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In this paper, a modified weak Galerkin method is proposed for the Stokes problem. The numerical scheme is based on a novel variational form of the Stokes problem. The degree of freedoms in the modified weak Galerkin method is less than that in the original weak Galerkin method, while the accuracy stays the same. In this paper, the optimal convergence orders are given and some numerical experiments are presented to verify the theory. [ABSTRACT FROM AUTHOR]

This paper seeks insight into stabilization mechanisms for periodic walking gaits in 3D bipedal robots. Based on this insight, a control strategy based on virtual constraints, which imposes coordination between joints rather than a temporal evolution, will be proposed for achieving asymptotic convergence toward a periodic motion. For planar bipeds with one degree of underactuation, it is known that a vertical displacement of the center of mass – with downward velocity at the step transition – inducesstability of a walking gait. This paper concerns the qualitative extension of this type of property to 3D walking with two degrees of underactuation. It is shown that a condition on the position of the center of mass in the horizontal plane at the transition between steps induces synchronization between the motions in the sagittal and frontal planes. A combination of the conditions for self-synchronization and vertical oscillations leads to stable gaits. The algorithm for self-stabilization of 3D walking gaits is first developed for a simplified model of a walking robot (an inverted pendulum with variable length legs), and then it is extended to a complex model of the humanoid robot Romeo using the notion of Hybrid Zero Dynamics. Simulations of the model of the robot illustrate the efficacy of the method and its robustness. [ABSTRACT FROM AUTHOR]

This paper is devoted to numerical global optimization algorithms applying several ideas to reduce the problem dimension. Two approaches to the dimensionality reduction are considered. The first one is based on the nested optimization scheme that reduces the multidimensional problem to a family of one-dimensional subproblems connected in a recursive way. The second approach as a reduction scheme uses Peano-type space-filling curves mapping multidimensional domains onto one-dimensional intervals. In the frameworks of both the approaches, several univariate algorithms belonging to the characteristical class of optimization techniques are used for carrying out the one-dimensional optimization. Theoretical part of the paper contains a substantiation of global convergence for the considered methods. The efficiency of the compared global search methods is evaluated experimentally on the well-known GKLS test class generator used broadly for testing global optimization algorithms. Results for representative problem sets of different dimensions demonstrate a convincing advantage of the adaptive nested optimization scheme with respect to other tested methods. [ABSTRACT FROM AUTHOR]

In this paper, meshless weak form techniques are applied to find the numerical solution of nonlinear biharmonic Sivashinsky equation arising in the alloy solidification problem. Stability and convergence analysis of time-discrete scheme are proved. An error analysis of meshless global weak form method based on radial point interpolation technique is proposed for this nonlinear biharmonic equation. In addition, a comparison between meshless global and local weak form methods is done from the perspective of accuracy and efficiency. The main purpose of this paper is to show that the meshless weak form techniques can be used for solving the nonlinear biharmonic partial differential equations especially Sivashinsky equation. The numerical results confirm the good efficiency of the proposed methods for solving this nonlinear biharmonic model. [ABSTRACT FROM AUTHOR]

This paper presents a new method to synthesize safe reversible Markov chains via extending the classical Metropolis–Hastings (M–H) algorithm. The classical M–H algorithm does not impose safety upper bound constraints on the probability vector, discrete probability density function, that evolves with the resulting Markov chain. This paper presents a new M–H algorithm for Markov chain synthesis that ensures such safety constraints together with reversibility and convergence to a desired stationary (steady-state) distribution. Specifically, we provide a convex synthesis method that incorporates the safety constraints via designing the proposal matrix for the M–H algorithm. It is shown that the M–H algorithm with this proposal matrix, safe M–H algorithm, ensures safety for a well-characterized convex set of stationary probability distributions, i.e., it is robustly safe with respect to this set of stationary distributions. The size of the safe set is then incorporated in the design problem to further enhance the robustness of the synthesized M–H proposal matrix. Numerical simulations are provided to demonstrate that multi-agent systems, swarms, can utilize the safe M–H algorithm to control the swarm density distribution. The controlled swarm density tracks time-varying desired distributions, while satisfying the safety constraints. Numerical simulations suggest that there is insignificant trade-off between the speed of convergence and the robustness. [ABSTRACT FROM AUTHOR]

We further develop the Multivariate Decomposition Method (MDM) for the Lebesgue integration of functions of infinitely many variables x 1 , x 2 , x 3 , … with respect to a corresponding product of a one dimensional probability measure. The method is designed for functions that admit a dominantly convergent decomposition f = ∑ u f u , where u runs over all finite subsets of positive integers, and for each u = { i 1 , … , i k } the function f u depends only on x i 1 , … , x i k . Although a number of concepts of infinite-dimensional integrals have been used in the literature, questions of uniqueness and compatibility have mostly not been studied. We show that, under appropriate convergence conditions, the Lebesgue integral equals the ‘anchored’ integral, independently of the anchor. For approximating the integral, the MDM assumes that point values of f u are available for important subsets u , at some known cost. In this paper, we introduce a new setting, in which it is assumed that each f u belongs to a normed space F u , and that bounds B u on ‖ f u ‖ F u are known. This contrasts with the assumption in many papers that weights γ u , appearing in the norm of the infinite-dimensional function space, are somehow known. Often such weights γ u were determined by minimizing an error bound depending on the B u , the γ u and the chosen algorithm, resulting in weights that depend on the algorithm. In contrast, in this paper, only the bounds B u are assumed to be known. We give two examples in which we specialize the MDM: in the first case, F u is the | u | -fold tensor product of an anchored reproducing kernel Hilbert space; in the second case, it is a particular non-Hilbert space for integration over an unbounded domain. [ABSTRACT FROM AUTHOR]

The problem of consistency of a solution over time remains an important issue in cooperative dynamic games. Payoffs to players prescribed by an inconsistent solution may not be achievable since such a solution is extremely sensitive to its revision in the course of a game developing along an agreed upon cooperative behavior. The paper proposes a strong time-consistent payment scheme which is stable to a revision of cooperative set solutions, e.g., the core. Using a linear transformation of the solution, it becomes possible to obtain non-negative payments to players. In the paper, we also deal with a limit linear transformation of the solution whose convergence is proved. Developing a non-negative strong time-consistent payment scheme in a closed form, we guarantee that the solution supported by the scheme will not be revised over time. [ABSTRACT FROM AUTHOR]

The paper develops strong approximation schemes for solutions of stochastic differential equations with Markovian switching (SDEwMSs). The convergent orders of existing strong numerical schemes all are 0.5. This paper provides a convergence theorem for the construction of strong approximations of any given order of convergence for SDEwMSs, and then constructs the order 1 scheme, the order 1.5 scheme. The paper also develops a new way to simulate the Markov chain and hence the order 1 scheme. Finally, a numerical example is provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper considers the problem of measurement matrix optimization for compressed sensing (CS) in which the dictionary is assumed to be given, such that it leads to an effective sensing matrix. Due to important properties of equiangular tight frames (ETFs) to achieve Welch bound equality, the measurement matrix optimization based on ETF has received considerable attention and many algorithms have been proposed for this aim. These methods produce sensing matrix with low mutual coherence based on initializing the measurement matrix with random Gaussian ensembles. This paper, use incoherent unit norm tight frame (UNTF) as an important frame with the aim of low mutual coherence and proposes a new method to construction a measurement matrix of any dimension while measurement matrix initialized by partial Fourier matrix. Simulation results show that the obtained measurement matrix effectively reduces the mutual coherence of sensing matrix and has a fast convergence to Welch bound compared with other methods. [ABSTRACT FROM AUTHOR]

Over the last four decades, Environmental Accounting tools have been developed to conceptualise and quantify the direct and indirect effects of human activity on the environment, to enable decision-makers to track and measure progress towards sustainability outcomes and goals. These environmental accounting methods range from ecological footprinting, carbon footprinting, energy analysis, emergy analysis, ecological pricing and life cycle assessment to environmental input-output analysis. Regrettably, the contemporaneous development of these tools has frequently occurred in isolation from each other, even though they often seek to serve common analytical and evaluative purposes, as well as serving similar communities of interest. It is the central argument of this paper that, in spite of this isolation, the environmental accounting methods have a number of common features − that is, they can be mathematically reduced to similar analytics, and they often confront the same methodological issues − e.g., joint production (co-products) problem, weighting, commensuration, double counting and boundary setting. In this regard the paper reviews how the various environmental accounting tools can ‘learn’ from each other − e.g., how the mathematics of ecological pricing can address the joint production problem in a number of the other environmental accounting methods; and how the insights from input-output analysis can be used in system boundary setting. The paper concludes by agreeing with previous authors, that a better understanding of any given environmental issue is likely to be achieved by using a mix of these environmental accounting tools, rather than relying on just one tool, one perspective or one criterion. [ABSTRACT FROM AUTHOR]

Construction of support characteristic curves is an important aspect of the implementation of the convergence-confinement method of tunnel support design. This paper presents a detailed analysis of the equations required to construct the support characteristic curve of a combined support system consisting of closed circular steel sets linked to the periphery of the tunnel by equally spaced prismatic wood blocks. This particular problem has been treated in the classical literature of underground excavation design in rock, although without providing details of the origin or validity of the equations. This paper fills this gap, providing the derivation and validation of all the equations required to construct the support characteristic curve for the combined support system. The paper shows that both the stiffness and maximum load that the combined support system can take increases as the angle between equally spaced wood blocks is decreased (or the number of blocks for the steel section is increased). In the limit, when the angle between wood blocks is assumed to be zero, the paper shows that the classical equations for construction of support characteristic curve for a steel set subjected to uniform radial load are recovered. The paper presents also a practical example illustrating the application of all equations needed to construct the support characteristic curve for the combined support system. [ABSTRACT FROM AUTHOR]

In the current paper, an efficient numerical method based on two-dimensional hybrid of block-pulse functions and Legendre polynomials is developed to approximate the solutions of two-dimensional nonlinear Fredholm, Volterra and Volterra–Fredholm integral equations of the second kind. The main idea of the presented method is based upon some of the important benefits of the hybrid functions such as high accuracy, wide applicability and adjustability of the orders of block-pulse functions and Legendre polynomials to achieve highly accurate numerical solutions. By using the numerical integration and collocation method, two-dimensional nonlinear integral equations are reduced to a system of nonlinear algebraic equations. The focus of this paper is to obtain an error estimate and to show the convergence analysis for the numerical approach under the L 2 -norm. Numerical results are presented and compared with the results from other existing methods to illustrate the efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

In a recent paper, a distributed algorithm was proposed for solving linear algebraic equations of the form A x = b assuming that the equation has at least one solution. The equation is presumed to be solved by m agents assuming that each agent knows a subset of the rows of the matrix A b , the current estimates of the equation’s solution generated by each of its neighbors, and nothing more. Neighbor relationships are represented by a time-dependent directed graph N ( t ) whose vertices correspond to agents and whose arcs characterize neighbor relationships. Sufficient conditions on N ( t ) were derived under which the algorithm can cause all agents’ estimates to converge exponentially fast to the same solution to A x = b . These conditions were also shown to be necessary for exponential convergence, provided the data about A b available to the agents is “non-redundant”. The aim of this paper is to relax this “non-redundant” assumption. This is accomplished by establishing exponential convergence under conditions which are the weakest possible for the problem at hand; the conditions are based on a new notion of graph connectivity. An improved bound on the convergence rate is also derived. [ABSTRACT FROM AUTHOR]

This paper proposes the introduction of a connectivity constraint in the Bi-directional Evolutionary Structural Optimisation (BESO) method, which avoids the possibility of arriving at highly non-optimal local optima. By developing a constraint that looks at the usefulness of complete members, rather than just elements, local optima are shown to be avoided. This problem, which affects both evolutionary and discrete optimisation techniques, has divided the optimisation community and resulted in significant discussion. This discussion has led to the development of what is now known in the literature as the Zhou-Rozvany (Z-R) problem. After analysing previous attempts at solving this problem, an updated formulation for the convergence criteria of the proposed BESO algorithm is presented. The convergence of the sequence is calculated by the structure's ability to safely carry the applied loads without breaking the constraints. The Z-R problem is solved for both stress minimisation and minimum compliance, further highlighting the flexibility of the proposed formulation. Finally, this paper aims to give some new insights into the uniqueness of the Z-R problem and to discuss the reasons for which discrete methods struggle to find suitable global optima. [ABSTRACT FROM AUTHOR]

The unconditional convergence of finite element method for two-dimensional time-dependent viscoelastic flow with an Oldroyd B constitutive equation is given in this paper, while all previous works require certain time-step restrictions. The approximation is stabilized by using the Discontinuous Galerkin (DG) approximation for the constitutive equation. The analysis bases on a splitting of the error into two parts: the error from the time discretization of the PDEs and the error from the finite element approximation of corresponding iterated time-discrete PDEs. The approach used in this paper can be applied to more general couple nonlinear parabolic and hyperbolic systems. [ABSTRACT FROM AUTHOR]

The paper presents studies on the Green’s function for thermomagnetoelectroelastic medium and its reduction to the contour integral. Based on the previous studies the thermomagnetoelectroelastic Green’s function is presented as a surface integral over a half-sphere. The latter is then reduced to the double integral, which inner integral is evaluated explicitly using the complex variable calculus and the Stroh formalism. Thus, the Green’s function is reduced to the contour integral. Since the latter is evaluated over the period of the integrand, the paper proposes to use trapezoid rule for its numerical evaluation with exponential convergence. Several numerical examples are presented, which shows efficiency of the proposed approach for evaluation of Green’s function in thermomagnetoelectroelastic anisotropic solids. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a generalization of Kowalsky diagonal condition and that of Fischer diagonal condition respectively, namely Kowalsky ⊤-diagonal condition and Fischer ⊤-diagonal condition. We show that our Fischer ⊤-diagonal condition assures a complete-MV-algebra-valued convergence space, proposed in this paper, is strong L -topological, and Kowalsky ⊤-diagonal condition assures a principle (or pretopological) complete-MV-algebra-valued convergence space is strong L -topological also. As applications, we give a “dual form” of our Fischer ⊤-diagonal condition and obtain a concept of regular ⊤-convergence space. In addition, we present an extension theorem for continuous maps from a dense subspace to a regular ⊤-convergence space to show that our ⊤-diagonal conditions works indeed. [ABSTRACT FROM AUTHOR]

In this paper, an iteration process, referred to in short as MMP, will be considered. This iteration is related to finding the maximum modulus of a complex polynomial over a unit disc on the complex plane creating intriguing images. Kalantari calls these images polynomiographs independently from whether they are generated by the root finding or maximum modulus finding process applied to any polynomial. We show that the images can be easily modified using different MMP methods (pseudo-Newton, MMP-Householder, methods from the MMP-Basic, MMP-Parametric Basic or MMP-Euler–Schröder Families of Iterations) with various kinds of non-standard iterations. Such images are interesting from three points of views: scientific, educational and artistic. We present the results of experiments showing automatically generated non-trivial images obtained for different modifications of root finding MMP-methods. The colouring by iteration reveals the dynamic behaviour of the used root finding process and its speed of convergence. The results of the present paper extend Kalantari’s recent results in finding the maximum modulus of a complex polynomial based on Newton’s process with the Picard iteration to other MMP-processes with various non-standard iterations. [ABSTRACT FROM AUTHOR]

Multitask learning can be defined as the joint learning of related tasks using shared representations, such that each task can help other tasks to perform better. One of the various multitask learning frameworks is the regularized convex minimization problem, for which many optimization techniques are available in the literature. In this paper, we consider solving the non-smooth convex minimization problem with sparsity-inducing regularizers for the multitask learning framework, which can be efficiently solved using proximal algorithms. Due to slow convergence of traditional proximal gradient methods, a recent trend is to introduce acceleration to these methods, which increases the speed of convergence. In this paper, we present a new accelerated gradient method for the multitask regression framework, which not only outperforms its non-accelerated counterpart and traditional accelerated proximal gradient method but also improves the prediction accuracy. We also prove the convergence and stability of the algorithm under few specific conditions. To demonstrate the applicability of our method, we performed experiments with several real multitask learning benchmark datasets. Empirical results exhibit that our method outperforms the previous methods in terms of convergence, accuracy and computational time. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the numerical approximation of a general second order parabolic stochastic partial differential equation(SPDE) driven by multiplicative and additive noise. Our main interest is on such SPDEs where the nonlinear part is stronger than the linear part, usually called stochastic dominated transport equations. Most standard numerical schemes lose their good stability properties on such equations, including the current linear implicit Euler method. We discretize the SPDE in space by the finite element method and propose a novel scheme called stochastic Rosenbrock-type scheme for temporal discretization. Our scheme is based on the local linearization of the semi-discrete problem obtained after space discretization and is more appropriate for such equations. We provide a strong convergence of the new fully discrete scheme toward the exact solution for multiplicative and additive noise and obtain optimal rates of convergence. Numerical experiments to sustain our theoretical results are provided. [ABSTRACT FROM AUTHOR]

This paper studies the parameter identification problem for a large-scale multivariable systems. In terms of the identification obstacle causing by huge amounts of parameters of large-scale systems, a separable gradient (synthesis) identification algorithm is developed in accordance with the hierarchical computation principle. For the large-scale multivariable equation-error systems, the whole parameters are detached into several sub-parameter matrices based on the scales of the coefficient matrices of the inputs and outputs. On the basis of the detached parameter matrices, multiple parameter estimation sub-algorithms are presented for estimating the parameters of each sub-matrix through using the gradient search and multi-innovation theory from real-time measurements. Concerning the problem that the sub-algorithms are not effective because of the unknown parameters existing in the recursive computation, the previous estimates of the unknown parameters and the interactive estimation are introduced into the sub-algorithms to eliminate the associated items that make the sub-algorithms impossible to implement. In order to analyze the convergence of the proposed algorithms theoretically, we prove the convergence by using martingale convergence theory and stochastic principle. Finally, the performance tests of the proposed identification approaches for large-scale multivariable systems are carried out on several numerical examples and the simulation results demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, we modify the general iterative method to approximate a common element of the set of solutions of split variational inclusion problem and the set of common fixed points of a finite family of k -strictly pseudo-contractive nonself mappings. Strong convergence theorem is established under some suitable conditions in a real Hilbert space, which also solves some variational inequality problems. Results presented in this paper may be viewed as a refinement and important generalizations of the previously known results announced by many other authors. Finally, some examples to study the rate of convergence and some illustrative numerical examples are presented. [ABSTRACT FROM AUTHOR]

In this paper, an interior-point trust-region algorithm to generate a Pareto optimal solution for a multi-objective optimal load flow (MOLF) problem is introduced. A weighted Tchebychev approach is used in this paper to transform (MOLF) problem to a single objective optimization problem. In the algorithm, an interior-point Newton method is used with Coleman-Li scaling matrix and a trust-region globalization strategy to insure global convergence. The trust region technique is suitable for multi-objective optimal load flow problem such that its objective functions may be ill-defined or having a non-convex Pareto-optimal front. A projected Hessian technique is used in the algorithm to handling the difficulty of having an infeasible trust region subproblems. The proposed algorithm is carried out on the standard IEEE 30-bus 6-generator test systems to assert the efficacy of the algorithm used to solve the multi-objective (MOLF) problem. Our results have been compared to those reported in the literature. The comparison demonstrates the superiority of the proposed approach and confirm its potential to generate the Pareto optimal solution for (MOLF) problem. [ABSTRACT FROM AUTHOR]

In this paper a new semi-analytical solution for the moving mass problem is presented. Firstly, the problem of a mass traversing a finite beam on an elastic foundation is reviewed and some new aspects are added. Then, the new semi-analytical solution is deduced for an infinite beam. The semi-analytical solution of the displacement under the mass is derived with the help of integral transforms and the full deflection shape is obtained by linking together two semi-infinite beams. An iterative procedure is suggested for the determination of the frequency of the oscillation induced by the moving mass. Results deduced for infinite beams are confirmed by analysis of long finite beams, with the help of derivations given in the first part of this paper. Convergence analysis on finite beams is also presented, and, in addition, the effects of the normal force, of the harmonic component of the vertical force and of the foundation damping are discussed. [ABSTRACT FROM AUTHOR]

This paper deals with the finite-time synchronization issue of time-varying delayed neural networks (DNNs) with discontinuous activations. Based on master-slave concept, several sufficient conditions are given to guarantee the finite-time synchronization of discontinuous DNNs. In order to control the synchronization error to converge zero in a finite time, we design three classes of novel switching state-feedback controllers which involve time-delays and discontinuous factors. The analysis in this paper employs the extended differential inclusion theory, the famous finite-time stability theorem, inequality techniques and generalized Lyapunov approach. Moreover, the upper bounds of the settling time of synchronization are estimated. Finally, the validity of proposed design method and theoretical results are illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

This paper presents an iterative convex programming algorithm for the complex ascent trajectory planning problem. Due to the nonlinear dynamics and constraints, ascent trajectory planning problems are always difficult to be solved rapidly. With deterministic convergence, convex programming is becoming increasingly attractive to such problems. In this paper, first, path constraints (dynamic pressure, load and bending moment) are convexified by a change of variables and a reasonable approximation. Then, based on the Newton–Kantorovich/Pseudospectral (N–K/PS) approach, the dynamic equations are transcribed into linearized algebraic equality constraints with a given initial guess, and the ascent trajectory planning problem is formulated as a convex programming problem. At last, by iteratively solving the convex programming problem with readily available convex optimization methods and successively updating the initial guess with the Newton–Kantorovich iteration, the trajectory planning problem can be solved accurately and rapidly. The convergence of the proposed iterative convex programming method is proved theoretically, and numerical simulations show that the method proposed can potentially be implemented onboard a launch vehicle for real-time applications. [ABSTRACT FROM AUTHOR]

We extend in this paper an optimal family of three-step eighth-order methods developed by Džunić et al. (2011) with higher-order weight functions employed in the second and third sub-steps and investigate their dynamics under the relevant extraneous fixed points among which purely imaginary ones are specially treated for the analysis of the rich dynamics. Their theoretical and computational properties are fully investigated along with a main theorem describing the order of convergence and the asymptotic error constant as well as proper choices of special cases. A wide variety of relevant numerical examples are illustrated to confirm the underlying theoretical development. In addition, this paper investigates the dynamics of selected existing optimal eighth-order iterative maps with the help of illustrative basins of attraction for various polynomials. [ABSTRACT FROM AUTHOR]

This paper investigates identification of Wiener systems with quantized inputs and binary-valued output observations. By parameterizing the static nonlinear function and incorporating both linear and nonlinear parts, we begin by investigating system identifiability under the input and output constraints. Then a three-step algorithm is proposed to estimate the unknown parameters by using the empirical measure, input persistent patterns, and information on noise statistics. Convergence properties of the algorithm, including strong convergence and mean-square convergence rate, are established. Furthermore, by selecting a suitable transformation matrix, the asymptotic efficiency of the algorithm is proved in terms of the Cramér–Rao lower bound. Finally, numerical simulations are presented to illustrate the main results of this paper. [ABSTRACT FROM AUTHOR]

Transmitter localization is used extensively in civilian and military applications. In this paper, we focus on the Direct Position Determination (DPD) approach, based on Time of Arrival (TOA) measurements, in which the transmitter location is obtained directly, in one step, from the signals intercepted by all sensors. The DPD objective function is often non-convex and therefore finding the maximum usually require s exhaustive search, since gradient based methods usually converge to local maxima. In this paper we present an efficient technique for finding the extremum of the objective function that corresponds to the transmitter location. The proposed method is based on the Expectation-Maximization (EM) algorithm. The EM algorithm is designed to find the Maximum Likelihood (ML) estimate when the available data can be viewed as “incomplete data”, while the “complete data” is hidden in the model. By choosing the appropriate “incomplete data” we replace the high dimensional search, associated with the ML algorithm, with several sub-problems that require only one dimensional search. We demonstrate that although the EM algorithm does not guarantee a convergence to the global maximum, it does so with high probability and therefore it outperforms the common gradient-based methods. [ABSTRACT FROM AUTHOR]

This paper considers identification of nonlinear rational systems defined as the ratio of two nonlinear functions of past inputs and outputs. Despite its long history, a globally consistent identification algorithm remains illusive. This paper proposes a globally convergent identification algorithm for such nonlinear rational systems. To the best of our knowledge, this is the first globally convergent algorithm for the nonlinear rational systems. The technique employed is a two-step estimator. Though two-step estimators are known to produce consistent nonlinear least squares estimates if a N consistent estimate can be determined in the first step, how to find such a N consistent estimate in the first step for nonlinear rational systems is nontrivial and is not answered by any two-step estimators. The technical contribution of the paper is to develop a globally consistent estimator for nonlinear rational systems in the first step. This is achieved by involving model transformation, bias analysis, noise variance estimation, and bias compensation in the paper. Two simulation examples and a practical example are provided to verify the good performance of the proposed two-step estimator. [ABSTRACT FROM AUTHOR]

The null space pursuit (NSP) algorithm is an operator-based signal separation approach which separates a signal into a set of additive subcomponents using adaptively estimated operators and parameters. In this paper, a new operator termed complex-valued differential (CD) operator is proposed. Combining with the CD operator, this paper proposes NSP-CD algorithm to solve the CD operator-based signal separation problem. The NSP-CD algorithm can separate the multi-component signal into sum of amplitude-modulated and frequency-modulated (AM–FM) signals in the form of A ( t ) exp ( j ) ( ϕ ( t ) ) . The proposed NSP-CD algorithm has many advantages. Firstly, the proposed CD operator can ensure that the AM–FM signal totally lies in the null space of the operator rather than close to the null space that the original used operator may reach. Secondly, compared with the original NSP algorithm, our algorithm provides a more reasonable strategy to update the regularization parameter λ and the leakage factor γ . Finally, we have proved that the proposed algorithm has quadric convergence theoretically. Experiments on both synthetic and real-life signals demonstrate that the NSP-CD algorithm is more robust and effective than other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In this paper we study the multigrid methods for adaptively refined finite element meshes. In our multigrid iterations, on each level we only perform relaxation on new nodes and the old nodes whose support of nodal basis function have changed. The convergence analysis of the algorithm is based on the framework of subspace decomposition and subspace correction. In order to decompose the functions from the finest finite element space into each level, a new projection is presented in this paper. Briefly speaking, this new projection can be seemed as the weighted average of the local L 2 projection. We can perform our subspace decomposition through this new projection by its localization property. Other properties of this new projection are also presented and by these properties we prove the uniform convergence of the algorithm in both 2D and 3D. We also present some numerical examples to illustrate our conclusion. [ABSTRACT FROM AUTHOR]

This paper uses a divergence-conforming B-spline fluid discretization to address the long-standing issue of poor mass conservation in immersed methods for computational fluid–structure interaction (FSI) that represent the influence of the structure as a forcing term in the fluid subproblem. We focus, in particular, on the immersogeometric method developed in our earlier work, analyze its convergence for linear model problems, then apply it to FSI analysis of heart valves, using divergence-conforming B-splines to discretize the fluid subproblem. Poor mass conservation can manifest as effective leakage of fluid through thin solid barriers. This leakage disrupts the qualitative behavior of FSI systems such as heart valves, which exist specifically to block flow. Divergence-conforming discretizations can enforce mass conservation exactly, avoiding this problem. To demonstrate the practical utility of immersogeometric FSI analysis with divergence-conforming B-splines, we use the methods described in this paper to construct and evaluate a computational model of an in vitro experiment that pumps water through an artificial valve. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed localization problem of sensor networks with mixed measurements. Each node holds a local coordinate system without a common orientation and is capable of measuring only one type of information (either distance, bearing, or relative position) to near-by nodes. Thus, three types of measurements are mixed in the sensor networks. Moreover, the communication topologies in the sensor networks may be time-varying due to unreliable communications. This paper develops a fully distributed algorithm called BCDL (Barycentric Coordinate based Distributed Localization) where each node starts from a random initial guess about its true coordinate and converges to the true coordinate via only local node interactions. The key idea in BCDL is to establish a unified linear equation constraints for the sensor coordinates by using the barycentric coordinates of each node with respect to its neighbors though the sensor nodes may have different types of measurements. Then a distributed iterative algorithm is proposed to solve the linear equations under time-varying communication networks. A necessary and sufficient graphical condition is obtained to ensure global convergence of the distributed algorithm. [ABSTRACT FROM AUTHOR]

Convergence rate result for a modified steepest descent method and a modified minimal error method for the solution of nonlinear ill-posed operator equation have been proved with noisy data. To our knowledge, convergence rate result for the steepest descent method and minimal error method with noisy data are not known. We provide a convergence rate results for these methods with noisy data. The result in this paper are obtained under less computational cost when compared to the steepest descent method and minimal error method. We present an academic example which satisfies the assumptions of this paper. [ABSTRACT FROM AUTHOR]

Remote medical resources configuration and management involves complex combinatorial Multi-Objective Optimization problem, whose computational complexity is a typical NP problem. Based on the MOEA/D framework, this paper applies the two-way local search strategy and the new selection strategy based on domination amount and proposes the IMOEA/D framework, following which each individual produces two individuals in mutation. In this paper, by using a new selection strategy, the parent individual is compared with two mutated offspring individuals, and the more excellent one is selected for the next generation of evolution. The proposed algorithm IMOEA/D is compared with eMOEA, MOEA/D and NSGA-II, and experimental results show that for most test functions, IMOEA/D proposed is superior to the other three algorithms in terms of convergence rate and distribution. [ABSTRACT FROM AUTHOR]

This paper introduces a new method for the integration of localized surface geometry with fully parameterized absolute nodal coordinate formulation (ANCF) finite elements. In this investigation, ANCF finite elements are used to create the global geometry and perform the finite element (FE)/multibody system (MBS) analysis of deformable bodies. The localized surface geometry details can be described on ANCF element surfaces without the need for mesh refinement. The localized surface is represented using a standard computational geometry method, Non-uniform rational B-spline surface (NURBS), which can describe both conic surface and freeform surface efficiently and accurately. The basic idea of the integration of localized surface geometry with ANCF elements lies in the inclusion of such detail in the element mass matrix and forces. The integration can be implemented by overlapping the localized surface geometry on the original ANCF element or by directly trimming the ANCF element domain to fit the required shape. During the integration process, a mapping between ANCF local coordinates and NURBS localized geometric parameters is used for a consistent implementation of the overlapping and trimming methods. Additionally, two numerical integration methods are compared for the rate of convergence. The results show that the proposed subdomain integration method is better, since it is optimized for dealing with complex geometry. The proposed subdomain method can be used with any fully parameterized ANCF element. In order to analyze the accuracy of the proposed method, a cantilever plate example with localized surface geometry is used, and the simulation results with the proposed method are compared with the simulation results obtained using a commercial FE code. Two other examples that include contact with ground and localized surface geometry are also provided. These examples are a simple plate structure with surface geometry and a tire with tread details. The incompressible hyperelastic Mooney–Rivlin material model is used to describe the material used in the tire tread. It is shown through the tire contact patch that the proposed method can successfully capture the effect of the tread grooves. The rate of convergence and locking of fully parameterized ANCF elements are also discussed in this paper. [ABSTRACT FROM AUTHOR]

This paper addresses the structurally constrained sparse decomposition of multi-dimensional signals onto overcomplete families of vectors, called dictionaries. The contribution of the paper is threefold. Firstly, a generic spatio-temporal regularization term is designed and used together with the standard ℓ 1 regularization term to enforce a sparse decomposition preserving the spatio-temporal structure of the signal. Secondly, an optimization algorithm based on the split Bregman approach is proposed to handle the associated optimization problem, and its convergence is analyzed. Our well-founded approach yields same accuracy as the other algorithms at the state of the art, with significant gains in terms of convergence speed. Thirdly, the empirical validation of the approach on artificial and real-world problems demonstrates the generality and effectiveness of the method. On artificial problems, the proposed regularization subsumes the Total Variation minimization and recovers the expected decomposition. On the real-world problem of electro-encephalography brainwave decomposition, the approach outperforms similar approaches in terms of P300 evoked potentials detection, using structured spatial priors to guide the decomposition. [ABSTRACT FROM AUTHOR]

This paper is devoted to the numerical analysis of a first order fractional-step time-scheme (via decomposition of the viscosity) and “inf-sup” stable finite-element spatial approximations applied to the Primitive Equations of the Ocean. The aim of the paper is twofold. First, we prove that the scheme is unconditionally stable and convergent towards weak solutions of the Primitive Equations. Second, optimal error estimates for velocity and pressure are provided of order O ( k + h l ) for l = 1 or l = 2 considering either first or second order finite-element approximations ( k and h being the time step and the mesh size, respectively). In both cases, these error estimates are obtained under the same constraint k ≤ C h 2 . [ABSTRACT FROM AUTHOR]

Since contours of multi-dimensional depth functions often characterize the distribution, it has become of interest to consider structural properties and limit theorems for the sample contours (see Zuo and Serfling (2000)). For finite dimensional data Massé and Theodorescu (1994) [14] and Kong and Mizera (2012) have made connections of directional quantile envelopes to level sets of half-space (Tukey) depth. In the recent paper (Kuelbs and Zinn, 2014) we showed that half-space depth regions determined by evaluation maps of a stochastic process are not only uniquely determined by related upper and lower quantile functions for the process, but limit theorems have also been obtained. In this paper we study the consequences of these results when applied to finite dimensional data in greater detail. The methods we employ here are based on Kuelbs and Zinn (2015) and Kuelbs and Zinn (2013). [ABSTRACT FROM AUTHOR]

The paper is a potpourri of short sections. There will be some reminiscences about Evarist (from the early 1970s), then some on infinite-dimensional limit theorems from 1950 through 1990. A section reviews a case of slow convergence in the central limit theorem for empirical processes (Beck, 1985) and another the “fast” convergence of Komlós–Major–Tusnády. The paper does an experimental exploration of bootstrap confidence intervals for the mean (of Pareto distributions) and (as less commonly seen) for the variance, of normal and Pareto distributions. [ABSTRACT FROM AUTHOR]

This paper presents a class of stationary iterative processes with convergence order equal to the growth rate of generalized Fibonacci sequences. We prove that the informational and computational efficiency of the processes of our class tends to 2 from below. The paper illustrates a connection of the methods of the class with the nonstationary iterative method suggested by our previous paper, whose efficiency index equals to 2. We prove that the efficiency of the nonstationary iterative method, measured by Ostrowski–Traub criteria, is maximal among all iterative processes of order 2. [ABSTRACT FROM AUTHOR]

This paper discusses the continuous-time consensus problems for directed multi-agent networks under certain coupling or control. Since agents are driven not only by their neighbors' states but also by their derivatives in many realistic situations, dynamical networks described by singular systems are appropriate to study. Consensus problems for such multi-agent networks are considered when the agents communicate in the presence or absence of time delays. The maximum tolerated time-delay is obtained when the multi-agent network asymptotically reaches consensus. The results of this paper indicate that such multi-agent networks can achieve consensus with a demanding convergent speed through agents' interactions. Numerical examples are given to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]