Two-level Method Research Articles

Reducing Alignment Time Complexity of Ultra-Large Sets of Sequences.

The alignment of three or more protein or nucleotide sequences is known as Multiple Sequence Alignment problem. The complexity of this problem increases exponentially with the number of sequences; therefore, many of the current approaches published in the literature suffer a computational overhead when thousands of sequences are required to be aligned. We introduce a new approach for dealing with ultra-large sets of sequences. A two-level clustering method is considered. The first level clusters the input sequences by using their biological composition, that is, the number of positive, negative, polar, special, and hydrophobic amino acids. In the second level, each cluster is divided into different clusters according to their similarity. Then, each cluster is aligned by using any method/aligner. After aligning the centroid sequences of each second-level cluster, we extrapolate the new gaps to each cluster of sequences to obtain the final alignment. We present a study on biological data with up to ∼100,000 sequences, showing that the proposed approach is able to obtain accurate alignments in a reduced amount of time; for example, in >10,000 sequences datasets, it is able to reduce up to ∼45 times the required runtime of the well-known Kalign.

Identification of influential users by neighbors in online social networks

Identification and ranking of influential users in social networks for the sake of news spreading and advertising has recently become an attractive field of research. Given the large number of users in social networks and also the various relations that exist among them, providing an effective method to identify influential users has been gradually considered as an essential factor. In most of the already-provided methods, those users who are located in an appropriate structural position of the network are regarded as influential users. These methods do not usually pay attention to the interactions among users, and also consider those relations as being binary in nature. This paper, therefore, proposes a new method to identify influential users in a social network by considering those interactions that exist among the users. Since users tend to act within the frame of communities, the network is initially divided into different communities. Then the amount of interaction among users is used as a parameter to set the weight of relations existing within the network. Afterward, by determining the neighbors’ role for each user, a two-level method is proposed for both detecting users’ influence and also ranking them. Simulation and experimental results on twitter data shows that those users who are selected by the proposed method, comparing to other existing ones, are distributed in a more appropriate distance. Moreover, the proposed method outperforms the other ones in terms of both the influential speed and capacity of the users it selects.

Multigrid algorithms for $$\varvec{hp}$$ h p -version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes

In this paper we analyze the convergence properties of two-level and W-cycle multigrid solvers for the numerical solution of the linear system of equations arising from hp-version symmetric interior penalty discontinuous Galerkin discretizations of second-order elliptic partial differential equations on polygonal/polyhedral meshes. We prove that the two-level method converges uniformly with respect to the granularity of the grid and the polynomial approximation degree p, provided that the number of smoothing steps, which depends on p, is chosen sufficiently large. An analogous result is obtained for the W-cycle multigrid algorithm, which is proved to be uniformly convergent with respect to the mesh size, the polynomial approximation degree, and the number of levels, provided the latter remains bounded and the number of smoothing steps is chosen sufficiently large. Numerical experiments are presented which underpin the theoretical predictions; moreover, the proposed multilevel solvers are shown to be convergent in practice, even when some of the theoretical assumptions are not fully satisfied.

Recent Methods for the Study of Measurement Invariance With Many Groups

This article reviews and compares recently proposed factor analytic and item response theory approaches to the study of invariance across groups. Two methods are described and contrasted. The alignment method considers the groups as a fixed mode of variation, while the random-intercept, random-loading two-level method considers the groups as a random mode of variation. Both maximum likelihood and Bayesian analyses are applied. A survey of close to 50,000 subjects in 26 countries is used as an illustration. In addition, the two methods are studied by Monte Carlo simulations. A list of considerations for choosing between the two methods is presented.

Spatial and temporal ecological risk assessment of unionized ammonia nitrogen in Tai Lake, China (2004–2015)

Ammonia toxicity varies largely due to its pH- and temperature-dependent speciation (unionized ammonia nitrogen, NH3-N). The seasonal and long-term trend of ammonia risk in ecologically significant sections of Tai Lake, China was unknown. In this study, a two-level (deterministic and quantitative) method was developed to assess the special ecological risks posed by NH3-N at 37 sites during two seasons (February and September) of 2014 in Tai Lake. The long-term temporal (2004–2015) risk posed by NH3-N was also assessed by comparing annual quantitative risk values (probability of exceeding acute or chronic threshold values) in three key sections of Tai Lake. The results indicated the species living in the Tai Lake were at a 0.04% and 32.45% chance of risk due to acute exposure, and a 1.97% and 92.05% chance of risk due to chronic exposure in February and September of 2014, respectively. Alarmingly, the chronic ecological risks of NH3-N in the Lanshanzui section of the Tai Lake remained >30% from 2004 to 2011. The chronic risk of NH3-N in all three key sections of Tai Lake started to decrease in 2011. This was likely the consequence of the control practice of eutrophication implemented in the Tai Lake. A significant decline in diversity of the benthic invertebrate community of the Tai Lake could be associated with continuous exposure to ammonia over decades given different sensitivity of taxa to ammonia. The results laid a scientific foundation for risk assessment and management of ammonia in Tai Lake, China, and the developed two-level risk assessment approach can also be applied to other similar aquatic regions.

A two-level method of production planning and scheduling for bi-objective reentrant hybrid flow shops

This research deals with a two-level method of production planning and scheduling problems of the reentrant hybrid flow shops. The hybrid flow shop has serial stages where each stage consists of identical parallel machines. Products can be processed at any one of the parallel machines at a stage in the hybrid flow shop. Also a product may have reentrant operations which require revisits of some stages several times. We consider a two-level hierarchical process on production planning and scheduling of the reentrant hybrid flow shop with the bi-objective function to improve productivity and customer satisfaction. Computational experiments show that the combination of preemptive goal programming based production planning algorithms and Pareto genetic based scheduling algorithms outperforms other two-level algorithms. Also we provide results of the application of the proposed method to both randomly generated problems and a real world Thin Film Transistor and Liquid Crystal Display (TFT-LCD) industry.

High Accuracy Compact Operator Methods for Two-Dimensional Fourth Order Nonlinear Parabolic Partial Differential Equations

Abstract In this study, we develop and implement numerical schemes to solve classes of two-dimensional fourth-order partial differential equations. These methods are fourth-order accurate in space and second-order accurate in time and require only nine spatial grid points of a single compact cell. The proposed discretizations allow the use of Dirichlet boundary conditions only without the need to discretize the derivative boundary conditions and thus avoids the use of ghost points. No transformation or linearization technique is used to handle nonlinearity and the obtained block tri-diagonal nonlinear system has been solved by Newton’s block iteration method. It is discussed how our formulation is able to tackle linear singular problems and it is ensured that the methods retain their orders and accuracy everywhere in the solution region. The proposed two-level method is shown to be unconditionally stable for a class of two-dimensional fourth-order linear parabolic equation. We also discuss the alternating direction implicit (ADI) method for solving two-dimensional fourth-order linear parabolic equation. The proposed difference methods has been successfully tested on the two-dimensional vibration problem, Boussinesq equation, extended Fisher–Kolmogorov equation and Kuramoto–Sivashinsky equation. Numerical results demonstrate that the schemes are highly accurate in solving a large class of physical problems.

Symmetric Interior Penalty Discontinuous Galerkin Discretizations and Block Preconditioning for Heterogeneous Stokes Flow

Provable stable arbitrary order symmetric interior penalty (SIP) discontinuous Galerkin discretizations of heterogeneous, incompressible Stokes flow utilizing $Q^2_k$--$Q_{k-1}$ elements and hierarchical Legendre basis polynomials are developed and investigated. For solving the resulting linear system, a block preconditioned iterative method is proposed. The nested viscous problem is solved by a $hp$-multilevel preconditioned Krylov subspace method. For the $p$-coarsening, a two-level method utilizing element-block Jacobi preconditioned iterations as a smoother is employed. Piecewise bilinear ($Q^2_1$) and piecewise constant ($Q^2_0$) $p$-coarse spaces are considered. Finally, Galerkin $h$-coarsening is proposed and investigated for the two $p$-coarse spaces considered. Through a number of numerical experiments, we demonstrate that utilizing the $Q^2_1$ coarse space results in the most robust $hp$-multigrid method for heterogeneous Stokes flow. Using this $Q^2_1$ coarse space we observe that the convergen...

Two-level Visual Method and the Practice of Cultural Expression: Visual Anthropological Value and the Inspiration of Tea Ceremony

Two-level Visual Method and the Practice of Cultural Expression: Visual Anthropological Value and the Inspiration of Tea Ceremony

Direct Torque Control of Induction Motor with Common-Mode Voltage Elimination

If the common-mode voltage in the induction motor drive is not eliminated, it may cause failure of motor bearings and malfunctioning of the electrical equipment associated with the drive. This article proposes the modified direct torque control technique to control the induction motor fed by three-level inverter, commonly called a neutral-point-clamped inverter. The selective voltage vectors in three-level inverter determine elimination of the common-mode voltage. The classic three-level direct torque control based on selection of 6-full, 6-half, and 2-zero voltage vectors out of available 27 is modified so that the 6-intermediate voltage vectors and a zero voltage vector are employed. A comparative investigation with another three-level direct torque control method which reduces both common-mode voltage and torque ripple is also carried out. These methods are compared with classic two-level direct torque control method in context of common-mode voltage, torque ripple, current total harmonic distortion (THD) and DC-link utilization. The simulation and experimental results validate the proposed common-mode voltage elimination and common-mode voltage reduction direct torque control techniques.

A two-level stochastic collocation method for semilinear elliptic equations with random coefficients

In this work, we propose a novel two-level discretization for solving semilinear elliptic equations with random coefficients. Motivated by the two-grid method for deterministic partial differential equations (PDEs) introduced by Xu (1994), our two-level stochastic collocation method utilizes a two-grid finite element discretization in the physical space and a two-level collocation method in the random domain. In particular, we solve semilinear equations on a coarse mesh TH with a low level stochastic collocation (corresponding to the polynomial space PP) and solve linearized equations on a fine mesh Th using high level stochastic collocation (corresponding to the polynomial space Pp). We prove that the approximated solution obtained from this method achieves the same order of accuracy as that from solving the original semilinear problem directly by stochastic collocation method with Th and Pp. The two-level method is computationally more efficient than the standard stochastic collocation method for solving nonlinear problems with random coefficients. Numerical experiments are provided to verify the theoretical results.

Optimal design of the stacking sequences of a corrugated central cylinder in a satellite

This Case Study is to describe an application of a two-level approximation method in optimally determining the stacking sequences of a practical corrugated central cylinder. Being housed in the center of a practical satellite, this cylinder can support many of the structural components and functional devices in the satellite. For the purpose of reducing its mass meanwhile maintaining good mechanical properties, the stacking sequences of this cylinder are to be optimally designed under given constraints in this paper. To address this problem, an optimization model was first established by minimizing the structural mass based on initial lay-ups. With the given lay-ups for multi-parts of this cylinder, the existence of each ply was to be determined in terms of discrete variables. Meanwhile, the ply thicknesses were also treated as continuous variables. The two-level approximation method combined with a genetic algorithm previously proposed by the authors was adopted as the optimization method. According to the practical engineering considerations, multiple optimizations were conducted by starting from different initial lay-ups to search more possible optimization designs. After optimization, it was found that compared with the empirical designs, the mass of the main cylinder could be significantly decreased by obtaining some reasonable stacking sequences.

A two-level consistent splitting scheme for the navier-stokes equations

A fully discrete two-level consistent splitting scheme is considered for solving the time-dependent Navier-Stokes equations. To overcome the incompressible constraint which couples the velocity and the pressure, we apply the consistent splitting scheme which is a projection type method to decouple the velocity and the pressure. To overcome the difficulty caused by nonlinearity, we consider a two-level method which only solves a nonlinear equation in the coarse-level subspace and a linear problem in the fine-level subspace. The analysis shows that our method can reach the same accuracy as the one-level method with a very fine mesh size h by an appropriate choice of coarse mesh size H. Numerical examples are provided that confirm both the theoretical analysis and the corresponding improvement in computational efficiency.

Application of the conditional gradient method to resource allocation in wireless networks

We propose a new two-level iterative method for solution of a general problem of optimal allocation of a homogeneous resource (bandwidth) in a wireless communication network. It is divided into service zones (clusters) and the network manager can buy external volumes of this resource. This approach leads to a convex optimization problem, which is solved with a dual Lagrangian method, where calculation of the cost function value decomposes into a system of independent zonal optimization problems. Each of them is treated as a market equilibrium problem. This optimization problem is solved with conditional gradient method for different information exchange schemes for participants. Besides, we suggest several ways to adjust the basic problemto the case of moving nodes. We give some results of numerical experiments on the proposed method which confirm its preference over the previous ones.

A two-level perturbation method for connecting unstable periodic orbits with low fuel cost and short time of flight: application to a lunar observation mission

The proposed method connects two unstable periodic orbits by employing trajectories of their associated invariant manifolds that are perturbed in two levels. A first level of velocity perturbations is applied on the trajectories of the discretized manifolds at the points where they approach the nominal unstable periodic orbit in order to accelerate them. A second level of structured velocity perturbations is applied to trajectories that have already been subjected to first level perturbations in order to approximately meet the necessary conditions for a low \(\varDelta \text {V}\) transfer. Due to this two-level perturbation approach, the number of the trajectories obtained is significantly larger compared with approaches that employ traditional invariant manifolds. For this reason, the problem of connecting two unstable periodic orbits through perturbed trajectories of their manifolds is transformed into an equivalent discrete optimization problem that is solved with a very low computational complexity algorithm that is proposed in this paper. Finally, the method is applied to a lunar observation mission of practical interest and is found to perform considerably better in terms of \(\varDelta \text {V}\) cost and time of flight when compared with previous techniques applied to the same project.

An Additive Schwarz Method Type Theory for Lions's Algorithm and a Symmetrized Optimized Restricted Additive Schwarz Method

Optimized Schwarz methods (OSMs) are very popular methods which were introduced by P. L. Lions in [On the Schwarz alternating method III: A variant for nonoverlapping subdomains, in 3rd International Symposium on Domain Decomposition Methods for Partial Differential Equations (Houston, TX, 1989), T. F. Chan, R. Glowinski, J. Periaux, and O. Widlund, eds., SIAM, Philadelphia, 1990, pp. 202--223] for elliptic problems and by B. Despres in [C. R. Acad. Sci. Paris Ser. I Math., 311 (1990), pp. 313--316] for propagative wave phenomena. We give here a theory for Lions's algorithm that is the genuine counterpart of the theory developed over the years for the Schwarz algorithm. The first step is to introduce a symmetric variant of the optimized restricted additive Schwarz (ORAS) algorithm [A. St-Cyr, M. J. Gander, and S. J. Thomas, SIAM J. Sci. Comput., 29 (2007), pp. 2402--2425] that is suitable for the analysis of a two-level method. Then we build a coarse space for which the convergence rate of the two-level m...

Iterative penalty finite element methods for the steady incompressible magnetohydrodynamic problem

In the paper we consider the one-level and two-level iterative penalty finite element methods for the steady incompressible magnetohydrodynamic problem based on the iteration of pressure with a factor of penalty parameter. Firstly, the $$\mathbf {H}^1$$ and $$\mathbf {L}^2$$ error estimates of numerical solutions of one-level iterative penalty finite element method are provided. Secondly, the stability and convergence of two-level iterative penalty finite element method are analyzed. Finally, some numerical results are provided to verify the effectiveness of the developed numerical schemes.

Three-dimensional (3D) facial recognition and prediction

This paper provides solution to the problem in identifying humans from their 3D facial characteristics. For this reason, a standard 3D facial recognition system was built and used in this research work. This work proposes two novel fusion schemes where the first one employs a confidence-aided combination approach, and the second one implements a two-level serial integration method. Recognition simulations performed on the 3DRMA and the FRGC databases show that: (1) generic face template-based rigid registration of faces is better than the non-rigid variant, (2) principal curvature directions and surface normal have better discriminative power, (3) representing faces using local patch descriptors can both reduce the feature dimensionality and improve the identification rate, and (4) confidence-assisted fusion rules and serial two-stage fusion schemes have a potential to improve the accuracy when compared to other decision-level fusion rules.

A Two-Level Method for Pressure Projection Stabilized P1 Nonconforming Approximation of the Semi-Linear Elliptic Equations

Abstract.In this paper, we study a new stabilized method based on the local pressure projection to solve the semi-linear elliptic equation. The proposed scheme combines nonconforming finite element pairs NCP1–P1 triangle element and two-level method, which has a number of attractive computational properties: parameter-free, avoiding higher-order derivatives or edge-based data structures, but have more favorable stability and less support sets. Stability analysis and error estimates have been done. Finally, numerical experiments to check estimates are presented.

Two-level finite element variational multiscale method based on bubble functions for the steady incompressible MHD flow

ABSTRACTIn this paper, a finite element variational multiscale method (VMM) is developed for the stationary incompressible magnetohydrodynamics (MHD) problem and the corresponding stability and convergence are established. Our VMM is based on the polynomial bubble functions as a subgrid scale and the numerical implementation is based on the local Gauss integrations. Compared to the common VMM, our method does not introduce any extra variable. Furthermore, the two-level finite element VMM is also developed. Compared to the one-level VMM, the two-level VMM consists of solving a nonlinear MHD problem on a coarse mesh with mesh size H, and then a linearized magnetohydrodynamic problem based on the Oseen iteration on a fine mesh is solved with mesh size . Stability and convergence of numerical approximations in two-level VMM are presented. Finally, some numerical examples are provided to demonstrate the effectiveness of the developed numerical algorithms.