Optimal Partition Research Articles

Constructing Perturbation Matrices of Prototypes for Enhancing the Performance of Fuzzy Decoding Mechanism

Granular computing (GrC) embraces a spectrum of concepts, methodologies, methods, and applications, which dwells upon information granules and their processing. Fuzzy C-means (FCM) based encoding and decoding (granulation-degranulation) mechanism plays a visible role in granular computing. Fuzzy decoding mechanism, also known as the reconstruction (degranulation) problem, has become an intensively studied category in recent years. This study mainly focuses on the improvement of the fuzzy decoding mechanism, and an augmented version achieved through constructing perturbation matrices of prototypes is put forward. Particle swarm optimization is employed to determine a group of optimal perturbation matrices to optimize the prototype matrix and obtain an optimal partition matrix. A series of experiments are carried out to show the enhancement of the proposed method. The experimental results are consistent with the theoretical analysis and demonstrate that the developed method outperforms the traditional FCM-based decoding mechanism.

Urban Dominant Trees Followed the Optimal Partitioning Theory and Increased Root Biomass Allocation and Nutrient Uptake under Elevated Nitrogen Deposition

Nitrogen (N) is one of the limiting nutrients for plant growth and metabolism in terrestrial ecosystems. Numerous studies have explored the effects of N addition on the eco-physiological traits and biomass production of plants, but the underlying mechanism of how N deposition influences biomass allocation patterns remains controversial, especially for urban greening trees. A greenhouse experiment was conducted for 7 months, using two dominant tree species of urban streets in North China, including the coniferous tree species Pinus tabuliformis and the broadleaved tree Fraxinus chinensis, under three levels of N addition: ambient, low N addition, and high N addition (0, 3.5, and 10.5 gN m−2 year−1). The plant growth, biomass distribution, functional traits, and soil nutrient properties of the two trees were determined. Overall, N addition had positive effects on the aboveground and belowground biomass of P. tabuliformis, which also shifted its functional traits to an acquisitive strategy, while F. chinensis only increased root biomass distribution and fast traits as N increased. Furthermore, N supply increased the soil N and phosphorus availability of both trees and improved their root nutrient uptake capacity, resulting in an increase in their root–shoot ratio. Optimal partitioning theory could better explain why trees would invest more resources in roots, changing root structure and nutrient uptake, thus increasing root biomass allocation to adapt to a resource-poor environment. These findings highlight the importance of plant functional traits in driving the responses of biomass allocation to environmental changes for urban greening dominant tree species and could help to come up with new tree growth strategies in silvicultural practice for urban green space.

Determining optimal channel partition for 2:4 fine grained structured sparsity

Determining optimal channel partition for 2:4 fine grained structured sparsity

Subspace learning machine (SLM): Methodology and performance evaluation

Inspired by the feedforward multilayer perceptron (FF-MLP), decision tree (DT) and extreme learning machine (ELM), a new classification model, called the subspace learning machine (SLM), is proposed in this work. SLM first identifies a discriminant subspace, S0, by examining the discriminant power of each input feature. Then, it uses probabilistic projections of features in S0 to yield 1D subspaces and finds the optimal partition for each of them. This is equivalent to partitioning S0 with hyperplanes. A criterion is developed to choose the best q partitions that yield 2q partitioned subspaces among them. We assign S0 to the root node of a decision tree and the intersections of 2q subspaces to its child nodes of depth one. The partitioning process is recursively applied at each child node to build an SLM tree. When the samples at a child node are sufficiently pure, the partitioning process stops and each leaf node makes a prediction. The idea can be generalized to regression, leading to the subspace learning regressor (SLR). Furthermore, ensembles of SLM/SLR trees can yield a stronger predictor. Extensive experiments are conducted for performance benchmarking among SLM/SLR trees, ensembles and classical classifiers/regressors.

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.

Root overlap and allocation of above- and belowground growth of European beech in pure and mixed stands of Douglas fir and Norway spruce

Site conditions and species identity have a combined effect on fine root growth of trees in pure and mixed stands. However, mechanisms that may contribute to this effect are rarely studied, even though they are essential to assess the potential of species to cope with climate change. This study examined fine root overlap and the linkage between fine root and stem growth of European beech (Fagus sylvatica) growing in pure and mixed stands with Douglas fir (Pseudotsuga menziesii) or Norway spruce (Picea abies) at two different study sites in northwestern Germany.The study sites represented substantially different soil and climate conditions. At each site, three stands, and at each stand, three pairs of trees were studied. In the pure beech stand, the pairs consisted of two beech trees, while in the mixed stands each pair was composed of a beech tree and a conifer. Between each pair, three evenly spaced soil cores were taken monthly throughout the growing season. In the pure beech stands, microsatellite markers were used to assign the fine roots to individual trees. Changes in stem diameter of beech were quantified and then upscaled to aboveground wood productivity with automatic high-resolution circumference dendrometers.We found that fine root overlap between neighboring trees varied independently of the distance between the paired trees or the stand types (pure versus mixed stands), indicating that there was no territorial competition. Aboveground wood productivity (wood NPP) and fine root productivity (root NPP) showed similar unimodal seasonal patterns, peaking in June. However, this pattern was more distinct for root NPP, and root NPP started earlier and lasted longer than wood NPP. The influence of site conditions on the variation in wood and root NPP of beech was stronger than that of stand type. Wood NPP was, as expected, higher at the richer site than at the poorer site. In contrast, root NPP was higher at the poorer than at the richer site.We concluded that beech can respond to limited resources not only above- but also belowground and that the negative relationship between above- and belowground growth across the study sites suggests an ‘optimal partitioning’ of growth under stress.

Joint Optimization of Device Placement and Model Partitioning for Cooperative DNN Inference in Heterogeneous Edge Computing

Joint Optimization of Device Placement and Model Partitioning for Cooperative DNN Inference in Heterogeneous Edge Computing

Optimal Service Area Partitioning for Wireless Communication Systems and a Multibeam Antenna with Contoured Beams for the Equipotential Coverage of This Area

Optimal Service Area Partitioning for Wireless Communication Systems and a Multibeam Antenna with Contoured Beams for the Equipotential Coverage of This Area

A Novel Multi-objective Synchronous Optimal Subarray Partition Method for Transmitting Array in Microwave Wireless Power Transmission

A Novel Multi-objective Synchronous Optimal Subarray Partition Method for Transmitting Array in Microwave Wireless Power Transmission

An Efficient and Scalable RFID Anti-Collision Algorithm on Optimal Partition and Collided Block Bit-Mapping

In RFID systems, many anti-collision algorithms, driven by the concept of rescheduling the response sequence between the reader and unidentified tags, have been put forward to solve tag collision problem, including ALOHA-based, tree-based and hybrid algorithms. In this paper, we propose a novel RFID anti-collision algorithm called EAQ-CBB, which adopts three main approaches: tag population estimation based on collided bit detection method, optimal partitions and trimmed query tree based on the strategy of collided block bit-mapping (QTCBB). The relatively accurate estimation of tag backlog and optimal partition ensure a great reduction of collisions in the initial phase. For each collided partition, a QTCBB process is introduced immediately, which eliminates all the empty slots and significantly reduces the collided slots. Simulation results show that EAQ-CBB performs good stability and scalability when the key parameters change. Compared with the existing algorithms, such as DFSA, QTI, T-GDFSA and CT, EAQ-CBB outperforms the others with high system throughput, low normalized latency and low normalized overhead at a low cost of energy, which makes it easier to be used widely in the efficient-aware and energy-aware applications.

Trade-off in the partitioning of recent photosynthate carbon under global change.

There may be trade-offs in the allocation patterns of recent photosynthetic carbon (RPC) allocation in response to environmental changes, with a greater proportion of RPC being directed towards compartments experiencing limited resource availability. Alternatively, the allocation of RPC could shift from sources to sinks as plants processing excess photosynthates. It prompts the question: Does the pattern of RPC allocation vary under global changes? If so, is this variation driven by optimal or by residual C allocation strategies? We conducted a meta-analysis by complicating 273 pairwise observations from 55 articles with 13 C or 14 C pulse or continuous labeling to assess the partitioning of RPC in biomass (leaf, stem, shoot, and root), soil pools (soil organic C, rhizosphere, and microbial biomass C) and CO2 fluxes under elevated CO2 (eCO2 ), warming, drought and nitrogen (N) addition. We propose that the increased allocation of RPC to belowground under sufficient CO2 results from the excretion of excess photosynthates. Warming led to a significant reduction in the percentage of RPC allocated to shoots, alongside an increase in roots allocation, although this was not statistically significant. This pattern is due to the reduced water availability resulting from warming. In conditions of drought, there was a notable increase in the partitioning of RPC to stems (+7.25%) and roots (+36.38%), indicative of a greater investment of RPC in roots for accessing water from deeper soil. Additionally, N addition led to a heightened allocation of RPC in leaves (+10.18%) and shoots (+5.78%), while reducing its partitioning in soil organic C (-8.92%). Contrary to the residual C partitioning observed under eCO2 , the alterations in RPC partitioning in response to warming, drought, and N supplementation are more comprehensively explained through the lens of optimal partitioning theory, showing a trade-off in the partitioning of RPC under global change.

A general approach analyzing transient dynamics in plant biomass allocation patterns

Allometric biomass allocation theory and optimal partitioning theory are the most important theoretical frameworks for explaining and predicting plant biomass allocation patterns. But their focus on equilibrium conditions does not advance our understanding of transient allocation patterns. To address this limitation, we develop a heuristic approach with a quantitative metric to theoretically analyze transient patterns of plant allocation of photosynthetic products to different plant organs. The approach is also used to ask how various factors can drive transient patterns. A case study is analyzed, showing how periodic perturbations of transient patterns of plant leaf and stem biomass can decrease or increase in response to plant height, crown diameter, and projected crown area. The predictions are consistent with global data on forest plants. The approach here addresses the limitations of optimal partitioning theory by revealing the variation in plant photosynthetic partitioning over short time scales. Given the central role of plant biomass allocation patterns for both empirical and theoretical studies, there is a large scope for applying this approach to improve estimations of carbon stock, and stabilized yields in forest management.

Serverless application composition leveraging function fusion: Theory and algorithms

Serverless computing is a novel cloud computing paradigm enabling flexible, cost-efficient and fine-granular development of cloud-native applications, although without any guarantees on scheduling or execution times. Thus, various high-level solutions have been proposed in recent years to find proper configurations of individual FaaS functions, while considering user-given QoS requirements. However, the ever-increasing complexity of invocation patterns among stateless functions, externalized management of intermediate states, and diverse public cloud resources pose new challenges to the composition of highly data-intensive serverless applications. In this paper, we fill this gap by proposing novel algorithms based on the emerging function fusion technique, along with the related cost/performance models of composite functions supporting implicit instance parallelization and internal state propagation. We prove the NP-completeness of the underlying latency-constrained tree partitioning problem, and design a bicriteria approximation scheme and a greedy heuristic to derive cost-efficient deployment configurations in polynomial time. With the help of extensive simulations using synthetic call graphs generated from public cloud traces, we demonstrate the applicability and superior runtime performance of our proposed methods compared to state-of-the-art solutions. In addition, we showcase that further cost-reduction of up to 3–6 % can be achieved compared to the optimal partitioning with the allowance of tolerable latency violations.

NOCAP: Near-Optimal Correlation-Aware Partitioning Joins

Storage-based joins are still commonly used today because the memory budget does not always scale with the data size. One of the many join algorithms developed that has been widely deployed and proven to be efficient is the Hybrid Hash Join (HHJ), which is designed to exploit any available memory to maximize the data that is joined directly in memory. However, HHJ cannot fully exploit detailed knowledge of the join attribute correlation distribution. In this paper, we show that given a correlation skew in the join attributes, HHJ partitions data in a suboptimal way. To do that, we derive the optimal partitioning using a new cost-based analysis of partitioning-based joins that is tailored for primary key - foreign key (PK-FK) joins, one of the most common join types. This optimal partitioning strategy has a high memory cost, thus, we further derive an approximate algorithm that has tunable memory cost and leads to near-optimal results. Our algorithm, termed NOCAP (Near-Optimal Correlation-Aware Partitioning) join, outperforms the state of the art for skewed correlations by up to 30%, and the textbook Grace Hash Join by up to 4×. Further, for a limited memory budget, NOCAP outperforms HHJ by up to 10%, even for uniform correlation. Overall, NOCAP dominates state-of-the-art algorithms and mimics the best algorithm for a memory budget varying from below √||relation|| to more than ||relation||.

Dynamic trajectory partition optimization method based on historical trajectory data

Partitioning dynamic trajectory data can improve the efficiency and accuracy of trajectory data processing, provide a foundation for trajectory data mining and analysis. However, with the continuous growth of trajectory data scales and the urgent demand for trajectory query efficiency and accuracy, partitioning methods have become crucial. The partitioning method of dynamic trajectory data faces significant challenges in terms of spatiotemporal trajectory locality, partition load balancing, and partition time. To address these challenges, we propose a method based on historical trajectory pre-partitioning, which can store data more effectively in distributed systems. We partition similar historical trajectory data to achieve preliminary partitioning of the data. In addition, we also construct a cost model to ensure that the workload of each partition is close to consistency. Extensive experiments have demonstrated the excellent partitioning efficiency and query efficiency achieved by our design compared to other partitioning methods.

Multiagent, Multitarget Path Planning in Markov Decision Processes

Missions for autonomous systems often require agents to visit multiple targets in complex operating conditions. This work considers the problem of visiting a set of targets in minimum time by a team of non-communicating agents in a Markov decision process (MDP). The single-agent problem is at least NP-complete by reducing it to a Hamiltonian path problem. We first discuss an optimal algorithm based on Bellman's optimality equation that is exponential in the number of target states. Then, we trade-off optimality for time complexity by presenting a suboptimal algorithm that is polynomial at each time step. We prove that the proposed algorithm generates optimal policies for certain classes of MDPs. Extending our procedure to the multi-agent case, we propose a target partitioning algorithm that approximately minimizes the expected time to visit the targets. We prove that our algorithm generates optimal partitions for clustered target scenarios. We present the performance of our algorithms on random MDPs and gridworld environments inspired by ocean dynamics. We show that our algorithms are much faster than the optimal procedure and more optimal than the currently available heuristic.

A DEA-based model for grouped internal carbon pricing: An analysis of a large coal producer

As a strategic lever, internal carbon pricing allows enterprises to cope with potential climate-related risks and motivate their low-carbon transformation. But internal carbon pricing, still in its early exploratory stage, lacks standard criteria for optimization. The traditional goal of cost minimization or profit maximization is not directly applicable to internal carbon pricing because internal payment for carbon emissions does not affect enterprises' aggregated costs or profits. How to optimize internal carbon prices to reduce carbon emissions more efficiently becomes an important issue. This study proposed a grouped internal carbon pricing method considering both internal carbon pricing and comprehensive efficiency. We found that there exists an optimal partition of internal units with corresponding differentiated carbon prices. Compared with other internal carbon pricing methods, the average efficiency of differentiated carbon pricing was significantly higher than the average efficiency of uniform carbon pricing. We then applied the method to a large coal producer with 16 subdivisions in China. The results showed that if the enterprise adopted the grouped internal carbon pricing under its current technology level, the carbon emissions would reach an optimal level, and its comprehensive efficiency would be significantly improved.

An efficient topology partitioning algorithm for system-level parallel simulation of mega satellite constellation communication networks

Satellite Internet, as an important component of the integrated space-ground information network, is a hot research hotspot nowadays. Many scholars have undertaken research in the areas of constellation networking design, network protocol design, and communication performance assessment, and their main research tool is software simulation. Traditional stand-alone network simulation simulators based on OPNET or NS3 are constrained in the simulation efficiency of mega satellite networks because of the limitations of computer hardware conditions and software performance. Based on the above characteristics, we propose a parallel network simulation architecture based on low correlation between different areas of the global satellite network, and in order to improve the parallel network simulation performance, the network topology needs to be divided effectively. Therefore, firstly we consider CPU and memory resource consumption as a measure of topology partitioning performance indicators, propose a resource assessment algorithm and use the result of this assessment as the topology partitioning optimization objective; secondly, we propose a load balancing based intelligent topology partitioning algorithm (LBTP); thirdly, we propose a time slice algorithm (TSA) for parallel simulation in each time cycle. To demonstrate the algorithm proposed in this paper, we built a simulation platform based on the combination of STK (Satellite Tool Kit), OPNET and Proxmox VE, and experimentally verified that the proposed architecture and algorithm significantly improve the simulation efficiency.

Nunchaku: optimally partitioning data into piece-wise contiguous segments.

When analyzing 1D time series, scientists are often interested in identifying regions where one variable depends linearly on the other. Typically, they use an ad hoc and therefore often subjective method to do so. Here, we develop a statistically rigorous, Bayesian approach to infer the optimal partitioning of a dataset not only into contiguous piece-wise linear segments, but also into contiguous segments described by linear combinations of arbitrary basis functions. We therefore present a general solution to the problem of identifying discontinuous change points. Focusing on microbial growth, we use the algorithm to find the range of optical density where this density is linearly proportional to the number of cells and to automatically find the regions of exponential growth for both Escherichia coli and Saccharomyces cerevisiae. For budding yeast, we consequently are able to infer the Monod constant for growth on fructose. Our algorithm lends itself to automation and high throughput studies, increases reproducibility, and should facilitate data analyses for a broad range of scientists. The corresponding Python package, entitled Nunchaku, is available at PyPI: https://pypi.org/project/nunchaku.

Remaining useful life prediction of ball screw based on integrating preload and precision

Ball screw remaining useful life (RUL) prediction is of great interest to industry and academia. However, the lack of a reliable prediction model limits accuracy. To address this, a hybrid method that combines physical-based and data-driven methods is proposed. A novel integrated index is developed to capture wear degradation by integrating the preload and precision parameters, and the optimum partitioning method is used for wear stage categorization. A physical-based method of a two-stage empirical model is constructed to characterize the randomness and nonlinearity of the degradation process. Model parameters are initialized and updated using particle filtering (PF) through a data-driven method for RUL prediction. To address discontinuous predictions in the empirical model, the random forest with PF (RF-PF) method is employed. The effectiveness of this approach is evaluated through experiments and comparisons with other methods.