Terms Of Convergence Properties Research Articles

Some Properties of Deferred Nörlund I-Statistical Convergence in Probability, Mean, and Distribution for Sequences of Random Variables

This paper investigates the concept of deferred Nörlund I -statistical convergence in probability, mean of order r, distribution, and explores the relationships among these notions. We present a novel approach to deferred Nörlund I-statistical convergence, which allows for a deeper understanding of the convergence behavior in various contexts. We examine the convergence properties in terms of probability, mean of order r, and distribution, providing a comprehensive analysis of their interdependencies. Our findings contribute to the field of statistical convergence theory, shedding light on the deferred Nörlund I-statistical convergence and its connections with probability, mean of order r, and distribution.

The Weighted Kalman Filter

This paper proposes a new version of the Kalman filter, referred to as weighted Kalman filter (WKF). In the WKF some recent results on the weighted linearization of nonlinear systems are exploited to incorporate modifications in the equations of the extended Kalman filter (EKF). More specifically, the computation of the Jacobian matrices at the current mean of the estimated state is replaced by the multiple integral over the state space of the Jacobian matrix functions multiplied by a weighting function. Similar modifications are introduced in the equations used to account for the available nonlinear model and compute the so-called a priori state and output estimates. The weighting function is chosen to be a multivariable Gaussian function where the generalized variance is selected as proportional to the current covariance matrix of the state estimate. An illustrative example is used to describe the step-by-step derivation of the WKF equations and compare its performance against the EKF in terms of convergence properties and estimation error performance.

Structurally Constrained Initial Impedance Modeling for Poststack Seismic Inversion

The establishment of initial subsurface model is a crucial step for seismic inversion. An accurate and reasonable initial model can mitigate the ill-posedness of seismic inversion and improve the quality of inversion result. A common method for building initial model is the well-log data interpolation. However, the traditional well-log interpolation method ignores the structural information of the subsurface, resulting in the constructed initial model lacking geological meaning. We propose a novel structurally constrained modeling method (SCMM) to obtain a geologically reasonable initial impedance model for poststack seismic inversion. Well-log interpolation can be represented as an inverse problem. SCMM constrains the inversion process by using a regularization operator that forces the well-log data to be extended to the entire seismic working area along the subsurface local structural direction. First, we calculate the seismic dip from the poststack seismic profile. Then, we design the structural operator based on the estimated seismic dip information to constrain the interpolation process. Under the framework of inversion, the interpolation objective function can be established by combining the structural operator with the well-log data misfit term, and it can be solved efficiently by the conjugate gradient algorithm. Synthetic and field data tests show that the initial model built by SCMM is more consistent with the geological rules than that built by traditional method, and the poststack impedance inversion using SCMM is better than that using traditional modeling method in terms of convergence property and accuracy of inversion result.

L2-Norm Based a Posteriori Error Estimates of Compressible and Nearly-Incompressible Elastic Finite Element Solutions

The displacement and stress-based error estimates in a posteriori error recovery of compressible and nearly-incompressible elastic finite element solutions is investigated in the present study. The errors in the finite element solutions, i.e., in displacement and stress, at local and global levels are computed in L2-norm of quantity of interest, namely, displacements and gradients. The error estimation techniques are based on the least square fitting of higher order polynomials to stress and displacement in a patch comprising of node/elements surrounding and including the node/elements under consideration. The benchmark examples of compressible and incompressible elastic bodies, with known solutions employing triangular discretization schemes, are implemented to measure the finite element errors in displacements and gradients. The mixed formulation involving displacement and pressure is used for incompressible elastic analysis. The performance of error estimation is measured in terms of convergence properties, effectivity and mesh required for predefined precision. The error convergence rate, in FEM original solution, recovered solution using displacement recovery-based and stress-based error recovery technique for stresses, are obtained as (1.9714, 2.8999, and 2.5018) and (0.9818, 1.7805, and 1.4952) respectively for compressible and incompressible self-loaded elastic plate benchmark example using higher order triangular elements. It is concluded from the study that displacement fitting technique for extracting higher order derivatives shows a very effective technique for recovery of compressible and nearly-incompressible finite element analysis errors.

Performance Analysis of Orthogonal Gradient Sign Algorithm Using Spline-based Hammerstein Model for Smart Application

This paper presents a spline-based Hammerstein model for adaptive filtering based on a sign algorithm with the normalised orthogonal gradient algorithm. Spline-based Hammerstein architecture consists of an interpolation spline-based adaptive lookup table in the part of nonlinear filter and an adaptive finite impulse response filter used in the part of linear filter. Hammerstein spline adaptive filter (HSAF) is a nonlinear filter for the nonlinear systems among the advantages in the low computational cost and high performance. An adaptive lookup table and spline control points are determined and derived with the orthogonal gradient-based mechanism. Performance analysis in terms of convergence properties and mean square analysis based on the mean square error (MSE) constraint are proven by using the Taylor series expansion of the estimation error in the form of the excess MSE. Experimental results indicate the robust performance of the proposed algorithm can provide the better performance than the other models based on the conventional least mean square Hammerstein spline adaptive filtering algorithm.

Lagrangian Vortex computations of turbine wakes: recent improvements using Poletto’s Synthetic Eddy Method (SEM) to account for ambient turbulence

This paper presents possible techniques for modelling ambient turbulence in the Lagrangian Vortex Method formalism. Due to the fact that regular Synthetic Eddy Method (SEM) already presented in previous studies is not divergence free by definition; improvements were necessary to develop a similar SEM method with such a divergence free property. The recent improvements formulated by R. Poletto give the way to such a possibility. This new Divergence Free Synthetic Eddy Method (DFSEM) is presented here in comparison with the regular SEM. Obtained numerical velocity fields are compared in terms of convergence properties, Power Spectral Density and also Taylor macro-scale. Finally, turbine wakes are computed with both the recent Poletto’s DFSEM and the regular Jarrin’s SEM to highlight differences. At this stage of development, the DFSEM seems very promising even though some improvements are still necessary.

A modified Taylor Galerkin scheme for turbulent compressible flow simulation

As already demonstrated by different authors, the Taylor-Galerkin (TG) scheme, in the context of the Finite Element Method (FEM), is particularly suitable for the solution of supersonic flows. The TG scheme, using hexahedral finite elements with analytical evaluation of element matrices, is applied in this work. Tools to avoid locking and a shock capturing technique for the solution of supersonic viscous and non-viscous compressible flows are also employed. However, TG scheme usually presents instabilities in subsonic flows. Even in cases in which the free stream Mach number corresponds to supersonic flows, there are always flow regions, specifically near the walls of the immersed obstacles, where the speed is lower and the local Mach number corresponds to a subsonic flow. The Characteristic Based Split (CBS) scheme was developed in order to obtain a single method to improve the behavior with respect to TG method in subsonic and supersonic regimes. In the last two decades some works have shown advantages in convergence rates of the CBS method when compared to the TG algorithm. However, simulation time increases in the CBS method since split operations, typical of this algorithm, imply in additional element loops. In this paper a hybrid algorithm called Modified-Taylor-Galerkin scheme (MTG) is proposed. This algorithm presents advantages with respect to TG and CBS schemes in terms of convergence properties and computational processing time. In order to get an efficient algorithm, the element matrices are analytically integrated. This is performed with two different approaches. In the first approach the inverse matrix and the determinant of the Jacobian matrix at element level are evaluated with a reduced integration form, using the point located in the center of the element for mass, convective, diffusive and stabilization element matrices; all these matrices are integrated analytically. In the second approach, mass and convective matrices are calculated by a complete integration scheme (including the inverse matrix and the determinant of the Jacobian matrix at element level in the analytical expression to be integrated) and the diffusive and stabilization matrices are calculated with a reduced integration form, using the point located at the center of the element to calculate the inverse matrix and the determinant of the Jacobian matrix at element level. Finally, this work incorporates the Spalart-Allmaras (S-A) turbulence model using a conservative version of the transport equation, as proposed by the authors of the original S-A model in a later paper. Algorithms are tested to determine convergence rate improvements in both laminar and turbulent cases and for different Mach numbers (supersonic, transonic and subsonic flows).&nbsp

Efficient admission control and resource allocation mechanisms for public safety communications over 5G network slice

The deployment of a broadband public safety (PS) mobile network can be undertaken in different ways. One method involves combining commercial networks with private ones to reduce their deployment cost and time to market. In shared commercial networks, priorities should be defined to differentiate traffic not only between consumers and PS users but also between different PS organizations and type of services. Prioritization must also ensure that emergency calls are always served under normal conditions and during disasters. The recent advent of the fifth generation (5G) wireless standard introduces new technologies, such as network slicing (NS), which allows the provision of logical PS networks in a shared 5G system wherein each slice can be dedicated to an organization or to a type of service. However, 5G management and orchestration become a challenging task with NS, e.g., in handling resource allocation between slices with diverse requirements. Therefore, efficient solutions for slice resource allocation are required to facilitate this task. In this paper, we present a review of adaptive and dynamic resource allocation leveraging on heuristic and reinforcement learning-based algorithms that have been proposed in the recent literatures. The challenge in implementing these algorithms is to find the most suitable one for our problem, i.e., an algorithm that is highly scalable, able to solve problems immediately, and exhibits the best convergence properties in terms of speed and ability to find the global optimum.

Finite-Time Convergence Adaptive Neural Network Control for Nonlinear Servo Systems

Although adaptive control design with function approximators, for example, neural networks (NNs) and fuzzy logic systems, has been studied for various nonlinear systems, the classical adaptive laws derived based on the gradient descent algorithm with σ -modification or e -modification cannot guarantee the parameter estimation convergence. These nonconvergent learning methods may lead to sluggish response in the control system and make the parameter tuning complex. The aim of this paper is to propose a new learning strategy driven by the estimation error to design the alternative adaptive laws for adaptive control of nonlinear servo systems. The parameter estimation error is extracted and used as a new leakage term in the adaptive laws. By using this new learning method, the convergence of both the estimated parameters and the tracking error can be achieved simultaneously. The proposed learning algorithm is further tailored to retain finite-time convergence. To handle unknown nonlinearities in the servomechanisms, an augmented NN with a new friction model is used, where both the NN weights and some friction model coefficients are estimated online via the proposed algorithms. Comparisons with the σ -modification algorithm are addressed in terms of convergence property and robustness. Simulations and practical experiments are given to show the superior performance of the suggested adaptive algorithms.

Bayesian Coalition Formation Game for Virtual 5G Core Network Functions

The network function virtualization (NFV) enables the virtual network functions (VNFs) to run as software components upon a virtualization system hosted in a cloud. Recently, due to its high flexibility and elasticity in terms of network services and functions deploying, NFV has been considered as one of the key enabling techniques of the fifth-generation (5G) wireless systems. Moreover, the creation of the core network functions is the key to the implementation of 5G. Currently, there are extensive studies researching into how to deploy cooperatively VNFs over a federated cloud for multiple cloud providers (CPs) to create the 5G Core. These studies have a critical assumption that each CP participating in the cooperation is fully informed of all the information about other CPs. However, the assumption may not hold in practice. Since CPs adopt diverse virtualization technologies (e.g., XEN, KVM, or containers), the cost to create an instance of one VNF for each CP may be different. Moreover, the cost information is private and will not be shared with each other. Consequently, it is difficult for each CP to determine whether to cooperate with others and the way of cooperation. Therefore, in this paper, we utilize the Bayesian coalition formation game (BCFG) to tackle this challenging situation with the unknown information about CPs and formulate the optimal coalition that can deploy cooperatively each VNFs of 5G Core. Specifically, we address the optimal number of VNF instances to instantiate, the number of virtual resources for each instance, and the placement decision in a specific CP over a federated cloud. We propose a BCFG-based non-myopic and full negotiation approach for the creation of the virtual 5G Core network functions. Simulation results demonstrate the comprehensive performance of the proposed method in terms of convergence properties and the profits that each participating CP can obtain.

Improved approximation and error estimations by King type (p, q)-Szász-Mirakjan Kantorovich operators

In the present paper, two different modifications are proposed for (p, q)-Szász-Mirakjan-Kantorovich operators which preserve some test functions. Some approximation results with the help of better-known Korovkin’s theorem and weighted Korovkin’s theorem for these operators are presented. Furthermore, convergence properties in terms of modulus of continuity and class of Lipschitz functions are studied. It has been shown that for a given absolute error bound, King type modified (p, q)-Szász-Mirakjan-Kantorovich operators require lesser value of m and elapsed time within some subintervals. Further for comparisons, some graphics and error estimation tables are presented using MATLAB(R2018a).

Iterative coupling algorithms for large multidomain problems with the boundary element method

SummaryA new parallel Robin‐Robin adaptive iterative coupling algorithm with dynamic relaxation parameters is proposed for the boundary element method (BEM), and relaxation parameters are derived for other existing iterative coupling algorithms. The performances of the new algorithm and of the modified existing algorithms are investigated in terms of convergence properties with respect to the number of subdomains, mesh density, interface mesh conformity, and BEM element types. Results show that the number of subdomains and the refinement level of the mesh are the two dominant factors affecting the performances of the considered algorithms. The proposed parallel Robin‐Robin algorithm shows the best overall convergence behavior for the tested large problems, thanks to its effectiveness in handling complex boundary conditions and large number of subdomains, thus resulting to be very promising for efficient parallel BEM computing and large coupling problems.Source code is available at https://github.com/BinWang0213/PyBEM2D.

A new unified approach for the state estimation and bad data analysis of electric power transmission systems with multi-terminal VSC-based HVDC networks

The aim of this paper is the proposal of a static state estimation approach suitable for electric power transmission systems containing fully controlled multi-terminal high voltage direct current networks. An integrated electric circuit model of the voltage source converter station, including its on-load tap-changer (OLTC) transformer, is used to determine the state variables associated with the AC–DC interface. These controllable variables are added to the state vector, together with the nodal voltages associated with the AC and DC networks, as well as the duty cycle of the DC–DC converters, for a unified SE solution in a single frame of reference. The SE problem is formulated based on Hachtel’s augmented matrix method in order to directly consider the operational constraints associated with the AC–DC network. In addition, a new technique for performing multiple bad data analysis is proposed in which the original level of measurement redundancy is maintained unaltered during the estimation process. The applicability of the proposed SE approach and bad data analysis is demonstrated by estimating the operating state of two integrated AC–DC multi-terminal transmission networks. The numerical results show that the proposal retains good convergence properties in terms of the number of iterations required to achieve a reliable state estimation as well as robustness to deal with bad data.

Efficient OFDMA for LiFi Downlink

Light-fidelity (LiFi) relies on visible light communication to provide multiuser access in a small cell. For higher throughput, this paper studies the resource allocation problem for an orthogonal frequency-division multiplexing access scheme for LiFi downlink transmissions and presents a joint design of the bias level, power and subcarrier allocation. Decomposing the original optimization into subproblems, we first develop an efficient algorithm for the bias optimization, along with its performance analysis in terms of convergence properties and the global optimality. We then propose several power and subcarrier allocation strategies, including an optimal algorithm and a near-optimal simplified method, to satisfy different complexity and accuracy requirements. Finally, we present two algorithms to jointly optimize the bias, power, and subcarrier, and analyze the convergence properties in terms of both the objective and the solution. Comprehensive simulation results under practical LiFi system setups illustrate the effectiveness of the proposed algorithms.

Adaptive dynamic programming for discrete-time linear quadratic regulation based on multirate generalised policy iteration

ABSTRACTIn this paper, we propose two multirate generalised policy iteration (GPI) algorithms applied to discrete-time linear quadratic regulation problems. The proposed algorithms are extensions of the existing GPI algorithm that consists of the approximate policy evaluation and policy improvement steps. The two proposed schemes, named heuristic dynamic programming (HDP) and dual HDP (DHP), based on multirate GPI, use multi-step estimation (M-step Bellman equation) at the approximate policy evaluation step for estimating the value function and its gradient called costate, respectively. Then, we show that these two methods with the same update horizon can be considered equivalent in the iteration domain. Furthermore, monotonically increasing and decreasing convergences, so called value iteration (VI)-mode and policy iteration (PI)-mode convergences, are proved to hold for the proposed multirate GPIs. Further, general convergence properties in terms of eigenvalues are also studied. The data-driven online implementation methods for the proposed HDP and DHP are demonstrated and finally, we present the results of numerical simulations performed to verify the effectiveness of the proposed methods.

Dunkl generalization of q-Szász-Mirakjan Kantorovich operators which preserve some test functions

In this paper we introduce q-Szasz-Mirakjan-Kantorovich operators generated by a Dunkl generalization of the exponential function and we propose two different modifications of the q-Szasz-Mirakjan-Kantorovich operators which preserve some test functions. We obtain some approximation results with the help of the well-known Korovkin theorem and the weighted Korovkin theorem for these operators. Furthermore, we study convergence properties in terms of the modulus of continuity and the class of Lipschitz functions. This type of operator modification enables better error estimation than the classical ones. We also obtain a Voronovskaja-type theorem for these operators.

${\mathcal{T}}$-REx. II. RETRIEVAL OF EMISSION SPECTRA

-REx (Tau Retrieval of Exoplanets) is a novel, fully Bayesian atmospheric retrieval code custom built for extrasolar atmospheres. In Waldmann et al., the transmission spectroscopic case was introduced, and here we present the emission spectroscopy spectral retrieval for the -REx framework. Compared to transmission spectroscopy, the emission case is often significantly more degenerate due to the need to retrieve the full atmospheric temperature–pressure (TP) profile. This is particularly true in the case of current measurements of exoplanetary atmospheres, which are either of low signal-to-noise, low spectral resolution, or both. We present a new way of combining two existing approaches to the modeling of the said TP profile: (1) the parametric profile, where the atmospheric TP structure is analytically approximated by a few model parameters, (2) the layer-by-layer approach, where individual atmospheric layers are modeled. Both of these approaches have distinct advantages and disadvantages in terms of convergence properties and potential model biases. The -REx hybrid model presented here is a new two-stage TP profile retrieval, which combines the robustness of the analytic solution with the accuracy of the layer-by-layer approach. The retrieval process is demonstrated using simulations of the hot-Jupiter WASP-76b and the hot-super-Earth 55 Cnc e as well as the secondary eclipse measurements of HD 189733b.

CAPRI: efficient inference of cancer progression models from cross-sectional data.

We devise a novel inference algorithm to effectively solve the cancer progression model reconstruction problem. Our empirical analysis of the accuracy and convergence rate of our algorithm, CAncer PRogression Inference (CAPRI), shows that it outperforms the state-of-the-art algorithms addressing similar problems. Several cancer-related genomic data have become available (e.g. The Cancer Genome Atlas, TCGA) typically involving hundreds of patients. At present, most of these data are aggregated in a cross-sectional fashion providing all measurements at the time of diagnosis. Our goal is to infer cancer 'progression' models from such data. These models are represented as directed acyclic graphs (DAGs) of collections of 'selectivity' relations, where a mutation in a gene A 'selects' for a later mutation in a gene B. Gaining insight into the structure of such progressions has the potential to improve both the stratification of patients and personalized therapy choices. The CAPRI algorithm relies on a scoring method based on a probabilistic theory developed by Suppes, coupled with bootstrap and maximum likelihood inference. The resulting algorithm is efficient, achieves high accuracy and has good complexity, also, in terms of convergence properties. CAPRI performs especially well in the presence of noise in the data, and with limited sample sizes. Moreover CAPRI, in contrast to other approaches, robustly reconstructs different types of confluent trajectories despite irregularities in the data. We also report on an ongoing investigation using CAPRI to study atypical Chronic Myeloid Leukemia, in which we uncovered non trivial selectivity relations and exclusivity patterns among key genomic events. CAPRI is part of the TRanslational ONCOlogy R package and is freely available on the web at: http://bimib.disco.unimib.it/index.php/Tronco daniele.ramazzotti@disco.unimib.it Supplementary data are available at Bioinformatics online.

Chaotic biogeography-based optimization approach to target detection in UAV surveillance

This paper describes a novel chaotic biogeography-based optimization (CBBO) algorithm for target detection by means of template matching to meet the request of unmanned aerial vehicle (UAV) surveillance. Template matching has been widely applied in movement tracking and other fields and makes excellent performances in visual navigation. Biogeography-based optimization (BBO) algorithm emerges as a new kind of optimization method on the basis of biogeography concept. The idea of migration and mutation strategy of species in BBO contributes to solving optimization problems. Our work adds chaotic searching strategy into BBO and applies CBBO in template matching. By utilizing chaotic strategy, the population ergodicity and global searching ability are improved, thus avoiding local optimal solutions during evolution. Applying the algorithm to resolving template matching problem overcomes the defects of common image matching. Series of experimental results demonstrate the feasibility and effectiveness of our modified approach over other algorithms in solving template matching problems. Our modified BBO algorithm performs better in terms of convergence property and robustness when compared with basic BBO.

Experimental Analysis of the Power Auto-Correlation-Based Chromatic Dispersion Estimation Method

We experimentally investigate the performance of the signal power autocorrelation-based method for chromatic dispersion (CD) estimation in a polarization-multiplexing quadrature phase-shift keying (PM-QPSK) 100G coherent optical system conveying optical channel transport unit level-4 (OTU4) frames. It is shown that the typical laboratory setup, where the signal components are generated from delayed versions of the same pseudorandom binary sequence (PRBS), is inadequate for experimental validation because of artifacts in the signal auto-correlation function. This problem is circumvented by the use of a commercial line card transporting independent data sequences. The algorithm is used to estimate accumulated CD values from 0 to 50 000 ps/nm under up to 80-ps differential group delay (DGD). We further evaluate its convergence properties in terms of the length of the sample vector required for correct CD estimation and address the hardware resource requirements. The CD-shifted version of the algorithm yielded a maximum estimation error of 186 ps/nm in all tested conditions.