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Including polynomials with small degree and stencil when designing very high order reconstructions is surely beneficial for their non oscillatory properties, but may bring loss of accuracy on smooth data unless special care is exerted. In this paper we address this issue with a new Central WENOZ (CWENOZ ) approach, in which the reconstruction polynomial is computed from a single set of non linear weights, but the linear weights of the polynomials with very low degree (compared to the final desired accuracy) are infinitesimal with respect to the grid size. After proving general results that guide the choice of the CWENOZ parameters, we study a concrete example of a reconstruction that blends polynomials of degree six, four and two, mimicking already published Adaptive Order WENO reconstructions (Arbogast et al. in SIAM J Numer Anal 56(3):1818-1947, 2018),(Balsara et al. in J Comput Phys 326:780-804, 2016). The novel reconstruction yields similar accuracy and oscillations with respect to the previous ones, but saves up to 20% computational time since it does not rely on a hierarchic approach and thus does not compute multiple sets of nonlinear weights in each cell. [ABSTRACT FROM AUTHOR]

This paper presents a computational technique based on cubic trigonometric B-splines for the time fractional Burgers' equation. The nonlinear advection term is approximated by a new linearization technique which is very efficient and significantly reduces the computational cost. The usual finite difference formulation is used to approximate the Caputo time fractional derivative while the derivative in space is discretized using cubic trigonometric B-spline functions. The proposed technique is proved to be globally unconditionally stable. A convergence analysis is discussed to measure the accuracy of the solution. Computational experiments are performed to further confirm the accuracy and stability of the method. Numerical results are compared with those obtained by a scheme based on parametric spline functions. The comparison reveals that the proposed scheme is quite accurate and effective. [ABSTRACT FROM AUTHOR]

A geometric construction of a Bézier curve is presented by a unifiable way from the mentioned literature with some modification. A closed-form solution to the inverse problem in cubic Bézier-spline interpolation will be obtained. Calculations in the given examples are performed by a Maple procedure using this solution. [ABSTRACT FROM AUTHOR]

We present an approximation problem of surfaces of a generalized offset surface with offset variable distances and directions. Such approximating surface fits some given data points and minimizes a Sobolev's semi-norm of order 3. The study of the new results, from a mathematical point of view, carefully establishing the proof of the convergence between the generalized offset surface and its approximating spline in an adequate parametric bicubic spline space. Moreover, the approximating spline function is computed and an estimation of the relative error is introduced. Finally, some numerical and graphic examples are shown in order to prove the useful and the effectiveness of our method. [ABSTRACT FROM AUTHOR]

• We propose a module to predict boundary shapes and boxes with a new masking scheme. • We comprehensively investigate proposed frameworks with various masking methods. • The proposed modularizable component can easily be applied to existing models. • BshapeNet + improves accuracy notably compared to the baselines, Faster and Mask RCNN. • We achieved highly competitive results with SOTA detection and segmentation models. We propose a modularizable component that can predict the boundary shapes and boxes of an image, along with a new masking scheme for improving object detection and instance segmentation. Specifically, we introduce two types of novel masks: a bounding box (bbox) mask and a bounding shape (bshape) mask. For each of these types, we consider two variants—the "Thick" model and the "Scored" model—both of which have the same morphology but differ in ways that make their boundaries thicker. To evaluate our masks, we design extended frameworks by adding a bshape mask (or a bbox mask) branch to a Faster R-CNN, and call this BshapeNet (or BboxNet). Furthermore, we propose BshapeNet+, a network that combines a bshape mask branch with a Mask R-CNN. Among our various models, BshapeNet+ demonstrates the best performance in both tasks. In addition, BshapeNet+ markedly outperforms the baseline models on MS COCO and Cityscapes and achieves highly competitive results with state-of-the-art models. In particular, the experimental results show that our branch works well on small objects and is easily applicable to various models, such as PANet as well as Faster R-CNN and Mask R-CNN. [ABSTRACT FROM AUTHOR]

Essentially non-oscillatory (ENO) and weighted ENO (WENO) methods on equidistant Cartesian grids are widely used to solve partial differential equations with discontinuous solutions. However, stable ENO/WENO methods on unstructured grids are less well studied. We propose a high-order ENO method based on radial basis function (RBF) to solve hyperbolic conservation laws on general two-dimensional grids. The radial basis function reconstruction offers a flexible way to deal with ill-conditioned cell constellations. We introduce a smoothness indicator based on RBFs and a stencil selection algorithm suitable for general meshes. Furthermore, we develop a stable method to evaluate the RBF reconstruction in the finite volume setting which circumvents the stagnation of the error and keeps the condition number of the reconstruction bounded. We conclude with several challenging numerical examples in two dimensions to show the robustness of the method. [ABSTRACT FROM AUTHOR]

In this paper we present a trivariate algorithm for fast computation of tetrahedral Shepard interpolants. Though the tetrahedral Shepard method achieves an approximation order better than classical Shepard formulas, it requires to detect suitable configurations of tetrahedra whose vertices are given by the set of data points. In doing that, we propose the use of a fast searching procedure based on the partitioning of domain and nodes in cubic blocks. This allows us to find the nearest neighbor points associated with each ball that need to be used in the 3D interpolation scheme. Numerical experiments show good performance of our interpolation algorithm. [ABSTRACT FROM AUTHOR]

This paper presents convergence analysis of kernel-based quadrature rules in misspecified settings, focusing on deterministic quadrature in Sobolev spaces. In particular, we deal with misspecified settings where a test integrand is less smooth than a Sobolev RKHS based on which a quadrature rule is constructed. We provide convergence guarantees based on two different assumptions on a quadrature rule: one on quadrature weights and the other on design points. More precisely, we show that convergence rates can be derived (i) if the sum of absolute weights remains constant (or does not increase quickly), or (ii) if the minimum distance between design points does not decrease very quickly. As a consequence of the latter result, we derive a rate of convergence for Bayesian quadrature in misspecified settings. We reveal a condition on design points to make Bayesian quadrature robust to misspecification, and show that, under this condition, it may adaptively achieve the optimal rate of convergence in the Sobolev space of a lesser order (i.e., of the unknown smoothness of a test integrand), under a slightly stronger regularity condition on the integrand. [ABSTRACT FROM AUTHOR]

We study some procedures for the approximation of three-dimensional data on a grid with a hypothesis of periodicity. The first part proposes a generalization of a discrete periodic approximation defined by Dunham Jackson. The functions used have the advantage of owning an analytical explicit expression in terms of the samples (specific values) of the original function or data. In the second part, we describe a continuous approximation function for the same problem, defined through an integral. Some results of the rate of convergence and bounds of the approximation error are presented, with the single hypothesis of Hölder continuity or continuity of the original function. [ABSTRACT FROM AUTHOR]

In this paper, we study how to construct a planar cubic G1 Hermite interpolation curve with minimal length and curvature variation energy. This problem is solved by a bi-objective optimization model. We prove that there is a unique solution to this problem and give the expression of the solution. Some numerical examples show that the proposed method makes the curvature variation energy of the curve as small as possible when the length of the curve as short as possible. [ABSTRACT FROM AUTHOR]

We are concerned with a noncausal approach to the numerical evaluation of the stochastic integral ∫ f d W t with respect to Brownian motion. Viewed as a special case of the numerical solution (in strong sense) of the SDE, it may be believed that the precision level of such an approximation scheme that uses only a finite number of increments Δ k W = W (t k + 1) - W (t k) of Brownian motion, would not exceed the order O (1 n) where n is the number of steps for discretization. We present in this note a simple but not trivial example showing that this belief is not correct. The discussion is developed on the basis of the noncausal theory of stochastic calculus introduced by the author. [ABSTRACT FROM AUTHOR]

Tempered fractional derivatives and the corresponding tempered fractional differential equations have played a key role in physical science. In this paper, for solving the tempered fractional ordinary differential equation, the predictor–corrector (PC) methods with uniform and non-uniform meshes of Deng et al. (Numer Algorithms 74(3):717–754, 2017) are developed, by using the piecewise quadratic interpolation polynomial. The error bounds of proposed predictor–corrector schemes with uniform and equidistributing meshes are obtained. We proved that the presented numerical method has a higher-order convergence order O (h 3) . Also, some numerical examples are constructed to demonstrate the efficacy and usefulness of the numerical methods. Finally, the results of PC schemes with uniform and non-uniform given in Deng et al. (2017) and presented schemes (improved PC with uniform and non-uniform meshes) are compared for different values of parameters. [ABSTRACT FROM AUTHOR]

In the current paper, authors proposed a computational model based on the cubic B-spline method to solve linear 6th order BVPs arising in astrophysics. The prescribed method transforms the boundary problem to a system of linear equations. The algorithm we are going to develop in this paper is not only simply the approximation solution of the 6th order BVPs using cubic B-spline, but it also describes the estimated derivatives of 1st order to 6th order of the analytic solution at the same time. This novel technique has lesser computational cost than numerous other techniques and is second order convergent. To show the efficiency of the proposed method, four numerical examples have been tested. The results are described using error tables and graphs and are compared with the results existing in the literature. [ABSTRACT FROM AUTHOR]

We give compact formulae of the Lagrange interpolation polynomials and cubature formulae based on the common zeros of product Chebyshev polynomials of the second kind. Further, for 0 < p ≤ 2 , we study the mean convergence of the Lagrange interpolation polynomials. [ABSTRACT FROM AUTHOR]

It is known that discrete sets of uniformly distributed points on the hypersphere S d ⊂ ℝ d + 1 can be obtained from minimizing the energy functional corresponding to Riesz s-kernels k s (x , y) = ∥ x − y ∥ − s (s > 0) or the logarithmic kernel k log (x , y) = − log ∥ x − y ∥ + log 2 . We prove the same for the kernel k log (x , y) = ∥ x − y ∥ (log ∥ x − y ∥ 2 − 1) + 2 which is a front-extension of the sequence of derivatives k log , k 1 , k 2 , k 3 , ... , up to sign and constants. The boundedness of the kernel simplifies the classical potential-theoretical proof of the asymptotic uniformity of the point distributions. Still, the property of a singular derivative for x → y is preserved, with the physical interpretation of infinite repulsive forces for touching particles. The quality of the resulting point distributions is exemplary compared with that of Riesz- and classical logarithmic point sets, and found to be competitive. Originally motivated by problems of high-dimensional data, the applicability of log -optimal point sets with a novel concentric interpolation and differentiation scheme is demonstrated. The method is significantly optimized by the introduction of symmetrized kernels for both the generation of the minimum energy points and the spherical basis functions. Both the point generation and the Concentric Interpolation software are available as Open Source software and selected point sets are provided. [ABSTRACT FROM AUTHOR]

We describe a systematic mathematical approach to the geometric discretization of gauge field theories that is based on Dirac and multi-Dirac mechanics and geometry, which provide a unified mathematical framework for describing Lagrangian and Hamiltonian mechanics and field theories, as well as degenerate, interconnected, and nonholonomic systems. Variational integrators yield geometric structure-preserving numerical methods that automatically preserve the symplectic form and momentum maps, and exhibit excellent long-time energy stability. The construction of momentum-preserving variational integrators relies on the use of group-equivariant function spaces, and we describe a general construction for functions taking values in symmetric spaces. This is motivated by the geometric discretization of general relativity, which is a second-order covariant gauge field theory on the symmetric space of Lorentzian metrics. [ABSTRACT FROM AUTHOR]

A new flux-based hybrid subcell-remapping algorithm for staggered multimaterial arbitrary Lagrangian-Eulerian (MMALE) methods is presented. This new method is an effective generalization of the original subcell-remapping method to the multi-material regime (LOUBÈRE, R. and SHASHKOV, M. A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods. Journal of Computational Physics, 209, 105–138 (2005)). A complete remapping procedure of all fluid quantities is described detailedly in this paper. In the pure material regions, remapping of mass and internal energy is performed by using the original subcell-remapping method. In the regions near the material interfaces, remapping of mass and internal energy is performed with the intersection-based fluxes where intersections are performed between the swept regions and pure material polygons in the Lagrangian mesh, and an approximate approach is then introduced for constructing the subcell mass fluxes. In remapping of the subcell momentum, the mass fluxes are used to construct the momentum fluxes by multiplying a reconstructed velocity in the swept region. The nodal velocity is then conservatively recovered. Some numerical examples simulated in the full MMALE regime and several purely cyclic remapping examples are presented to prove the properties of the remapping method. [ABSTRACT FROM AUTHOR]

In this work, we introduce a modification into the technique, presented in A. Cordero, J.L. Hueso, E. Martínez, and J.R. Torregrosa [Increasing the convergence order of an iterative method for nonlinear systems, Appl. Math. Lett. 25 (2012), pp. 2369–2374], that increases by two units the convergence order of an iterative method. The main idea is to compose a given iterative method of order p with a modification of Newton's method that introduces just one evaluation of the function, obtaining a new method of order p+2, avoiding the need to compute more than one derivative, so we improve the efficiency index in the scalar case. This procedure can be repeated n times, with the same approximation to the derivative, obtaining new iterative methods of order p+2n. We perform different numerical tests that confirm the theoretical results. By applying this procedure to Newton's method one obtains the well known fourth order Ostrowski's method. We finally analyse its dynamical behaviour on second and third degree real polynomials. [ABSTRACT FROM AUTHOR]

This paper introduces the software TiGL: TiGL is an open source geometry modeler that is used in the conceptual and preliminary aircraft and helicopter design phase. It creates full three-dimensional models of aircraft from their parametric CPACS description. Due to its parametric nature, it is typically used for aircraft design analysis and optimization. First, we present the use-case and architecture of TiGL. Then, we discuss its geometry module, which is used to generate the B-spline based surfaces of the aircraft. The backbone of TiGL is its surface generator for curve network interpolation, based on Gordon surfaces. One major part of this paper explains the mathematical foundation of Gordon surfaces on B-splines and how we achieve the required curve network compatibility. Finally, TiGL's aircraft component module is introduced, which is used to create the external and internal parts of aircraft, such as wings, flaps, fuselages, engines or structural elements. [ABSTRACT FROM AUTHOR]

As this paper is concerned with a class of multistep numerical difference techniques to solve one-dimensional parabolic inverse problems with source control parameter , we apply the linear multistep method combining with Lagrange interpolation to develop three different numerical difference schemes. The problem of numerical differentiation with noisy scattered data is mildly ill-posed, the smoothing spline model based on Tikhonov regularization method is developed to compute numerical derivative contaminated by noise error. Simultaneously, the truncation error estimations and the convergence conclusions are proposed for the above difference methods respectively. The results of numerical tests with different noise levels are given to show that the presented algorithms are accurate and effective. [ABSTRACT FROM AUTHOR]

The stability properties of the Newton interpolation formula depend on the order of the nodes and can be measured through a condition number. Increasing and Leja orderings have been previously considered (Carnicer et al. in J Approx Theory, 2017. https://doi.org/10.1016/j.jat.2017.07.005; Reichel in BIT 30:332–346, 1990). We analyze central orderings for equidistant nodes on a bounded real interval. A bound for conditioning is given. We demonstrate in particular that this ordering provides a more stable Newton formula than the natural increasing order. We also analyze of a central ordering with respect to the evaluation point, which provides low bounds for the conditioning. Numerical examples are included. [ABSTRACT FROM AUTHOR]

In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. Recently a new unfitted finite element method was introduced which achieves a high order approximation of the geometry for domains which are implicitly described by smooth level set functions. This method is based on a parametric mapping which transforms a piecewise planar interface (or surface) reconstruction to a high order approximation. In the paper [C. Lehrenfeld and A. Reusken, IMA J. Numer. Anal. 38 (2018), No. 3, 1351–1387] an a priori error analysis of the method applied to an interface problem is presented. The analysis reveals optimal order discretization error bounds in the H1-norm. In this paper we extend this analysis and derive optimal L2-error bounds. [ABSTRACT FROM AUTHOR]

This paper studies well-definedness and convergence of subdivision schemes which operate on Riemannian manifolds with nonpositive sectional curvature. These schemes are constructed from linear ones by replacing affine averages by the Riemannian centre of mass. In contrast to previous work, we consider schemes without any sign restriction on the mask, and our results apply to all input data. We also analyse the Hölder continuity of the resulting limit curves. Our main result states that if the norm of the derived scheme (resp. iterated derived scheme) is smaller than the corresponding dilation factor then the adapted scheme converges. In this way, we establish that convergence of a linear subdivision scheme is almost equivalent to convergence of its nonlinear manifold counterpart. [ABSTRACT FROM AUTHOR]

This work discusses the problem of fitting a regular curve γ based on reduced data points Q m = (q 0 , q 1 , ⋯ , q m) in arbitrary Euclidean space. The corresponding interpolation knots T = (t 0 , t 1 , ⋯ , t m) are assumed to be unknown. In this paper the missing knots are estimated by T λ = (t ^ 0 , t ^ 1 , ⋯ , t ^ m) in accordance with the so-called exponential parameterization (see Kvasov in Methods of shape-preserving spline approximation, World Scientific Publishing Company, Singapore, 2000) controlled by a single parameter λ ∈ [ 0 , 1 ] . In order to fit (T ^ λ , Q m) , a modified Hermite interpolant γ ^ H (a C 1 piecewise-cubic) introduced in Kozera and Noakes (Fundam Inf 61(3–4):285–301, 2004) is used. The sharp quartic convergence order for estimating γ ∈ C 4 by γ ^ H is proved in Kozera (Stud Inf 25(4B-61):1–140, 2004) and Kozera and Noakes (2004) only for λ = 1 and within the general class of admissible samplings. The main result of this paper extends the latter to the remaining cases of exponential parameterization covering all λ ∈ [ 0 , 1) . A slower linear convergence order in trajectory estimation is established for any λ ∈ [ 0 , 1) and arbitrary more-or-less uniform sampling. The numerical tests conducted in Mathematica indicate the sharpness of the latter and confirm the necessity of more-or-less uniformity. Other interpolation schemes used to fit reduced data Q m and based on T λ together with some relevant applications are also briefly recalled in this paper. [ABSTRACT FROM AUTHOR]

This paper examines the problem of extrapolation of an analytic function for x > 1 given N + 1 perturbed samples from an equally spaced grid on [ - 1 , 1 ] . For a function f on [ - 1 , 1 ] that is analytic in a Bernstein ellipse with parameter ρ > 1 , and for a uniform perturbation level ε on the function samples, we construct an asymptotically best extrapolant e(x) as a least squares polynomial approximant of degree M ∗ determined explicitly. We show that the extrapolant e(x) converges to f(x) pointwise in the interval I ρ ∈ [ 1 , (ρ + ρ - 1) / 2) as ε → 0 , at a rate given by a x-dependent fractional power of ε . More precisely, for each x ∈ I ρ we have | f (x) - e (x) | = O ε - log r (x) / log ρ , r (x) = x + x 2 - 1 ρ , up to log factors, provided that an oversampling conditioning is satisfied, viz. M ∗ ≤ 1 2 N , which is known to be needed from approximation theory. In short, extrapolation enjoys a weak form of stability, up to a fraction of the characteristic smoothness length. The number of function samples does not bear on the size of the extrapolation error provided that it obeys the oversampling condition. We also show that one cannot construct an asymptotically more accurate extrapolant from equally spaced samples than e(x), using any other linear or nonlinear procedure. The proofs involve original statements on the stability of polynomial approximation in the Chebyshev basis from equally spaced samples and these are expected to be of independent interest. [ABSTRACT FROM AUTHOR]

We investigate adaptivity issues for the approximation of Poisson equations via radial basis function-based partition of unity collocation. The adaptive residual subsampling approach is performed with quasi-uniform node sequences leading to a flexible tool which however might suffer from numerical instability due to ill-conditioning of the collocation matrices. We thus develop a hybrid method which makes use of the so-called variably scaled kernels. The proposed algorithm numerically ensures the convergence of the adaptive procedure. [ABSTRACT FROM AUTHOR]

In this note, we show that the degree of the interpolation polynomial for equidistant base points is characterized by the regularity of matrices of combinatorical type. [ABSTRACT FROM AUTHOR]

Interpolatory splines are usually useful to reconstruct data that present certain regularity. This paper is devoted to the construction and analysis of a new technique that allows to improve the accuracy of splines near corner singularities in the point values and jump discontinuities in the cell averages. The detection of discontinuities is easily done through the processing of the right hand side of the system of equations of the spline, that contains divided differences. The process of adaption will require some knowledge about the position of the discontinuity and the values of the function and its derivatives at the discontinuity. Using Harten's multiresolution we can adapt splines to the presence of corner singularities and jump discontinuities. Thanks to the adaption, the smearing of corner singularities does not appear in the reconstruction obtained in the point values and Gibbs phenomenon and diffusion of jump discontinuities is also eliminated. These numerical effects are a consequence of assuming that the data used in the reconstruction comes from the discretization of a continuous function with certain regularity and this might not be true. [ABSTRACT FROM AUTHOR]

In the past few years, Bogoya, Böttcher, Grudsky, and Maximenko obtained the precise asymptotic expansion for the eigenvalues of a Toeplitz matrix Tn(f), under suitable assumptions on the generating function f, as the matrix size n goes to infinity. On the basis of several numerical experiments, it was conjectured by Serra-Capizzano that a completely analogous expansion also holds for the eigenvalues of the preconditioned Toeplitz matrix Tn(u)− 1Tn(v), provided f = v/u is monotone and further conditions on u and v are satisfied. Based on this expansion, we here propose and analyze an interpolation-extrapolation algorithm for computing the eigenvalues of Tn(u)− 1Tn(v). The algorithm is suited for parallel implementation and it may be called "matrix-less" as it does not need to store the entries of the matrix. We illustrate the performance of the algorithm through numerical experiments and we also present its generalization to the case where f = v/u is non-monotone. [ABSTRACT FROM AUTHOR]

We show how a recently developed multivariate data fitting technique enables to solve a variety of scientific computing problems in filtering, queueing, networks, metamodelling, computational finance, graphics, and more. We can capture linear as well as nonlinear phenomena because the method uses a generalized multivariate rational model. The technique is a refinement of the basic ideas developed in Salazar et al. (Numer Algorithms 45:375-388, 2007. https://doi.org/10.1007/s11075-007-9077-3) and interpolates interval data. Intervals allow to take the inherent data error in measurements and simulation into consideration, whilst guaranteeing an upper bound on the tolerated range of uncertainty. The latter is the main difference with a best approximation or least squares technique which does as well as it can, but without respecting an a priori imposed threshold on the approximation error. Compared to the best approximations, the interval interpolant is relatively easy to compute. In applications where industry standards need to be guaranteed, the interval interpolation technique may be a valuable alternative. [ABSTRACT FROM AUTHOR]

In this paper, a novel hybrid trust-region algorithm using radial basis function (RBF) interpolations is proposed. The new algorithm is an improved version of ORBIT algorithm based on two novel ideas. Because the accuracy and stability of RBF interpolation depends on a shape parameter, so it is more appropriate to select this parameter according to the optimization problem. In the new algorithm, the appropriate shape parameter value is determined according to the optimization problem based on an effective statistical approach, while the ORBIT algorithm in all problems uses a fixed shape parameter value. In addition, the new algorithm is equipped with a new intelligent nonmonotone strategy which improves the speed of convergence, while the monotonicity of the sequence of objective function values in the ORBIT may decrease the rate of convergence, especially when an iteration is trapped near a narrow curved valley. The global convergence of the new hybrid algorithm is analyzed under some mild assumptions. The numerical results significantly indicate the superiority of the new algorithm compared with the original version. [ABSTRACT FROM AUTHOR]

We introduce a new class of Pythagorean-Hodograph (PH) space curves - called Algebraic-Trigonometric Pythagorean-Hodograph (ATPH) space curves - that are defined over a six-dimensional space mixing algebraic and trigonometric polynomials. After providing a general definition for this new class of curves, their quaternion representation is introduced and the fundamental properties are discussed. Then, as previously done with their quintic polynomial counterpart, a constructive approach to solve the first-order Hermite interpolation problem in ℝ3 is provided. Comparisons with the polynomial case are illustrated to point out the greater flexibility of ATPH curves with respect to polynomial PH curves. [ABSTRACT FROM AUTHOR]

Highlights • We propose trainable feature extractors for representation of skeleton poses. • We employ the proposed feature extractor for classification of human actions. • We designed an human action classification method based on string kernel. • We carried out experiments on the MHAD, MSRDA and MIVIA-S action datasets. • We publicly released the MIVIA-S dataset for research purpose. Abstract Automatic interpretation of human actions gained strong interest among researchers in patter recognition and computer vision because of its wide range of applications, such as in social and home robotics, elderly people health care, surveillance, among others. In this paper, we propose a method for recognition of human actions by analysis of skeleton poses. The method that we propose is based on novel trainable feature extractors, which can learn the representation of prototype skeleton examples and can be employed to recognize skeleton poses of interest. We combine the proposed feature extractors with an approach for classification of pose sequences based on string kernels. We carried out experiments on three benchmark data sets (MIVIA-S, MSRSDA and MHAD) and the results that we achieved are comparable or higher than the ones obtained by other existing methods. A further important contribution of this work is the MIVIA-S dataset, that we collected and made publicly available. [ABSTRACT FROM AUTHOR]