Non-uniform Partition Research Articles

On the convergence of a linearly implicit finite element method for the nonlinear Schrödinger equation

AbstractWe consider a model initial‐ and Dirichlet boundary–value problem for a nonlinear Schrödinger equation in two and three space dimensions. The solution to the problem is approximated by a conservative numerical method consisting of a standard conforming finite element space discretization and a second‐order, linearly implicit time stepping, yielding approximations at the nodes and at the midpoints of a nonuniform partition of the time interval. We investigate the convergence of the method by deriving optimal‐order error estimates in the and the norm, under certain assumptions on the partition of the time interval and avoiding the enforcement of a Courant‐Friedrichs‐Lewy (CFL) condition between the space mesh size and the time step sizes.

An autonomic parallel strategy for exhaustive search tree algorithms on shared or heterogeneous systems

SummaryBacktracking branch‐and‐prune (BP) algorithms and their variants are exhaustive search tree techniques widely employed to solve optimization problems in many scientific areas. However, they characteristically often demand significant amounts of computing power for problem sizes representative of real‐world scenarios. Given that their search domains can often be partitioned, these algorithms are frequently designed to execute in parallel by harnessing distributed computing systems. However, to achieve efficient parallel execution times, an effective strategy is required to balance the nonuniform partition workloads across the available resources. Furthermore, with the increasing integration of servers with heterogeneous resources and the adoption of resource sharing, balancing workloads is becoming complex. This paper proposes a strategy to execute parallel BP algorithms more efficiently on even shared or heterogeneous distributed systems. The approach integrates a self‐adjusting dynamic partitioning method in the BP algorithm with a dynamic scheduler, provided by an application middleware, which manages the parallel execution while addressing any issues of imbalance. Empirical results indicate better scalability with efficiencies above 90% for instances of an application case study for the discretizable molecular distance geometry problem (DMDGP). Improvements of up to 38% were obtained in execution speed‐ups compared to a more traditional parallel BP implementation for DMDGP.

Adaptive non-uniform partition algorithm based on linear canonical transform

This paper proposes a new signal representation method of adaptive non-uniform partition algorithm based on linear canonical transform, which can partition the signal in independent regions to further improve the reconstruction quality of the signal thus extending its application range. That means the partial signal in each sub-region can be approximated by a determined linear canonical transform series after applying the least squares approximation. The partition process is guided by a set control error so that it can more effectively reflect the regional characteristics of the signal. Compared with the signal reconstructed effect by both the original adaptive non-uniform partition algorithm and Fourier transform through simulation experiments, the results prove that the proposed algorithm has better performance in signal representation and reconstruction under the same approximation condition. On the other hand, through the comparison of simulation experiments with wavelet transform and the original rectangular non-uniform partition algorithm for one-dimensional signal denoising, it can be concluded that the proposed method has certain potential in signal denoising.

Image representation method based on Gaussian function and non-uniform partition

Image representation method based on Gaussian function and non-uniform partition

New Algorithm to Solve Mixed Integer Quadratically Constrained Quadratic Programming Problems Using Piecewise Linear Approximation

Techniques and methods of linear optimization underwent a significant improvement in the 20th century which led to the development of reliable mixed integer linear programming (MILP) solvers. It would be useful if these solvers could handle mixed integer nonlinear programming (MINLP) problems. Piecewise linear approximation (PLA) is one of most popular methods used to transform nonlinear problems into linear ones. This paper will introduce PLA with brief a background and literature review, followed by describing our contribution before presenting the results of computational experiments and our findings. The goals of this paper are (a) improving PLA models by using nonuniform domain partitioning, and (b) proposing an idea of applying PLA partially on MINLP problems, making them easier to handle. The computational experiments were done using quadratically constrained quadratic programming (QCQP) and MIQCQP and they showed that problems under PLA with nonuniform partition resulted in more accurate solutions and required less time compared to PLA with uniform partition.

Computational Experience with Piecewise Linear Relaxations for Petroleum Refinery Planning

Refinery planning optimization is a challenging problem as regards handling the nonconvex bilinearity, mainly due to pooling operations in processes such as crude oil distillation and product blending. This work investigated the performance of several representative piecewise linear (or piecewise affine) relaxation schemes (referred to as McCormick, bm, nf5, and nf6t) and de (which is a new approach proposed based on eigenvector decomposition) that mainly give rise to mixed-integer optimization programs to convexify a bilinear term using predetermined univariate partitioning for instances of uniform and non-uniform partition sizes. The computational results showed that applying these schemes improves the relaxation tightness compared to only applying convex and concave envelopes as estimators. Uniform partition sizes typically perform better in terms of relaxation solution quality and convergence behavior. It was also seen that there is a limit on the number of partitions that contribute to relaxation tightness, which does not necessarily correspond to a larger number of partitions, while a direct relationship between relaxation size and tightness does not always hold for non-uniform partition sizes.

NN Search based on Non-uniform Space Partition on Air

It is one of most important challenges in information services based on location to support a huge number of clients to process the NN query for a given query point. A scheme of NN query processing based on wireless data broadcasting is an effective way to overcome the challenge. In this paper, we propose an indexing scheme NSPI (Non-uniform Space Partition Index) for quick NN search over wireless data broadcasting. For implementing the aim, we use a non-uniform spatial partition and provide an index based on the partition for equidistance between indexes on the wireless channel. The index scheme enables the clients to process NN quickly by lessening the time for the clients to meet the index on the channel. To show the effectiveness of the proposed scheme, we compare the access time and tuning time of the clients with existing indexing schemes by simulation studies. The proposed NSPI shows shorter access time than the other existing scheme. Also, NSPI outperforms in the aspect of tuning time than the others.

Thermal modelling of cutting tool temperatures and heat partition in orthogonal machining of high-strength alloy steel

Cutting temperatures and heat partition into the cutting tool are critical factors that significantly affect tool life and part accuracy during metal removal operations, especially in dry machining. Among many thermal modelling studies, uniform heat partition ratio, and/or uniform heat intensity along the tool-chip interface are frequently assumed. This assumption is not valid in actual machining and can lead to erroneous estimated results in the presence of sticking and sliding friction zones. Therefore, it is necessary to accurately predict the cutting tool temperature and heat partition during machining. This paper presents an analytical thermal modelling approach which considers the combined effect of the primary and the secondary heat sources and determines the temperature rise and non-uniform heat partition ratio along the tool-chip interface. Cutting tests were conducted on AISI/SAE 4140 high-strength alloy steel using carbide cutting tools over a wide range of cutting speeds. Cutting temperatures were measured experimentally using an infrared thermal imaging camera. Experimentally established sticking and sliding friction regions were used to evaluate non-uniform frictional heat intensity along the tool-chip interface. The temperature matching condition along the tool-chip interface leads to the solution of distributed non-uniform heat partition ratio by solving a set of linear equations through programming in MATLAB®. Experimental results show to be consistent well with those obtained from the thermal model, yielding a relative difference of predicted average tool-chip interface temperature from −0.8% to 6.3%. It is found that average heat partition into the cutting tool ( RT) varies from 35% down to 15% for the entire range of cutting speeds. These results suggest that, to address the thermal problem in metal cutting, the research and development of tooling should also focus on reducing friction on the tool rake face in addition to the contribution of the combined effect of primary and secondary heat sources on temperature rise at the tool-chip interface.

A clustering algorithm based on nonuniform partition for WSNs

Abstract Wireless sensor networks (WSNs) have great application potential in partition parameter observation, such as forest fire detection. Due to the limited battery capacity of sensor nodes, how to reduce energy consumption is an important technical challenge. In this paper, we propose an energy efficient routing algorithm of adaptive double cluster head (CH) based on nonuniform partition for WSN. Firstly, according to the distance information from the base station (BS) to every sensor node, the network is divided into several uneven partitions. Secondly, CH is selected for each partition as the primary cluster head (PCH). Because of the cluster-level routing, the CHs close to the BS need to forward more data than the CHs in other areas, which consumes more energy. Therefore, an adaptive double CH method can be used to generate a secondary cluster head (SCH) in the cluster near the BS according to the parameters. Finally, the PCH is responsible for data collection, data integration, and data transmission. while the SCH is in charge of data routing. Simulation results show that the proposed algorithm can reduce the energy consumption and extend the life of the WSNs, compared with LEACH protocol and the HEED protocol.

Fine-Grained Query Authorization With Integrity Verification Over Encrypted Spatial Data in Cloud Storage

In this article, a fine-grained query authorization scheme with integrity verification is proposed over encrypted spatial data for location-based services (LBS). The fine-grained query authorization is enabled based on a distribution of the spatial data by employing a non-uniform partition in the spatial domain to generate a density-based space filling curve (DSC), which can be used to generate index values for querying and transformation keys. The transformation keys can be used to generate query tokens for a secure spatial query as well as construct a transformation key tree whose subtree can be distributed by the LBS provider to an authorized user as transformation key for query tokens generation. Furthermore, the proposed scheme constructs a Merkle quad tree (MQ-tree) to support integrity verification by aggregating a digest of the spatial data based on the DSC and employing the MQ-tree as a verification structure. The LBS provider can share a subtree of the MQ-tree to authorized user as his verification structure, which corresponds to the transformation key of the authorized user. In this way, the authorized user can only generate the valid query tokens and verify the query results in his authorized region. The security properties of the proposed scheme is discussed, and extensive experimental results demonstrate the high efficiency of verification structure generation and verification operations.

MT-IVSN: a novel model for vehicle re-identification

Image re-identification is usually used to find specific images from image libraries or video sequences. In recent years, convolutional neural networks have gradually become the dominant method in this field. In this paper, a Multitask Identification-Verification Siamese Network for vehicles is proposed, which combines color feature vectors with the inherent structure, category and other attributes of the vehicle. A vehicle 2D structural model and a method of image viewpoint normalization are also presented to ensure the high consistency of features in the expression of images from different angles. In addition, based on the vehicle 2D structural model, a dynamic annular non-uniform partition color super-pixel sampling strategy for vehicle face is investigated to construct a color feature vector. In the experiments, the proposed model and method are evaluated on the public vehicles and VeRi datasets. The experimental results show that the proposed method and model have made great progress.

Effects of non-uniform porosity on thermochemical performance of solar driven methane reforming

As one of the effective methods for solving the greenhouse problem, methane reforming has received increasing attention. The performance of a reactor is strongly influenced by the foam structure with different parameters. In this study, the idea of non-uniform partition design of porosity (an expansion kind of hierarchical porous structure) in a porous media reactor was put forward and investigated. The heat and mass transfer phenomena and thermochemical properties of methane reforming under high convergence solar radiation were numerically studied. Finite volume method coupled with thermochemical kinetics is considered to solve this problem. Based on a constant pore size, the porosity of the porous medium is divided into two layers and combined in different forms in an axial direction. The effects of non-uniform porosity on thermochemical performance of solar driven methane reforming are analyzed and an optimization method for non-uniform porosity is proposed. The results show that methane conversion in a reactor with uniform porous media increases with growth up of the porosity. In addition, a reactor with non-uniform porous media exhibits better thermochemical performance and reforming performance compared to one with uniform porous media. Finally, different non-uniform partitions have an impact on methane conversion. When the porosity is constant, methane conversion decreases with an increase of the length of the first layer of porous media, and the maximum methane conversion (82.42%) was achieved at L1 = 0.01 m with φ1 = 0.75, φ2 = 0.9.

Simplification of locomotive running gear three-dimensional point cloud based on non-uniform division

The 3D point cloud data obtained from the laser line structured light scanner has redundancy, and a point cloud simplification algorithm based on the two order non-uniform partition is designed and implemented to deal with locomotive running department in this paper. First, according to the intrinsic shape signature (ISS), the point cloud normal vector of the detected object are estimated and the feature points of the point cloud are extracted. Then, according to the distribution of the feature point cloud, the point cloud is first divided non-uniformly to obtain uneven initial cloud patches. Finally, the divided cloud points are mapped to different Gaussian spheres for further subdivision. The mean shift clustering is performed on the Gauss sphere to extract the center of gravity of each cluster in the actual three-dimensional space. The set of the center of gravity is the result of simplification. Experimental results verified the effectiveness of the proposed method. It can keep the details information of the point cloud while ensuring a high simplification rate. Comparing with the existing method, this method balances the speed and accuracy, and is more suitable for the on-line locomotive automated detection system.

Analysis of the accuracy of the gradient method for determining the mean integral refractive index of air

The article is devoted to the problem of improving the accuracy of taking into account the influence of the Earth’s atmosphere on the results of distance measurements carried out using electromagnetic waves. The main influencing factors in such measurements are the difference between the speed of propagation of an electromagnetic signal in the atmosphere and the speed of light in a vacuum, as well as the refractive distortion of the trajectory along which the signal propagates.To eliminate the influence of the atmosphere, special corrections are used, which are applied into the measurement results in order to compensate for the above influencing factors. The most important among them is the correction, which takes into account the mean integral refractive index of air along the trace being measured.At present, as a rule, model methods for determining the correction are used, taking into account the mean integral refractive index of air. These methods use a point approximation of continuous functions describing the spatial distribution of temperature, pressure and air humidity on the trace being measured, as well as the representation of the finite sum of a certain integral specifying the exact correlation for the correction. Due to these limitations in the framework of the commonly used model methods, it is not always possible to achieve the required accuracy of the results of distance measurements. As for the well-known hardware methods, which are potentially more accurate, they are still under development. In this regard, new possibilities of improving the accuracy of model methods, in particular, the recently proposed gradient method, are considered.Theoretical studies of the accuracy of the gradient method for determining the mean integral refractive index of air in distance measurements on near-Earth traces are carried out. It is shown that it is more accurate than the well-known trapezium method. The equations of measurement of the gradient method obtained with the use of Hermite interpolation polynomials, which are valid for non-uniform partition of the measured trace by points in which the local values of the refractive index are determined, are considered. The requirements for the procedure and accuracy of measurements of the parameters necessary for determining the gradients of the refractive index of air at the end points of the trace in the framework of the gradient method are substantiated.The results of the studies provide a rigorous justification for new methods for determining the mean integral refractive index of air on near-Earth traces with a non-uniform profile of the underlying surface in the presence of significant elevation differences.

TF-DMB: A traffic flow theory-based dynamic multi-hop broadcast protocol

In order to ensure traffic safety, the emergency warning message should be transmitted quickly and reliably in vehicular ad hoc networks by multi-hop broadcast. In this article, we propose a traffic flow theory-based dynamic multi-hop broadcast protocol to address the issue of emergency warning message dissemination in vehicular ad hoc networks. The main goal of our protocol is to reduce delay and enhance reliability no matter the traffic density is high or low. First, according to the simulations of the distribution of vehicles under different traffic densities, a method of dynamically dividing the communication range is proposed, which, to a large extent, could find the candidate forwarders by one non-uniform partition. Next, a mechanism of dynamically adjusting the contention window size and boundary is designed, and the minimum waiting time difference is considered. The complete execution process of theory-based dynamic multi-hop broadcast protocol and corresponding retransmission strategies are included for high reliability. Through extensive simulations, we demonstrate the superior performance of our protocol in terms of one-hop delay, one-hop message processing, and delivery ratio compared with other existing schemes.

Hybrid fuzzy polynomial neural networks with the aid of weighted fuzzy clustering method and fuzzy polynomial neurons

It is well-known that any nonlinear complex system can be modeled by using a collection of "if źthen" fuzzy rules. In spite of a number of successful models reported in the literature, there are still two open issues: (1) one is not able to reflect the heterogeneous partition of the input space; (2) it becomes very difficult to deal effectively with high dimensionality of the problem (data). In this study, we present a parallel fuzzy polynomial neural networks (PFPNNs) with the aid of heterogeneous partition of the input space. Like fuzzy rules encountered in fuzzy models, the PFPNNs comprises a collection of premise and consequent parts. In the design of the premise part of the rule a weighted fuzzy clustering method is used not only to realize a nonuniform partition of the input space but to overcome a possible curse dimensionality. While in the design of consequent part, fuzzy polynomial neural networks are exploited to construct optimal local models (high order polynomials) that describe the relationship between the input variables and output variable within some local region of the input space. Two types of information granulation-based fuzzy polynomial neurons are developed for FPNNs. Particle swarm optimization (PSO) is employed to adjust the design parameters of parallel fuzzy polynomial neural networks. To evaluate the performance of PFPNNs a series of experiments based on several benchmarks are included. A comparative analysis demonstrates that the proposed model comes with higher accuracy and generalization capabilities in comparison with some previous models reported in the literature.

Analysis on block-centered finite differences of numerical simulation of semiconductor device detector

A finite difference scheme on block-centered method is presented on nonuniform partition to simulate numerically three-dimensional transient problems of semiconductor detector of photoconduction. Applying the method of mixed finite element, the principle of duality, the induction hypothesis, the prior error theory of differential equations and other special techniques, we give error estimates of second-order accuracy in l2-norm. The numerical simulation is super-convergent for the electric field intensity, really important in actual applications.

IDEMPOTENT RANK IN THE ENDOMORPHISM MONOID OF A NONUNIFORM PARTITION

We calculate the rank and idempotent rank of the semigroup ${\mathcal{E}}(X,{\mathcal{P}})$ generated by the idempotents of the semigroup ${\mathcal{T}}(X,{\mathcal{P}})$ which consists of all transformations of the finite set $X$ preserving a nonuniform partition ${\mathcal{P}}$. We also classify and enumerate the idempotent generating sets of minimal possible size. This extends results of the first two authors in the uniform case.

Convergence of the Swartztrauber-Sweet Method for Parabolic Problems on a Disk with Singularities

In this article, we study the convergence analysis for the initial and boundary value problem of parabolic equations on a disk with singular solutions. It is assumed that the exact solution performs singular properties that its derivatives go to infinity at the boundary of the disk. We propose a fully implicit time-stepping numerical scheme. A stretching polynomial-like function with a parameter is used to construct a local grid refinement. Over the nonuniform partition, we combine the Swartztrauber-Sweet scheme and the backward Euler method in spatial and temporal discretization, respectively. We carry out convergence analysis and analyze the effects of the parameter. It is shown that our numerical scheme is of first order accuracy for temporal discretization and of almost second order accuracy for spatial discretization. Numerical experiments are performed to illustrate our analysis results and show that there exists an optimal value for the parameter to obtain a best approximate solution.

A Non-Uniform Regional Partition Coding of One Dimension Signal and its Application

In this paper, a novel method for one-dimension-signal coding based on non-uniform regional partition is proposed. A given 1D signal can automatically be partitioned into different regions with different lengths and the one-variable polynomial is used to do the Least Square Approximation for signal values in each sub-region. When the approximation error and initial partition are specified, a specific signal partition result is obtained. Based on this algorithm, an effective denoising scheme of 1D signal is implemented and some of the experimental examples are illustrated to prove that the quality of the re-constructed signal, the denoising effect are all satisfactory and can be referenced by other researchers.