 26 s. By contrast, an alternative GPlates method completed the same task within 96 s. The proposed method supports CSV, EXCEL, SHP, and other data formats, thereby avoiding possible software switching requirements when using methods associated with GPlates. Using synthetic and real paleontological data as experimental datasets, BPPR proved to be nine times more efficient than GPlates when rotating 900,000 points. This efficiency improvement significantly enhanced data-driven paleogeographic analysis. The parallel strategy employed can be broadly applied to massive data analysis in geoscience.

Solving the Problem of Fuzzy Partition-Distribution with Determination of the Location of Subset Centers

A large number of real-world problems from various fields of human activity can be reduced to optimal partitioning-allocation problems with the purpose of minimizing the partitioning quality criterion. A typical representative of such problem is an infinite-dimensional transportation problem and more generalized problems—infinite-dimensional problems of production centers placement along with the partitioning of the area of continuously distributed consumers with the purpose of minimizing transportation and production costs. The relevant problems are characterized by some kind of uncertainty level of a not-probabilistic nature. A method is proposed to solve an optimal fuzzy partitioning-allocation problem with the subsets centers placement for sets of n-dimensional Euclidean space. The method is based on the synthesis of the methods of fuzzy theory and optimal partitioning-allocation theory, which is a new science field in infinite-dimensional mathematical programming with Boolean variables. A theorem was proved that determines the form of the optimal solution of the corresponding optimal fuzzy partitioning-allocation problem with the subsets centers placement for sets of n-dimensional Euclidean space. An algorithm for solving fuzzy partitioning-allocation problems is proposed, which is based on the proved theorem and on a variant of Shor’s r-algorithm—a non-differential optimization method. The application of the proposed method is demonstrated on model tasks, where the coefficient of mistrust is integrated to interpret the obtained result—the minimum value of the membership function, which allows each point of the set partition to be assigned to a specific fuzzy subset.

Multi-Grained Point Cloud Geometry Compression via Dual-Model Prediction with Extended Octree

The state-of-the-art geometry-based point cloud compression (G-PCC) (Octree) is the fine-grained approach, which uses the octree to partition point clouds into voxels and predicts them based on neighbor occupancy in narrower spaces. However, G-PCC (Octree) is less effective at compressing dense point clouds than multi-grained approaches (such as G-PCC (Trisoup)), which exploit the continuous point distribution in nodes partitioned by the pruned octree over larger spaces. Therefore, we propose a lossy multi-grained compression with extended octree and dual-model prediction. The extended octree, where each partitioned node contains intra-block and extra-block points, is applied to address poor prediction (such as overfitting) at the node edges of the octree partition. For the points of each multi-grained node, dual-model prediction fits surfaces and projects residuals onto the surfaces, reducing projection residuals for efficient 2D compression and fitting complexity. In addition, a hybrid DWT-DCT transform for 2D projection residuals mitigates the resolution degradation of DWT and the blocking effect of DCT during high compression. Experimental results demonstrate the superior performance of our method over advanced G-PCC (Octree), achieving BD-Rate gains of 55.9% and 45.3% for point-to-point ( D1 ) and point-to-plane ( D2 ) distortions, respectively. Our approach also outperforms G-PCC (Octree) and G-PCC (Trisoup) in subjective evaluation.

A global springback compensation method for manufacturing metallic seal ring with complex cross-section and submillimeter precision

The fabrication of complex thin-walled components with irregular cross-sectional geometries often necessitates multi-pass forming processes. The springback phenomena at the microscale level contribute significantly difficulty to the precise control of geometrical accuracy for such components. To achieve submillimeter precision control of micro features in metal seal rings, this research proposed a global springback compensation method to facilitate the attainment of the optimized surfaces of dies. Through the analysis of changes in cross-sectional shape, stress distribution and bending moment in the multiple stages, several partition points were set up to divide the cross-section into four zones. For a partitional control of the manufactured surface, the compensation magnitudes for each segment are determined by iteratively refining the compensation factors using the secant method. The iteration of compensation factors is based on the deviation of dimensions measured by finite element simulation, which greatly saves experimental costs. The experimental results indicate that the predictive dimensional alterations by the global compensation agree with the experimental ones exhibiting a maximum error of less than 3 %. Furthermore, the springback behavior during the unloading and trimming stages coupling caused a dimensional error of 14.9 % for the wave width and 8.3 % for the peak width. Following the application of coupled compensation through two iterations, a distinct decrease in the relative average errors of springback values for both part width and peak width, achieving reductions to 2.4 % and 0.6 %, respectively. Compared to the traditional single springback compensation technique, the global compensation strategy effectively mitigates the out-of-tolerance issues induced by the trimming process.

Research on Human Lung Impedance Tomography Based on Soft Thresholding Image Segmentation and Reduced-Order Tikhonov Regularization

The lung is one of the most vital organs in the human body, and its condition is closely correlated with overall health. Electrical impedance tomography (EIT), as a biomedical imaging technique, often produces low-quality reconstructed images due to its inherent ill-posedness in solving the inverse problem. To address this issue, this paper proposes a soft-threshold region segmentation algorithm with a relaxation factor. This algorithm segments the reconstructed lung images into internal regions, edge regions, and background regions, resulting in clearer boundaries in the reconstructed images. This facilitates the intuitive identification of regions of interest by healthcare professionals. Additionally, this segmentation algorithm is suitably combined with a dimension-reduced Tikhonov regularization algorithm. By utilizing the joint capabilities of these algorithms, the partition points belonging to the background region can be excluded from the sought grayscale vector, thereby improving the ill-posedness of the image reconstruction process and enhancing the quality of image reconstruction. Finally, a 16-electrode human lung EIT simulation model is established for the thoracic region and verified through simulation. Experimental validation is conducted using a human lung tank simulation platform to further demonstrate the effectiveness of the proposed method.

Game-Based Adaptive FLOPs and Partition Point Decision Mechanism With Latency and Energy-Efficient Tradeoff for Edge Intelligence

Game-Based Adaptive FLOPs and Partition Point Decision Mechanism With Latency and Energy-Efficient Tradeoff for Edge Intelligence

FTPipeHD: A Fault-Tolerant Pipeline-Parallel Distributed Training Approach for Heterogeneous Edge Devices

With the increasing proliferation of Internet-of-Things (IoT) devices, there is a growing trend towards distributing the power of deep learning (DL) among edge devices rather than centralizing it at the cloud. To deploy deep and complex models at edge devices with limited resources, model partitioning of deep neural network (DNN) models has been widely studied. However, most of the existing literature only considers distributing the inference model while still training the model at the cloud. In this paper, we propose FTPipeHD, a novel DNN training approach that trains DNN models across distributed heterogeneous devices with the fault-tolerance mechanism. To accelerate the training with the time-varying computing power of each device, we optimize the partition points dynamically according to real-time computing capacities. We also propose a novel weight redistribution approach that replicates the weights to both the neighboring nodes and the central node periodically, which combats the failure of multiple devices during training while incurring limited communication costs. Our numerical results demonstrate that FTPipeHD is 6.8 times faster in training than the state-of-the-art method when the computing capacity of the best device is 10 times greater than the worst one. It is also shown that the proposed method is able to accelerate the training even with the existence of device failures.

Dynamic planning of office building elevator scheduling

Every morning rush hour is the most crowded time for elevators in office buildings, and many office workers will be late because they can't wait for the elevator. How to reasonably call the existing elevator resources has become a problem we need to pay attention to. In this paper, we will discuss the modeling of elevator scheduling optimization problem for office buildings. In this paper, the background and significance of the research is firstly explained, and then the elevator group linkage control system is briefly understood and analyzed, and the evaluation indexes are determined according to its multi-objective and diversified characteristics, and then the group control method focusing on making the elevator run time the shortest is adopted, and the principle of the ratio of elevator running period/total running time equal to the number of passengers transported/total passengers transported by the elevator in one cycle is followed to compare several common elevator running methods, and the results are summarized in the following table. Common elevator operation methods are compared, the most effective way to arrive at, and finally use dynamic programming to solve the partition point, to establish the optimal scheme of elevator scheduling for the office building division. Since it is not possible to expand the elevator in the office building, reducing the number of stops of each elevator to shorten the time required for the elevator to carry passengers becomes the most feasible method. After comparing the common elevator operation methods, it can be found that zoning can shorten the final average arrival time of passengers more than no zoning. That is, the elevators in an office building are divided into different zones, and each zone has a designated elevator serving a designated floor segment. In order to solve the floor segment allocation problem, the shortest path algorithm is used in this paper. The paper concludes with a summary and future outlook of the resulting optimization model.

Novel Robust Stability Criteria for Lur’e Systems with Time-Varying Delay

This paper focuses on addressing the issue of absolute stability for uncertain Lur’e systems with time-varying delay using a delay-segmentation approach. The approach involves decomposing the delay interval into two distinct subintervals of unequal lengths. This allows for the introduction of a delay-segmentation-based augmented Lyapunov–Krasovskii functional that ensures piecewise continuity at the partition points. By selecting two sets of Lyapunov matrices for the time-varying delay in each interval, the obtained results are less conservative, providing a more accurate assessment of absolute stability. Finally, a numerical example is given to demonstrate the superiority of the delay-segmentation approach.

A DNN partitioning framework with controlled lossy mechanisms for edge-cloud collaborative intelligence

Collaborative intelligence (CI) is an approach used to accelerate deep neural network computations on IoT edge devices by offloading certain DNN computations to high-performance cloud servers. This offloading process involves transferring a large volume of feature data between the IoT edge device and the cloud servers, resulting in significant transfer time overhead that contributes to the overall end-to-end latency. Despite its importance, CI research has largely overlooked the impact of an unstable network environment on transfer time, leading to suboptimal latency in real-world scenarios. In light of this, we propose CO-PILOT, a novel partition framework that aims to minimize end-to-end latency while preserving the original model accuracy. CO-PILOT achieves this by finely controlling various lossy mechanisms, such as compression level and transport protocol, and strategically selecting error-robust layers as partition points to enhance resilience against network conditions and lossy mechanisms. The results demonstrate that CO-PILOT can reduce end-to-end latency by up to 85% with less than 1% accuracy degradation, all without requiring model retraining.

PArtNNer: Platform-Agnostic Adaptive Edge-Cloud DNN Partitioning for Minimizing End-to-End Latency

The last decade has seen the emergence of Deep Neural Networks (DNNs) as the de facto algorithm for various computer vision applications. In intelligent edge devices, sensor data streams acquired by the device are processed by a DNN application running on either the edge device itself or in the cloud. However, “edge-only” and “cloud-only” execution of State-of-the-Art DNNs may not meet an application’s latency requirements due to the limited compute, memory, and energy resources in edge devices, dynamically varying bandwidth of edge-cloud connectivity networks, and temporal variations in the computational load of cloud servers. This work investigates distributed (partitioned) inference across edge devices (mobile/end device) and cloud servers to minimize end-to-end DNN inference latency. We study the impact of temporally varying operating conditions and the underlying compute and communication architecture on the decision of whether to run the inference solely on the edge, entirely in the cloud, or by partitioning the DNN model execution among the two. Leveraging the insights gained from this study and the wide variation in the capabilities of various edge platforms that run DNN inference, we propose PArtNNer , a platform-agnostic adaptive DNN partitioning algorithm that finds the optimal partitioning point in DNNs to minimize inference latency. PArtNNer can adapt to dynamic variations in communication bandwidth and cloud server load without requiring pre-characterization of underlying platforms. Experimental results for six image classification and object detection DNNs on a set of five commercial off-the-shelf compute platforms and three communication standards indicate that PArtNNer results in 10.2× and 3.2× (on average) and up to 21.1× and 6.7× improvements in end-to-end inference latency compared to execution of the DNN entirely on the edge device or entirely on a cloud server, respectively. Compared to pre-characterization-based partitioning approaches, PArtNNer converges to the optimal partitioning point 17.6× faster.

Hastening Stream Offloading of Inference via Multi-Exit DNNs in Mobile Edge Computing

As the primary driver of intelligent mobile applications, deep neural networks (DNNs) have gradually deployed to millions of mobile devices, producing massive latency-sensitive and computation-intensive tasks daily. Mobile edge computing facilitates the deployment of computing resources at the edge, which enables fine-grained offloading of DNN inference tasks from mobile devices to edge nodes. However, most existing studies have not systematically considered three crucial performance aspects: scheduling multiple streams of DNN inference tasks, leveraging multi-exit models to hasten task processing, and partitioning inference models for partial offloading. To this end, this paper proposes an adaptive inference framework in mobile edge computing, which can dynamically select the exit point and partition point for multiple inference task streams. We design a dynamic programming algorithm to obtain an efficient solution under the ideal condition that task arrival information is known. Further, we design a learning-based algorithm for online scheduling, whose training efficiency is improved based on historical experience initialization and priority experience replay. Experimental results show that compared with the Greedy algorithm, the online algorithm improves the performance on two environmental parameters by an average of 5.9% and 32%, respectively.

Density-Based Clustering by Means of Bridge Point Identification

Density-based clustering focuses on defining clusters consisting of contiguous regions characterized by similar densities of points. Traditional approaches identify core points first, whereas more recent ones initially identify the cluster borders and then propagate cluster labels within the delimited regions. Both strategies encounter issues in presence of multi-density regions or when clusters are characterized by noisy borders. To overcome the above issues, we present a new clustering algorithm that relies on the concept of bridge point. A bridge point is a point whose neighborhood includes points of different clusters. The key idea is to use bridge points, rather than border points, to partition points into clusters. We have proved that a correct bridge point identification yields a cluster separation consistent with the expectation. To correctly identify bridge points in absence of a priori cluster information we leverage an established unsupervised outlier detection algorithm. Specifically, we empirically show that, in most cases, the detected outliers are actually a superset of the bridge point set. Therefore, to define clusters we spread cluster labels like a wildfire until an outlier, acting as a candidate bridge point, is reached. The proposed algorithm performs statistically better than state-of-the-art methods on a large set of benchmark datasets and is particularly robust to the presence of intra-cluster multiple densities and noisy borders.

Low-Latency Federated Learning via Dynamic Model Partitioning for Healthcare IoT.

Federated learning (FL) is receiving much attention in the Healthcare Internet of Things (H-IoT) to support various instantaneous E-health services. Today, the deployment of FL suffers from several challenges, such as high training latency and data privacy leakage risks, especially for resource-constrained medical devices. In this article, we develop a three-layer FL architecture to decrease training latency by introducing split learning into FL. We formulate a long-term optimization problem to minimize the local model training latency while preserving the privacy of the original medical data in H-IoT. Specially, a Privacy-ware Model Partitioning Algorithm (PMPA) is proposed to solve the formulated problem based on the Lyapunov optimization theory. In PMPA, the local model is partitioned properly between a resource-constrained medical end device and an edge server, which meets privacy requirements and energy consumption constraints. The proposed PMPA is separated into two phases. In the first phase, a partition point set is obtained using Kullback-Leibler (KL) divergence to meet the privacy requirement. In the second phase, we employ the model partitioning function, derived through Lyapunov optimization, to select the partition point from the partition point set that that satisfies the energy consumption constraints. Simulation results show that compared with traditional FL, the proposed algorithm can significantly reduce the local training latency. Moreover, the proposed algorithm improves the efficiency of medical image classification while ensuring medical data security.

Slope deformation partitioning and monitoring points optimization based on cluster analysis

Slope deformation partitioning and monitoring points optimization based on cluster analysis

OctFormer: Octree-based Transformers for 3D Point Clouds

We propose octree-based transformers, named OctFormer, for 3D point cloud learning. OctFormer can not only serve as a general and effective backbone for 3D point cloud segmentation and object detection but also have linear complexity and is scalable for large-scale point clouds. The key challenge in applying transformers to point clouds is reducing the quadratic, thus overwhelming, computation complexity of attentions. To combat this issue, several works divide point clouds into non-overlapping windows and constrain attentions in each local window. However, the point number in each window varies greatly, impeding the efficient execution on GPU. Observing that attentions are robust to the shapes of local windows, we propose a novel octree attention, which leverages sorted shuffled keys of octrees to partition point clouds into local windows containing a fixed number of points while permitting shapes of windows to change freely. And we also introduce dilated octree attention to expand the receptive field further. Our octree attention can be implemented in 10 lines of code with open-sourced libraries and runs 17 times faster than other point cloud attentions when the point number exceeds 200 k. Built upon the octree attention, OctFormer can be easily scaled up and achieves state-of-the-art performances on a series of 3D semantic segmentation and 3D object detection benchmarks, surpassing previous sparse-voxel-based CNNs and point cloud transformers in terms of both efficiency and effectiveness. Notably, on the challenging ScanNet200 dataset, OctFormer outperforms sparse-voxel-based CNNs by 7.3 in mIoU. Our code and trained models are available at https://wang-ps.github.io/octformer.

CNNParted: An open source framework for efficient Convolutional Neural Network inference partitioning in embedded systems

Applications such as autonomous driving or assistive robotics heavily rely on the usage of Deep Neural Networks. In particular, Convolutional Neural Networks (CNNs) provide precise and reliable results in image processing tasks like camera-based object detection or semantic segmentation. However, to achieve even better results, CNNs are becoming more and more complex. Deploying these networks in distributed embedded systems thereby imposes new challenges, due to additional constraints regarding performance and energy consumption in the near-sensor compute platforms, i.e. the sensor nodes. Processing all data in the central node, however, is disadvantageous since raw data of camera consumes large bandwidth and running CNN inference of multiple tasks requires certain performance. Moreover, sending raw data over the interconnect is not advisable for privacy reasons. Hence, offloading CNN workload to the sensor nodes in the system can lead to reduced traffic on the link and a higher level of data security.However, due to the limited hardware-resources on the sensor nodes, partitioning CNNs has to be done carefully to meet overall latency requirements and energy constraints. Therefore, we present CNNParted, an open-source framework for efficient, hardware-aware CNN inference partitioning targeting embedded AI applications. It automatically searches for potential partitioning points in the CNN to find a beneficial workload distribution between sensor nodes and a central edge node. Thereby, CNNParted not only analyzes the CNN architecture but also takes hardware components, such as dedicated hardware accelerators and memories, into consideration to evaluate inference partitioning regarding latency and energy consumption.Exemplary, we apply CNNParted to three commonly used feed forward CNNs in embedded systems. Thereby, the framework first searches for several potential partitioning points and then evaluates the latter regarding inference latency and energy consumption. Based on the results, beneficial partitioning points can be identified depending on the system constraints. Using the framework, we are able to find and evaluate 10 potential partitioning points for FCN ResNet-50, 13 partitioning points for GoogLeNet, and 8 partitioning points for SqueezeNet V1.1 within 520 s, 330 s, and 140 s, respectively, on an AMD EPYC 7702P running 8 concurrent threads. For GoogLeNet, we determine two partitioning points that provide a good trade-off between required bandwidth, latency and energy consumption. We also provide insights into further interesting findings that can be derived from the evaluation results.