Adaptive Basis Function Research Articles

Two-phase greedy pursuit algorithm for automatic detection and characterization of transient calcium signaling.

Ca(2+) plays an important role in the regulation of cellular functions. Local calcium events, e.g., calcium sparks, not only bring insights into Ca(2+) signaling but also contribute to the understanding of various cellular processes. However, it is challenging to detect calcium sparks, due to their transient properties and high level of nonstationary noises in microscopic images. Most of existing algorithms tend to have limitations for the detection of calcium sparks, e.g., empirically defined hard thresholds or poor applicability to nonstationary conditions. This paper presents a novel two-phase greedy pursuit (TPGP) algorithm for automatic detection and characterization of calcium sparks. In Phase I, a coarse-grained search is conducted across the whole image to identify the predominant sparks. In Phase II, adaptive basis function model is developed for the fine-grained representation of detected sparks. It may be noted that the proposed TPGP algorithms overcome the drawback of hard thresholding in most of previous approaches. Furthermore, the morphology of detected sparks is effectively modeled with multiscale basis functions in Phase II, thereby facilitating the analysis of physiological features. We evaluated and validated the TPGP algorithms using both real-word and synthetic images with multiple noise levels and varying baselines. Experimental results show that TPGP algorithms yield better performances than previous hard-thresholding approaches in terms of both sensitivities and positive predicted values. The present research provides the community a robust tool for the automatic detection and characterization of transient calcium signaling.

Efficient iterative solution of electromagnetic scattering using adaptive cross approximation enhanced characteristic basis function method

A new hybrid adaptive cross approximation-characteristic basis function method (ACA-CBFM) is proposed to efficiently solve the electromagnetic scattering problems. In the conventional ACA-CBFM, the ACA is only applied to speed up the construction of the reduced matrix that is directly solved and stored. However, with the increase of the size of the targets under analysis, the reduced matrix will become so large that it is difficult to directly solve and store. In this study, the reduced matrix is further compressed by the adaptive cross approximation-singular value decomposition (ACA-SVD) and solved by an iterative method, which leads to reduced storage and accelerated matrix vector product. Furthermore, the ACA-SVD is adapted to efficiently generate the characteristic basis functions (CBFs), which reduces both the time of generating initial CBFs and the SVD time of initial CBFs. Numerical results about the electromagnetic scattering from perfect electric conducting targets are given to demonstrate the merits of the proposed methods.

<i>A posteriori</i> error estimator for adaptive local basis functions to solve Kohn–Sham density functional theory

Kohn-Sham density functional theory is one of the most widely used electronic structure theories. The recently developed adaptive local basis functions form an accurate and systematically improvable basis set for solving Kohn-Sham density functional theory using discontinuous Galerkin methods, requiring a small number of basis functions per atom. In this paper we develop residual-based a posteriori error estimates for the adaptive local basis approach, which can be used to guide non-uniform basis refinement for highly inhomogeneous systems such as surfaces and large molecules. The adaptive local basis functions are non-polynomial basis functions, and standard a posteriori error estimates for $hp$-refinement using polynomial basis functions do not directly apply. We generalize the error estimates for $hp$-refinement to non-polynomial basis functions. We demonstrate the practical use of the a posteriori error estimator in performing three-dimensional Kohn-Sham density functional theory calculations for quasi-2D aluminum surfaces and a single-layer graphene oxide system in water.

Adaptive structure radial basis function network model for processes with operating region migration

An adaptive structure radial basis function (RBF) network model is proposed in this paper to model nonlinear processes with operating point migration. The recursive orthogonal least squares algorithm (ROLS) is adopted to select new centers on-line, as well as to train the network weights. Based on the R matrix in the orthogonal decomposition, an initial center bank is formed and updated in each sample period. A new learning strategy is proposed to gain information from the new data for network structure adaptation. A center grouping algorithm is also developed to divide the centers into active and non-active groups, so that a structure with a smaller size is maintained in the final network model used for output prediction. The proposed RBF model is evaluated and compared with the three existing adaptive structure RBF networks by modeling a nonlinear time-varying numerical example. Simulation results demonstrate that the proposed algorithm has several advantages in term of the adaptive tracking ability and a better recovery speed over the existing methods during the migration of system׳s operating point.

Planetary gearbox condition monitoring of ship-based satellite communication antennas using ensemble multiwavelet analysis method

Satellite communication antennas are key devices of a measurement ship to support voice, data, fax and video integration services. Condition monitoring of mechanical equipment from the vibration measurement data is significant for guaranteeing safe operation and avoiding the unscheduled breakdown. So, condition monitoring system for ship-based satellite communication antennas is designed and developed. Planetary gearboxes play an important role in the transmission train of satellite communication antenna. However, condition monitoring of planetary gearbox still faces challenges due to complexity and weak condition feature. This paper provides a possibility for planetary gearbox condition monitoring by proposing ensemble a multiwavelet analysis method. Benefit from the property on multi-resolution analysis and the multiple wavelet basis functions, multiwavelet has the advantage over characterizing the non-stationary signal. In order to realize the accurate detection of the condition feature and multi-resolution analysis in the whole frequency band, adaptive multiwavelet basis function is constructed via increasing multiplicity and then vibration signal is processed by the ensemble multiwavelet transform. Finally, normalized ensemble multiwavelet transform information entropy is computed to describe the condition of planetary gearbox. The effectiveness of proposed method is first validated through condition monitoring of experimental planetary gearbox. Then this method is used for planetary gearbox condition monitoring of ship-based satellite communication antennas and the results support its feasibility.

An Adaptive Radial Point Interpolation Meshless Method for Simulation of Electromagnetic and Optical Fields

This paper is going to handle an adaptive meshless method by which a wide range of microwave problems in terms of frequency are numerically solved whose accuracy and computational time are acceptable with respect to some other numerical schemes. As the origin, in the process of imposing the conventional radial point interpolation method (CRPIM) to laser problems, a special function was found, which results in a well-behaved basis function for CRPIM. This basis function possesses two fundamental advantages in view of meshless methods. At first, and in contradiction with conventional basis functions, the shape parameters are deterministic, which results in a higher accuracy than conventional basis functions. Second, it will construct the shape functions without any need for the middle matrix inversion step. Also, the adaptive basis function inherits the fundamental properties of fields. Hence, the computational time is reduced, approximately by half, comparing with the conventional basis functions. To investigate the proposed adaptive method named quantum radial point interpolation method in different areas of interest, it has been employed to solve three classes of partial differential equations in computational electromagnetics, i.e., Schrodinger's equation in a quantum wave laser, Laplace and electromagnetic wave equations. The results are more accurate and faster than the CRPIM and the finite-element method.

Adaptive Regression and Classification Models with Applications in Insurance

Abstract Nowadays, in the insurance industry the use of predictive modeling by means of regression and classification techniques is becoming increasingly important and popular. The success of an insurance company largely depends on the ability to perform such tasks as credibility estimation, determination of insurance premiums, estimation of probability of claim, detecting insurance fraud, managing insurance risk. This paper discusses regression and classification modeling for such types of prediction problems using the method of Adaptive Basis Function Construction

Self-learning PID Control for X-Y NC Position Table with Uncertainty Base on Neural Network

An adaptive radical basis function (RBF) neural network PID control scheme for X-Y position table is proposed by the paper. Firstly, X-Y position table model is established, controller based on neutral network is used to learn adaptive and compensate uncertainty model of X-Y position table, neutral network is used to study model. PID neural network controller base on augmented variable method is designed. PID controller is used as assistant direction error controller, neural network parameters base on stochastic gradient algorithm can be adjust adaptive on line. The simulation results show that the presented controller has important engineering value.

T-x frequency filtering of high resolution seismic reflection data using singular spectral analysis

Abstract We develop here an efficient approach using singular spectral analysis (SSA) for frequency filtering of seismic reflection data in t-x domain. The abrupt change in geophysical records creates ringing artifacts in the Fourier based filtering operations. We use here complete data adaptive basis functions in SSA filtering, which enables the self-similarity of the data in reconstruction of such sudden changes. We first tested the SSA based filtering algorithm on synthetic seismic data and then applied to real seismic reflection data from Singareni coalfields, Andhra Pradesh, India. The individual trace from each channel in the shot gathers is processed and compared with Fourier and multichannel SSA filtered output. Our analysis demonstrates that SSA filtering attenuated the low frequency ground role and high frequency noise embedded in the seismic record in a more efficient way than the other two methods. The coal formations and faults identified in the stack section of filtered data match quite well with the geological information available in the study region.

Digital Predistortion Using Adaptive Basis Functions

This paper is concerned with digital predistortion (DPD) for linearization of radio frequency (RF) high power amplifiers (PAs). We propose an adaptive scheme for selecting basis functions for both direct and indirect learning digital predistortion architectures. The adaptive scheme has the advantage of reducing the complexity and, at the same time, increasing the stability of digital predistortion. Simulation and lab experimental results are presented to demonstrate the effectiveness of using adaptive basis functions in a hardware platform with a solid state high power amplifier.

Confinement effects of solvation on a molecule physisorbed on a polarizable continuum particle

We investigate the effects of solvation on the static properties of a molecule physisorbed on a spherical polarizable continuum particle, with a static dielectric constant. The effective polarizability of the physisorbed molecule is enhanced by a factor of 105 in vacuo and by only 102 when solvated. The electrostatic interaction between molecules and the polarizable continuum particle (PCP) results in a magnified reflected electric field with a magnitude that depends on the PCP-molecule separation. A similar and greater magnification effect in reflected field also results from the PCP-field (external electric field) interaction. The variation of the polarizability of the molecules with respect to the changes in their environment illustrates the importance of electrostatic interaction in the enhancement of the effective polarizability. In the course of the investigation, the solute and the continuous body are represented with the same adaptive multi-wavelet basis functions, thereby, within the user specified precision, eliminating basis set error.

Multiscale Adaptive Basis Function Modeling of Spatiotemporal Vectorcardiogram Signals

Mathematical modeling of cardiac electrical signals facilitates the simulation of realistic cardiac electrical behaviors, the evaluation of algorithms, and the characterization of underlying space-time patterns. However, there are practical issues pertinent to model efficacy, robustness, and generality. This paper presents a multiscale adaptive basis function modeling approach to characterize not only temporal but also spatial behaviors of vectorcardiogram (VCG) signals. Model parameters are adaptively estimated by the "best matching" projections of VCG characteristic waves onto a dictionary of nonlinear basis functions. The model performance is experimentally evaluated with respect to the number of basis functions, different types of basis function (i.e., Gaussian, Mexican hat, customized wavelet, and Hermitian wavelets), and various cardiac conditions, including 80 healthy controls and different myocardial infarctions (i.e., 89 inferior, 77 anterior-septal, 56 inferior-lateral, 47 anterior, and 43 anterior-lateral). Multiway analysis of variance shows that the basis function and the model complexity have significant effects on model performances while cardiac conditions are not significant. The customized wavelet is found to be an optimal basis function for the modeling of spacetime VCG signals. The comparison of QT intervals shows small relative errors (<;5%) between model representations and realworld VCG signals when the model complexity is greater than 10. The proposed model shows great potentials to model space-time cardiac pathological behaviors and can lead to potential benefits in feature extraction, data compression, algorithm evaluation, and disease prognostics.

Identification of nonlinear dynamic systems using convex combinations of multiple adaptive radius basis function networks

To improve performance of nonlinear adaptive filter based on radius basis function (RBF) networks, a generalized combination scheme is proposed for nonlinear dynamic system identification in this paper. The nonlinear filter proposed is constructed by the convex combination of multiple RBF networks (MCRBF). Its adaptive algorithm with different step sizes is derived by the gradient descent rule, and can overcome the contradiction between convergence speed and precision of the stochastic gradient (SG) algorithm for RBF networks, which is imposed by the selection of a fixed value for the adaption step. Computer simulations demonstrate that the performance of the nonlinear filter proposed is superior to the RBF for nonlinear dynamic system identification in terms of convergence speed, steady state error and tracking capability.

Multigrid and multilevel preconditioners for computational photography

This paper unifies multigrid and multilevel (hierarchical) preconditioners, two widely-used approaches for solving computational photography and other computer graphics simulation problems. It provides detailed experimental comparisons of these techniques and their variants, including an analysis of relative computational costs and how these impact practical algorithm performance. We derive both theoretical convergence rates based on the condition numbers of the systems and their preconditioners, and empirical convergence rates drawn from real-world problems. We also develop new techniques for sparsifying higher connectivity problems, and compare our techniques to existing and newly developed variants such as algebraic and combinatorial multigrid. Our experimental results demonstrate that, except for highly irregular problems, adaptive hierarchical basis function preconditioners generally outperform alternative multigrid techniques, especially when computational complexity is taken into account.

Wave scattering from random sets of closely spaced objects through linear embedding via Green's operators

In this paper we present the application of linear embedding via Green's operators (LEGO) to the solution of the electromagnetic scattering from clusters of arbitrary (both conducting and penetrable) bodies randomly placed in a homogeneous background medium. In the LEGO method the objects are enclosed within simple-shaped bricks described in turn via scattering operators of equivalent surface current densities. Such operators have to be computed only once for a given frequency, and hence they can be re-used to perform the study of many distributions comprising the same objects located in different positions. The surface integral equations of LEGO are solved via the Moments Method combined with Adaptive Cross Approximation (to save memory) and Arnoldi basis functions (to compress the system). By means of purposefully selected numerical experiments we discuss the time requirements with respect to the geometry of a given distribution. Besides, we derive an approximate relationship between the (near-field) accuracy of the computed solution and the number of Arnoldi basis functions used to obtain it. This result endows LEGO with a handy practical criterion for both estimating the error and keeping it in check.

Incremental State Aggregation for Value Function Estimation in Reinforcement Learning

In reinforcement learning, large state and action spaces make the estimation of value functions impractical, so a value function is often represented as a linear combination of basis functions whose linear coefficients constitute parameters to be estimated. However, preparing basis functions requires a certain amount of prior knowledge and is, in general, a difficult task. To overcome this difficulty, an adaptive basis function construction technique has been proposed by Keller recently, but it requires excessive computational cost. We propose an efficient approach to this difficulty, in which the problem of approximating the value function is decomposed into a number of subproblems, each of which can be solved with small computational cost. Computer experiments show that the CPU time needed by our method is much smaller than that by the existing method.

An adaptive fuzzy model using orthonormal basis functions based on multifractal characteristics applied to network traffic control

In this paper, we present an adaptive predictive orthonormal basis functions (OBF)-fuzzy model that considers the multifractal behavior of network traffic flows. To this end, we model the traffic flows using orthonormal basis functions obtained through multifractal analysis. We insert the orthonormal basis functions into a fuzzy model trained with an adaptive clustering algorithm. Further, we propose a predictive flow control scheme for broadband networks. Also, using the fuzzy model parameters, we derive an expression for the optimal traffic source rate. Comparisons to other predictive control schemes prove the efficiency of the proposed adaptive OBF-fuzzy based control and training algorithm.

Reduced-Rank Linear Interference Suppression for DS-UWB Systems Based on Switched Approximations of Adaptive Basis Functions

In this paper, we propose a novel low-complexity reduced-rank scheme and consider its application to linear interference suppression in direct-sequence ultrawideband systems (DS-UWB). First, we investigate a generic reduced-rank scheme that jointly optimizes a projection vector and a reduced-rank filter by using the minimum mean square error (MMSE) criterion. Then, a low-complexity scheme, which are denoted the switched approximation of adaptive basis functions (SAABFs), is proposed. The SAABF scheme is an extension of the generic scheme, in which the complexity reduction is achieved by using a multibranch framework to simplify the structure of the projection vector. Adaptive implementations for the SAABF scheme are developed by using least mean squares (LMS) and recursive least squares (RLS) algorithms. We also develop algorithms for selecting the branch number and the model order of the SAABF scheme. Simulations show that, in the scenarios with severe intersymbol interference (ISI) and multiple-access interference (MAI), the proposed SAABF scheme has fast convergence and remarkable interference suppression performance with low complexity.

ELECTROMAGNETIC SCATTERING AND DOPPLER ANALYSIS OF THREE-DIMENSIONAL BREAKING WAVE CRESTS AT LOW-GRAZING ANGLES

The electromagnetic scattering of the synthesized three- dimensional (3-D) breaking wave crests which are formed by azimuthally aligning the individual 2-D breaking wave proflles has been numerically studied at the low-grazing angles (LGA) by using the multilevel fast multipole algorithm (MLFMA) with adaptive higher order hierarchical Legendre basis functions. Difierent from the specular (or quasi-specular) re∞ection and Bragg scattering, the \sea-spike phenomenon which is characterized by that horizontally polarization (HH) signals greatly exceed vertically polarization (V V ) signals has been demonstrated by analyzing both the backscattering of 3-D LONGTANK series and a plunging breaker. For the time- dependent evolution of the plunging breaker, the Doppler shifts and Doppler splitting efiects are investigated by applying the fast Fourier transform (FFT) with a moving Hamming window. The spectrum of HH scattering has the feature of concentration, while the spectrum of V V scattering shows the Doppler splitting efiects.

Ｈ．２６４のＩｎｔｒａ予測残差に対する適応的変換基底関数を用いた映像符号化方式

Ｈ．２６４のＩｎｔｒａ予測残差に対する適応的変換基底関数を用いた映像符号化方式