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We present a numerical Tikhonov regularization method that can be used to reconstruct past ground surface temperature (GST) records from borehole temperatures. The present ground temperature preserves past climatic signals according to the heat diffusion process in permafrost-affected soils. To track past surface temperature, we employ an inverse method based on a physical connection between GST and measured borehole temperatures. We validate this method by applying it to two synthetic surface temperature cases. Since measured borehole data include uncertainty, we add random noise to our synthetic input borehole data to simulate the process of noise suppression. GST recovered with corresponding uncertainty shows a close match with synthetic surface temperature for both cases. We show that this method can successfully suppress the noise disturbance and achieve smoother solutions.The ability of borehole temperature data to resolve past climatic events is investigated using the Tikhonov method. We investigated past GST of Wudaoliang on Qinghai-Tibet plateau and the inversion result shows the increasing trend of 1.8 (±1.6) in the past 308 years. This GST trend fits the air temperature observation trend but has small value deviation caused by local topography and surface energy budgets of the ground surface. [ABSTRACT FROM AUTHOR]

A stabilized version of the fundamental solution method to catch ill-conditioning effects is investigated with focus on the computation of complex-valued elastic interior transmission eigenvalues in two dimensions for homogeneous and isotropic media. Its algorithm can be implemented very shortly and adopts to many similar partial differential equation-based eigenproblems as long as the underlying fundamental solution function can be easily generated. We develop a corroborative approximation analysis which also implicates new basic results for transmission eigenfunctions and present some numerical examples which together prove successful feasibility of our eigenvalue recovery approach. [ABSTRACT FROM AUTHOR]

The paper presents a novel decoupling method, based on blending the input and output signals of linear dynamical systems. For this purpose, blend vectors are introduced and calculated such that the minimum sensitivity of the controlled mode is maximised, while the worst case gain of the other subsystems is minimised from the blended input to the blended output. The problem is transformed to a standard optimisation program subject to Linear Matrix Inequality constraints. An arising rank constraint is resolved by an alternating projection scheme. The method is presented based on the decoupling of a single mode, but the extension to decouple multiple modes is also discussed. Numerical examples are given to validate the method and to illustrate how the proposed approach can be applied for control engineering problems. [ABSTRACT FROM AUTHOR]

We consider the problem of estimating community memberships of nodes in a network, where every node is associated with a vector determining its degree of membership in each community. Existing provably consistent algorithms often require strong assumptions about the population, are computationally expensive, and only provide an overall error bound for the whole community membership matrix. This article provides uniform rates of convergence for the inferred community membership vector of each node in a network generated from the mixed membership stochastic blockmodel (MMSB); to our knowledge, this is the first work to establish per-node rates for overlapping community detection in networks. We achieve this by establishing sharp row-wise eigenvector deviation bounds for MMSB. Based on the simplex structure inherent in the eigen-decomposition of the population matrix, we build on established corner-finding algorithms from the optimization community to infer the community membership vectors. Our results hold over a broad parameter regime where the average degree only grows poly-logarithmically with the number of nodes. Using experiments with simulated and real datasets, we show that our method achieves better error with lower variability over competing methods, and processes real world networks of up to 100,000 nodes within tens of seconds. for this article are available online. [ABSTRACT FROM AUTHOR]

We derive an explicit k-dependence in W m , p error estimates for P k Lagrange finite elements. Two laws of probability are established to measure the relative accuracy between P k 1 and P k 2 finite elements, ( k 1 < k 2 ), in terms of W m , p -norms. We further prove a weak asymptotic relation in D ′ (R) between these probabilistic laws when difference k 2 − k 1 goes to infinity. Moreover, as expected, one finds that P k 2 finite element is surely more accurate than P k 1 , for sufficiently small values of the mesh size h. Nevertheless, our results also highlight cases where P k 1 is more likely accurate than P k 2 , for a range of values of h. Hence, this approach brings a new perspective on how to compare two finite elements, which is not limited to the rate of convergence. [ABSTRACT FROM AUTHOR]

In this paper, the Crank–Nicolson (CN) and rotated four-point Fractional Explicit Decoupled Group (FEDG) methods are introduced to solve the two-dimensional reaction–subdiffusion equation with Caputo–Fabrizio operator. The FEDG method is derived by 45 ∘ rotation of CN method around the x and y axes. The restarted GMRES with left preconditioner L, based on incomplete LU factorization is used to solve the discretized system obtained by our proposed methods. The FEDG method shows more superior capability in the term of CPU timings and the number of iteration compared to CN method on the standard grid but with same order of accuracy. The stability and convergence analysis in the approximate schemes are investigated. Some numerical experiments performed to show the efficiency of the presented methods in terms of accuracy and CPU time. [ABSTRACT FROM AUTHOR]

Robust stability problem of integral delay systems with uncertain kernel matrix functions is addressed in this paper. On the basis of the characteristic equation and the argument principle, an algorithm is generated, which is shown to outperform the Lyapunov-Krasovskii (LK) approaches with respect to conservatism in the presented examples. Despite the conventional manual use of the Nyquist criterion, the proposed algorithm is fully algebraic, cheaper and easily implemented in computer programs. The kernel matrix function in this method is not limited to the exponential type and can include any bounded real function as its elements. [ABSTRACT FROM AUTHOR]

The high-dimensional linear model y = X β 0 + ϵ is considered and the focus is put on the problem of recovering the support S0 of the sparse vector β 0. We introduce a new l 1 -based estimator, called Lasso-Zero, whose novelty resides in the repeated use of noise dictionaries concatenated to X for overfitting the response. Lasso-Zero is an extension of thresholded basis pursuit (TBP), for which we prove sign consistency for correlated Gaussian designs. Both theoretical and empirical results motivate the use of noise dictionaries to improve TBP when the coefficients' amplitude is low. To select the threshold of Lasso-Zero, we suggest to employ a pivotal version of the quantile universal threshold (QUT) that exploits a byproduct of Lasso-Zero to avoid the need to estimate the noise level. Numerical simulations show that Lasso-Zero tuned by QUT performs well in terms of support recovery and provides an excellent trade-off between high power and few false discoveries compared to competitors. Supplemental materials for this article are available online. [ABSTRACT FROM AUTHOR]

We consider a measurement constrained supervised learning problem, that is, (i) full sample of the predictors are given; (ii) the response observations are unavailable and expensive to measure. Thus, it is ideal to select a subsample of predictor observations, measure the corresponding responses, and then fit the supervised learning model on the subsample of the predictors and responses. However, model fitting is a trial and error process, and a postulated model for the data could be misspecified. Our empirical studies demonstrate that most of the existing subsampling methods have unsatisfactory performances when the models are misspecified. In this paper, we develop a novel subsampling method, called "LowCon," which outperforms the competing methods when the working linear model is misspecified. Our method uses orthogonal Latin hypercube designs to achieve a robust estimation. We show that the proposed design-based estimator approximately minimizes the so-called worst-case bias with respect to many possible misspecification terms. Both the simulated and real-data analyses demonstrate the proposed estimator is more robust than several subsample least-squares estimators obtained by state-of-the-art subsampling methods. for this article are available online. [ABSTRACT FROM AUTHOR]

In this paper, the mode matching (MM) method is applied to analyze the dispersion of the newly proposed transmission line (TL), centrosymmetric double-slotted line (CSDSL). For simplicity, the lateral metallic vias are replaced with the electric walls (EWs). Furthermore, four magnetic walls (MWs) are added to guarantee the boundary condition (BC) of MM. The proposed method is compared with the 3D electromagnetic field analysis (HFSS). The result shows a good agreement between the dispersions of the dominant mode obtained using MM method and HFSS. Additionally, the dispersions of the higher modes of CSDSL are also provided using the proposed method with convergent results. [ABSTRACT FROM AUTHOR]

A trigonometric quintic B-spline method is proposed for the solution of a class of turning point singularly perturbed boundary value problems (SP-BVPs) whose solution exhibits either twin boundary layers near both endpoints of the interval of consideration or an interior layer near the turning point. To resolve the boundary/interior layer(s) trigonometric quintic B-spline basis functions are used with a piecewise-uniform mesh generated with the help of a transition parameter that separates the layer and regular regions. The proposed method reduces the problem into a system of algebraic equations which can be written in matrix form with the penta-diagonal coefficient matrix. The well-known fast penta-diagonal system solver algorithm is used to solve the system. The method is shown almost fourth-order convergent irrespective of the size of the diffusion parameter ϵ. The theoretical error bounds are verified by taking some relevant test examples computationally. [ABSTRACT FROM AUTHOR]

The natural perturbation orbital (NPO) method, combined with the gauge-including atomic orbital (GIAO), was applied to nuclear magnetic resonance (NMR) chemical shifts. The substituent effects of electron-donating (NH2) and electron-withdrawing (NO2) groups on the 13C NMR chemical shifts of monosubstituted benzenes were analysed using NPOs. 13C chemical shifts at the ortho-, meta- and para-positions were efficiently decomposed into contributions from two NPO pairs ( σ x − π x ∗ , σ y − π y ∗ ). These contributions were further divided into two factors, namely electron density in the vicinity of resonance nuclei and orbital energy gaps. Trends in the electron density matched with the ortho-, meta- and para-directions of the substituent effects. Specifically, NH2 shielded the ortho- and para-carbons, while NO2 deshielded the same carbons. The orbital energy gaps of ortho-carbons in NH2- and NO2-benzenes were significantly decreased, showing that these substituents shielded the ortho-carbons. [ABSTRACT FROM AUTHOR]

The parameterized generalized inverse eigenvalue problems containing multiplicative and additive inverse eigenvalue problems appear in vibrating systems design, structural design, and inverse Sturm–Liouville problems. In this article, by using the Cholesky factorization and the Jacobi method, we propose two efficient algorithms based on Newton's method and the L-BFGS-B method for solving these problems. To demonstrate the effectiveness of the algorithms, we present three numerical examples. [ABSTRACT FROM AUTHOR]

Newton method is one of the most powerful methods for finding solutions of nonlinear equations and for proving their existence. In its 'pure' form it has fast convergence near the solution, but small convergence domain. On the other hand damped Newton method has slower convergence rate, but weaker conditions on the initial point. We provide new versions of Newton-like algorithms, resulting in combinations of Newton and damped Newton method with special step-size choice, and estimate its convergence domain. Under some assumptions the convergence is global. Explicit complexity results are also addressed. The adaptive version of the algorithm (with no a priori constants knowledge) is presented. The method is applicable for under-determined equations (with m< n , m being the number of equations and n being the number of variables). The results are specified for systems of quadratic equations, for composite mappings and for one-dimensional equations and inequalities. [ABSTRACT FROM AUTHOR]

Ridge or more formally l 2 regularization shows up in many areas of statistics and machine learning. It is one of those essential devices that any good data scientist needs to master for their craft. In this brief ridge fest, I have collected together some of the magic and beauty of ridge that my colleagues and I have encountered over the past 40 years in applied statistics. [ABSTRACT FROM AUTHOR]

In this paper, we propose a Padé-type approximation based on truncated total least squares (P – TTLS) and compare it with three commonly used smoothing methods: Penalized spline, Kernel smoothing and smoothing spline methods that have become very powerful smoothing techniques in the nonparametric regression setting. We consider the nonparametric regression model, y i = g (x i) + ε i , and discuss how to estimate smooth regression function g where we are unsure of the underlying functional form of g. The Padé approximation provides a linear model with multi-collinearities and errors in all its variables. The P – TTLS method is primarily designed to address these issues, especially for solving error-contaminated systems and ill-conditioned problems. To demonstrate the ability of the method, we conduct Monte Carlo simulations under different conditions and employ a real data example. The outcomes of the experiments show that the fitted curve solved by P – TTLS is superior to and more stable than the benchmarked penalized spline (B – PS), Kernel smoothing (KS) and smoothing spline (SS) techniques. [ABSTRACT FROM AUTHOR]

The development of interpretable and readable diagnosis support models in the medical field is becoming an active research area. Neuroimaging technology has been widely used in the study of various brain diseases, supported by several kind of machine learning algorithms. Such algorithms, in spite of their accuracy, have often a lack of interpretability. In order to address these issues, in this paper, a new classifier based on functional networks, revised from a granular perspective is proposed. Granular architectures allow high accuracy, without losing interpretability. Two classes of neurodevelopmental disorders, that is Attention Deficit Hyperactivity Disorder and Autism Spectrum Disorder, will be considered to perform numerical experiments on publicly available data. The numerical results against state-of-the-art methods show the good performance of the proposed scheme, by confirming some theoretical achievements. [ABSTRACT FROM AUTHOR]

In this work, we describe a method for estimating the muscle activity without drawing any assumptions regarding optimality principles in human motor control strategies; further, the method does not require any neural circuitry modeling which limits the neurophysiological terms and estimability of the method. We introduce the concept of system observability, which can reconstruct states from outputs and their derivatives based on system dynamics. Based on neuromuscular system observability, we estimate the muscle activity from joint torques and kinematics of multiple locomotive gaits, while considering the unknown neural inputs as system disturbances. Moreover, to quantify the robustness of the method, the degree of observability and parameter sensitivity are evaluated. Finally, the neurophysiological implications and generality of the method are addressed. [ABSTRACT FROM AUTHOR]

Some improved rigorous perturbation bounds with normwise perturbation for the block Cholesky downdating problem are first derived by combining the modified matrix-vector equation approach with the strategy for Lyapunov majorant function and the Banach fixed point theorem. Then, we investigate four distinct kinds of condition numbers, i.e. two normwise ones, and mixed and componentwise ones, for this problem, and present their explicit expressions. Furthermore, using the probabilistic spectral norm estimator and the small-sample statistical condition estimation method, we also consider the statistical estimation of these condition numbers and design two algorithms. The obtained results are illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

We propose a novel linear discriminant analysis (LDA) approach for the classification of high-dimensional matrix-valued data that commonly arises from imaging studies. Motivated by the equivalence of the conventional LDA and the ordinary least squares, we consider an efficient nuclear norm penalized regression that encourages a low-rank structure. Theoretical properties including a nonasymptotic risk bound and a rank consistency result are established. Simulation studies and an application to electroencephalography data show the superior performance of the proposed method over the existing approaches. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel multiple input multiple output (MIMO) linear parameter varying (LPV) state-space refinement system identification algorithm that uses tensor networks. Its novelty mainly lies in representing the LPV sub-Markov parameters, data and state-revealing matrix condensely and in exact manner using specific tensor networks. These representations circumvent the 'curse-of-dimensionality' as they inherit the properties of tensor trains. The proposed algorithm is 'curse-of-dimensionality'-free in memory and computation and has conditioning guarantees. Its performance is illustrated using simulation cases and additionally compared with existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we present a software-based approach for collision avoidance that can be applied in human–robot collaboration scenarios. One of the contributions is a method for converting clustered 3D sensor data into computationally efficient convex hull representations used for robot-obstacle distance computation. Based on the computed distance vectors, we generate collision avoidance motions using a potential field approach and integrate them with other simultaneously running robot tasks in a constraint-based control framework. In order to improve control performance, we apply evolutionary techniques for parameter optimization within this framework based on selected quality criteria. Experiments are performed on a dual-arm robotic system equipped with several depth cameras. The approach is able to generate task-compliant avoidance motions in dynamic environments with high performance. [ABSTRACT FROM AUTHOR]

Regression is a common technique in engineering when physical laws are unknown. Practitioners usually look for a unique set of true parameters that optimally explain the observed data. This is, for instance, the case in concrete strength estimation where engineers have been looking for an universal law to estimate this magnitude. We show that this approach is incorrect if the uncertainty of the regression problem is not properly taken into account. The uncertainty analysis of linear regression problems is revisited providing an analytical expression for the direction of maximum uncertainty where most of the models are sampled when partial information is used. We also analyse the case of 1D nonlinear regression models (exponential and potential models) and the multivariate case. We show a simple way of sampling the posterior distribution of the model parameters by performing least-squares of different data bags (bootstrap), introducing the percentile curves for the concrete strength estimation, comparing the results obtained from the linearized and nonlinear bootstrap procedures in the case of the nonlinear regression models. The methodology introduced in this paper constitutes a robust and simple way of assessing the intrincic uncertainty of these well-known parameter identification problems and adopting more robust decisions. [ABSTRACT FROM AUTHOR]

This paper provides a procedure for designing a sliding mode observer for a nonlinear system in the presence of Gaussian input disturbances and sensor noises. The paper first proposes a novel candidate for Lyapunov stability, termed a Time-averaged Lyapunov (TAL) function. The TAL averages the Lyapunov analysis over a small finite time interval, allowing for intuitive analysis of noises and disturbance. The paper then provides the necessary and sufficient condition for the design of the sliding observer gainsusing the TAL in the form of Linear Matrix Inequality (LMI). The LMIs can then be explicitly solved offline using commercial LMI solvers. The paper compares the LMIs for the two observer designs to demonstrate the design of the sliding mode observer using TAL can greatly enhance the scope of observer design for nonlinear systems. [ABSTRACT FROM AUTHOR]

The paper considers the fault detection problem over finite-frequency domain for a class of discrete time-delayed networked systems subject to round-robin protocol. This protocol is a periodic one to schedule the information transmitted via a shared communication network with an intent to prevent the data from collisions. In this scenario, the error dynamics can be regarded as a periodic protocol-induced system. The aim of the problem addressed is to design a fault detection filter that (1) the sensitivity of the residual to the fault is enhanced by means of a maximised H − index and (2) the effect from the exogenous disturbances on the residual is decreased with considering a minimised H ∞ index. By resorting to a Lyapunov function, an improved version of generalised Kalman–Yakubovich–Popov lemma (GKYP) is first developed for protocol-induced periodic system. Then, in light of such a lemma, sufficient conditions are derived to guarantee both the fault sensitivity and the disturbance attenuation capability by solving a set of matrix inequalities. Finally, the usefulness of the presented fault detection algorithm is utilised via a numerical simulation. [ABSTRACT FROM AUTHOR]

In this paper, we study the numerical solution of singularly perturbed degenerate parabolic convection–diffusion problem on a rectangular domain. The solution of the problem exhibits a parabolic boundary layer in the neighbourhood of x=0. First, we use the backward-Euler finite difference scheme to discretize the time derivative of the continuous problem on uniform mesh in the temporal direction. Then, to discretize the spatial derivatives of the resulting time semidiscrete problem, we apply the hybrid finite difference scheme, which is a combination of central difference scheme and midpoint upwind scheme on piecewise uniform Shishkin mesh. We derive the error estimates, which show that the proposed hybrid scheme is ϵ-uniform convergent of almost second-order (up to a logarithmic factor) in space and first-order in time. Some numerical results have been carried out to validate the theoretical results. [ABSTRACT FROM AUTHOR]

A numerical scheme for a class of two-point singularly perturbed boundary value problems with an interior turning point having an interior layer or twin boundary layers is proposed. The solution of this type of problem exhibits a transition region between rapid oscillations and the exponential behaviour. The problem with interior turning point represents a one-dimensional version of stationary convection-diffusion problems with a dominant convective term and a speed field that changes its sign in the catch basin. To solve these problems numerically, we consider a scheme which comprises quintic B-spline collocation method on an appropriate piecewise-uniform mesh, which is dense in the neighbourhood of the interior/boundary layer(s). The method is shown to be parameter-uniform with respect to the singular perturbation parameter ϵ. Some relevant numerical examples are illustrated to verify the theoretical aspects computationally. The results compared with other existing methods show that the proposed method provides more accurate solutions. [ABSTRACT FROM AUTHOR]

This paper investigates the prescribed performance distributed output consensus problem under directed graphs. With the utilisation of a filter, the original system of each follower can be converted into a strict-feedback system. Then, we design a prescribed performance output feedback distributed control protocol by applying the backstepping approach in the converted system. The proposed protocol can guarantee that the consensus tracking error of each agent evolves in predefined decaying bounds to achieve the prescribed performance, that is, the consensus tracking error of each agent converges to a predetermined residual set at a convergence rate no less than a prespecified value and exhibiting a maximum overshoot less than a preassigned constant. Moreover, during the process of consensus, all the signals in the closed-loop system are globally uniformly bounded. A simulation example is given to verify the effectiveness of the proposed control protocol. [ABSTRACT FROM AUTHOR]

In this paper, we have developed a new algorithm for solving nonconvex large-scale problems. The new algorithm performs explicit matrix modifications adaptively, mimicing the implicit modifications used by trust-region methods. Thus, it shares the equivalent theoretical strength of trust-region approaches, without needing to accommodate an explicit step-size constraint. We show that the algorithm is well suited for solving very large-scale nonconvex problems whenever Hessian-vector products are available. The numerical results on the CUTEr problems demonstrate the effectiveness of this approach in the context of a line-search method for large-scale unconstrained nonconvex optimization. Moreover, applications in deep-learning problems further illustrate the usefulness of this algorithm. It does not share any of the prohibitive traits of popular matrix-free algorithms such as truncated conjugate gradient (CG) due to the difficult nature of deep-learning problems. Thus the proposed algorithm serves to bridge the gap between the needs of data-mining community and existing state-of-the-art approaches embraced foremost by the optimization community. Moreover, the proposed approach can be realized with minimal modification to the CG algorithm itself with negligible storage and computational overhead. [ABSTRACT FROM AUTHOR]

When we speak about parametric programming, sensitivity analysis or related topics, we usually mean the problem of studying specified perturbations of the data such that for a given optimization problem some optimality criterion remains satisfied. In this paper, we turn to another question. Suppose that A is a matrix having a specific property . What are the maximal allowable variations of the data such that the property still remains valid for the matrix? We study two basic forms of perturbations. The first is a perturbation in a given direction, which is closely related to parametric programming. The second type consists of all possible data variations in a neighbourhood specified by a certain matrix norm; this is related to the tolerance approach to sensitivity analysis or to stability. The matrix properties discussed in this paper are positive definiteness; M-matrix, H-matrix and P-matrix property; total positivity; inverse M-matrix property and inverse nonnegativity. [ABSTRACT FROM AUTHOR]

In this article, a collocation method for the problems where the second-order derivative is multiplied by a small perturbation parameter ϵ, the coefficient of the convection term vanishes at a point within the domain of interest, and the shift δ is of is proposed. Similar boundary value problems are encountered while simulating several real-life processes, for instance, first exit time problem in the modelling of neuronal variability. The presence of turning point results into twin boundary layers or an interior layer in the solution of the problem under consideration. A rigorous analysis is carried out and it has been shown theoretically that the numerical solution generated by the method converges uniformly to the solution of the continuous problem with respect to the singular perturbation parameter. The effect of the small shift on the boundary/interior layer(s) has also been observed. Several numerical examples are presented to support the theoretical analysis developed in this article. [ABSTRACT FROM AUTHOR]

The problems of unconstrained optimisation and establishing asymptotic stability have much in common. Understanding the analogy between these two sheds light on their interconnection and may lead to a number of new results. For instance, in this paper, we provide estimates of the rate of convergence when analysing asymptotic stability of differential equations, rather than just ascertain the very fact of stability. Also, standard methods for the design of Lyapunov functions (e.g. those having the meaning of the full energy of the system) turn out to be unsatisfactory from this point of view and have to be modified. These claims are exemplified in the paper by considering the heavy-ball method for function minimisation ‘in parallel’ with the problem of asymptotic stability for the synchronous motor equation. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach to include stochastic variation in the framework of a macroscopic traffic model. Simultaneously, the effects of insufficient data quality and consequent inaccurate identification are investigated. The traffic density distribution over time and space provides a deeper understanding of the evolution of jams, which in turn is vital for the development of traffic network control algorithms. Model parameters are estimated using both Eulerian and Lagrangian sensing. Instead of using deterministic model parameters directly, this work proposes to use stochastic model parameters. Therefore, in addition to the estimated mean of model parameters, a corresponding covariance matrix is estimated as well. The utilized traffic model supports arbitrary Fundamental Diagrams defined by (a combination of) model parameters. Using an analytic approach to define the resulting variation in the Fundamental Diagram is generally impossible, due to the nonlinear combination of random variables in the parameterization of the Fundamental Diagram. A general approach to deal with complex combinations of random variables in the definition of Fundamental Diagrams and, consequently, in the traffic model, is proposed. The core idea is to utilize Monte Carlo Simulation to create a discretized lookup table for the density-speed relationship. Thereby computational effort is significantly reduced, while preserving the ability of the traffic model to reflect variation in the driving behavior. The proposed approach is validated via simulation with state-of-the-art software and Monte Carlo Simulations. [ABSTRACT FROM AUTHOR]

The linear regression model is widely used in empirical work in economics, statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We give inference methods that allow for many covariates and heteroscedasticity. Our results are obtained using high-dimensional approximations, where the number of included covariates is allowed to grow as fast as the sample size. We find that all of the usual versions of Eicker-White heteroscedasticity consistent standard error estimators for linear models are inconsistent under this asymptotics. We then propose a new heteroscedasticity consistent standard error formula that is fully automatic and robust to both (conditional) heteroscedasticity of unknown form and the inclusion of possibly many covariates. We apply our findings to three settings: parametric linear models with many covariates, linear panel models with many fixed effects, and semiparametric semi-linear models with many technical regressors. Simulation evidence consistent with our theoretical results is provided, and the proposed methods are also illustrated with an empirical application. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

The numerical solution of the inverse problem is usually obtained by solving a set of linear algebraic equations, while the system of equations may suffer from ill-posedness due to insufficient data. Regularisation is a technique for making the estimation problems well posed by adding indirect constraints on the estimated model, but the regularisation parameter selection is difficult. In geophysics, without explicit calculation methods and quantitative evaluation criteria, it is usually based on the experience of the inversion engineers to try to achieve the best inversion results by continuously modifying the regularisation parameter. For prestack amplitude variation with offset (AVO) inversion for real seismic data, fixed regularisation parameters cannot satisfy the optimisation conditions in the seismic data with different signal-to-noise (SNR) in one area. Besides, fixed regularisation parameter may cause that the model constraint misfit is too large or too small compared to data misfit, which may guide the inversion to generate undesirable results. Therefore, adaptive selection of regularisation parameter according to the seismic data can help guarantee a good inversion result. Based on the traditional Lcurve criterion, we derive the theoretical formula of the adaptive computation of the regularisation parameter, which can be applied to any norm constraint. Weproposed the application of this selection scheme in prestackAVOinversion. Model tests show that the improved L-curve method has better stability than its main competitor, the generalised cross-validation (GCV) method. PrestackAVOinversion on logging data and real seismic data demonstrate that the proposed method can improve the accuracy of the inversion, and it is more immune to strong noise. [ABSTRACT FROM AUTHOR]

Realistic leaf models are significant for numerous applications in the plant sciences, for instance, modelling pesticide droplet movement on the leaf surface. In this framework, a smooth surface is necessary to structure the foundation for a theoretical revision of a droplets motion on leaves. The radial basis function is convenient for scattered d-dimensional interpolation and usually extended by a polynomial Pk (x) of degree (k) to improve the method stability. In this research paper, we proposed a new technique for modelling a real leaf surface, which is based on enhancing a cubic polynomial term P3 (x) to the multiquadric Radial basis function (CMRBF). The precision of the CMRBF method is confirmed by applying it to a virtual data and then to a real Frangipani and Anthurium data sets sampled using a laser scanner. It is concluded that the proposed CMRBF method produces a realistic and accurate representation of the leaf surface. [ABSTRACT FROM AUTHOR]

The introduction of new operation enhancement technologies plus increasing application of power electronics, coupled with the continuous increase in load demand, has increased the risk of power networks to voltage instability and susceptibility to voltage collapse. This frequent occurrence of voltage collapse in modern power system has been a growing concern among power system utilities. This paper proposes alternative techniques for the identification of critical nodes that are liable to voltage instability in a power system. The first method is based on the critical mode corresponding to the smallest eigenvalues, while the second technique is based on the centrality measure to identify the most influential node of the networks. The eigenvector centrality measure is formulated from the response matrices of both the load and generator nodes of the networks. The effectiveness of the suggested approaches is tested using the IEEE 30-bus and the Southern Indian 10-bus power networks. The results are compared with the techniques based on the traditional power flow. The whole procedure of the results involved in the identification of critical nodes through the proposed methods is totally non-iterative and thereby saves time and requires less computational burden. [ABSTRACT FROM AUTHOR]

In this paper, two new approaches for handling multiple tasks in redundant manipulators based on predefined allocated priorities are proposed. The first approach is an integrated scheme which employs null-space base vector for handling prioritized tasks. Clear task and null-space representation, better execution of the lower priority tasks, and intuitive formulation are its basic features. The second approach aims to improve the performance of all the prioritized tasks, especially during algorithmic singularities beside clear null-space dynamics representation. This approach can be considered as a modification and extension of the Reverse Priority (RP) algorithm in acceleration level. The commands related to each tasks are added to each other following reverse order of priorities and by suitable projectors. The projector definition is given using minimal representation of the null-space. Clear null-space dynamics in the proposed methods facilitate the stability analysis. A detailed evaluation by means of computer simulation in various cases is reported. Tasks accomplishment using the proposed approaches is compared with the classic method. The results, in general, show higher performance and accuracy of the tasks by the proposed approaches. [ABSTRACT FROM AUTHOR]

A multivariate model that allows for both a time-varying cointegrating matrix and time-varying cointegrating rank is presented. The model addresses the issue that, in real data, the validity of a constant cointegrating relationship may be questionable. The model nests the submodels implied by alternative cointegrating matrix ranks and allows for transitions between stationarity and nonstationarity, and cointegrating and noncointegrating relationships in accordance with the observed behavior of the data. A Bayesian test of cointegration is also developed. The model is used to assess the validity of the Fisher effect and is also applied to equity market data. [ABSTRACT FROM AUTHOR]

The numerical solution of saddle point systems has received a lot of attention over the past few years in a wide variety of applications such as constrained optimization, computational fluid dynamics and optimal control, to name a few. In this paper, we focus on the saddle point formulation of a large-scale variational data assimilation problem, where the computations involving the constraint blocks are supposed to be much more expensive than those related to the (1, 1) block of the saddle point matrix. New low-rank limited memory preconditioners exploiting the particular structure of the problem are proposed and analysed theoretically. Numerical experiments performed within the Object-Oriented Prediction System are presented to highlight the relevance of the proposed preconditioners. [ABSTRACT FROM AUTHOR]

In this paper, the relationship between the degree of controllability (DOC) of controlled plants and the corresponding quadratic optimal performance index in LQR control is investigated for the electro-hydraulic synchronising servo control systems and wind turbine systems, respectively. It is shown that for these two types of systems, the higher the DOC of a controlled plant is, the better the quadratic optimal performance index is. It implies that in some LQR controller designs, the measure of the DOC of a controlled plant can be used as an index for the optimisation of adjustable plant parameters, by which the plant can be controlled more effectively. [ABSTRACT FROM PUBLISHER]

Low rank approximation of matrices has been well studied in literature. Singular value decomposition, QR decomposition with column pivoting, rank revealing QR factorization, Interpolative decomposition, etc. are classical deterministic algorithms for low rank approximation. But these techniques are very expensive (O(n3) operations are required for n×n matrices). There are several randomized algorithms available in the literature which are not so expensive as the classical techniques (but the complexity is not linear in n). So, it is very expensive to construct the low rank approximation of a matrix if the dimension of the matrix is very large. There are alternative techniques like Cross/Skeleton approximation which gives the low-rank approximation with linear complexity in n. In this article we review low rank approximation techniques briefly and give extensive references of many techniques. [ABSTRACT FROM AUTHOR]

We propose a modelling framework for risk-neutral stochastic processes nested in a real-world stochastic process. The framework is important for insurers that deal with the valuation of embedded options and in particular at future points in time. We make use of the class of State Space Hidden Markov models for modelling the joint behaviour of the parameters of a risk-neutral model and the dynamics of option market instruments. This modelling concept enables us to perform non-linear estimation, forecasting and robust calibration. The proposed method is applied to the Heston model for which we find highly satisfactory results. We use the estimated Heston model to compute the required capital of an insurance company under Solvency II and we find large differences compared to a basic calibration method. [ABSTRACT FROM PUBLISHER]

In this paper, new results on the open-loop balanced representation of continuous time linear time-invariant systems are reported. More particularly, the effect of lossless positive real transformations on open-loop balanced representations is investigated with specific attention to the problem of model order reduction. The properties of systems where a lossless positive real transformation has been applied are discussed showing that, if the original system is open-loop balanced, the resulting transformed system is still open-loop balanced. Furthermore, the singular values of the transformed system are related to those of the original one. These results allow to derive a model order reduction strategy for this class of systems that leads to a consistent decrease of the numerical complexity. The proposed approach reveals to be of particular interest for the design of reduced-order systems with specific amplitude responses, including analog multiband filters. [ABSTRACT FROM AUTHOR]

In this article, the Ridge–GME parameter estimator, which combines Ridge Regression and Generalized Maximum Entropy, is improved in order to eliminate the subjectivity in the analysis of the ridge trace. A serious concern with the visual inspection of the ridge trace to define the supports for the parameters in the Ridge–GME parameter estimator is the misinterpretation of some ridge traces, in particular where some of them are very close to the axes. A simulation study and two empirical applications are used to illustrate the performance of the improved estimator. A MATLAB code is provided as supplementary material. [ABSTRACT FROM AUTHOR]

The detection and reconstruction of fatigue fractures is of great interest in quality assurance. In the framework of nondestructive testing, Lorentz force evaluation (LFE) is an evaluation technique to estimate flaws in electrically conductive materials based on measured Lorentz forces. In the forward solution for LFE, a defect can be interpreted as a distributed current source. This has motivated the authors to propose current density reconstructions (CDRs) calculated with minimum norm estimates to estimate defect geometries. TheL1andL2norms tend to produce a solution which is either very focused or very smeared. To balance these constraints, the generalLpnorm with 1 ≤p ≤2 was used and the inverse solutions compared. This approach was applied to measured data obtained from a laminated composite and simulated data from a monolithic material. The results show that theL1.5norm provides the most accurate inverse solutions. The location and extent of the defect are determined with an error of 15 % relative to the size of the defect. The depth estimation has a deviation of 50 %. It can be concluded that CDRs are a powerful method to reconstruct and characterize defects in LFE. [ABSTRACT FROM PUBLISHER]

The ability to approximate a set of data by a parametric cylinder in a general position is required in a diverse range of fields in metrology. A new technique for cylinder fitting based on the minimization of the sum of orthogonal squared distances is considered. A descent algorithm is proposed and illustrated using numerical examples. [ABSTRACT FROM PUBLISHER]

Compressible flow over a flat plate with two localised and well-separated roughness elements is analysed by global frequency-response analysis. This analysis reveals a sustained feedback loop consisting of a convectively unstable shear-layer instability, triggered at the upstream roughness, and an upstream-propagating acoustic wave, originating at the downstream roughness and regenerating the shear-layer instability at the upstream protrusion. A typical multi-peaked frequency response is recovered from the numerical simulations. In addition, the optimal forcing and response clearly extract the components of this feedback loop and isolate flow regions of pronounced sensitivity and amplification. An efficient parametric-sensitivity framework is introduced and applied to the reference case which shows that first-order increases in Reynolds number and roughness height act destabilising on the flow, while changes in Mach number or roughness separation cause corresponding shifts in the peak frequencies. This information is gained with negligible effort beyond the reference case and can easily be applied to more complex flows. [ABSTRACT FROM PUBLISHER]