Algorithm For Fast Computation Research Articles

Fast approximate shortest paths in the congested clique

We design fast deterministic algorithms for distance computation in the Congested Clique model. Our key contributions include:A (2+epsilon )-approximation for all-pairs shortest paths in O(log ^2{n} / epsilon ) rounds on unweighted undirected graphs. With a small additional additive factor, this also applies for weighted graphs. This is the first sub-polynomial constant-factor approximation for APSP in this model.A (1+epsilon )-approximation for multi-source shortest paths from O(sqrt{n}) sources in O(log ^2{n} / epsilon ) rounds on weighted undirected graphs. This is the first sub-polynomial algorithm obtaining this approximation for a set of sources of polynomial size. Our main techniques are new distance tools that are obtained via improved algorithms for sparse matrix multiplication, which we leverage to construct efficient hopsets and shortest paths. Furthermore, our techniques extend to additional distance problems for which we improve upon the state-of-the-art, including diameter approximation, and an exact single-source shortest paths algorithm for weighted undirected graphs in tilde{O}(n^{1/6}) rounds.

Hierarchical Cubical Tensor Decomposition through Low Complexity Orthogonal Transforms

In this work, new approaches are proposed for the 3D decomposition of a cubical tensor of size N × N × N for N = 2n through hierarchical deterministic orthogonal transforms with low computational complexity, whose kernels are based on the Walsh-Hadamard Transform (WHT) and the Complex Hadamard Transform (CHT). On the basis of the symmetrical properties of the real and complex Walsh-Hadamard matrices are developed fast computational algorithms whose computational complexity is compared with that of the famous deterministic transforms: the 3D Fast Fourier Transform, the 3D Discrete Wavelet Transform and the statistical Hierarchical Tucker decomposition. The comparison results show the lower computational complexity of the offered algorithms. Additionally, they ensure the high energy concentration of the original tensor into a small number of coefficients of the so calculated transformed spectrum tensor. The main advantage of the proposed algorithms is the reduction of the needed calculations due to the low number of hierarchical levels compared to the significant number of iterations needed to achieve the required decomposition accuracy based on the statistical methods. The choice of the 3D hierarchical decomposition is defined by the requirements and limitations related to the corresponding application area.

Estimation in linear errors-in-variables models with unknown error distribution

Summary Parameter estimation in linear errors-in-variables models typically requires that the measurement error distribution be known or estimable from replicate data. A generalized method of moments approach can be used to estimate model parameters in the absence of knowledge of the error distributions, but it requires the existence of a large number of model moments. In this paper, parameter estimation based on the phase function, a normalized version of the characteristic function, is considered. This approach requires the model covariates to have asymmetric distributions, while the error distributions are symmetric. Parameters are estimated by minimizing a distance function between the empirical phase functions of the noisy covariates and the outcome variable. No knowledge of the measurement error distribution is needed to calculate this estimator. Both asymptotic and finite-sample properties of the estimator are studied. The connection between the phase function approach and method of moments is also discussed. The estimation of standard errors is considered and a modified bootstrap algorithm for fast computation is proposed. The newly proposed estimator is competitive with the generalized method of moments, despite making fewer model assumptions about the moment structure of the measurement error. Finally, the proposed method is applied to a real dataset containing measurements of air pollution levels.

A Fast Algorithm for Calculation of Thêo1.

Thêo1 is a frequency stability statistic that is similar to the Allan variance but can provide stability estimates at longer averaging factors and with higher confidence. However, the calculation of Thêo1 is significantly slower than that of the Allan variance, particularly for large data sets, due to a worse computational complexity. A faster algorithm for calculating the "all- τ " version of Thêo1 is developed by identifying certain repeated sums and removing them with a recurrence relation. The new algorithm has a reduced computational complexity, which is equal to that of the Allan variance. Computation time is reduced by orders of magnitude for many data sets. The new, faster algorithm does introduce an error due to accumulated floating-point errors in very large data sets. The error can be compensated for by increasing the numerical precision used at critical steps. The new algorithm can also be used to increase the speed of ThêoBr and ThêoH that are more sophisticated statistics derived from Thêo1.

Signal Reconstruction Using New Biorthogonal Frequency-Modified Kravchenko Wavelets When Representing the Measurement Process as a Convolution Model

Abstract—A new biorthogonal system of wavelet bases has been constructed, which is oriented toward reconstructing the useful signal of a measuring system if the measurement process is represented as a convolution model. New biorthogonal wavelet bases are obtained by using a instrumental function to modify a Kravchenko orthogonal wavelet system with a finite spectrum. The properties of new biorthogonal frequency-modified wavelets are studied, and digital filters that realize fast computational algorithms are constructed. Schemes for multiresolution analysis are proposed, which, during discrete wavelet transform, immediately solve the problem of reconstructing the useful signal, as well as effective noise suppression, which can significantly speed up computations.

Fast Computation of LSP Frequencies Using the Bairstow Method

Linear prediction is the kernel technology in speech processing. It has been widely applied in speech recognition, synthesis, and coding, and can efficiently and correctly represent the speech frequency spectrum with only a few parameters. Line Spectrum Pairs (LSPs) frequencies, as an alternative representation of Linear Predictive Coding (LPC), have the advantages of good quantization accuracy and low spectral sensitivity. However, computing the LSPs frequencies takes a long time. To address this issue, a fast computation algorithm, based on the Bairstow method for computing LSPs frequencies from linear prediction coefficients, is proposed in this paper. The algorithm process first transforms the symmetric and antisymmetric polynomial to general polynomial, then extracts the polynomial roots. Associated with the short-term stationary property of speech signal, an adaptive initial method is applied to reduce the average iteration numbers by 26%, as compared to the statics in the initial method, with a Perceptual Evaluation of Speech Quality (PESQ) score reaching 3.46. Experimental results show that the proposed method can extract the polynomial roots efficiently and accurately with significantly reduced computation complexity. Compared to previous works, the proposed method is 17 times faster than Tschirnhus Transform, and has a 22% PESQ improvement on the Birge-Vieta method with an almost comparable computation time.

An Efficient Trivariate Algorithm for Tetrahedral Shepard Interpolation

In this paper we present a trivariate algorithm for fast computation of tetrahedral Shepard interpolants. Though the tetrahedral Shepard method achieves an approximation order better than classical Shepard formulas, it requires to detect suitable configurations of tetrahedra whose vertices are given by the set of data points. In doing that, we propose the use of a fast searching procedure based on the partitioning of domain and nodes in cubic blocks. This allows us to find the nearest neighbor points associated with each ball that need to be used in the 3D interpolation scheme. Numerical experiments show good performance of our interpolation algorithm.

Energy modeling of solar water heating systems with on-off control and thermally stratified storage using a fast computation algorithm

This work presents a simplified model for the rapid computation of the yearly solar fraction of direct solar water heating systems using on-off control. Thermal stratification was included using a simple one-dimensional multi-node model. A time-step dependency analysis showed that a time step of 0.05h is a good compromise between accuracy and computation speed. The solar fraction increases with collector flow rate when the flow rate is low. In fully-mixed storage, the solar fraction keeps increasing with flow rate, although with a decreasing rate of increase. However, in stratified storage, the solar fraction reaches a maximum at an optimum flow rate, before it starts decreasing with flow rate. When the number of tank nodes increases from 1 to 4, the maximum solar fraction increases 5–28%; this increase is superior for less efficient collectors and lower collector areas. In low-stratified systems, the optimum flow rate is the maximum allowed by the system. However, in stratified systems, the optimum flow rate is reduced to values of 0.006–0.016m3h−1 per square meter of collector area. Unless the tank walls are covered by a rather thick layer of thermal insulation (about 0.2m), storage tank losses cannot be ignored.

Orthogonal and Non-Orthogonal Signal Representations Using New Transformation Matrices Having NPM Structure

In this paper, we introduce two types of real-valued sums known as Complex Conjugate Pair Sums (CCPSs) denoted as CCPS$^{(1)}$ and CCPS$^{(2)}$, and discuss a few of their properties. Using each type of CCPSs and their circular shifts, we construct two non-orthogonal Nested Periodic Matrices (NPMs). As NPMs are non-singular, this introduces two non-orthogonal transforms known as Complex Conjugate Periodic Transforms (CCPTs) denoted as CCPT$^{(1)}$ and CCPT$^{(2)}$. We propose another NPM, which uses both types of CCPSs such that its columns are mutually orthogonal, this transform is known as Orthogonal CCPT (OCCPT). After a brief study of a few OCCPT properties like periodicity, circular shift, etc., we present two different interpretations of it. Further, we propose a Decimation-In-Time (DIT) based fast computation algorithm for OCCPT (termed as FOCCPT), whenever the length of the signal is equal to $2^v,\ v{\in} \mathbb{N}$. The proposed sums and transforms are inspired by Ramanujan sums and Ramanujan Period Transform (RPT). Finally, we show that the period (both divisor and non-divisor) and frequency information of a signal can be estimated using the proposed transforms with a significant reduction in the computational complexity over Discrete Fourier Transform (DFT).

Linking statistical literacy and data stewardship in Public Universities of Niger: Lessons learned from the collaboration with the national statistics institute

This paper aims at highlighting the lessons learned from recent initiatives between public universities of Niger and the national statistics institute. Our investigation of the existing national statistical system revealed the need to increase the number of qualified human resources with advanced skills in open data, big data, data visualisation, machine learning, mathematical modeling and data-driven innovations. Moreover, the existing statistical literacy and data crowdsourcing activities need to be validated and upscaled; and we have found a lack of experience in managing big data and in the development of mathematical methods and fast computational algorithms to analyze them. Finally, the aforementioned collaboration can be improved by working closely with private sector, civil society and the data science community to generate new approaches to emerging issues including climate change and sustainable development.

Multiscale radial kernels with high-order generalized Strang-Fix conditions

The paper provides a general and simple approach for explicitly constructing multiscale radial kernels with high-order generalized Strang-Fix conditions from a given univariate generator. The resulting kernels are constructed by taking a linear functional to the scaled f -form of the generator with respect to the scale variable. Equivalent divided difference forms of the kernels are also derived; based on which, a pyramid-like algorithm for fast and stable computation of multiscale radial kernels is proposed. In addition, characterizations of the kernels in both the spatial and frequency domains are given, which show that the generalized Strang-Fix condition, the moment condition, and the condition of polynomial reproduction in the convolution sense are equivalent to each other. Hence, as a byproduct, the paper provides a unified view of these three classical concepts. These kernels can be used to construct quasi-interpolation with high approximation accuracy and construct convolution operators with high approximation orders, to name a few. As an example, we construct a quasi-interpolation scheme for irregularly spaced data and derived its error estimates and choices of scale parameters of multiscale radial kernels. Numerical results of approximating a bivariate Franke function using our quasi-interpolation are presented at the end of the paper. Both theoretical and numerical results show that quasi-interpolation with multiscale radial kernels satisfying high-order generalized Strang-Fix conditions usually provides high approximation orders.

Fast Nonseparable Gaussian Stochastic Process With Application to Methylation Level Interpolation

Gaussian stochastic process (GaSP) has been widely used as a prior over functions due to its flexibility and tractability in modeling. However, the computational cost in evaluating the likelihood is , where n is the number of observed points in the process, as it requires to invert the covariance matrix. This bottleneck prevents GaSP being widely used in large-scale data. We propose a general class of nonseparable GaSP models for multiple functional observations with a fast and exact algorithm, in which the computation is linear (O(n)) and exact, requiring no approximation to compute the likelihood. We show that the commonly used linear regression and separable models are special cases of the proposed nonseparable GaSP model. Through the study of an epigenetic application, the proposed nonseparable GaSP model can accurately predict the genome-wide DNA methylation levels and compares favorably to alternative methods, such as linear regression, random forest, and localized Kriging method. The supplementary materials of this article are online and the algorithm for fast computation is implemented in the FastGaSP R package on CRAN. Supplemental materials for this article are available online.

Thresholds of Absorbing Sets Under Scaled Min-Sum LDPC Decoding

In this paper, the definition of threshold of elementary absorbing sets is extended to scaled Min-Sum low-density parity-check (LDPC) decoding. Based on the analysis of the behavior of scaled Min-Sum LDPC decoders in the Tanner graph of the absorbing set, it is proven that correct decoding is guaranteed with received channel messages above threshold. A fast algorithm for the threshold computation is derived. Many examples of absorbing sets taken from LDPC codes of various variable node degrees are investigated, and it is shown that all of them can be deactivated with low enough scaling factors.

1268A comparison between the diagnostic performance of quantitative flow ratio and non-invasive imaging modalities for diagnosing myocardial ischemia defined by FFR, a PACIFIC-trial interim analysis

Abstract Background Quantitative flow ratio (QFR) uses fast computational algorithms based on 3-dimensional quantitative coronary angiography and estimation of contrast flow velocity during invasive coronary angiography (ICA) to obtain QFR values equivalent to fractional flow reserve (FFR). Objective To compare the diagnostic performance of QFR with coronary computed tomography angiography (CCTA), single-photon emission tomography (SPECT), and positron emission tomography (PET) for diagnosing myocardial ischemia defined by FFR. Method QFR computation was attempted in 109 patients (286 vessels without a subtotal/total lesion) of the 208 patients included in the PACIFIC-trial. Patients underwent 256-slice CCTA, Tetrofosmin SPECT, and [15O]H2O PET prior to ICA in conjunction with 3 vessel FFR measurements. ICA images were obtained without the use of a dedicated QFR acquistion protocol. QFR was calculated using a fixed empiric hyperemic flow velocity (fQFR) as well as using a patient specific flow velocity based on contrast passage through the coronary (cQFR). All analysis were performed on a per vessel level. Results Fixed QFR computation succeeded in 152 (53%) vessels while cQFR analysis was successful in 140 (49%) vessels. A good correlation between FFR and fQFR/cQFR was observed (R=0.774, p<0.001/R=0.790, p<0.001). The diagnostic performance in terms of sensitivity, specificity, negative predictive value, positive predictive value, and accuracy is presented in table 1. In total, 133 vessels with matched FFR, fQFR, cQFR, CCTA, SPECT, and PET results were available for the comparative C-statistic analysis, figure 1. The diagnostic performance of fQFR and cQFR was comparable (p=0.451) and superior to CCTA (p=0.004/p=0.003), SPECT (p<0.001/p<0.001), and PET (p=0.008/p=0.006), figure 1. CCTA, and PET performed alike (p=0.568) and outperformed SPECT (p=0.023, p=0.002). Table 1 % (95% Confidence Interval) fQFR n=152 cQFR (n=140) CCTA (n=152) SPECT (n=150) PET (n=149) Sensitivity 76 (59–89) 71 (53–86) 70 (51–84) 30 (16–49) 76 (58–89) Specificity 94 (88–98) 93 (86–97) 73 (64–81) 96 (90–99) 80 (72–87) Negative Predictive Value 93 (88–96) 92 (86–95) 90 (84–94) 83 (79–86) 92 (86–96) Positive Predictive Value 79 (64–89) 74 (59–85) 42 (33–51) 67 (42–84) 52 (42–62) Accuracy 90 (84–94) 88 (81–93) 72 (65–79) 81 (74–87) 79 (72–85) Figure 1. Conclusion Fixed QFR and cQFR correlate well with FFR with a high diagnostic accuracy as result. QFR outperformed CCTA, SPECT, and PET for the diagnosis of myocardial ischemia on a per vessel basis with the important footnote that fQFR and cQFR could only be computed in 53%, and 49% of the vessels.

A fast algorithm for radiative transport in isotropic media

Constructing efficient numerical solution methods for the equation of radiative transfer (ERT) remains as a challenging task in scientific computing despite of the tremendous development on the subject in recent years. We present in this work a simple fast computational algorithm for solving the ERT in isotropic media. The algorithm we developed has two steps. In the first step, we solve a volume integral equation for the angularly-averaged ERT solution using iterative schemes such as the GMRES method. The computation in this step is accelerated with a fast multipole method (FMM). In the second step, we solve a scattering-free transport equation to recover the angular dependence of the ERT solution. The algorithm does not require the underlying medium be homogeneous. We present numerical simulations under various scenarios to demonstrate the performance of the proposed numerical algorithm for both homogeneous and heterogeneous media.

Automatic Defect Detection for Web Offset Printing Based on Machine Vision

In the printing industry, defect detection is of crucial importance for ensuring the quality of printed matter. However, rarely has research been conducted for web offset printing. In this paper, we propose an automatic defect detection method for web offset printing, which consists of determining first row of captured images, image registration and defect detection. Determining the first row of captured images is a particular problem of web offset printing, which has not been studied before. To solve this problem, a fast computational algorithm based on image projection is given, which can convert 2D image searching into 1D feature matching. For image registration, a shape context descriptor is constructed by considering the shape concave-convex feature, which can effectively reduce the dimension of features compared with the traditional image registration method. To tolerate the position difference and brightness deviation between the detected image and the reference image, a modified image subtraction is proposed for defect detection. The experimental results demonstrate the effectiveness of the proposed method.

Fast computation algorithm for the random consideration set model

This paper proposes a fast and reliable computation algorithm for the random consideration set model. A simple and numerically tractable representation of the model is developed to reduce the computational burden. I show that the new algorithm outperforms existing methods in terms of accuracy and speed.

Verified Newton–Raphson Iteration for Multiplicative Inverses Modulo Powers of Any Base

We identify two faults in a published algorithm for fast computation of multiplicative inverses modulo prime powers. We patch the algorithm and present machine-assisted proofs of correctness of the repair. Our formal proofs also reveal that being prime is an unnecessary demand for the power base, thus attributing a wider scope of applications to the repaired algorithm.

MIMR-DGSA: Unsupervised hyperspectral band selection based on information theory and a modified discrete gravitational search algorithm

Band selection plays an important role in hyperspectral data analysis as it can improve the performance of data analysis without losing information about the constitution of the underlying data. We propose a MIMR-DGSA algorithm for band selection by following the Maximum-Information-Minimum-Redundancy (MIMR) criterion that maximises the information carried by individual features of a subset and minimises redundant information between them. Subsets are generated with a modified Discrete Gravitational Search Algorithm (DGSA) where we definine a neighbourhood concept for feature subsets. A fast algorithm for pairwise mutual information calculation that incorporates variable bandwidths of hyperspectral bands called VarBWFastMI is also developed. Classification results on three hyperspectral remote sensing datasets show that the proposed MIMR-DGSA performs similar to the original MIMR with Clonal Selection Algorithm (CSA) but is computationally more efficient and easier to handle as it has fewer parameters for tuning.

A novel level set approach for image segmentation with landmark constraints

Level set methods are widely used in image segmentation and shape analysis. However, most of the current research focuses on fast computational algorithms, initial value selection, and practical applications in various areas. To the best of our knowledge, no research has been conducted on segmentation with level set models where the segmentation contours have to pass through some prior landmark points. In this paper, we propose a new variational model for image segmentation based on the classical Chan-Vese model for this new problem. The new model incorporates prior landmarks information as constraints in a formulated optimization problem. Then, we investigate the theoretical solvability of the new model and design a new algorithm based on the Split Bregman algorithm for numerical implementation. Finally, we conduct some segmentation experiments on gray images and compare with the original Chan-Vese model. The obtained results show many advantages of the proposed model with broad applications. Additionally, we give some critical analysis of the proposed algorithm.