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Forward and backward reaching inverse kinematics (FABRIK) is an efficient two-stage iterative solver for inverse kinematics of spherical-joint manipulator without the calculation of Jacobian matrix. Based on FABRIK, this paper presents an incremental control scheme for a free-floating space manipulator consists of revolute joints and rigid links with the consideration of joint constraints and dynamic coupling effect. Due to the characteristics of FABRIK, it can induce large angular movements on specific joints. Apart from that, FABRIK maps three dimensional (3D) problem into two dimensional (2D) problem by a simple geometric projection. This operation can cause infinite loops in some cases. In order to overcome these issues and apply FABRIK on space manipulators, an increments allocation method is developed to constrain the angular movements as well as to re-orient the end-effector. The manipulator is re-positioned based on the momentum conservation law. Instead of pure target position tracking, the orientation control of the end-effector is also considered. Numerical simulation is performed to testify and demonstrate the effectiveness and reliability of the proposed incremental control approach.

Dimensionality reduction (DR) technique has been frequently used to alleviate information redundancy and reduce computational complexity. Traditional DR methods generally are inability to deal with nonlinear data and have high computational complexity. To cope with the problems, we propose a fast unsupervised projection (FUP) method. The simplified graph of FUP is constructed by samples and representative points, where the number of the representative points selected through iterative optimization is less than that of samples. By generating the presented graph, it is proved that large-scale data can be projected faster in numerous scenarios. Thereafter, the orthogonality FUP (OFUP) method is proposed to ensure the orthogonality of projection matrix. Specifically, the OFUP method is proved to be equivalent to PCA upon certain parameter setting. Experimental results on benchmark data sets show the effectiveness in retaining the essential information.

We design a virtual element method for the numerical treatment of the two-dimensional parabolic variational inequality problem on unstructured polygonal meshes. Due to the expected low regularity of the exact solution, the virtual element method is based on the lowest-order virtual element space that contains the subspace of the linear polynomials defined on each element. The connection between the nonnegativity of the virtual element functions and the nonnegativity of the degrees of freedom, i.e., the values at the mesh vertices, is established by applying the Maximum and Minimum Principle Theorem. The mass matrix is computed through an approximate L 2 polynomial projection, whose properties are carefully investigated in the paper. We prove the well-posedness of the resulting scheme in two different ways that reveal the contractive nature of the VEM and its connection with the minimization of quadratic functionals. The convergence analysis requires the existence of a nonnegative quasi-interpolation operator, whose construction is also discussed in the paper. The variational crime introduced by the virtual element setting produces five error terms that we control by estimating a suitable upper bound. Numerical experiments confirm the theoretical convergence rate for the refinement in space and time on three different mesh families including distorted squares, nonconvex elements, and Voronoi tesselations.

In this article, considering the supervised dimensionality reduction, we first propose a model, called infinite Bayesian max-margin linear discriminant projection (iMMLDP), by assembling a set of local regions, where we make use of Bayesian nonparametric priors to handle the model selection problem, for example, the underlying number of local regions. In each local region, our model jointly learns a discriminative subspace and the corresponding classifier. Under this framework, iMMLDP combines dimensionality reduction, clustering, and classification in a principled way. Moreover, to deal with more complex data, for example, a local nonlinear separable structure, we extend the linear projection to a nonlinear case based on the kernel trick and develop an infinite kernel max-margin discriminant projection (iKMMDP) model. Thanks to the conjugate property, the parameters in these two models can be inferred efficiently via the Gibbs sampler. Finally, we implement our models on synthesized and real-world data, including multimodally distributed datasets and measured radar image data, to validate their efficiency and effectiveness.

We show that the endomorphism ring of any nonzero finitely generated projective module over the Leavitt path algebra $L_K(E)$ of an arbitrary graph $E$ with coefficients in a field $K$ is isomorphic to a Steinberg algebra. This yields in particular that every nonzero corner of the Leavitt path algebra of an arbitrary graph is isomorphic to a Steinberg algebra. This in its turn gives that every $K$-algebra with local units which is Morita equivalent to the Leavitt path algebra of a row-countable graph is isomorphic to a Steinberg algebra. Moreover, we prove that a corner by a projection of a $C^*$-algebra of a countable graph is isomorphic to the $C^*$-algebra of an ample groupoid., Comment: 31 pages

Many wave propagation problems involve discontinuous material properties. We propose to solve such problems by non-overlapping domain decomposition combined with the method of difference potentials (MDP). The MDP reduces the Helmholtz equation on each subdomain to a Calderon's boundary equation with projection on the boundary. The unknowns for the Calderon's equation are the Dirichlet and Neumann data. Coupling between neighboring subdomains is rendered by applying their respective Calderon's equations to the same data at the common interface. Solutions on individual subdomains are computed concurrently using a direct solver. Our method proves to be insensitive to large jumps in the wavenumber for transmission problems, as well as interior cross-points and mixed boundary conditions, which may be a challenge to many other domain decomposition methods.

In this paper, we consider the port-Hamiltonian (PH) modeling of general RLC circuits, then explore the model order reduction (MOR) of corresponding port-Hamiltonian differential algebra equation (PH-DAE) systems. Specifically, by directed graphs, the general RLC circuits are firstly modeled as PH-DAE systems which imply the important passivity property. Based on e-embedding and parametric moment matching techniques, MOR is implemented to the PH-DAE system, and the corresponding reduced system preserves PH-DAE structure and then preserves the passivity property. In addition, we prove that the reduced parametric PH system obtained by only one-side projection can preserve three times moments which indicates better accuracy in theory, and the error estimation between PH-DAE system and parametric PH system is also provided.

Traditional proper orthogonal decomposition (POD)-Galerkin projection for reduced-order models (ROMs) of fluid flows is based on a fixed domain. The current method removes this limitation by consid...

The issue of sliding-mode control (SMC) design is studied for a class of nonlinear semi-Markovian switching systems (S-MSSs) via T-S fuzzy approach. Compared with previous literature, novel integral sliding-mode surfaces (ISMSs) are developed to depend on the designed controller gains and projection matrices. The aim of this work is to design an appropriate fuzzy SMC law under complex stochastic semi-Markovian switching process. For this purpose, the novel ISMSs are developed under the T-S fuzzy modeling framework. Then, based on the weak infinitesimal operator theory, sufficient conditions are given for stochastic stability criteria relying on the sojourn-time. Furthermore, an appropriate fuzzy SMC law is proposed to drive the state signals onto the predefined fuzzy manifold. Finally, an electric circuit model illustrates the effectiveness of the theoretical findings.

Feature selection is one of the most important techniques to deal with the high-dimensional data for a variety of machine learning and data mining tasks, such clustering, classification, and retrieval, etc. Fuzziness is a widespread nature of data in nature human society. However, most existing feature selection methods ignore the existence of fuzziness in the data, resulting in sub-optimal feature subsets. To address the problem, we propose a novel unsupervised feature selection method, called Unsupervised Discriminative Projection for Feature Selection (UDPFS) to select discriminative features by conducting fuzziness learning and sparse learning, simultaneously. Specifically, we use projection matrix transform data as its low-dimensional representation, which are partitioned to clusters by using membership matrix with sparse constrain. In addition, L2, 1-norm regularization is applied to the projection matrix. Then, a discriminative projection matrix with row sparse is obtained by perform fuzziness learning and sparse learning, simultaneously. An effective alternative optimization algorithm is proposed to solve the objective function. Evaluate experimental results on several real-world datasets show the effectiveness and superiority of the proposed unsupervised feature selection method.

In this paper, we propose two inertial projection methods to solve mixed variational inequalities without assuming monotonicity on the cost operator. Consequently, we show that the sequence of iterates generated by our proposed methods converge globally to a solution of the mixed variational inequality under the condition that the set of solutions of the dual mixed variational inequality is nonempty. Our convergence results are obtained without assuming any further stringent condition imposed in other related results in the literature. Moreover, our results improve on many important related results in the literature. Some numerical illustrations are given to show the efficiency of our proposed methods.

In this article, a comprehensive method for parametric representation of wire trajectories, allowing accurate geometric description of complex and arbitrarily oriented wire bundles, is introduced. This is the starting point to develop a computationally efficient numerical transmission-line (TL) model for predicting the radiated susceptibility of arbitrarily oriented bundles of wires, illuminated by (possibly) nonuniform electromagnetic fields. The proposed method foresees solution of the field-to-wire coupling problem through suitable discretization and sampling of the bundle geometry and the incident electromagnetic field. Differently from previous models, where bundles parallel to ground were assumed, the proposed model allows for arbitrary bundle orientation by exploiting, first, exact projection of the external field onto the bundle direction, and second, evaluation of the actual wire length (instead of the longitudinal one) of each TL section. Accuracy and computational efficiency of the proposed method are assessed versus full-wave simulation for two application examples, involving parabola-shaped and trefoil knot-shaped wiring structures above ground. Although the strong nonuniformity affecting these structures forces TL theory to work very close to its limits, the achieved agreement is satisfactory and the significant reduction of computational times makes the proposed method suitable for approximate yet efficient prediction of radiated susceptibility characteristics of complex wire bundles.

The paper aims to develop a class of high-order explicit exponential time differencing energy-preserving schemes for some conservative fractional PDEs based on the general Hamiltonian form of these equations. The equation is first reformulated into an equivalent system that possesses a new quadratic energy by introducing an auxiliary variable. Then, explicit schemes are derived via applying the exponential time differencing Runge-Kutta method approximations for time integration and Fourier pseudo-spectral discretization in space, which can maintain the accuracy and improve the stability to the system with stiffness. Subsequently, highly efficient energy-preserving schemes are given by combining the proposed explicit schemes and the projection technique. Finally, the advantages of the proposed schemes are illustrated by the numerical results of the fractional nonlinear Schrodinger equation.

This work presents a method for conforming fluid flow to tensor fields in particle-in-cell simulations. Our focus is on the use of tensor fields as a medium to deflect fluids for computer graphics applications. The anisotropic fluid simulation here presented adapts the Fluid-Implicit-Particle (FLIP) method, by including the tensor field information in the advection and projection steps. Numerical solutions are proposed for adapting the anisotropic advection to the particle-in-cell model and for solving the anisotropic Helmholtz projection for Marker-and-Cell (MAC) grids. Suitable boundary conditions are also provided to ensure proper anisotropic fluid behavior. To evidence the capabilities of this approach, we present simulations with different tensor fields composed of isotropic, linear, and planar tensors. Experimental results show that our method is capable of deflecting or withholding flow in specific directions, according to the characteristics of the underlying tensor field, producing visual outcomes typically encountered in anisotropic media, such as permeable-like effects.

Owing to the strong correlation between the spectral bands of hyperspectral images (HSIs), many feature extraction (FE) methods have been proposed to reduce the redundancy of hyperspectral data. However, Euclidean distance-based FE methods are sensitive to noise. To address this issue, this letter proposed a new unsupervised FE method called robust projection learning (RPL) by integrating the low-rank and sparse decomposition with projection learning. Specifically, in order to enhance the discrimination of traditional robust principal component analysis (RPCA), discriminative RPCA (DRPCA) is first proposed by decomposing the raw data into a low-rank part, a discriminative sparse part, and a structured noise. Moreover, for the purpose of redundancy reduction, projection learning is integrated into DRPCA to obtain a projection matrix with robustness and discrimination. To verify the validity of RPL, two real hyperspectral data sets are used for basic comparison and robust analysis. The corresponding experimental results demonstrate that RPL outperforms the comparative FE methods.

Let L ( H ) be the space of linear operators acting from the finite-dimensional real Hilbert space into itself. The purpose of this paper is to present results concerning the geometric properties of some subspaces of L ( H ) . In particular, vertices of the closed unit ball of those subspaces are discussed. The problem of best approximation in the space L ( l 2 2 ) is investigated. Moreover, in this paper we show an example of an effective method seeking a unique minimal projection which is strongly unique.

Radial basis function (RBF) has been accurately used for the spatial discretization to solve PDE problems. In this paper, a practical stabilization of the local formulation of the radial basis function (RBF) method is presented to solve the incompressible fluid flows with heat transport problems. To avoid the nonlinearity of the convective term, we include the modified method of characteristics to construct stable and efficient methods. The governing equations are the incompressible Navier–Stokes equations/Boussinesq approximation coupled with the heat transport equation. The spatial discretization carried out using the local radial basis function (LRBF) method on a uniform and non-uniform nodes distribution in a complex domain. The proposed method can be described as a fractional step splitting where the convective and generalized Stokes parts are treated separately. To solve the generalized Stokes problem, we used a projection/fractional step method that requires velocity–pressure decoupling. The proposed approach’s performance is tested on three benchmark problems and natural convection flow in a regular and irregular domains. We compare the results with different numerical solutions published in the literature. The obtained numerical results demonstrate the accuracy and stability of the proposed meshless method.

An effective unsupervised hashing algorithm leads to compact binary codes preserving the neighborhood structure of data as much as possible. One of the most established schemes for unsupervised hashing is to reduce the dimensionality of data and then find a rigid (neighborhood-preserving) transformation that reduces the quantization error. Although employing rigid transformations is effective, we may not reduce quantization loss to the ultimate limits. As well, reducing dimensionality and quantization loss in two separate steps seems to be sub-optimal. Motivated by these shortcomings, we propose to employ both rigid and non-rigid transformations to reduce quantization error and dimensionality simultaneously. We relax the orthogonality constraint on the projection in a PCA-formulation and regularize this by a quantization term. We show that both the non-rigid projection matrix and rotation matrix contribute towards minimizing quantization loss but in different ways. A scalable nested coordinate descent approach is proposed to optimize this mixed-integer optimization problem. We evaluate the proposed method on five public benchmark datasets providing almost half a million images. Comparative results indicate that the proposed method mostly outperforms state-of-art linear methods and competes with end-to-end deep solutions.

This letter quantifies the effect of random model uncertainty on finite horizon linear time-varying (LTV) systems. Mean and standard deviation field are approximated with high accuracy and efficiency by a Hilbert space technique called polynomial chaos expansion (PCE). The deterministic expansion coefficients of the generalized Fourier series are determined via orthogonal projection, also known as Galerkin projection. We propose the projection of uncertain systems in linear fractional representation (LFR), which can have computational benefits. The technique is benchmarked on a two-link robotic manipulator.

Projecting the original data into a low-dimensional target space for feature extraction is a common method. Recently, presentation-based approaches have been widely concerned and many feature extraction algorithms based on this have been proposed. However, in the process of acquiring real data, the pollution of complex noise cannot always be avoided, which will greatly increase the difficulty of feature extraction and even lead to failed feature extraction results. Thus, a robust image feature extraction model based on Orthogonal Low-Rank Projection Learning (OLRPL) is proposed, in which the introduction of orthogonal matrix can encourage the preservation of the main components of the sample. Particularly, the row sparsity constraint introduced on the projection matrix can encourage the features to be more compact, discriminative and interpretable. In particular, the Weighted Truncated Schatten \emph{p}-norm (WTSN) is proposed to better solve the optimization problem of low-rank constraints. At the same time, the correntropy is applied in OLRPL to suppress the complex noise in the data and thus improve the robustness of the model. Finally, we specially design a robust classification loss function so that our model can be fitted the supervised scene effectively. Experiments on five general databases have proved that OLRPL has better effectiveness and robustness than existing advanced methods.

This paper investigates the problems of stochastic admissibility and extended dissipativity analysis as well as state feedback controller design for interval type-2 singular systems with nonhomogeneous Markovian switching. By utilizing matrix decomposition technique to deal with the time-dependent transition rates, a sufficient condition is established to guarantee that the systems under consideration are regular, impulse-free, stochastically asymptotically stable and extended dissipative. For developing the state feedback controller in light of the obtained sufficient condition, a novel lemma is proposed inspired by Projection lemma, based on which an approach of controller design is provided. It should be pointed out that no conservatism is introduced in controller design due to the sufficiency and necessity of this lemma. Finally, simulation examples are provided to show the effectiveness of the proposed approach.

An a priori analysis for a generalized local projection stabilized finite element approximation of the Stokes, and the Darcy flow equations are presented in this paper. A first-order conforming P 1 c finite element space is used to approximate both the velocity and pressure. It is shown that the stabilized discrete bilinear form satisfies the inf-sup condition in the generalized local projection norm. Moreover, a priori error estimates are established in a mesh-dependent norm as well as in the L 2 -norm for the velocity and pressure. The optimal and quasi-optimal convergence properties are derived for the Stokes and the Darcy flow problems. Finally, the derived estimates are numerically validated with appropriate examples.

We propose a novel constraint-handling technique for the covariance matrix adaptation evolution strategy (CMA-ES). The proposed technique is aimed at solving explicitly constrained black-box continuous optimization problems, in which the explicit constraint is a constraint whereby the computational time for the constraint violation and its (numerical) gradient are negligible compared to that for the objective function. This method is designed to realize two invariance properties: invariance to the affine transformation of the search space, and invariance to the increasing transformation of the objective and constraint functions. The CMA-ES is designed to possess these properties for handling difficulties that appear in black-box optimization problems, such as non-separability, ill-conditioning, ruggedness, and the different orders of magnitude in the objective. The proposed constraint-handling technique (CHT), known as ARCH, modifies the underlying CMA-ES only in terms of the ranking of the candidate solutions. It employs a repair operator and an adaptive ranking aggregation strategy to compute the ranking. We developed test problems to evaluate the effects of the invariance properties, and performed experiments to empirically verify the invariance of the algorithm. We compared the proposed method with other CHTs on the CEC 2006 constrained optimization benchmark suite to demonstrate its efficacy. Empirical studies reveal that ARCH is able to exploit the explicitness of the constraint functions effectively, sometimes even more efficiently than an existing box-constraint handling technique on box-constrained problems, while exhibiting the invariance properties. Moreover, ARCH overwhelmingly outperforms CHTs by not exploiting the explicit constraints in terms of the number of objective function calls., Accepted to Evolutionary Computation (MIT Press)

We consider three-dimensional cubic barcodes, consisting of smaller cubes, each built from one of two possible materials and carry one bit of information. To retrieve the information stored in the barcode, we measure a 2-D projection of the barcode using a penetrating wave such as X-rays, either using parallel-beam or cone-beam scanners from an unknown direction. We derive a theoretical representation of this scanning process and show that for a known barcode pose with respect to the scanner, the projection operator is linear and can be easily inverted. Moreover, we provide a method to estimate the unknown pose of the barcode from a single 2-D scan. We also propose coding schemes to correct errors and ambiguities in the reconstruction process. Finally, we test our designed barcode and reconstruction algorithms with several simulations, as well as a real-world barcode acquired with an X-ray cone-beam scanner, as a proof of concept.

We consider hyperbolic links that admit alternating projections on surfaces in compact, irreducible 3-manifolds. We show that, under some mild hypotheses, the volume of the complement of such a link is bounded below in terms of a Kauffman bracket function defined on link diagrams on the surface. In the case that the 3-manifold is a thickened surface, this Kauffman bracket function leads to a Jones-type polynomial that is an isotopy invariant of links. We show that coefficients of this polynomial provide 2-sided linear bounds on the volume of hyperbolic alternating links in the thickened surface. As a corollary of the proof of this result, we deduce that the twist number of a reduced, twist reduced, checkerboard alternating link projection with disk regions, is an invariant of the link., 24 pages, 6 figures; To be published in Fundamenta Mathematicae; V2: Corrected typos, updated references

The set-theoretical convergence of models of continuous and discrete synthesis processes in the compositions of metals and non-metals at the action of ray sources is shown. The non-metal density function obtained by the IDS thermal impulses on the temperature axis projection has a periodic view with fi xed stationary temperatures. They coincide with the boundaries of diff erent areas of change in the speeds of metal heating. This convergence of models to the general periodic operator is possible under four conditions of beam scanning: separation, compactness, property of states, stability. Then the current reciprocity ratios of the system (metals/non-metals) allow the use of the temperature of stationary non-metals as support for metals and serves to determine the parameters of ray sources when synthesizing structures in the compositions of the volume of the material.

We propose a nonlinear reduced basis method for the efficient approximation of parametrized partial differential equations (PDEs), exploiting kernel proper orthogonal decomposition (KPOD) for the generation of a reduced order space and neural networks for the evaluation of the reduced order approximation. In particular, we use KPOD in place of the more classical POD, on a set of high-fidelity solutions of the problem at hand to extract a reduced basis. This method provides a more accurate approximation of the snapshots' set featuring a lower dimension, while maintaining the same efficiency as POD. A neural network (NN) is then used to find the coefficients of the reduced basis by following a supervised learning paradigm and shown to be effective in learning the map between the time/parameter values and the projection of the high-fidelity snapshots onto the reduced space. In this NN, both the number of hidden layers and the number of neurons vary according to the intrinsic dimension of the differential problem at hand and the size of the reduced space. This adaptively built NN attains good performances in both the learning and the testing phases. Our approach is then tested on two benchmark problems, a one-dimensional wave equation and a two-dimensional nonlinear lid-driven cavity problem. We finally compare the proposed KPOD-NN technique with a POD-NN strategy, showing that KPOD allows a reduction of the number of modes that must be retained to reach a given accuracy in the reduced basis approximation. For this reason, the NN built to find the coefficients of the KPOD expansion is smaller, easier and less computationally demanding to train than the one used in the POD-NN strategy.

This paper studies the Schatten-q error of low-rank matrix estimation by singular value decomposition under perturbation. We specifically establish a perturbation bound on the low-rank matrix estimation via a perturbation projection error bound. Then, we establish lower bounds to justify the tightness of the upper bound on the low-rank matrix estimation error. We further develop a user-friendly sinΘ bound for singular subspace perturbation based on the matrix perturbation projection error bound. Finally, we demonstrate the advantage of our results over the ones in the literature by simulation.

Model order reduction of electronic devices and on-chip interconnects plays an important role in determining the performance of very large scale IC (Integrated Circuit) designs. The ever shrinking process technology continues to increase complexity of these systems with the current Intel device technology node standing at 10 nm. In the analysis of high-speed IC interconnects, the reduced model is often required to approximate the original system in the desired frequency range. In this paper, an efficient Statistically Inspired Multi-shift Arnoldi (SIMA) Method is proposed, which dynamically selects normally distributed shifts to determine the projection matrix. The SIMA is implemented by developing an iterative algorithm for approximation of large-scale systems as an eigenvalue problem using statistically generated interpolation points. The motivation of selecting these points weighted with the Gaussian kernel is derived from the fact that there exist many natural phenomenon, which follow normal distribution. Simulation results have shown better accuracy for the proposed method as compared to other existing model order reduction techniques.

We propose a method for testing hypothesis on parametric family of transition probabilities of a Markov sequence, when the asymptotic distribution of the empirical processes involved is, largely, independent from the specific form of the parametric family. We first consider function-parametric empirical process for the Markov sequence and describe its weak limit as a certain projection. Then we establish equivalence between testing different families of transition probabilities and show how the empirical process for one testing problem can be transformed into empirical process in another testing problem. This creates wide equivalence classes and allows distribution free testing.

In this paper, four accelerated subgradient extragradient methods are proposed to solve the variational inequality problem with a pseudo-monotone operator in real Hilbert spaces. These iterative schemes employ two new adaptive stepsize strategies that are significant when the Lipschitz constant of the mapping involved is unknown. Strong convergence theorems for the proposed algorithms are established under the condition that the operators are Lipschitz continuous and non-Lipschitz continuous. Numerical experiments on finite- and infinite-dimensional spaces and applications in optimal control problems are reported to demonstrate the advantages and efficiency of the proposed algorithms over some existing results.

In this work, we construct two numerical approximations methods to deal with approximations of a linear Fredholm integro-differential equation. In order to show the existence and uniqueness of the solution we start by the reformulation of the integro-differential equation to a system of integral equations. We explain the general framework of the projection method which helps to clarify the basic ideas of the Collocation and Kantorovich methods. We introduce a new iterative method to avoid inversing the block operator matrix. Next, we apply the iterative projection methods and we present theorems to show the convergence of the constructed solutions to the exact solution. Finally, to observe the error behavior of the two methods, we give two numerical examples.

In this paper, we study a new generalization of the Lorentz cone $$\mathcal{L}^n_+$$ L + n , called the monotone extended second-order cone (MESOC). We investigate basic properties of MESOC including computation of its Lyapunov rank and proving its reducibility. Moreover, we show that in an ambient space, a cylinder is an isotonic projection set with respect to MESOC. We also examine a nonlinear complementarity problem on a cylinder, which is equivalent to a suitable mixed complementarity problem, and provide a computational example illustrating applicability of MESOC.

Under a fourth-order moment condition on the branching and a second-order moment condition on the immigration mechanisms, we show that an appropriately scaled projection of a supercritical and irreducible continuous-state and continuous-time branching process with immigration on certain left non-Perron eigenvectors of the branching mean matrix is asymptotically mixed normal. With an appropriate random scaling, under some conditional probability measure, we prove asymptotic normality as well. In the case of a non-trivial process, under a first-order moment condition on the immigration mechanism, we also prove the convergence of the relative frequencies of distinct types of individuals on a suitable event; for instance, if the immigration mechanism does not vanish, then this convergence holds almost surely.

Due to sensor drift, instrumental variation, or change of measurement object, the distributions of the datasets (domains) acquired by the sensors are often different. A domain adaptive framework called MCSP-SSS is proposed to reduce the distribution discrepancy across domains for high-accuracy sensor data classification. The framework consists of two key parts: Multi-Constraint Subspace Projection (MCSP) and Source Sample Selection (SSS). MCSP is a subspace-projection-based approach, which introduces four constraints to get an optimized projection matrix: Principal Component Analysis (PCA) is used to reduce the redundancy of features; Mean Distribution Discrepancy (MDD) is applied to minimize the difference between source and target data; Hilbert-Schmidt Independence Criterion (HSIC) is adopted to maximizing the dependence between features and labels; A so-called weighted-within-class scatter matrix is introduced to minimize the within-class variance to avoid samples with different labels to overlap in the subspace. SSS is designed to remove the outliers in projected source samples so as to reduce distribution discrepancy between the source and target samples projected by MCSP. Experimental results show that our framework can achieve the best accuracies in all classification tasks in comparison with other state-of-the-art approaches. The accuracy of MCSP-SSS is 3.57 percentage points (pps) higher on average than that of the second best approach for single-source domain adaptation, and 7.00 pps for multi-source domain adaptation. Source code is available at https://github.com/threedteam/tsc_subspace_projection .

Thermodynamic assessment of the ternary system B-Hf-Zr has been conducted by modeling the Gibbs energy of all individual phases using the CALPHAD (CALculation of PHAse Diagrams) approach. There is no ternary compound in this system. The individual solution phases, i.e., liquid, (βHf,βZr), HfB and (Hf,Zr)B2 have been modeled. The modeling covers the whole composition and temperature ranges. The Gibbs energies of HfB2 and HfB in the B-Hf system were reassessed using the two-sublattice models (B,Hf)1(B,Hf)2 and (Hf)1(B,Hf)1, respectively. A set of self-consistent thermodynamic parameters for the B-Hf-Zr system was obtained by considering the phase diagram data in the ternary system. Comprehensive comparisons between the calculated and measured phase diagram and thermodynamic data show that the experimental information was satisfactorily accounted for by the present thermodynamic description. The liquidus projection and reaction scheme of the B-Hf-Zr system are also presented.

We describe a robust method for determining Pipek-Mezey (PM) Wannier functions (WF), recently introduced by Jonsson et al. (J. Chem. Theor. Chem.2017,13, 460), which provide some formal advantages over the more common Boys (also known as maximally-localized) Wannier functions. The Broyden-Fletcher-Goldfarb-Shanno-based PMWF solver is demonstrated to yield dramatically faster convergence compared to the alternatives (steepest ascent and conjugate gradient) in a variety of one-, two-, and three-dimensional solids (including some with vanishing gaps) and can be used to obtain Wannier functions robustly in supercells with thousands of atoms. Evaluation of the PM functional and its gradient in periodic linear combination of atomic orbital representation used a particularly simple definition of atomic charges obtained by Moore-Penrose pseudoinverse projection onto the minimal atomic orbital basis. An automated "canonicalize phase then randomize" method for generating the initial guess for WFs contributes significantly to the robustness of the solver.

Model-order reduction is an important tool in the computational exploration of complex physical phenomena, such as kinetic plasmas. A popular strategy to achieve model reduction is the so- called projection methods, such as the proper orthogonal decomposition (POD), where the dynamics of interest are decomposed into a set of global modes and the problem is then projected onto those modes. While very successful, in general, the conventional POD technique is not suited for certain advection-dominated problems or “transport” problems where moving localized features cannot be well represented by global modes. In this work, we apply an extension of the POD technique to obtain an efficient reduced-order model of advection-dominated kinetic plasma problems from finite-element particle-in-cell (PIC) simulations. The results obtained showcase the efficacy of this strategy for obtaining a parsimonious representation of the degrees of freedom of the problem that serves to both reduce simulation costs and provide added physical insight into the problem.

The Prandtl–Ishlinskii (PI) operator is a mathematical model for hysteresis, and it is comprised of weighted superposition of multiple play (backlash) operators. The PI operator has been widely used in modeling and compensation of hysteresis in smart material actuators, robots, and mechanical systems. The behavior of a PI operator is determined by both the weights and the radii of individual play operators. However, existing modeling work has mostly been focused on the identification of the weight parameters by assuming the play radii to be known. While the latter approach is convenient due to the linear relationship between the operator output and the weight parameters, it often requires a large number of plays with preassigned radii in order to adequately capture the hysteresis in a given application. In this work, for the first time, we propose an adaptive estimation algorithm to identify the play radii of a PI operator, to enable accurate modeling of hysteresis with a small number of plays and, thus, reduce the complexity in control. The major challenge lies in the nonlinear, complex, time-varying relationship between the PI operator output and the play radii. The proposed algorithm utilizes available measurement and information, including the instantaneous slope of the hysteretic input–output graph, to derive a modified estimation error function that is proportional to the parameter error. With a mild condition on the input, we establish the persistent excitation of the resulting regressor vector and the parameter convergence under a gradient algorithm with parameter projection. Both simulation and experimental results are presented to illustrate the proposed approach. In particular, comparison results based on experimental data from a piezoelectric nanopositioner show that, with the proposed method, the resulting PI operator outperforms identified PI operators of larger numbers of plays with preassigned radius values.

In this article, we study the recursive algorithms for a class of separable nonlinear models (SNLMs) in which the parameters can be partitioned into a linear part and a nonlinear part. Such models are very common in machine learning, system identification, and signal processing. Utilizing the special structure of the SNLMs, we propose a recursive variable projection (RVP) algorithm, in which at each recursion, the linear parameters of the model are eliminated, and the nonlinear parameters are updated by the recursive Levenberg-Marquart algorithm. Then, based on the updated nonlinear parameters, the linear parameters are updated by the recursive least-squares algorithm. According to a convergence analysis of the RVP algorithm, the parameter estimation error is mean-square bounded. Numerical examples confirm the satisfactory performance of the proposed algorithm.

In this paper a milli-sized traveling wave actuator is designed by optimizing the polarization direction. Two different sets of electrodes are needed to generate the traveling wave. The topology optimization method is used to get the optimal sets of electrodes that minimize the difference between a pure traveling wave and the deflection generated. Classical issues in topology optimization problem such as mesh-dependence or intermediate densities are overcome by using filtering and projection techniques. Examples with different boundary conditions are presented in order to validate the model.

We study the construction of nonlinear impulse responses in linear structural dynamic models that include nonlinearly transformed regressors. We derive the closed-form solution for the population impulse responses to a given shock and propose a control function approach to estimating these responses without taking a stand on how the remainder of the model is identified. Our plug-in estimator dispenses with the need for simulations and, unlike conventional local projection (LP) estimators, is consistent. A modified LP estimator is shown to be consistent in special cases, but less accurate in finite samples than the plug-in estimator.

Principal component analysis (PCA) and Kernel principal component analysis (KPCA) are fundamental methods in machine learning for dimensionality reduction. The former is a technique for finding this approximation in finite dimensions and the latter is often in an infinite dimensional reproducing Kernel Hilbert-space (RKHS). In this paper, we present a geometric framework for computing the principal linear subspaces in both (finite and infinite) situations as well as for the robust PCA case, that amounts to computing the intrinsic average on the space of all subspaces: the Grassmann manifold. Points on this manifold are defined as the subspaces spanned by $K$ K -tuples of observations. The intrinsic Grassmann average of these subspaces are shown to coincide with the principal components of the observations when they are drawn from a Gaussian distribution. We show similar results in the RKHS case and provide an efficient algorithm for computing the projection onto the this average subspace. The result is a method akin to KPCA which is substantially faster. Further, we present a novel online version of the KPCA using our geometric framework. Competitive performance of all our algorithms are demonstrated on a variety of real and synthetic data sets.

In this paper, we consider a new class of quasi-variational inequalities, which is called the general quasi-variational inequality. Using the projection operator technique, we establish the equivalence between the general quasi-variational inequalities and the fixed point problems. We use this alternate formulation to propose some new inertial iterative schemes for solving the general quasi-variational inequalities. The convergence criteria of the new inertial projection methods under some appropriate conditions is investigated. Since the general quasi-variational inequalities include the quasi-variational inequalities, variational inequalities, complementarity problems and the related optimization problems as special cases, our results continue to hold for these problems. It is an interesting problem to compare the efficiency of the proposed methods with other known methods.

Humans prefer visual representations for the analysis of large databases. In this work, we suggest a method for the visualization of the chemical reaction space. Our technique uses the t-SNE approach that is parameterized by a deep neural network (parametric t-SNE). We demonstrated that the parametric t-SNE combined with reaction difference fingerprints can provide a tool for the projection of chemical reactions onto a low-dimensional manifold for easy exploration of reaction space. We showed that the global reaction landscape, been projected onto a 2D plane, corresponds well with already known reaction types. The application of a pretrained parametric t-SNE model to new reactions allows chemists to study these reactions on a global reaction space. We validated the feasibility of this approach for two marketed drugs: darunavir and oseltamivir. We believe that our method can help explore reaction space and inspire chemists to find new reactions and synthetic ways.

Skew braces have recently attracted attention as a method to study set-theoretical solutions of the Yang-Baxter equation. Here, we present a new approach to these solutions by studying Hopf algebras in the category, SupLat, of complete lattices and join-preserving morphisms. We connect the two methods by showing that any Hopf algebra, H in SupLat, has a corresponding group, R ( H ) , which we call its remnant and a co-quasitriangular structure on H induces a YBE solution on R ( H ) , which is compatible with its group structure. Conversely, any group with a compatible YBE solution can be realised in this way. Additionally, it is well-known that any such group has an induced secondary group structure, making it a skew left brace. By realising the group as the remnant of a co-quasitriangular Hopf algebra, H , this secondary group structure appears as the projection of the transmutation of H . Finally, for any YBE solution, we obtain a SupLat-FRT Hopf algebra in SupLat, whose remnant recovers the universal skew brace of the solution.

A proper orthogonal decomposition-based B-splines B\'ezier elements method (POD-BSBEM) is proposed as a non-intrusive reduced-order model for uncertainty propagation analysis for stochastic time-dependent problems. The method uses a two-step proper orthogonal decomposition (POD) technique to extract the reduced basis from a collection of high-fidelity solutions called snapshots. A third POD level is then applied on the data of the projection coefficients associated with the reduced basis to separate the time-dependent modes from the stochastic parametrized coefficients. These are approximated in the stochastic parameter space using B-splines basis functions defined in the corresponding B\'ezier element. The accuracy and the efficiency of the proposed method are assessed using benchmark steady-state and time-dependent problems and compared to the reduced order model-based artificial neural network (POD-ANN) and to the full-order model-based polynomial chaos expansion (Full-PCE). The POD-BSBEM is then applied to analyze the uncertainty propagation through a flood wave flow stemming from a hypothetical dam-break in a river with a complex bathymetry. The results confirm the ability of the POD-BSBEM to accurately predict the statistical moments of the output quantities of interest with a substantial speed-up for both offline and online stages compared to other techniques., Comment: 45 pages, 15 figures

We propose a new framework to design controllers for high-dimensional nonlinear systems. The control is designed through the iterative linear quadratic regulator (ILQR), an algorithm that computes control by iteratively applying the linear quadratic regulator on the local linearization of the system at each time step. Since ILQR is computationally expensive, we propose to first construct reduced-order models (ROMs) of the high-dimensional nonlinear system. We derive nonlinear ROMs via projection, where the basis is computed via balanced truncation (BT) and LQG balanced truncation (LQG-BT). Numerical experiments are performed on a semi-discretized nonlinear Burgers equation. We find that the ILQR algorithm produces good control on ROMs constructed either by BT or LQG-BT, with BT-ROM based controllers outperforming LQG-BT slightly for very low-dimensional systems.

The algebraic singularity method is a framework for analyzing collider events with missing energy. It provides a way to draw out a set of singularity variables that can catch singular features originating from the projection of full phase space onto the observable phase space of measured particle momenta. It is a promising approach applicable to various physics processes with missing energy but still requires more studies for use in practice. Meanwhile, in the double-sided decay topology with an invisible particle on each side, the $M_{T2}$ variable has been known to be a useful collider observable for measuring particle masses from missing energy events or setting signal regions of collider searches. We investigate the relation between the two different types of kinematic variables in double-sided decay topology. We find that the singularity variables contain the $M_{T2}$ variable in many cases, although the former is not a strict superset of the latter., 1+25 pages, 6 figures; matches published version

In this paper, by combining the Solodov and Svaiter projection technique with the conjugate gradient method for unconstrained optimization proposed by Mohamed et al. (2020), we develop a derivative-free conjugate gradient method to solve nonlinear equations with convex constraints. The proposed method involves a spectral parameter which satisfies the sufficient descent condition. The global convergence is proved under the assumption that the underlying mapping is Lipschitz continuous and satisfies a weaker monotonicity condition. Numerical experiment shows that the proposed method is efficient.