SIR phasing by combination of SOLVE/RESOLVE and dual-space fragment extension involving OASIS

A new phasing procedure has been proposed for dealing with single isomorphous replacement (SIR) x-ray diffraction data. The procedure combines {SOLVE/RESOLVE} with the dual-space fragment extension involving {OASIS}. Two sets of SIR data at 0.28~nm resolution taken from the protein (R)-phycoerythrin (PDB code: 1LIA) were used in the test. For one of the two SIR data sets, a default run of {SOLVE/RESOLVE} based on the heavy-atom substructure found by {SHLEXD} led automatically to an interpretable electron density map. {OASIS} could not effectively improve the result. For the other set of SIR data, {SOLVE/RESOLVE} resulted in a fragmented model consisting of 454 of the total 668 residues, in which only 29 residues were docked into the sequence. Based on this model, 7 iteration cycles of {OASIS-DM-RESOLVE} (build only) yielded automatically a model of 547 residues with 133 residues docked into the sequence. The overall-averaged phase error decreased considerably and the quality of electron density map was improved significantly. Two more cycles of iterative {OASIS}-{DM}-{RESOLVE} were carried out, in which the output phases and figures of merit from {DM} were merged with that from the original run of {SOLVE/RESOLVE} before they were passed onto {RESOLVE} (build only). This led automatically to a model containing 452 residues with 173 docked into the sequence. The resultant electron density map is manually traceable. It is concluded that when results of {SOLVE/RESOLVE} are not sufficiently satisfactory, the combination of {SOLVE/RESOLVE} and {OASIS}-{DM}-{RESOLVE} (build only) may significantly improve them.     

Use of iterative OASIS with low resolution SAD laboratory X-ray source (Cr Kα) data sets

Anomalous scattering methods are widely used for phasing macromolecular structures. OASIS program works on a direct methods procedure and is used to break the phase ambiguity intrinsic in a single wavelength anomalous diffraction (SAD) experiment. An iterative phasing/model-building procedure for processing SAD data includes the initial direct method phasing of SAD data, density modification, automatic model building and direct methods phasing of SAD data with feed back from partial structure information. This dual-space procedure has been tested on two experimental Cr Kα SAD data sets, 2.3 ? for S-SAD and 2.4 ? for I-SAD, of an enzyme glucose isomerase with an approximate molecular weight of 44 kDa (388 residues). HYSS in PHENIX was used to locate the anomalous scatterers for both the data sets (11 sulfurs for 2.3 ? data and 9 iodines for 2.4 ? data). Phasing and density modification were carried out using OASIS, DM and model building was then carried out using ARP/wARP. Two iterative cycles were necessary for the successful structure solution and refinement of the 2.3 ? data set which built 384 residues out of 388. Regular ARP/wARP failed for the 2.4 ? resolution data and hence the modified version of REFMAC5 was used in ARP/wARP. A successful model could be built after three iterative cycles of OASIS using this modified version which built 382 residues out of 388 residues. Minimal manual model building was required at this stage and the structure determination was completed using regular REFMAC5. All the computations mentioned here were carried out using Pentium IV PC.     

Phase iteration and spacing iteration algorithms for speckle fringe pattern processing

Speckle fringe pattern is characterized by speckle noise because the speckle is the information carrier. Phase iteration and Spacing iteration are algorithms that are able to extract the information as well as suppress noise. Phase iteration is a loop of smoothing, phase calculation, and pattern reconstruction. Spacing Iteration is a repetition of correlation, phase calculation, and least-squares fit. The two algorithms are reviewed and compared in this paper. The modern computer provides the capability to explore all sorts of convergent methods by simply ‘do it again’. Phase iteration and Spacing iteration are two of the convergent methods in processing optical metrology fringe pattern.     

Inverse iteration for damped natural vibration

Inverse iteration is extended to internally and/or externally damped natural vibration. Each iteration involves one matrix multiplication and one linear equation solution of order n. The symmetric band form of the original undamped eigenvalue problem is preserved. If the undamped mode is taken as the first approximation, the inverse iteration will converse to the corresponding damped mode in about four iterations. However, the one step method is divergent for heavy damping. Therefore, it is advisible to subdivide the damping into successive steps if inverse iteration does not converge in say five iterations. The method is successful for both discrete systems and distributed systems. The implementation is very simple by means of complex arithmetic which is readily available in many FORTRAN compilers.     

Design of quantum VQ iteration and quantum VQ encoding algorithm taking O（√N） steps for data compression

Vector quantization (VQ) is an important data compression method. The key of the encoding of VQ is to find the closest vector among N vectors for a feature vector. Many classical linear search algorithms take $O(N)$ steps of distance computing between two vectors. The quantum VQ iteration and corresponding quantum VQ encoding algorithm that takes $O(\sqrt N )$ steps are presented in this paper. The unitary operation of distance computing can be performed on a number of vectors simultaneously because the quantum state exists in a superposition of states. The quantum VQ iteration comprises three oracles, by contrast many quantum algorithms have only one oracle, such as Shor's factorization algorithm and Grover's algorithm. Entanglement state is generated and used, by contrast the state in Grover's algorithm is not an entanglement state. The quantum VQ iteration is a rotation over subspace, by contrast the Grover iteration is a rotation over global space. The quantum VQ iteration extends the Grover iteration to the more complex search that requires more oracles. The method of the quantum VQ iteration is universal.     

SAD phasing by OASIS at different resolutions down to 0.30nm and below

Single-wavelength anomalous diffraction (SAD) phasing is increasingly important in solving de novo protein structures. Direct methods have been proved very efficient in SAD phasing. This paper aims at probing the low-resolution limit of direct-method SAD phasing. Two known proteins TT0570 and Tom70p were used as test samples. Sulfur-SAD data of the protein TT0570 were collected with conventional Cu-K\alpha source at 0.18nm resolution. Its truncated subsets respectively at 0.21, 0.30, 0.35 and 0.40nm resolutions were used in the test. TT0570 Cu-K$\alpha$ sulfur-SAD data have an expected Bijvoet ratio <\vert\Delta F\vert>/\ \sim 0.55%. In the 0.21nm case, a single run of OASIS-DM-ARP/wARP led automatically to a model containing 1178 of the total 1206 residues all docked into the sequence. In 0.30 and 0.35nm cases, SAD phasing by OASIS-DM led to traceable electron density maps. In the 0.40nm case, SAD phasing by OASIS-DM resulted in a degraded electron density map, which may be difficult to trace but still contains useful secondary-structure information. Test on real 0.33nm selenium-SAD data of the protein Tom70p showed that even automatic model building was not successful, the combination of manual tracing and direct-method fragment extension was capable of significantly improving the electron-density map. This provides the possibility of effectively improving the manually built model before structure refinement is performed.     

SAD phasing by OASIS at different resolutions down to 0.30 nm and below

Single-wavelength anomalous diffraction （SAD） phasing is increasingly important in solving de novo protein structures. Direct methods have been proved very efficient in SAD phasing. This paper aims at probing the low-resolution limit of direct-method SAD phasing. Two known proteins TT0570 and Tom70p were used as test samples. Sulfur-SAD data of the protein TT0570 were collected with conventional Cu-Kα source at 0.18 nm resolution. Its truncated subsets respectively at 0.21, 0.30, 0.35 and 0.40 nm resolutions were used in the test. TT0570 Cu-Kα sulfur-SAD data have an expected Bijvoet ratio 〈 ｜△F｜ 〉 / 〈 F 〉 ～ 0.55%. In the 0.21 nm case, a single run of OASIS-DM-ARP/wARP led automatically to a model containing 1178 of the total 1206 residues all docked into the sequence. In 0.30 and 0.35 nm cases, SAD phasing by OASIS-DM led to traceable electron density maps. In the 0.40 nm case, SAD phasing by OASIS-DM resulted in a degraded electron density map, which may be difficult to trace but still contains useful secondary-structure information. Test on real 0.33 nm selenium-SAD data of the protein Tom70p showed that even automatic model building was not successful, the combination of manual tracing and direct-method fragment extension was capable of significantly improving the electron-density map. This provides the possibility of effectively improving the manually built model before structure refinement is performed.     

Variational iteration method for solving biharmonic equations

By means of the variational iteration method the numerical solution of biharmonic equations are obtained. Biharmonic equation has significant applications in physics and engineering. There is a difficulty to solve the biharmonic equation due to the existence of fourth order derivatives. For this reason, we use the variational iteration method to solve this equation. Test problems, are used to validate this algorithm which is found to be more accurate and efficient than previous ones.     

Adaptive window iteration algorithm for enhancing 3D shape recovery from image focus

Depth from focus(DFF) is a technique for estimating the depth and three-dimensional(3D) shape of an object from a multi-focus image sequence. At present, focus evaluation algorithms based on DFF technology will always cause inaccuracies in deep map recovery from image focus. There are two main reasons behind this issue. The first is that the window size of the focus evaluation operator has been fixed. Therefore, for some pixels, enough neighbor information cannot be covered in a fixed window and is easily disturbed by noise, which results in distortion of the model. For other pixels, the fixed window is too large, which increases the computational burden. The second is the level of difficulty to get the full focus pixels, even though the focus evaluation calculation in the actual calculation process has been completed. In order to overcome these problems, an adaptive window iteration algorithm is proposed to enhance image focus for accurate depth estimation. This algorithm will automatically adjust the window size based on gray differences in a window that aims to solve the fixed window problem.Besides that, it will also iterate evaluation values to enhance the focus evaluation of each pixel. Comparative analysis of the evaluation indicators and model quality has shown the effectiveness of the proposed adaptive window iteration algorithm.     

A fully automatic three-step liver segmentation method on LDA-based probability maps for multiple contrast MR images

Automatic 3D liver segmentation in magnetic resonance (MR) data sets has proven to be a very challenging task in the domain of medical image analysis. There exist numerous approaches for automatic 3D liver segmentation on computer tomography data sets that have influenced the segmentation of MR images. In contrast to previous approaches to liver segmentation in MR data sets, we use all available MR channel information of different weightings and formulate liver tissue and position probabilities in a probabilistic framework. We apply multiclass linear discriminant analysis as a fast and efficient dimensionality reduction technique and generate probability maps then used for segmentation. We develop a fully automatic three-step 3D segmentation approach based upon a modified region growing approach and a further threshold technique. Finally, we incorporate characteristic prior knowledge to improve the segmentation results. This novel 3D segmentation approach is modularized and can be applied for normal and fat accumulated liver tissue properties.     

Application of He's variational iteration method to nonlinear heat transfer equations

Instead of finding a small parameter for solving nonlinear problems through perturbation method, a new analytical method called He's variational iteration method (VIM) is introduced to be applied to solve nonlinear heat transfer equations in this Letter. In this research, variational iteration method is used to solve an unsteady nonlinear convective-radiative equation and a nonlinear convective-radiative-conduction equation containing two small parameters of ε₁ and ε₂ and evaluate the efficiency of straight fins. VIM can apply to the nonlinear equations with boundary or initial conditions defined in different points just with developing the correction functional using the extra parameters such as Cn, as used in this Letter.     

OASIS4.0—a new version of the program OASIS for phasing protein diffraction data

<正>The program OASIS4.0 has been released.Apart from the improved single-wavelength anomalous diffraction (SAD) phasing algorithm described in a separate paper,an important new feature in this version is the automation of the iterative phasing and model-building process in solving protein structures.A new graphical user's interface(GUI) is provided for controlling and real-time monitoring the dual-space iterative process.The GUI is discussed in detail in the present paper.     

On the iteration of a rational function: Computer experiments with Newton's method

Using Newton's method to look for roots of a polynomial in the complex plane amounts to iterating a certain rational function. This article describes the behavior of Newton iteration for cubic polynomials. After a change of variables, these polynomials can be parametrized by a single complex parameter, and the Newton transformation has a single critical point other than its fixed points at the roots of the polynomial. We describe the behavior of the orbit of the free critical point as the parameter is varied. The Julia set, points where Newton's method fail to converge, is also pictured. These sets exhibit an unexpected stability of their gross structure while the changes in small scale structure are intricate and subtle.     

A novel content-based active contour model for brain tumor segmentation

Brain tumor segmentation is a crucial step in surgical and treatment planning. Intensity-based active contour models such as gradient vector flow (GVF), magneto static active contour (MAC) and fluid vector flow (FVF) have been proposed to segment homogeneous objects/tumors in medical images. In this study, extensive experiments are done to analyze the performance of intensity-based techniques for homogeneous tumors on brain magnetic resonance (MR) images. The analysis shows that the state-of-art methods fail to segment homogeneous tumors against similar background or when these tumors show partial diversity toward the background. They also have preconvergence problem in case of false edges/saddle points. However, the presence of weak edges and diffused edges (due to edema around the tumor) leads to oversegmentation by intensity-based techniques. Therefore, the proposed method content-based active contour (CBAC) uses both intensity and texture information present within the active contour to overcome above-stated problems capturing large range in an image. It also proposes a novel use of Gray-Level Co-occurrence Matrix to define texture space for tumor segmentation. The effectiveness of this method is tested on two different real data sets (55 patients - more than 600 images) containing five different types of homogeneous, heterogeneous, diffused tumors and synthetic images (non-MR benchmark images). Remarkable results are obtained in segmenting homogeneous tumors of uniform intensity, complex content heterogeneous, diffused tumors on MR images (T1-weighted, postcontrast T1-weighted and T2-weighted) and synthetic images (non-MR benchmark images of varying intensity, texture, noise content and false edges). Further, tumor volume is efficiently extracted from 2-dimensional slices and is named as 2.5-dimensional segmentation.     

Modified variational iteration method

In this Letter, we introduce a modified variational iteration method by inserting some unknown parameters into the correctional functional. The main advantage of this method is that one can avoid the uncontrollability problems, of the nonzero endpoint conditions, encountered in the traditional variational iteration method. Moreover, the method is applied to some nonlinear equations and the numerical solutions reveal that the modified method is accurate and efficient to solve a large class of nonlinear differential equations. Furthermore, the method does not share the drawbacks of the conventional variational iteration method, namely the restriction of the order of the nonlinearity term or even the form of the boundary conditions.     

Fractional variational iteration method and its application

Fractional differential equations have been investigated by variational iteration method. However, the previous works avoid the term of fractional derivative and handle them as a restricted variation. We propose herein a fractional variational iteration method with modified Riemann Liouville derivative which is more efficient to solve the fractional differential equations.     

Chirp-coefficient bisection iteration method for phase-intensity reconstruction of chirped pulses

A new method is proposed to systematically measure the phase-intensity information of chirped pulses that is based on the chirp-coefficient bisection iteration (CBI) concept. Through the CBI procedure with measured spectrum and temporal intensity profiles (or intensity autocorrelations), spectral and temporal amplitude–phase information can be rapidly retrieved. We experimentally verified that our method has high precision for nanosecond- and picosecond-level pulses and low precision for femtosecond-level pulses. Our proposed method does not require a sophisticated setup and has the advantage of accurate determination of temporal and spectral chirp coefficients with various orders. It also has lower cost, simple operation, in particular covers a wider measurement range than the main current methods. Moreover, the retrieved waveforms can reveal both the pulse shape and the actual intensity with spectral and temporal chirped coefficients of various orders, which can be directly used in various pulse propagation analyses such as chirped pulse amplification.     

Complex denoising of MR data via wavelet analysis: application for functional MRI

A fast post-processing method for noise reduction of MR images, termed complex-denoising, is presented. The method is based on shrinking noisy discrete wavelet transform coefficients via thresholding, and it can be used for any MRI data-set with no need for high power computers. Unlike previous wavelet application to MR images, the denoising algorithm is applied, separately, to the two orthogonal sets of the complex MR image. The norm of the combined data are used to construct the image. With this method, signal-noise decoupling and Gaussian white noise assumptions used in the wavelet noise suppression scheme, are better fulfilled. The performance of the method is tested by carrying out a qualitative and quantitative comparison of a single-average image, complex-denoised image, multiple-average images, and a magnitude-denoised image, of a standard phantom. The comparison shows that the complex-denoising scheme improves the signal-to-noise and contrast-to-noise ratios more than the magnitude-denoising scheme, particularly in low SNR regions. To demonstrate the method strength, it is applied to fMRI data of somatosensory rat stimulation. It is shown that the activation area in a cross-correlation analysis is approximately 63% larger in the complex-denoised versus original data sets when equal threshold value is used. Application of the method of Principal Component Analysis to the complex-denoised, magnitude-denoised, and original data sets results in a similar but higher variance of the first few principal components obtained from the former data set as compared to those obtained from the later two sets.     

Asymptotic iteration approach to supersymmetric bistable potentials

We examine quasi exactly solvable bistable potentials and their supersymmetric partners within the framework of the asymptotic iteration method (AIM). It is shown that the AIM produces excellent approximate spectra and that some×it is found to be more useful to use the partner potential for computation. We also discuss the direct application of the AIM to the Fokker-Planck equation.     

基于优化迭代算法的细胞荧光光谱解析

使用光谱测量方法进行细胞多色荧光分析时, 发射光谱会产生部分光谱重叠, 为定性和定量分析造成了一定的困难。为此, 提出基于优化迭代算法的细胞荧光光谱解析算法, 建立重叠峰模型并确定单峰顶点; 根据每次构造峰面积的大小, 重新确定构造峰的构造方式, 最终得到模拟峰的顶点及面积信息。利用该算法对高斯函数叠加形成的重叠峰进行解析, 并与常规方法进行对比, 结果表明优化迭代算法解析误差稳定在0.15%以内; 加入随机噪声后, 解析误差可稳定在0.85%以内, 均优于另外两种算法。此外, 计算了该算法下的迭代效率, 结果表明该算法较常规方法提高了32.2%。