Algorithm For Fast Computation Research Articles

First Derivative Approximations and Applications

In this paper, we consider constructions of first derivative approximations using the generating function. The weights of the approximations contain the powers of a parameter whose modulus is less than one. The values of the initial weights are determined, and the convergence and order of the approximations are proved. The paper discusses applications of approximations of the first derivative for the numerical solution of ordinary and partial differential equations and proposes an algorithm for fast computation of the numerical solution. Proofs of the convergence and accuracy of the numerical solutions are presented and the performance of the numerical methods considered is compared with the Euler method. The main goal of constructing approximations for integer-order derivatives of this type is their application in deriving high-order approximations for fractional derivatives, whose weights have specific properties. The paper proposes the construction of an approximation for the fractional derivative and its application for numerically solving fractional differential equations. The theoretical results for the accuracy and order of the numerical methods are confirmed by the experimental results presented in the paper.

Implementation and validation of a very-high-energy electron model in the matRad treatment planning system.

While electron beams of up to 20 MeV are commonly used in radiotherapy, the use of very-high-energy electrons (VHEEs) in the range of 100-200 MeV is now becoming a realistic option thanks to the recent advancements in accelerator technology. Indeed, VHEE offers several clinically attractive features and can be delivered using various conformation methods (including scanning, collimation, and focussing) at ultra-high dose rates. To date, there is a lack of research tools for fast simulation of treatment plans using VHEE beams. This work aims to implement and validate a simple and fast dose calculation algorithm based on the Fermi-Eyges theory of multiple Coulomb scattering for VHEE radiation therapy, with energies up to 200 MeV. A treatment planning system (TPS) toolkit with VHEE modality would indeed allow for further preclinical investigations, including treatment plan optimization and evaluation, and thus contribute to the gradual introduction of VHEE radiotherapy in clinical practice. A VHEE pencil beam scanning double Gaussian model was introduced into the open-source TPS matRad environment along with new functions and options dedicated to VHEE dose calculations. Various geometries and field configurations were then calculated in matRad (up to 200 MeV and 15×15 cm2, with complex bone or lung heterogeneities) and the results were compared to Monte Carlo simulations in the TOPAS/Geant4 toolkit. Two types of beam model (divergent or focused) were also tested. Examples of clinical treatment plans were computed, and the results were compared between the two codes. VHEE modality was fully implemented in matRad with GUI capabilities while preserving all original TPS features. New relevant options such as the importation of specific spot-lists or adjustment of the lateral dose calculation cutoff to optimize the calculation speed were validated. Single spot and square field dose distributions were validated in water alone as well as in clinically relevant inhomogeneities. Dose maps from the VHEE model in matRad were in good agreement with TOPAS (2D gamma index [2%/1mm] with passing rates superior to 90%, <6% mean dose differences), except for large interface heterogeneities. This work describes the implementation of a simple but efficient VHEE simulation model in matRad. A few configurations were studied in order to validate the model against accurate Monte Carlo simulations, demonstrating its usefulness for carrying out preliminary studies involving VHEE radiotherapy.

A comprehensive propulsion system analysis: an integrated approach utilising engine simulation and free-running model experiments

Regulations concerning the environmental impact and energy efficiency of ships are becoming increasingly stringent. To meet these demanding criteria, new technologies are actively being developed to achieve emission reductions while maintaining efficient fuel energy conversion into propulsion power. However, the propulsion system behaviour in a dynamic environment of the actual sea is highly nonlinear and complex, and a profound understanding of the mutual interactions is still lacking. This paper proposes an integrated approach for comprehensive propulsion system analysis. The key feature of this technique is the utilisation of an intelligent propeller drive controlled by a marine diesel engine simulator (MDES) to drive the free-running model of a ship, providing real-like behaviour of the engine model in real-time in response to actual measured values. The core of the MDES consists of a continuous cycle-mean value dynamic engine model supplemented with a detailed combustion cycle evaluation. The developed fast calculation algorithm of crank-angle resolved thermodynamic equations of the gas state in the engine cylinder enables the complete engine model to be integrated into the real-time environment of a physical model ship. Thus, the propulsion system's performance can be analysed under conditions that closely mimic those of the actual sea environment.

Novel Partitioned Time-Stepping Algorithms for Fast Computation of Random Interface-Coupled Problems with Uncertain Parameters

Novel Partitioned Time-Stepping Algorithms for Fast Computation of Random Interface-Coupled Problems with Uncertain Parameters

2772: Fast and accurate dose calculation algorithm based on multi-level U-Net for IMRT

2772: Fast and accurate dose calculation algorithm based on multi-level U-Net for IMRT

Non-Cooperative LEO Satellite Orbit Determination Using Single Station for Space-Based Opportunistic Positioning

Space-based opportunistic positioning is a crucial component of resilient positioning, navigation, and timing (PNT) systems, and it requires the acquisition of orbit information for non-cooperative low Earth orbit (LEO) satellites. Traditional methods for orbit determination (OD) of non-cooperative LEO satellites have difficulty in achieving a balance between reliability, hardware costs, and availability duration. To address these challenges, this study proposes a framework for single-station orbit determination of non-cooperative LEO satellites. By utilizing signals of opportunity (SOPs) captured by a single ground station, the system performs initial orbit determination (IOD), precise orbit determination (POD), and orbit prediction (OP), enabling the long-term determination of satellite positions and velocities. Under the proposed framework, the reliability and real-time performance are dependent on the initial orbit determination and the orbit calculation based on the dynamical model. To achieve initial orbit determination, a three-step algorithm is designed. (1) An improved search method is employed to estimate a coarse orbit using single-pass Doppler measurements. (2) Data association is conducted to obtain multi-pass Doppler observations. (3) The least squares (LS) is implemented to determine the initial orbit using the associated multi-pass Doppler measurements and the coarse orbit. Additionally, to enhance computational efficiency, two fast orbit calculation algorithms are devised. These algorithms leverage the numerical stability of the Runge–Kutta integrator to reduce computations and exploit the strong correlation among nearby time intervals of orbits with small eccentricities to minimize redundant calculations, thereby achieving orbit calculation efficiently. Finally, through positioning experiments, the determined orbits are demonstrated to have accuracy comparable to that of two-line elements (TLE) updated by the North American Aerospace Defense Command (NORAD).

Time and memory scalable algorithms for clustering tendency assessment of big data

Large-volume and high-dimensional big datasets are being generated quickly. They are expected to provide data-driven solutions for various pressing challenges such as cybersecurity, credit card fraud, network intrusion detection, etc. The visual assessment of clustering tendency (VAT) family of algorithms provides an excellent tool for assessing clustering tendency and subsequent clustering of these novel datasets to extract groups and anomalies to better understand the data generation phenomenon. However, VAT and improved VAT (iVAT) algorithms are plagued with O(n2) time and space complexity as they use Prim's algorithm for building Euclidean minimum spanning tree (EMST) of the data points, leaving it inapplicable to large datasets. This paper develops three novel time- and memory-scalable algorithms for fast computation of VAT EMST by reducing the search space of the following possible EMST edge and using an efficient data structure, the k-d tree. Next, we develop a novel approach to compute iVAT reordered dissimilarity image (RDI) in a novel memory-preserving manner using the EMST edge lengths calculated previously without having to compute memory intensive n×n VAT RDI. We experimented on several synthetic and real-life datasets to showcase that the proposed approaches can help quickly assess their clustering tendency in a memory-saving manner. We also demonstrate the applicability of the proposed methods for the anomaly detection task in large volumes of high-dimensional data.

De-cluttering Scatterplots with Integral Images.

Scatterplots provide a visual representation of bivariate data (or 2D embeddings of multivariate data) that allows for effective analyses of data dependencies, clusters, trends, and outliers. Unfortunately, classical scatterplots suffer from scalability issues, since growing data sizes eventually lead to overplotting and visual clutter on a screen with a fixed resolution, which hinders the data analysis process. We propose an algorithm that compensates for irregular sample distributions by a smooth transformation of the scatterplot's visual domain. Our algorithm evaluates the scatterplot's density distribution to compute a regularization mapping based on integral images of the rasterized density function. The mapping preserves the samples' neighborhood relations. Few regularization iterations suffice to achieve a nearly uniform sample distribution that efficiently uses the available screen space. We further propose approaches to visually convey the transformation that was applied to the scatterplot and compare them in a user study. We present a novel parallel algorithm for fast GPU-based integral-image computation, which allows for integrating our de-cluttering approach into interactive visual data analysis systems.

Accurate and Fast Geodesic Distance Calculation Algorithm for Superpixel Segmentation

Accurate and Fast Geodesic Distance Calculation Algorithm for Superpixel Segmentation

Algorithms for fast calculation of energization overvoltage of hybrid overhead line-cable transmission lines based on full frequency-dependent parameters

Algorithms for fast calculation of energization overvoltage of hybrid overhead line-cable transmission lines based on full frequency-dependent parameters

Horseshoe prior Bayesian quantile regression

Abstract This paper extends the horseshoe prior to Bayesian quantile regression and provides a fast sampling algorithm for computation in high dimensions. Compared to alternative shrinkage priors, our method yields better performance in coefficient bias and forecast error, especially in sparse designs and in estimating extreme quantiles. In a high-dimensional growth-at-risk forecasting application, we forecast tail risks and complete forecast densities using a database covering over 200 macroeconomic variables. Quantile specific and density calibration score functions show that our method provides competitive performance compared to competing Bayesian quantile regression priors, especially at short- and medium-run horizons.

Comparative study of single precision floating point division using different computational algorithms

&lt;span&gt;This paper presents different computational algorithms to implement single precision floating point division on field programmable gate arrays (FPGA). Fast division computation algorithms can apply to all division cases by which an efficient result will be obtained in terms of delay time and power consumption. 24-bit Vedic multiplication (Urdhva-Triyakbhyam-sutra) technique enhances the computational speed of the mantissa module and this module is used to design a 32-bit floating point multiplier which is the crucial feature of this proposed design, which yields a higher computational speed and reduced delay time. The proposed design of floating-point divider using fast computational algorithms synthesized using Verilog hardware description language has a 32-bit floating point multiplier module unit and a 32-bit floating point subtractor module unit. Xilinx Spartan 6 SP605 evaluation platform is used to verify this proposed design on FPGA. Synthesis results provide the device utilization and propagation delay parameters for the proposed design and a comparative study is done with previous work. Input to the divider is provided in IEEE 754 32-bit formats.&lt;/span&gt;

RegularSearch, a fast performance algorithm for typical testors computation

RegularSearch, a fast performance algorithm for typical testors computation

Fast Grayscale Morphology for Circular Window

AbstractMorphological operations are among the most popular classic image filters. The filter assumes the maximum or minimum value within a window and is often used for light object thickening and thinning operations, which are important components of various workflows, such as object recognition and stylization. Circular windows are preferred over rectangular windows for obtaining isotropic filter results. However, the existing efficient algorithms focus on rectangular or binary input images. Efficient morphological operations with circular windows for grayscale images remain challenging. In this study, we present a fast grayscale morphology heuristic computation algorithm that decomposes circular windows using the convex hull of circles. We significantly accelerate traditional methods based on Minkowski addition by introducing new decomposition rules specialized for circular windows. As our morphological operation using a convex hull can be computed independently for each pixel, the algorithm is efficient for modern multithreaded hardware.

Rapid and Efficient Computation of Cell Paths During Ultrasonic Focusing.

This biophysical analysis explores the first-principles physics of movement of white blood cell sized particles, suspended in an aqueous fluid and experiencing progressive or standing waves of acoustic pressure. In many current applications the cells are gradually nudged or herded toward the nodes of the standing wave, providing a degree of acoustic focusing and concentration of the cells in layers perpendicular to the direction of sound propagation. Here the underlying biomechanics of this phenomenon are analyzed specifically for the viscous regime of water and for small diameter microscopic spheroids such as living cells. The resulting mathematical model leads to a single algebraic expression for the creep or drift velocity as a function of sound frequency, amplitude, wavelength, fluid viscosity, boundary dimensions, and boundary reflectivity. This expression can be integrated numerically by a simple and fast computer algorithm to demonstrate net movement of particles as a function of time, providing a guide to optimization in a variety of emerging applications of ultrasonic cell focusing.

Directional lifting wavelet transform for image edge analysis

In this paper, we propose a new two-dimensional directional discrete wavelet transform that can decompose an image into 12 multiscale directional edge components. The proposed transform is designed in a fully discrete setting and thus is easy to implement in actual computations. The proposed transform is viewed as a category of redundant discrete wavelet transforms implemented by fast in-place computational algorithms by a lifting scheme that has been modified to incorporate redundancy. The redundancy is limited to (N×J+1)/4, where N=12 is the directional selectivity and J is a decomposition level of the multiscale transform. Numerical experiments in edge analysis using various images demonstrate the advantages of the proposed method over some conventional standard methods. The proposed method outperforms several conventional edge detection methods in identifying both the location and orientation of edges, and well captures the directional and geometrical features of images.

Real-time computing for a holographic 3D display based on the sparse distribution of a 3D object and requisite Fourier spectrum.

In holographic three-dimensional (3D) displays, the surface structures of 3D objects are reconstructed without their internal parts. In diffraction calculations using 3D fast Fourier transform (FFT), this sparse distribution of 3D objects can reduce the calculation time as the Fourier transform can be analytically solved in the depth direction and the 3D FFT can be resolved into multiple two-dimensional (2D) FFTs. Moreover, the Fourier spectrum required for hologram generation is not the entire 3D spectrum but a partial 2D spectrum located on the hemispherical surface. This sparsity of the required Fourier spectrum also reduces the number of 2D FFTs and improves the acceleration. In this study, a fast calculation algorithm based on two sparsities is derived theoretically and explained in detail. Our proposed algorithm demonstrated a 24-times acceleration improvement compared with a conventional algorithm and realized real-time hologram computing at a rate of 170Hz.

Evolution of pore structure in nanoparticle deposits from unimodal to bimodal pore size distributions: Focus on structural features of dendritic structures

Nanoparticle deposits can exhibit various structures, including compact and dendritic structures, depending on the deposition conditions. While previous studies have characterized deposit structures using factors such as porosity and spatial autocorrelation index, the pore size distribution (PSD), which is an essential structural property, has only been explored in compact structures. In this study, we investigate the PSDs of the entire nanoparticle deposits, ranging from compact to dendritic structures. Deposits are formed using an off-lattice Monte Carlo simulation, and deposition conditions are represented by two dimensionless numbers (KnD, χF). The diffusive Knudsen number (KnD) ranges from 10−1.5 to 101.5, while the dimensionless translational energy of a particle (χF) ranges from 10−3 to 101.5. We use the Delaunay triangulation algorithm for fast PSD calculation, and validate the calculation method using theoretical values of ideal structures and experimental literature data. Our results show that bimodal PSDs appear under thermally-dominated conditions with high values of KnD, while unimodal PSDs with a constant mode radius (∼2.5 rp) are observed under highly advective conditions with high values of χF. We present the geometric mean radii and mode radii of pores as color-filled contours to show their variation trends with KnD and χF. Additionally, we propose a simple model that predicts dendrite width by combining the overall porosity and mode radii of pores. Our model's predictions reasonably match the dendrite width data obtained using a density-based clustering algorithm.

A Multithreaded Algorithm for the Computation of Sample Entropy

Many popular entropy definitions for signals, including approximate and sample entropy, are based on the idea of embedding the time series into an m-dimensional space, aiming to detect complex, deeper and more informative relationships among samples. However, for both approximate and sample entropy, the high computational cost is a severe limitation. Especially when large amounts of data are processed, or when parameter tuning is employed premising a large number of executions, the necessity of fast computation algorithms becomes urgent. In the past, our research team proposed fast algorithms for sample, approximate and bubble entropy. In the general case, the bucket-assisted algorithm was the one presenting the lowest execution times. In this paper, we exploit the opportunities given by the multithreading technology to further reduce the computation time. Without special requirements in hardware, since today even our cost-effective home computers support multithreading, the computation of entropy definitions can be significantly accelerated. The aim of this paper is threefold: (a) to extend the bucket-assisted algorithm for multithreaded processors, (b) to present updated execution times for the bucket-assisted algorithm since the achievements in hardware and compiler technology affect both execution times and gain, and (c) to provide a Python library which wraps fast C implementations capable of running in parallel on multithreaded processors.

FTA-GAN: A Computation-Efficient Accelerator for GANs With Fast Transformation Algorithm.

Nowadays, generative adversarial network (GAN) is making continuous breakthroughs in many machine learning tasks. The popular GANs usually involve computation-intensive deconvolution operations, leading to limited real-time applications. Prior works have brought several accelerators for deconvolution, but all of them suffer from severe problems, such as computation imbalance and large memory requirements. In this article, we first introduce a novel fast transformation algorithm (FTA) for deconvolution computation, which well solves the computation imbalance problem and removes the extra memory requirement for overlapped partial sums. Besides, it can reduce the computation complexity for various types of deconvolutions significantly. Based on FTA, we develop a fast computing core (FCC) and the corresponding computing array so that the deconvolution can be efficiently computed. We next optimize the dataflow and storage scheme to further reuse on-chip memory and improve the computation efficiency. Finally, we present a computation-efficient hardware architecture for GANs and validate it on several GAN benchmarks, such as deep convolutional GAN (DCGAN), energy-based GAN (EBGAN), and Wasserstein GAN (WGAN). The experimental results show that our design can reach 2211 GOPS under 185-MHz working frequency on Intel Stratix 10SX field-programmable gate array (FPGA) board with satisfactory visual results. In brief, the proposed design can achieve more than 2× hardware efficiency improvement over previous designs, and it can reduce the storage requirement drastically.