The completion of a crystal structure determination is often hampered by the presence of embedded solvent molecules or ions that are seriously disordered. Their contribution to the calculated ...structure factors in the least‐squares refinement of a crystal structure has to be included in some way. Traditionally, an atomistic solvent disorder model is attempted. Such an approach is generally to be preferred, but it does not always lead to a satisfactory result and may even be impossible in cases where channels in the structure are filled with continuous electron density. This paper documents the SQUEEZE method as an alternative means of addressing the solvent disorder issue. It conveniently interfaces with the 2014 version of the least‐squares refinement program SHELXL Sheldrick (2015). Acta Cryst. C71. In the press and other refinement programs that accept externally provided fixed contributions to the calculated structure factors. The PLATON SQUEEZE tool calculates the solvent contribution to the structure factors by back‐Fourier transformation of the electron density found in the solvent‐accessible region of a phase‐optimized difference electron‐density map. The actual least‐squares structure refinement is delegated to, for example, SHELXL. The current versions of PLATON SQUEEZE and SHELXL now address several of the unnecessary complications with the earlier implementation of the SQUEEZE procedure that were a necessity because least‐squares refinement with the now superseded SHELXL97 program did not allow for the input of fixed externally provided contributions to the structure‐factor calculation. It is no longer necessary to subtract the solvent contribution temporarily from the observed intensities to be able to use SHELXL for the least‐squares refinement, since that program now accepts the solvent contribution from an external file (.fab file) if the ABIN instruction is used. In addition, many twinned structures containing disordered solvents are now also treatable by SQUEEZE. The details of a SQUEEZE calculation are now automatically included in the CIF archive file, along with the unmerged reflection data. The current implementation of the SQUEEZE procedure is described, and discussed and illustrated with three examples. Two of them are based on the reflection data of published structures and one on synthetic reflection data generated for a published structure.
Abnormal Event Detection at 150 FPS in MATLAB Lu, Cewu; Shi, Jianping; Jia, Jiaya
2013 IEEE International Conference on Computer Vision,
12/2013
Conference Proceeding, Journal Article
Speedy abnormal event detection meets the growing demand to process an enormous number of surveillance videos. Based on inherent redundancy of video structures, we propose an efficient sparse ...combination learning framework. It achieves decent performance in the detection phase without compromising result quality. The short running time is guaranteed because the new method effectively turns the original complicated problem to one in which only a few costless small-scale least square optimization steps are involved. Our method reaches high detection rates on benchmark datasets at a speed of 140-150 frames per second on average when computing on an ordinary desktop PC using MATLAB.
Abstract
Based on partial least squares, the dimethyl monomethyme content was measured. The original spectroscopy, smooth, first-order differential, second-order differential, multi-scattered ...correction, standard regular conversion, the main cause of the child were effectively used. The results show that the model performance of 6 main factors established separately, the correction set coefficient and verification set coefficient of correction set is 0.9999 and 0.9991, respectively, and the correlation set prediction standard deviation is 0.00356, respectively. And 0.0178. This optimal model is used to measure the blind sample of modeling. As a result, the deviation of the measurement results is between -0.028% ∼ 0.012%, the average deviation is from 0.014%, the standard deviation is 0.014%, and the relative standard deviation is 2.9%. The result is satisfactory.
Baseline correction methods based on penalized least squares are successfully applied to various spectral analyses. The methods change the weights iteratively by estimating a baseline. If a signal is ...below a previously fitted baseline, large weight is given. On the other hand, no weight or small weight is given when a signal is above a fitted baseline as it could be assumed to be a part of the peak. As noise is distributed above the baseline as well as below the baseline, however, it is desirable to give the same or similar weights in either case. For the purpose, we propose a new weighting scheme based on the generalized logistic function. The proposed method estimates the noise level iteratively and adjusts the weights correspondingly. According to the experimental results with simulated spectra and measured Raman spectra, the proposed method outperforms the existing methods for baseline correction and peak height estimation.
Baseline correction methods based on penalized least squares are successfully applied to various spectral analyses.
This paper proposes a novel nonlinear dynamical system identification method based on the sparse regression algorithm and the separable least squares method. To effectively avoid solving the second ...derivative of the displacement signal and reduce the effect of noise, the Duhamel's integral is adopted to represent the dynamic relationship between the system input and output. In the expression form of Duhamel's integral, nonlinear dynamical system identification can be cast as a separable least squares problem. Thus, the separable least squares method is leveraged to separately identify the parameters of the linear subsystem and the coefficients corresponding to nonlinearities among the nonlinear dynamical system. During the identification process of nonlinear restoring forces, one complete set of nonlinear basis functions are used to represent the nonlinear restoring forces. Not all the candidate nonlinear terms are contributing, however, thus the sparse regression algorithm is adopted to select the actual contributing nonlinear components in the candidate nonlinear terms and eliminate the non-contributing nonlinear components, and then the corresponding parameters of contributing nonlinear components are estimated by the unbiased least squares method. Finally, one RKHS (Reproducing Kernel Hilbert Space)-based non-parametric de-noise method is further proposed to reduce the noise in the vibration displacement and obtain the noise-reduced velocity from the displacement signal. The numerical simulation about the identification of the rotating blade-casing system and the dynamic experiment of the HSLDS (high-static-low-dynamic stiffness) isolator system verify the effectiveness of the new identification method for nonlinear dynamical systems proposed in this paper.
Abstract In response to the issue of harmonic data anomalies affecting harmonic impedance estimation, a method based on improved rank regression is proposed, building upon the foundation of rank ...estimation. This method utilizes harmonic data sampled from the point of common coupling, treating harmonic impedance as regression parameters. Initially, the least squares method is employed to solve for regression parameters. Subsequently, Bayesian optimization is applied to refine these parameters. The optimized parameters are then incorporated into the rank estimation function derived from the residual rank matrix for weighted iteration. The final calculation results are determined through this iterative process. Simulation analysis demonstrates that this method can effectively mitigate the impact of outliers, yielding more accurate harmonic impedance values.
The presence of fine particles has reduced the quality of water resources. Unfortunately, the fine particles normally take a longer time to be removed. Realizing this, the present study aims to ...employ a magnetic adsorbent to assist a fast separation of the fine particles from their solution. Here, micron-sized SiO
2
particles were used as the model fine particles; meanwhile, the magnetic adsorbent was designed by functionalizing iron oxide nanoparticles (IONPs) with chitosan. A process study was done based on the effects of medium pH, IONPs concentration, and contact time. Results implied that both bare IONPs and chitosan functionalized-IONPs (denoted as CF-IONPs) were best in removing SiO
2
at pH 4 owing to the electrostatic attraction force. However, as compared to the bare counterpart, CF-IONPs is more suitable for large scale application as it is effective in a wider pH range, requires lesser adsorbent dosage and shorter adsorption time. Despite that, removal of SiO
2
using both types of adsorbents were found to follow pseudo-second order kinetic. The obtained data was modeled using either the moving least squares (MLS) or multivariable power least squares (MPLS) method. In particular, the indices of each parameter obtained from the MPLS-generated equation indicated that the most dominant parameter that governing the SiO
2
removal by bare IONPs is medium pH, while the one for CF-IONPs is contact time.
The current article evaluates least-squares-based approaches for estimating parameters of the two-parameter Pareto distribution. The algebraic expressions for least squares (LS), relative least ...squares (RLS) and weighted least squares (WLS) estimators are derived by generating empirical cumulative distribution function (CDF) using mean rank, median rank and symmetrical CDF methods. The performance of the estimation approaches is evaluated through Monte Carlo simulations for different combinations of parameter values and sample sizes. The performance of the regression-based methods is then compared with one another and with the traditional maximum likelihood (ML) estimation method. Our simulation results unveil that among the regression-based methods, RLS has an improved or better performance compared to the other two regression-based approaches for samples of all sizes. Moreover, RLS performs better than the ML method for small samples. Among the rank methods used for generating empirical CDF, it is observed that the mean rank method outperformed other two rank methods. The simulation results are further corroborated by the application of all the methods on two real-life datasets representing damages caused by natural catastrophes.
We present a robust sharp-interface immersed boundary method for numerically studying high speed flows of compressible and viscous fluids interacting with arbitrarily shaped either stationary or ...moving rigid solids. The Navier–Stokes equations are discretized on a rectangular Cartesian grid based on a low-diffusion flux splitting method for inviscid fluxes and conservative high-order central-difference schemes for the viscous components. Discontinuities such as those introduced by shock waves and contact surfaces are captured by using a high-resolution weighted essentially non-oscillatory (WENO) scheme. Ghost cells in the vicinity of the fluid–solid interface are introduced to satisfy boundary conditions on the interface. Values of variables in the ghost cells are found by using a constrained moving least squares method (CMLS) that eliminates numerical instabilities encountered in the conventional MLS formulation. The solution of the fluid flow and the solid motion equations is advanced in time by using the third-order Runge–Kutta and the implicit Newmark integration schemes, respectively. The performance of the proposed method has been assessed by computing results for the following four problems: shock-boundary layer interaction, supersonic viscous flows past a rigid cylinder, moving piston in a shock tube and lifting off from a flat surface of circular, rectangular and elliptic cylinders triggered by shock waves, and comparing computed results with those available in the literature.
•WENO scheme used for compressible viscous flows around moving irregular-shaped rigid solids.•Proposed constrained moving least-squares sharp interface method for satisfying fluid–solid interface boundary conditions.•Robustness and accuracy of the method assessed by solving four challenging problems.•Lifting off of an elliptical cylinder by viscous flow of Reynolds number 100 analyzed.•Supersonic flow past a stationary circular rigid cylinder of Reynolds number 300 studied.
Based on the least-squares method, a new approach is proposed to the problem of regression modeling of imprecise quantities. In this approach, the available data, of both explanatory variable(s) and ...the response variable, as well as the parameters of the model, are assumed to be Atanassov's intuitionistic fuzzy numbers. Therefore, the proposed model is a fully intuitionistic fuzzy model. Based on the similarity measure and the squared errors, two indices are proposed to investigate the goodness of fit of such models. Inside, using a real dataset, the application of the proposed approach in modeling some soil characteristics is studied. The predictive ability of the obtained model is evaluated by using the cross-validation method.
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