Fast Multiple Method Research Articles

A fast temporal multiple sparse Bayesian learning-based channel estimation method for time-varying underwater acoustic OFDM systems

In this paper, a fast temporal multiple sparse Bayesian learning (FTMSBL)-based channel estimation method for underwater acoustic (UWA) orthogonal frequency division multiplexing (OFDM) systems is proposed, which is optimized using the fast marginalized likelihood maximization method. The algorithm fully uses the consistent sparse structure and time-domain correlation properties of channels to improve the reconstruction performance and computational efficiency, offering better performance and higher computational efficiency than the traditional Bayesian learning algorithms. At the same time, the FTMSBL algorithm does not require computing the inverse of large matrices and consumes very little storage resources in the operation, making it suitable for hardware implementation. Simulation and sea trial results show that the FTMSBL-based underwater channel estimation algorithm achieves higher channel estimation accuracy than the orthogonal matching tracking algorithm, and the system bit error rate (BER) is significantly reduced; specifically, the FTMSBL algorithm can achieve optimal performance in strong time-dependent channels.

A multiresolution method for modelling galaxy and massive black hole mergers

ABSTRACT The coalescence of the most massive black hole (MBH) binaries releases gravitational waves (GWs) within the detectable frequency range of pulsar timing arrays (PTAs; 10−9 to 10−6 Hz). The incoherent superposition of GWs from MBH mergers, the stochastic gravitational wave background (GWB), can provide unique information on MBH parameters and the large-scale structure of the Universe. The recent evidence for a GWB reported by the PTAs opens an exciting new window on to MBHs and their host galaxies. However, the astrophysical interpretation of the GWB requires accurate estimations of MBH merger time-scales for a statistically representative sample of galaxy mergers. This is numerically challenging; a high numerical resolution is required to avoid spurious relaxation and stochastic effects, while a large number of simulations are needed to sample a cosmologically representative volume. Here, we present a new multimass modelling method to increase the central resolution of a galaxy model at a fixed particle number. We follow mergers of galaxies hosting central MBHs with the fast multiple method code griffin at two reference resolutions and with two refinement schemes. We show that both refinement schemes are effective at increasing central resolution, reducing spurious relaxation and stochastic effects. A particle number of N ≥ 106 within a radius of five times the sphere of influence of the MBHs is required to reduce numerical scatter in the binary eccentricity and the coalescence time-scale to <30 per cent, a resolution that can only be reached at present with the mass refinement scheme.

The Spherical Fast Multipole Method (sFMM) for Gravitational Lensing Simulation

In this paper, we present a spherical Fast Multipole Method (sFMM) for ray-tracing simulation of gravitational lensing on a curved sky. The sFMM is a nontrivial extension of the Fast Multiple Method to sphere , and it can accurately solve the Poisson equation with time complexity of , where N is the number of particles. It is found that the time complexity of the sFMM is near O(N) and the computational accuracy can reach 10−10 in our test. In addition, compared with the Fast Spherical Harmonic Transform, the sFMM is not only faster but also more accurate, as it has the ability to reserve high-frequency components of the density field. These merits make the sFMM an optimum method to simulate the gravitational lensing on a curved sky, which is the case for upcoming large-area sky surveys, such as the Vera Rubin Observatory and the China Space Station Telescope.

3D gravity inversion based on mixed-norm regularization in spherical coordinates with application to the lunar Moscoviense Basin

Three-dimensional gravity inversion has been widely used to infer density structures and tectonic movements of the earth and Moon. However, two problems (the nonuniqueness and low depth resolution) of current gravity inversion methods still exist and are not completely resolved, which affect the reliability of the inversion results and the corresponding geologic interpretation. To improve the depth resolution of the 3D gravity inversion, we propose an efficient inversion method in spherical coordinates based on a mixed smooth and focused regularization with depth-weighting functions. In the inversion, we also use the kernel matrix equivalence strategy and the fast kernel-vector multiplication method based on a fast Fourier transform in each iteration to increase computational efficiency. Two synthetic inversion examples indicate that the proposed method can recover more complex density structures compared with the often used smooth-constraint inversion approach. Finally, the proposed inversion approach is applied to the latest lunar gravitational field model GL1500E to study the 3D density structures of the Moscoviense Basin. The inverted results indicate that the density structure with high-positive anomalies is principally distributed at depths ranging from 5 to 70 km, forming a giant asymmetrical high-density structure inclining from the southwest to the northeast. We may conclude that the Moscoviense Basin was formed by the double impact, where the second collision occurred in the southwest of the basin center of the first collision.

A local current based iterative physical optics method for computing the RCS of target above sea surface

A local current based iterative physical optics (LC-IPO) scheme, for the analysis of the scattering from large complex targets on sea surface, is proposed. By employing ray tracing mechanism, the current radiation iterations are limited to local region and performed for each “bounce” in the IPO scheme. This approach alleviates the need for expensive computation of simulations. Meanwhile, the resulting method makes use of field integrals which are accelerable using a fast multiple method algorithm. GPU acceleration technique is also used to accelerating the scattering analyzing. Numerical examples illustrate that the accelerated local current technique can greatly improve the computational efficiency of the iterative physical optics method, and the accuracy is as good as the previous method without acceleration.

A parallel Monte Carlo method for solving electromagnetic scattering in clusters of dielectric objects

In this work, we develop a novel Monte Carlo method for solving the electromagnetic scattering problem for clusters of photonic particles. The method is based on a formal solution of the scattering problem as a modified Born series whose coefficients are found by a conformal transformation. The terms of the Born series are approximated by sampling random elements of its matrix representation, computed by the Method of Moments. Unlike other techniques like the Fast Multiple Method, this Monte Carlo method does not require communication between processors, which makes it suitable for large parallel executions.

Sparse Bayesian multiple sources localization using variational approximation for Laplace priors

Multiple sources localization (MSL) has been playing an important role in various applications of wireless sensor networks. In this paper, sparse representation-based MSL with received signal strength (RSS) as observations is addressed within the sparse Bayesian learning framework. Conventional approaches are usually based on the assumption of Gaussian prior for the sparse coefficients. In this paper, Laplacian prior is employed to model the sparse coefficient for improved sparsity performance. To tackle the problem that Laplace prior is not conjugate to Gaussian likelihood, a variational approximation is employed for Bayesian inference. Finally, a multiple sources localization method is developed. Furthermore, to reduce the computing complexity and promote sparsity, a fast multiple sources localization method is further developed. In the proposed methods, the source locations, sparse coefficients, and all necessary model parameters are adaptively deduced solely from the RSS observations. Meanwhile, by employing Laplacian prior for the sparse coefficients, better sparse recovery can be achieved. Experimental results demonstrate the effectiveness of the proposed methods.

Multiple Zero-Watermarking of Medical Images for Internet of Medical Things

The Internet of Medical Things (IoMT) plays a vital role in healthcare systems to increase electronic devices’ accuracy, reliability, and productivity. This paper presents fast multiple zero-watermarking methods based on Multi-channel Fractional Legendre Fourier moments (MFrLFMs) for medical image security and copyright protection in IoMT applications without deforming the original medical images. The MFrLFMs are utilized due to their high accuracy, numerical stability, geometric invariances, and high resistance to various attacks. Based on the most significant features generated from MFrLFMs, after scrambling using a two-dimensional Discrete Henon Map, then XORed with binary scrambled watermark to construct owner share. The proposed watermarking method is implemented using a low-cost Raspberry Pi Linux microprocessor, which ensures the suitability of medical devices in the IoMT environment. We evaluated the robustness of the proposed algorithm against different geometric and common signal processing attacks using various medical images. The proposed method gives better BER, NC, and SSIM values than existing methods.

A novel fast multiple nucleotide sequence alignment method based on FM-index

Multiple sequence alignment (MSA) is fundamental to many biological applications. But most classical MSA algorithms are difficult to handle large-scale multiple sequences, especially long sequences. Therefore, some recent aligners adopt an efficient divide-and-conquer strategy to divide long sequences into several short sub-sequences. Selecting the common segments (i.e. anchors) for division of sequences is very critical as it directly affects the accuracy and time cost. So, we proposed a novel algorithm, FMAlign, to improve the performance of multiple nucleotide sequence alignment. We use FM-index to extract long common segments at a low cost rather than using a space-consuming hash table. Moreover, after finding the longer optimal common segments, the sequences are divided by the longer common segments. FMAlign has been tested on virus and bacteria genome and human mitochondrial genome datasets, and compared with existing MSA methods such as MAFFT, HAlign and FAME. The experiments show that our method outperforms the existing methods in terms of running time, and has a high accuracy on long sequence sets. All the results demonstrate that our method is applicable to the large-scale nucleotide sequences in terms of sequence length and sequence number. The source code and related data are accessible in https://github.com/iliuh/FMAlign.

Fast Multiple Edge Response Method Based on the Design of Experiment and Machine Learning

The multiple edge response (MER) method can accurately capture the nonlinear characteristics in signal integrity simulations. However, transient simulation is time-consuming to obtain all the edge responses for high-order MER. A fast method based on the design of experiment (DoE) and machine learning is proposed in this letter to obtain all the edge responses for a severe nonlinear link. The DoE is used to generate a few training sets for an artificial neural network (ANN). The ANN uses the generated training sets to build a precise model. The developed ANN model predicts the remaining edge responses. The proposed method takes 9.8 min to obtain all the responses, which is 92 min for transient simulations for the ninth-order MER. The results show that the eye height and width error between the proposed method and measurement is less than 5%.

A hybrid Fast Multipole Method for cosmological N-body simulations

We investigate a hybrid numerical algorithm aimed at large-scale cosmological N-body simulation for on-going and future high precision sky surveys. It makes use of a truncated Fast Multiple Method (FMM) for short-range gravity, incorporating a Particle Mesh (PM) method for long-range potential, which is applied to deal with extremely large particle number. In this work, we present a specific strategy to modify a conventional FMM by a Gaussian shaped factor and provide quantitative expressions for the interaction kernels between multipole expansions. Moreover, a proper Multipole Acceptance Criterion for the hybrid method is introduced to solve potential precision loss induced by the truncation. Such procedures reduce the amount of computation compared to an original FMM and decouple the global communication. A simplified version of code is introduced to verify the hybrid algorithm, accuracy and parallel implementation.

A Fast and Effective Multiple Kernel Clustering Method on Incomplete Data

Multiple kernel clustering is an unsupervised data analysis method that has been used in various scenarios where data is easy to be collected but hard to be labeled. However, multiple kernel clustering for incomplete data is a critical yet challenging task. Although the existing absent multiple kernel clustering methods have achieved remarkable performance on this task, they may fail when data has a high value-missing rate, and they may easily fall into a local optimum. To address these problems, in this paper, we propose an absent multiple kernel clustering (AMKC) method on incomplete data. The AMKC method first clusters the initialized incomplete data. Then, it constructs a new multiple-kernel-based data space, referred to as <i>K</i>-space, from multiple sources to learn kernel combination coefficients. Finally, it seamlessly integrates an incomplete-kernel-imputation objective, a multiple-kernel-learning objective, and a kernel-clustering objective in order to achieve absent multiple kernel clustering. The three stages in this process are carried out simultaneously until the convergence condition is met. Experiments on six datasets with various characteristics demonstrate that the kernel imputation and clustering performance of the proposed method is significantly better than state-of-the-art competitors. Meanwhile, the proposed method gains fast convergence speed.

Extraction of winding parameters for 33/11 kV, 30 MVA transformer based on finite element method for frequency response modelling.

This paper proposes an alternative approach to extract transformer’s winding parameters of resistance (R), inductance (L), capacitance (C) and conductance (G) based on Finite Element Method (FEM). The capacitance and conductance were computed based on Fast Multiple Method (FMM) and Method of Moment (MoM) through quasi-electrostatics approach. The AC resistances and inductances were computed based on MoM through quasi-magnetostatics approach. Maxwell's equations were used to compute the DC resistances and inductances. Based on the FEM computed parameters, the frequency response of the winding was obtained through the Bode plot function. The simulated frequency response by FEM model was compared with the simulated frequency response based on the Multi-conductor Transmission Line (MTL) model and the measured frequency response of a 33/11 kV, 30 MVA transformer. The statistical indices such as Root Mean Square Error (RMSE) and Absolute Sum of Logarithmic Error (ASLE) were used to analyze the performance of the proposed FEM model. It is found that the simulated frequency response by FEM model is quite close to measured frequency response at low and mid frequency regions as compared to simulated frequency response by MTL model based on RMSE and ASLE analysis.

Defeating stochasticity: coalescence time-scales of massive black holes in galaxy mergers

ABSTRACT The coalescence of massive black hole binaries (BHBs) in galactic mergers is the primary source of gravitational waves (GWs) at low frequencies. Current estimates of GW detection rates for the Laser Interferometer Space Antenna and the Pulsar Timing Array vary by three orders of magnitude. To understand this variation, we simulate the merger of equal-mass, eccentric, galaxy pairs with central massive black holes and shallow inner density cusps. We model the formation and hardening of a central BHB using the fast multiple method as a force solver, which features a O(N) scaling with the number N of particles and obtains results equivalent to direct-summation simulations. At N ∼ 5 × 105, typical for contemporary studies, the eccentricity of the BHBs can vary significantly for different random realizations of the same initial condition, resulting in a substantial variation of the merger time-scale. This scatter owes to the stochasticity of stellar encounters with the BHB and decreases with increasing N. We estimate that N ∼ 107 within the stellar half-light radius suffices to reduce the scatter in the merger time-scale to ∼10 per cent. Our results suggest that at least some of the uncertainty in low-frequency GW rates owes to insufficient numerical resolution.

Модификация алгоритма Валианта для задачи поиска подстрок

The theory of formal languages and, particularly, context-free grammars has been extensively studied and applied in different areas. For example, several approaches to the recognition and classification problems in bioinformatics are based on searching the genomic subsequences possessing some specific features which can be described by a context-free grammar. Therefore, the string-matching problem can be reduced to parsing – verification if some subsequence can be derived in this grammar. Such field of application as bioinformatics requires working with a large amount of data, so it is necessary to improve the existing parsing techniques. The most asymptotically efficient parsing algorithm that can be applied to any context-free grammar is a matrix-based algorithm proposed by Valiant. This paper aims to present Valiant’s algorithm modification, which main advantage is the possibility to divide the parsing table into successively computed layers of disjoint submatrices where each submatrix of the layer can be processed independently. Moreover, our approach is easily adapted for the string-matching problem. Our evaluation shows that the proposed modification retains all benefits of Valiant’s algorithm, especially its high performance achieved by using fast matrix multiplication methods. Also, the modified version decreases a large amount of excessive computations and accelerates the substrings searching.

A fast multiplex real-time PCR assay for simultaneous detection of pork, chicken, and beef in commercial processed meat products

As rapid and efficient methods for species identification were required, we developed a fast multiplex real-time polymerase chain reaction (PCR) assay based on TaqMan® probes to simultaneously detect pork, chicken, and beef in processed meat samples within 40 min. For multiplex PCR reactions, the 5’ ends of the pork-, chicken-, and beef-specific probes were labeled with FAM, VIC, and NED, respectively. The specificity of this assay was evaluated using 20 animal species and no cross-contamination was observed. The absolute detection limit was 0.1 pg of DNA extracted for all three target species, and the limit of detection (LOD) of reference meat mixtures was determined to be 0.5%. The optimized method was applied to 66 commercial processed products and specific targets were successfully amplified in under 40 min. Therefore, the fast multiple real-time PCR method can be utilized for easily and rapidly monitoring the presence of three meat species in various processed meat products.

The Multiplication Method with Scaling the Result for High-Precision Residue Positional Interval Logarithmic Computations

Introduction. The solution of the simulation problems critical to rounding errors, including the problems of computational mathematics, mathematical physics, optimal control, biochemistry, quantum mechanics, mathematical programming and cryptography, requires the accuracy from 100 to 1 000 decimal digits and more. The main lack of high-precision software libraries is a significant decrease of the speed-in-action, unacceptable for practical problems, in particular, when performing multiplication. A way to increase computation performance over very long numbers is using the residue number system. In this work, we discuss a new fast multiplication method with scaling the result using original hybrid residue positional interval logarithmic floating-point number representation. Materials and Methods. The new way of the organizing numerical information is a residue positional interval logarithmic number representation in which the mantissa is presented in the residue number system, and information on an absolute value (the characteristic) in the interval logarithmic number system that makes it possible to accelerate performance of comparison and scaling is developed to increase the speed of calculations; to compare modular numbers, the provisions of interval analysis are used; to scale modular numbers, the properties of the logarithmic number system and approximate interval calculations using the Chinese reminder theorem are used. Results. A new fast multiplication method of floating-point residue-represented numbers is developed and patented; the authors evaluated the developed method speed-in action, compared the developed method with classical and pipelined multiplication methods of long numbers. Discussion and Conclusion. The developed method is 2.4–4.0 times faster than the pipelined multiplication method, and is 6.4–12.9 times faster than classical multiplication methods.

Actinides AMS on the VEGA accelerator

The VEGA 1MV accelerator at ANSTO is designed to be a highly versatile AMS instrument. In this paper we focus on describing those aspects of the system that are designed to optimise its performance for actinides isotopic analysis, in particular the implementation of fast isotope cycling and multiple isotope detection methods to enable isotope detection across a wide range of rates and currents. Charge state yields are reported in the energy range from 0.3 to 1.0 MeV with helium gas stripping, showing that the highest yield for the 3+ charge state occurs around 1 MeV and exceeds 40%. Accuracy and precision for uranium isotope ratios are shown to approach 1% over a wide range of concentrations and isotope ratios. The ionisation efficiency for plutonium is shown to exceed 3%, leading to overall detection efficiency over 1%. In the absence of background, this leads to sub-attogram detection limits for several Pu isotopes including 244Pu.

Electromagnetic scattering of coated objects over sea surface based on SBR-SDFSM

An efficient approach to analyze the electromagnetic (EM) scattering from coated objects above a three-dimensional (3-D) dielectric random rough surface is proposed in this paper. The electric and magnetic current densities on the sea surface are analytically realized using the semi-deterministic facet scattering model (SDFSM). Considering Fresnel reflection coefficient, a scheme combining the shooting and bouncing rays (SBR) and the physical theory of diffraction (PTD) is developed to calculate the scattering of the coated objects. Simulation results obtained with the combined method are verified by comparison with exact simulations using the multilevel fast multiple method (MLFMM). Scattering of large coated objects over sea surface composite model are too large and complex to be calculated using exact methods. With the asymptotic approach in this paper, the scattering performance can be analyzed with rather moderate computational efforts. Numerical results of composite scattering from an electric large three-dimensional model, e.g. an airplane target over a randomly rough surface with Pierson Moskowitz (PM) spectrum are presented and discussed.

Atomistic modelling of magnetic nano-granular thin films

In this work, a complete model for studying the magnetic behaviour of polycrystalline thin films at nanoscale was processed. This model includes terms as exchange interaction, dipolar interaction and various types of anisotropies. For the first term, exchange interaction dependence of the distance n was used with purpose of quantify the interaction, mainly in grain boundaries. The third term includes crystalline, surface and boundary anisotropies. Special attention was paid to the disorder vector that determines the loss of cubic symmetry in the crystalline structure. For the case of the dipolar interaction, a similar implementation of the fast multiple method (FMM) was performed. Using these tools, modelling and simulations were developed varying the number of grains, and the results obtained presented a great dependence of the magnetic properties on this parameter. Comparisons between critical temperature and magnetization of saturation depending on the number of grains were performed for samples with and without factors as the surface and boundary anisotropies, and the dipolar interaction. It was observed that the inclusion of these parameters produced a decrease in the critical temperature and the magnetization of saturation; furthermore, in both cases, including and not including the disorder parameters, not only the critical temperature, but also the magnetization of saturation exhibited a range of values that also depend on the number of grains. This presence of a critical interval is due to each grain can transit toward the ferromagnetic state at different values of critical temperature. The processes of Zero field cooling (ZFC), Field cooling (FCC) and field cooling in warming mode (FCW) were necessary for understanding the mono-domain regime around of transition temperature, due to the high probabilities of a Super-paramagnetic (SPM) state.