Space Partitioning Research Articles

On the optimality of DIA-estimators: theory and applications

In this contribution, we introduce, in analogy to penalized ambiguity resolution, the concept of penalized misclosure space partitioning, with the goal of directing the performance of the DIA-estimator towards its application-dependent tolerable risk objectives. We assign penalty functions to each of the decision regions in misclosure space and use the distribution of the misclosure vector to determine the optimal partitioning by minimizing the mean penalty. As each minimum mean penalty partitioning depends on the given penalty functions, different choices can be made, in dependence of the application. For the DIA-estimator, we introduce a special set of penalty functions that penalize its unwanted outcomes. It is shown how this set allows one to construct the optimal DIA-estimator, being the estimator that within its class has the largest probability of lying inside a user specified tolerance region. Further elaboration shows how these penalty functions are driven by the influential biases of the different hypotheses and how they can be used operationally. Hereby the option is included of extending the misclosure partitioning with an additional undecided region to accommodate situations when it will be hard to discriminate between some of the hypotheses or when identification is unconvincing. By extending the analogy with integer ambiguity resolution to that of integer-equivariant ambiguity resolution, we also introduce the maximum probability estimator within the similar larger class.

A layer assigned probability space partition method for structural small failure probability problem

The Physical Synthesis Method (PSM) stands out as a robust framework for conducting structural reliability analyses due to its clear conceptual foundation. However, this approach often necessitates significant computational resources when addressing scenarios with small failure probabilities. In response to this challenge, this study introduces a layer assigned probability space partition method designed to identify pivotal points based on the ultimate bearing capacity failure criterion of structural components within the PSM framework. Drawing inspiration from Harbitz's β-sphere, this method effectively utilizes the minimum reliability index of components to discern essential representative points within the probability space, thus streamlining computations. The efficacy of this approach is showcased through two case studies: a simply supported beam and a six-story reinforced concrete frame. The outcomes demonstrate that the proposed method, when integrated with PSM, exhibits a substantial enhancement in efficiency compared to the conventional Monte Carlo method. Besides, under equivalent computational resources, it achieves superior computational accuracy compared to the importance sampling method, particularly in scenarios with small failure probabilities. Furthermore, by introducing the notion of a common safe domain, this method addresses challenges in structural reliability analyses involving multiple failure surfaces.

Sensitivity analysis of aircraft structural fatigue reliability under mixed uncertainty

Fatigue is the main failure mode of the structure. The aircraft structure is subject to multi-level cyclic loading, which is prone to fatigue damage, reduces reliability, and affects flight safety. Various uncertainties are inevitably associated with the factors related to the fatigue performance of the structure. In particular, for the variables with insufficient information, their uncertainties are hard to describe by the probability density function. In this paper, these variables are treated as interval variables. The sensitivity analysis of the aircraft structure fatigue reliability model under mixed uncertainties is studied. On the basis of the definition of the distance between interval numbers, the interval distance indexes are proposed as a global sensitivity measure for a mixed random-interval model system. To reduce the computational cost, the method combining the space partition with unscented transformation (SP-UT) is used to calculate the proposed indexes. Lastly, the proposed indexes and method are applied to solve the aircraft structure fatigue problem. Compared with the traditional MCS method, the proposed method has proved to be more conducive and efficient.

Incremental Fuzzy Clustering-Based Neural Networks Driven With the Aid of Dynamic Input Space Partition and Quasi-Fuzzy Local Models.

Fuzzy clustering-based neural networks (FCNNs) based on information granulation techniques have been shown to be effective Takagi-Sugeno (TS)-type fuzzy models. However, the existing FCNNs could not cope well with sequential learning tasks. In this study, we introduce incremental FCNNs (IFCNNs), which could dynamically update themselves whenever new learning data (e.g., single datum or block data) are incorporated into the dataset. Specifically, we employ dynamic (incremental) fuzzy C-means (FCMs) clustering algorithms to reveal a structure in data and divide the entire input space into several subregions. In the aforementioned partition, the dynamic FCM adaptively adjusts the position of its prototypes by using sequential data. Due to the time-sharing arrival of training data, compared with batch learning models, incremental learning methods may lose classification (prediction) accuracy. In order to tackle this challenge, we utilize quasi-fuzzy local models (QFLMs) based on modified Schmidt neural networks to replace the popular linear functions in TS-type fuzzy models to refine and enhance the ability to represent the behavior of fuzzy subspaces. Meanwhile, the recursive least square error (LSE) estimation is utilized to update the weights of QFLMs from one-by-one or block-by-block (fixed or varying block size) learning data. In addition, the L2 regularization is considered to ameliorate the deterioration of generalization abilities caused by potential overfitting when carrying out weight estimation. The proposed method leads to the construction of FCNNs in a new way, which can effectively deal with incremental data as well as deliver sound generalization capability. Extensive machine-learning datasets and a real-world application are employed to show the validity and performance of the presented methods. From the experimental results, we show that the proposal can maintain sound classification accuracy when effectively processing sequential data.

Spatial partitioning of terrestrial precipitation reveals varying dataset agreement across different environments

The study of the water cycle at planetary scale is crucial for our understanding of large-scale climatic processes. However, very little is known about how terrestrial precipitation is distributed across different environments. In this study, we address this gap by employing a 17-dataset ensemble to provide, for the first time, precipitation estimates over a suite of land cover types, biomes, elevation zones, and precipitation intensity classes. We estimate annual terrestrial precipitation at approximately 114,000 ± 9400 km3, with about 70% falling over tropical, subtropical and temperate regions. Our results highlight substantial inconsistencies, mainly, over the arid and the mountainous areas. To quantify the overall discrepancies, we utilize the concept of dataset agreement and then explore the pairwise relationships among the datasets in terms of “genealogy”, concurrency, and distance. The resulting uncertainty-based partitioning demonstrates how precipitation is distributed over a wide range of environments and improves our understanding on how their conditions influence observational fidelity.

A Novel Fast and Body-Fitted Particle Generation Technique for Large-Scale SPH Simulations

Particle generation is important for particle-based methods. The reasonable initial particle distribution has a profound impact on the computational accuracy and the stability of particle-based methods. We propose a particle generation method that generates the body-fitted and uniform particles fast. This method first generates initial body-fitted and locally uniformly distributed particles on the geometric facets, following the spatial partitioning, particle hashing, particle sorting, and particle merging. The surface particles become body-fitted and uniform. In addition, we combine several other generation methods of boundary-level particles and inner particles to provide a unified framework for the pre-processing process of the smoothed particle hydrodynamics (SPH) method. Some particle generation examples of complex geometric models demonstrate the feasibility and effectiveness of this method. The proposed method can generate large-scale particles of complex geometric models, improve the handling capacity of pre-processing techniques, and keep up with the scale of solvers.

Convergence Diagnostics for Entity Resolution

Entity resolution is the process of merging and removing duplicate records from multiple data sources, often in the absence of unique identifiers. Bayesian models for entity resolution allow one to include a priori information, quantify uncertainty in important applications, and directly estimate a partition of the records. Markov chain Monte Carlo (MCMC) sampling is the primary computational method for approximate posterior inference in this setting, but due to the high dimensionality of the space of partitions, there are no agreed upon standards for diagnosing nonconvergence of MCMC sampling. In this article, we review Bayesian entity resolution, with a focus on the specific challenges that it poses for the convergence of a Markov chain. We review prior methods for convergence diagnostics, discussing their weaknesses. We provide recommendations for using MCMC sampling for Bayesian entity resolution, focusing on the use of modern diagnostics that are commonplace in applied Bayesian statistics. Using simulated data, we find that a commonly used Gibbs sampler performs poorly compared with two alternatives.

О методах исследования динамических систем

Wide application of dynamical systems resulted in designing many various methods for investigations, both analytical and computer-oriented ones. In this paper we consider methods based on ideas of symbolic dynamics, and discuss the application of dynamical systems for solving identification and prognosis problems. The representation of the system dynamics by an oriented graph constructed in accordance with the system and a finite partition of the phase space gives a possibility to matchtrajectories paths on the graph. By this method one may construct approximation to invariant sets and invariant measures, and the Morse spectrum as well. Using dynamical systems in identification problems is consideredon examples of probability chainsfor the modeling social and economic resource distribution, and the method of nonlinear dynamics for reconstruction of an attractor on a given time series.

How electrons still guard the space: Electron number distribution functions based on QTAIM∩ELF intersections.

Despite the importance of the one-particle picture provided by the orbital paradigm, a rigorous understanding of the spatial distribution of electrons in molecules is still of paramount importance to chemistry. Considerable progress has been made following the introduction of topological approaches, capable of partitioning space into chemically meaningful regions. They usually provide atomic partitions, for example, through the attraction basins of the electron density in the quantum theory of atoms in molecules (QTAIM) or electron-pair decompositions, as in the case of the electron localization function (ELF). In both cases, the so-called electron distribution functions (EDFs) provide a rich statistical description of the electron distribution in these spatial domains. Here, we take the EDF concept to a new fine-grained limit by calculating EDFs in the QTAIM ∩ ELF intersection domains. As shown in AHn systems based on main group elements, as well as in the CO, NO, and BeO molecules, this approach provides an exquisitely detailed picture of the electron distribution in molecules, allowing for an insightful combination of the distribution of electrons between Lewis entities (such as bonds and lone pairs) and atoms at the same time. Besides mean-field calculations, we also explore the impact of electron correlation through Hartree-Fock (HF), density functional theory (DFT) (B3LYP), and CASSCF calculations.

To lose is to win: Long‐term co‐occurrence of two asexual populations realized by a dormant strategy of the inferior competitor

Abstract Asexual organisms are ubiquitous. While being members of a single species with the same ecological requirements, multiple asexual genotypes within a species are often found in a single habitat. Niche partitioning in time and space among genotypes has been proposed to explain this phenomenon. However, it is not clear whether these different genotypes co‐occur in the long term. Therefore, we examined the population dynamics of two asexual Daphnia cf. pulex genotypes (JPN1 and JPN2) over 9 years in a small mountain lake. These two genotypes consistently occurred in the same seasons and layers, suggesting that niche partitioning cannot explain their long‐term co‐occurrence. The abundance of JPN1 was typically higher in most years. However, the abundance of dormant eggs in lake sediments was at the same level between the genotypes. Results of a laboratory experiment showed that JPN1 competitively excluded JPN2. However, many JPN2 individuals produced dormant eggs before JPN1 competitively excluded them from the experiment. Furthermore, the competitively inferior JPN2 produced dormant eggs abundantly in the medium containing a crowding cue from JPN1 while no such trend was observed for JPN1. These results showed that a competitively inferior asexual genotype could maintain a population with a competitively superior genotype for a long period of time because it had the ability to detect an increase in competitors and produce dormant eggs each year before being competitively eliminated. Based on these results, we suggest that the variation in genotype‐specific response in dormant egg production to environmental change plays a key role in the long‐term co‐occurrence of different asexual genotypes in single habitats. Read the free Plain Language Summary for this article on the Journal blog.

Unraveling microbial community structure–function relationships in the horizontal and vertical spatial dimensions in extreme environments

A fundamental challenge in soil macroecology is to understand how microbial community structure shapes ecosystem function along environmental gradients of the land surface at broad spatial scales (i.e. the horizontal dimension). However, little is known about microbial community structure–function relationships in extreme environments along environmental gradients of soil depth at finer spatial scales (i.e. the vertical dimension). Here, we propose a general spatial dimension partitioning approach for assessing the patterns and drivers of soil microbial community structure–function relationships across horizontal and vertical spatial gradients simultaneously. We leveraged a 200‐km desert soil salinity gradient created by a 12‐year saline‐water irrigation in the Tarim basin of Taklamakan Desert. Specifically, using a general linear model, hierarchical variance partitioning, and a path model, we assessed the patterns and key ecological processes controlling spatial turnover in microbial community structure (i.e. β‐diversity) and enzymatic activity relevant to carbon, nitrogen, and phosphorus cycling along soil salinity gradients across study sites (horizontal dimension) and soil depths (vertical dimension). We found a decoupled relationship between soil microbial β‐diversity and enzymatic activity. Differences in soil depth (on the scale of meters) were as important as geographic distance (on the scale of kilometers) in shaping bacterial and fungal β‐diversity. However, the vertical and horizontal turnover in enzymatic activity was largely attributed to an increase in the heterogeneity of soil properties, such as soil texture, water content, and pH. Our findings suggest that dispersal limitation controls microbial community β‐diversity and that environmental heterogeneity, rather than soil salinization, controls enzymatic activity. Taken together, this work highlights that in the face of ongoing environmental alterations, soil depth is an under‐explored spatial dimension that must be considered in soil conservation efforts as a critical factor in determining microbial community structure and function in extreme environments.

Optimization of Cabin Virus Transmission Suppression Technology Based on Hanging Curtain Physical Isolation

This study presents an innovative physical isolation measure for commercial scenarios, namely, hanging curtains, to prevent the spread of respiratory infections. Using computational fluid dynamics simulation techniques, the closed spaces within cruise cabins were modeled and numerically analyzed, focusing on the dispersion characteristics of droplets. Additionally, orthogonal methods were employed to investigate various arrangements of hanging curtains and their effects on droplet dispersion based on spatial positioning. The research findings indicated that hanging curtains can effectively alter the airflow within a space, realizing the innovative concept of localized pollutant containment. It was found that the spatial partitioning method based on the location of individuals contributes more to reducing droplet dispersion than other methods. Moreover, the sag height of curtains emerges as the most influential factor on individual infection risk, while the scheme for hanging curtain positions has the least impact. Finally, the optimal configuration recommendation is provided: a curtain bottom coordinate of Z = 2.3 m and a top coordinate of Z = 2.8 m when the infection source was positioned at the center of the space. This configuration has also been validated by varying the location of the infection source. The research findings provide valuable insights for formulating preventive measures for passengers on cruise ships and for pandemic control in similar scenarios.

An algorithm for constructing spatial vector data storage based on KD-tree and density estimation

With the widespread application of spatial vector data in various fields, this paper proposes a novel algorithm for constructing spatial vector data storage. The algorithm is based on KD-tree and density estimation techniques, aiming to improve the storage efficiency and query performance of large-scale spatial vector data. The algorithm first efficiently organizes spatial vector data using KD-tree, and then performs density estimation based on the Locality Sensitive Hashing (LSH) algorithm. Algorithm optimizations for spatial partitioning are applied to the KD-tree construction algorithm, reducing the search range during queries and improving retrieval speed. By testing with Green Tide data, the algorithm based on KD-tree and density estimation demonstrates higher query efficiency and better scalability across multiple test datasets. Particularly, when dealing with large-scale datasets characterized by non-uniform data distributions, this algorithm significantly improves data retrieval speed while maintaining low storage overhead.

Machine Failure Prediction Using Multilabel Classification Methods

Early detection of machine failure is crucial in every industrial setting as it may prevent unexpected process downtimes as well as system failures. However, machine learning (ML) models are increasingly being utilized to forecast system failures in industrial maintenance, and among them, multilabel classification techniques act as efficient methods. Therefore, this study analyzed machine failure data with five types of machine failures. Initially, a feature selection approach was also carried out in this study to determine the variables which directly cause machine failure. Furthermore, multilabel k-nearest neighbours (MLkNN), multilabel adaptive resonance associative map (MLARAM), and multilabel twin support vector machine classifier (MLTSVM) in adapted algorithms, Binary Relevance, ClassifierChain, and LabelPowerSet in problem transformation approaches, and Random Label Space Partitioning with Label Powerset (RakelD) in ensemble classifiers were employed. To train these models, both the original data set as well as data frame after the feature selection was used, and hamming loss, accuracy, macro, and micro averages were calculated for each of these classifiers. According to the results, MLkNN in adapted algorithms and LabelPowerset in problem transformation approaches performed better than other classifiers used in this study. Therefore, it can be concluded that MLkNN and LabelPowerset could be used to classify multilabel with positive results. KEYWORDS: adapted algorithms, ensemble classifiers, feature selection, machine failure, machine learning, multilabel classification, problem transformation.

Interval type-2 possibilistic picture C-means clustering incorporating local information for noisy image segmentation

Picture fuzzy C-means clustering is a novel computational intelligence method that has some advantages over fuzzy clustering in pattern analysis and machine intelligence. However, picture fuzzy clustering is easily affected by noise and weighting exponent, which seriously limits its widespread application. To address this issue, this paper proposes a new robust possibilistic clustering method called “interval type-2 possibilistic picture C-means clustering with local information”. This method combines interval type-2 fuzzy sets with possibilistic C-means clustering based on picture fuzzy sets, strengthening the noise resistance of picture fuzzy clustering. Firstly, this paper creatively extends an improved possibilistic clustering with double weighing exponents to picture fuzzy sets, solving the problem of consistency clustering in existing possibilistic picture clustering. Second, this paper originally introduces a new picture local information factor in possibilistic picture clustering and further enhances the anti-noise robustness of the method by using spatial possibilistic picture partition information. Finally, this paper skillfully extends this clustering method to interval type-2 fuzzy sets, which can handle more flexibly high-order uncertainties than type-1 clustering method. Experimental results indicate that this proposed method has better segmentation performance and stronger noise suppression ability compared with existing picture fuzzy clustering and interval type-2 fuzzy clustering. In summary, this work has made significant contributions to the development of picture fuzzy clustering theory and its applications.

Performance modeling and running strategy of parallel cdugksFOAM program

The cdugksFOAM program realizes the physical space grid and the velocity space grid in parallel at the same time. Its distinguishing feature lies in its potential for large-scale parallelism. However, the running time of the cdugksFOAM program is significantly dependent on the number of physical and velocity space partitions. In order to find the optimal partitioning strategies for a specific CFD problem running on a parallel computer, we performed performance modeling of the cdugksFOAM program. Firstly, we proposed a floating-point operations model, a MPI communication volume model, and a memory consumption model. Based on these models, we established a Roofline model to predict the computational time, and a model to predict communication time. According to the computational time model and the communication time model, the execution time model was proposed and its effectiveness was verified with two cases. Finally, the optimal running strategy that minimizes the product of the number of computing nodes and execution time was identified, providing meaningful guidance for the economic execution of the program.

Learning Only When It Matters: Cost-Aware Long-Tailed Classification

Most current long-tailed classification approaches assume the cost-agnostic scenario, where the training distribution of classes is long-tailed while the testing distribution of classes is balanced. Meanwhile, the misclassification costs of all instances are the same. On the other hand, in many real-world applications, it is more proper to assume that the training and testing distributions of classes are the same, while the misclassification cost of tail-class instances is varied. In this work, we model such a scenario as cost-aware long-tailed classification, in which the identification of high-cost tail instances and focusing learning on them thereafter is essential. In consequence, we propose the learning strategy of augmenting new instances based on adaptive region partition in the feature space. We conduct theoretical analysis to show that under the assumption that the feature-space distance and the misclassification cost are correlated, the identification of high-cost tail instances can be realized by building region partitions with a low variance of risk within each region. The resulting AugARP approach could significantly outperform baseline approaches on both benchmark datasets and real-world product sales datasets.

Convolutional Channel-Wise Competitive Learning for the Forward-Forward Algorithm

The Forward-Forward (FF) Algorithm has been recently proposed to alleviate the issues of backpropagation (BP) commonly used to train deep neural networks. However, its current formulation exhibits limitations such as the generation of negative data, slower convergence, and inadequate performance on complex tasks. In this paper we take the main ideas of FF and improve them by leveraging channel-wise competitive learning in the context of convolutional neural networks for image classification tasks. A layer-wise loss function is introduced that promotes competitive learning and eliminates the need for negative data construction. To enhance both the learning of compositional features and feature space partitioning, a channel-wise feature separator and extractor block is proposed that complements the competitive learning process. Our method outperforms recent FF-based models on image classification tasks, achieving testing errors of 0.58%, 7.69%, 21.89%, and 48.77% on MNIST, Fashion-MNIST, CIFAR-10 and CIFAR-100 respectively. Our approach bridges the performance gap between FF learning and BP methods, indicating the potential of our proposed approach to learn useful representations in a layer-wise modular fashion, enabling more efficient and flexible learning. Our source code and supplementary material are available at https://github.com/andreaspapac/CwComp.

Biomechanical adaptations enable phoretic mite species to occupy distinct spatial niches on host burying beetles.

Niche theory predicts that ecologically similar species coexist by minimizing interspecific competition through niche partitioning. Therefore, understanding the mechanisms of niche partitioning is essential for predicting interactions and coexistence between competing organisms. Here, we study two phoretic mite species, Poecilochirus carabi and Macrocheles nataliae that coexist on the same host burying beetle Nicrophorus vespilloides and use it to 'hitchhike' between reproductive sites. Field observations revealed clear spatial partitioning between species in distinct host body parts. Poecilochirus carabi preferred the ventral side of the thorax, whereas M. nataliae were exclusively found ventrally at the hairy base of the abdomen. Experimental manipulations of mite density showed that each species preferred these body parts, largely regardless of the density of the other mite species on the host beetle. Force measurements indicated that this spatial distribution is mediated by biomechanical adaptations, because each mite species required more force to be removed from their preferred location on the beetle. While P. carabi attached with large adhesive pads to the smooth thorax cuticle, M. nataliae gripped abdominal setae with their chelicerae. Our results show that specialist biomechanical adaptations for attachment can mediate spatial niche partitioning among species sharing the same host.

Research on charging demands of commercial electric vehicles based on Voronoi diagram and spatial econometrics model: An empirical study in Chongqing China

In order to address the mismatch between the current charging demand of electric vehicles and the layout of charging stations, this paper collects multi-source heterogeneous data that may affect charging demand, and explores their spatiotemporal distributions in depth. Then, this paper proposes a Voronoi polygon spatial partitioning method based on charging demand clustering and two spatial econometric models, spatial lag model (SLM) and spatial error model (SEM), to quantitatively analyze the influences of various elements on charging demands. Empirical research in Chongqing, China reveals that the spatiotemporal distribution of charging demand is uneven, with peak areas and periods for charging, and the division of Voronoi polygon can better reflect the spatial heterogeneity of charging demands than regular grid division. The positive factors include the low SOC, parking lot density, population density, and road network density, especially the low SOC and parking lot density, and the negative items contain consumption related Point Of Interest (POI), tourism related POI, and transportation hub related POI. Among them, population density and road network density, as static data, have similar influences on charging demands at different intervals, while the impact of other factors on charging demand varies with periods, with obvious peak-valley characteristics. There is spatial dependence and lag effect between charging demands within polygons, causing SLM outperforms SEM. The research results are beneficial for the rational siting and optimization of charging stations.