Sparse Form Research Articles

Compressive Sensing Sparse Sampling Method for Composite Material Based on Principal Component Analysis

Signals can be sampled by compressive sensing theory with a much less rate than those by traditional Nyquist sampling theorem, and reconstructed with high probability, only when signals are sparse in the time domain or a transform domain. Most signals are not sparse in real world, but can be expressed in sparse form by some kind of sparse transformation. Commonly used sparse transformations will lose some information, because their transform bases are generally fixed. In this paper, we use principal component analysis for data reduction, and select new variable with low dimension and linearly correlated to the original variable, instead of the original variable with high dimension, thus the useful data of the original signals can be included in the sparse signals after dimensionality reduction with maximize portability. Therefore, the loss of data can be reduced as much as possible, and the efficiency of signal reconstruction can be improved. Finally, the composite material plate is used for the experimental verification. The experimental result shows that the sparse representation of signals based on principal component analysis can reduce signal distortion and improve signal reconstruction efficiency.

Gelatin Methacryloyl Hydrogels in the Absence of a Crosslinker as 3D Glioblastoma Multiforme (GBM)-Mimetic Microenvironment.

3D platforms are important for monitoring tumor progression and screening drug candidates to eradicate tumors such as glioblastoma multiforme (GBM), a malignant type of human brain tumor. Here, a new strategy is reported that exploits visible-light-induced crosslinking of gelatin where the reaction is carried out in the absence of an additional crosslinker. Visible light-induced crosslinking promotes the design of cancer microenvironment-mimetic system without compromising the cell viability during the process and absence of crosslinker facilitates the synthesis of the unique construct. Suspension and spheroid-based models of GBM are used to investigate cellular behavior, expression profiles of malignancy, and apoptosis-related genes within this unique network. Furthermore, sensitivity to an anticancer drug, Digitoxigenin, treatment is investigated in detail. The data suggest that U373 cells, in sparse or spheroid form, have significantly decreased expressions of apoptosis-activating genes, Bad, Puma, and Caspase-3, and a high expression of prosurvival Bcl-2 gene within GelMA hydrogels. Matrix-metalloproteinase genes are also upregulated within GelMA, suggesting positive contribution of gels on extracellular remodeling of cancer cells. This unique photocurable gelatin holds great potential for clinical translation of cancer research through the analysis of 3D malignant cancer cell behavior, and hence for more efficient treatment methods for GBM.

Improved Algorithms and Implementations for Integer to $\tau $ NAF Conversion for Koblitz Curves

The conversion from an integer scalar to a short and sparse τ-adic nonadjacent form (τNAF) is crucial for efficient elliptic curve scalar multiplication over Koblitz curves. Currently the conversion is costly both in time and area, limiting the application of Koblitz curves. In this paper, we propose improved algorithms and implementations for both the single-digit and double-digit scalar conversions. Area reduction is achieved by removing the τ-and-add calculation of the remainder upon division by τ m for lazy reduction or the τ2-and-add one for the double lazy reduction. The τNAF and the double τNAF algorithms are modified accordingly to support a mixed-formreduced scalar from the new reduction algorithms. Furthermore, fair pipelining is explored to speed up conversion with only a slight increase in area. Implementation results on Altera Stratix II FPGA show that the proposed single-digit converters are both smaller and faster than existing works, and the 4-stage pipelined one achieves at least 42.3% area reduction and 78.9% better area-time product (ATP) performance. On Xilinx Virtex IV, our non-pipelined double-digit converters are at least 44.5% smaller but slightly slower, while the 4-stage pipelined one can run faster with averagely 46.6% better ATP than previous equivalent works.

TensorLightning: A Traffic-Efficient Distributed Deep Learning on Commodity Spark Clusters

With the recent success of deep learning, the amount of data and computation continues to grow daily. Hence a distributed deep learning system that shares the training workload has been researched extensively. Although a scale-out distributed environment using commodity servers is widely used, not only is there a limit due to synchronous operation and communication traffic but also combining deep neural network (DNN) training with existing clusters often demands additional hardware and migration between different cluster frameworks or libraries, which is highly inefficient. Therefore, we propose TensorLightning which integrates the widely used data pipeline of Apache Spark with powerful deep learning libraries, Caffe and TensorFlow. TensorLightning embraces a brand-new parameter aggregation algorithm and parallel asynchronous parameter managing schemes to relieve communication discrepancies and overhead. We redesign the elastic averaging stochastic gradient descent algorithm with pruned and sparse form parameters. Our approach provides the fast and flexible DNN training with high accessibility. We evaluated our proposed framework with convolutional neural network and recurrent neural network models; the framework reduces network traffic by 67% with faster convergence.

Compressive sensing-based electrostatic sensor array signal processing and exhausted abnormal debris detecting

Abstract When faults happen at gas path components of gas turbines, some sparsely-distributed and charged debris will be generated and released into the exhaust gas. The debris is called abnormal debris. Electrostatic sensors can detect the debris online and further indicate the faults. It is generally considered that, under a specific working condition, a more serious fault generates more and larger debris, and a piece of larger debris carries more charge. Therefore, the amount and charge of the abnormal debris are important indicators of the fault severity. However, because an electrostatic sensor can only detect the superposed effect on the electrostatic field of all the debris, it can hardly identify the amount and position of the debris. Moreover, because signals of electrostatic sensors depend on not only charge but also position of debris, and the position information is difficult to acquire, measuring debris charge accurately using the electrostatic detecting method is still a technical difficulty. To solve these problems, a hemisphere-shaped electrostatic sensors’ circular array (HSESCA) is used, and an array signal processing method based on compressive sensing (CS) is proposed in this paper. To research in a theoretical framework of CS, the measurement model of the HSESCA is discretized into a sparse representation form by meshing. In this way, the amount and charge of the abnormal debris are described as a sparse vector. It is further reconstructed by constraining l1-norm when solving an underdetermined equation. In addition, a pre-processing method based on singular value decomposition and a result calibration method based on weighted-centroid algorithm are applied to ensure the accuracy of the reconstruction. The proposed method is validated by both numerical simulations and experiments. Reconstruction errors, characteristics of the results and some related factors are discussed.

On the inherent competition between valid and spurious inductive inferences in Boolean data

Inductive inference is the process of extracting general rules from specific observations. This problem also arises in the analysis of biological networks, such as genetic regulatory networks, where the interactions are complex and the observations are incomplete. A typical task in these problems is to extract general interaction rules as combinations of Boolean covariates, that explain a measured response variable. The inductive inference process can be considered as an incompletely specified Boolean function synthesis problem. This incompleteness of the problem will also generate spurious inferences, which are a serious threat to valid inductive inference rules. Using random Boolean data as a null model, here we attempt to measure the competition between valid and spurious inductive inference rules from a given data set. We formulate two greedy search algorithms, which synthesize a given Boolean response variable in a sparse disjunct normal form, and respectively a sparse generalized algebraic normal form of the variables from the observation data, and we evaluate numerically their performance.

Reduced-order modeling and calculation of vortex-induced vibration for large-span bridges

The Volterra theory-based reduced-order modeling (ROM) technique is utilized for simulating fluid-structure interactions of bridge decks during vortex-induced vibration (VIV). To improve the order of nonlinearity adopted in the Volterra series, sparse form kernels are adopted in this study. To illustrate and validate the performance of ROM in simulating fluid-structure interactions of VIV, a real bridge deck is used as a case study. The kernels in the Volterra series are identified using least squares with input–output pairs obtained from a CFD approach. Results indicate that ROM can well reproduce the inherent nature of nonlinearities existing in fluid-structure interactions described by the CFD approach. A method for calculating the VIV of bridges by combining ROM with the structural finite element model is also proposed. The VIV performance of a real bridge is obtained through the proposed method and is compared with field measurements.

Sparse Low-Rank Matrix Approximation for Data Compression

Low-rank matrix approximation (LRMA) is a powerful technique for signal processing and pattern analysis. However, its potential for data compression has not yet been fully investigated. In this paper, we propose sparse LRMA (SLRMA), an effective computational tool for data compression. SLRMA extends conventional LRMA by exploring both the intra and inter coherence of data samples simultaneously. With the aid of prescribed orthogonal transforms (e.g., discrete cosine/wavelet transform and graph transform), SLRMA decomposes a matrix into a product of two smaller matrices, where one matrix is made up of extremely sparse and orthogonal column vectors and the other consists of the transform coefficients. Technically, we formulate SLRMA as a constrained optimization problem, i.e., minimizing the approximation error in the least-squares sense regularized by the $\ell _{0}$ -norm and orthogonality, and solve it using the inexact augmented Lagrangian multiplier method. Through extensive tests on real-world data, such as 2D image sets and 3D dynamic meshes, we observe that: 1) SLRMA empirically converges well; 2) SLRMA can produce approximation error comparable to LRMA but in a much sparse form; and 3) SLRMA-based compression schemes significantly outperform the state of the art in terms of rate-distortion performance.

Sparse bilinear forms for Bochner Riesz multipliers and applications

We use the very recent approach developed by Lacey in [An elementary proof of the A 2 Bound, Israel J. Math., to appear] and extended by Bernicot, Frey and Petermichl in [Sharp weighted norm estimates beyond Calderón-Zygmund theory, Anal. PDE 9 (2016) 1079–1113], in order to control Bochner–Riesz operators by a sparse bilinear form. In this way, new quantitative weighted estimates, as well as vector-valued inequalities are deduced.

Closed-Form Orthogonal Ramanujan Integer Basis

In this letter, a closed-form orthogonal Ramanujan integer basis is proposed and obtained by performing Gram–Schmidt process from the Ramanujan sum and its circular shift. It has a surprisingly simple and sparse form, which is better than the original complete Ramanujan basis. The relationship between the original basis and proposed basis is also clearly illustrated. Therefore, the original basis can be replaced easily.

Generation of complementary sampled phase-only holograms.

If an image is uniformly down-sampled into a sparse form and converted into a hologram, the phase component alone will be adequate to reconstruct the image. However, the appearance of the reconstructed image is degraded with numerous empty holes. In this paper, we present a low complexity and non-iterative solution to this problem. Briefly, two phase-only holograms are generated for an image, each based on a different down-sampling lattice. Subsequently, the holograms are displayed alternately at high frame rate. The reconstructed images of the 2 holograms will appear to be a single, densely sampled image with enhance visual quality.

Sparse reconstruction time delay estimation algorithm based on backtracking filter

The time delay estimation is widely used in wireless location field, and is the research emphasis in complex environment of this field. The current delay estimation algorithms can be classified as five methods of correlation, high-order statistics, self-adaption, maximum likelihood and subspace. However, the existing algorithms can hardly achieve an ideal performance in small sample（single snapshot) and low signal-to-noise ratio environment during wireless location. In order to solve the problem about the insufficiency of the current algorithms in the above conditions, many new methods have been introduced into the delay estimation problem. The compressed sensing sparse reconstruction method has been applied to the signal processing field as a newly-proposed algorithm in recent years. The delay estimation is realized by using the method of sparse reconstruction, in which the sparse representation of the signal is the premise. The rational construction of the measurement matrix and the design of the signal reconstruction algorithm are the core of correct estimation.The purpose of this article is to deal with the lack of measurement data in small sample（single snapshot) and low signal-to-noise ratio environment during wireless location. In the model of wireless location, the signal can be represented as a sparse matrix form by selecting suitable sparse representation matrix. The wireless multi-channel is measured in the time domain, the propagation delay varies with channel and the delay representation in the time domain is sparse, so that it can be directly constructed into the form of sparse signal. Since the necessary and the sufficient condition of the coefficient sparse matrix successfully reconstructed by the measurement matrix are the measurement matrix meeting the restricted isometry property（RIP). The orthogonal measurement matrix based on the steering vector by the method of Gram-Schmidt is proven to achieve the RIP. A novel sparse reconstruction algorithm based on backtracking filter is constructed to estimate the time delay. In order to guarantee that the first selection includes the optimal atom, several atoms are selected. And then the backtracking mechanism is introduced, and the selected atoms are approached by the method of the minimum square to sequence the obtained signals and select the optimal atom. Therefore, this method can be used to guarantee that the optimal atom is selected. The presented algorithm can achieve the delay estimation by using the corresponding relation between the time delay and the measurement matrix in a high precision. Furthermore, the Cramer-Rao bound（CRB) of this model is derived. Finally, simulations show that the proposed approach is suitable for small sample（single snapshot) and low signal-to-noise ratio environment. The proposed method can achieve a higher precision than Root-Music and improve performance at low complexity cost compared with OMP algorithm. The simulation result proves that the algorithm is stable and reliable.

Preconditioners for hierarchical matrices based on their extended sparse form

AbstractIn this paper we consider linear systems with dense-matrices which arise from numerical solution of boundary integral equations. Such matrices can be well-approximated with ℋ

Sparse grids‐based stochastic approximations with applications to aerodynamics sensitivity analysis

SummaryThis work compares sample‐based polynomial surrogates, well suited for moderately high‐dimensional stochastic problems. In particular, generalized polynomial chaos in its sparse pseudospectral form and stochastic collocation methods based on both isotropic and dimension‐adapted sparse grids are considered. Both classes of approximations are compared, and an improved version of a stochastic collocation with dimension adaptivity driven by global sensitivity analysis is proposed. The stochastic approximations efficiency is assessed on multivariate test function and airfoil aerodynamics simulations. The latter study addresses the probabilistic characterization of global aerodynamic coefficients derived from viscous subsonic steady flow about a NACA0015 airfoil in the presence of geometrical and operational uncertainties with both simplified aerodynamics model and Reynolds‐Averaged Navier‐Stokes (RANS) simulation. Sparse pseudospectral and collocation approximations exhibit similar level of performance for isotropic sparse simulation ensembles. Computational savings and accuracy gain of the proposed adaptive stochastic collocation driven by Sobol' indices are patent but remain problem‐dependent. Copyright © 2015 John Wiley & Sons, Ltd.

Numerical Simulation of Antennas with Improved Integral Equation Method* *Supported by in part China Postdoctoral Science Foundation under Grant No. 2014M550839, and in part by the Key Research Program of the Chinese Academy of Sciences under Grant No. KGZD-EW-603

Simulating antennas around a conducting object is a challenge task in computational electromagnetism, which is concerned with the behaviour of electromagnetic fields. To analyze this model efficiently, an improved integral equation-fast Fourier transform (IE-FFT) algorithm is presented in this paper. The proposed scheme employs two Cartesian grids with different size and location to enclose the antenna and the other object, respectively. On the one hand, IE-FFT technique is used to store matrix in a sparse form and accelerate the matrix-vector multiplication for each sub-domain independently. On the other hand, the mutual interaction between sub-domains is taken as the additional exciting voltage in each matrix equation. By updating integral equations several times, the whole electromagnetic system can achieve a stable status. Finally, the validity of the presented method is verified through the analysis of typical antennas in the presence of a conducting object.

Efficient and robust implementation of the TLISMNI method

The dynamics of large scale and complex multibody systems (MBS) that include flexible bodies and contact/impact pairs is governed by stiff equations. Because explicit integration methods can be inefficient and often fail in the case of stiff problems, the use of implicit numerical integration methods is recommended in this case. This paper presents a new and efficient implementation of the two-loop implicit sparse matrix numerical integration (TLISMNI) method proposed for the solution of constrained rigid and flexible MBS differential and algebraic equations. The TLISMNI method has desirable features that include avoiding numerical differentiation of the forces, allowing for an efficient sparse matrix implementation, and ensuring that the kinematic constraint equations are satisfied at the position, velocity and acceleration levels. In this method, a sparse Lagrangian augmented form of the equations of motion that ensures that the constraints are satisfied at the acceleration level is used to solve for all the accelerations and Lagrange multipliers. The generalized coordinate partitioning or recursive methods can be used to satisfy the constraint equations at the position and velocity levels. In order to improve the efficiency and robustness of the TLISMNI method, the simple iteration and the Jacobian-Free Newton−Krylov approaches are used in this investigation. The new implementation is tested using several low order formulas that include Hilber–Hughes–Taylor (HHT), L-stable Park, A-stable Trapezoidal, and A-stable BDF methods. The HHT method allows for including numerical damping. Discussion on which method is more appropriate to use for a certain application is provided. The paper also discusses TLISMNI implementation issues including the step size selection, the convergence criteria, the error control, and the effect of the numerical damping. The use of the computer algorithm described in this paper is demonstrated by solving complex rigid and flexible tracked vehicle models, railroad vehicle models, and very stiff structure problems. The results, obtained using these low order formulas, are compared with the results obtained using the explicit Adams–Bashforth predictor-corrector method. Using the TLISMNI method, which does not require numerical differentiation of the forces and allows for an efficient sparse matrix implementation, for solving complex and stiff structure problems leads to significant computational cost saving as demonstrated in this paper. In some problems, it was found that the new TLISMNI implementation is 35 times faster than the explicit Adams–Bashforth method.

Sparsifying Preconditioner for the Lippmann--Schwinger Equation

The Lippmann--Schwinger equation is an integral equation formulation for acoustic and electromagnetic scattering from an inhomogeneous medium and quantum scattering from a localized potential. We present the sparsifying preconditioner for accelerating the iterative solution of the Lippmann--Schwinger equation. This new preconditioner transforms the discretized Lippmann--Schwinger equation into sparse form and leverages the efficient sparse linear algebra algorithms for computing an approximate inverse. This preconditioner is efficient and easy to implement. When combined with standard iterative methods, it results in almost frequency-independent iteration counts. We provide two- and three-dimensional numerical results to demonstrate the effectiveness of this new preconditioner.

Improving Width-3 Joint Sparse Form to Attain Asymptotically Optimal Complexity on Average Case

Improving Width-3 Joint Sparse Form to Attain Asymptotically Optimal Complexity on Average Case

Classical and Quasi-Newton Methods for a Meteorological Parameters Prediction Boundary Value Problem

We study the numerical solution of a Boundary Value problem for second order quadratic differential equations which arises in the numerical prediction of meteorological parameters. In the present work, we use finite differences and focus on the numerical solution of the resulting nonlinear system. More precisely, we apply classical Newton’s and Quasi-Newton methods paying attention to the special sparse form of the Jacobian matrix and modify appropriately the LU factorization in order to reduce significantly the required floating point operations. Furthermore, we implement and study in depth the behavior of all the proposed procedures in respect of their accuracy, stability and complexity, using data from South East Mediterranean Sea. All the methods are tested with a variety of initial values and their performance is presented and discussed leading to interesting results on the sensitivity of the selected starting point.

Analysis of the Binary Asymmetric Joint Sparse Form

We consider redundant binary joint digital expansions of integer vectors. The redundancy is used to minimize the Hamming weight,i.e., the number of non-zero digit vectors. This leads to efficient linear combination algorithms in abelian groups, which are used in elliptic curve cryptography, for instance.If the digit set is a set of contiguous integers containing zero, a special syntactical condition is known to minimize the weight. We analyse the optimal weight of all non-negative integer vectors with maximum entry less thanN. The expectation and the variance are given with a main term and a periodic fluctuation in the second-order term. Finally, we prove asymptotic normality.