Half-space albedo problem for the Anlı-Güngör scattering function

One speed, time-independent and homogeneous medium neutron transport equation is solved for second order scattering using the Anlı-Güngör scattering function which is a recently investigated scattering function. The scattering function depends on Legendre polynomials and the t parameter which is defined on the interval [−1, 1]. A half-space albedo problem is examined with the FN method and the recently developed SVD method. Albedo values are calculated with two methods and tabulated. Thus, the albedo values for the Anlı-Güngör scattering are compared with these methods. The behaviour of the scattering function is similar to İnönü’s scattering function according to calculated results.

Fast mining method of network heterogeneous fault tolerant data based on K-means clustering

In the traditional network heterogeneous fault-tolerant data mining process, there are some problems such as low accuracy and slow speed. This paper proposes a fast mining method based on K-means clustering for network heterogeneous fault-tolerant data. The confidence space of heterogeneous fault-tolerant data is determined, and the range of motion of fault-tolerant data is obtained; Singular value decomposition (SVD) method is used to construct the classified data model to obtain the characteristics of heterogeneous fault-tolerant data; The redundant data in fault-tolerant data is deleted by unsupervised feature selection algorithm, and the square sum and Euclidean distance of fault-tolerant data clustering center are determined by K-means algorithm. The discrete data clustering space is constructed, and the objective optimal function of network heterogeneous fault-tolerant data clustering is obtained, Realize fault-tolerant data fast mining. The results show that the mining accuracy of the proposed method can reach 97%.

Receiver phase alignment using fitted SVD derived sensitivities from routine prescans

Magnetic resonance imaging radio frequency arrays are composed of multiple receive coils that have their signals combined to form an image. Combination requires an estimate of the radio frequency coil sensitivities to align signal phases and prevent destructive interference. At lower fields this can be accomplished using a uniform physical reference coil. However, at higher fields, uniform volume coils are lacking and, when available, suffer from regions of low receive sensitivity that result in poor sensitivity estimation and combination. Several approaches exist that do not require a physical reference coil but require manual intervention, specific prescans, or must be completed post-acquisition. This makes these methods impractical for large multi-volume datasets such as those collected for novel types of functional MRI or quantitative susceptibility mapping, where magnitude and phase are important. This pilot study proposes a fitted SVD method which utilizes existing combination methods to create a phase sensitive combination method targeted at large multi-volume datasets. This method uses any multi-image prescan to calculate the relative receive sensitivities using voxel-wise singular value decomposition. These relative sensitivities are fitted to the solid harmonics using an iterative least squares fitting algorithm. Fits of the relative sensitivities are used to align the phases of the receive coils and improve combination in subsequent acquisitions during the imaging session. This method is compared against existing approaches in the human brain at 7 Tesla by examining the combined data for the presence of singularities and changes in phase signal-to-noise ratio. Two additional applications of the method are also explored, using the fitted SVD method in an asymmetrical coil and in a case with subject motion. The fitted SVD method produces singularity-free images and recovers between 95–100% of the phase signal-to-noise ratio depending on the prescan data resolution. Using solid harmonic fitting to interpolate singular value decomposition derived receive sensitivities from existing prescans allows the fitted SVD method to be used on all acquisitions within a session without increasing exam duration. Our fitted SVD method is able to combine imaging datasets accurately without supervision during online reconstruction.

Distributed Singular Value Decomposition Method for Fast Data Processing in Recommendation Systems

The problem of analyzing a big amount of user data to determine their preferences and, based on these data, to provide recommendations on new products is important. Depending on the correctness and timeliness of the recommendations, significant profits or losses can be obtained. The task of analyzing data on users of services of companies is carried out in special recommendation systems. However, with a large number of users, the data for processing become very big, which causes complexity in the work of recommendation systems. For efficient data analysis in commercial systems, the Singular Value Decomposition (SVD) method can perform intelligent analysis of information. With a large amount of processed information we proposed to use distributed systems. This approach allows reducing time of data processing and recommendations to users. For the experimental study, we implemented the distributed SVD method using Message Passing Interface, Hadoop and Spark technologies and obtained the results of reducing the time of data processing when using distributed systems compared to non-distributed ones.

Golub–Kahan vs. Monte Carlo: a comparison of bidiagonlization and a randomized SVD method for the solution of linear discrete ill-posed problems

Randomized methods can be competitive for the solution of problems with a large matrix of low rank. They also have been applied successfully to the solution of large-scale linear discrete ill-posed problems by Tikhonov regularization (Xiang and Zou in Inverse Probl 29:085008, 2013). This entails the computation of an approximation of a partial singular value decomposition of a large matrix A that is of numerical low rank. The present paper compares a randomized method to a Krylov subspace method based on Golub–Kahan bidiagonalization with respect to accuracy and computing time and discusses characteristics of linear discrete ill-posed problems that make them well suited for solution by a randomized method.

Excitation of Oxygen Ion Cyclotron Harmonic Waves in the Inner Magnetosphere

<p>Oxygen ion cyclotron harmonic waves, with discrete spectral peaks at multiple harmonics of the oxygen ion cyclotron frequency, have been observed in the inner magnetosphere. Their excitation mechanism has remained unclear, because the singular value decomposition (SVD) method commonly used in satellite wave data analysis suggests that the waves have quasi-parallel propagation, whereas plasma theory reveals unstable modes at nearly perpendicular propagation. Hybrid simulations are carried out to investigate the excitation of these waves. The simulation results show that waves at multiple harmonics of the oxygen ion cyclotron frequency can be excited by energetic oxygen ions of a ring-like velocity distribution. More importantly, analyzing the simulated waves in a three-dimensional simulation using the common SVD method demonstrates that, while the excited waves have quasi-perpendicular propagation, the superposition of multiple waves with different azimuthal angles causes the SVD method to yield incorrectly small wave normal angles. In addition, the scattering of oxygen ions by the excited waves is examined in the simulations. The waves can cause significant transverse heating of the relatively cool background oxygen ions, through cyclotron resonance. The waves may also scatter energetic radiation belt electrons through bounce resonance and transit time scattering, like fast magnetosonic waves.</p>

Two Models Based on Social Relations and SVD++ Method for Recommendation System

Recently, Recommender Systems (RSs) have attracted many researchers whose goal is to improve the performance of the prediction accuracy of recommendation systems by alleviating RSs drawbacks. The most common limitations are sparsity and the cold-start problem. This article proposes two models to mitigate the effects of these limitations. The proposed models exploit five sources of information: rating information, which involves two sources, namely explicit and implicit, which can be extracted via users’ ratings, and two types of social relations: explicit and implicit relations, the last source is confidence values that are included in the first model only. The whole sources are combined into the Singular Value Decomposition plus (SVD++) method. First, to extract implicit relations, each non-friend pair of users, the Multi-Steps Resource Allocation (MSRA) method is adopted to compute the probability of being friends. If the probability has accepted value which exceeds a threshold, an implicit relationship will be created. Second, the similarity of explicit and implicit social relationships for each pair of users is computed. Regarding the first model, a confidence value between each pair of users is computed by dividing the number of common items by the total number of items which have also rated by the first user of this pair. The confidence values are combined with the similarity values to produce the weight factor. Furthermore, the weight factor, explicit, and implicit feedback information are integrated into the SVD++ method to compute the missing prediction values. Additionally, three standard datasets are utilized in this study, namely Last.Fm, Ciao, and FilmTrust, to evaluate our models. The experimental results have revealed that the proposed models outperformed state-of-the-art approaches in terms of accuracy.