Joint sparse representation for robust multimodal biometrics recognition.

PubMed

Shekhar, Sumit; Patel, Vishal M; Nasrabadi, Nasser M; Chellappa, Rama

2014-01-01

Traditional biometric recognition systems rely on a single biometric signature for authentication. While the advantage of using multiple sources of information for establishing the identity has been widely recognized, computational models for multimodal biometrics recognition have only recently received attention. We propose a multimodal sparse representation method, which represents the test data by a sparse linear combination of training data, while constraining the observations from different modalities of the test subject to share their sparse representations. Thus, we simultaneously take into account correlations as well as coupling information among biometric modalities. A multimodal quality measure is also proposed to weigh each modality as it gets fused. Furthermore, we also kernelize the algorithm to handle nonlinearity in data. The optimization problem is solved using an efficient alternative direction method. Various experiments show that the proposed method compares favorably with competing fusion-based methods.

An information theoretic approach of designing sparse kernel adaptive filters.

PubMed

Liu, Weifeng; Park, Il; Principe, José C

2009-12-01

This paper discusses an information theoretic approach of designing sparse kernel adaptive filters. To determine useful data to be learned and remove redundant ones, a subjective information measure called surprise is introduced. Surprise captures the amount of information a datum contains which is transferable to a learning system. Based on this concept, we propose a systematic sparsification scheme, which can drastically reduce the time and space complexity without harming the performance of kernel adaptive filters. Nonlinear regression, short term chaotic time-series prediction, and long term time-series forecasting examples are presented.

The application of nonlinear programming and collocation to optimal aeroassisted orbital transfers

NASA Astrophysics Data System (ADS)

Shi, Y. Y.; Nelson, R. L.; Young, D. H.; Gill, P. E.; Murray, W.; Saunders, M. A.

1992-01-01

Sequential quadratic programming (SQP) and collocation of the differential equations of motion were applied to optimal aeroassisted orbital transfers. The Optimal Trajectory by Implicit Simulation (OTIS) computer program codes with updated nonlinear programming code (NZSOL) were used as a testbed for the SQP nonlinear programming (NLP) algorithms. The state-of-the-art sparse SQP method is considered to be effective for solving large problems with a sparse matrix. Sparse optimizers are characterized in terms of memory requirements and computational efficiency. For the OTIS problems, less than 10 percent of the Jacobian matrix elements are nonzero. The SQP method encompasses two phases: finding an initial feasible point by minimizing the sum of infeasibilities and minimizing the quadratic objective function within the feasible region. The orbital transfer problem under consideration involves the transfer from a high energy orbit to a low energy orbit.

Sampling schemes and parameter estimation for nonlinear Bernoulli-Gaussian sparse models

NASA Astrophysics Data System (ADS)

Boudineau, Mégane; Carfantan, Hervé; Bourguignon, Sébastien; Bazot, Michael

2016-06-01

We address the sparse approximation problem in the case where the data are approximated by the linear combination of a small number of elementary signals, each of these signals depending non-linearly on additional parameters. Sparsity is explicitly expressed through a Bernoulli-Gaussian hierarchical model in a Bayesian framework. Posterior mean estimates are computed using Markov Chain Monte-Carlo algorithms. We generalize the partially marginalized Gibbs sampler proposed in the linear case in [1], and build an hybrid Hastings-within-Gibbs algorithm in order to account for the nonlinear parameters. All model parameters are then estimated in an unsupervised procedure. The resulting method is evaluated on a sparse spectral analysis problem. It is shown to converge more efficiently than the classical joint estimation procedure, with only a slight increase of the computational cost per iteration, consequently reducing the global cost of the estimation procedure.

The Joker: A Custom Monte Carlo Sampler for Binary-star and Exoplanet Radial Velocity Data

NASA Astrophysics Data System (ADS)

Price-Whelan, Adrian M.; Hogg, David W.; Foreman-Mackey, Daniel; Rix, Hans-Walter

2017-03-01

Given sparse or low-quality radial velocity measurements of a star, there are often many qualitatively different stellar or exoplanet companion orbit models that are consistent with the data. The consequent multimodality of the likelihood function leads to extremely challenging search, optimization, and Markov chain Monte Carlo (MCMC) posterior sampling over the orbital parameters. Here we create a custom Monte Carlo sampler for sparse or noisy radial velocity measurements of two-body systems that can produce posterior samples for orbital parameters even when the likelihood function is poorly behaved. The six standard orbital parameters for a binary system can be split into four nonlinear parameters (period, eccentricity, argument of pericenter, phase) and two linear parameters (velocity amplitude, barycenter velocity). We capitalize on this by building a sampling method in which we densely sample the prior probability density function (pdf) in the nonlinear parameters and perform rejection sampling using a likelihood function marginalized over the linear parameters. With sparse or uninformative data, the sampling obtained by this rejection sampling is generally multimodal and dense. With informative data, the sampling becomes effectively unimodal but too sparse: in these cases we follow the rejection sampling with standard MCMC. The method produces correct samplings in orbital parameters for data that include as few as three epochs. The Joker can therefore be used to produce proper samplings of multimodal pdfs, which are still informative and can be used in hierarchical (population) modeling. We give some examples that show how the posterior pdf depends sensitively on the number and time coverage of the observations and their uncertainties.

Robust representation and recognition of facial emotions using extreme sparse learning.

PubMed

Shojaeilangari, Seyedehsamaneh; Yau, Wei-Yun; Nandakumar, Karthik; Li, Jun; Teoh, Eam Khwang

2015-07-01

Recognition of natural emotions from human faces is an interesting topic with a wide range of potential applications, such as human-computer interaction, automated tutoring systems, image and video retrieval, smart environments, and driver warning systems. Traditionally, facial emotion recognition systems have been evaluated on laboratory controlled data, which is not representative of the environment faced in real-world applications. To robustly recognize the facial emotions in real-world natural situations, this paper proposes an approach called extreme sparse learning, which has the ability to jointly learn a dictionary (set of basis) and a nonlinear classification model. The proposed approach combines the discriminative power of extreme learning machine with the reconstruction property of sparse representation to enable accurate classification when presented with noisy signals and imperfect data recorded in natural settings. In addition, this paper presents a new local spatio-temporal descriptor that is distinctive and pose-invariant. The proposed framework is able to achieve the state-of-the-art recognition accuracy on both acted and spontaneous facial emotion databases.

A Sparse Matrix Approach for Simultaneous Quantification of Nystagmus and Saccade

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.; Stone, Lee; Boyle, Richard D.

2012-01-01

The vestibulo-ocular reflex (VOR) consists of two intermingled non-linear subsystems; namely, nystagmus and saccade. Typically, nystagmus is analysed using a single sufficiently long signal or a concatenation of them. Saccade information is not analysed and discarded due to insufficient data length to provide consistent and minimum variance estimates. This paper presents a novel sparse matrix approach to system identification of the VOR. It allows for the simultaneous estimation of both nystagmus and saccade signals. We show via simulation of the VOR that our technique provides consistent and unbiased estimates in the presence of output additive noise.

Rational Variety Mapping for Contrast-Enhanced Nonlinear Unsupervised Segmentation of Multispectral Images of Unstained Specimen

PubMed Central

Kopriva, Ivica; Hadžija, Mirko; Popović Hadžija, Marijana; Korolija, Marina; Cichocki, Andrzej

2011-01-01

A methodology is proposed for nonlinear contrast-enhanced unsupervised segmentation of multispectral (color) microscopy images of principally unstained specimens. The methodology exploits spectral diversity and spatial sparseness to find anatomical differences between materials (cells, nuclei, and background) present in the image. It consists of rth-order rational variety mapping (RVM) followed by matrix/tensor factorization. Sparseness constraint implies duality between nonlinear unsupervised segmentation and multiclass pattern assignment problems. Classes not linearly separable in the original input space become separable with high probability in the higher-dimensional mapped space. Hence, RVM mapping has two advantages: it takes implicitly into account nonlinearities present in the image (ie, they are not required to be known) and it increases spectral diversity (ie, contrast) between materials, due to increased dimensionality of the mapped space. This is expected to improve performance of systems for automated classification and analysis of microscopic histopathological images. The methodology was validated using RVM of the second and third orders of the experimental multispectral microscopy images of unstained sciatic nerve fibers (nervus ischiadicus) and of unstained white pulp in the spleen tissue, compared with a manually defined ground truth labeled by two trained pathophysiologists. The methodology can also be useful for additional contrast enhancement of images of stained specimens. PMID:21708116

A scalable nonlinear fluid-structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

NASA Astrophysics Data System (ADS)

Kong, Fande; Cai, Xiao-Chuan

2017-07-01

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear in many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexact Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here "geometry" includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.

A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

DOE PAGES

Kong, Fande; Cai, Xiao-Chuan

2017-03-24

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexactmore » Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here ''geometry'' includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.« less

Convergence Speed of a Dynamical System for Sparse Recovery

NASA Astrophysics Data System (ADS)

Balavoine, Aurele; Rozell, Christopher J.; Romberg, Justin

2013-09-01

This paper studies the convergence rate of a continuous-time dynamical system for L1-minimization, known as the Locally Competitive Algorithm (LCA). Solving L1-minimization} problems efficiently and rapidly is of great interest to the signal processing community, as these programs have been shown to recover sparse solutions to underdetermined systems of linear equations and come with strong performance guarantees. The LCA under study differs from the typical L1 solver in that it operates in continuous time: instead of being specified by discrete iterations, it evolves according to a system of nonlinear ordinary differential equations. The LCA is constructed from simple components, giving it the potential to be implemented as a large-scale analog circuit. The goal of this paper is to give guarantees on the convergence time of the LCA system. To do so, we analyze how the LCA evolves as it is recovering a sparse signal from underdetermined measurements. We show that under appropriate conditions on the measurement matrix and the problem parameters, the path the LCA follows can be described as a sequence of linear differential equations, each with a small number of active variables. This allows us to relate the convergence time of the system to the restricted isometry constant of the matrix. Interesting parallels to sparse-recovery digital solvers emerge from this study. Our analysis covers both the noisy and noiseless settings and is supported by simulation results.

Incomplete Gröbner basis as a preconditioner for polynomial systems

NASA Astrophysics Data System (ADS)

Sun, Yang; Tao, Yu-Hui; Bai, Feng-Shan

2009-04-01

Precondition plays a critical role in the numerical methods for large and sparse linear systems. It is also true for nonlinear algebraic systems. In this paper incomplete Gröbner basis (IGB) is proposed as a preconditioner of homotopy methods for polynomial systems of equations, which transforms a deficient system into a system with the same finite solutions, but smaller degree. The reduced system can thus be solved faster. Numerical results show the efficiency of the preconditioner.

Rational variety mapping for contrast-enhanced nonlinear unsupervised segmentation of multispectral images of unstained specimen.

PubMed

Kopriva, Ivica; Hadžija, Mirko; Popović Hadžija, Marijana; Korolija, Marina; Cichocki, Andrzej

2011-08-01

A methodology is proposed for nonlinear contrast-enhanced unsupervised segmentation of multispectral (color) microscopy images of principally unstained specimens. The methodology exploits spectral diversity and spatial sparseness to find anatomical differences between materials (cells, nuclei, and background) present in the image. It consists of rth-order rational variety mapping (RVM) followed by matrix/tensor factorization. Sparseness constraint implies duality between nonlinear unsupervised segmentation and multiclass pattern assignment problems. Classes not linearly separable in the original input space become separable with high probability in the higher-dimensional mapped space. Hence, RVM mapping has two advantages: it takes implicitly into account nonlinearities present in the image (ie, they are not required to be known) and it increases spectral diversity (ie, contrast) between materials, due to increased dimensionality of the mapped space. This is expected to improve performance of systems for automated classification and analysis of microscopic histopathological images. The methodology was validated using RVM of the second and third orders of the experimental multispectral microscopy images of unstained sciatic nerve fibers (nervus ischiadicus) and of unstained white pulp in the spleen tissue, compared with a manually defined ground truth labeled by two trained pathophysiologists. The methodology can also be useful for additional contrast enhancement of images of stained specimens. Copyright © 2011 American Society for Investigative Pathology. Published by Elsevier Inc. All rights reserved.

Nonlinear Hebbian Learning as a Unifying Principle in Receptive Field Formation.

PubMed

Brito, Carlos S N; Gerstner, Wulfram

2016-09-01

The development of sensory receptive fields has been modeled in the past by a variety of models including normative models such as sparse coding or independent component analysis and bottom-up models such as spike-timing dependent plasticity or the Bienenstock-Cooper-Munro model of synaptic plasticity. Here we show that the above variety of approaches can all be unified into a single common principle, namely nonlinear Hebbian learning. When nonlinear Hebbian learning is applied to natural images, receptive field shapes were strongly constrained by the input statistics and preprocessing, but exhibited only modest variation across different choices of nonlinearities in neuron models or synaptic plasticity rules. Neither overcompleteness nor sparse network activity are necessary for the development of localized receptive fields. The analysis of alternative sensory modalities such as auditory models or V2 development lead to the same conclusions. In all examples, receptive fields can be predicted a priori by reformulating an abstract model as nonlinear Hebbian learning. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities.

Nonlinear Hebbian Learning as a Unifying Principle in Receptive Field Formation

PubMed Central

Gerstner, Wulfram

2016-01-01

The development of sensory receptive fields has been modeled in the past by a variety of models including normative models such as sparse coding or independent component analysis and bottom-up models such as spike-timing dependent plasticity or the Bienenstock-Cooper-Munro model of synaptic plasticity. Here we show that the above variety of approaches can all be unified into a single common principle, namely nonlinear Hebbian learning. When nonlinear Hebbian learning is applied to natural images, receptive field shapes were strongly constrained by the input statistics and preprocessing, but exhibited only modest variation across different choices of nonlinearities in neuron models or synaptic plasticity rules. Neither overcompleteness nor sparse network activity are necessary for the development of localized receptive fields. The analysis of alternative sensory modalities such as auditory models or V2 development lead to the same conclusions. In all examples, receptive fields can be predicted a priori by reformulating an abstract model as nonlinear Hebbian learning. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities. PMID:27690349

Applications of compressed sensing image reconstruction to sparse view phase tomography

NASA Astrophysics Data System (ADS)

Ueda, Ryosuke; Kudo, Hiroyuki; Dong, Jian

2017-10-01

X-ray phase CT has a potential to give the higher contrast in soft tissue observations. To shorten the measure- ment time, sparse-view CT data acquisition has been attracting the attention. This paper applies two major compressed sensing (CS) approaches to image reconstruction in the x-ray sparse-view phase tomography. The first CS approach is the standard Total Variation (TV) regularization. The major drawbacks of TV regularization are a patchy artifact and loss in smooth intensity changes due to the piecewise constant nature of image model. The second CS method is a relatively new approach of CS which uses a nonlinear smoothing filter to design the regularization term. The nonlinear filter based CS is expected to reduce the major artifact in the TV regular- ization. The both cost functions can be minimized by the very fast iterative reconstruction method. However, in the past research activities, it is not clearly demonstrated how much image quality difference occurs between the TV regularization and the nonlinear filter based CS in x-ray phase CT applications. We clarify the issue by applying the two CS applications to the case of x-ray phase tomography. We provide results with numerically simulated data, which demonstrates that the nonlinear filter based CS outperforms the TV regularization in terms of textures and smooth intensity changes.

Statistical inference methods for sparse biological time series data.

PubMed

Ndukum, Juliet; Fonseca, Luís L; Santos, Helena; Voit, Eberhard O; Datta, Susmita

2011-04-25

Comparing metabolic profiles under different biological perturbations has become a powerful approach to investigating the functioning of cells. The profiles can be taken as single snapshots of a system, but more information is gained if they are measured longitudinally over time. The results are short time series consisting of relatively sparse data that cannot be analyzed effectively with standard time series techniques, such as autocorrelation and frequency domain methods. In this work, we study longitudinal time series profiles of glucose consumption in the yeast Saccharomyces cerevisiae under different temperatures and preconditioning regimens, which we obtained with methods of in vivo nuclear magnetic resonance (NMR) spectroscopy. For the statistical analysis we first fit several nonlinear mixed effect regression models to the longitudinal profiles and then used an ANOVA likelihood ratio method in order to test for significant differences between the profiles. The proposed methods are capable of distinguishing metabolic time trends resulting from different treatments and associate significance levels to these differences. Among several nonlinear mixed-effects regression models tested, a three-parameter logistic function represents the data with highest accuracy. ANOVA and likelihood ratio tests suggest that there are significant differences between the glucose consumption rate profiles for cells that had been--or had not been--preconditioned by heat during growth. Furthermore, pair-wise t-tests reveal significant differences in the longitudinal profiles for glucose consumption rates between optimal conditions and heat stress, optimal and recovery conditions, and heat stress and recovery conditions (p-values <0.0001). We have developed a nonlinear mixed effects model that is appropriate for the analysis of sparse metabolic and physiological time profiles. The model permits sound statistical inference procedures, based on ANOVA likelihood ratio tests, for testing the significance of differences between short time course data under different biological perturbations.

Configurable hardware integrate and fire neurons for sparse approximation.

PubMed

Shapero, Samuel; Rozell, Christopher; Hasler, Paul

2013-09-01

Sparse approximation is an important optimization problem in signal and image processing applications. A Hopfield-Network-like system of integrate and fire (IF) neurons is proposed as a solution, using the Locally Competitive Algorithm (LCA) to solve an overcomplete L1 sparse approximation problem. A scalable system architecture is described, including IF neurons with a nonlinear firing function, and current-based synapses to provide linear computation. A network of 18 neurons with 12 inputs is implemented on the RASP 2.9v chip, a Field Programmable Analog Array (FPAA) with directly programmable floating gate elements. Said system uses over 1400 floating gates, the largest system programmed on a FPAA to date. The circuit successfully reproduced the outputs of a digital optimization program, converging to within 4.8% RMS, and an objective cost only 1.7% higher on average. The active circuit consumed 559 μA of current at 2.4 V and converges on solutions in 25 μs, with measurement of the converged spike rate taking an additional 1 ms. Extrapolating the scaling trends to a N=1000 node system, the spiking LCA compares favorably with state-of-the-art digital solutions, and analog solutions using a non-spiking approach. Copyright © 2013 Elsevier Ltd. All rights reserved.

Precession missile feature extraction using sparse component analysis of radar measurements

NASA Astrophysics Data System (ADS)

Liu, Lihua; Du, Xiaoyong; Ghogho, Mounir; Hu, Weidong; McLernon, Des

2012-12-01

According to the working mode of the ballistic missile warning radar (BMWR), the radar return from the BMWR is usually sparse. To recognize and identify the warhead, it is necessary to extract the precession frequency and the locations of the scattering centers of the missile. This article first analyzes the radar signal model of the precessing conical missile during flight and develops the sparse dictionary which is parameterized by the unknown precession frequency. Based on the sparse dictionary, the sparse signal model is then established. A nonlinear least square estimation is first applied to roughly extract the precession frequency in the sparse dictionary. Based on the time segmented radar signal, a sparse component analysis method using the orthogonal matching pursuit algorithm is then proposed to jointly estimate the precession frequency and the scattering centers of the missile. Simulation results illustrate the validity of the proposed method.

Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions.

PubMed

Omori, Toshiaki; Kuwatani, Tatsu; Okamoto, Atsushi; Hukushima, Koji

2016-09-01

It is essential to extract nonlinear dynamics from time-series data as an inverse problem in natural sciences. We propose a Bayesian statistical framework for extracting nonlinear dynamics of surface heterogeneous reactions from sparse and noisy observable data. Surface heterogeneous reactions are chemical reactions with conjugation of multiple phases, and they have the intrinsic nonlinearity of their dynamics caused by the effect of surface-area between different phases. We adapt a belief propagation method and an expectation-maximization (EM) algorithm to partial observation problem, in order to simultaneously estimate the time course of hidden variables and the kinetic parameters underlying dynamics. The proposed belief propagation method is performed by using sequential Monte Carlo algorithm in order to estimate nonlinear dynamical system. Using our proposed method, we show that the rate constants of dissolution and precipitation reactions, which are typical examples of surface heterogeneous reactions, as well as the temporal changes of solid reactants and products, were successfully estimated only from the observable temporal changes in the concentration of the dissolved intermediate product.

Nonlinear effects in the time measurement device based on surface acoustic wave filter excitation.

PubMed

Prochazka, Ivan; Panek, Petr

2009-07-01

A transversal surface acoustic wave filter has been used as a time interpolator in a time interval measurement device. We are presenting the experiments and results of an analysis of the nonlinear effects in such a time interpolator. The analysis shows that the nonlinear distortion in the time interpolator circuits causes a deterministic measurement error which can be understood as the time interpolation nonlinearity. The dependence of this error on time of the measured events can be expressed as a sparse Fourier series thus it usually oscillates very quickly in comparison to the clock period. The theoretical model is in good agreement with experiments carried out on an experimental two-channel timing system. Using highly linear amplifiers in the time interpolator and adjusting the filter excitation level to the optimum, we have achieved the interpolation nonlinearity below 0.2 ps. The overall single-shot precision of the experimental timing device is 0.9 ps rms in each channel.

Nonlinear Estimation With Sparse Temporal Measurements

DTIC Science & Technology

2016-09-01

Kalman filter , the extended Kalman filter (EKF) and unscented Kalman filter (UKF) are commonly used in practical application. The Kalman filter is an...optimal estimator for linear systems; the EKF and UKF are sub-optimal approximations of the Kalman filter . The EKF uses a first-order Taylor series...propagated covariance is compared for similarity with a Monte Carlo propagation. The similarity of the covariance matrices is shown to predict filter

Linear and nonlinear trending and prediction for AVHRR time series data

NASA Technical Reports Server (NTRS)

Smid, J.; Volf, P.; Slama, M.; Palus, M.

1995-01-01

The variability of AVHRR calibration coefficient in time was analyzed using algorithms of linear and non-linear time series analysis. Specifically we have used the spline trend modeling, autoregressive process analysis, incremental neural network learning algorithm and redundancy functional testing. The analysis performed on available AVHRR data sets revealed that (1) the calibration data have nonlinear dependencies, (2) the calibration data depend strongly on the target temperature, (3) both calibration coefficients and the temperature time series can be modeled, in the first approximation, as autonomous dynamical systems, (4) the high frequency residuals of the analyzed data sets can be best modeled as an autoregressive process of the 10th degree. We have dealt with a nonlinear identification problem and the problem of noise filtering (data smoothing). The system identification and filtering are significant problems for AVHRR data sets. The algorithms outlined in this study can be used for the future EOS missions. Prediction and smoothing algorithms for time series of calibration data provide a functional characterization of the data. Those algorithms can be particularly useful when calibration data are incomplete or sparse.

Experiments with conjugate gradient algorithms for homotopy curve tracking

NASA Technical Reports Server (NTRS)

Irani, Kashmira M.; Ribbens, Calvin J.; Watson, Layne T.; Kamat, Manohar P.; Walker, Homer F.

1991-01-01

There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Here, variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. The test problems used include actual large scale, sparse structural mechanics problems.

Signal-Preserving Erratic Noise Attenuation via Iterative Robust Sparsity-Promoting Filter

DOE PAGES

Zhao, Qiang; Du, Qizhen; Gong, Xufei; ...

2018-04-06

Sparse domain thresholding filters operating in a sparse domain are highly effective in removing Gaussian random noise under Gaussian distribution assumption. Erratic noise, which designates non-Gaussian noise that consists of large isolated events with known or unknown distribution, also needs to be explicitly taken into account. However, conventional sparse domain thresholding filters based on the least-squares (LS) criterion are severely sensitive to data with high-amplitude and non-Gaussian noise, i.e., the erratic noise, which makes the suppression of this type of noise extremely challenging. Here, in this paper, we present a robust sparsity-promoting denoising model, in which the LS criterion ismore » replaced by the Huber criterion to weaken the effects of erratic noise. The random and erratic noise is distinguished by using a data-adaptive parameter in the presented method, where random noise is described by mean square, while the erratic noise is downweighted through a damped weight. Different from conventional sparse domain thresholding filters, definition of the misfit between noisy data and recovered signal via the Huber criterion results in a nonlinear optimization problem. With the help of theoretical pseudoseismic data, an iterative robust sparsity-promoting filter is proposed to transform the nonlinear optimization problem into a linear LS problem through an iterative procedure. The main advantage of this transformation is that the nonlinear denoising filter can be solved by conventional LS solvers. Lastly, tests with several data sets demonstrate that the proposed denoising filter can successfully attenuate the erratic noise without damaging useful signal when compared with conventional denoising approaches based on the LS criterion.« less

Signal-Preserving Erratic Noise Attenuation via Iterative Robust Sparsity-Promoting Filter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Qiang; Du, Qizhen; Gong, Xufei

Sparse domain thresholding filters operating in a sparse domain are highly effective in removing Gaussian random noise under Gaussian distribution assumption. Erratic noise, which designates non-Gaussian noise that consists of large isolated events with known or unknown distribution, also needs to be explicitly taken into account. However, conventional sparse domain thresholding filters based on the least-squares (LS) criterion are severely sensitive to data with high-amplitude and non-Gaussian noise, i.e., the erratic noise, which makes the suppression of this type of noise extremely challenging. Here, in this paper, we present a robust sparsity-promoting denoising model, in which the LS criterion ismore » replaced by the Huber criterion to weaken the effects of erratic noise. The random and erratic noise is distinguished by using a data-adaptive parameter in the presented method, where random noise is described by mean square, while the erratic noise is downweighted through a damped weight. Different from conventional sparse domain thresholding filters, definition of the misfit between noisy data and recovered signal via the Huber criterion results in a nonlinear optimization problem. With the help of theoretical pseudoseismic data, an iterative robust sparsity-promoting filter is proposed to transform the nonlinear optimization problem into a linear LS problem through an iterative procedure. The main advantage of this transformation is that the nonlinear denoising filter can be solved by conventional LS solvers. Lastly, tests with several data sets demonstrate that the proposed denoising filter can successfully attenuate the erratic noise without damaging useful signal when compared with conventional denoising approaches based on the LS criterion.« less

Blended particle filters for large-dimensional chaotic dynamical systems

PubMed Central

Majda, Andrew J.; Qi, Di; Sapsis, Themistoklis P.

2014-01-01

A major challenge in contemporary data science is the development of statistically accurate particle filters to capture non-Gaussian features in large-dimensional chaotic dynamical systems. Blended particle filters that capture non-Gaussian features in an adaptively evolving low-dimensional subspace through particles interacting with evolving Gaussian statistics on the remaining portion of phase space are introduced here. These blended particle filters are constructed in this paper through a mathematical formalism involving conditional Gaussian mixtures combined with statistically nonlinear forecast models compatible with this structure developed recently with high skill for uncertainty quantification. Stringent test cases for filtering involving the 40-dimensional Lorenz 96 model with a 5-dimensional adaptive subspace for nonlinear blended filtering in various turbulent regimes with at least nine positive Lyapunov exponents are used here. These cases demonstrate the high skill of the blended particle filter algorithms in capturing both highly non-Gaussian dynamical features as well as crucial nonlinear statistics for accurate filtering in extreme filtering regimes with sparse infrequent high-quality observations. The formalism developed here is also useful for multiscale filtering of turbulent systems and a simple application is sketched below. PMID:24825886

An Optimization Code for Nonlinear Transient Problems of a Large Scale Multidisciplinary Mathematical Model

NASA Astrophysics Data System (ADS)

Takasaki, Koichi

This paper presents a program for the multidisciplinary optimization and identification problem of the nonlinear model of large aerospace vehicle structures. The program constructs the global matrix of the dynamic system in the time direction by the p-version finite element method (pFEM), and the basic matrix for each pFEM node in the time direction is described by a sparse matrix similarly to the static finite element problem. The algorithm used by the program does not require the Hessian matrix of the objective function and so has low memory requirements. It also has a relatively low computational cost, and is suited to parallel computation. The program was integrated as a solver module of the multidisciplinary analysis system CUMuLOUS (Computational Utility for Multidisciplinary Large scale Optimization of Undense System) which is under development by the Aerospace Research and Development Directorate (ARD) of the Japan Aerospace Exploration Agency (JAXA).

An adaptive sparse-grid high-order stochastic collocation method for Bayesian inference in groundwater reactive transport modeling

NASA Astrophysics Data System (ADS)

Zhang, Guannan; Lu, Dan; Ye, Ming; Gunzburger, Max; Webster, Clayton

2013-10-01

Bayesian analysis has become vital to uncertainty quantification in groundwater modeling, but its application has been hindered by the computational cost associated with numerous model executions required by exploring the posterior probability density function (PPDF) of model parameters. This is particularly the case when the PPDF is estimated using Markov Chain Monte Carlo (MCMC) sampling. In this study, a new approach is developed to improve the computational efficiency of Bayesian inference by constructing a surrogate of the PPDF, using an adaptive sparse-grid high-order stochastic collocation (aSG-hSC) method. Unlike previous works using first-order hierarchical basis, this paper utilizes a compactly supported higher-order hierarchical basis to construct the surrogate system, resulting in a significant reduction in the number of required model executions. In addition, using the hierarchical surplus as an error indicator allows locally adaptive refinement of sparse grids in the parameter space, which further improves computational efficiency. To efficiently build the surrogate system for the PPDF with multiple significant modes, optimization techniques are used to identify the modes, for which high-probability regions are defined and components of the aSG-hSC approximation are constructed. After the surrogate is determined, the PPDF can be evaluated by sampling the surrogate system directly without model execution, resulting in improved efficiency of the surrogate-based MCMC compared with conventional MCMC. The developed method is evaluated using two synthetic groundwater reactive transport models. The first example involves coupled linear reactions and demonstrates the accuracy of our high-order hierarchical basis approach in approximating high-dimensional posteriori distribution. The second example is highly nonlinear because of the reactions of uranium surface complexation, and demonstrates how the iterative aSG-hSC method is able to capture multimodal and non-Gaussian features of PPDF caused by model nonlinearity. Both experiments show that aSG-hSC is an effective and efficient tool for Bayesian inference.

Local structure preserving sparse coding for infrared target recognition

PubMed Central

Han, Jing; Yue, Jiang; Zhang, Yi; Bai, Lianfa

2017-01-01

Sparse coding performs well in image classification. However, robust target recognition requires a lot of comprehensive template images and the sparse learning process is complex. We incorporate sparsity into a template matching concept to construct a local sparse structure matching (LSSM) model for general infrared target recognition. A local structure preserving sparse coding (LSPSc) formulation is proposed to simultaneously preserve the local sparse and structural information of objects. By adding a spatial local structure constraint into the classical sparse coding algorithm, LSPSc can improve the stability of sparse representation for targets and inhibit background interference in infrared images. Furthermore, a kernel LSPSc (K-LSPSc) formulation is proposed, which extends LSPSc to the kernel space to weaken the influence of the linear structure constraint in nonlinear natural data. Because of the anti-interference and fault-tolerant capabilities, both LSPSc- and K-LSPSc-based LSSM can implement target identification based on a simple template set, which just needs several images containing enough local sparse structures to learn a sufficient sparse structure dictionary of a target class. Specifically, this LSSM approach has stable performance in the target detection with scene, shape and occlusions variations. High performance is demonstrated on several datasets, indicating robust infrared target recognition in diverse environments and imaging conditions. PMID:28323824

Online sparse Gaussian process based human motion intent learning for an electrically actuated lower extremity exoskeleton.

PubMed

Long, Yi; Du, Zhi-Jiang; Chen, Chao-Feng; Dong, Wei; Wang, Wei-Dong

2017-07-01

The most important step for lower extremity exoskeleton is to infer human motion intent (HMI), which contributes to achieve human exoskeleton collaboration. Since the user is in the control loop, the relationship between human robot interaction (HRI) information and HMI is nonlinear and complicated, which is difficult to be modeled by using mathematical approaches. The nonlinear approximation can be learned by using machine learning approaches. Gaussian Process (GP) regression is suitable for high-dimensional and small-sample nonlinear regression problems. GP regression is restrictive for large data sets due to its computation complexity. In this paper, an online sparse GP algorithm is constructed to learn the HMI. The original training dataset is collected when the user wears the exoskeleton system with friction compensation to perform unconstrained movement as far as possible. The dataset has two kinds of data, i.e., (1) physical HRI, which is collected by torque sensors placed at the interaction cuffs for the active joints, i.e., knee joints; (2) joint angular position, which is measured by optical position sensors. To reduce the computation complexity of GP, grey relational analysis (GRA) is utilized to specify the original dataset and provide the final training dataset. Those hyper-parameters are optimized offline by maximizing marginal likelihood and will be applied into online GP regression algorithm. The HMI, i.e., angular position of human joints, will be regarded as the reference trajectory for the mechanical legs. To verify the effectiveness of the proposed algorithm, experiments are performed on a subject at a natural speed. The experimental results show the HMI can be obtained in real time, which can be extended and employed in the similar exoskeleton systems.

Advanced Kalman Filter for Real-Time Responsiveness in Complex Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Welch, Gregory Francis; Zhang, Jinghe

2014-06-10

Complex engineering systems pose fundamental challenges in real-time operations and control because they are highly dynamic systems consisting of a large number of elements with severe nonlinearities and discontinuities. Today’s tools for real-time complex system operations are mostly based on steady state models, unable to capture the dynamic nature and too slow to prevent system failures. We developed advanced Kalman filtering techniques and the formulation of dynamic state estimation using Kalman filtering techniques to capture complex system dynamics in aiding real-time operations and control. In this work, we looked at complex system issues including severe nonlinearity of system equations, discontinuitiesmore » caused by system controls and network switches, sparse measurements in space and time, and real-time requirements of power grid operations. We sought to bridge the disciplinary boundaries between Computer Science and Power Systems Engineering, by introducing methods that leverage both existing and new techniques. While our methods were developed in the context of electrical power systems, they should generalize to other large-scale scientific and engineering applications.« less

Investigation into image quality difference between total variation and nonlinear sparsifying transform based compressed sensing

NASA Astrophysics Data System (ADS)

Dong, Jian; Kudo, Hiroyuki

2017-03-01

Compressed sensing (CS) is attracting growing concerns in sparse-view computed tomography (CT) image reconstruction. The most standard approach of CS is total variation (TV) minimization. However, images reconstructed by TV usually suffer from distortions, especially in reconstruction of practical CT images, in forms of patchy artifacts, improper serrate edges and loss of image textures. Most existing CS approaches including TV achieve image quality improvement by applying linear transforms to object image, but linear transforms usually fail to take discontinuities into account, such as edges and image textures, which is considered to be the key reason for image distortions. Actually, discussions on nonlinear filter based image processing has a long history, leading us to clarify that the nonlinear filters yield better results compared to linear filters in image processing task such as denoising. Median root prior was first utilized by Alenius as nonlinear transform in CT image reconstruction, with significant gains obtained. Subsequently, Zhang developed the application of nonlocal means-based CS. A fact is gradually becoming clear that the nonlinear transform based CS has superiority in improving image quality compared with the linear transform based CS. However, it has not been clearly concluded in any previous paper within the scope of our knowledge. In this work, we investigated the image quality differences between the conventional TV minimization and nonlinear sparsifying transform based CS, as well as image quality differences among different nonlinear sparisying transform based CSs in sparse-view CT image reconstruction. Additionally, we accelerated the implementation of nonlinear sparsifying transform based CS algorithm.

Online learning control using adaptive critic designs with sparse kernel machines.

PubMed

Xu, Xin; Hou, Zhongsheng; Lian, Chuanqiang; He, Haibo

2013-05-01

In the past decade, adaptive critic designs (ACDs), including heuristic dynamic programming (HDP), dual heuristic programming (DHP), and their action-dependent ones, have been widely studied to realize online learning control of dynamical systems. However, because neural networks with manually designed features are commonly used to deal with continuous state and action spaces, the generalization capability and learning efficiency of previous ACDs still need to be improved. In this paper, a novel framework of ACDs with sparse kernel machines is presented by integrating kernel methods into the critic of ACDs. To improve the generalization capability as well as the computational efficiency of kernel machines, a sparsification method based on the approximately linear dependence analysis is used. Using the sparse kernel machines, two kernel-based ACD algorithms, that is, kernel HDP (KHDP) and kernel DHP (KDHP), are proposed and their performance is analyzed both theoretically and empirically. Because of the representation learning and generalization capability of sparse kernel machines, KHDP and KDHP can obtain much better performance than previous HDP and DHP with manually designed neural networks. Simulation and experimental results of two nonlinear control problems, that is, a continuous-action inverted pendulum problem and a ball and plate control problem, demonstrate the effectiveness of the proposed kernel ACD methods.

Sparse bursts optimize information transmission in a multiplexed neural code.

PubMed

Naud, Richard; Sprekeler, Henning

2018-06-22

Many cortical neurons combine the information ascending and descending the cortical hierarchy. In the classical view, this information is combined nonlinearly to give rise to a single firing-rate output, which collapses all input streams into one. We analyze the extent to which neurons can simultaneously represent multiple input streams by using a code that distinguishes spike timing patterns at the level of a neural ensemble. Using computational simulations constrained by experimental data, we show that cortical neurons are well suited to generate such multiplexing. Interestingly, this neural code maximizes information for short and sparse bursts, a regime consistent with in vivo recordings. Neurons can also demultiplex this information, using specific connectivity patterns. The anatomy of the adult mammalian cortex suggests that these connectivity patterns are used by the nervous system to maintain sparse bursting and optimal multiplexing. Contrary to firing-rate coding, our findings indicate that the physiology and anatomy of the cortex may be interpreted as optimizing the transmission of multiple independent signals to different targets. Copyright © 2018 the Author(s). Published by PNAS.

Three-dimensional image authentication scheme using sparse phase information in double random phase encoded integral imaging.

PubMed

Yi, Faliu; Jeoung, Yousun; Moon, Inkyu

2017-05-20

In recent years, many studies have focused on authentication of two-dimensional (2D) images using double random phase encryption techniques. However, there has been little research on three-dimensional (3D) imaging systems, such as integral imaging, for 3D image authentication. We propose a 3D image authentication scheme based on a double random phase integral imaging method. All of the 2D elemental images captured through integral imaging are encrypted with a double random phase encoding algorithm and only partial phase information is reserved. All the amplitude and other miscellaneous phase information in the encrypted elemental images is discarded. Nevertheless, we demonstrate that 3D images from integral imaging can be authenticated at different depths using a nonlinear correlation method. The proposed 3D image authentication algorithm can provide enhanced information security because the decrypted 2D elemental images from the sparse phase cannot be easily observed by the naked eye. Additionally, using sparse phase images without any amplitude information can greatly reduce data storage costs and aid in image compression and data transmission.

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

DOE PAGES

Desai, Ajit; Khalil, Mohammad; Pettit, Chris; ...

2017-09-21

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolutionmore » in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.« less

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Desai, Ajit; Khalil, Mohammad; Pettit, Chris

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolutionmore » in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.« less

Sparsity-Cognizant Algorithms with Applications to Communications, Signal Processing, and the Smart Grid

NASA Astrophysics Data System (ADS)

Zhu, Hao

Sparsity plays an instrumental role in a plethora of scientific fields, including statistical inference for variable selection, parsimonious signal representations, and solving under-determined systems of linear equations - what has led to the ground-breaking result of compressive sampling (CS). This Thesis leverages exciting ideas of sparse signal reconstruction to develop sparsity-cognizant algorithms, and analyze their performance. The vision is to devise tools exploiting the 'right' form of sparsity for the 'right' application domain of multiuser communication systems, array signal processing systems, and the emerging challenges in the smart power grid. Two important power system monitoring tasks are addressed first by capitalizing on the hidden sparsity. To robustify power system state estimation, a sparse outlier model is leveraged to capture the possible corruption in every datum, while the problem nonconvexity due to nonlinear measurements is handled using the semidefinite relaxation technique. Different from existing iterative methods, the proposed algorithm approximates well the global optimum regardless of the initialization. In addition, for enhanced situational awareness, a novel sparse overcomplete representation is introduced to capture (possibly multiple) line outages, and develop real-time algorithms for solving the combinatorially complex identification problem. The proposed algorithms exhibit near-optimal performance while incurring only linear complexity in the number of lines, which makes it possible to quickly bring contingencies to attention. This Thesis also accounts for two basic issues in CS, namely fully-perturbed models and the finite alphabet property. The sparse total least-squares (S-TLS) approach is proposed to furnish CS algorithms for fully-perturbed linear models, leading to statistically optimal and computationally efficient solvers. The S-TLS framework is well motivated for grid-based sensing applications and exhibits higher accuracy than existing sparse algorithms. On the other hand, exploiting the finite alphabet of unknown signals emerges naturally in communication systems, along with sparsity coming from the low activity of each user. Compared to approaches only accounting for either one of the two, joint exploitation of both leads to statistically optimal detectors with improved error performance.

Compressive sensing for single-shot two-dimensional coherent spectroscopy

NASA Astrophysics Data System (ADS)

Harel, E.; Spencer, A.; Spokoyny, B.

2017-02-01

In this work, we explore the use of compressive sensing for the rapid acquisition of two-dimensional optical spectra that encodes the electronic structure and ultrafast dynamics of condensed-phase molecular species. Specifically, we have developed a means to combine multiplexed single-element detection and single-shot and phase-resolved two-dimensional coherent spectroscopy. The method described, which we call Single Point Array Reconstruction by Spatial Encoding (SPARSE) eliminates the need for costly array detectors while speeding up acquisition by several orders of magnitude compared to scanning methods. Physical implementation of SPARSE is facilitated by combining spatiotemporal encoding of the nonlinear optical response and signal modulation by a high-speed digital micromirror device. We demonstrate the approach by investigating a well-characterized cyanine molecule and a photosynthetic pigment-protein complex. Hadamard and compressive sensing algorithms are demonstrated, with the latter achieving compression factors as high as ten. Both show good agreement with directly detected spectra. We envision a myriad of applications in nonlinear spectroscopy using SPARSE with broadband femtosecond light sources in so-far unexplored regions of the electromagnetic spectrum.

Discovering governing equations from data by sparse identification of nonlinear dynamics

NASA Astrophysics Data System (ADS)

Brunton, Steven

The ability to discover physical laws and governing equations from data is one of humankind's greatest intellectual achievements. A quantitative understanding of dynamic constraints and balances in nature has facilitated rapid development of knowledge and enabled advanced technology, including aircraft, combustion engines, satellites, and electrical power. There are many more critical data-driven problems, such as understanding cognition from neural recordings, inferring patterns in climate, determining stability of financial markets, predicting and suppressing the spread of disease, and controlling turbulence for greener transportation and energy. With abundant data and elusive laws, data-driven discovery of dynamics will continue to play an increasingly important role in these efforts. This work develops a general framework to discover the governing equations underlying a dynamical system simply from data measurements, leveraging advances in sparsity-promoting techniques and machine learning. The resulting models are parsimonious, balancing model complexity with descriptive ability while avoiding overfitting. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions. This perspective, combining dynamical systems with machine learning and sparse sensing, is explored with the overarching goal of real-time closed-loop feedback control of complex systems. This is joint work with Joshua L. Proctor and J. Nathan Kutz. Video Abstract: https://www.youtube.com/watch?v=gSCa78TIldg

Generative models for discovering sparse distributed representations.

PubMed Central

Hinton, G E; Ghahramani, Z

1997-01-01

We describe a hierarchical, generative model that can be viewed as a nonlinear generalization of factor analysis and can be implemented in a neural network. The model uses bottom-up, top-down and lateral connections to perform Bayesian perceptual inference correctly. Once perceptual inference has been performed the connection strengths can be updated using a very simple learning rule that only requires locally available information. We demonstrate that the network learns to extract sparse, distributed, hierarchical representations. PMID:9304685

Digital Self-Interference Cancellation for Asynchronous In-Band Full-Duplex Underwater Acoustic Communication.

PubMed

Qiao, Gang; Gan, Shuwei; Liu, Songzuo; Ma, Lu; Sun, Zongxin

2018-05-24

To improve the throughput of underwater acoustic (UWA) networking, the In-band full-duplex (IBFD) communication is one of the most vital pieces of research. The major drawback of IBFD-UWA communication is Self-Interference (SI). This paper presents a digital SI cancellation algorithm for asynchronous IBFD-UWA communication system. We focus on two issues: one is asynchronous communication dissimilar to IBFD radio communication, the other is nonlinear distortion caused by power amplifier (PA). First, we discuss asynchronous IBFD-UWA signal model with the nonlinear distortion of PA. Then, we design a scheme for asynchronous IBFD-UWA communication utilizing the non-overlapping region between SI and intended signal to estimate the nonlinear SI channel. To cancel the nonlinear distortion caused by PA, we propose an Over-Parameterization based Recursive Least Squares (RLS) algorithm (OPRLS) to estimate the nonlinear SI channel. Furthermore, we present the OPRLS with a sparse constraint to estimate the SI channel, which reduces the requirement of the length of the non-overlapping region. Finally, we verify our concept through simulation and the pool experiment. Results demonstrate that the proposed digital SI cancellation scheme can cancel SI efficiently.

Thermodynamics of random reaction networks.

PubMed

Fischer, Jakob; Kleidon, Axel; Dittrich, Peter

2015-01-01

Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models (Erdős-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha) and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa -1.5 for linear and -1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks.

Thermodynamics of Random Reaction Networks

PubMed Central

Fischer, Jakob; Kleidon, Axel; Dittrich, Peter

2015-01-01

Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models (Erdős-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha) and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa −1.5 for linear and −1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks. PMID:25723751

Close Encounters of a Sparse Kind.

ERIC Educational Resources Information Center

Westerberg, Arthur W.

1980-01-01

By providing an example problem in solving sets of nonlinear algebraic equations, the advantages and disadvantages of two methods for its solution, the tearing approach v the Newton-Raphson approach, are elucidated. (CS)

A modified sparse reconstruction method for three-dimensional synthetic aperture radar image

NASA Astrophysics Data System (ADS)

Zhang, Ziqiang; Ji, Kefeng; Song, Haibo; Zou, Huanxin

2018-03-01

There is an increasing interest in three-dimensional Synthetic Aperture Radar (3-D SAR) imaging from observed sparse scattering data. However, the existing 3-D sparse imaging method requires large computing times and storage capacity. In this paper, we propose a modified method for the sparse 3-D SAR imaging. The method processes the collection of noisy SAR measurements, usually collected over nonlinear flight paths, and outputs 3-D SAR imagery. Firstly, the 3-D sparse reconstruction problem is transformed into a series of 2-D slices reconstruction problem by range compression. Then the slices are reconstructed by the modified SL0 (smoothed l0 norm) reconstruction algorithm. The improved algorithm uses hyperbolic tangent function instead of the Gaussian function to approximate the l0 norm and uses the Newton direction instead of the steepest descent direction, which can speed up the convergence rate of the SL0 algorithm. Finally, numerical simulation results are given to demonstrate the effectiveness of the proposed algorithm. It is shown that our method, compared with existing 3-D sparse imaging method, performs better in reconstruction quality and the reconstruction time.

Sparse distributed memory: understanding the speed and robustness of expert memory

PubMed Central

Brogliato, Marcelo S.; Chada, Daniel M.; Linhares, Alexandre

2014-01-01

How can experts, sometimes in exacting detail, almost immediately and very precisely recall memory items from a vast repertoire? The problem in which we will be interested concerns models of theoretical neuroscience that could explain the speed and robustness of an expert's recollection. The approach is based on Sparse Distributed Memory, which has been shown to be plausible, both in a neuroscientific and in a psychological manner, in a number of ways. A crucial characteristic concerns the limits of human recollection, the “tip-of-tongue” memory event—which is found at a non-linearity in the model. We expand the theoretical framework, deriving an optimization formula to solve this non-linearity. Numerical results demonstrate how the higher frequency of rehearsal, through work or study, immediately increases the robustness and speed associated with expert memory. PMID:24808842

An hp symplectic pseudospectral method for nonlinear optimal control

NASA Astrophysics Data System (ADS)

Peng, Haijun; Wang, Xinwei; Li, Mingwu; Chen, Biaosong

2017-01-01

An adaptive symplectic pseudospectral method based on the dual variational principle is proposed and is successfully applied to solving nonlinear optimal control problems in this paper. The proposed method satisfies the first order necessary conditions of continuous optimal control problems, also the symplectic property of the original continuous Hamiltonian system is preserved. The original optimal control problem is transferred into a set of nonlinear equations which can be solved easily by Newton-Raphson iterations, and the Jacobian matrix is found to be sparse and symmetric. The proposed method, on one hand, exhibits exponent convergence rates when the number of collocation points are increasing with the fixed number of sub-intervals; on the other hand, exhibits linear convergence rates when the number of sub-intervals is increasing with the fixed number of collocation points. Furthermore, combining with the hp method based on the residual error of dynamic constraints, the proposed method can achieve given precisions in a few iterations. Five examples highlight the high precision and high computational efficiency of the proposed method.

Estimating the state of a geophysical system with sparse observations: time delay methods to achieve accurate initial states for prediction

NASA Astrophysics Data System (ADS)

An, Zhe; Rey, Daniel; Ye, Jingxin; Abarbanel, Henry D. I.

2017-01-01

The problem of forecasting the behavior of a complex dynamical system through analysis of observational time-series data becomes difficult when the system expresses chaotic behavior and the measurements are sparse, in both space and/or time. Despite the fact that this situation is quite typical across many fields, including numerical weather prediction, the issue of whether the available observations are "sufficient" for generating successful forecasts is still not well understood. An analysis by Whartenby et al. (2013) found that in the context of the nonlinear shallow water equations on a β plane, standard nudging techniques require observing approximately 70 % of the full set of state variables. Here we examine the same system using a method introduced by Rey et al. (2014a), which generalizes standard nudging methods to utilize time delayed measurements. We show that in certain circumstances, it provides a sizable reduction in the number of observations required to construct accurate estimates and high-quality predictions. In particular, we find that this estimate of 70 % can be reduced to about 33 % using time delays, and even further if Lagrangian drifter locations are also used as measurements.

Multiple Kernel Sparse Representation based Orthogonal Discriminative Projection and Its Cost-Sensitive Extension.

PubMed

Zhang, Guoqing; Sun, Huaijiang; Xia, Guiyu; Sun, Quansen

2016-07-07

Sparse representation based classification (SRC) has been developed and shown great potential for real-world application. Based on SRC, Yang et al. [10] devised a SRC steered discriminative projection (SRC-DP) method. However, as a linear algorithm, SRC-DP cannot handle the data with highly nonlinear distribution. Kernel sparse representation-based classifier (KSRC) is a non-linear extension of SRC and can remedy the drawback of SRC. KSRC requires the use of a predetermined kernel function and selection of the kernel function and its parameters is difficult. Recently, multiple kernel learning for SRC (MKL-SRC) [22] has been proposed to learn a kernel from a set of base kernels. However, MKL-SRC only considers the within-class reconstruction residual while ignoring the between-class relationship, when learning the kernel weights. In this paper, we propose a novel multiple kernel sparse representation-based classifier (MKSRC), and then we use it as a criterion to design a multiple kernel sparse representation based orthogonal discriminative projection method (MK-SR-ODP). The proposed algorithm aims at learning a projection matrix and a corresponding kernel from the given base kernels such that in the low dimension subspace the between-class reconstruction residual is maximized and the within-class reconstruction residual is minimized. Furthermore, to achieve a minimum overall loss by performing recognition in the learned low-dimensional subspace, we introduce cost information into the dimensionality reduction method. The solutions for the proposed method can be efficiently found based on trace ratio optimization method [33]. Extensive experimental results demonstrate the superiority of the proposed algorithm when compared with the state-of-the-art methods.

Sequential-Optimization-Based Framework for Robust Modeling and Design of Heterogeneous Catalytic Systems

DOE PAGES

Rangarajan, Srinivas; Maravelias, Christos T.; Mavrikakis, Manos

2017-11-09

Here, we present a general optimization-based framework for (i) ab initio and experimental data driven mechanistic modeling and (ii) optimal catalyst design of heterogeneous catalytic systems. Both cases are formulated as a nonlinear optimization problem that is subject to a mean-field microkinetic model and thermodynamic consistency requirements as constraints, for which we seek sparse solutions through a ridge (L 2 regularization) penalty. The solution procedure involves an iterative sequence of forward simulation of the differential algebraic equations pertaining to the microkinetic model using a numerical tool capable of handling stiff systems, sensitivity calculations using linear algebra, and gradient-based nonlinear optimization.more » A multistart approach is used to explore the solution space, and a hierarchical clustering procedure is implemented for statistically classifying potentially competing solutions. An example of methanol synthesis through hydrogenation of CO and CO 2 on a Cu-based catalyst is used to illustrate the framework. The framework is fast, is robust, and can be used to comprehensively explore the model solution and design space of any heterogeneous catalytic system.« less

Sequential-Optimization-Based Framework for Robust Modeling and Design of Heterogeneous Catalytic Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rangarajan, Srinivas; Maravelias, Christos T.; Mavrikakis, Manos

Here, we present a general optimization-based framework for (i) ab initio and experimental data driven mechanistic modeling and (ii) optimal catalyst design of heterogeneous catalytic systems. Both cases are formulated as a nonlinear optimization problem that is subject to a mean-field microkinetic model and thermodynamic consistency requirements as constraints, for which we seek sparse solutions through a ridge (L 2 regularization) penalty. The solution procedure involves an iterative sequence of forward simulation of the differential algebraic equations pertaining to the microkinetic model using a numerical tool capable of handling stiff systems, sensitivity calculations using linear algebra, and gradient-based nonlinear optimization.more » A multistart approach is used to explore the solution space, and a hierarchical clustering procedure is implemented for statistically classifying potentially competing solutions. An example of methanol synthesis through hydrogenation of CO and CO 2 on a Cu-based catalyst is used to illustrate the framework. The framework is fast, is robust, and can be used to comprehensively explore the model solution and design space of any heterogeneous catalytic system.« less

RZA-NLMF algorithm-based adaptive sparse sensing for realizing compressive sensing

NASA Astrophysics Data System (ADS)

Gui, Guan; Xu, Li; Adachi, Fumiyuki

2014-12-01

Nonlinear sparse sensing (NSS) techniques have been adopted for realizing compressive sensing in many applications such as radar imaging. Unlike the NSS, in this paper, we propose an adaptive sparse sensing (ASS) approach using the reweighted zero-attracting normalized least mean fourth (RZA-NLMF) algorithm which depends on several given parameters, i.e., reweighted factor, regularization parameter, and initial step size. First, based on the independent assumption, Cramer-Rao lower bound (CRLB) is derived as for the performance comparisons. In addition, reweighted factor selection method is proposed for achieving robust estimation performance. Finally, to verify the algorithm, Monte Carlo-based computer simulations are given to show that the ASS achieves much better mean square error (MSE) performance than the NSS.

Time-domain finite elements in optimal control with application to launch-vehicle guidance. PhD. Thesis

NASA Technical Reports Server (NTRS)

Bless, Robert R.

1991-01-01

A time-domain finite element method is developed for optimal control problems. The theory derived is general enough to handle a large class of problems including optimal control problems that are continuous in the states and controls, problems with discontinuities in the states and/or system equations, problems with control inequality constraints, problems with state inequality constraints, or problems involving any combination of the above. The theory is developed in such a way that no numerical quadrature is necessary regardless of the degree of nonlinearity in the equations. Also, the same shape functions may be employed for every problem because all strong boundary conditions are transformed into natural or weak boundary conditions. In addition, the resulting nonlinear algebraic equations are very sparse. Use of sparse matrix solvers allows for the rapid and accurate solution of very difficult optimization problems. The formulation is applied to launch-vehicle trajectory optimization problems, and results show that real-time optimal guidance is realizable with this method. Finally, a general problem solving environment is created for solving a large class of optimal control problems. The algorithm uses both FORTRAN and a symbolic computation program to solve problems with a minimum of user interaction. The use of symbolic computation eliminates the need for user-written subroutines which greatly reduces the setup time for solving problems.

Bypassing the Limits of Ll Regularization: Convex Sparse Signal Processing Using Non-Convex Regularization

NASA Astrophysics Data System (ADS)

Parekh, Ankit

Sparsity has become the basis of some important signal processing methods over the last ten years. Many signal processing problems (e.g., denoising, deconvolution, non-linear component analysis) can be expressed as inverse problems. Sparsity is invoked through the formulation of an inverse problem with suitably designed regularization terms. The regularization terms alone encode sparsity into the problem formulation. Often, the ℓ1 norm is used to induce sparsity, so much so that ℓ1 regularization is considered to be `modern least-squares'. The use of ℓ1 norm, as a sparsity-inducing regularizer, leads to a convex optimization problem, which has several benefits: the absence of extraneous local minima, well developed theory of globally convergent algorithms, even for large-scale problems. Convex regularization via the ℓ1 norm, however, tends to under-estimate the non-zero values of sparse signals. In order to estimate the non-zero values more accurately, non-convex regularization is often favored over convex regularization. However, non-convex regularization generally leads to non-convex optimization, which suffers from numerous issues: convergence may be guaranteed to only a stationary point, problem specific parameters may be difficult to set, and the solution is sensitive to the initialization of the algorithm. The first part of this thesis is aimed toward combining the benefits of non-convex regularization and convex optimization to estimate sparse signals more effectively. To this end, we propose to use parameterized non-convex regularizers with designated non-convexity and provide a range for the non-convex parameter so as to ensure that the objective function is strictly convex. By ensuring convexity of the objective function (sum of data-fidelity and non-convex regularizer), we can make use of a wide variety of convex optimization algorithms to obtain the unique global minimum reliably. The second part of this thesis proposes a non-linear signal decomposition technique for an important biomedical signal processing problem: the detection of sleep spindles and K-complexes in human sleep electroencephalography (EEG). We propose a non-linear model for the EEG consisting of three components: (1) a transient (sparse piecewise constant) component, (2) a low-frequency component, and (3) an oscillatory component. The oscillatory component admits a sparse time-frequency representation. Using a convex objective function, we propose a fast non-linear optimization algorithm to estimate the three components in the proposed signal model. The low-frequency and oscillatory components are then used to estimate the K-complexes and sleep spindles respectively. The proposed detection method is shown to outperform several state-of-the-art automated sleep spindles detection methods.

Estimating the state of a geophysical system with sparse observations: time delay methods to achieve accurate initial states for prediction

DOE PAGES

An, Zhe; Rey, Daniel; Ye, Jingxin; ...

2017-01-16

The problem of forecasting the behavior of a complex dynamical system through analysis of observational time-series data becomes difficult when the system expresses chaotic behavior and the measurements are sparse, in both space and/or time. Despite the fact that this situation is quite typical across many fields, including numerical weather prediction, the issue of whether the available observations are "sufficient" for generating successful forecasts is still not well understood. An analysis by Whartenby et al. (2013) found that in the context of the nonlinear shallow water equations on a β plane, standard nudging techniques require observing approximately 70 % of themore » full set of state variables. Here we examine the same system using a method introduced by Rey et al. (2014a), which generalizes standard nudging methods to utilize time delayed measurements. Here, we show that in certain circumstances, it provides a sizable reduction in the number of observations required to construct accurate estimates and high-quality predictions. In particular, we find that this estimate of 70 % can be reduced to about 33 % using time delays, and even further if Lagrangian drifter locations are also used as measurements.« less

Estimating the state of a geophysical system with sparse observations: time delay methods to achieve accurate initial states for prediction

DOE Office of Scientific and Technical Information (OSTI.GOV)

An, Zhe; Rey, Daniel; Ye, Jingxin

The problem of forecasting the behavior of a complex dynamical system through analysis of observational time-series data becomes difficult when the system expresses chaotic behavior and the measurements are sparse, in both space and/or time. Despite the fact that this situation is quite typical across many fields, including numerical weather prediction, the issue of whether the available observations are "sufficient" for generating successful forecasts is still not well understood. An analysis by Whartenby et al. (2013) found that in the context of the nonlinear shallow water equations on a β plane, standard nudging techniques require observing approximately 70 % of themore » full set of state variables. Here we examine the same system using a method introduced by Rey et al. (2014a), which generalizes standard nudging methods to utilize time delayed measurements. Here, we show that in certain circumstances, it provides a sizable reduction in the number of observations required to construct accurate estimates and high-quality predictions. In particular, we find that this estimate of 70 % can be reduced to about 33 % using time delays, and even further if Lagrangian drifter locations are also used as measurements.« less

Sequential quadratic programming-based fast path planning algorithm subject to no-fly zone constraints

NASA Astrophysics Data System (ADS)

Liu, Wei; Ma, Shunjian; Sun, Mingwei; Yi, Haidong; Wang, Zenghui; Chen, Zengqiang

2016-08-01

Path planning plays an important role in aircraft guided systems. Multiple no-fly zones in the flight area make path planning a constrained nonlinear optimization problem. It is necessary to obtain a feasible optimal solution in real time. In this article, the flight path is specified to be composed of alternate line segments and circular arcs, in order to reformulate the problem into a static optimization one in terms of the waypoints. For the commonly used circular and polygonal no-fly zones, geometric conditions are established to determine whether or not the path intersects with them, and these can be readily programmed. Then, the original problem is transformed into a form that can be solved by the sequential quadratic programming method. The solution can be obtained quickly using the Sparse Nonlinear OPTimizer (SNOPT) package. Mathematical simulations are used to verify the effectiveness and rapidity of the proposed algorithm.

Optimization of Stability Constrained Geometrically Nonlinear Shallow Trusses Using an Arc Length Sparse Method with a Strain Energy Density Approach

NASA Technical Reports Server (NTRS)

Hrinda, Glenn A.; Nguyen, Duc T.

2008-01-01

A technique for the optimization of stability constrained geometrically nonlinear shallow trusses with snap through behavior is demonstrated using the arc length method and a strain energy density approach within a discrete finite element formulation. The optimization method uses an iterative scheme that evaluates the design variables' performance and then updates them according to a recursive formula controlled by the arc length method. A minimum weight design is achieved when a uniform nonlinear strain energy density is found in all members. This minimal condition places the design load just below the critical limit load causing snap through of the structure. The optimization scheme is programmed into a nonlinear finite element algorithm to find the large strain energy at critical limit loads. Examples of highly nonlinear trusses found in literature are presented to verify the method.

k-t Acceleration in pure phase encode MRI to monitor dynamic flooding processes in rock core plugs

NASA Astrophysics Data System (ADS)

Xiao, Dan; Balcom, Bruce J.

2014-06-01

Monitoring the pore system in sedimentary rocks with MRI when fluids are introduced is very important in the study of petroleum reservoirs and enhanced oil recovery. However, the lengthy acquisition time of each image, with pure phase encode MRI, limits the temporal resolution. Spatiotemporal correlations can be exploited to undersample the k-t space data. The stacked frames/profiles can be well approximated by an image matrix with rank deficiency, which can be recovered by nonlinear nuclear norm minimization. Sparsity of the x-t image can also be exploited for nonlinear reconstruction. In this work the results of a low rank matrix completion technique were compared with k-t sparse compressed sensing. These methods are demonstrated with one dimensional SPRITE imaging of a Bentheimer rock core plug and SESPI imaging of a Berea rock core plug, but can be easily extended to higher dimensionality and/or other pure phase encode measurements. These ideas will enable higher dimensionality pure phase encode MRI studies of dynamic flooding processes in low magnetic field systems.

Response of selected binomial coefficients to varying degrees of matrix sparseness and to matrices with known data interrelationships

USGS Publications Warehouse

Archer, A.W.; Maples, C.G.

1989-01-01

Numerous departures from ideal relationships are revealed by Monte Carlo simulations of widely accepted binomial coefficients. For example, simulations incorporating varying levels of matrix sparseness (presence of zeros indicating lack of data) and computation of expected values reveal that not only are all common coefficients influenced by zero data, but also that some coefficients do not discriminate between sparse or dense matrices (few zero data). Such coefficients computationally merge mutually shared and mutually absent information and do not exploit all the information incorporated within the standard 2 ?? 2 contingency table; therefore, the commonly used formulae for such coefficients are more complicated than the actual range of values produced. Other coefficients do differentiate between mutual presences and absences; however, a number of these coefficients do not demonstrate a linear relationship to matrix sparseness. Finally, simulations using nonrandom matrices with known degrees of row-by-row similarities signify that several coefficients either do not display a reasonable range of values or are nonlinear with respect to known relationships within the data. Analyses with nonrandom matrices yield clues as to the utility of certain coefficients for specific applications. For example, coefficients such as Jaccard, Dice, and Baroni-Urbani and Buser are useful if correction of sparseness is desired, whereas the Russell-Rao coefficient is useful when sparseness correction is not desired. ?? 1989 International Association for Mathematical Geology.

Mapping visual stimuli to perceptual decisions via sparse decoding of mesoscopic neural activity.

PubMed

Sajda, Paul

2010-01-01

In this talk I will describe our work investigating sparse decoding of neural activity, given a realistic mapping of the visual scene to neuronal spike trains generated by a model of primary visual cortex (V1). We use a linear decoder which imposes sparsity via an L1 norm. The decoder can be viewed as a decoding neuron (linear summation followed by a sigmoidal nonlinearity) in which there are relatively few non-zero synaptic weights. We find: (1) the best decoding performance is for a representation that is sparse in both space and time, (2) decoding of a temporal code results in better performance than a rate code and is also a better fit to the psychophysical data, (3) the number of neurons required for decoding increases monotonically as signal-to-noise in the stimulus decreases, with as little as 1% of the neurons required for decoding at the highest signal-to-noise levels, and (4) sparse decoding results in a more accurate decoding of the stimulus and is a better fit to psychophysical performance than a distributed decoding, for example one imposed by an L2 norm. We conclude that sparse coding is well-justified from a decoding perspective in that it results in a minimum number of neurons and maximum accuracy when sparse representations can be decoded from the neural dynamics.

On A Nonlinear Generalization of Sparse Coding and Dictionary Learning.

PubMed

Xie, Yuchen; Ho, Jeffrey; Vemuri, Baba

2013-01-01

Existing dictionary learning algorithms are based on the assumption that the data are vectors in an Euclidean vector space ℝ d , and the dictionary is learned from the training data using the vector space structure of ℝ d and its Euclidean L 2 -metric. However, in many applications, features and data often originated from a Riemannian manifold that does not support a global linear (vector space) structure. Furthermore, the extrinsic viewpoint of existing dictionary learning algorithms becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to the application. This paper proposes a novel framework for sparse coding and dictionary learning for data on a Riemannian manifold, and it shows that the existing sparse coding and dictionary learning methods can be considered as special (Euclidean) cases of the more general framework proposed here. We show that both the dictionary and sparse coding can be effectively computed for several important classes of Riemannian manifolds, and we validate the proposed method using two well-known classification problems in computer vision and medical imaging analysis.

On A Nonlinear Generalization of Sparse Coding and Dictionary Learning

PubMed Central

Xie, Yuchen; Ho, Jeffrey; Vemuri, Baba

2013-01-01

Existing dictionary learning algorithms are based on the assumption that the data are vectors in an Euclidean vector space ℝd, and the dictionary is learned from the training data using the vector space structure of ℝd and its Euclidean L2-metric. However, in many applications, features and data often originated from a Riemannian manifold that does not support a global linear (vector space) structure. Furthermore, the extrinsic viewpoint of existing dictionary learning algorithms becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to the application. This paper proposes a novel framework for sparse coding and dictionary learning for data on a Riemannian manifold, and it shows that the existing sparse coding and dictionary learning methods can be considered as special (Euclidean) cases of the more general framework proposed here. We show that both the dictionary and sparse coding can be effectively computed for several important classes of Riemannian manifolds, and we validate the proposed method using two well-known classification problems in computer vision and medical imaging analysis. PMID:24129583

Sparseness- and continuity-constrained seismic imaging

NASA Astrophysics Data System (ADS)

Herrmann, Felix J.

2005-04-01

Non-linear solution strategies to the least-squares seismic inverse-scattering problem with sparseness and continuity constraints are proposed. Our approach is designed to (i) deal with substantial amounts of additive noise (SNR < 0 dB); (ii) use the sparseness and locality (both in position and angle) of directional basis functions (such as curvelets and contourlets) on the model: the reflectivity; and (iii) exploit the near invariance of these basis functions under the normal operator, i.e., the scattering-followed-by-imaging operator. Signal-to-noise ratio and the continuity along the imaged reflectors are significantly enhanced by formulating the solution of the seismic inverse problem in terms of an optimization problem. During the optimization, sparseness on the basis and continuity along the reflectors are imposed by jointly minimizing the l1- and anisotropic diffusion/total-variation norms on the coefficients and reflectivity, respectively. [Joint work with Peyman P. Moghaddam was carried out as part of the SINBAD project, with financial support secured through ITF (the Industry Technology Facilitator) from the following organizations: BG Group, BP, ExxonMobil, and SHELL. Additional funding came from the NSERC Discovery Grants 22R81254.

Dense modifiable interconnections utilizing photorefractive volume holograms

NASA Astrophysics Data System (ADS)

Psaltis, Demetri; Qiao, Yong

1990-11-01

This report describes an experimental two-layer optical neural network built at Caltech. The system uses photorefractive volume holograms to implement dense, modifiable synaptic interconnections and liquid crystal light valves (LCVS) to perform nonlinear thresholding operations. Kanerva's Sparse, Distributed Memory was implemented using this network and its ability to recognize handwritten character-alphabet (A-Z) has been demonstrated experimentally. According to Kanerva's model, the first layer has fixed, random weights of interconnections and the second layer is trained by sum-of-outer-products rule. After training, the recognition rates of the network on the training set (104 patterns) and test set (520 patterns) are 100 and 50 percent, respectively.

Implicit solvers for unstructured meshes

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, Dimitri J.

1991-01-01

Implicit methods for unstructured mesh computations are developed and tested. The approximate system which arises from the Newton-linearization of the nonlinear evolution operator is solved by using the preconditioned generalized minimum residual technique. These different preconditioners are investigated: the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over-relaxation (SSOR). The preconditioners have been optimized to have good vectorization properties. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also investigated. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Coulomb disorder in three-dimensional Dirac materials

NASA Astrophysics Data System (ADS)

Skinner, Brian

2015-03-01

In three-dimensional materials with a Dirac spectrum, weak short-ranged disorder is essentially irrelevant near the Dirac point. This is manifestly not the case for Coulomb disorder, where the long-ranged nature of the potential produced by charged impurities implies large fluctuations of the disorder potential even when impurities are sparse, and these fluctuations are screened by the formation of electron/hole puddles. Here I outline a theory of such nonlinear screening of Coulomb disorder in three-dimensional Dirac systems, and present results for the typical magnitude of the disorder potential, the corresponding density of states, and the size and density of electron/hole puddles. The resulting conductivity is also discussed.

Ordering Unstructured Meshes for Sparse Matrix Computations on Leading Parallel Systems

NASA Technical Reports Server (NTRS)

Oliker, Leonid; Li, Xiaoye; Heber, Gerd; Biswas, Rupak

2000-01-01

The ability of computers to solve hitherto intractable problems and simulate complex processes using mathematical models makes them an indispensable part of modern science and engineering. Computer simulations of large-scale realistic applications usually require solving a set of non-linear partial differential equations (PDES) over a finite region. For example, one thrust area in the DOE Grand Challenge projects is to design future accelerators such as the SpaHation Neutron Source (SNS). Our colleagues at SLAC need to model complex RFQ cavities with large aspect ratios. Unstructured grids are currently used to resolve the small features in a large computational domain; dynamic mesh adaptation will be added in the future for additional efficiency. The PDEs for electromagnetics are discretized by the FEM method, which leads to a generalized eigenvalue problem Kx = AMx, where K and M are the stiffness and mass matrices, and are very sparse. In a typical cavity model, the number of degrees of freedom is about one million. For such large eigenproblems, direct solution techniques quickly reach the memory limits. Instead, the most widely-used methods are Krylov subspace methods, such as Lanczos or Jacobi-Davidson. In all the Krylov-based algorithms, sparse matrix-vector multiplication (SPMV) must be performed repeatedly. Therefore, the efficiency of SPMV usually determines the eigensolver speed. SPMV is also one of the most heavily used kernels in large-scale numerical simulations.

Modeling an aquatic ecosystem: application of an evolutionary algorithm with genetic doping to reduce prediction uncertainty

NASA Astrophysics Data System (ADS)

Friedel, Michael; Buscema, Massimo

2016-04-01

Aquatic ecosystem models can potentially be used to understand the influence of stresses on catchment resource quality. Given that catchment responses are functions of natural and anthropogenic stresses reflected in sparse and spatiotemporal biological, physical, and chemical measurements, an ecosystem is difficult to model using statistical or numerical methods. We propose an artificial adaptive systems approach to model ecosystems. First, an unsupervised machine-learning (ML) network is trained using the set of available sparse and disparate data variables. Second, an evolutionary algorithm with genetic doping is applied to reduce the number of ecosystem variables to an optimal set. Third, the optimal set of ecosystem variables is used to retrain the ML network. Fourth, a stochastic cross-validation approach is applied to quantify and compare the nonlinear uncertainty in selected predictions of the original and reduced models. Results are presented for aquatic ecosystems (tens of thousands of square kilometers) undergoing landscape change in the USA: Upper Illinois River Basin and Central Colorado Assessment Project Area, and Southland region, NZ.

Vertically homogeneous stationary tornado-type vortex

NASA Astrophysics Data System (ADS)

Rutkevich, P. B.; Rutkevych, P. P.

2010-05-01

Tornado is regarded as one of the most dangerous atmosphere phenomena. The tornado phenomenon has been intensively studied so far, however, there is still no established and accepted theory of how tornadoes form, an uncertainty still exists concerning extreme winds and pressure drops in tornadoes. It is commonly accepted that it is possible to describe tornado from the set of nonlinear hydrodynamical equations, however, it is still unclear which non-linear processes are responsible for its formation. Nonlinear terms in the system are associated with either centrifugal force, or entropy transport, or transport of humidity. It appears that the amount and spatial distribution of precipitation with the convection are important indicators of the weather phenomena associated with a particular storm. The low-precipitation supercells that produce relatively little precipitation and yet show clear visual signs of rotation. Low-precipitation supercells occur most often near the surface dryline and, owing to the sparse precipitation and relatively dry environments with little cloudiness. Low-precipitation storms are frequently non-tornadic and many are non-severe despite exhibiting persistent rotation. On the other hand, the so-called high-precipitation storms are characterized by substantial precipitation within their mesocyclonic circulations. When high-precipitation storms have a recognizable hook radar echo, reflectivity in the hook is comparable to those in the precipitation core. High-precipitation supercells are probably the most common form of supercell and produce severe weather of all types including tornadoes. Therefore, in this work we consider a hydrodynamic system with only one nonlinear term associated with atmosphere humidity, which yields energy to the system. The tornado vortex is usually to a good approximation cylindrical so we use cylindrical geometry and homogeneity in vertical direction. In this case the problem reduces to a system of ordinary differential equations. Rotation in the vortex is associated with compressibility so we also take into account the compressibility of the gas. Under certain approximations the problem reduces to a single high-order nonlinear equation. Numerical solution of the obtained high-order equation describes all three velocity components and all thermodynamic parameters in the system. The system exhibits high rotation and strong vertical air flow in the middle part of the vortex.

Total recall in distributive associative memories

NASA Technical Reports Server (NTRS)

Danforth, Douglas G.

1991-01-01

Iterative error correction of asymptotically large associative memories is equivalent to a one-step learning rule. This rule is the inverse of the activation function of the memory. Spectral representations of nonlinear activation functions are used to obtain the inverse in closed form for Sparse Distributed Memory, Selected-Coordinate Design, and Radial Basis Functions.

MR Image Reconstruction Using Block Matching and Adaptive Kernel Methods.

PubMed

Schmidt, Johannes F M; Santelli, Claudio; Kozerke, Sebastian

2016-01-01

An approach to Magnetic Resonance (MR) image reconstruction from undersampled data is proposed. Undersampling artifacts are removed using an iterative thresholding algorithm applied to nonlinearly transformed image block arrays. Each block array is transformed using kernel principal component analysis where the contribution of each image block to the transform depends in a nonlinear fashion on the distance to other image blocks. Elimination of undersampling artifacts is achieved by conventional principal component analysis in the nonlinear transform domain, projection onto the main components and back-mapping into the image domain. Iterative image reconstruction is performed by interleaving the proposed undersampling artifact removal step and gradient updates enforcing consistency with acquired k-space data. The algorithm is evaluated using retrospectively undersampled MR cardiac cine data and compared to k-t SPARSE-SENSE, block matching with spatial Fourier filtering and k-t ℓ1-SPIRiT reconstruction. Evaluation of image quality and root-mean-squared-error (RMSE) reveal improved image reconstruction for up to 8-fold undersampled data with the proposed approach relative to k-t SPARSE-SENSE, block matching with spatial Fourier filtering and k-t ℓ1-SPIRiT. In conclusion, block matching and kernel methods can be used for effective removal of undersampling artifacts in MR image reconstruction and outperform methods using standard compressed sensing and ℓ1-regularized parallel imaging methods.

Dimension Reduction With Extreme Learning Machine.

PubMed

Kasun, Liyanaarachchi Lekamalage Chamara; Yang, Yan; Huang, Guang-Bin; Zhang, Zhengyou

2016-08-01

Data may often contain noise or irrelevant information, which negatively affect the generalization capability of machine learning algorithms. The objective of dimension reduction algorithms, such as principal component analysis (PCA), non-negative matrix factorization (NMF), random projection (RP), and auto-encoder (AE), is to reduce the noise or irrelevant information of the data. The features of PCA (eigenvectors) and linear AE are not able to represent data as parts (e.g. nose in a face image). On the other hand, NMF and non-linear AE are maimed by slow learning speed and RP only represents a subspace of original data. This paper introduces a dimension reduction framework which to some extend represents data as parts, has fast learning speed, and learns the between-class scatter subspace. To this end, this paper investigates a linear and non-linear dimension reduction framework referred to as extreme learning machine AE (ELM-AE) and sparse ELM-AE (SELM-AE). In contrast to tied weight AE, the hidden neurons in ELM-AE and SELM-AE need not be tuned, and their parameters (e.g, input weights in additive neurons) are initialized using orthogonal and sparse random weights, respectively. Experimental results on USPS handwritten digit recognition data set, CIFAR-10 object recognition, and NORB object recognition data set show the efficacy of linear and non-linear ELM-AE and SELM-AE in terms of discriminative capability, sparsity, training time, and normalized mean square error.

Optimal Couple Projections for Domain Adaptive Sparse Representation-based Classification.

PubMed

Zhang, Guoqing; Sun, Huaijiang; Porikli, Fatih; Liu, Yazhou; Sun, Quansen

2017-08-29

In recent years, sparse representation based classification (SRC) is one of the most successful methods and has been shown impressive performance in various classification tasks. However, when the training data has a different distribution than the testing data, the learned sparse representation may not be optimal, and the performance of SRC will be degraded significantly. To address this problem, in this paper, we propose an optimal couple projections for domain-adaptive sparse representation-based classification (OCPD-SRC) method, in which the discriminative features of data in the two domains are simultaneously learned with the dictionary that can succinctly represent the training and testing data in the projected space. OCPD-SRC is designed based on the decision rule of SRC, with the objective to learn coupled projection matrices and a common discriminative dictionary such that the between-class sparse reconstruction residuals of data from both domains are maximized, and the within-class sparse reconstruction residuals of data are minimized in the projected low-dimensional space. Thus, the resulting representations can well fit SRC and simultaneously have a better discriminant ability. In addition, our method can be easily extended to multiple domains and can be kernelized to deal with the nonlinear structure of data. The optimal solution for the proposed method can be efficiently obtained following the alternative optimization method. Extensive experimental results on a series of benchmark databases show that our method is better or comparable to many state-of-the-art methods.

A Nonlinear Model for Gene-Based Gene-Environment Interaction.

PubMed

Sa, Jian; Liu, Xu; He, Tao; Liu, Guifen; Cui, Yuehua

2016-06-04

A vast amount of literature has confirmed the role of gene-environment (G×E) interaction in the etiology of complex human diseases. Traditional methods are predominantly focused on the analysis of interaction between a single nucleotide polymorphism (SNP) and an environmental variable. Given that genes are the functional units, it is crucial to understand how gene effects (rather than single SNP effects) are influenced by an environmental variable to affect disease risk. Motivated by the increasing awareness of the power of gene-based association analysis over single variant based approach, in this work, we proposed a sparse principle component regression (sPCR) model to understand the gene-based G×E interaction effect on complex disease. We first extracted the sparse principal components for SNPs in a gene, then the effect of each principal component was modeled by a varying-coefficient (VC) model. The model can jointly model variants in a gene in which their effects are nonlinearly influenced by an environmental variable. In addition, the varying-coefficient sPCR (VC-sPCR) model has nice interpretation property since the sparsity on the principal component loadings can tell the relative importance of the corresponding SNPs in each component. We applied our method to a human birth weight dataset in Thai population. We analyzed 12,005 genes across 22 chromosomes and found one significant interaction effect using the Bonferroni correction method and one suggestive interaction. The model performance was further evaluated through simulation studies. Our model provides a system approach to evaluate gene-based G×E interaction.

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. II. Linear scaling domain based pair natural orbital coupled cluster theory

NASA Astrophysics Data System (ADS)

Riplinger, Christoph; Pinski, Peter; Becker, Ute; Valeev, Edward F.; Neese, Frank

2016-01-01

Domain based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)) is a highly efficient local correlation method. It is known to be accurate and robust and can be used in a black box fashion in order to obtain coupled cluster quality total energies for large molecules with several hundred atoms. While previous implementations showed near linear scaling up to a few hundred atoms, several nonlinear scaling steps limited the applicability of the method for very large systems. In this work, these limitations are overcome and a linear scaling DLPNO-CCSD(T) method for closed shell systems is reported. The new implementation is based on the concept of sparse maps that was introduced in Part I of this series [P. Pinski, C. Riplinger, E. F. Valeev, and F. Neese, J. Chem. Phys. 143, 034108 (2015)]. Using the sparse map infrastructure, all essential computational steps (integral transformation and storage, initial guess, pair natural orbital construction, amplitude iterations, triples correction) are achieved in a linear scaling fashion. In addition, a number of additional algorithmic improvements are reported that lead to significant speedups of the method. The new, linear-scaling DLPNO-CCSD(T) implementation typically is 7 times faster than the previous implementation and consumes 4 times less disk space for large three-dimensional systems. For linear systems, the performance gains and memory savings are substantially larger. Calculations with more than 20 000 basis functions and 1000 atoms are reported in this work. In all cases, the time required for the coupled cluster step is comparable to or lower than for the preceding Hartree-Fock calculation, even if this is carried out with the efficient resolution-of-the-identity and chain-of-spheres approximations. The new implementation even reduces the error in absolute correlation energies by about a factor of two, compared to the already accurate previous implementation.

Nonlinear damage detection in composite structures using bispectral analysis

NASA Astrophysics Data System (ADS)

Ciampa, Francesco; Pickering, Simon; Scarselli, Gennaro; Meo, Michele

2014-03-01

Literature offers a quantitative number of diagnostic methods that can continuously provide detailed information of the material defects and damages in aerospace and civil engineering applications. Indeed, low velocity impact damages can considerably degrade the integrity of structural components and, if not detected, they can result in catastrophic failure conditions. This paper presents a nonlinear Structural Health Monitoring (SHM) method, based on ultrasonic guided waves (GW), for the detection of the nonlinear signature in a damaged composite structure. The proposed technique, based on a bispectral analysis of ultrasonic input waveforms, allows for the evaluation of the nonlinear response due to the presence of cracks and delaminations. Indeed, such a methodology was used to characterize the nonlinear behaviour of the structure, by exploiting the frequency mixing of the original waveform acquired from a sparse array of sensors. The robustness of bispectral analysis was experimentally demonstrated on a damaged carbon fibre reinforce plastic (CFRP) composite panel, and the nonlinear source was retrieved with a high level of accuracy. Unlike other linear and nonlinear ultrasonic methods for damage detection, this methodology does not require any baseline with the undamaged structure for the evaluation of the nonlinear source, nor a priori knowledge of the mechanical properties of the specimen. Moreover, bispectral analysis can be considered as a nonlinear elastic wave spectroscopy (NEWS) technique for materials showing either classical or non-classical nonlinear behaviour.

Dimensionality reduction of collective motion by principal manifolds

NASA Astrophysics Data System (ADS)

Gajamannage, Kelum; Butail, Sachit; Porfiri, Maurizio; Bollt, Erik M.

2015-01-01

While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods is not amenable to the analysis of such manifolds. This is mainly due to the necessary spectral decomposition step, which limits control over the mapping from the original high-dimensional space to the embedding space. Here, we propose an alternative approach that demands a two-dimensional embedding which topologically summarizes the high-dimensional data. In this sense, our approach is closely related to the construction of one-dimensional principal curves that minimize orthogonal error to data points subject to smoothness constraints. Specifically, we construct a two-dimensional principal manifold directly in the high-dimensional space using cubic smoothing splines, and define the embedding coordinates in terms of geodesic distances. Thus, the mapping from the high-dimensional data to the manifold is defined in terms of local coordinates. Through representative examples, we show that compared to existing nonlinear dimensionality reduction methods, the principal manifold retains the original structure even in noisy and sparse datasets. The principal manifold finding algorithm is applied to configurations obtained from a dynamical system of multiple agents simulating a complex maneuver called predator mobbing, and the resulting two-dimensional embedding is compared with that of a well-established nonlinear dimensionality reduction method.

Learning partial differential equations via data discovery and sparse optimization

NASA Astrophysics Data System (ADS)

Schaeffer, Hayden

2017-01-01

We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection.

Learning partial differential equations via data discovery and sparse optimization.

PubMed

Schaeffer, Hayden

2017-01-01

We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection.

Learning partial differential equations via data discovery and sparse optimization

PubMed Central

2017-01-01

We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection. PMID:28265183

Evidence of chaotic pattern in solar flux through a reproducible sequence of period-doubling-type bifurcations

NASA Technical Reports Server (NTRS)

Ashrafi, S.; Roszman, L.

1991-01-01

A preliminary study of the limits to solar flux intensity prediction, and of whether the general lack of predictability in the solar flux arises from the nonlinear chaotic nature of the Sun's physical activity is presented. Statistical analysis of a chaotic signal can extract only its most gross features, and detailed physical models fail, since even the simplest equations of motion for a nonlinear system can exhibit chaotic behavior. A recent theory by Feigenbaum suggests that nonlinear systems that can be led into chaotic behavior through a sequence of period-doubling bifurcations will exhibit a universal behavior. As the control parameter is increased, the bifurcation points occur in such a way that a proper ratio of these will approach the universal Feigenbaum number. Experimental evidence supporting the applicability of the Feigenbaum scenario to solar flux data is sparse. However, given the hypothesis that the Sun's convection zones are similar to a Rayleigh-Bernard mechanism, we can learn a great deal from the remarkable agreement observed between the prediction by theory (period doubling - a universal route to chaos) and the amplitude decrease of the signal's regular subharmonics. It is shown that period-doubling-type bifurcation is a possible route to a chaotic pattern of solar flux that is distinguishable from the logarithm of its power spectral density. This conclusion is the first positive step toward a reformulation of solar flux by a nonlinear chaotic approach. The ultimate goal of this research is to be able to predict an estimate of the upper and lower bounds for solar flux within its predictable zones. Naturally, it is an important task to identify the time horizons beyond which predictability becomes incompatible with computability.

Evidence of chaotic pattern in solar flux through a reproducible sequence of period-doubling-type bifurcations

NASA Technical Reports Server (NTRS)

Ashrafi, S.; Roszman, L.

1991-01-01

Presented here is a preliminary study of the limits to solar flux intensity prediction, and of whether the general lack of predictability in the solar flux arises from the nonlinear chaotic nature of the Sun's physical activity. Statistical analysis of a chaotic signal can extract only its most gross features, and detailed physical models fail, since even the simplest equations of motion for a nonlinear system can exhibit chaotic behavior. A recent theory by Feigenbaum suggests that nonlinear systems that can be led into chaotic behavior through a sequence of period-doubling bifurcations will exhibit a universal behavior. As the control parameter is increased, the bifurcation points occur in such a way that a proper ratio of these will approach the universal Feigenbaum number. Experimental evidence supporting the applicability of the Feigenbaum scenario to solar flux data is sparse. However, given the hypothesis that the Sun's convection zones are similar to a Rayleigh-Bernard mechanism, we can learn a great deal from the remarkable agreement observed between the prediction by theory (period doubling - a universal route to chaos) and the amplitude decrease of the signal's regular subharmonics. The authors show that period-doubling-type bifurcation is a possible route to a chaotic pattern of solar flux that is distinguishable from the logarithm of its power spectral density. This conclusion is the first positive step toward a reformulation of solar flux by a nonlinear chaotic approach. The ultimate goal of this research is to be able to predict an estimate of the upper and lower bounds for solar flux within its predictable zones. Naturally, it is an important task to identify the time horizons beyond which predictability becomes incompatible with computability.

Application of Four-Point Newton-EGSOR iteration for the numerical solution of 2D Porous Medium Equations

NASA Astrophysics Data System (ADS)

Chew, J. V. L.; Sulaiman, J.

2017-09-01

Partial differential equations that are used in describing the nonlinear heat and mass transfer phenomena are difficult to be solved. For the case where the exact solution is difficult to be obtained, it is necessary to use a numerical procedure such as the finite difference method to solve a particular partial differential equation. In term of numerical procedure, a particular method can be considered as an efficient method if the method can give an approximate solution within the specified error with the least computational complexity. Throughout this paper, the two-dimensional Porous Medium Equation (2D PME) is discretized by using the implicit finite difference scheme to construct the corresponding approximation equation. Then this approximation equation yields a large-sized and sparse nonlinear system. By using the Newton method to linearize the nonlinear system, this paper deals with the application of the Four-Point Newton-EGSOR (4NEGSOR) iterative method for solving the 2D PMEs. In addition to that, the efficiency of the 4NEGSOR iterative method is studied by solving three examples of the problems. Based on the comparative analysis, the Newton-Gauss-Seidel (NGS) and the Newton-SOR (NSOR) iterative methods are also considered. The numerical findings show that the 4NEGSOR method is superior to the NGS and the NSOR methods in terms of the number of iterations to get the converged solutions, the time of computation and the maximum absolute errors produced by the methods.

Finite element method for optimal guidance of an advanced launch vehicle

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Bless, Robert R.; Calise, Anthony J.; Leung, Martin

1992-01-01

A temporal finite element based on a mixed form of Hamilton's weak principle is summarized for optimal control problems. The resulting weak Hamiltonian finite element method is extended to allow for discontinuities in the states and/or discontinuities in the system equations. An extension of the formulation to allow for control inequality constraints is also presented. The formulation does not require element quadrature, and it produces a sparse system of nonlinear algebraic equations. To evaluate its feasibility for real-time guidance applications, this approach is applied to the trajectory optimization of a four-state, two-stage model with inequality constraints for an advanced launch vehicle. Numerical results for this model are presented and compared to results from a multiple-shooting code. The results show the accuracy and computational efficiency of the finite element method.

Two-step superresolution approach for surveillance face image through radial basis function-partial least squares regression and locality-induced sparse representation

NASA Astrophysics Data System (ADS)

Jiang, Junjun; Hu, Ruimin; Han, Zhen; Wang, Zhongyuan; Chen, Jun

2013-10-01

Face superresolution (SR), or face hallucination, refers to the technique of generating a high-resolution (HR) face image from a low-resolution (LR) one with the help of a set of training examples. It aims at transcending the limitations of electronic imaging systems. Applications of face SR include video surveillance, in which the individual of interest is often far from cameras. A two-step method is proposed to infer a high-quality and HR face image from a low-quality and LR observation. First, we establish the nonlinear relationship between LR face images and HR ones, according to radial basis function and partial least squares (RBF-PLS) regression, to transform the LR face into the global face space. Then, a locality-induced sparse representation (LiSR) approach is presented to enhance the local facial details once all the global faces for each LR training face are constructed. A comparison of some state-of-the-art SR methods shows the superiority of the proposed two-step approach, RBF-PLS global face regression followed by LiSR-based local patch reconstruction. Experiments also demonstrate the effectiveness under both simulation conditions and some real conditions.

A network model of successive partitioning-limited solute diffusion through the stratum corneum.

PubMed

Schumm, Phillip; Scoglio, Caterina M; van der Merwe, Deon

2010-02-07

As the most exposed point of contact with the external environment, the skin is an important barrier to many chemical exposures, including medications, potentially toxic chemicals and cosmetics. Traditional dermal absorption models treat the stratum corneum lipids as a homogenous medium through which solutes diffuse according to Fick's first law of diffusion. This approach does not explain non-linear absorption and irregular distribution patterns within the stratum corneum lipids as observed in experimental data. A network model, based on successive partitioning-limited solute diffusion through the stratum corneum, where the lipid structure is represented by a large, sparse, and regular network where nodes have variable characteristics, offers an alternative, efficient, and flexible approach to dermal absorption modeling that simulates non-linear absorption data patterns. Four model versions are presented: two linear models, which have unlimited node capacities, and two non-linear models, which have limited node capacities. The non-linear model outputs produce absorption to dose relationships that can be best characterized quantitatively by using power equations, similar to the equations used to describe non-linear experimental data.

Nonlinear hyperspectral unmixing based on sparse non-negative matrix factorization

NASA Astrophysics Data System (ADS)

Li, Jing; Li, Xiaorun; Zhao, Liaoying

2016-01-01

Hyperspectral unmixing aims at extracting pure material spectra, accompanied by their corresponding proportions, from a mixed pixel. Owing to modeling more accurate distribution of real material, nonlinear mixing models (non-LMM) are usually considered to hold better performance than LMMs in complicated scenarios. In the past years, numerous nonlinear models have been successfully applied to hyperspectral unmixing. However, most non-LMMs only think of sum-to-one constraint or positivity constraint while the widespread sparsity among real materials mixing is the very factor that cannot be ignored. That is, for non-LMMs, a pixel is usually composed of a few spectral signatures of different materials from all the pure pixel set. Thus, in this paper, a smooth sparsity constraint is incorporated into the state-of-the-art Fan nonlinear model to exploit the sparsity feature in nonlinear model and use it to enhance the unmixing performance. This sparsity-constrained Fan model is solved with the non-negative matrix factorization. The algorithm was implemented on synthetic and real hyperspectral data and presented its advantage over those competing algorithms in the experiments.

Compressive Spectral Method for the Simulation of the Nonlinear Gravity Waves

PubMed Central

Bayındır, Cihan

2016-01-01

In this paper an approach for decreasing the computational effort required for the spectral simulations of the fully nonlinear ocean waves is introduced. The proposed approach utilizes the compressive sampling algorithm and depends on the idea of using a smaller number of spectral components compared to the classical spectral method. After performing the time integration with a smaller number of spectral components and using the compressive sampling technique, it is shown that the ocean wave field can be reconstructed with a significantly better efficiency compared to the classical spectral method. For the sparse ocean wave model in the frequency domain the fully nonlinear ocean waves with Jonswap spectrum is considered. By implementation of a high-order spectral method it is shown that the proposed methodology can simulate the linear and the fully nonlinear ocean waves with negligible difference in the accuracy and with a great efficiency by reducing the computation time significantly especially for large time evolutions. PMID:26911357

Implicit solvers for unstructured meshes

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, Dimitri J.

1991-01-01

Implicit methods were developed and tested for unstructured mesh computations. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (Generalized Minimum Residual) technique. Three different preconditioners were studied, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over relaxation (SSOR). The preconditioners were optimized to have good vectorization properties. SSOR and ILU were also studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also studied. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Design of Warped Stretch Transform

PubMed Central

Mahjoubfar, Ata; Chen, Claire Lifan; Jalali, Bahram

2015-01-01

Time stretch dispersive Fourier transform enables real-time spectroscopy at the repetition rate of million scans per second. High-speed real-time instruments ranging from analog-to-digital converters to cameras and single-shot rare-phenomena capture equipment with record performance have been empowered by it. Its warped stretch variant, realized with nonlinear group delay dispersion, offers variable-rate spectral domain sampling, as well as the ability to engineer the time-bandwidth product of the signal’s envelope to match that of the data acquisition systems. To be able to reconstruct the signal with low loss, the spectrotemporal distribution of the signal spectrum needs to be sparse. Here, for the first time, we show how to design the kernel of the transform and specifically, the nonlinear group delay profile dictated by the signal sparsity. Such a kernel leads to smart stretching with nonuniform spectral resolution, having direct utility in improvement of data acquisition rate, real-time data compression, and enhancement of ultrafast data capture accuracy. We also discuss the application of warped stretch transform in spectrotemporal analysis of continuous-time signals. PMID:26602458

Storage of sparse files using parallel log-structured file system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bent, John M.; Faibish, Sorin; Grider, Gary

A sparse file is stored without holes by storing a data portion of the sparse file using a parallel log-structured file system; and generating an index entry for the data portion, the index entry comprising a logical offset, physical offset and length of the data portion. The holes can be restored to the sparse file upon a reading of the sparse file. The data portion can be stored at a logical end of the sparse file. Additional storage efficiency can optionally be achieved by (i) detecting a write pattern for a plurality of the data portions and generating a singlemore » patterned index entry for the plurality of the patterned data portions; and/or (ii) storing the patterned index entries for a plurality of the sparse files in a single directory, wherein each entry in the single directory comprises an identifier of a corresponding sparse file.« less

Curvelet-based compressive sensing for InSAR raw data

NASA Astrophysics Data System (ADS)

Costa, Marcello G.; da Silva Pinho, Marcelo; Fernandes, David

2015-10-01

The aim of this work is to evaluate the compression performance of SAR raw data for interferometry applications collected by airborne from BRADAR (Brazilian SAR System operating in X and P bands) using the new approach based on compressive sensing (CS) to achieve an effective recovery with a good phase preserving. For this framework is desirable a real-time capability, where the collected data can be compressed to reduce onboard storage and bandwidth required for transmission. In the CS theory, a sparse unknown signals can be recovered from a small number of random or pseudo-random measurements by sparsity-promoting nonlinear recovery algorithms. Therefore, the original signal can be significantly reduced. To achieve the sparse representation of SAR signal, was done a curvelet transform. The curvelets constitute a directional frame, which allows an optimal sparse representation of objects with discontinuities along smooth curves as observed in raw data and provides an advanced denoising optimization. For the tests were made available a scene of 8192 x 2048 samples in range and azimuth in X-band with 2 m of resolution. The sparse representation was compressed using low dimension measurements matrices in each curvelet subband. Thus, an iterative CS reconstruction method based on IST (iterative soft/shrinkage threshold) was adjusted to recover the curvelets coefficients and then the original signal. To evaluate the compression performance were computed the compression ratio (CR), signal to noise ratio (SNR), and because the interferometry applications require more reconstruction accuracy the phase parameters like the standard deviation of the phase (PSD) and the mean phase error (MPE) were also computed. Moreover, in the image domain, a single-look complex image was generated to evaluate the compression effects. All results were computed in terms of sparsity analysis to provides an efficient compression and quality recovering appropriated for inSAR applications, therefore, providing a feasibility for compressive sensing application.

ODEion--a software module for structural identification of ordinary differential equations.

PubMed

Gennemark, Peter; Wedelin, Dag

2014-02-01

In the systems biology field, algorithms for structural identification of ordinary differential equations (ODEs) have mainly focused on fixed model spaces like S-systems and/or on methods that require sufficiently good data so that derivatives can be accurately estimated. There is therefore a lack of methods and software that can handle more general models and realistic data. We present ODEion, a software module for structural identification of ODEs. Main characteristic features of the software are: • The model space is defined by arbitrary user-defined functions that can be nonlinear in both variables and parameters, such as for example chemical rate reactions. • ODEion implements computationally efficient algorithms that have been shown to efficiently handle sparse and noisy data. It can run a range of realistic problems that previously required a supercomputer. • ODEion is easy to use and provides SBML output. We describe the mathematical problem, the ODEion system itself, and provide several examples of how the system can be used. Available at: http://www.odeidentification.org.

Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems

DOE PAGES

Bavier, Eric; Hoemmen, Mark; Rajamanickam, Sivasankaran; ...

2012-01-01

Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples themore » algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.« less

Sparse distributed memory overview

NASA Technical Reports Server (NTRS)

Raugh, Mike

1990-01-01

The Sparse Distributed Memory (SDM) project is investigating the theory and applications of massively parallel computing architecture, called sparse distributed memory, that will support the storage and retrieval of sensory and motor patterns characteristic of autonomous systems. The immediate objectives of the project are centered in studies of the memory itself and in the use of the memory to solve problems in speech, vision, and robotics. Investigation of methods for encoding sensory data is an important part of the research. Examples of NASA missions that may benefit from this work are Space Station, planetary rovers, and solar exploration. Sparse distributed memory offers promising technology for systems that must learn through experience and be capable of adapting to new circumstances, and for operating any large complex system requiring automatic monitoring and control. Sparse distributed memory is a massively parallel architecture motivated by efforts to understand how the human brain works. Sparse distributed memory is an associative memory, able to retrieve information from cues that only partially match patterns stored in the memory. It is able to store long temporal sequences derived from the behavior of a complex system, such as progressive records of the system's sensory data and correlated records of the system's motor controls.

Joint Sparse Representation for Robust Multimodal Biometrics Recognition

DTIC Science & Technology

2014-01-01

comprehensive multimodal dataset and a face database are described in section V. Finally, in section VI, we discuss the computational complexity of...fingerprint, iris, palmprint , hand geometry and voice from subjects of different age, gender and ethnicity as described in Table I. It is a...Taylor, “Constructing nonlinear discriminants from multiple data views,” Machine Learning and Knowl- edge Discovery in Databases , pp. 328–343, 2010

A Stabilized Sparse-Matrix U-D Square-Root Implementation of a Large-State Extended Kalman Filter

NASA Technical Reports Server (NTRS)

Boggs, D.; Ghil, M.; Keppenne, C.

1995-01-01

The full nonlinear Kalman filter sequential algorithm is, in theory, well-suited to the four-dimensional data assimilation problem in large-scale atmospheric and oceanic problems. However, it was later discovered that this algorithm can be very sensitive to computer roundoff, and that results may cease to be meaningful as time advances. Implementations of a modified Kalman filter are given.

A 3D Freehand Ultrasound System for Multi-view Reconstructions from Sparse 2D Scanning Planes

PubMed Central

2011-01-01

Background A significant limitation of existing 3D ultrasound systems comes from the fact that the majority of them work with fixed acquisition geometries. As a result, the users have very limited control over the geometry of the 2D scanning planes. Methods We present a low-cost and flexible ultrasound imaging system that integrates several image processing components to allow for 3D reconstructions from limited numbers of 2D image planes and multiple acoustic views. Our approach is based on a 3D freehand ultrasound system that allows users to control the 2D acquisition imaging using conventional 2D probes. For reliable performance, we develop new methods for image segmentation and robust multi-view registration. We first present a new hybrid geometric level-set approach that provides reliable segmentation performance with relatively simple initializations and minimum edge leakage. Optimization of the segmentation model parameters and its effect on performance is carefully discussed. Second, using the segmented images, a new coarse to fine automatic multi-view registration method is introduced. The approach uses a 3D Hotelling transform to initialize an optimization search. Then, the fine scale feature-based registration is performed using a robust, non-linear least squares algorithm. The robustness of the multi-view registration system allows for accurate 3D reconstructions from sparse 2D image planes. Results Volume measurements from multi-view 3D reconstructions are found to be consistently and significantly more accurate than measurements from single view reconstructions. The volume error of multi-view reconstruction is measured to be less than 5% of the true volume. We show that volume reconstruction accuracy is a function of the total number of 2D image planes and the number of views for calibrated phantom. In clinical in-vivo cardiac experiments, we show that volume estimates of the left ventricle from multi-view reconstructions are found to be in better agreement with clinical measures than measures from single view reconstructions. Conclusions Multi-view 3D reconstruction from sparse 2D freehand B-mode images leads to more accurate volume quantification compared to single view systems. The flexibility and low-cost of the proposed system allow for fine control of the image acquisition planes for optimal 3D reconstructions from multiple views. PMID:21251284

A 3D freehand ultrasound system for multi-view reconstructions from sparse 2D scanning planes.

PubMed

Yu, Honggang; Pattichis, Marios S; Agurto, Carla; Beth Goens, M

2011-01-20

A significant limitation of existing 3D ultrasound systems comes from the fact that the majority of them work with fixed acquisition geometries. As a result, the users have very limited control over the geometry of the 2D scanning planes. We present a low-cost and flexible ultrasound imaging system that integrates several image processing components to allow for 3D reconstructions from limited numbers of 2D image planes and multiple acoustic views. Our approach is based on a 3D freehand ultrasound system that allows users to control the 2D acquisition imaging using conventional 2D probes.For reliable performance, we develop new methods for image segmentation and robust multi-view registration. We first present a new hybrid geometric level-set approach that provides reliable segmentation performance with relatively simple initializations and minimum edge leakage. Optimization of the segmentation model parameters and its effect on performance is carefully discussed. Second, using the segmented images, a new coarse to fine automatic multi-view registration method is introduced. The approach uses a 3D Hotelling transform to initialize an optimization search. Then, the fine scale feature-based registration is performed using a robust, non-linear least squares algorithm. The robustness of the multi-view registration system allows for accurate 3D reconstructions from sparse 2D image planes. Volume measurements from multi-view 3D reconstructions are found to be consistently and significantly more accurate than measurements from single view reconstructions. The volume error of multi-view reconstruction is measured to be less than 5% of the true volume. We show that volume reconstruction accuracy is a function of the total number of 2D image planes and the number of views for calibrated phantom. In clinical in-vivo cardiac experiments, we show that volume estimates of the left ventricle from multi-view reconstructions are found to be in better agreement with clinical measures than measures from single view reconstructions. Multi-view 3D reconstruction from sparse 2D freehand B-mode images leads to more accurate volume quantification compared to single view systems. The flexibility and low-cost of the proposed system allow for fine control of the image acquisition planes for optimal 3D reconstructions from multiple views.

Data based identification and prediction of nonlinear and complex dynamical systems

NASA Astrophysics Data System (ADS)

Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso

2016-07-01

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The "inverse" problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear dynamical systems theories with tools from statistical physics, optimization, engineering control, applied mathematics, and scientific computing enables the development of a number of paradigms to address the problem of nonlinear and complex systems reconstruction. In this Review, we describe the recent advances in this forefront and rapidly evolving field, with a focus on compressive sensing based methods. In particular, compressive sensing is a paradigm developed in recent years in applied mathematics, electrical engineering, and nonlinear physics to reconstruct sparse signals using only limited data. It has broad applications ranging from image compression/reconstruction to the analysis of large-scale sensor networks, and it has become a powerful technique to obtain high-fidelity signals for applications where sufficient observations are not available. We will describe in detail how compressive sensing can be exploited to address a diverse array of problems in data based reconstruction of nonlinear and complex networked systems. The problems include identification of chaotic systems and prediction of catastrophic bifurcations, forecasting future attractors of time-varying nonlinear systems, reconstruction of complex networks with oscillatory and evolutionary game dynamics, detection of hidden nodes, identification of chaotic elements in neuronal networks, reconstruction of complex geospatial networks and nodal positioning, and reconstruction of complex spreading networks with binary data.. A number of alternative methods, such as those based on system response to external driving, synchronization, and noise-induced dynamical correlation, will also be discussed. Due to the high relevance of network reconstruction to biological sciences, a special section is devoted to a brief survey of the current methods to infer biological networks. Finally, a number of open problems including control and controllability of complex nonlinear dynamical networks are discussed. The methods outlined in this Review are principled on various concepts in complexity science and engineering such as phase transitions, bifurcations, stabilities, and robustness. The methodologies have the potential to significantly improve our ability to understand a variety of complex dynamical systems ranging from gene regulatory systems to social networks toward the ultimate goal of controlling such systems.

Melanin-targeted nonlinear microscopy for label-free molecular diagnosis and staining (Conference Presentation)

NASA Astrophysics Data System (ADS)

Warren, Warren S.

2017-02-01

Visible absorption in tissue is dominated by a very small number of chromophores (hemoglobins and melanins) with broad optical spectra; for melanins in particular, the optical absorption spectrum is typically featureless. In addition, scattering limits penetration depth. As a result, the most common microscopy application by far is with excised tissue, which can be stained. However, nonlinear optical methods have the additional advantages of greater penetration depth and reduced sensitivity to scattering. Traditional nonlinear microscopy relies on mechanisms which produce light of a different color than the irradiating lasers, such as second harmonic generation or two photon induced fluorescence, and this contrast is sparse in biological issue without expressing or injecting different chromophores. Recently, stable laser sources and pulse shaping/pulse train modulation methods have made it possible to detect a much wider range of nonlinear molecular signatures, even at modest laser powers (much less than a laser pointer). Here we show the utility of a variety of such signatures (pump-probe, pulse-shaped stimulated Raman, cross-phase modulation) to quantitatively image the biochemical composition of transparent or pigmented tissue in a variety of applications, ranging from thin, unstained tissue sections to live knockout mice. The rich biochemical information provided by this method can be used as an indicator of melanocyte activity, which in turn (for example) reflects the status of melanocytic lesions. Comparisons with model systems (synthetic melanin nanoparticles, sepia melanin) and analysis of melanin degradation pathways in vivo have led to a quantitative understanding of the molecular basis of these changes.

State estimation and prediction using clustered particle filters.

PubMed

Lee, Yoonsang; Majda, Andrew J

2016-12-20

Particle filtering is an essential tool to improve uncertain model predictions by incorporating noisy observational data from complex systems including non-Gaussian features. A class of particle filters, clustered particle filters, is introduced for high-dimensional nonlinear systems, which uses relatively few particles compared with the standard particle filter. The clustered particle filter captures non-Gaussian features of the true signal, which are typical in complex nonlinear dynamical systems such as geophysical systems. The method is also robust in the difficult regime of high-quality sparse and infrequent observations. The key features of the clustered particle filtering are coarse-grained localization through the clustering of the state variables and particle adjustment to stabilize the method; each observation affects only neighbor state variables through clustering and particles are adjusted to prevent particle collapse due to high-quality observations. The clustered particle filter is tested for the 40-dimensional Lorenz 96 model with several dynamical regimes including strongly non-Gaussian statistics. The clustered particle filter shows robust skill in both achieving accurate filter results and capturing non-Gaussian statistics of the true signal. It is further extended to multiscale data assimilation, which provides the large-scale estimation by combining a cheap reduced-order forecast model and mixed observations of the large- and small-scale variables. This approach enables the use of a larger number of particles due to the computational savings in the forecast model. The multiscale clustered particle filter is tested for one-dimensional dispersive wave turbulence using a forecast model with model errors.

Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitions

NASA Astrophysics Data System (ADS)

Bui, Quan M.; Wang, Lu; Osei-Kuffuor, Daniel

2018-04-01

Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switching technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to deal with problems of this type. We demonstrate the effectiveness of the method through numerical results for the case of two-phase, two-component flow with phase appearance/disappearance. We also show that the strategy is efficient and scales optimally with problem size.

State estimation and prediction using clustered particle filters

PubMed Central

Lee, Yoonsang; Majda, Andrew J.

2016-01-01

Particle filtering is an essential tool to improve uncertain model predictions by incorporating noisy observational data from complex systems including non-Gaussian features. A class of particle filters, clustered particle filters, is introduced for high-dimensional nonlinear systems, which uses relatively few particles compared with the standard particle filter. The clustered particle filter captures non-Gaussian features of the true signal, which are typical in complex nonlinear dynamical systems such as geophysical systems. The method is also robust in the difficult regime of high-quality sparse and infrequent observations. The key features of the clustered particle filtering are coarse-grained localization through the clustering of the state variables and particle adjustment to stabilize the method; each observation affects only neighbor state variables through clustering and particles are adjusted to prevent particle collapse due to high-quality observations. The clustered particle filter is tested for the 40-dimensional Lorenz 96 model with several dynamical regimes including strongly non-Gaussian statistics. The clustered particle filter shows robust skill in both achieving accurate filter results and capturing non-Gaussian statistics of the true signal. It is further extended to multiscale data assimilation, which provides the large-scale estimation by combining a cheap reduced-order forecast model and mixed observations of the large- and small-scale variables. This approach enables the use of a larger number of particles due to the computational savings in the forecast model. The multiscale clustered particle filter is tested for one-dimensional dispersive wave turbulence using a forecast model with model errors. PMID:27930332

Mid-frequency MTF compensation of optical sparse aperture system.

PubMed

Zhou, Chenghao; Wang, Zhile

2018-03-19

Optical sparse aperture (OSA) can greatly improve the spatial resolution of optical system. However, because of its aperture dispersion and sparse, its mid-frequency modulation transfer function (MTF) are significantly lower than that of a single aperture system. The main focus of this paper is on the mid-frequency MTF compensation of the optical sparse aperture system. Firstly, the principle of the mid-frequency MTF decreasing and missing of optical sparse aperture are analyzed. This paper takes the filling factor as a clue. The method of processing the mid-frequency MTF decreasing with large filling factor and method of compensation mid-frequency MTF with small filling factor are given respectively. For the MTF mid-frequency decreasing, the image spatial-variant restoration method is proposed to restore the mid-frequency information in the image; for the mid-frequency MTF missing, two images obtained by two system respectively are fused to compensate the mid-frequency information in optical sparse aperture image. The feasibility of the two method are analyzed in this paper. The numerical simulation of the system and algorithm of the two cases are presented using Zemax and Matlab. The results demonstrate that by these two methods the mid-frequency MTF of OSA system can be compensated effectively.

Using absolute gravimeter data to determine vertical gravity gradients

USGS Publications Warehouse

Robertson, D.S.

2001-01-01

The position versus time data from a free-fall absolute gravimeter can be used to estimate the vertical gravity gradient in addition to the gravity value itself. Hipkin has reported success in estimating the vertical gradient value using a data set of unusually good quality. This paper explores techniques that may be applicable to a broader class of data that may be contaminated with "system response" errors of larger magnitude than were evident in the data used by Hipkin. This system response function is usually modelled as a sum of exponentially decaying sinusoidal components. The technique employed here involves combining the x0, v0 and g parameters from all the drops made during a site occupation into a single least-squares solution, and including the value of the vertical gradient and the coefficients of system response function in the same solution. The resulting non-linear equations must be solved iteratively and convergence presents some difficulties. Sparse matrix techniques are used to make the least-squares problem computationally tractable.

Analysis of Monte Carlo accelerated iterative methods for sparse linear systems: Analysis of Monte Carlo accelerated iterative methods for sparse linear systems

DOE PAGES

Benzi, Michele; Evans, Thomas M.; Hamilton, Steven P.; ...

2017-03-05

Here, we consider hybrid deterministic-stochastic iterative algorithms for the solution of large, sparse linear systems. Starting from a convergent splitting of the coefficient matrix, we analyze various types of Monte Carlo acceleration schemes applied to the original preconditioned Richardson (stationary) iteration. We expect that these methods will have considerable potential for resiliency to faults when implemented on massively parallel machines. We also establish sufficient conditions for the convergence of the hybrid schemes, and we investigate different types of preconditioners including sparse approximate inverses. Numerical experiments on linear systems arising from the discretization of partial differential equations are presented.

Variable is better than invariable: sparse VSS-NLMS algorithms with application to adaptive MIMO channel estimation.

PubMed

Gui, Guan; Chen, Zhang-xin; Xu, Li; Wan, Qun; Huang, Jiyan; Adachi, Fumiyuki

2014-01-01

Channel estimation problem is one of the key technical issues in sparse frequency-selective fading multiple-input multiple-output (MIMO) communication systems using orthogonal frequency division multiplexing (OFDM) scheme. To estimate sparse MIMO channels, sparse invariable step-size normalized least mean square (ISS-NLMS) algorithms were applied to adaptive sparse channel estimation (ACSE). It is well known that step-size is a critical parameter which controls three aspects: algorithm stability, estimation performance, and computational cost. However, traditional methods are vulnerable to cause estimation performance loss because ISS cannot balance the three aspects simultaneously. In this paper, we propose two stable sparse variable step-size NLMS (VSS-NLMS) algorithms to improve the accuracy of MIMO channel estimators. First, ASCE is formulated in MIMO-OFDM systems. Second, different sparse penalties are introduced to VSS-NLMS algorithm for ASCE. In addition, difference between sparse ISS-NLMS algorithms and sparse VSS-NLMS ones is explained and their lower bounds are also derived. At last, to verify the effectiveness of the proposed algorithms for ASCE, several selected simulation results are shown to prove that the proposed sparse VSS-NLMS algorithms can achieve better estimation performance than the conventional methods via mean square error (MSE) and bit error rate (BER) metrics.

Variable Is Better Than Invariable: Sparse VSS-NLMS Algorithms with Application to Adaptive MIMO Channel Estimation

PubMed Central

Gui, Guan; Chen, Zhang-xin; Xu, Li; Wan, Qun; Huang, Jiyan; Adachi, Fumiyuki

2014-01-01

Channel estimation problem is one of the key technical issues in sparse frequency-selective fading multiple-input multiple-output (MIMO) communication systems using orthogonal frequency division multiplexing (OFDM) scheme. To estimate sparse MIMO channels, sparse invariable step-size normalized least mean square (ISS-NLMS) algorithms were applied to adaptive sparse channel estimation (ACSE). It is well known that step-size is a critical parameter which controls three aspects: algorithm stability, estimation performance, and computational cost. However, traditional methods are vulnerable to cause estimation performance loss because ISS cannot balance the three aspects simultaneously. In this paper, we propose two stable sparse variable step-size NLMS (VSS-NLMS) algorithms to improve the accuracy of MIMO channel estimators. First, ASCE is formulated in MIMO-OFDM systems. Second, different sparse penalties are introduced to VSS-NLMS algorithm for ASCE. In addition, difference between sparse ISS-NLMS algorithms and sparse VSS-NLMS ones is explained and their lower bounds are also derived. At last, to verify the effectiveness of the proposed algorithms for ASCE, several selected simulation results are shown to prove that the proposed sparse VSS-NLMS algorithms can achieve better estimation performance than the conventional methods via mean square error (MSE) and bit error rate (BER) metrics. PMID:25089286

Sparse Event Modeling with Hierarchical Bayesian Kernel Methods

DTIC Science & Technology

2016-01-05

SECURITY CLASSIFICATION OF: The research objective of this proposal was to develop a predictive Bayesian kernel approach to model count data based on...several predictive variables. Such an approach, which we refer to as the Poisson Bayesian kernel model , is able to model the rate of occurrence of...which adds specificity to the model and can make nonlinear data more manageable. Early results show that the 1. REPORT DATE (DD-MM-YYYY) 4. TITLE

Catchments as non-linear filters: evaluating data-driven approaches for spatio-temporal predictions in ungauged basins

NASA Astrophysics Data System (ADS)

Bellugi, D. G.; Tennant, C.; Larsen, L.

2016-12-01

Catchment and climate heterogeneity complicate prediction of runoff across time and space, and resulting parameter uncertainty can lead to large accumulated errors in hydrologic models, particularly in ungauged basins. Recently, data-driven modeling approaches have been shown to avoid the accumulated uncertainty associated with many physically-based models, providing an appealing alternative for hydrologic prediction. However, the effectiveness of different methods in hydrologically and geomorphically distinct catchments, and the robustness of these methods to changing climate and changing hydrologic processes remain to be tested. Here, we evaluate the use of machine learning techniques to predict daily runoff across time and space using only essential climatic forcing (e.g. precipitation, temperature, and potential evapotranspiration) time series as model input. Model training and testing was done using a high quality dataset of daily runoff and climate forcing data for 25+ years for 600+ minimally-disturbed catchments (drainage area range 5-25,000 km2, median size 336 km2) that cover a wide range of climatic and physical characteristics. Preliminary results using Support Vector Regression (SVR) suggest that in some catchments this nonlinear-based regression technique can accurately predict daily runoff, while the same approach fails in other catchments, indicating that the representation of climate inputs and/or catchment filter characteristics in the model structure need further refinement to increase performance. We bolster this analysis by using Sparse Identification of Nonlinear Dynamics (a sparse symbolic regression technique) to uncover the governing equations that describe runoff processes in catchments where SVR performed well and for ones where it performed poorly, thereby enabling inference about governing processes. This provides a robust means of examining how catchment complexity influences runoff prediction skill, and represents a contribution towards the integration of data-driven inference and physically-based models.

Numerical study of heat transfer and fluid flow for steady crystal growth in a vertical Bridgman device

NASA Astrophysics Data System (ADS)

Pohlman, Matthew Michael

The study of heat transfer and fluid flow in a vertical Bridgman device is motivated by current industrial difficulties in growing crystals with as few defects as possible. For example, Gallium Arsenide (GaAs) is of great interest to the semiconductor industry but remains an uneconomical alternative to silicon because of the manufacturing problems. This dissertation is a two dimensional study of the fluid in an idealized Bridgman device. The model nonlinear PDEs are discretized using second order finite differencing. Newton's method solves the resulting nonlinear discrete equations. The large sparse linear systems involving the Jacobian are solved iteratively using the Generalized Minimum Residual method (GMRES). By adapting fast direct solvers for elliptic equations with simple boundary conditions, a good preconditioner is developed which is essential for GMRES to converge quickly. Trends of the fluid flow and heat transfer for typical ranges of the physical parameters are determined. Also, the size of the terms in the mathematical model are found by numerical investigation, in order to find what terms are in balance as the physical parameters vary. The results suggest the plausibility of simpler asymptotic solutions.

Comparison and analysis of nonlinear algorithms for compressed sensing in MRI.

PubMed

Yu, Yeyang; Hong, Mingjian; Liu, Feng; Wang, Hua; Crozier, Stuart

2010-01-01

Compressed sensing (CS) theory has been recently applied in Magnetic Resonance Imaging (MRI) to accelerate the overall imaging process. In the CS implementation, various algorithms have been used to solve the nonlinear equation system for better image quality and reconstruction speed. However, there are no explicit criteria for an optimal CS algorithm selection in the practical MRI application. A systematic and comparative study of those commonly used algorithms is therefore essential for the implementation of CS in MRI. In this work, three typical algorithms, namely, the Gradient Projection For Sparse Reconstruction (GPSR) algorithm, Interior-point algorithm (l(1)_ls), and the Stagewise Orthogonal Matching Pursuit (StOMP) algorithm are compared and investigated in three different imaging scenarios, brain, angiogram and phantom imaging. The algorithms' performances are characterized in terms of image quality and reconstruction speed. The theoretical results show that the performance of the CS algorithms is case sensitive; overall, the StOMP algorithm offers the best solution in imaging quality, while the GPSR algorithm is the most efficient one among the three methods. In the next step, the algorithm performances and characteristics will be experimentally explored. It is hoped that this research will further support the applications of CS in MRI.

Optimal bipedal interactions with dynamic terrain: synthesis and analysis via nonlinear programming

NASA Astrophysics Data System (ADS)

Hubicki, Christian; Goldman, Daniel; Ames, Aaron

In terrestrial locomotion, gait dynamics and motor control behaviors are tuned to interact efficiently and stably with the dynamics of the terrain (i.e. terradynamics). This controlled interaction must be particularly thoughtful in bipeds, as their reduced contact points render them highly susceptible to falls. While bipedalism under rigid terrain assumptions is well-studied, insights for two-legged locomotion on soft terrain, such as sand and dirt, are comparatively sparse. We seek an understanding of how biological bipeds stably and economically negotiate granular media, with an eye toward imbuing those abilities in bipedal robots. We present a trajectory optimization method for controlled systems subject to granular intrusion. By formulating a large-scale nonlinear program (NLP) with reduced-order resistive force theory (RFT) models and jamming cone dynamics, the optimized motions are informed and shaped by the dynamics of the terrain. Using a variant of direct collocation methods, we can express all optimization objectives and constraints in closed-form, resulting in rapid solving by standard NLP solvers, such as IPOPT. We employ this tool to analyze emergent features of bipedal locomotion in granular media, with an eye toward robotic implementation.

Time-Frequency Analysis of Non-Stationary Biological Signals with Sparse Linear Regression Based Fourier Linear Combiner.

PubMed

Wang, Yubo; Veluvolu, Kalyana C

2017-06-14

It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC). In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976) ratio and outperforms existing methods such as short-time Fourier transfrom (STFT), continuous Wavelet transform (CWT) and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error.

Sparse gammatone signal model optimized for English speech does not match the human auditory filters.

PubMed

Strahl, Stefan; Mertins, Alfred

2008-07-18

Evidence that neurosensory systems use sparse signal representations as well as improved performance of signal processing algorithms using sparse signal models raised interest in sparse signal coding in the last years. For natural audio signals like speech and environmental sounds, gammatone atoms have been derived as expansion functions that generate a nearly optimal sparse signal model (Smith, E., Lewicki, M., 2006. Efficient auditory coding. Nature 439, 978-982). Furthermore, gammatone functions are established models for the human auditory filters. Thus far, a practical application of a sparse gammatone signal model has been prevented by the fact that deriving the sparsest representation is, in general, computationally intractable. In this paper, we applied an accelerated version of the matching pursuit algorithm for gammatone dictionaries allowing real-time and large data set applications. We show that a sparse signal model in general has advantages in audio coding and that a sparse gammatone signal model encodes speech more efficiently in terms of sparseness than a sparse modified discrete cosine transform (MDCT) signal model. We also show that the optimal gammatone parameters derived for English speech do not match the human auditory filters, suggesting for signal processing applications to derive the parameters individually for each applied signal class instead of using psychometrically derived parameters. For brain research, it means that care should be taken with directly transferring findings of optimality for technical to biological systems.

Electromagnetic Formation Flight (EMFF) for Sparse Aperture Arrays

NASA Technical Reports Server (NTRS)

Kwon, Daniel W.; Miller, David W.; Sedwick, Raymond J.

2004-01-01

Traditional methods of actuating spacecraft in sparse aperture arrays use propellant as a reaction mass. For formation flying systems, propellant becomes a critical consumable which can be quickly exhausted while maintaining relative orientation. Additional problems posed by propellant include optical contamination, plume impingement, thermal emission, and vibration excitation. For these missions where control of relative degrees of freedom is important, we consider using a system of electromagnets, in concert with reaction wheels, to replace the consumables. Electromagnetic Formation Flight sparse apertures, powered by solar energy, are designed differently from traditional propulsion systems, which are based on V. This paper investigates the design of sparse apertures both inside and outside the Earth's gravity field.

Fast Sparse Coding for Range Data Denoising with Sparse Ridges Constraint.

PubMed

Gao, Zhi; Lao, Mingjie; Sang, Yongsheng; Wen, Fei; Ramesh, Bharath; Zhai, Ruifang

2018-05-06

Light detection and ranging (LiDAR) sensors have been widely deployed on intelligent systems such as unmanned ground vehicles (UGVs) and unmanned aerial vehicles (UAVs) to perform localization, obstacle detection, and navigation tasks. Thus, research into range data processing with competitive performance in terms of both accuracy and efficiency has attracted increasing attention. Sparse coding has revolutionized signal processing and led to state-of-the-art performance in a variety of applications. However, dictionary learning, which plays the central role in sparse coding techniques, is computationally demanding, resulting in its limited applicability in real-time systems. In this study, we propose sparse coding algorithms with a fixed pre-learned ridge dictionary to realize range data denoising via leveraging the regularity of laser range measurements in man-made environments. Experiments on both synthesized data and real data demonstrate that our method obtains accuracy comparable to that of sophisticated sparse coding methods, but with much higher computational efficiency.

Performance assessment of a single-pixel compressive sensing imaging system

NASA Astrophysics Data System (ADS)

Du Bosq, Todd W.; Preece, Bradley L.

2016-05-01

Conventional electro-optical and infrared (EO/IR) systems capture an image by measuring the light incident at each of the millions of pixels in a focal plane array. Compressive sensing (CS) involves capturing a smaller number of unconventional measurements from the scene, and then using a companion process known as sparse reconstruction to recover the image as if a fully populated array that satisfies the Nyquist criteria was used. Therefore, CS operates under the assumption that signal acquisition and data compression can be accomplished simultaneously. CS has the potential to acquire an image with equivalent information content to a large format array while using smaller, cheaper, and lower bandwidth components. However, the benefits of CS do not come without compromise. The CS architecture chosen must effectively balance between physical considerations (SWaP-C), reconstruction accuracy, and reconstruction speed to meet operational requirements. To properly assess the value of such systems, it is necessary to fully characterize the image quality, including artifacts and sensitivity to noise. Imagery of the two-handheld object target set at range was collected using a passive SWIR single-pixel CS camera for various ranges, mirror resolution, and number of processed measurements. Human perception experiments were performed to determine the identification performance within the trade space. The performance of the nonlinear CS camera was modeled with the Night Vision Integrated Performance Model (NV-IPM) by mapping the nonlinear degradations to an equivalent linear shift invariant model. Finally, the limitations of CS modeling techniques will be discussed.

[Formula: see text]-regularized recursive total least squares based sparse system identification for the error-in-variables.

PubMed

Lim, Jun-Seok; Pang, Hee-Suk

2016-01-01

In this paper an [Formula: see text]-regularized recursive total least squares (RTLS) algorithm is considered for the sparse system identification. Although recursive least squares (RLS) has been successfully applied in sparse system identification, the estimation performance in RLS based algorithms becomes worse, when both input and output are contaminated by noise (the error-in-variables problem). We proposed an algorithm to handle the error-in-variables problem. The proposed [Formula: see text]-RTLS algorithm is an RLS like iteration using the [Formula: see text] regularization. The proposed algorithm not only gives excellent performance but also reduces the required complexity through the effective inversion matrix handling. Simulations demonstrate the superiority of the proposed [Formula: see text]-regularized RTLS for the sparse system identification setting.

A general method to determine sampling windows for nonlinear mixed effects models with an application to population pharmacokinetic studies.

PubMed

Foo, Lee Kien; McGree, James; Duffull, Stephen

2012-01-01

Optimal design methods have been proposed to determine the best sampling times when sparse blood sampling is required in clinical pharmacokinetic studies. However, the optimal blood sampling time points may not be feasible in clinical practice. Sampling windows, a time interval for blood sample collection, have been proposed to provide flexibility in blood sampling times while preserving efficient parameter estimation. Because of the complexity of the population pharmacokinetic models, which are generally nonlinear mixed effects models, there is no analytical solution available to determine sampling windows. We propose a method for determination of sampling windows based on MCMC sampling techniques. The proposed method attains a stationary distribution rapidly and provides time-sensitive windows around the optimal design points. The proposed method is applicable to determine sampling windows for any nonlinear mixed effects model although our work focuses on an application to population pharmacokinetic models. Copyright © 2012 John Wiley & Sons, Ltd.

Analog system for computing sparse codes

DOEpatents

Rozell, Christopher John; Johnson, Don Herrick; Baraniuk, Richard Gordon; Olshausen, Bruno A.; Ortman, Robert Lowell

2010-08-24

A parallel dynamical system for computing sparse representations of data, i.e., where the data can be fully represented in terms of a small number of non-zero code elements, and for reconstructing compressively sensed images. The system is based on the principles of thresholding and local competition that solves a family of sparse approximation problems corresponding to various sparsity metrics. The system utilizes Locally Competitive Algorithms (LCAs), nodes in a population continually compete with neighboring units using (usually one-way) lateral inhibition to calculate coefficients representing an input in an over complete dictionary.

A monolithic homotopy continuation algorithm with application to computational fluid dynamics

NASA Astrophysics Data System (ADS)

Brown, David A.; Zingg, David W.

2016-09-01

A new class of homotopy continuation methods is developed suitable for globalizing quasi-Newton methods for large sparse nonlinear systems of equations. The new continuation methods, described as monolithic homotopy continuation, differ from the classical predictor-corrector algorithm in that the predictor and corrector phases are replaced with a single phase which includes both a predictor and corrector component. Conditional convergence and stability are proved analytically. Using a Laplacian-like operator to construct the homotopy, the new algorithm is shown to be more efficient than the predictor-corrector homotopy continuation algorithm as well as an implementation of the widely-used pseudo-transient continuation algorithm for some inviscid and turbulent, subsonic and transonic external aerodynamic flows over the ONERA M6 wing and the NACA 0012 airfoil using a parallel implicit Newton-Krylov finite-difference flow solver.

On the regularization for nonlinear tomographic absorption spectroscopy

NASA Astrophysics Data System (ADS)

Dai, Jinghang; Yu, Tao; Xu, Lijun; Cai, Weiwei

2018-02-01

Tomographic absorption spectroscopy (TAS) has attracted increased research efforts recently due to the development in both hardware and new imaging concepts such as nonlinear tomography and compressed sensing. Nonlinear TAS is one of the emerging modality that bases on the concept of nonlinear tomography and has been successfully demonstrated both numerically and experimentally. However, all the previous demonstrations were realized using only two orthogonal projections simply for ease of implementation. In this work, we examine the performance of nonlinear TAS using other beam arrangements and test the effectiveness of the beam optimization technique that has been developed for linear TAS. In addition, so far only smoothness prior has been adopted and applied in nonlinear TAS. Nevertheless, there are also other useful priors such as sparseness and model-based prior which have not been investigated yet. This work aims to show how these priors can be implemented and included in the reconstruction process. Regularization through Bayesian formulation will be introduced specifically for this purpose, and a method for the determination of a proper regularization factor will be proposed. The comparative studies performed with different beam arrangements and regularization schemes on a few representative phantoms suggest that the beam optimization method developed for linear TAS also works for the nonlinear counterpart and the regularization scheme should be selected properly according to the available a priori information under specific application scenarios so as to achieve the best reconstruction fidelity. Though this work is conducted under the context of nonlinear TAS, it can also provide useful insights for other tomographic modalities.

Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitions [Algebraic multigrid preconditioners for multiphase flow in porous media with phase transitions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bui, Quan M.; Wang, Lu; Osei-Kuffuor, Daniel

Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switchingmore » technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to deal with problems of this type. We demonstrate the effectiveness of the method through numerical results for the case of two-phase, two-component flow with phase appearance/disappearance. In conclusion, we also show that the strategy is efficient and scales optimally with problem size.« less

Algebraic multigrid preconditioners for two-phase flow in porous media with phase transitions [Algebraic multigrid preconditioners for multiphase flow in porous media with phase transitions

DOE PAGES

Bui, Quan M.; Wang, Lu; Osei-Kuffuor, Daniel

2018-02-06

Multiphase flow is a critical process in a wide range of applications, including oil and gas recovery, carbon sequestration, and contaminant remediation. Numerical simulation of multiphase flow requires solving of a large, sparse linear system resulting from the discretization of the partial differential equations modeling the flow. In the case of multiphase multicomponent flow with miscible effect, this is a very challenging task. The problem becomes even more difficult if phase transitions are taken into account. A new approach to handle phase transitions is to formulate the system as a nonlinear complementarity problem (NCP). Unlike in the primary variable switchingmore » technique, the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this study, we explore the effectiveness of a new multilevel strategy, based on the multigrid reduction technique, to deal with problems of this type. We demonstrate the effectiveness of the method through numerical results for the case of two-phase, two-component flow with phase appearance/disappearance. In conclusion, we also show that the strategy is efficient and scales optimally with problem size.« less

Gravitational clustering in the expanding universe - Controlled high-resolution studies in two dimensions

NASA Technical Reports Server (NTRS)

Beacom, John Francis; Dominik, Kurt G.; Melott, Adrian L.; Perkins, Sam P.; Shandarin, Sergei F.

1991-01-01

Results are presented from a series of gravitational clustering simulations in two dimensions. These simulations are a significant departure from previous work, since in two dimensions one can have large dynamic range in both length scale and mass using present computer technology. Controlled experiments were conducted by varying the slope of power-law initial density fluctuation spectra and varying cutoffs at large k, while holding constant the phases of individual Fourier components and the scale of nonlinearity. Filaments are found in many different simulations, even with pure power-law initial conditions. By direct comparison, filaments, called 'second-generation pancakes' are shown to arise as a consequence of mild nonlinearity on scales much larger than the correlation length and are not relics of an initial lattice or due to sparse sampling of the Fourier components. Bumps of low amplitude in the two-point correlation are found to be generic but usually only statistical fluctuations. Power spectra are much easier to relate to initial conditions, and seem to follow a simple triangular shape (on log-log plot) in the nonlinear regime. The rms density fluctuation with Gaussian smoothing is the most stable indicator of nonlinearity.

Fast Sparse Coding for Range Data Denoising with Sparse Ridges Constraint

PubMed Central

Lao, Mingjie; Sang, Yongsheng; Wen, Fei; Zhai, Ruifang

2018-01-01

Light detection and ranging (LiDAR) sensors have been widely deployed on intelligent systems such as unmanned ground vehicles (UGVs) and unmanned aerial vehicles (UAVs) to perform localization, obstacle detection, and navigation tasks. Thus, research into range data processing with competitive performance in terms of both accuracy and efficiency has attracted increasing attention. Sparse coding has revolutionized signal processing and led to state-of-the-art performance in a variety of applications. However, dictionary learning, which plays the central role in sparse coding techniques, is computationally demanding, resulting in its limited applicability in real-time systems. In this study, we propose sparse coding algorithms with a fixed pre-learned ridge dictionary to realize range data denoising via leveraging the regularity of laser range measurements in man-made environments. Experiments on both synthesized data and real data demonstrate that our method obtains accuracy comparable to that of sophisticated sparse coding methods, but with much higher computational efficiency. PMID:29734793

Kanerva's sparse distributed memory: An associative memory algorithm well-suited to the Connection Machine

NASA Technical Reports Server (NTRS)

Rogers, David

1988-01-01

The advent of the Connection Machine profoundly changes the world of supercomputers. The highly nontraditional architecture makes possible the exploration of algorithms that were impractical for standard Von Neumann architectures. Sparse distributed memory (SDM) is an example of such an algorithm. Sparse distributed memory is a particularly simple and elegant formulation for an associative memory. The foundations for sparse distributed memory are described, and some simple examples of using the memory are presented. The relationship of sparse distributed memory to three important computational systems is shown: random-access memory, neural networks, and the cerebellum of the brain. Finally, the implementation of the algorithm for sparse distributed memory on the Connection Machine is discussed.

Resonance-Based Sparse Signal Decomposition and its Application in Mechanical Fault Diagnosis: A Review.

PubMed

Huang, Wentao; Sun, Hongjian; Wang, Weijie

2017-06-03

Mechanical equipment is the heart of industry. For this reason, mechanical fault diagnosis has drawn considerable attention. In terms of the rich information hidden in fault vibration signals, the processing and analysis techniques of vibration signals have become a crucial research issue in the field of mechanical fault diagnosis. Based on the theory of sparse decomposition, Selesnick proposed a novel nonlinear signal processing method: resonance-based sparse signal decomposition (RSSD). Since being put forward, RSSD has become widely recognized, and many RSSD-based methods have been developed to guide mechanical fault diagnosis. This paper attempts to summarize and review the theoretical developments and application advances of RSSD in mechanical fault diagnosis, and to provide a more comprehensive reference for those interested in RSSD and mechanical fault diagnosis. Followed by a brief introduction of RSSD's theoretical foundation, based on different optimization directions, applications of RSSD in mechanical fault diagnosis are categorized into five aspects: original RSSD, parameter optimized RSSD, subband optimized RSSD, integrated optimized RSSD, and RSSD combined with other methods. On this basis, outstanding issues in current RSSD study are also pointed out, as well as corresponding instructional solutions. We hope this review will provide an insightful reference for researchers and readers who are interested in RSSD and mechanical fault diagnosis.

Resonance-Based Sparse Signal Decomposition and Its Application in Mechanical Fault Diagnosis: A Review

PubMed Central

Huang, Wentao; Sun, Hongjian; Wang, Weijie

2017-01-01

Mechanical equipment is the heart of industry. For this reason, mechanical fault diagnosis has drawn considerable attention. In terms of the rich information hidden in fault vibration signals, the processing and analysis techniques of vibration signals have become a crucial research issue in the field of mechanical fault diagnosis. Based on the theory of sparse decomposition, Selesnick proposed a novel nonlinear signal processing method: resonance-based sparse signal decomposition (RSSD). Since being put forward, RSSD has become widely recognized, and many RSSD-based methods have been developed to guide mechanical fault diagnosis. This paper attempts to summarize and review the theoretical developments and application advances of RSSD in mechanical fault diagnosis, and to provide a more comprehensive reference for those interested in RSSD and mechanical fault diagnosis. Followed by a brief introduction of RSSD’s theoretical foundation, based on different optimization directions, applications of RSSD in mechanical fault diagnosis are categorized into five aspects: original RSSD, parameter optimized RSSD, subband optimized RSSD, integrated optimized RSSD, and RSSD combined with other methods. On this basis, outstanding issues in current RSSD study are also pointed out, as well as corresponding instructional solutions. We hope this review will provide an insightful reference for researchers and readers who are interested in RSSD and mechanical fault diagnosis. PMID:28587198

Real-time model learning using Incremental Sparse Spectrum Gaussian Process Regression.

PubMed

Gijsberts, Arjan; Metta, Giorgio

2013-05-01

Novel applications in unstructured and non-stationary human environments require robots that learn from experience and adapt autonomously to changing conditions. Predictive models therefore not only need to be accurate, but should also be updated incrementally in real-time and require minimal human intervention. Incremental Sparse Spectrum Gaussian Process Regression is an algorithm that is targeted specifically for use in this context. Rather than developing a novel algorithm from the ground up, the method is based on the thoroughly studied Gaussian Process Regression algorithm, therefore ensuring a solid theoretical foundation. Non-linearity and a bounded update complexity are achieved simultaneously by means of a finite dimensional random feature mapping that approximates a kernel function. As a result, the computational cost for each update remains constant over time. Finally, algorithmic simplicity and support for automated hyperparameter optimization ensures convenience when employed in practice. Empirical validation on a number of synthetic and real-life learning problems confirms that the performance of Incremental Sparse Spectrum Gaussian Process Regression is superior with respect to the popular Locally Weighted Projection Regression, while computational requirements are found to be significantly lower. The method is therefore particularly suited for learning with real-time constraints or when computational resources are limited. Copyright © 2012 Elsevier Ltd. All rights reserved.

Epileptic Seizure Detection with Log-Euclidean Gaussian Kernel-Based Sparse Representation.

PubMed

Yuan, Shasha; Zhou, Weidong; Wu, Qi; Zhang, Yanli

2016-05-01

Epileptic seizure detection plays an important role in the diagnosis of epilepsy and reducing the massive workload of reviewing electroencephalography (EEG) recordings. In this work, a novel algorithm is developed to detect seizures employing log-Euclidean Gaussian kernel-based sparse representation (SR) in long-term EEG recordings. Unlike the traditional SR for vector data in Euclidean space, the log-Euclidean Gaussian kernel-based SR framework is proposed for seizure detection in the space of the symmetric positive definite (SPD) matrices, which form a Riemannian manifold. Since the Riemannian manifold is nonlinear, the log-Euclidean Gaussian kernel function is applied to embed it into a reproducing kernel Hilbert space (RKHS) for performing SR. The EEG signals of all channels are divided into epochs and the SPD matrices representing EEG epochs are generated by covariance descriptors. Then, the testing samples are sparsely coded over the dictionary composed by training samples utilizing log-Euclidean Gaussian kernel-based SR. The classification of testing samples is achieved by computing the minimal reconstructed residuals. The proposed method is evaluated on the Freiburg EEG dataset of 21 patients and shows its notable performance on both epoch-based and event-based assessments. Moreover, this method handles multiple channels of EEG recordings synchronously which is more speedy and efficient than traditional seizure detection methods.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chow, Edmond

Solving sparse problems is at the core of many DOE computational science applications. We focus on the challenge of developing sparse algorithms that can fully exploit the parallelism in extreme-scale computing systems, in particular systems with massive numbers of cores per node. Our approach is to express a sparse matrix factorization as a large number of bilinear constraint equations, and then solving these equations via an asynchronous iterative method. The unknowns in these equations are the matrix entries of the factorization that is desired.

Image fusion using sparse overcomplete feature dictionaries

DOEpatents

Brumby, Steven P.; Bettencourt, Luis; Kenyon, Garrett T.; Chartrand, Rick; Wohlberg, Brendt

2015-10-06

Approaches for deciding what individuals in a population of visual system "neurons" are looking for using sparse overcomplete feature dictionaries are provided. A sparse overcomplete feature dictionary may be learned for an image dataset and a local sparse representation of the image dataset may be built using the learned feature dictionary. A local maximum pooling operation may be applied on the local sparse representation to produce a translation-tolerant representation of the image dataset. An object may then be classified and/or clustered within the translation-tolerant representation of the image dataset using a supervised classification algorithm and/or an unsupervised clustering algorithm.

A sparse reconstruction method for the estimation of multiresolution emission fields via atmospheric inversion

DOE PAGES

Ray, J.; Lee, J.; Yadav, V.; ...

2014-08-20

We present a sparse reconstruction scheme that can also be used to ensure non-negativity when fitting wavelet-based random field models to limited observations in non-rectangular geometries. The method is relevant when multiresolution fields are estimated using linear inverse problems. Examples include the estimation of emission fields for many anthropogenic pollutants using atmospheric inversion or hydraulic conductivity in aquifers from flow measurements. The scheme is based on three new developments. Firstly, we extend an existing sparse reconstruction method, Stagewise Orthogonal Matching Pursuit (StOMP), to incorporate prior information on the target field. Secondly, we develop an iterative method that uses StOMP tomore » impose non-negativity on the estimated field. Finally, we devise a method, based on compressive sensing, to limit the estimated field within an irregularly shaped domain. We demonstrate the method on the estimation of fossil-fuel CO 2 (ffCO 2) emissions in the lower 48 states of the US. The application uses a recently developed multiresolution random field model and synthetic observations of ffCO 2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of two. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.« less

AZTEC. Parallel Iterative method Software for Solving Linear Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hutchinson, S.; Shadid, J.; Tuminaro, R.

1995-07-01

AZTEC is an interactive library that greatly simplifies the parrallelization process when solving the linear systems of equations Ax=b where A is a user supplied n X n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. AZTEC is intended as a software tool for users who want to avoid cumbersome parallel programming details but who have large sparse linear systems which require an efficiently utilized parallel processing system. A collection of data transformation tools are provided that allow for easy creation of distributed sparse unstructured matricesmore » for parallel solutions.« less

Development of a steady potential solver for use with linearized, unsteady aerodynamic analyses

NASA Technical Reports Server (NTRS)

Hoyniak, Daniel; Verdon, Joseph M.

1991-01-01

A full potential steady flow solver (SFLOW) developed explicitly for use with an inviscid unsteady aerodynamic analysis (LINFLO) is described. The steady solver uses the nonconservative form of the nonlinear potential flow equations together with an implicit, least squares, finite difference approximation to solve for the steady flow field. The difference equations were developed on a composite mesh which consists of a C grid embedded in a rectilinear (H grid) cascade mesh. The composite mesh is capable of resolving blade to blade and far field phenomena on the H grid, while accurately resolving local phenomena on the C grid. The resulting system of algebraic equations is arranged in matrix form using a sparse matrix package and solved by Newton's method. Steady and unsteady results are presented for two cascade configurations: a high speed compressor and a turbine with high exit Mach number.

Comparison of empirical and data driven hydrometeorological hazard models on coastal cities of São Paulo, Brazil

NASA Astrophysics Data System (ADS)

Koga-Vicente, A.; Friedel, M. J.

2010-12-01

Every year thousands of people are affected by floods and landslide hazards caused by rainstorms. The problem is more serious in tropical developing countries because of the susceptibility as a result of the high amount of available energy to form storms, and the high vulnerability due to poor economic and social conditions. Predictive models of hazards are important tools to manage this kind of risk. In this study, a comparison of two different modeling approaches was made for predicting hydrometeorological hazards in 12 cities on the coast of São Paulo, Brazil, from 1994 to 2003. In the first approach, an empirical multiple linear regression (MLR) model was developed and used; the second approach used a type of unsupervised nonlinear artificial neural network called a self-organized map (SOM). By using twenty three independent variables of susceptibility (precipitation, soil type, slope, elevation, and regional atmospheric system scale) and vulnerability (distribution and total population, income and educational characteristics, poverty intensity, human development index), binary hazard responses were obtained. Model performance by cross-validation indicated that the respective MLR and SOM model accuracy was about 67% and 80%. Prediction accuracy can be improved by the addition of information, but the SOM approach is preferred because of sparse data and highly nonlinear relations among the independent variables.

Scalable implicit incompressible resistive MHD with stabilized FE and fully-coupled Newton–Krylov-AMG

DOE PAGES

Shadid, J. N.; Pawlowski, R. P.; Cyr, E. C.; ...

2016-02-10

Here, we discuss that the computational solution of the governing balance equations for mass, momentum, heat transfer and magnetic induction for resistive magnetohydrodynamics (MHD) systems can be extremely challenging. These difficulties arise from both the strong nonlinear, nonsymmetric coupling of fluid and electromagnetic phenomena, as well as the significant range of time- and length-scales that the interactions of these physical mechanisms produce. This paper explores the development of a scalable, fully-implicit stabilized unstructured finite element (FE) capability for 3D incompressible resistive MHD. The discussion considers the development of a stabilized FE formulation in context of the variational multiscale (VMS) method,more » and describes the scalable implicit time integration and direct-to-steady-state solution capability. The nonlinear solver strategy employs Newton–Krylov methods, which are preconditioned using fully-coupled algebraic multilevel preconditioners. These preconditioners are shown to enable a robust, scalable and efficient solution approach for the large-scale sparse linear systems generated by the Newton linearization. Verification results demonstrate the expected order-of-accuracy for the stabilized FE discretization. The approach is tested on a variety of prototype problems, that include MHD duct flows, an unstable hydromagnetic Kelvin–Helmholtz shear layer, and a 3D island coalescence problem used to model magnetic reconnection. Initial results that explore the scaling of the solution methods are also presented on up to 128K processors for problems with up to 1.8B unknowns on a CrayXK7.« less

CGRO Guest Investigator Program

NASA Technical Reports Server (NTRS)

Begelman, Mitchell C.

1997-01-01

The following are highlights from the research supported by this grant: (1) Theory of gamma-ray blazars: We studied the theory of gamma-ray blazars, being among the first investigators to propose that the GeV emission arises from Comptonization of diffuse radiation surrounding the jet, rather than from the synchrotron-self-Compton mechanism. In related work, we uncovered possible connections between the mechanisms of gamma-ray blazars and those of intraday radio variability, and have conducted a general study of the role of Compton radiation drag on the dynamics of relativistic jets. (2) A Nonlinear Monte Carlo code for gamma-ray spectrum formation: We developed, tested, and applied the first Nonlinear Monte Carlo (NLMC) code for simulating gamma-ray production and transfer under much more general (and realistic) conditions than are accessible with other techniques. The present version of the code is designed to simulate conditions thought to be present in active galactic nuclei and certain types of X-ray binaries, and includes the physics needed to model thermal and nonthermal electron-positron pair cascades. Unlike traditional Monte-Carlo techniques, our method can accurately handle highly non-linear systems in which the radiation and particle backgrounds must be determined self-consistently and in which the particle energies span many orders of magnitude. Unlike models based on kinetic equations, our code can handle arbitrary source geometries and relativistic kinematic effects In its first important application following testing, we showed that popular semi-analytic accretion disk corona models for Seyfert spectra are seriously in error, and demonstrated how the spectra can be simulated if the disk is sparsely covered by localized 'flares'.

Adaptive regulation of sparseness by feedforward inhibition

PubMed Central

Assisi, Collins; Stopfer, Mark; Laurent, Gilles; Bazhenov, Maxim

2014-01-01

In the mushroom body of insects, odors are represented by very few spikes in a small number of neurons, a highly efficient strategy known as sparse coding. Physiological studies of these neurons have shown that sparseness is maintained across thousand-fold changes in odor concentration. Using a realistic computational model, we propose that sparseness in the olfactory system is regulated by adaptive feedforward inhibition. When odor concentration changes, feedforward inhibition modulates the duration of the temporal window over which the mushroom body neurons may integrate excitatory presynaptic input. This simple adaptive mechanism could maintain the sparseness of sensory representations across wide ranges of stimulus conditions. PMID:17660812

A new approach for solving seismic tomography problems and assessing the uncertainty through the use of graph theory and direct methods

NASA Astrophysics Data System (ADS)

Bogiatzis, P.; Ishii, M.; Davis, T. A.

2016-12-01

Seismic tomography inverse problems are among the largest high-dimensional parameter estimation tasks in Earth science. We show how combinatorics and graph theory can be used to analyze the structure of such problems, and to effectively decompose them into smaller ones that can be solved efficiently by means of the least squares method. In combination with recent high performance direct sparse algorithms, this reduction in dimensionality allows for an efficient computation of the model resolution and covariance matrices using limited resources. Furthermore, we show that a new sparse singular value decomposition method can be used to obtain the complete spectrum of the singular values. This procedure provides the means for more objective regularization and further dimensionality reduction of the problem. We apply this methodology to a moderate size, non-linear seismic tomography problem to image the structure of the crust and the upper mantle beneath Japan using local deep earthquakes recorded by the High Sensitivity Seismograph Network stations.

Transformer fault diagnosis using continuous sparse autoencoder.

PubMed

Wang, Lukun; Zhao, Xiaoying; Pei, Jiangnan; Tang, Gongyou

2016-01-01

This paper proposes a novel continuous sparse autoencoder (CSAE) which can be used in unsupervised feature learning. The CSAE adds Gaussian stochastic unit into activation function to extract features of nonlinear data. In this paper, CSAE is applied to solve the problem of transformer fault recognition. Firstly, based on dissolved gas analysis method, IEC three ratios are calculated by the concentrations of dissolved gases. Then IEC three ratios data is normalized to reduce data singularity and improve training speed. Secondly, deep belief network is established by two layers of CSAE and one layer of back propagation (BP) network. Thirdly, CSAE is adopted to unsupervised training and getting features. Then BP network is used for supervised training and getting transformer fault. Finally, the experimental data from IEC TC 10 dataset aims to illustrate the effectiveness of the presented approach. Comparative experiments clearly show that CSAE can extract features from the original data, and achieve a superior correct differentiation rate on transformer fault diagnosis.

Variational Assimilation of Sparse and Uncertain Satellite Data For 1D Saint-Venant River Models

NASA Astrophysics Data System (ADS)

Garambois, P. A.; Brisset, P.; Monnier, J.; Roux, H.

2016-12-01

Profusion of satellites are providing increasingly accurate measurements of continental water cyle, and water bodies variations while in situ observability is declining. The future Surface Water and Ocean Topography (SWOT) mission will provide maps of river surface elevations widths and slopes with an almost global coverage and temporal revisits. This will offer the possibility to address a larger variety of inverse problems in surface hydrology. Data assimilation techniques, that are broadly used in several scientific fields, aim to optimally combine models, system observations and prior information. Variational assimilation consists in iterative minimization of a discrepency measure between model outputs and observations, here for retrieving boundary conditions and parameters of a 1D Saint Venant model. Nevertheless, inferring river discharge and hydraulic parameters thanks to the observation of river surface is not straightforward. This is particularly true in the case of sparse and uncertain observations of flow state variables since they are governed by nonlinear physical processes. This paper investigates the identifiability of hydraulic controls given sparse and uncertain satellite observations of a river. The identifiability of river discharge alone and with roughness is tested for several spatio temporal patterns of river observations, including SWOT like observations. A new 1D Shallow water model with variational data assimilation, within the DassFlow chain is presented as well as postprocessing and observation operator dedicated to the future SWOT and SWOT simulator data. In view to decrease inverse problem dimensionality discharge is represented in a reduced basis. Moreover we introduce an original and reduced parametrization of the flow resistance that can account for various flow regimes along with a cross section design dedicated to remote sensing. We show which discharge temporal frequencies can be identified w.r.t observation ones and at which accuracy. Eventually the important question of the discharge identifiability potential between observation times and depending on the spatio-temporal sampling is adressed with respect to the wave lengths of the hydrological signals.

Individual Differences in Boys’ and Girls’ Timing and Tempo of Puberty: Modeling Development With Nonlinear Growth Models

PubMed Central

Marceau, Kristine; Ram, Nilam; Houts, Renate M.; Grimm, Kevin J.; Susman, Elizabeth J.

2014-01-01

Pubertal development is a nonlinear process progressing from prepubescent beginnings through biological, physical, and psychological changes to full sexual maturity. To tether theoretical concepts of puberty with sophisticated longitudinal, analytical models capable of articulating pubertal development more accurately, we used nonlinear mixed-effects models to describe both the timing and tempo of pubertal development in the sample of 364 White boys and 373 White girls measured across 6 years as part of the National Institute of Child Health and Human Development Study of Early Child Care and Youth Development. Individual differences in timing and tempo were extracted with models of logistic growth. Differential relations emerged for how boys’ and girls’ timing and tempo of development were related to physical characteristics (body mass index, height, and weight) and psychological outcomes (internalizing problems, externalizing problems, and risky sexual behavior). Timing and tempo are associated in boys but not girls. Pubertal timing and tempo are particularly important for predicting psychological outcomes in girls but only sparsely related to boys’ psychological outcomes. Results highlight the importance of considering the nonlinear nature of puberty and expand the repertoire of possibilities for examining important aspects of how and when pubertal processes contribute to development. PMID:21639623

Method and apparatus for distinguishing actual sparse events from sparse event false alarms

DOEpatents

Spalding, Richard E.; Grotbeck, Carter L.

2000-01-01

Remote sensing method and apparatus wherein sparse optical events are distinguished from false events. "Ghost" images of actual optical phenomena are generated using an optical beam splitter and optics configured to direct split beams to a single sensor or segmented sensor. True optical signals are distinguished from false signals or noise based on whether the ghost image is presence or absent. The invention obviates the need for dual sensor systems to effect a false target detection capability, thus significantly reducing system complexity and cost.

Predictive uncertainty analysis of plume distribution for geological carbon sequestration using sparse-grid Bayesian method

NASA Astrophysics Data System (ADS)

Shi, X.; Zhang, G.

2013-12-01

Because of the extensive computational burden, parametric uncertainty analyses are rarely conducted for geological carbon sequestration (GCS) process based multi-phase models. The difficulty of predictive uncertainty analysis for the CO2 plume migration in realistic GCS models is not only due to the spatial distribution of the caprock and reservoir (i.e. heterogeneous model parameters), but also because the GCS optimization estimation problem has multiple local minima due to the complex nonlinear multi-phase (gas and aqueous), and multi-component (water, CO2, salt) transport equations. The geological model built by Doughty and Pruess (2004) for the Frio pilot site (Texas) was selected and assumed to represent the 'true' system, which was composed of seven different facies (geological units) distributed among 10 layers. We chose to calibrate the permeabilities of these facies. Pressure and gas saturation values from this true model were then extracted and used as observations for subsequent model calibration. Random noise was added to the observations to approximate realistic field conditions. Each simulation of the model lasts about 2 hours. In this study, we develop a new approach that improves computational efficiency of Bayesian inference by constructing a surrogate system based on an adaptive sparse-grid stochastic collocation method. This surrogate response surface global optimization algorithm is firstly used to calibrate the model parameters, then prediction uncertainty of the CO2 plume position is quantified due to the propagation from parametric uncertainty in the numerical experiments, which is also compared to the actual plume from the 'true' model. Results prove that the approach is computationally efficient for multi-modal optimization and prediction uncertainty quantification for computationally expensive simulation models. Both our inverse methodology and findings can be broadly applicable to GCS in heterogeneous storage formations.

KEEN Wave Simulations: Comparing various PIC to various fixed grid Vlasov to Phase-Space Adaptive Sparse Tiling & Effective Lagrangian (PASTEL) Techniques

NASA Astrophysics Data System (ADS)

Afeyan, Bedros; Larson, David; Shadwick, Bradley; Sydora, Richard

2017-10-01

We compare various ways of solving the Vlasov-Poisson and Vlasov-Maxwell equations on rather demanding nonlinear kinetic phenomena associated with KEEN and KEEPN waves. KEEN stands for Kinetic, Electrostatic, Electron Nonlinear, and KEEPN, for electron-positron or pair plasmas analogs. Because these self-organized phase space structures are not steady-state, or single mode, or fluid or low order moment equation limited, typical techniques with low resolution or too much noise will distort the answer too much, too soon, and fail. This will be shown via Penrose criteria triggers for instability at the formation stage as well as particle orbit statistics in fully formed KEEN waves and KEEN-KEEN and KEEN-EPW interacting states. We will argue that PASTEL is a viable alternative to traditional methods with reasonable chances of success in higher dimensions. Work supported by a Grant from AFOSR PEEP.

Joint sparsity based heterogeneous data-level fusion for target detection and estimation

NASA Astrophysics Data System (ADS)

Niu, Ruixin; Zulch, Peter; Distasio, Marcello; Blasch, Erik; Shen, Dan; Chen, Genshe

2017-05-01

Typical surveillance systems employ decision- or feature-level fusion approaches to integrate heterogeneous sensor data, which are sub-optimal and incur information loss. In this paper, we investigate data-level heterogeneous sensor fusion. Since the sensors monitor the common targets of interest, whose states can be determined by only a few parameters, it is reasonable to assume that the measurement domain has a low intrinsic dimensionality. For heterogeneous sensor data, we develop a joint-sparse data-level fusion (JSDLF) approach based on the emerging joint sparse signal recovery techniques by discretizing the target state space. This approach is applied to fuse signals from multiple distributed radio frequency (RF) signal sensors and a video camera for joint target detection and state estimation. The JSDLF approach is data-driven and requires minimum prior information, since there is no need to know the time-varying RF signal amplitudes, or the image intensity of the targets. It can handle non-linearity in the sensor data due to state space discretization and the use of frequency/pixel selection matrices. Furthermore, for a multi-target case with J targets, the JSDLF approach only requires discretization in a single-target state space, instead of discretization in a J-target state space, as in the case of the generalized likelihood ratio test (GLRT) or the maximum likelihood estimator (MLE). Numerical examples are provided to demonstrate that the proposed JSDLF approach achieves excellent performance with near real-time accurate target position and velocity estimates.

Robust Small Target Co-Detection from Airborne Infrared Image Sequences.

PubMed

Gao, Jingli; Wen, Chenglin; Liu, Meiqin

2017-09-29

In this paper, a novel infrared target co-detection model combining the self-correlation features of backgrounds and the commonality features of targets in the spatio-temporal domain is proposed to detect small targets in a sequence of infrared images with complex backgrounds. Firstly, a dense target extraction model based on nonlinear weights is proposed, which can better suppress background of images and enhance small targets than weights of singular values. Secondly, a sparse target extraction model based on entry-wise weighted robust principal component analysis is proposed. The entry-wise weight adaptively incorporates structural prior in terms of local weighted entropy, thus, it can extract real targets accurately and suppress background clutters efficiently. Finally, the commonality of targets in the spatio-temporal domain are used to construct target refinement model for false alarms suppression and target confirmation. Since real targets could appear in both of the dense and sparse reconstruction maps of a single frame, and form trajectories after tracklet association of consecutive frames, the location correlation of the dense and sparse reconstruction maps for a single frame and tracklet association of the location correlation maps for successive frames have strong ability to discriminate between small targets and background clutters. Experimental results demonstrate that the proposed small target co-detection method can not only suppress background clutters effectively, but also detect targets accurately even if with target-like interference.

On the role of sparseness in the evolution of modularity in gene regulatory networks

PubMed Central

2018-01-01

Modularity is a widespread property in biological systems. It implies that interactions occur mainly within groups of system elements. A modular arrangement facilitates adjustment of one module without perturbing the rest of the system. Therefore, modularity of developmental mechanisms is a major factor for evolvability, the potential to produce beneficial variation from random genetic change. Understanding how modularity evolves in gene regulatory networks, that create the distinct gene activity patterns that characterize different parts of an organism, is key to developmental and evolutionary biology. One hypothesis for the evolution of modules suggests that interactions between some sets of genes become maladaptive when selection favours additional gene activity patterns. The removal of such interactions by selection would result in the formation of modules. A second hypothesis suggests that modularity evolves in response to sparseness, the scarcity of interactions within a system. Here I simulate the evolution of gene regulatory networks and analyse diverse experimentally sustained networks to study the relationship between sparseness and modularity. My results suggest that sparseness alone is neither sufficient nor necessary to explain modularity in gene regulatory networks. However, sparseness amplifies the effects of forms of selection that, like selection for additional gene activity patterns, already produce an increase in modularity. That evolution of new gene activity patterns is frequent across evolution also supports that it is a major factor in the evolution of modularity. That sparseness is widespread across gene regulatory networks indicates that it may have facilitated the evolution of modules in a wide variety of cases. PMID:29775459

On the role of sparseness in the evolution of modularity in gene regulatory networks.

PubMed

Espinosa-Soto, Carlos

2018-05-01

Modularity is a widespread property in biological systems. It implies that interactions occur mainly within groups of system elements. A modular arrangement facilitates adjustment of one module without perturbing the rest of the system. Therefore, modularity of developmental mechanisms is a major factor for evolvability, the potential to produce beneficial variation from random genetic change. Understanding how modularity evolves in gene regulatory networks, that create the distinct gene activity patterns that characterize different parts of an organism, is key to developmental and evolutionary biology. One hypothesis for the evolution of modules suggests that interactions between some sets of genes become maladaptive when selection favours additional gene activity patterns. The removal of such interactions by selection would result in the formation of modules. A second hypothesis suggests that modularity evolves in response to sparseness, the scarcity of interactions within a system. Here I simulate the evolution of gene regulatory networks and analyse diverse experimentally sustained networks to study the relationship between sparseness and modularity. My results suggest that sparseness alone is neither sufficient nor necessary to explain modularity in gene regulatory networks. However, sparseness amplifies the effects of forms of selection that, like selection for additional gene activity patterns, already produce an increase in modularity. That evolution of new gene activity patterns is frequent across evolution also supports that it is a major factor in the evolution of modularity. That sparseness is widespread across gene regulatory networks indicates that it may have facilitated the evolution of modules in a wide variety of cases.

Representation-Independent Iteration of Sparse Data Arrays

NASA Technical Reports Server (NTRS)

James, Mark

2007-01-01

An approach is defined that describes a method of iterating over massively large arrays containing sparse data using an approach that is implementation independent of how the contents of the sparse arrays are laid out in memory. What is unique and important here is the decoupling of the iteration over the sparse set of array elements from how they are internally represented in memory. This enables this approach to be backward compatible with existing schemes for representing sparse arrays as well as new approaches. What is novel here is a new approach for efficiently iterating over sparse arrays that is independent of the underlying memory layout representation of the array. A functional interface is defined for implementing sparse arrays in any modern programming language with a particular focus for the Chapel programming language. Examples are provided that show the translation of a loop that computes a matrix vector product into this representation for both the distributed and not-distributed cases. This work is directly applicable to NASA and its High Productivity Computing Systems (HPCS) program that JPL and our current program are engaged in. The goal of this program is to create powerful, scalable, and economically viable high-powered computer systems suitable for use in national security and industry by 2010. This is important to NASA for its computationally intensive requirements for analyzing and understanding the volumes of science data from our returned missions.

Compressed-sensing-based content-driven hierarchical reconstruction: Theory and application to C-arm cone-beam tomography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Langet, Hélène; Laboratoire des Signaux et Systèmes, CentraleSupélec, Gif-sur-Yvette F-91192; Center for Visual Computing, CentraleSupélec, Châtenay-Malabry F-92295

2015-09-15

Purpose: This paper addresses the reconstruction of x-ray cone-beam computed tomography (CBCT) for interventional C-arm systems. Subsampling of CBCT is a significant issue with C-arms due to their slow rotation and to the low frame rate of their flat panel x-ray detectors. The aim of this work is to propose a novel method able to handle the subsampling artifacts generally observed with analytical reconstruction, through a content-driven hierarchical reconstruction based on compressed sensing. Methods: The central idea is to proceed with a hierarchical method where the most salient features (high intensities or gradients) are reconstructed first to reduce the artifactsmore » these features induce. These artifacts are addressed first because their presence contaminates less salient features. Several hierarchical schemes aiming at streak artifacts reduction are introduced for C-arm CBCT: the empirical orthogonal matching pursuit approach with the ℓ{sub 0} pseudonorm for reconstructing sparse vessels; a convex variant using homotopy with the ℓ{sub 1}-norm constraint of compressed sensing, for reconstructing sparse vessels over a nonsparse background; homotopy with total variation (TV); and a novel empirical extension to nonlinear diffusion (NLD). Such principles are implemented with penalized iterative filtered backprojection algorithms. For soft-tissue imaging, the authors compare the use of TV and NLD filters as sparsity constraints, both optimized with the alternating direction method of multipliers, using a threshold for TV and a nonlinear weighting for NLD. Results: The authors show on simulated data that their approach provides fast convergence to good approximations of the solution of the TV-constrained minimization problem introduced by the compressed sensing theory. Using C-arm CBCT clinical data, the authors show that both TV and NLD can deliver improved image quality by reducing streaks. Conclusions: A flexible compressed-sensing-based algorithmic approach is proposed that is able to accommodate for a wide range of constraints. It is successfully applied to C-arm CBCT images that may not be so well approximated by piecewise constant functions.« less

Multi-dimensional Fokker-Planck equation analysis using the modified finite element method

NASA Astrophysics Data System (ADS)

Náprstek, J.; Král, R.

2016-09-01

The Fokker-Planck equation (FPE) is a frequently used tool for the solution of cross probability density function (PDF) of a dynamic system response excited by a vector of random processes. FEM represents a very effective solution possibility, particularly when transition processes are investigated or a more detailed solution is needed. Actual papers deal with single degree of freedom (SDOF) systems only. So the respective FPE includes two independent space variables only. Stepping over this limit into MDOF systems a number of specific problems related to a true multi-dimensionality must be overcome. Unlike earlier studies, multi-dimensional simplex elements in any arbitrary dimension should be deployed and rectangular (multi-brick) elements abandoned. Simple closed formulae of integration in multi-dimension domain have been derived. Another specific problem represents the generation of multi-dimensional finite element mesh. Assembling of system global matrices should be subjected to newly composed algorithms due to multi-dimensionality. The system matrices are quite full and no advantages following from their sparse character can be profited from, as is commonly used in conventional FEM applications in 2D/3D problems. After verification of partial algorithms, an illustrative example dealing with a 2DOF non-linear aeroelastic system in combination with random and deterministic excitations is discussed.

Sparse, decorrelated odor coding in the mushroom body enhances learned odor discrimination.

PubMed

Lin, Andrew C; Bygrave, Alexei M; de Calignon, Alix; Lee, Tzumin; Miesenböck, Gero

2014-04-01

Sparse coding may be a general strategy of neural systems for augmenting memory capacity. In Drosophila melanogaster, sparse odor coding by the Kenyon cells of the mushroom body is thought to generate a large number of precisely addressable locations for the storage of odor-specific memories. However, it remains untested how sparse coding relates to behavioral performance. Here we demonstrate that sparseness is controlled by a negative feedback circuit between Kenyon cells and the GABAergic anterior paired lateral (APL) neuron. Systematic activation and blockade of each leg of this feedback circuit showed that Kenyon cells activated APL and APL inhibited Kenyon cells. Disrupting the Kenyon cell-APL feedback loop decreased the sparseness of Kenyon cell odor responses, increased inter-odor correlations and prevented flies from learning to discriminate similar, but not dissimilar, odors. These results suggest that feedback inhibition suppresses Kenyon cell activity to maintain sparse, decorrelated odor coding and thus the odor specificity of memories.

An efficient method for model refinement in diffuse optical tomography

NASA Astrophysics Data System (ADS)

Zirak, A. R.; Khademi, M.

2007-11-01

Diffuse optical tomography (DOT) is a non-linear, ill-posed, boundary value and optimization problem which necessitates regularization. Also, Bayesian methods are suitable owing to measurements data are sparse and correlated. In such problems which are solved with iterative methods, for stabilization and better convergence, the solution space must be small. These constraints subject to extensive and overdetermined system of equations which model retrieving criteria specially total least squares (TLS) must to refine model error. Using TLS is limited to linear systems which is not achievable when applying traditional Bayesian methods. This paper presents an efficient method for model refinement using regularized total least squares (RTLS) for treating on linearized DOT problem, having maximum a posteriori (MAP) estimator and Tikhonov regulator. This is done with combination Bayesian and regularization tools as preconditioner matrices, applying them to equations and then using RTLS to the resulting linear equations. The preconditioning matrixes are guided by patient specific information as well as a priori knowledge gained from the training set. Simulation results illustrate that proposed method improves the image reconstruction performance and localize the abnormally well.

A theoretical model of strong and moderate El Niño regimes

NASA Astrophysics Data System (ADS)

Takahashi, Ken; Karamperidou, Christina; Dewitte, Boris

2018-02-01

The existence of two regimes for El Niño (EN) events, moderate and strong, has been previously shown in the GFDL CM2.1 climate model and also suggested in observations. The two regimes have been proposed to originate from the nonlinearity in the Bjerknes feedback, associated with a threshold in sea surface temperature (T_c ) that needs to be exceeded for deep atmospheric convection to occur in the eastern Pacific. However, although the recent 2015-16 EN event provides a new data point consistent with the sparse strong EN regime, it is not enough to statistically reject the null hypothesis of a unimodal distribution based on observations alone. Nevertheless, we consider the possibility suggestive enough to explore it with a simple theoretical model based on the nonlinear Bjerknes feedback. In this study, we implemented this nonlinear mechanism in the recharge-discharge (RD) ENSO model and show that it is sufficient to produce the two EN regimes, i.e. a bimodal distribution in peak surface temperature (T) during EN events. The only modification introduced to the original RD model is that the net damping is suppressed when T exceeds T_c , resulting in a weak nonlinearity in the system. Due to the damping, the model is globally stable and it requires stochastic forcing to maintain the variability. The sustained low-frequency component of the stochastic forcing plays a key role for the onset of strong EN events (i.e. for T>T_c ), at least as important as the precursor positive heat content anomaly (h). High-frequency forcing helps some EN events to exceed T_c , increasing the number of strong events, but the rectification effect is small and the overall number of EN events is little affected by this forcing. Using the Fokker-Planck equation, we show how the bimodal probability distribution of EN events arises from the nonlinear Bjerknes feedback and also propose that the increase in the net feedback with increasing T is a necessary condition for bimodality in the RD model. We also show that the damping strength determines both the adjustment time-scale and equilibrium value of the ensemble spread associated with the stochastic forcing.

Semi-Supervised Sparse Representation Based Classification for Face Recognition With Insufficient Labeled Samples

NASA Astrophysics Data System (ADS)

Gao, Yuan; Ma, Jiayi; Yuille, Alan L.

2017-05-01

This paper addresses the problem of face recognition when there is only few, or even only a single, labeled examples of the face that we wish to recognize. Moreover, these examples are typically corrupted by nuisance variables, both linear (i.e., additive nuisance variables such as bad lighting, wearing of glasses) and non-linear (i.e., non-additive pixel-wise nuisance variables such as expression changes). The small number of labeled examples means that it is hard to remove these nuisance variables between the training and testing faces to obtain good recognition performance. To address the problem we propose a method called Semi-Supervised Sparse Representation based Classification (S$^3$RC). This is based on recent work on sparsity where faces are represented in terms of two dictionaries: a gallery dictionary consisting of one or more examples of each person, and a variation dictionary representing linear nuisance variables (e.g., different lighting conditions, different glasses). The main idea is that (i) we use the variation dictionary to characterize the linear nuisance variables via the sparsity framework, then (ii) prototype face images are estimated as a gallery dictionary via a Gaussian Mixture Model (GMM), with mixed labeled and unlabeled samples in a semi-supervised manner, to deal with the non-linear nuisance variations between labeled and unlabeled samples. We have done experiments with insufficient labeled samples, even when there is only a single labeled sample per person. Our results on the AR, Multi-PIE, CAS-PEAL, and LFW databases demonstrate that the proposed method is able to deliver significantly improved performance over existing methods.

Delay differential analysis of time series.

PubMed

Lainscsek, Claudia; Sejnowski, Terrence J

2015-03-01

Nonlinear dynamical system analysis based on embedding theory has been used for modeling and prediction, but it also has applications to signal detection and classification of time series. An embedding creates a multidimensional geometrical object from a single time series. Traditionally either delay or derivative embeddings have been used. The delay embedding is composed of delayed versions of the signal, and the derivative embedding is composed of successive derivatives of the signal. The delay embedding has been extended to nonuniform embeddings to take multiple timescales into account. Both embeddings provide information on the underlying dynamical system without having direct access to all the system variables. Delay differential analysis is based on functional embeddings, a combination of the derivative embedding with nonuniform delay embeddings. Small delay differential equation (DDE) models that best represent relevant dynamic features of time series data are selected from a pool of candidate models for detection or classification. We show that the properties of DDEs support spectral analysis in the time domain where nonlinear correlation functions are used to detect frequencies, frequency and phase couplings, and bispectra. These can be efficiently computed with short time windows and are robust to noise. For frequency analysis, this framework is a multivariate extension of discrete Fourier transform (DFT), and for higher-order spectra, it is a linear and multivariate alternative to multidimensional fast Fourier transform of multidimensional correlations. This method can be applied to short or sparse time series and can be extended to cross-trial and cross-channel spectra if multiple short data segments of the same experiment are available. Together, this time-domain toolbox provides higher temporal resolution, increased frequency and phase coupling information, and it allows an easy and straightforward implementation of higher-order spectra across time compared with frequency-based methods such as the DFT and cross-spectral analysis.

A feasibility study for compressed sensing combined phase contrast MR angiography reconstruction

NASA Astrophysics Data System (ADS)

Lee, Dong-Hoon; Hong, Cheol-Pyo; Lee, Man-Woo; Han, Bong-Soo

2012-02-01

Phase contrast magnetic resonance angiography (PC MRA) is a technique for flow velocity measurement and vessels visualization, simultaneously. The PC MRA takes long scan time because each flow encoding gradients which are composed bipolar gradient type need to reconstruct the angiography image. Moreover, it takes more image acquisition time when we use the PC MRA at the low-tesla MRI system. In this study, we studied and evaluation of feasibility for CS MRI reconstruction combined PC MRA which data acquired by low-tesla MRI system. We used non-linear reconstruction algorithm which named Bregman iteration for CS image reconstruction and validate the usefulness of CS combined PC MRA reconstruction technique. The results of CS reconstructed PC MRA images provide similar level of image quality between fully sampled reconstruction data and sparse sampled reconstruction using CS technique. Although our results used half of sampling ratio and do not used specification hardware device or performance which are improving the temporal resolution of MR image acquisition such as parallel imaging reconstruction using phased array coil or non-cartesian trajectory, we think that CS combined PC MRA technique will be helpful to increase the temporal resolution and at low-tesla MRI system.

Large-scale optimal control of interconnected natural gas and electrical transmission systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiang, Nai-Yuan; Zavala, Victor M.

2016-04-01

We present a detailed optimal control model that captures spatiotemporal interactions between gas and electric transmission networks. We use the model to study flexibility and economic opportunities provided by coordination. A large-scale case study in the Illinois system reveals that coordination can enable the delivery of significantly larger amounts of natural gas to the power grid. In particular, under a coordinated setting, gas-fired generators act as distributed demand response resources that can be controlled by the gas pipeline operator. This enables more efficient control of pressures and flows in space and time and overcomes delivery bottlenecks. We demonstrate that themore » additional flexibility not only can benefit the gas operator but can also lead to more efficient power grid operations and results in increased revenue for gas-fired power plants. We also use the optimal control model to analyze computational issues arising in these complex models. We demonstrate that the interconnected Illinois system with full physical resolution gives rise to a highly nonlinear optimal control problem with 4400 differential and algebraic equations and 1040 controls that can be solved with a state-of-the-art sparse optimization solver. (C) 2016 Elsevier Ltd. All rights reserved.« less

Mathematical modeling and simulation in animal health. Part III: Using nonlinear mixed-effects to characterize and quantify variability in drug pharmacokinetics.

PubMed

Bon, C; Toutain, P L; Concordet, D; Gehring, R; Martin-Jimenez, T; Smith, J; Pelligand, L; Martinez, M; Whittem, T; Riviere, J E; Mochel, J P

2018-04-01

A common feature of human and veterinary pharmacokinetics is the importance of identifying and quantifying the key determinants of between-patient variability in drug disposition and effects. Some of these attributes are already well known to the field of human pharmacology such as bodyweight, age, or sex, while others are more specific to veterinary medicine, such as species, breed, and social behavior. Identification of these attributes has the potential to allow a better and more tailored use of therapeutic drugs both in companion and food-producing animals. Nonlinear mixed effects (NLME) have been purposely designed to characterize the sources of variability in drug disposition and response. The NLME approach can be used to explore the impact of population-associated variables on the relationship between drug administration, systemic exposure, and the levels of drug residues in tissues. The latter, while different from the method used by the US Food and Drug Administration for setting official withdrawal times (WT) can also be beneficial for estimating WT of approved animal drug products when used in an extralabel manner. Finally, NLME can also prove useful to optimize dosing schedules, or to analyze sparse data collected in situations where intensive blood collection is technically challenging, as in small animal species presenting limited blood volume such as poultry and fish. © 2017 John Wiley & Sons Ltd.

A framelet-based iterative maximum-likelihood reconstruction algorithm for spectral CT

NASA Astrophysics Data System (ADS)

Wang, Yingmei; Wang, Ge; Mao, Shuwei; Cong, Wenxiang; Ji, Zhilong; Cai, Jian-Feng; Ye, Yangbo

2016-11-01

Standard computed tomography (CT) cannot reproduce spectral information of an object. Hardware solutions include dual-energy CT which scans the object twice in different x-ray energy levels, and energy-discriminative detectors which can separate lower and higher energy levels from a single x-ray scan. In this paper, we propose a software solution and give an iterative algorithm that reconstructs an image with spectral information from just one scan with a standard energy-integrating detector. The spectral information obtained can be used to produce color CT images, spectral curves of the attenuation coefficient μ (r,E) at points inside the object, and photoelectric images, which are all valuable imaging tools in cancerous diagnosis. Our software solution requires no change on hardware of a CT machine. With the Shepp-Logan phantom, we have found that although the photoelectric and Compton components were not perfectly reconstructed, their composite effect was very accurately reconstructed as compared to the ground truth and the dual-energy CT counterpart. This means that our proposed method has an intrinsic benefit in beam hardening correction and metal artifact reduction. The algorithm is based on a nonlinear polychromatic acquisition model for x-ray CT. The key technique is a sparse representation of iterations in a framelet system. Convergence of the algorithm is studied. This is believed to be the first application of framelet imaging tools to a nonlinear inverse problem.

Determination of nonlinear genetic architecture using compressed sensing.

PubMed

Ho, Chiu Man; Hsu, Stephen D H

2015-01-01

One of the fundamental problems of modern genomics is to extract the genetic architecture of a complex trait from a data set of individual genotypes and trait values. Establishing this important connection between genotype and phenotype is complicated by the large number of candidate genes, the potentially large number of causal loci, and the likely presence of some nonlinear interactions between different genes. Compressed Sensing methods obtain solutions to under-constrained systems of linear equations. These methods can be applied to the problem of determining the best model relating genotype to phenotype, and generally deliver better performance than simply regressing the phenotype against each genetic variant, one at a time. We introduce a Compressed Sensing method that can reconstruct nonlinear genetic models (i.e., including epistasis, or gene-gene interactions) from phenotype-genotype (GWAS) data. Our method uses L1-penalized regression applied to nonlinear functions of the sensing matrix. The computational and data resource requirements for our method are similar to those necessary for reconstruction of linear genetic models (or identification of gene-trait associations), assuming a condition of generalized sparsity, which limits the total number of gene-gene interactions. An example of a sparse nonlinear model is one in which a typical locus interacts with several or even many others, but only a small subset of all possible interactions exist. It seems plausible that most genetic architectures fall in this category. We give theoretical arguments suggesting that the method is nearly optimal in performance, and demonstrate its effectiveness on broad classes of nonlinear genetic models using simulated human genomes and the small amount of currently available real data. A phase transition (i.e., dramatic and qualitative change) in the behavior of the algorithm indicates when sufficient data is available for its successful application. Our results indicate that predictive models for many complex traits, including a variety of human disease susceptibilities (e.g., with additive heritability h (2)∼0.5), can be extracted from data sets comprised of n ⋆∼100s individuals, where s is the number of distinct causal variants influencing the trait. For example, given a trait controlled by ∼10 k loci, roughly a million individuals would be sufficient for application of the method.

Solution of matrix equations using sparse techniques

NASA Technical Reports Server (NTRS)

Baddourah, Majdi

1994-01-01

The solution of large systems of matrix equations is key to the solution of a large number of scientific and engineering problems. This talk describes the sparse matrix solver developed at Langley which can routinely solve in excess of 263,000 equations in 40 seconds on one Cray C-90 processor. It appears that for large scale structural analysis applications, sparse matrix methods have a significant performance advantage over other methods.

Hyperspherical Sparse Approximation Techniques for High-Dimensional Discontinuity Detection

DOE PAGES

Zhang, Guannan; Webster, Clayton G.; Gunzburger, Max; ...

2016-08-04

This work proposes a hyperspherical sparse approximation framework for detecting jump discontinuities in functions in high-dimensional spaces. The need for a novel approach results from the theoretical and computational inefficiencies of well-known approaches, such as adaptive sparse grids, for discontinuity detection. Our approach constructs the hyperspherical coordinate representation of the discontinuity surface of a function. Then sparse approximations of the transformed function are built in the hyperspherical coordinate system, with values at each point estimated by solving a one-dimensional discontinuity detection problem. Due to the smoothness of the hypersurface, the new technique can identify jump discontinuities with significantly reduced computationalmore » cost, compared to existing methods. Several approaches are used to approximate the transformed discontinuity surface in the hyperspherical system, including adaptive sparse grid and radial basis function interpolation, discrete least squares projection, and compressed sensing approximation. Moreover, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. In conclusion, rigorous complexity analyses of the new methods are provided, as are several numerical examples that illustrate the effectiveness of our approach.« less

Period Estimation for Sparsely-sampled Quasi-periodic Light Curves Applied to Miras

NASA Astrophysics Data System (ADS)

He, Shiyuan; Yuan, Wenlong; Huang, Jianhua Z.; Long, James; Macri, Lucas M.

2016-12-01

We develop a nonlinear semi-parametric Gaussian process model to estimate periods of Miras with sparsely sampled light curves. The model uses a sinusoidal basis for the periodic variation and a Gaussian process for the stochastic changes. We use maximum likelihood to estimate the period and the parameters of the Gaussian process, while integrating out the effects of other nuisance parameters in the model with respect to a suitable prior distribution obtained from earlier studies. Since the likelihood is highly multimodal for period, we implement a hybrid method that applies the quasi-Newton algorithm for Gaussian process parameters and search the period/frequency parameter space over a dense grid. A large-scale, high-fidelity simulation is conducted to mimic the sampling quality of Mira light curves obtained by the M33 Synoptic Stellar Survey. The simulated data set is publicly available and can serve as a testbed for future evaluation of different period estimation methods. The semi-parametric model outperforms an existing algorithm on this simulated test data set as measured by period recovery rate and quality of the resulting period-luminosity relations.

Task-driven dictionary learning.

PubMed

Mairal, Julien; Bach, Francis; Ponce, Jean

2012-04-01

Modeling data with linear combinations of a few elements from a learned dictionary has been the focus of much recent research in machine learning, neuroscience, and signal processing. For signals such as natural images that admit such sparse representations, it is now well established that these models are well suited to restoration tasks. In this context, learning the dictionary amounts to solving a large-scale matrix factorization problem, which can be done efficiently with classical optimization tools. The same approach has also been used for learning features from data for other purposes, e.g., image classification, but tuning the dictionary in a supervised way for these tasks has proven to be more difficult. In this paper, we present a general formulation for supervised dictionary learning adapted to a wide variety of tasks, and present an efficient algorithm for solving the corresponding optimization problem. Experiments on handwritten digit classification, digital art identification, nonlinear inverse image problems, and compressed sensing demonstrate that our approach is effective in large-scale settings, and is well suited to supervised and semi-supervised classification, as well as regression tasks for data that admit sparse representations.

Portable implementation model for CFD simulations. Application to hybrid CPU/GPU supercomputers

NASA Astrophysics Data System (ADS)

Oyarzun, Guillermo; Borrell, Ricard; Gorobets, Andrey; Oliva, Assensi

2017-10-01

Nowadays, high performance computing (HPC) systems experience a disruptive moment with a variety of novel architectures and frameworks, without any clarity of which one is going to prevail. In this context, the portability of codes across different architectures is of major importance. This paper presents a portable implementation model based on an algebraic operational approach for direct numerical simulation (DNS) and large eddy simulation (LES) of incompressible turbulent flows using unstructured hybrid meshes. The strategy proposed consists in representing the whole time-integration algorithm using only three basic algebraic operations: sparse matrix-vector product, a linear combination of vectors and dot product. The main idea is based on decomposing the nonlinear operators into a concatenation of two SpMV operations. This provides high modularity and portability. An exhaustive analysis of the proposed implementation for hybrid CPU/GPU supercomputers has been conducted with tests using up to 128 GPUs. The main objective consists in understanding the challenges of implementing CFD codes on new architectures.

The adaptive parallel UKF inversion method for the shape of space objects based on the ground-based photometric data

NASA Astrophysics Data System (ADS)

Du, Xiaoping; Wang, Yang; Liu, Hao

2018-04-01

The space object in highly elliptical orbit is always presented as an image point on the ground-based imaging equipment so that it is difficult to resolve and identify the shape and attitude directly. In this paper a novel algorithm is presented for the estimation of spacecraft shape. The apparent magnitude model suitable for the inversion of object information such as shape and attitude is established based on the analysis of photometric characteristics. A parallel adaptive shape inversion algorithm based on UKF was designed after the achievement of dynamic equation of the nonlinear, Gaussian system involved with the influence of various dragging forces. The result of a simulation study demonstrate the viability and robustness of the new filter and its fast convergence rate. It realizes the inversion of combination shape with high accuracy, especially for the bus of cube and cylinder. Even though with sparse photometric data, it still can maintain a higher success rate of inversion.

Regulatory networks and connected components of the neutral space. A look at functional islands

NASA Astrophysics Data System (ADS)

Boldhaus, G.; Klemm, K.

2010-09-01

The functioning of a living cell is largely determined by the structure of its regulatory network, comprising non-linear interactions between regulatory genes. An important factor for the stability and evolvability of such regulatory systems is neutrality - typically a large number of alternative network structures give rise to the necessary dynamics. Here we study the discretized regulatory dynamics of the yeast cell cycle [Li et al., PNAS, 2004] and the set of networks capable of reproducing it, which we call functional. Among these, the empirical yeast wildtype network is close to optimal with respect to sparse wiring. Under point mutations, which establish or delete single interactions, the neutral space of functional networks is fragmented into ≈ 4.7 × 108 components. One of the smaller ones contains the wildtype network. On average, functional networks reachable from the wildtype by mutations are sparser, have higher noise resilience and fewer fixed point attractors as compared with networks outside of this wildtype component.

Sparse magnetic resonance imaging reconstruction using the bregman iteration

NASA Astrophysics Data System (ADS)

Lee, Dong-Hoon; Hong, Cheol-Pyo; Lee, Man-Woo

2013-01-01

Magnetic resonance imaging (MRI) reconstruction needs many samples that are sequentially sampled by using phase encoding gradients in a MRI system. It is directly connected to the scan time for the MRI system and takes a long time. Therefore, many researchers have studied ways to reduce the scan time, especially, compressed sensing (CS), which is used for sparse images and reconstruction for fewer sampling datasets when the k-space is not fully sampled. Recently, an iterative technique based on the bregman method was developed for denoising. The bregman iteration method improves on total variation (TV) regularization by gradually recovering the fine-scale structures that are usually lost in TV regularization. In this study, we studied sparse sampling image reconstruction using the bregman iteration for a low-field MRI system to improve its temporal resolution and to validate its usefulness. The image was obtained with a 0.32 T MRI scanner (Magfinder II, SCIMEDIX, Korea) with a phantom and an in-vivo human brain in a head coil. We applied random k-space sampling, and we determined the sampling ratios by using half the fully sampled k-space. The bregman iteration was used to generate the final images based on the reduced data. We also calculated the root-mean-square-error (RMSE) values from error images that were obtained using various numbers of bregman iterations. Our reconstructed images using the bregman iteration for sparse sampling images showed good results compared with the original images. Moreover, the RMSE values showed that the sparse reconstructed phantom and the human images converged to the original images. We confirmed the feasibility of sparse sampling image reconstruction methods using the bregman iteration with a low-field MRI system and obtained good results. Although our results used half the sampling ratio, this method will be helpful in increasing the temporal resolution at low-field MRI systems.

An approach to predict water quality in data-sparse catchments using hydrological catchment similarity

NASA Astrophysics Data System (ADS)

Pohle, Ina; Glendell, Miriam; Stutter, Marc I.; Helliwell, Rachel C.

2017-04-01

An understanding of catchment response to climate and land use change at a regional scale is necessary for the assessment of mitigation and adaptation options addressing diffuse nutrient pollution. It is well documented that the physicochemical properties of a river ecosystem respond to change in a non-linear fashion. This is particularly important when threshold water concentrations, relevant to national and EU legislation, are exceeded. Large scale (regional) model assessments required for regulatory purposes must represent the key processes and mechanisms that are more readily understood in catchments with water quantity and water quality data monitored at high spatial and temporal resolution. While daily discharge data are available for most catchments in Scotland, nitrate and phosphorus are mostly available on a monthly basis only, as typified by regulatory monitoring. However, high resolution (hourly to daily) water quantity and water quality data exist for a limited number of research catchments. To successfully implement adaptation measures across Scotland, an upscaling from data-rich to data-sparse catchments is required. In addition, the widespread availability of spatial datasets affecting hydrological and biogeochemical responses (e.g. soils, topography/geomorphology, land use, vegetation etc.) provide an opportunity to transfer predictions between data-rich and data-sparse areas by linking processes and responses to catchment attributes. Here, we develop a framework of catchment typologies as a prerequisite for transferring information from data-rich to data-sparse catchments by focusing on how hydrological catchment similarity can be used as an indicator of grouped behaviours in water quality response. As indicators of hydrological catchment similarity we use flow indices derived from observed discharge data across Scotland as well as hydrological model parameters. For the latter, we calibrated the lumped rainfall-runoff model TUWModel using multiple objective functions. The relationships between indicators of hydrological catchment similarity, physical catchment characteristics and nitrate and phosphorus concentrations in rivers are then investigated using multivariate statistics. This understanding of the relationship between catchment characteristics, hydrological processes and water quality will allow us to implement more efficient regulatory water quality monitoring strategies, to improve existing water quality models and to model mitigation and adaptation scenarios to global change in data-sparse catchments.

A sparse reconstruction method for the estimation of multi-resolution emission fields via atmospheric inversion

DOE PAGES

Ray, J.; Lee, J.; Yadav, V.; ...

2015-04-29

Atmospheric inversions are frequently used to estimate fluxes of atmospheric greenhouse gases (e.g., biospheric CO 2 flux fields) at Earth's surface. These inversions typically assume that flux departures from a prior model are spatially smoothly varying, which are then modeled using a multi-variate Gaussian. When the field being estimated is spatially rough, multi-variate Gaussian models are difficult to construct and a wavelet-based field model may be more suitable. Unfortunately, such models are very high dimensional and are most conveniently used when the estimation method can simultaneously perform data-driven model simplification (removal of model parameters that cannot be reliably estimated) andmore » fitting. Such sparse reconstruction methods are typically not used in atmospheric inversions. In this work, we devise a sparse reconstruction method, and illustrate it in an idealized atmospheric inversion problem for the estimation of fossil fuel CO 2 (ffCO 2) emissions in the lower 48 states of the USA. Our new method is based on stagewise orthogonal matching pursuit (StOMP), a method used to reconstruct compressively sensed images. Our adaptations bestow three properties to the sparse reconstruction procedure which are useful in atmospheric inversions. We have modified StOMP to incorporate prior information on the emission field being estimated and to enforce non-negativity on the estimated field. Finally, though based on wavelets, our method allows for the estimation of fields in non-rectangular geometries, e.g., emission fields inside geographical and political boundaries. Our idealized inversions use a recently developed multi-resolution (i.e., wavelet-based) random field model developed for ffCO 2 emissions and synthetic observations of ffCO 2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of 2. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.« less

A sparse reconstruction method for the estimation of multi-resolution emission fields via atmospheric inversion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ray, J.; Lee, J.; Yadav, V.

Atmospheric inversions are frequently used to estimate fluxes of atmospheric greenhouse gases (e.g., biospheric CO 2 flux fields) at Earth's surface. These inversions typically assume that flux departures from a prior model are spatially smoothly varying, which are then modeled using a multi-variate Gaussian. When the field being estimated is spatially rough, multi-variate Gaussian models are difficult to construct and a wavelet-based field model may be more suitable. Unfortunately, such models are very high dimensional and are most conveniently used when the estimation method can simultaneously perform data-driven model simplification (removal of model parameters that cannot be reliably estimated) andmore » fitting. Such sparse reconstruction methods are typically not used in atmospheric inversions. In this work, we devise a sparse reconstruction method, and illustrate it in an idealized atmospheric inversion problem for the estimation of fossil fuel CO 2 (ffCO 2) emissions in the lower 48 states of the USA. Our new method is based on stagewise orthogonal matching pursuit (StOMP), a method used to reconstruct compressively sensed images. Our adaptations bestow three properties to the sparse reconstruction procedure which are useful in atmospheric inversions. We have modified StOMP to incorporate prior information on the emission field being estimated and to enforce non-negativity on the estimated field. Finally, though based on wavelets, our method allows for the estimation of fields in non-rectangular geometries, e.g., emission fields inside geographical and political boundaries. Our idealized inversions use a recently developed multi-resolution (i.e., wavelet-based) random field model developed for ffCO 2 emissions and synthetic observations of ffCO 2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of 2. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.« less

Dynamical systems, attractors, and neural circuits.

PubMed

Miller, Paul

2016-01-01

Biology is the study of dynamical systems. Yet most of us working in biology have limited pedagogical training in the theory of dynamical systems, an unfortunate historical fact that can be remedied for future generations of life scientists. In my particular field of systems neuroscience, neural circuits are rife with nonlinearities at all levels of description, rendering simple methodologies and our own intuition unreliable. Therefore, our ideas are likely to be wrong unless informed by good models. These models should be based on the mathematical theories of dynamical systems since functioning neurons are dynamic-they change their membrane potential and firing rates with time. Thus, selecting the appropriate type of dynamical system upon which to base a model is an important first step in the modeling process. This step all too easily goes awry, in part because there are many frameworks to choose from, in part because the sparsely sampled data can be consistent with a variety of dynamical processes, and in part because each modeler has a preferred modeling approach that is difficult to move away from. This brief review summarizes some of the main dynamical paradigms that can arise in neural circuits, with comments on what they can achieve computationally and what signatures might reveal their presence within empirical data. I provide examples of different dynamical systems using simple circuits of two or three cells, emphasizing that any one connectivity pattern is compatible with multiple, diverse functions.

BinTree Seeking: A Novel Approach to Mine Both Bi-Sparse and Cohesive Modules in Protein Interaction Networks

PubMed Central

Shen, Hong-Bin

2011-01-01

Modern science of networks has brought significant advances to our understanding of complex systems biology. As a representative model of systems biology, Protein Interaction Networks (PINs) are characterized by a remarkable modular structures, reflecting functional associations between their components. Many methods were proposed to capture cohesive modules so that there is a higher density of edges within modules than those across them. Recent studies reveal that cohesively interacting modules of proteins is not a universal organizing principle in PINs, which has opened up new avenues for revisiting functional modules in PINs. In this paper, functional clusters in PINs are found to be able to form unorthodox structures defined as bi-sparse module. In contrast to the traditional cohesive module, the nodes in the bi-sparse module are sparsely connected internally and densely connected with other bi-sparse or cohesive modules. We present a novel protocol called the BinTree Seeking (BTS) for mining both bi-sparse and cohesive modules in PINs based on Edge Density of Module (EDM) and matrix theory. BTS detects modules by depicting links and nodes rather than nodes alone and its derivation procedure is totally performed on adjacency matrix of networks. The number of modules in a PIN can be automatically determined in the proposed BTS approach. BTS is tested on three real PINs and the results demonstrate that functional modules in PINs are not dominantly cohesive but can be sparse. BTS software and the supporting information are available at: www.csbio.sjtu.edu.cn/bioinf/BTS/. PMID:22140454

Generation of 3-D hydrostratigraphic zones from dense airborne electromagnetic data to assess groundwater model prediction error

USGS Publications Warehouse

Christensen, Nikolaj K; Minsley, Burke J.; Christensen, Steen

2017-01-01

We present a new methodology to combine spatially dense high-resolution airborne electromagnetic (AEM) data and sparse borehole information to construct multiple plausible geological structures using a stochastic approach. The method developed allows for quantification of the performance of groundwater models built from different geological realizations of structure. Multiple structural realizations are generated using geostatistical Monte Carlo simulations that treat sparse borehole lithological observations as hard data and dense geophysically derived structural probabilities as soft data. Each structural model is used to define 3-D hydrostratigraphical zones of a groundwater model, and the hydraulic parameter values of the zones are estimated by using nonlinear regression to fit hydrological data (hydraulic head and river discharge measurements). Use of the methodology is demonstrated for a synthetic domain having structures of categorical deposits consisting of sand, silt, or clay. It is shown that using dense AEM data with the methodology can significantly improve the estimated accuracy of the sediment distribution as compared to when borehole data are used alone. It is also shown that this use of AEM data can improve the predictive capability of a calibrated groundwater model that uses the geological structures as zones. However, such structural models will always contain errors because even with dense AEM data it is not possible to perfectly resolve the structures of a groundwater system. It is shown that when using such erroneous structures in a groundwater model, they can lead to biased parameter estimates and biased model predictions, therefore impairing the model's predictive capability.

Generation of 3-D hydrostratigraphic zones from dense airborne electromagnetic data to assess groundwater model prediction error

NASA Astrophysics Data System (ADS)

Christensen, N. K.; Minsley, B. J.; Christensen, S.

2017-02-01

We present a new methodology to combine spatially dense high-resolution airborne electromagnetic (AEM) data and sparse borehole information to construct multiple plausible geological structures using a stochastic approach. The method developed allows for quantification of the performance of groundwater models built from different geological realizations of structure. Multiple structural realizations are generated using geostatistical Monte Carlo simulations that treat sparse borehole lithological observations as hard data and dense geophysically derived structural probabilities as soft data. Each structural model is used to define 3-D hydrostratigraphical zones of a groundwater model, and the hydraulic parameter values of the zones are estimated by using nonlinear regression to fit hydrological data (hydraulic head and river discharge measurements). Use of the methodology is demonstrated for a synthetic domain having structures of categorical deposits consisting of sand, silt, or clay. It is shown that using dense AEM data with the methodology can significantly improve the estimated accuracy of the sediment distribution as compared to when borehole data are used alone. It is also shown that this use of AEM data can improve the predictive capability of a calibrated groundwater model that uses the geological structures as zones. However, such structural models will always contain errors because even with dense AEM data it is not possible to perfectly resolve the structures of a groundwater system. It is shown that when using such erroneous structures in a groundwater model, they can lead to biased parameter estimates and biased model predictions, therefore impairing the model's predictive capability.

Highly undersampled contrast-enhanced MRA with iterative reconstruction: Integration in a clinical setting.

PubMed

Stalder, Aurelien F; Schmidt, Michaela; Quick, Harald H; Schlamann, Marc; Maderwald, Stefan; Schmitt, Peter; Wang, Qiu; Nadar, Mariappan S; Zenge, Michael O

2015-12-01

To integrate, optimize, and evaluate a three-dimensional (3D) contrast-enhanced sparse MRA technique with iterative reconstruction on a standard clinical MR system. Data were acquired using a highly undersampled Cartesian spiral phyllotaxis sampling pattern and reconstructed directly on the MR system with an iterative SENSE technique. Undersampling, regularization, and number of iterations of the reconstruction were optimized and validated based on phantom experiments and patient data. Sparse MRA of the whole head (field of view: 265 × 232 × 179 mm(3) ) was investigated in 10 patient examinations. High-quality images with 30-fold undersampling, resulting in 0.7 mm isotropic resolution within 10 s acquisition, were obtained. After optimization of the regularization factor and of the number of iterations of the reconstruction, it was possible to reconstruct images with excellent quality within six minutes per 3D volume. Initial results of sparse contrast-enhanced MRA (CEMRA) in 10 patients demonstrated high-quality whole-head first-pass MRA for both the arterial and venous contrast phases. While sparse MRI techniques have not yet reached clinical routine, this study demonstrates the technical feasibility of high-quality sparse CEMRA of the whole head in a clinical setting. Sparse CEMRA has the potential to become a viable alternative where conventional CEMRA is too slow or does not provide sufficient spatial resolution. © 2014 Wiley Periodicals, Inc.

Improving the energy efficiency of sparse linear system solvers on multicore and manycore systems.

PubMed

Anzt, H; Quintana-Ortí, E S

2014-06-28

While most recent breakthroughs in scientific research rely on complex simulations carried out in large-scale supercomputers, the power draft and energy spent for this purpose is increasingly becoming a limiting factor to this trend. In this paper, we provide an overview of the current status in energy-efficient scientific computing by reviewing different technologies used to monitor power draft as well as power- and energy-saving mechanisms available in commodity hardware. For the particular domain of sparse linear algebra, we analyse the energy efficiency of a broad collection of hardware architectures and investigate how algorithmic and implementation modifications can improve the energy performance of sparse linear system solvers, without negatively impacting their performance. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Sparse electrocardiogram signals recovery based on solving a row echelon-like form of system.

PubMed

Cai, Pingmei; Wang, Guinan; Yu, Shiwei; Zhang, Hongjuan; Ding, Shuxue; Wu, Zikai

2016-02-01

The study of biology and medicine in a noise environment is an evolving direction in biological data analysis. Among these studies, analysis of electrocardiogram (ECG) signals in a noise environment is a challenging direction in personalized medicine. Due to its periodic characteristic, ECG signal can be roughly regarded as sparse biomedical signals. This study proposes a two-stage recovery algorithm for sparse biomedical signals in time domain. In the first stage, the concentration subspaces are found in advance. Then by exploiting these subspaces, the mixing matrix is estimated accurately. In the second stage, based on the number of active sources at each time point, the time points are divided into different layers. Next, by constructing some transformation matrices, these time points form a row echelon-like system. After that, the sources at each layer can be solved out explicitly by corresponding matrix operations. It is noting that all these operations are conducted under a weak sparse condition that the number of active sources is less than the number of observations. Experimental results show that the proposed method has a better performance for sparse ECG signal recovery problem.

Advantage of population pharmacokinetic method for evaluating the bioequivalence and accuracy of parameter estimation of pidotimod.

PubMed

Huang, Jihan; Li, Mengying; Lv, Yinghua; Yang, Juan; Xu, Ling; Wang, Jingjing; Chen, Junchao; Wang, Kun; He, Yingchun; Zheng, Qingshan

2016-09-01

This study was aimed at exploring the accuracy of population pharmacokinetic method in evaluating the bioequivalence of pidotimod with sparse data profiles and whether this method is suitable for bioequivalence evaluation in special populations such as children with fewer samplings. Methods In this single-dose, two-period crossover study, 20 healthy male Chinese volunteers were randomized 1 : 1 to receive either the test or reference formulation, with a 1-week washout before receiving the alternative formulation. Noncompartmental and population compartmental pharmacokinetic analyses were conducted. Simulated data were analyzed to graphically evaluate the model and the pharmacokinetic characteristics of the two pidotimod formulations. Various sparse sampling scenarios were generated from the real bioequivalence clinical trial data and evaluated by population pharmacokinetic method. The 90% confidence intervals (CIs) for AUC0-12h, AUC0-∞, and Cmax were 97.3 - 118.7%, 96.9 - 118.7%, and 95.1 - 109.8%, respectively, within the 80 - 125% range for bioequivalence using noncompartmental analysis. The population compartmental pharmacokinetics of pidotimod were described using a one-compartment model with first-order absorption and lag time. In the comparison of estimations in different dataset, the estimation of random three- and< fixed four-point sampling strategies can provide results similar to those obtained through rich sampling. The nonlinear mixed-effects model requires fewer data points. Moreover, compared with the noncompartmental analysis method, the pharmacokinetic parameters can be more accurately estimated using nonlinear mixed-effects model. The population pharmacokinetic modeling method was used to assess the bioequivalence of two pidotimod formulations with relatively few sampling points and further validated the bioequivalence of the two formulations. This method may provide useful information for regulating bioequivalence evaluation in special populations.

Synthesis and Characterization of Novel Anchorlipids for Tethered Bilayer Lipid Membranes.

PubMed

Andersson, Jakob; Knobloch, Jacqueline J; Perkins, Michael V; Holt, Stephen A; Köper, Ingo

2017-05-09

Tethered bilayer lipid membranes are versatile solid-supported model membrane systems. Core to these systems is an anchorlipid that covalently links a lipid bilayer to a support. The molecular structure of these lipids can have a significant impact on the properties of the resulting bilayer. Here, the synthesis of anchorlipids containing ester groups in the tethering part is described. The lipids are used to form bilayer membranes, and the resulting structures are compared with membranes formed using conventional anchorlipids or sparsely tethered membranes. All membranes showed good electrical sealing properties; the disulphide-terminated anchorlipids could be used in a sparsely tethered system without significantly reducing the sealing properties of the lipid bilayers. The sparsely tethered systems also allowed for higher ion transport across the membrane, which is in good correlation with higher hydration of the spacer region as seen by neutron scattering.

Algorithms and Application of Sparse Matrix Assembly and Equation Solvers for Aeroacoustics

NASA Technical Reports Server (NTRS)

Watson, W. R.; Nguyen, D. T.; Reddy, C. J.; Vatsa, V. N.; Tang, W. H.

2001-01-01

An algorithm for symmetric sparse equation solutions on an unstructured grid is described. Efficient, sequential sparse algorithms for degree-of-freedom reordering, supernodes, symbolic/numerical factorization, and forward backward solution phases are reviewed. Three sparse algorithms for the generation and assembly of symmetric systems of matrix equations are presented. The accuracy and numerical performance of the sequential version of the sparse algorithms are evaluated over the frequency range of interest in a three-dimensional aeroacoustics application. Results show that the solver solutions are accurate using a discretization of 12 points per wavelength. Results also show that the first assembly algorithm is impractical for high-frequency noise calculations. The second and third assembly algorithms have nearly equal performance at low values of source frequencies, but at higher values of source frequencies the third algorithm saves CPU time and RAM. The CPU time and the RAM required by the second and third assembly algorithms are two orders of magnitude smaller than that required by the sparse equation solver. A sequential version of these sparse algorithms can, therefore, be conveniently incorporated into a substructuring for domain decomposition formulation to achieve parallel computation, where different substructures are handles by different parallel processors.

Efficient Implementations of the Quadrature-Free Discontinuous Galerkin Method

NASA Technical Reports Server (NTRS)

Lockard, David P.; Atkins, Harold L.

1999-01-01

The efficiency of the quadrature-free form of the dis- continuous Galerkin method in two dimensions, and briefly in three dimensions, is examined. Most of the work for constant-coefficient, linear problems involves the volume and edge integrations, and the transformation of information from the volume to the edges. These operations can be viewed as matrix-vector multiplications. Many of the matrices are sparse as a result of symmetry, and blocking and specialized multiplication routines are used to account for the sparsity. By optimizing these operations, a 35% reduction in total CPU time is achieved. For nonlinear problems, the calculation of the flux becomes dominant because of the cost associated with polynomial products and inversion. This component of the work can be reduced by up to 75% when the products are approximated by truncating terms. Because the cost is high for nonlinear problems on general elements, it is suggested that simplified physics and the most efficient element types be used over most of the domain.

Data-driven modeling of background and mine-related acidity and metals in river basins

USGS Publications Warehouse

Friedel, Michael J

2013-01-01

A novel application of self-organizing map (SOM) and multivariate statistical techniques is used to model the nonlinear interaction among basin mineral-resources, mining activity, and surface-water quality. First, the SOM is trained using sparse measurements from 228 sample sites in the Animas River Basin, Colorado. The model performance is validated by comparing stochastic predictions of basin-alteration assemblages and mining activity at 104 independent sites. The SOM correctly predicts (>98%) the predominant type of basin hydrothermal alteration and presence (or absence) of mining activity. Second, application of the Davies–Bouldin criteria to k-means clustering of SOM neurons identified ten unique environmental groups. Median statistics of these groups define a nonlinear water-quality response along the spatiotemporal hydrothermal alteration-mining gradient. These results reveal that it is possible to differentiate among the continuum between inputs of background and mine-related acidity and metals, and it provides a basis for future research and empirical model development.

Iterative algorithms for large sparse linear systems on parallel computers

NASA Technical Reports Server (NTRS)

Adams, L. M.

1982-01-01

Algorithms for assembling in parallel the sparse system of linear equations that result from finite difference or finite element discretizations of elliptic partial differential equations, such as those that arise in structural engineering are developed. Parallel linear stationary iterative algorithms and parallel preconditioned conjugate gradient algorithms are developed for solving these systems. In addition, a model for comparing parallel algorithms on array architectures is developed and results of this model for the algorithms are given.

Normalization for sparse encoding of odors by a wide-field interneuron.

PubMed

Papadopoulou, Maria; Cassenaer, Stijn; Nowotny, Thomas; Laurent, Gilles

2011-05-06

Sparse coding presents practical advantages for sensory representations and memory storage. In the insect olfactory system, the representation of general odors is dense in the antennal lobes but sparse in the mushroom bodies, only one synapse downstream. In locusts, this transformation relies on the oscillatory structure of antennal lobe output, feed-forward inhibitory circuits, intrinsic properties of mushroom body neurons, and connectivity between antennal lobe and mushroom bodies. Here we show the existence of a normalizing negative-feedback loop within the mushroom body to maintain sparse output over a wide range of input conditions. This loop consists of an identifiable "giant" nonspiking inhibitory interneuron with ubiquitous connectivity and graded release properties.

Simultaneous analysis of large INTEGRAL/SPI1 datasets: Optimizing the computation of the solution and its variance using sparse matrix algorithms

NASA Astrophysics Data System (ADS)

Bouchet, L.; Amestoy, P.; Buttari, A.; Rouet, F.-H.; Chauvin, M.

2013-02-01

Nowadays, analyzing and reducing the ever larger astronomical datasets is becoming a crucial challenge, especially for long cumulated observation times. The INTEGRAL/SPI X/γ-ray spectrometer is an instrument for which it is essential to process many exposures at the same time in order to increase the low signal-to-noise ratio of the weakest sources. In this context, the conventional methods for data reduction are inefficient and sometimes not feasible at all. Processing several years of data simultaneously requires computing not only the solution of a large system of equations, but also the associated uncertainties. We aim at reducing the computation time and the memory usage. Since the SPI transfer function is sparse, we have used some popular methods for the solution of large sparse linear systems; we briefly review these methods. We use the Multifrontal Massively Parallel Solver (MUMPS) to compute the solution of the system of equations. We also need to compute the variance of the solution, which amounts to computing selected entries of the inverse of the sparse matrix corresponding to our linear system. This can be achieved through one of the latest features of the MUMPS software that has been partly motivated by this work. In this paper we provide a brief presentation of this feature and evaluate its effectiveness on astrophysical problems requiring the processing of large datasets simultaneously, such as the study of the entire emission of the Galaxy. We used these algorithms to solve the large sparse systems arising from SPI data processing and to obtain both their solutions and the associated variances. In conclusion, thanks to these newly developed tools, processing large datasets arising from SPI is now feasible with both a reasonable execution time and a low memory usage.

Solving large tomographic linear systems: size reduction and error estimation

NASA Astrophysics Data System (ADS)

Voronin, Sergey; Mikesell, Dylan; Slezak, Inna; Nolet, Guust

2014-10-01

We present a new approach to reduce a sparse, linear system of equations associated with tomographic inverse problems. We begin by making a modification to the commonly used compressed sparse-row format, whereby our format is tailored to the sparse structure of finite-frequency (volume) sensitivity kernels in seismic tomography. Next, we cluster the sparse matrix rows to divide a large matrix into smaller subsets representing ray paths that are geographically close. Singular value decomposition of each subset allows us to project the data onto a subspace associated with the largest eigenvalues of the subset. After projection we reject those data that have a signal-to-noise ratio (SNR) below a chosen threshold. Clustering in this way assures that the sparse nature of the system is minimally affected by the projection. Moreover, our approach allows for a precise estimation of the noise affecting the data while also giving us the ability to identify outliers. We illustrate the method by reducing large matrices computed for global tomographic systems with cross-correlation body wave delays, as well as with surface wave phase velocity anomalies. For a massive matrix computed for 3.7 million Rayleigh wave phase velocity measurements, imposing a threshold of 1 for the SNR, we condensed the matrix size from 1103 to 63 Gbyte. For a global data set of multiple-frequency P wave delays from 60 well-distributed deep earthquakes we obtain a reduction to 5.9 per cent. This type of reduction allows one to avoid loss of information due to underparametrizing models. Alternatively, if data have to be rejected to fit the system into computer memory, it assures that the most important data are preserved.

A Spectral Reconstruction Algorithm of Miniature Spectrometer Based on Sparse Optimization and Dictionary Learning.

PubMed

Zhang, Shang; Dong, Yuhan; Fu, Hongyan; Huang, Shao-Lun; Zhang, Lin

2018-02-22

The miniaturization of spectrometer can broaden the application area of spectrometry, which has huge academic and industrial value. Among various miniaturization approaches, filter-based miniaturization is a promising implementation by utilizing broadband filters with distinct transmission functions. Mathematically, filter-based spectral reconstruction can be modeled as solving a system of linear equations. In this paper, we propose an algorithm of spectral reconstruction based on sparse optimization and dictionary learning. To verify the feasibility of the reconstruction algorithm, we design and implement a simple prototype of a filter-based miniature spectrometer. The experimental results demonstrate that sparse optimization is well applicable to spectral reconstruction whether the spectra are directly sparse or not. As for the non-directly sparse spectra, their sparsity can be enhanced by dictionary learning. In conclusion, the proposed approach has a bright application prospect in fabricating a practical miniature spectrometer.

A Spectral Reconstruction Algorithm of Miniature Spectrometer Based on Sparse Optimization and Dictionary Learning

PubMed Central

Zhang, Shang; Fu, Hongyan; Huang, Shao-Lun; Zhang, Lin

2018-01-01

The miniaturization of spectrometer can broaden the application area of spectrometry, which has huge academic and industrial value. Among various miniaturization approaches, filter-based miniaturization is a promising implementation by utilizing broadband filters with distinct transmission functions. Mathematically, filter-based spectral reconstruction can be modeled as solving a system of linear equations. In this paper, we propose an algorithm of spectral reconstruction based on sparse optimization and dictionary learning. To verify the feasibility of the reconstruction algorithm, we design and implement a simple prototype of a filter-based miniature spectrometer. The experimental results demonstrate that sparse optimization is well applicable to spectral reconstruction whether the spectra are directly sparse or not. As for the non-directly sparse spectra, their sparsity can be enhanced by dictionary learning. In conclusion, the proposed approach has a bright application prospect in fabricating a practical miniature spectrometer. PMID:29470406

Finger vein verification system based on sparse representation.

PubMed

Xin, Yang; Liu, Zhi; Zhang, Haixia; Zhang, Hong

2012-09-01

Finger vein verification is a promising biometric pattern for personal identification in terms of security and convenience. The recognition performance of this technology heavily relies on the quality of finger vein images and on the recognition algorithm. To achieve efficient recognition performance, a special finger vein imaging device is developed, and a finger vein recognition method based on sparse representation is proposed. The motivation for the proposed method is that finger vein images exhibit a sparse property. In the proposed system, the regions of interest (ROIs) in the finger vein images are segmented and enhanced. Sparse representation and sparsity preserving projection on ROIs are performed to obtain the features. Finally, the features are measured for recognition. An equal error rate of 0.017% was achieved based on the finger vein image database, which contains images that were captured by using the near-IR imaging device that was developed in this study. The experimental results demonstrate that the proposed method is faster and more robust than previous methods.

Adapting iterative algorithms for solving large sparse linear systems for efficient use on the CDC CYBER 205

NASA Technical Reports Server (NTRS)

Kincaid, D. R.; Young, D. M.

1984-01-01

Adapting and designing mathematical software to achieve optimum performance on the CYBER 205 is discussed. Comments and observations are made in light of recent work done on modifying the ITPACK software package and on writing new software for vector supercomputers. The goal was to develop very efficient vector algorithms and software for solving large sparse linear systems using iterative methods.

Optimized Design and Analysis of Sparse-Sampling fMRI Experiments

PubMed Central

Perrachione, Tyler K.; Ghosh, Satrajit S.

2013-01-01

Sparse-sampling is an important methodological advance in functional magnetic resonance imaging (fMRI), in which silent delays are introduced between MR volume acquisitions, allowing for the presentation of auditory stimuli without contamination by acoustic scanner noise and for overt vocal responses without motion-induced artifacts in the functional time series. As such, the sparse-sampling technique has become a mainstay of principled fMRI research into the cognitive and systems neuroscience of speech, language, hearing, and music. Despite being in use for over a decade, there has been little systematic investigation of the acquisition parameters, experimental design considerations, and statistical analysis approaches that bear on the results and interpretation of sparse-sampling fMRI experiments. In this report, we examined how design and analysis choices related to the duration of repetition time (TR) delay (an acquisition parameter), stimulation rate (an experimental design parameter), and model basis function (an analysis parameter) act independently and interactively to affect the neural activation profiles observed in fMRI. First, we conducted a series of computational simulations to explore the parameter space of sparse design and analysis with respect to these variables; second, we validated the results of these simulations in a series of sparse-sampling fMRI experiments. Overall, these experiments suggest the employment of three methodological approaches that can, in many situations, substantially improve the detection of neurophysiological response in sparse fMRI: (1) Sparse analyses should utilize a physiologically informed model that incorporates hemodynamic response convolution to reduce model error. (2) The design of sparse fMRI experiments should maintain a high rate of stimulus presentation to maximize effect size. (3) TR delays of short to intermediate length can be used between acquisitions of sparse-sampled functional image volumes to increase the number of samples and improve statistical power. PMID:23616742

Optimized design and analysis of sparse-sampling FMRI experiments.

PubMed

Perrachione, Tyler K; Ghosh, Satrajit S

2013-01-01

Sparse-sampling is an important methodological advance in functional magnetic resonance imaging (fMRI), in which silent delays are introduced between MR volume acquisitions, allowing for the presentation of auditory stimuli without contamination by acoustic scanner noise and for overt vocal responses without motion-induced artifacts in the functional time series. As such, the sparse-sampling technique has become a mainstay of principled fMRI research into the cognitive and systems neuroscience of speech, language, hearing, and music. Despite being in use for over a decade, there has been little systematic investigation of the acquisition parameters, experimental design considerations, and statistical analysis approaches that bear on the results and interpretation of sparse-sampling fMRI experiments. In this report, we examined how design and analysis choices related to the duration of repetition time (TR) delay (an acquisition parameter), stimulation rate (an experimental design parameter), and model basis function (an analysis parameter) act independently and interactively to affect the neural activation profiles observed in fMRI. First, we conducted a series of computational simulations to explore the parameter space of sparse design and analysis with respect to these variables; second, we validated the results of these simulations in a series of sparse-sampling fMRI experiments. Overall, these experiments suggest the employment of three methodological approaches that can, in many situations, substantially improve the detection of neurophysiological response in sparse fMRI: (1) Sparse analyses should utilize a physiologically informed model that incorporates hemodynamic response convolution to reduce model error. (2) The design of sparse fMRI experiments should maintain a high rate of stimulus presentation to maximize effect size. (3) TR delays of short to intermediate length can be used between acquisitions of sparse-sampled functional image volumes to increase the number of samples and improve statistical power.

NELasso: Group-Sparse Modeling for Characterizing Relations Among Named Entities in News Articles.

PubMed

Tariq, Amara; Karim, Asim; Foroosh, Hassan

2017-10-01

Named entities such as people, locations, and organizations play a vital role in characterizing online content. They often reflect information of interest and are frequently used in search queries. Although named entities can be detected reliably from textual content, extracting relations among them is more challenging, yet useful in various applications (e.g., news recommending systems). In this paper, we present a novel model and system for learning semantic relations among named entities from collections of news articles. We model each named entity occurrence with sparse structured logistic regression, and consider the words (predictors) to be grouped based on background semantics. This sparse group LASSO approach forces the weights of word groups that do not influence the prediction towards zero. The resulting sparse structure is utilized for defining the type and strength of relations. Our unsupervised system yields a named entities' network where each relation is typed, quantified, and characterized in context. These relations are the key to understanding news material over time and customizing newsfeeds for readers. Extensive evaluation of our system on articles from TIME magazine and BBC News shows that the learned relations correlate with static semantic relatedness measures like WLM, and capture the evolving relationships among named entities over time.

Data-driven discovery of partial differential equations.

PubMed

Rudy, Samuel H; Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan

2017-04-01

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg-de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable.

Fast integration-based prediction bands for ordinary differential equation models.

PubMed

Hass, Helge; Kreutz, Clemens; Timmer, Jens; Kaschek, Daniel

2016-04-15

To gain a deeper understanding of biological processes and their relevance in disease, mathematical models are built upon experimental data. Uncertainty in the data leads to uncertainties of the model's parameters and in turn to uncertainties of predictions. Mechanistic dynamic models of biochemical networks are frequently based on nonlinear differential equation systems and feature a large number of parameters, sparse observations of the model components and lack of information in the available data. Due to the curse of dimensionality, classical and sampling approaches propagating parameter uncertainties to predictions are hardly feasible and insufficient. However, for experimental design and to discriminate between competing models, prediction and confidence bands are essential. To circumvent the hurdles of the former methods, an approach to calculate a profile likelihood on arbitrary observations for a specific time point has been introduced, which provides accurate confidence and prediction intervals for nonlinear models and is computationally feasible for high-dimensional models. In this article, reliable and smooth point-wise prediction and confidence bands to assess the model's uncertainty on the whole time-course are achieved via explicit integration with elaborate correction mechanisms. The corresponding system of ordinary differential equations is derived and tested on three established models for cellular signalling. An efficiency analysis is performed to illustrate the computational benefit compared with repeated profile likelihood calculations at multiple time points. The integration framework and the examples used in this article are provided with the software package Data2Dynamics, which is based on MATLAB and freely available at http://www.data2dynamics.org helge.hass@fdm.uni-freiburg.de Supplementary data are available at Bioinformatics online. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Evaluating the relationship between topography and groundwater using outputs from a continental-scale integrated hydrology model

NASA Astrophysics Data System (ADS)

Condon, Laura E.; Maxwell, Reed M.

2015-08-01

We study the influence of topography on groundwater fluxes and water table depths across the contiguous United States (CONUS). Groundwater tables are often conceptualized as subdued replicas of topography. While it is well known that groundwater configuration is also controlled by geology and climate, nonlinear interactions between these drivers within large real-world systems are not well understood and are difficult to characterize given sparse groundwater observations. We address this limitation using the fully integrated physical hydrology model ParFlow to directly simulate groundwater fluxes and water table depths within a complex heterogeneous domain that incorporates all three primary groundwater drivers. Analysis is based on a first of its kind, continental-scale, high-resolution (1 km), groundwater-surface water simulation spanning more than 6.3 million km2. Results show that groundwater fluxes are most strongly driven by topographic gradients (as opposed to gradients in pressure head) in humid regions with small topographic gradients or low conductivity. These regions are generally consistent with the topographically controlled groundwater regions identified in previous studies. However, we also show that areas where topographic slopes drive groundwater flux do not generally have strong correlations between water table depth and elevation. Nonlinear relationships between topography and water table depth are consistent with groundwater flow systems that are dominated by local convergence and could also be influenced by local variability in geology and climate. One of the strengths of the numerical modeling approach is its ability to evaluate continental-scale groundwater behavior at a high resolution not possible with other techniques. This article was corrected on 11 SEP 2015. See the end of the full text for details.

Exploring nonlinear feature space dimension reduction and data representation in breast Cadx with Laplacian eigenmaps and t-SNE.

PubMed

Jamieson, Andrew R; Giger, Maryellen L; Drukker, Karen; Li, Hui; Yuan, Yading; Bhooshan, Neha

2010-01-01

In this preliminary study, recently developed unsupervised nonlinear dimension reduction (DR) and data representation techniques were applied to computer-extracted breast lesion feature spaces across three separate imaging modalities: Ultrasound (U.S.) with 1126 cases, dynamic contrast enhanced magnetic resonance imaging with 356 cases, and full-field digital mammography with 245 cases. Two methods for nonlinear DR were explored: Laplacian eigenmaps [M. Belkin and P. Niyogi, "Laplacian eigenmaps for dimensionality reduction and data representation," Neural Comput. 15, 1373-1396 (2003)] and t-distributed stochastic neighbor embedding (t-SNE) [L. van der Maaten and G. Hinton, "Visualizing data using t-SNE," J. Mach. Learn. Res. 9, 2579-2605 (2008)]. These methods attempt to map originally high dimensional feature spaces to more human interpretable lower dimensional spaces while preserving both local and global information. The properties of these methods as applied to breast computer-aided diagnosis (CADx) were evaluated in the context of malignancy classification performance as well as in the visual inspection of the sparseness within the two-dimensional and three-dimensional mappings. Classification performance was estimated by using the reduced dimension mapped feature output as input into both linear and nonlinear classifiers: Markov chain Monte Carlo based Bayesian artificial neural network (MCMC-BANN) and linear discriminant analysis. The new techniques were compared to previously developed breast CADx methodologies, including automatic relevance determination and linear stepwise (LSW) feature selection, as well as a linear DR method based on principal component analysis. Using ROC analysis and 0.632+bootstrap validation, 95% empirical confidence intervals were computed for the each classifier's AUC performance. In the large U.S. data set, sample high performance results include, AUC0.632+ = 0.88 with 95% empirical bootstrap interval [0.787;0.895] for 13 ARD selected features and AUC0.632+ = 0.87 with interval [0.817;0.906] for four LSW selected features compared to 4D t-SNE mapping (from the original 81D feature space) giving AUC0.632+ = 0.90 with interval [0.847;0.919], all using the MCMC-BANN. Preliminary results appear to indicate capability for the new methods to match or exceed classification performance of current advanced breast lesion CADx algorithms. While not appropriate as a complete replacement of feature selection in CADx problems, DR techniques offer a complementary approach, which can aid elucidation of additional properties associated with the data. Specifically, the new techniques were shown to possess the added benefit of delivering sparse lower dimensional representations for visual interpretation, revealing intricate data structure of the feature space.

Linear SFM: A hierarchical approach to solving structure-from-motion problems by decoupling the linear and nonlinear components

NASA Astrophysics Data System (ADS)

Zhao, Liang; Huang, Shoudong; Dissanayake, Gamini

2018-07-01

This paper presents a novel hierarchical approach to solving structure-from-motion (SFM) problems. The algorithm begins with small local reconstructions based on nonlinear bundle adjustment (BA). These are then joined in a hierarchical manner using a strategy that requires solving a linear least squares optimization problem followed by a nonlinear transform. The algorithm can handle ordered monocular and stereo image sequences. Two stereo images or three monocular images are adequate for building each initial reconstruction. The bulk of the computation involves solving a linear least squares problem and, therefore, the proposed algorithm avoids three major issues associated with most of the nonlinear optimization algorithms currently used for SFM: the need for a reasonably accurate initial estimate, the need for iterations, and the possibility of being trapped in a local minimum. Also, by summarizing all the original observations into the small local reconstructions with associated information matrices, the proposed Linear SFM manages to preserve all the information contained in the observations. The paper also demonstrates that the proposed problem formulation results in a sparse structure that leads to an efficient numerical implementation. The experimental results using publicly available datasets show that the proposed algorithm yields solutions that are very close to those obtained using a global BA starting with an accurate initial estimate. The C/C++ source code of the proposed algorithm is publicly available at https://github.com/LiangZhaoPKUImperial/LinearSFM.

Bayesian nonlinear structural FE model and seismic input identification for damage assessment of civil structures

NASA Astrophysics Data System (ADS)

Astroza, Rodrigo; Ebrahimian, Hamed; Li, Yong; Conte, Joel P.

2017-09-01

A methodology is proposed to update mechanics-based nonlinear finite element (FE) models of civil structures subjected to unknown input excitation. The approach allows to jointly estimate unknown time-invariant model parameters of a nonlinear FE model of the structure and the unknown time histories of input excitations using spatially-sparse output response measurements recorded during an earthquake event. The unscented Kalman filter, which circumvents the computation of FE response sensitivities with respect to the unknown model parameters and unknown input excitations by using a deterministic sampling approach, is employed as the estimation tool. The use of measurement data obtained from arrays of heterogeneous sensors, including accelerometers, displacement sensors, and strain gauges is investigated. Based on the estimated FE model parameters and input excitations, the updated nonlinear FE model can be interrogated to detect, localize, classify, and assess damage in the structure. Numerically simulated response data of a three-dimensional 4-story 2-by-1 bay steel frame structure with six unknown model parameters subjected to unknown bi-directional horizontal seismic excitation, and a three-dimensional 5-story 2-by-1 bay reinforced concrete frame structure with nine unknown model parameters subjected to unknown bi-directional horizontal seismic excitation are used to illustrate and validate the proposed methodology. The results of the validation studies show the excellent performance and robustness of the proposed algorithm to jointly estimate unknown FE model parameters and unknown input excitations.

Incomplete Sparse Approximate Inverses for Parallel Preconditioning

DOE PAGES

Anzt, Hartwig; Huckle, Thomas K.; Bräckle, Jürgen; ...

2017-10-28

In this study, we propose a new preconditioning method that can be seen as a generalization of block-Jacobi methods, or as a simplification of the sparse approximate inverse (SAI) preconditioners. The “Incomplete Sparse Approximate Inverses” (ISAI) is in particular efficient in the solution of sparse triangular linear systems of equations. Those arise, for example, in the context of incomplete factorization preconditioning. ISAI preconditioners can be generated via an algorithm providing fine-grained parallelism, which makes them attractive for hardware with a high concurrency level. Finally, in a study covering a large number of matrices, we identify the ISAI preconditioner as anmore » attractive alternative to exact triangular solves in the context of incomplete factorization preconditioning.« less

Sparse image reconstruction for molecular imaging.

PubMed

Ting, Michael; Raich, Raviv; Hero, Alfred O

2009-06-01

The application that motivates this paper is molecular imaging at the atomic level. When discretized at subatomic distances, the volume is inherently sparse. Noiseless measurements from an imaging technology can be modeled by convolution of the image with the system point spread function (psf). Such is the case with magnetic resonance force microscopy (MRFM), an emerging technology where imaging of an individual tobacco mosaic virus was recently demonstrated with nanometer resolution. We also consider additive white Gaussian noise (AWGN) in the measurements. Many prior works of sparse estimators have focused on the case when H has low coherence; however, the system matrix H in our application is the convolution matrix for the system psf. A typical convolution matrix has high coherence. This paper, therefore, does not assume a low coherence H. A discrete-continuous form of the Laplacian and atom at zero (LAZE) p.d.f. used by Johnstone and Silverman is formulated, and two sparse estimators derived by maximizing the joint p.d.f. of the observation and image conditioned on the hyperparameters. A thresholding rule that generalizes the hard and soft thresholding rule appears in the course of the derivation. This so-called hybrid thresholding rule, when used in the iterative thresholding framework, gives rise to the hybrid estimator, a generalization of the lasso. Estimates of the hyperparameters for the lasso and hybrid estimator are obtained via Stein's unbiased risk estimate (SURE). A numerical study with a Gaussian psf and two sparse images shows that the hybrid estimator outperforms the lasso.

Optimised robot-based system for the exploration of elastic joint properties.

PubMed

Frey, M; Burgkart, R; Regenfelder, F; Riener, R

2004-09-01

Numerous publications provide measured biomechanical data relating to synovial joints. However, in general, they do not reflect the non-linear elastic joint properties in detail or do not consider all degrees of freedom (DOF), or the quantity of data is sparse. To perform more comprehensive, extended measurements of elastic joint properties, an optimised robot-based approach was developed. The basis was an industrial, high-precision robot that was capable of applying loads to the joint and measuring the joint displacement in 6 DOF. The system was equipped with novel, custom-made control hardware. In contrast to the commonly used sampling rates that are below 100 Hz, a rate of 4 kHz was realised for each DOF. This made it possible to implement advanced, highly dynamic, quasi-continuous closed-loop controllers. Thus oscillations of the robot were avoided, and measurements were speeded up. The stiffness of the entire system was greater than 44 kNm(-1) and 22 Nm deg(-1), and the maximum difference between two successive measurements was less than 0.5 deg. A sophisticated CT-based referencing routine facilitated the matching of kinematic data with the individual anatomy of the tested joint. The detailed detection of the elastic varus-valgus properties of a human knee joint is described, and the need for high spatial resolution is demonstrated.

Automatic Reconstruction of Spacecraft 3D Shape from Imagery

NASA Astrophysics Data System (ADS)

Poelman, C.; Radtke, R.; Voorhees, H.

We describe a system that computes the three-dimensional (3D) shape of a spacecraft from a sequence of uncalibrated, two-dimensional images. While the mathematics of multi-view geometry is well understood, building a system that accurately recovers 3D shape from real imagery remains an art. A novel aspect of our approach is the combination of algorithms from computer vision, photogrammetry, and computer graphics. We demonstrate our system by computing spacecraft models from imagery taken by the Air Force Research Laboratory's XSS-10 satellite and DARPA's Orbital Express satellite. Using feature tie points (each identified in two or more images), we compute the relative motion of each frame and the 3D location of each feature using iterative linear factorization followed by non-linear bundle adjustment. The "point cloud" that results from this traditional shape-from-motion approach is typically too sparse to generate a detailed 3D model. Therefore, we use the computed motion solution as input to a volumetric silhouette-carving algorithm, which constructs a solid 3D model based on viewpoint consistency with the image frames. The resulting voxel model is then converted to a facet-based surface representation and is texture-mapped, yielding realistic images from arbitrary viewpoints. We also illustrate other applications of the algorithm, including 3D mensuration and stereoscopic 3D movie generation.

Simulations inform design of regional occupancy-based monitoring for a sparsely distributed, territorial species

Treesearch

Quresh S. Latif; Martha M. Ellis; Victoria A. Saab; Kim Mellen-McLean

2017-01-01

Sparsely distributed species attract conservation concern, but insufficient information on population trends challenges conservation and funding prioritization. Occupancy-based monitoring is attractive for these species, but appropriate sampling design and inference depend on particulars of the study system. We employed spatially explicit simulations to identify...

Robust Methods for Sensing and Reconstructing Sparse Signals

ERIC Educational Resources Information Center

Carrillo, Rafael E.

2012-01-01

Compressed sensing (CS) is an emerging signal acquisition framework that goes against the traditional Nyquist sampling paradigm. CS demonstrates that a sparse, or compressible, signal can be acquired using a low rate acquisition process. Since noise is always present in practical data acquisition systems, sensing and reconstruction methods are…

A New Approach to Model Pitch Perception Using Sparse Coding

PubMed Central

Furst, Miriam; Barak, Omri

2017-01-01

Our acoustical environment abounds with repetitive sounds, some of which are related to pitch perception. It is still unknown how the auditory system, in processing these sounds, relates a physical stimulus and its percept. Since, in mammals, all auditory stimuli are conveyed into the nervous system through the auditory nerve (AN) fibers, a model should explain the perception of pitch as a function of this particular input. However, pitch perception is invariant to certain features of the physical stimulus. For example, a missing fundamental stimulus with resolved or unresolved harmonics, or a low and high-level amplitude stimulus with the same spectral content–these all give rise to the same percept of pitch. In contrast, the AN representations for these different stimuli are not invariant to these effects. In fact, due to saturation and non-linearity of both cochlear and inner hair cells responses, these differences are enhanced by the AN fibers. Thus there is a difficulty in explaining how pitch percept arises from the activity of the AN fibers. We introduce a novel approach for extracting pitch cues from the AN population activity for a given arbitrary stimulus. The method is based on a technique known as sparse coding (SC). It is the representation of pitch cues by a few spatiotemporal atoms (templates) from among a large set of possible ones (a dictionary). The amount of activity of each atom is represented by a non-zero coefficient, analogous to an active neuron. Such a technique has been successfully applied to other modalities, particularly vision. The model is composed of a cochlear model, an SC processing unit, and a harmonic sieve. We show that the model copes with different pitch phenomena: extracting resolved and non-resolved harmonics, missing fundamental pitches, stimuli with both high and low amplitudes, iterated rippled noises, and recorded musical instruments. PMID:28099436

A New Approach to Model Pitch Perception Using Sparse Coding.

PubMed

Barzelay, Oded; Furst, Miriam; Barak, Omri

2017-01-01

Our acoustical environment abounds with repetitive sounds, some of which are related to pitch perception. It is still unknown how the auditory system, in processing these sounds, relates a physical stimulus and its percept. Since, in mammals, all auditory stimuli are conveyed into the nervous system through the auditory nerve (AN) fibers, a model should explain the perception of pitch as a function of this particular input. However, pitch perception is invariant to certain features of the physical stimulus. For example, a missing fundamental stimulus with resolved or unresolved harmonics, or a low and high-level amplitude stimulus with the same spectral content-these all give rise to the same percept of pitch. In contrast, the AN representations for these different stimuli are not invariant to these effects. In fact, due to saturation and non-linearity of both cochlear and inner hair cells responses, these differences are enhanced by the AN fibers. Thus there is a difficulty in explaining how pitch percept arises from the activity of the AN fibers. We introduce a novel approach for extracting pitch cues from the AN population activity for a given arbitrary stimulus. The method is based on a technique known as sparse coding (SC). It is the representation of pitch cues by a few spatiotemporal atoms (templates) from among a large set of possible ones (a dictionary). The amount of activity of each atom is represented by a non-zero coefficient, analogous to an active neuron. Such a technique has been successfully applied to other modalities, particularly vision. The model is composed of a cochlear model, an SC processing unit, and a harmonic sieve. We show that the model copes with different pitch phenomena: extracting resolved and non-resolved harmonics, missing fundamental pitches, stimuli with both high and low amplitudes, iterated rippled noises, and recorded musical instruments.

Addressing global uncertainty and sensitivity in first-principles based microkinetic models by an adaptive sparse grid approach

NASA Astrophysics Data System (ADS)

Döpking, Sandra; Plaisance, Craig P.; Strobusch, Daniel; Reuter, Karsten; Scheurer, Christoph; Matera, Sebastian

2018-01-01

In the last decade, first-principles-based microkinetic modeling has been developed into an important tool for a mechanistic understanding of heterogeneous catalysis. A commonly known, but hitherto barely analyzed issue in this kind of modeling is the presence of sizable errors from the use of approximate Density Functional Theory (DFT). We here address the propagation of these errors to the catalytic turnover frequency (TOF) by global sensitivity and uncertainty analysis. Both analyses require the numerical quadrature of high-dimensional integrals. To achieve this efficiently, we utilize and extend an adaptive sparse grid approach and exploit the confinement of the strongly non-linear behavior of the TOF to local regions of the parameter space. We demonstrate the methodology on a model of the oxygen evolution reaction at the Co3O4 (110)-A surface, using a maximum entropy error model that imposes nothing but reasonable bounds on the errors. For this setting, the DFT errors lead to an absolute uncertainty of several orders of magnitude in the TOF. We nevertheless find that it is still possible to draw conclusions from such uncertain models about the atomistic aspects controlling the reactivity. A comparison with derivative-based local sensitivity analysis instead reveals that this more established approach provides incomplete information. Since the adaptive sparse grids allow for the evaluation of the integrals with only a modest number of function evaluations, this approach opens the way for a global sensitivity analysis of more complex models, for instance, models based on kinetic Monte Carlo simulations.

Towards a Highly Efficient Meshfree Simulation of Non-Newtonian Free Surface Ice Flow: Application to the Haut Glacier d'Arolla

NASA Astrophysics Data System (ADS)

Shcherbakov, V.; Ahlkrona, J.

2016-12-01

In this work we develop a highly efficient meshfree approach to ice sheet modeling. Traditionally mesh based methods such as finite element methods are employed to simulate glacier and ice sheet dynamics. These methods are mature and well developed. However, despite of numerous advantages these methods suffer from some drawbacks such as necessity to remesh the computational domain every time it changes its shape, which significantly complicates the implementation on moving domains, or a costly assembly procedure for nonlinear problems. We introduce a novel meshfree approach that frees us from all these issues. The approach is built upon a radial basis function (RBF) method that, thanks to its meshfree nature, allows for an efficient handling of moving margins and free ice surface. RBF methods are also accurate and easy to implement. Since the formulation is stated in strong form it allows for a substantial reduction of the computational cost associated with the linear system assembly inside the nonlinear solver. We implement a global RBF method that defines an approximation on the entire computational domain. This method exhibits high accuracy properties. However, it suffers from a disadvantage that the coefficient matrix is dense, and therefore the computational efficiency decreases. In order to overcome this issue we also implement a localized RBF method that rests upon a partition of unity approach to subdivide the domain into several smaller subdomains. The radial basis function partition of unity method (RBF-PUM) inherits high approximation characteristics form the global RBF method while resulting in a sparse system of equations, which essentially increases the computational efficiency. To demonstrate the usefulness of the RBF methods we model the velocity field of ice flow in the Haut Glacier d'Arolla. We assume that the flow is governed by the nonlinear Blatter-Pattyn equations. We test the methods for different basal conditions and for a free moving surface. Both RBF methods are compared with a classical finite element method in terms of accuracy and efficiency. We find that the RBF methods are more efficient than the finite element method and well suited for ice dynamics modeling, especially the partition of unity approach.

Compressive sensing using optimized sensing matrix for face verification

NASA Astrophysics Data System (ADS)

Oey, Endra; Jeffry; Wongso, Kelvin; Tommy

2017-12-01

Biometric appears as one of the solutions which is capable in solving problems that occurred in the usage of password in terms of data access, for example there is possibility in forgetting password and hard to recall various different passwords. With biometrics, physical characteristics of a person can be captured and used in the identification process. In this research, facial biometric is used in the verification process to determine whether the user has the authority to access the data or not. Facial biometric is chosen as its low cost implementation and generate quite accurate result for user identification. Face verification system which is adopted in this research is Compressive Sensing (CS) technique, in which aims to reduce dimension size as well as encrypt data in form of facial test image where the image is represented in sparse signals. Encrypted data can be reconstructed using Sparse Coding algorithm. Two types of Sparse Coding namely Orthogonal Matching Pursuit (OMP) and Iteratively Reweighted Least Squares -ℓp (IRLS-ℓp) will be used for comparison face verification system research. Reconstruction results of sparse signals are then used to find Euclidean norm with the sparse signal of user that has been previously saved in system to determine the validity of the facial test image. Results of system accuracy obtained in this research are 99% in IRLS with time response of face verification for 4.917 seconds and 96.33% in OMP with time response of face verification for 0.4046 seconds with non-optimized sensing matrix, while 99% in IRLS with time response of face verification for 13.4791 seconds and 98.33% for OMP with time response of face verification for 3.1571 seconds with optimized sensing matrix.

Regularized two-step brain activity reconstruction from spatiotemporal EEG data

NASA Astrophysics Data System (ADS)

Alecu, Teodor I.; Voloshynovskiy, Sviatoslav; Pun, Thierry

2004-10-01

We are aiming at using EEG source localization in the framework of a Brain Computer Interface project. We propose here a new reconstruction procedure, targeting source (or equivalently mental task) differentiation. EEG data can be thought of as a collection of time continuous streams from sparse locations. The measured electric potential on one electrode is the result of the superposition of synchronized synaptic activity from sources in all the brain volume. Consequently, the EEG inverse problem is a highly underdetermined (and ill-posed) problem. Moreover, each source contribution is linear with respect to its amplitude but non-linear with respect to its localization and orientation. In order to overcome these drawbacks we propose a novel two-step inversion procedure. The solution is based on a double scale division of the solution space. The first step uses a coarse discretization and has the sole purpose of globally identifying the active regions, via a sparse approximation algorithm. The second step is applied only on the retained regions and makes use of a fine discretization of the space, aiming at detailing the brain activity. The local configuration of sources is recovered using an iterative stochastic estimator with adaptive joint minimum energy and directional consistency constraints.

PERIOD ESTIMATION FOR SPARSELY SAMPLED QUASI-PERIODIC LIGHT CURVES APPLIED TO MIRAS

DOE Office of Scientific and Technical Information (OSTI.GOV)

He, Shiyuan; Huang, Jianhua Z.; Long, James

2016-12-01

We develop a nonlinear semi-parametric Gaussian process model to estimate periods of Miras with sparsely sampled light curves. The model uses a sinusoidal basis for the periodic variation and a Gaussian process for the stochastic changes. We use maximum likelihood to estimate the period and the parameters of the Gaussian process, while integrating out the effects of other nuisance parameters in the model with respect to a suitable prior distribution obtained from earlier studies. Since the likelihood is highly multimodal for period, we implement a hybrid method that applies the quasi-Newton algorithm for Gaussian process parameters and search the period/frequencymore » parameter space over a dense grid. A large-scale, high-fidelity simulation is conducted to mimic the sampling quality of Mira light curves obtained by the M33 Synoptic Stellar Survey. The simulated data set is publicly available and can serve as a testbed for future evaluation of different period estimation methods. The semi-parametric model outperforms an existing algorithm on this simulated test data set as measured by period recovery rate and quality of the resulting period–luminosity relations.« less

Synaptic and Network Mechanisms of Sparse and Reliable Visual Cortical Activity during Nonclassical Receptive Field Stimulation

PubMed Central

Haider, Bilal; Krause, Matthew R.; Duque, Alvaro; Yu, Yuguo; Touryan, Jonathan; Mazer, James A.; McCormick, David A.

2011-01-01

SUMMARY During natural vision, the entire visual field is stimulated by images rich in spatiotemporal structure. Although many visual system studies restrict stimuli to the classical receptive field (CRF), it is known that costimulation of the CRF and the surrounding nonclassical receptive field (nCRF) increases neuronal response sparseness. The cellular and network mechanisms underlying increased response sparseness remain largely unexplored. Here we show that combined CRF + nCRF stimulation increases the sparseness, reliability, and precision of spiking and membrane potential responses in classical regular spiking (RSC) pyramidal neurons of cat primary visual cortex. Conversely, fast-spiking interneurons exhibit increased activity and decreased selectivity during CRF + nCRF stimulation. The increased sparseness and reliability of RSC neuron spiking is associated with increased inhibitory barrages and narrower visually evoked synaptic potentials. Our experimental observations were replicated with a simple computational model, suggesting that network interactions among neuronal subtypes ultimately sharpen recurrent excitation, producing specific and reliable visual responses. PMID:20152117

Rectified factor networks for biclustering of omics data.

PubMed

Clevert, Djork-Arné; Unterthiner, Thomas; Povysil, Gundula; Hochreiter, Sepp

2017-07-15

Biclustering has become a major tool for analyzing large datasets given as matrix of samples times features and has been successfully applied in life sciences and e-commerce for drug design and recommender systems, respectively. actor nalysis for cluster cquisition (FABIA), one of the most successful biclustering methods, is a generative model that represents each bicluster by two sparse membership vectors: one for the samples and one for the features. However, FABIA is restricted to about 20 code units because of the high computational complexity of computing the posterior. Furthermore, code units are sometimes insufficiently decorrelated and sample membership is difficult to determine. We propose to use the recently introduced unsupervised Deep Learning approach Rectified Factor Networks (RFNs) to overcome the drawbacks of existing biclustering methods. RFNs efficiently construct very sparse, non-linear, high-dimensional representations of the input via their posterior means. RFN learning is a generalized alternating minimization algorithm based on the posterior regularization method which enforces non-negative and normalized posterior means. Each code unit represents a bicluster, where samples for which the code unit is active belong to the bicluster and features that have activating weights to the code unit belong to the bicluster. On 400 benchmark datasets and on three gene expression datasets with known clusters, RFN outperformed 13 other biclustering methods including FABIA. On data of the 1000 Genomes Project, RFN could identify DNA segments which indicate, that interbreeding with other hominins starting already before ancestors of modern humans left Africa. https://github.com/bioinf-jku/librfn. djork-arne.clevert@bayer.com or hochreit@bioinf.jku.at. © The Author 2017. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com

Near real-time estimation of the seismic source parameters in a compressed domain

NASA Astrophysics Data System (ADS)

Rodriguez, Ismael A. Vera

Seismic events can be characterized by its origin time, location and moment tensor. Fast estimations of these source parameters are important in areas of geophysics like earthquake seismology, and the monitoring of seismic activity produced by volcanoes, mining operations and hydraulic injections in geothermal and oil and gas reservoirs. Most available monitoring systems estimate the source parameters in a sequential procedure: first determining origin time and location (e.g., epicentre, hypocentre or centroid of the stress glut density), and then using this information to initialize the evaluation of the moment tensor. A more efficient estimation of the source parameters requires a concurrent evaluation of the three variables. The main objective of the present thesis is to address the simultaneous estimation of origin time, location and moment tensor of seismic events. The proposed method displays the benefits of being: 1) automatic, 2) continuous and, depending on the scale of application, 3) of providing results in real-time or near real-time. The inversion algorithm is based on theoretical results from sparse representation theory and compressive sensing. The feasibility of implementation is determined through the analysis of synthetic and real data examples. The numerical experiments focus on the microseismic monitoring of hydraulic fractures in oil and gas wells, however, an example using real earthquake data is also presented for validation. The thesis is complemented with a resolvability analysis of the moment tensor. The analysis targets common monitoring geometries employed in hydraulic fracturing in oil wells. Additionally, it is presented an application of sparse representation theory for the denoising of one-component and three-component microseismicity records, and an algorithm for improved automatic time-picking using non-linear inversion constraints.

Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

DOE PAGES

Li, Ruipeng; Saad, Yousef

2017-08-01

This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisonsmore » with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.« less

A novel aliasing-free subband information fusion approach for wideband sparse spectral estimation

NASA Astrophysics Data System (ADS)

Luo, Ji-An; Zhang, Xiao-Ping; Wang, Zhi

2017-12-01

Wideband sparse spectral estimation is generally formulated as a multi-dictionary/multi-measurement (MD/MM) problem which can be solved by using group sparsity techniques. In this paper, the MD/MM problem is reformulated as a single sparse indicative vector (SIV) recovery problem at the cost of introducing an additional system error. Thus, the number of unknowns is reduced greatly. We show that the system error can be neglected under certain conditions. We then present a new subband information fusion (SIF) method to estimate the SIV by jointly utilizing all the frequency bins. With orthogonal matching pursuit (OMP) leveraging the binary property of SIV's components, we develop a SIF-OMP algorithm to reconstruct the SIV. The numerical simulations demonstrate the performance of the proposed method.

Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Ruipeng; Saad, Yousef

This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisonsmore » with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.« less

A critical analysis of computational protein design with sparse residue interaction graphs

PubMed Central

Georgiev, Ivelin S.

2017-01-01

Protein design algorithms enumerate a combinatorial number of candidate structures to compute the Global Minimum Energy Conformation (GMEC). To efficiently find the GMEC, protein design algorithms must methodically reduce the conformational search space. By applying distance and energy cutoffs, the protein system to be designed can thus be represented using a sparse residue interaction graph, where the number of interacting residue pairs is less than all pairs of mutable residues, and the corresponding GMEC is called the sparse GMEC. However, ignoring some pairwise residue interactions can lead to a change in the energy, conformation, or sequence of the sparse GMEC vs. the original or the full GMEC. Despite the widespread use of sparse residue interaction graphs in protein design, the above mentioned effects of their use have not been previously analyzed. To analyze the costs and benefits of designing with sparse residue interaction graphs, we computed the GMECs for 136 different protein design problems both with and without distance and energy cutoffs, and compared their energies, conformations, and sequences. Our analysis shows that the differences between the GMECs depend critically on whether or not the design includes core, boundary, or surface residues. Moreover, neglecting long-range interactions can alter local interactions and introduce large sequence differences, both of which can result in significant structural and functional changes. Designs on proteins with experimentally measured thermostability show it is beneficial to compute both the full and the sparse GMEC accurately and efficiently. To this end, we show that a provable, ensemble-based algorithm can efficiently compute both GMECs by enumerating a small number of conformations, usually fewer than 1000. This provides a novel way to combine sparse residue interaction graphs with provable, ensemble-based algorithms to reap the benefits of sparse residue interaction graphs while avoiding their potential inaccuracies. PMID:28358804

Sparse matrix methods based on orthogonality and conjugacy

NASA Technical Reports Server (NTRS)

Lawson, C. L.

1973-01-01

A matrix having a high percentage of zero elements is called spares. In the solution of systems of linear equations or linear least squares problems involving large sparse matrices, significant saving of computer cost can be achieved by taking advantage of the sparsity. The conjugate gradient algorithm and a set of related algorithms are described.

Summer Proceedings 2016: The Center for Computing Research at Sandia National Laboratories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carleton, James Brian; Parks, Michael L.

Solving sparse linear systems from the discretization of elliptic partial differential equations (PDEs) is an important building block in many engineering applications. Sparse direct solvers can solve general linear systems, but are usually slower and use much more memory than effective iterative solvers. To overcome these two disadvantages, a hierarchical solver (LoRaSp) based on H2-matrices was introduced in [22]. Here, we have developed a parallel version of the algorithm in LoRaSp to solve large sparse matrices on distributed memory machines. On a single processor, the factorization time of our parallel solver scales almost linearly with the problem size for three-dimensionalmore » problems, as opposed to the quadratic scalability of many existing sparse direct solvers. Moreover, our solver leads to almost constant numbers of iterations, when used as a preconditioner for Poisson problems. On more than one processor, our algorithm has significant speedups compared to sequential runs. With this parallel algorithm, we are able to solve large problems much faster than many existing packages as demonstrated by the numerical experiments.« less

Self-consistent phonons revisited. I. The role of thermal versus quantum fluctuations on structural transitions in large Lennard-Jones clusters.

PubMed

Georgescu, Ionuţ; Mandelshtam, Vladimir A

2012-10-14

The theory of self-consistent phonons (SCP) was originally developed to address the anharmonic effects in condensed matter systems. The method seeks a harmonic, temperature-dependent Hamiltonian that provides the "best fit" for the physical Hamiltonian, the "best fit" being defined as the one that optimizes the Helmholtz free energy at a fixed temperature. The present developments provide a scalable O(N) unified framework that accounts for anharmonic effects in a many-body system, when it is probed by either thermal (ℏ → 0) or quantum fluctuations (T → 0). In these important limits, the solution of the nonlinear SCP equations can be reached in a manner that requires only the multiplication of 3N × 3N matrices, with no need of diagonalization. For short range potentials, such as Lennard-Jones, the Hessian, and other related matrices are highly sparse, so that the scaling of the matrix multiplications can be reduced from O(N(3)) to ~O(N). We investigate the role of quantum effects by continuously varying the de-Boer quantum delocalization parameter Λ and report the N-Λ (T = 0), and also the classical N-T (Λ = 0) phase diagrams for sizes up to N ~ 10(4). Our results demonstrate that the harmonic approximation becomes inadequate already for such weakly quantum systems as neon clusters, or for classical systems much below the melting temperatures.

Inferring internal properties of Earth's core dynamics and their evolution from surface observations and a numerical geodynamo model

NASA Astrophysics Data System (ADS)

Aubert, J.; Fournier, A.

2011-10-01

Over the past decades, direct three-dimensional numerical modelling has been successfully used to reproduce the main features of the geodynamo. Here we report on efforts to solve the associated inverse problem, aiming at inferring the underlying properties of the system from the sole knowledge of surface observations and the first principle dynamical equations describing the convective dynamo. To this end we rely on twin experiments. A reference model time sequence is first produced and used to generate synthetic data, restricted here to the large-scale component of the magnetic field and its rate of change at the outer boundary. Starting from a different initial condition, a second sequence is next run and attempts are made to recover the internal magnetic, velocity and buoyancy anomaly fields from the sparse surficial data. In order to reduce the vast underdetermination of this problem, we use stochastic inversion, a linear estimation method determining the most likely internal state compatible with the observations and some prior knowledge, and we also implement a sequential evolution algorithm in order to invert time-dependent surface observations. The prior is the multivariate statistics of the numerical model, which are directly computed from a large number of snapshots stored during a preliminary direct run. The statistics display strong correlation between different harmonic degrees of the surface observations and internal fields, provided they share the same harmonic order, a natural consequence of the linear coupling of the governing dynamical equations and of the leading influence of the Coriolis force. Synthetic experiments performed with a weakly nonlinear model yield an excellent quantitative retrieval of the internal structure. In contrast, the use of a strongly nonlinear (and more realistic) model results in less accurate static estimations, which in turn fail to constrain the unobserved small scales in the time integration of the evolution scheme. Evaluating the quality of forecasts of the system evolution against the reference solution, we show that our scheme can improve predictions based on linear extrapolations on forecast horizons shorter than the system e-folding time. Still, in the perspective of forthcoming data assimilation activities, our study underlines the need of advanced estimation techniques able to cope with the moderate to strong nonlinearities present in the geodynamo.

Effects of partitioning and scheduling sparse matrix factorization on communication and load balance

NASA Technical Reports Server (NTRS)

Venugopal, Sesh; Naik, Vijay K.

1991-01-01

A block based, automatic partitioning and scheduling methodology is presented for sparse matrix factorization on distributed memory systems. Using experimental results, this technique is analyzed for communication and load imbalance overhead. To study the performance effects, these overheads were compared with those obtained from a straightforward 'wrap mapped' column assignment scheme. All experimental results were obtained using test sparse matrices from the Harwell-Boeing data set. The results show that there is a communication and load balance tradeoff. The block based method results in lower communication cost whereas the wrap mapped scheme gives better load balance.

Communication requirements of sparse Cholesky factorization with nested dissection ordering

NASA Technical Reports Server (NTRS)

Naik, Vijay K.; Patrick, Merrell L.

1989-01-01

Load distribution schemes for minimizing the communication requirements of the Cholesky factorization of dense and sparse, symmetric, positive definite matrices on multiprocessor systems are presented. The total data traffic in factoring an n x n sparse symmetric positive definite matrix representing an n-vertex regular two-dimensional grid graph using n exp alpha, alpha not greater than 1, processors are shown to be O(n exp 1 + alpha/2). It is O(n), when n exp alpha, alpha not smaller than 1, processors are used. Under the conditions of uniform load distribution, these results are shown to be asymptotically optimal.

Dynamic mode decomposition for plasma diagnostics and validation.

PubMed

Taylor, Roy; Kutz, J Nathan; Morgan, Kyle; Nelson, Brian A

2018-05-01

We demonstrate the application of the Dynamic Mode Decomposition (DMD) for the diagnostic analysis of the nonlinear dynamics of a magnetized plasma in resistive magnetohydrodynamics. The DMD method is an ideal spatio-temporal matrix decomposition that correlates spatial features of computational or experimental data while simultaneously associating the spatial activity with periodic temporal behavior. DMD can produce low-rank, reduced order surrogate models that can be used to reconstruct the state of the system with high fidelity. This allows for a reduction in the computational cost and, at the same time, accurate approximations of the problem, even if the data are sparsely sampled. We demonstrate the use of the method on both numerical and experimental data, showing that it is a successful mathematical architecture for characterizing the helicity injected torus with steady inductive (HIT-SI) magnetohydrodynamics. Importantly, the DMD produces interpretable, dominant mode structures, including a stationary mode consistent with our understanding of a HIT-SI spheromak accompanied by a pair of injector-driven modes. In combination, the 3-mode DMD model produces excellent dynamic reconstructions across the domain of analyzed data.

Dynamic mode decomposition for plasma diagnostics and validation

NASA Astrophysics Data System (ADS)

Taylor, Roy; Kutz, J. Nathan; Morgan, Kyle; Nelson, Brian A.

2018-05-01

We demonstrate the application of the Dynamic Mode Decomposition (DMD) for the diagnostic analysis of the nonlinear dynamics of a magnetized plasma in resistive magnetohydrodynamics. The DMD method is an ideal spatio-temporal matrix decomposition that correlates spatial features of computational or experimental data while simultaneously associating the spatial activity with periodic temporal behavior. DMD can produce low-rank, reduced order surrogate models that can be used to reconstruct the state of the system with high fidelity. This allows for a reduction in the computational cost and, at the same time, accurate approximations of the problem, even if the data are sparsely sampled. We demonstrate the use of the method on both numerical and experimental data, showing that it is a successful mathematical architecture for characterizing the helicity injected torus with steady inductive (HIT-SI) magnetohydrodynamics. Importantly, the DMD produces interpretable, dominant mode structures, including a stationary mode consistent with our understanding of a HIT-SI spheromak accompanied by a pair of injector-driven modes. In combination, the 3-mode DMD model produces excellent dynamic reconstructions across the domain of analyzed data.

Two-level image authentication by two-step phase-shifting interferometry and compressive sensing

NASA Astrophysics Data System (ADS)

Zhang, Xue; Meng, Xiangfeng; Yin, Yongkai; Yang, Xiulun; Wang, Yurong; Li, Xianye; Peng, Xiang; He, Wenqi; Dong, Guoyan; Chen, Hongyi

2018-01-01

A two-level image authentication method is proposed; the method is based on two-step phase-shifting interferometry, double random phase encoding, and compressive sensing (CS) theory, by which the certification image can be encoded into two interferograms. Through discrete wavelet transform (DWT), sparseness processing, Arnold transform, and data compression, two compressed signals can be generated and delivered to two different participants of the authentication system. Only the participant who possesses the first compressed signal attempts to pass the low-level authentication. The application of Orthogonal Match Pursuit CS algorithm reconstruction, inverse Arnold transform, inverse DWT, two-step phase-shifting wavefront reconstruction, and inverse Fresnel transform can result in the output of a remarkable peak in the central location of the nonlinear correlation coefficient distributions of the recovered image and the standard certification image. Then, the other participant, who possesses the second compressed signal, is authorized to carry out the high-level authentication. Therefore, both compressed signals are collected to reconstruct the original meaningful certification image with a high correlation coefficient. Theoretical analysis and numerical simulations verify the feasibility of the proposed method.

Analog "neuronal" networks in early vision.

PubMed Central

Koch, C; Marroquin, J; Yuille, A

1986-01-01

Many problems in early vision can be formulated in terms of minimizing a cost function. Examples are shape from shading, edge detection, motion analysis, structure from motion, and surface interpolation. As shown by Poggio and Koch [Poggio, T. & Koch, C. (1985) Proc. R. Soc. London, Ser. B 226, 303-323], quadratic variational problems, an important subset of early vision tasks, can be "solved" by linear, analog electrical, or chemical networks. However, in the presence of discontinuities, the cost function is nonquadratic, raising the question of designing efficient algorithms for computing the optimal solution. Recently, Hopfield and Tank [Hopfield, J. J. & Tank, D. W. (1985) Biol. Cybern. 52, 141-152] have shown that networks of nonlinear analog "neurons" can be effective in computing the solution of optimization problems. We show how these networks can be generalized to solve the nonconvex energy functionals of early vision. We illustrate this approach by implementing a specific analog network, solving the problem of reconstructing a smooth surface from sparse data while preserving its discontinuities. These results suggest a novel computational strategy for solving early vision problems in both biological and real-time artificial vision systems. PMID:3459172

Nonlinear frequency response based adaptive vibration controller design for a class of nonlinear systems

NASA Astrophysics Data System (ADS)

Thenozhi, Suresh; Tang, Yu

2018-01-01

Frequency response functions (FRF) are often used in the vibration controller design problems of mechanical systems. Unlike linear systems, the FRF derivation for nonlinear systems is not trivial due to their complex behaviors. To address this issue, the convergence property of nonlinear systems can be studied using convergence analysis. For a class of time-invariant nonlinear systems termed as convergent systems, the nonlinear FRF can be obtained. The present paper proposes a nonlinear FRF based adaptive vibration controller design for a mechanical system with cubic damping nonlinearity and a satellite system. Here the controller gains are tuned such that a desired closed-loop frequency response for a band of harmonic excitations is achieved. Unlike the system with cubic damping, the satellite system is not convergent, therefore an additional controller is utilized to achieve the convergence property. Finally, numerical examples are provided to illustrate the effectiveness of the proposed controller.

Tactical 3D Model Generation using Structure-From-Motion on Video from Unmanned Systems

DTIC Science & Technology

2015-04-01

available SfM application known as VisualSFM .6,7 VisualSFM is an end-user, “off-the-shelf” implementation of SfM that is easy to configure and used for...most 3D model generation applications from imagery. While the usual interface with VisualSFM is through their graphical user interface (GUI), we will be...of our system.5 There are two types of 3D model generation available within VisualSFM ; sparse and dense reconstruction. Sparse reconstruction begins

Sparse covariance estimation in heterogeneous samples*

PubMed Central

Rodríguez, Abel; Lenkoski, Alex; Dobra, Adrian

2015-01-01

Standard Gaussian graphical models implicitly assume that the conditional independence among variables is common to all observations in the sample. However, in practice, observations are usually collected from heterogeneous populations where such an assumption is not satisfied, leading in turn to nonlinear relationships among variables. To address such situations we explore mixtures of Gaussian graphical models; in particular, we consider both infinite mixtures and infinite hidden Markov models where the emission distributions correspond to Gaussian graphical models. Such models allow us to divide a heterogeneous population into homogenous groups, with each cluster having its own conditional independence structure. As an illustration, we study the trends in foreign exchange rate fluctuations in the pre-Euro era. PMID:26925189

Polarimetric SAR image classification based on discriminative dictionary learning model

NASA Astrophysics Data System (ADS)

Sang, Cheng Wei; Sun, Hong

2018-03-01

Polarimetric SAR (PolSAR) image classification is one of the important applications of PolSAR remote sensing. It is a difficult high-dimension nonlinear mapping problem, the sparse representations based on learning overcomplete dictionary have shown great potential to solve such problem. The overcomplete dictionary plays an important role in PolSAR image classification, however for PolSAR image complex scenes, features shared by different classes will weaken the discrimination of learned dictionary, so as to degrade classification performance. In this paper, we propose a novel overcomplete dictionary learning model to enhance the discrimination of dictionary. The learned overcomplete dictionary by the proposed model is more discriminative and very suitable for PolSAR classification.

Multi-frame linear regressive filter for the measurement of infrared pixel spatial response and MTF from sparse data.

PubMed

Huard, Edouard; Derelle, Sophie; Jaeck, Julien; Nghiem, Jean; Haïdar, Riad; Primot, Jérôme

2018-03-05

A challenging point in the prediction of the image quality of infrared imaging systems is the evaluation of the detector modulation transfer function (MTF). In this paper, we present a linear method to get a 2D continuous MTF from sparse spectral data. Within the method, an object with a predictable sparse spatial spectrum is imaged by the focal plane array. The sparse data is then treated to return the 2D continuous MTF with the hypothesis that all the pixels have an identical spatial response. The linearity of the treatment is a key point to estimate directly the error bars of the resulting detector MTF. The test bench will be presented along with measurement tests on a 25 μm pitch InGaAs detector.

Efficient convolutional sparse coding

DOEpatents

Wohlberg, Brendt

2017-06-20

Computationally efficient algorithms may be applied for fast dictionary learning solving the convolutional sparse coding problem in the Fourier domain. More specifically, efficient convolutional sparse coding may be derived within an alternating direction method of multipliers (ADMM) framework that utilizes fast Fourier transforms (FFT) to solve the main linear system in the frequency domain. Such algorithms may enable a significant reduction in computational cost over conventional approaches by implementing a linear solver for the most critical and computationally expensive component of the conventional iterative algorithm. The theoretical computational cost of the algorithm may be reduced from O(M.sup.3N) to O(MN log N), where N is the dimensionality of the data and M is the number of elements in the dictionary. This significant improvement in efficiency may greatly increase the range of problems that can practically be addressed via convolutional sparse representations.

Linear-scaling density-functional simulations of charged point defects in Al2O3 using hierarchical sparse matrix algebra.

PubMed

Hine, N D M; Haynes, P D; Mostofi, A A; Payne, M C

2010-09-21

We present calculations of formation energies of defects in an ionic solid (Al(2)O(3)) extrapolated to the dilute limit, corresponding to a simulation cell of infinite size. The large-scale calculations required for this extrapolation are enabled by developments in the approach to parallel sparse matrix algebra operations, which are central to linear-scaling density-functional theory calculations. The computational cost of manipulating sparse matrices, whose sizes are determined by the large number of basis functions present, is greatly improved with this new approach. We present details of the sparse algebra scheme implemented in the ONETEP code using hierarchical sparsity patterns, and demonstrate its use in calculations on a wide range of systems, involving thousands of atoms on hundreds to thousands of parallel processes.

A design methodology for nonlinear systems containing parameter uncertainty: Application to nonlinear controller design

NASA Technical Reports Server (NTRS)

Young, G.

1982-01-01

A design methodology capable of dealing with nonlinear systems, such as a controlled ecological life support system (CELSS), containing parameter uncertainty is discussed. The methodology was applied to the design of discrete time nonlinear controllers. The nonlinear controllers can be used to control either linear or nonlinear systems. Several controller strategies are presented to illustrate the design procedure.

Identification of spatially-localized initial conditions via sparse PCA

NASA Astrophysics Data System (ADS)

Dwivedi, Anubhav; Jovanovic, Mihailo

2017-11-01

Principal Component Analysis involves maximization of a quadratic form subject to a quadratic constraint on the initial flow perturbations and it is routinely used to identify the most energetic flow structures. For general flow configurations, principal components can be efficiently computed via power iteration of the forward and adjoint governing equations. However, the resulting flow structures typically have a large spatial support leading to a question of physical realizability. To obtain spatially-localized structures, we modify the quadratic constraint on the initial condition to include a convex combination with an additional regularization term which promotes sparsity in the physical domain. We formulate this constrained optimization problem as a nonlinear eigenvalue problem and employ an inverse power-iteration-based method to solve it. The resulting solution is guaranteed to converge to a nonlinear eigenvector which becomes increasingly localized as our emphasis on sparsity increases. We use several fluids examples to demonstrate that our method indeed identifies the most energetic initial perturbations that are spatially compact. This work was supported by Office of Naval Research through Grant Number N00014-15-1-2522.

Nonlinear Deep Kernel Learning for Image Annotation.

PubMed

Jiu, Mingyuan; Sahbi, Hichem

2017-02-08

Multiple kernel learning (MKL) is a widely used technique for kernel design. Its principle consists in learning, for a given support vector classifier, the most suitable convex (or sparse) linear combination of standard elementary kernels. However, these combinations are shallow and often powerless to capture the actual similarity between highly semantic data, especially for challenging classification tasks such as image annotation. In this paper, we redefine multiple kernels using deep multi-layer networks. In this new contribution, a deep multiple kernel is recursively defined as a multi-layered combination of nonlinear activation functions, each one involves a combination of several elementary or intermediate kernels, and results into a positive semi-definite deep kernel. We propose four different frameworks in order to learn the weights of these networks: supervised, unsupervised, kernel-based semisupervised and Laplacian-based semi-supervised. When plugged into support vector machines (SVMs), the resulting deep kernel networks show clear gain, compared to several shallow kernels for the task of image annotation. Extensive experiments and analysis on the challenging ImageCLEF photo annotation benchmark, the COREL5k database and the Banana dataset validate the effectiveness of the proposed method.

Selective Data Acquisition in NMR. The Quantification of Anti-phase Scalar Couplings

NASA Astrophysics Data System (ADS)

Hodgkinson, P.; Holmes, K. J.; Hore, P. J.

Almost all time-domain NMR experiments employ "linear sampling," in which the NMR response is digitized at equally spaced times, with uniform signal averaging. Here, the possibilities of nonlinear sampling are explored using anti-phase doublets in the indirectly detected dimensions of multidimensional COSY-type experiments as an example. The Cramér-Rao lower bounds are used to evaluate and optimize experiments in which the sampling points, or the extent of signal averaging at each point, or both, are varied. The optimal nonlinear sampling for the estimation of the coupling constant J, by model fitting, turns out to involve just a few key time points, for example, at the first node ( t= 1/ J) of the sin(π Jt) modulation. Such sparse sampling patterns can be used to derive more practical strategies, in which the sampling or the signal averaging is distributed around the most significant time points. The improvements in the quantification of NMR parameters can be quite substantial especially when, as is often the case for indirectly detected dimensions, the total number of samples is limited by the time available.

Keeping it Together: Advanced algorithms and software for magma dynamics (and other coupled multi-physics problems)

NASA Astrophysics Data System (ADS)

Spiegelman, M.; Wilson, C. R.

2011-12-01

A quantitative theory of magma production and transport is essential for understanding the dynamics of magmatic plate boundaries, intra-plate volcanism and the geochemical evolution of the planet. It also provides one of the most challenging computational problems in solid Earth science, as it requires consistent coupling of fluid and solid mechanics together with the thermodynamics of melting and reactive flows. Considerable work on these problems over the past two decades shows that small changes in assumptions of coupling (e.g. the relationship between melt fraction and solid rheology), can have profound changes on the behavior of these systems which in turn affects critical computational choices such as discretizations, solvers and preconditioners. To make progress in exploring and understanding this physically rich system requires a computational framework that allows more flexible, high-level description of multi-physics problems as well as increased flexibility in composing efficient algorithms for solution of the full non-linear coupled system. Fortunately, recent advances in available computational libraries and algorithms provide a platform for implementing such a framework. We present results from a new model building system that leverages functionality from both the FEniCS project (www.fenicsproject.org) and PETSc libraries (www.mcs.anl.gov/petsc) along with a model independent options system and gui, Spud (amcg.ese.ic.ac.uk/Spud). Key features from FEniCS include fully unstructured FEM with a wide range of elements; a high-level language (ufl) and code generation compiler (FFC) for describing the weak forms of residuals and automatic differentiation for calculation of exact and approximate jacobians. The overall strategy is to monitor/calculate residuals and jacobians for the entire non-linear system of equations within a global non-linear solve based on PETSc's SNES routines. PETSc already provides a wide range of solvers and preconditioners, from parallel sparse direct to algebraic multigrid, that can be chosen at runtime. In particular, we make extensive use of PETSc's FieldSplit block preconditioners that allow us to use optimal solvers for subproblems (such as Stokes, or advection/diffusion of temperature) as preconditioners for the full problem. Thus these routines let us reuse effective solving recipes/splittings from previous experience while monitoring the convergence of the global problem. These techniques often yield quadratic (Newton like) convergence for the work of standard Picard schemes. We will illustrate this new framework with examples from the Magma Dynamic Demonstration suite (MADDs) of well understood magma dynamics benchmark problems including stokes flow in ridge geometries, magmatic solitary waves and shear-driven melt bands. While development of this system has been driven by magma dynamics, this framework is much more general and can be used for a wide range of PDE based multi-physics models.

Multi-layer sparse representation for weighted LBP-patches based facial expression recognition.

PubMed

Jia, Qi; Gao, Xinkai; Guo, He; Luo, Zhongxuan; Wang, Yi

2015-03-19

In this paper, a novel facial expression recognition method based on sparse representation is proposed. Most contemporary facial expression recognition systems suffer from limited ability to handle image nuisances such as low resolution and noise. Especially for low intensity expression, most of the existing training methods have quite low recognition rates. Motivated by sparse representation, the problem can be solved by finding sparse coefficients of the test image by the whole training set. Deriving an effective facial representation from original face images is a vital step for successful facial expression recognition. We evaluate facial representation based on weighted local binary patterns, and Fisher separation criterion is used to calculate the weighs of patches. A multi-layer sparse representation framework is proposed for multi-intensity facial expression recognition, especially for low-intensity expressions and noisy expressions in reality, which is a critical problem but seldom addressed in the existing works. To this end, several experiments based on low-resolution and multi-intensity expressions are carried out. Promising results on publicly available databases demonstrate the potential of the proposed approach.

Development of Innovative Technology to Expand Precipitation Observations in Satellite Precipitation Validation in Under-developed Data-sparse Regions

NASA Astrophysics Data System (ADS)

Kucera, P. A.; Steinson, M.

2016-12-01

Accurate and reliable real-time monitoring and dissemination of observations of precipitation and surface weather conditions in general is critical for a variety of research studies and applications. Surface precipitation observations provide important reference information for evaluating satellite (e.g., GPM) precipitation estimates. High quality surface observations of precipitation, temperature, moisture, and winds are important for applications such as agriculture, water resource monitoring, health, and hazardous weather early warning systems. In many regions of the World, surface weather station and precipitation gauge networks are sparsely located and/or of poor quality. Existing stations have often been sited incorrectly, not well-maintained, and have limited communications established at the site for real-time monitoring. The University Corporation for Atmospheric Research (UCAR)/National Center for Atmospheric Research (NCAR), with support from USAID, has started an initiative to develop and deploy low-cost weather instrumentation including tipping bucket and weighing-type precipitation gauges in sparsely observed regions of the world. The goal is to improve the number of observations (temporally and spatially) for the evaluation of satellite precipitation estimates in data-sparse regions and to improve the quality of applications for environmental monitoring and early warning alert systems on a regional to global scale. One important aspect of this initiative is to make the data open to the community. The weather station instrumentation have been developed using innovative new technologies such as 3D printers, Raspberry Pi computing systems, and wireless communications. An initial pilot project have been implemented in the country of Zambia. This effort could be expanded to other data sparse regions around the globe. The presentation will provide an overview and demonstration of 3D printed weather station development and initial evaluation of observed precipitation datasets.

Synchronous Motions Across the Instrumental Climate Record

NASA Astrophysics Data System (ADS)

Carl, Peter

The Earth's climate system bears a rich variety of feedback mechanisms that may give rise to complex, evolving modal structures under internal and external control. Various types of synchronization may be identified in the system's motion when looking at representative time series of the instrumental period through the glasses of an advanced technique of sparse data approximation, the Matching Pursuit (MP) approach. To disentangle the emerging network of oscillatory modes to the degree that climate dynamics turns out to be separable, a large dictionary of "Gaussian logons," i.e. frequency modulated (FM) Gabor atoms, is applied. Though the extracted modes make up linear decompositions, this flexible analyzing signal matches highly nonlinear waveforms. Univariate analyses over the period 1870-1997 are presented of a set of customary time series in annual resolution, comprising global and regional climate, central European synoptic systems, German precipitation, and runoff of the Elbe river near Dresden. All the evidence from this first-generation MP-FM study, obtained in subsequent multivariate syntheses, points to dynamically excited regimes of an organized yet complex climate system under permanent change—perhaps a (pre)chaotic one at centennial timescales, suggesting a "chaos control" perspective on global climate dynamics and change. Findings and conclusions include, among others, internal structure of reconstructed insolation, the episodic nature of global warming as reflected in multidecadal temperature modes, their swarm of "interdomain" companions across the whole system that unveils an unknown regime character of interannual climate dynamics, and the apparent onset early in the 1990s of the present thermal stagnation.

Maximized Gust Loads of a Closed-Loop, Nonlinear Aeroelastic System Using Nonlinear Systems Theory

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1999-01-01

The problem of computing the maximized gust load for a nonlinear, closed-loop aeroelastic aircraft is discusses. The Volterra theory of nonlinear systems is applied in order to define a linearized system that provides a bounds on the response of the nonlinear system of interest. The method is applied to a simplified model of an Airbus A310.

Asymmetric nonlinear system is not sufficient for a nonreciprocal wave diode

NASA Astrophysics Data System (ADS)

Wu, Gaomin; Long, Yang; Ren, Jie

2018-05-01

We demonstrate symmetric wave propagations in asymmetric nonlinear systems. By solving the nonlinear Schördinger equation, we first analytically prove the existence of symmetric transmission in asymmetric systems with a single nonlinear delta-function interface. We then point out that a finite width of the nonlinear interface region is necessary to produce nonreciprocity in asymmetric systems. However, a geometrical resonant condition for breaking nonreciprocal propagation is then identified theoretically and verified numerically. With such a resonant condition, the nonlinear interface region of finite width behaves like a single nonlinear delta-barrier so that wave propagations in the forward and backward directions are identical under arbitrary incident wave intensity. As such, reciprocity reemerges periodically in the asymmetric nonlinear system when changing the width of interface region. Finally, similar resonant conditions of discrete nonlinear Schördinger equation are discussed. Therefore, we have identified instances of reciprocity that breaking spatial symmetry in nonlinear interface systems is not sufficient to produce nonreciprocal wave propagation.

Exploring nonlinear feature space dimension reduction and data representation in breast CADx with Laplacian eigenmaps and t-SNE

PubMed Central

Jamieson, Andrew R.; Giger, Maryellen L.; Drukker, Karen; Li, Hui; Yuan, Yading; Bhooshan, Neha

2010-01-01

Purpose: In this preliminary study, recently developed unsupervised nonlinear dimension reduction (DR) and data representation techniques were applied to computer-extracted breast lesion feature spaces across three separate imaging modalities: Ultrasound (U.S.) with 1126 cases, dynamic contrast enhanced magnetic resonance imaging with 356 cases, and full-field digital mammography with 245 cases. Two methods for nonlinear DR were explored: Laplacian eigenmaps [M. Belkin and P. Niyogi, “Laplacian eigenmaps for dimensionality reduction and data representation,” Neural Comput. 15, 1373–1396 (2003)] and t-distributed stochastic neighbor embedding (t-SNE) [L. van der Maaten and G. Hinton, “Visualizing data using t-SNE,” J. Mach. Learn. Res. 9, 2579–2605 (2008)]. Methods: These methods attempt to map originally high dimensional feature spaces to more human interpretable lower dimensional spaces while preserving both local and global information. The properties of these methods as applied to breast computer-aided diagnosis (CADx) were evaluated in the context of malignancy classification performance as well as in the visual inspection of the sparseness within the two-dimensional and three-dimensional mappings. Classification performance was estimated by using the reduced dimension mapped feature output as input into both linear and nonlinear classifiers: Markov chain Monte Carlo based Bayesian artificial neural network (MCMC-BANN) and linear discriminant analysis. The new techniques were compared to previously developed breast CADx methodologies, including automatic relevance determination and linear stepwise (LSW) feature selection, as well as a linear DR method based on principal component analysis. Using ROC analysis and 0.632+bootstrap validation, 95% empirical confidence intervals were computed for the each classifier’s AUC performance. Results: In the large U.S. data set, sample high performance results include, AUC0.632+=0.88 with 95% empirical bootstrap interval [0.787;0.895] for 13 ARD selected features and AUC0.632+=0.87 with interval [0.817;0.906] for four LSW selected features compared to 4D t-SNE mapping (from the original 81D feature space) giving AUC0.632+=0.90 with interval [0.847;0.919], all using the MCMC-BANN. Conclusions: Preliminary results appear to indicate capability for the new methods to match or exceed classification performance of current advanced breast lesion CADx algorithms. While not appropriate as a complete replacement of feature selection in CADx problems, DR techniques offer a complementary approach, which can aid elucidation of additional properties associated with the data. Specifically, the new techniques were shown to possess the added benefit of delivering sparse lower dimensional representations for visual interpretation, revealing intricate data structure of the feature space. PMID:20175497

Moving target detection for frequency agility radar by sparse reconstruction

NASA Astrophysics Data System (ADS)

Quan, Yinghui; Li, YaChao; Wu, Yaojun; Ran, Lei; Xing, Mengdao; Liu, Mengqi

2016-09-01

Frequency agility radar, with randomly varied carrier frequency from pulse to pulse, exhibits superior performance compared to the conventional fixed carrier frequency pulse-Doppler radar against the electromagnetic interference. A novel moving target detection (MTD) method is proposed for the estimation of the target's velocity of frequency agility radar based on pulses within a coherent processing interval by using sparse reconstruction. Hardware implementation of orthogonal matching pursuit algorithm is executed on Xilinx Virtex-7 Field Programmable Gata Array (FPGA) to perform sparse optimization. Finally, a series of experiments are performed to evaluate the performance of proposed MTD method for frequency agility radar systems.

Moving target detection for frequency agility radar by sparse reconstruction.

PubMed

Quan, Yinghui; Li, YaChao; Wu, Yaojun; Ran, Lei; Xing, Mengdao; Liu, Mengqi

2016-09-01

Frequency agility radar, with randomly varied carrier frequency from pulse to pulse, exhibits superior performance compared to the conventional fixed carrier frequency pulse-Doppler radar against the electromagnetic interference. A novel moving target detection (MTD) method is proposed for the estimation of the target's velocity of frequency agility radar based on pulses within a coherent processing interval by using sparse reconstruction. Hardware implementation of orthogonal matching pursuit algorithm is executed on Xilinx Virtex-7 Field Programmable Gata Array (FPGA) to perform sparse optimization. Finally, a series of experiments are performed to evaluate the performance of proposed MTD method for frequency agility radar systems.

Recognizing the ‘sparsely settled forest’: Multi-decade socioecological change dynamics and community exemplars

Treesearch

Derek B. Van Berkel; Bronwyn Rayfield; Sebastián Martinuzzi; Martin J. Lechowicz; Eric White; Kathleen P. Bell; Chris R. Colocousis; Kent F. Kovacs; Anita T. Morzillo; Darla K. Munroe; Benoit Parmentier; Volker C. Radeloff; Brian J. McGill

2018-01-01

Sparsely settled forests (SSF) are poorly studied, coupled natural and human systems involving rural communities in forest ecosystems that are neither largely uninhabited wildland nor forests on the edges of urban areas. We developed and applied a multidisciplinary approach to define, map, and examine changes in the spatial extent and structure of both the landscapes...

A Multilevel Algorithm for the Solution of Second Order Elliptic Differential Equations on Sparse Grids

NASA Technical Reports Server (NTRS)

Pflaum, Christoph

1996-01-01

A multilevel algorithm is presented that solves general second order elliptic partial differential equations on adaptive sparse grids. The multilevel algorithm consists of several V-cycles. Suitable discretizations provide that the discrete equation system can be solved in an efficient way. Numerical experiments show a convergence rate of order Omicron(1) for the multilevel algorithm.

Sparse Coding of Natural Human Motion Yields Eigenmotions Consistent Across People

NASA Astrophysics Data System (ADS)

Thomik, Andreas; Faisal, A. Aldo

2015-03-01

Providing a precise mathematical description of the structure of natural human movement is a challenging problem. We use a data-driven approach to seek a generative model of movement capturing the underlying simplicity of spatial and temporal structure of behaviour observed in daily life. In perception, the analysis of natural scenes has shown that sparse codes of such scenes are information theoretic efficient descriptors with direct neuronal correlates. Translating from perception to action, we identify a generative model of movement generation by the human motor system. Using wearable full-hand motion capture, we measure the digit movement of the human hand in daily life. We learn a dictionary of ``eigenmotions'' which we use for sparse encoding of the movement data. We show that the dictionaries are generally well preserved across subjects with small deviations accounting for individuality of the person and variability in tasks. Further, the dictionary elements represent motions which can naturally describe hand movements. Our findings suggest the motor system can compose complex movement behaviours out of the spatially and temporally sparse activation of ``eigenmotion'' neurons, and is consistent with data on grasp-type specificity of specialised neurons in the premotor cortex. Andreas is supported by the Luxemburg Research Fund (1229297).

A Bayesian least squares support vector machines based framework for fault diagnosis and failure prognosis

NASA Astrophysics Data System (ADS)

Khawaja, Taimoor Saleem

A high-belief low-overhead Prognostics and Health Management (PHM) system is desired for online real-time monitoring of complex non-linear systems operating in a complex (possibly non-Gaussian) noise environment. This thesis presents a Bayesian Least Squares Support Vector Machine (LS-SVM) based framework for fault diagnosis and failure prognosis in nonlinear non-Gaussian systems. The methodology assumes the availability of real-time process measurements, definition of a set of fault indicators and the existence of empirical knowledge (or historical data) to characterize both nominal and abnormal operating conditions. An efficient yet powerful Least Squares Support Vector Machine (LS-SVM) algorithm, set within a Bayesian Inference framework, not only allows for the development of real-time algorithms for diagnosis and prognosis but also provides a solid theoretical framework to address key concepts related to classification for diagnosis and regression modeling for prognosis. SVM machines are founded on the principle of Structural Risk Minimization (SRM) which tends to find a good trade-off between low empirical risk and small capacity. The key features in SVM are the use of non-linear kernels, the absence of local minima, the sparseness of the solution and the capacity control obtained by optimizing the margin. The Bayesian Inference framework linked with LS-SVMs allows a probabilistic interpretation of the results for diagnosis and prognosis. Additional levels of inference provide the much coveted features of adaptability and tunability of the modeling parameters. The two main modules considered in this research are fault diagnosis and failure prognosis. With the goal of designing an efficient and reliable fault diagnosis scheme, a novel Anomaly Detector is suggested based on the LS-SVM machines. The proposed scheme uses only baseline data to construct a 1-class LS-SVM machine which, when presented with online data is able to distinguish between normal behavior and any abnormal or novel data during real-time operation. The results of the scheme are interpreted as a posterior probability of health (1 - probability of fault). As shown through two case studies in Chapter 3, the scheme is well suited for diagnosing imminent faults in dynamical non-linear systems. Finally, the failure prognosis scheme is based on an incremental weighted Bayesian LS-SVR machine. It is particularly suited for online deployment given the incremental nature of the algorithm and the quick optimization problem solved in the LS-SVR algorithm. By way of kernelization and a Gaussian Mixture Modeling (GMM) scheme, the algorithm can estimate "possibly" non-Gaussian posterior distributions for complex non-linear systems. An efficient regression scheme associated with the more rigorous core algorithm allows for long-term predictions, fault growth estimation with confidence bounds and remaining useful life (RUL) estimation after a fault is detected. The leading contributions of this thesis are (a) the development of a novel Bayesian Anomaly Detector for efficient and reliable Fault Detection and Identification (FDI) based on Least Squares Support Vector Machines, (b) the development of a data-driven real-time architecture for long-term Failure Prognosis using Least Squares Support Vector Machines, (c) Uncertainty representation and management using Bayesian Inference for posterior distribution estimation and hyper-parameter tuning, and finally (d) the statistical characterization of the performance of diagnosis and prognosis algorithms in order to relate the efficiency and reliability of the proposed schemes.

A Novel Nonlinear Piezoelectric Energy Harvesting System Based on Linear-Element Coupling: Design, Modeling and Dynamic Analysis.

PubMed

Zhou, Shengxi; Yan, Bo; Inman, Daniel J

2018-05-09

This paper presents a novel nonlinear piezoelectric energy harvesting system which consists of linear piezoelectric energy harvesters connected by linear springs. In principle, the presented nonlinear system can improve broadband energy harvesting efficiency where magnets are forbidden. The linear spring inevitably produces the nonlinear spring force on the connected harvesters, because of the geometrical relationship and the time-varying relative displacement between two adjacent harvesters. Therefore, the presented nonlinear system has strong nonlinear characteristics. A theoretical model of the presented nonlinear system is deduced, based on Euler-Bernoulli beam theory, Kirchhoff’s law, piezoelectric theory and the relevant geometrical relationship. The energy harvesting enhancement of the presented nonlinear system (when n = 2, 3) is numerically verified by comparing with its linear counterparts. In the case study, the output power area of the presented nonlinear system with two and three energy harvesters is 268.8% and 339.8% of their linear counterparts, respectively. In addition, the nonlinear dynamic response characteristics are analyzed via bifurcation diagrams, Poincare maps of the phase trajectory, and the spectrum of the output voltage.

Nonlinear Flying Qualities Criteria for Large-Amplitude Maneuvers

DTIC Science & Technology

1984-12-01

theory which are pertinent to the formation of a nonlinear flying qualities methodology. This report surveys nonlinear system theory and describes...the development of an applied flying qualities methodology based on a canonical system theory and using research in relative controllability...The Nonlinear Flying Qualities (NFQ) for Large-Amplitude Maneuvers Program examined promising techniques from nonlinear analysis and nonlinear system

FRF decoupling of nonlinear systems

NASA Astrophysics Data System (ADS)

Kalaycıoğlu, Taner; Özgüven, H. Nevzat

2018-03-01

Structural decoupling problem, i.e. predicting dynamic behavior of a particular substructure from the knowledge of the dynamics of the coupled structure and the other substructure, has been well investigated for three decades and led to several decoupling methods. In spite of the inherent nonlinearities in a structural system in various forms such as clearances, friction and nonlinear stiffness, all decoupling studies are for linear systems. In this study, decoupling problem for nonlinear systems is addressed for the first time. A method, named as FRF Decoupling Method for Nonlinear Systems (FDM-NS), is proposed for calculating FRFs of a substructure decoupled from a coupled nonlinear structure where nonlinearity can be modeled as a single nonlinear element. Depending on where nonlinear element is, i.e., either in the known or unknown subsystem, or at the connection point, the formulation differs. The method requires relative displacement information between two end points of the nonlinear element, in addition to point and transfer FRFs at some points of the known subsystem. However, it is not necessary to excite the system from the unknown subsystem even when the nonlinear element is in that subsystem. The validation of FDM-NS is demonstrated with two different case studies using nonlinear lumped parameter systems. Finally, a nonlinear experimental test structure is used in order to show the real-life application and accuracy of FDM-NS.

Data-driven discovery of partial differential equations

PubMed Central

Rudy, Samuel H.; Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan

2017-01-01

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg–de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable. PMID:28508044

Improving subjective pattern recognition in chemical senses through reduction of nonlinear effects in evaluation of sparse data

NASA Astrophysics Data System (ADS)

Assadi, Amir H.; Rasouli, Firooz; Wrenn, Susan E.; Subbiah, M.

2002-11-01

Artificial neural network models are typically useful in pattern recognition and extraction of important features in large data sets. These models are implemented in a wide variety of contexts and with diverse type of input-output data. The underlying mathematics of supervised training of neural networks is ultimately tied to the ability to approximate the nonlinearities that are inherent in network"s generalization ability. The quality and availability of sufficient data points for training and validation play a key role in the generalization ability of the network. A potential domain of applications of neural networks is in analysis of subjective data, such as in consumer science, affective neuroscience and perception of chemical senses. In applications of ANN to subjective data, it is common to rely on knowledge of the science and context for data acquisition, for instance as a priori probabilities in the Bayesian framework. In this paper, we discuss the circumstances that create challenges for success of neural network models for subjective data analysis, such as sparseness of data and cost of acquisition of additional samples. In particular, in the case of affect and perception of chemical senses, we suggest that inherent ambiguity of subjective responses could be offset by a combination of human-machine expert. We propose a method of pre- and post-processing for blind analysis of data that that relies on heuristics from human performance in interpretation of data. In particular, we offer an information-theoretic smoothing (ITS) algorithm that optimizes that geometric visualization of multi-dimensional data and improves human interpretation of the input-output view of neural network implementations. The pre- and post-processing algorithms and ITS are unsupervised. Finally, we discuss the details of an example of blind data analysis from actual taste-smell subjective data, and demonstrate the usefulness of PCA in reduction of dimensionality, as well as ITS.

Infrared moving small target detection based on saliency extraction and image sparse representation

NASA Astrophysics Data System (ADS)

Zhang, Xiaomin; Ren, Kan; Gao, Jin; Li, Chaowei; Gu, Guohua; Wan, Minjie

2016-10-01

Moving small target detection in infrared image is a crucial technique of infrared search and tracking system. This paper present a novel small target detection technique based on frequency-domain saliency extraction and image sparse representation. First, we exploit the features of Fourier spectrum image and magnitude spectrum of Fourier transform to make a rough extract of saliency regions and use a threshold segmentation system to classify the regions which look salient from the background, which gives us a binary image as result. Second, a new patch-image model and over-complete dictionary were introduced to the detection system, then the infrared small target detection was converted into a problem solving and optimization process of patch-image information reconstruction based on sparse representation. More specifically, the test image and binary image can be decomposed into some image patches follow certain rules. We select the target potential area according to the binary patch-image which contains salient region information, then exploit the over-complete infrared small target dictionary to reconstruct the test image blocks which may contain targets. The coefficients of target image patch satisfy sparse features. Finally, for image sequence, Euclidean distance was used to reduce false alarm ratio and increase the detection accuracy of moving small targets in infrared images due to the target position correlation between frames.

Fuzzy model-based servo and model following control for nonlinear systems.

PubMed

Ohtake, Hiroshi; Tanaka, Kazuo; Wang, Hua O

2009-12-01

This correspondence presents servo and nonlinear model following controls for a class of nonlinear systems using the Takagi-Sugeno fuzzy model-based control approach. First, the construction method of the augmented fuzzy system for continuous-time nonlinear systems is proposed by differentiating the original nonlinear system. Second, the dynamic fuzzy servo controller and the dynamic fuzzy model following controller, which can make outputs of the nonlinear system converge to target points and to outputs of the reference system, respectively, are introduced. Finally, the servo and model following controller design conditions are given in terms of linear matrix inequalities. Design examples illustrate the utility of this approach.

Efficient image enhancement using sparse source separation in the Retinex theory

NASA Astrophysics Data System (ADS)

Yoon, Jongsu; Choi, Jangwon; Choe, Yoonsik

2017-11-01

Color constancy is the feature of the human vision system (HVS) that ensures the relative constancy of the perceived color of objects under varying illumination conditions. The Retinex theory of machine vision systems is based on the HVS. Among Retinex algorithms, the physics-based algorithms are efficient; however, they generally do not satisfy the local characteristics of the original Retinex theory because they eliminate global illumination from their optimization. We apply the sparse source separation technique to the Retinex theory to present a physics-based algorithm that satisfies the locality characteristic of the original Retinex theory. Previous Retinex algorithms have limited use in image enhancement because the total variation Retinex results in an overly enhanced image and the sparse source separation Retinex cannot completely restore the original image. In contrast, our proposed method preserves the image edge and can very nearly replicate the original image without any special operation.

Sparse matrix methods research using the CSM testbed software system

NASA Technical Reports Server (NTRS)

Chu, Eleanor; George, J. Alan

1989-01-01

Research is described on sparse matrix techniques for the Computational Structural Mechanics (CSM) Testbed. The primary objective was to compare the performance of state-of-the-art techniques for solving sparse systems with those that are currently available in the CSM Testbed. Thus, one of the first tasks was to become familiar with the structure of the testbed, and to install some or all of the SPARSPAK package in the testbed. A suite of subroutines to extract from the data base the relevant structural and numerical information about the matrix equations was written, and all the demonstration problems distributed with the testbed were successfully solved. These codes were documented, and performance studies comparing the SPARSPAK technology to the methods currently in the testbed were completed. In addition, some preliminary studies were done comparing some recently developed out-of-core techniques with the performance of the testbed processor INV.

Bayesian sparse channel estimation

NASA Astrophysics Data System (ADS)

Chen, Chulong; Zoltowski, Michael D.

2012-05-01

In Orthogonal Frequency Division Multiplexing (OFDM) systems, the technique used to estimate and track the time-varying multipath channel is critical to ensure reliable, high data rate communications. It is recognized that wireless channels often exhibit a sparse structure, especially for wideband and ultra-wideband systems. In order to exploit this sparse structure to reduce the number of pilot tones and increase the channel estimation quality, the application of compressed sensing to channel estimation is proposed. In this article, to make the compressed channel estimation more feasible for practical applications, it is investigated from a perspective of Bayesian learning. Under the Bayesian learning framework, the large-scale compressed sensing problem, as well as large time delay for the estimation of the doubly selective channel over multiple consecutive OFDM symbols, can be avoided. Simulation studies show a significant improvement in channel estimation MSE and less computing time compared to the conventional compressed channel estimation techniques.

Nonlinear hybrid modal synthesis based on branch modes for dynamic analysis of assembled structure

NASA Astrophysics Data System (ADS)

Huang, Xing-Rong; Jézéquel, Louis; Besset, Sébastien; Li, Lin; Sauvage, Olivier

2018-01-01

This paper describes a simple and fast numerical procedure to study the steady state responses of assembled structures with nonlinearities along continuous interfaces. The proposed strategy is based on a generalized nonlinear modal superposition approach supplemented by a double modal synthesis strategy. The reduced nonlinear modes are derived by combining a single nonlinear mode method with reduction techniques relying on branch modes. The modal parameters containing essential nonlinear information are determined and then employed to calculate the stationary responses of the nonlinear system subjected to various types of excitation. The advantages of the proposed nonlinear modal synthesis are mainly derived in three ways: (1) computational costs are considerably reduced, when analyzing large assembled systems with weak nonlinearities, through the use of reduced nonlinear modes; (2) based on the interpolation models of nonlinear modal parameters, the nonlinear modes introduced during the first step can be employed to analyze the same system under various external loads without having to reanalyze the entire system; and (3) the nonlinear effects can be investigated from a modal point of view by analyzing these nonlinear modal parameters. The proposed strategy is applied to an assembled system composed of plates and nonlinear rubber interfaces. Simulation results have proven the efficiency of this hybrid nonlinear modal synthesis, and the computation time has also been significantly reduced.

A Merged IQC/SOS Theory for Analysis and Synthesis of Nonlinear Control Systems

DTIC Science & Technology

2015-06-23

constraints. As mentioned previously, this enables new applications of IQCs to analyze the robustness of time-varying and nonlinear systems . This...enables new applications of IQCs to analyze the robustness of time-varying and nonlinear systems . This section considers the analysis of nonlinear systems ...AFRL-AFOSR-VA-TR-2016-0008 A Merged IQC/SOS Theory for Analysis and Synthesis of Nonlinear Control Systems Gary Balas REGENTS OF THE UNIVERSITY OF

Multiple model self-tuning control for a class of nonlinear systems

NASA Astrophysics Data System (ADS)

Huang, Miao; Wang, Xin; Wang, Zhenlei

2015-10-01

This study develops a novel nonlinear multiple model self-tuning control method for a class of nonlinear discrete-time systems. An increment system model and a modified robust adaptive law are proposed to expand the application range, thus eliminating the assumption that either the nonlinear term of the nonlinear system or its differential term is global-bounded. The nonlinear self-tuning control method can address the situation wherein the nonlinear system is not subject to a globally uniformly asymptotically stable zero dynamics by incorporating the pole-placement scheme. A novel, nonlinear control structure based on this scheme is presented to improve control precision. Stability and convergence can be confirmed when the proposed multiple model self-tuning control method is applied. Furthermore, simulation results demonstrate the effectiveness of the proposed method.

Fast sparsely synchronized brain rhythms in a scale-free neural network

NASA Astrophysics Data System (ADS)

Kim, Sang-Yoon; Lim, Woochang

2015-08-01

We consider a directed version of the Barabási-Albert scale-free network model with symmetric preferential attachment with the same in- and out-degrees and study the emergence of sparsely synchronized rhythms for a fixed attachment degree in an inhibitory population of fast-spiking Izhikevich interneurons. Fast sparsely synchronized rhythms with stochastic and intermittent neuronal discharges are found to appear for large values of J (synaptic inhibition strength) and D (noise intensity). For an intensive study we fix J at a sufficiently large value and investigate the population states by increasing D . For small D , full synchronization with the same population-rhythm frequency fp and mean firing rate (MFR) fi of individual neurons occurs, while for large D partial synchronization with fp> ( : ensemble-averaged MFR) appears due to intermittent discharge of individual neurons; in particular, the case of fp>4 is referred to as sparse synchronization. For the case of partial and sparse synchronization, MFRs of individual neurons vary depending on their degrees. As D passes a critical value D* (which is determined by employing an order parameter), a transition to unsynchronization occurs due to the destructive role of noise to spoil the pacing between sparse spikes. For D

Natural image sequences constrain dynamic receptive fields and imply a sparse code.

PubMed

Häusler, Chris; Susemihl, Alex; Nawrot, Martin P

2013-11-06

In their natural environment, animals experience a complex and dynamic visual scenery. Under such natural stimulus conditions, neurons in the visual cortex employ a spatially and temporally sparse code. For the input scenario of natural still images, previous work demonstrated that unsupervised feature learning combined with the constraint of sparse coding can predict physiologically measured receptive fields of simple cells in the primary visual cortex. This convincingly indicated that the mammalian visual system is adapted to the natural spatial input statistics. Here, we extend this approach to the time domain in order to predict dynamic receptive fields that can account for both spatial and temporal sparse activation in biological neurons. We rely on temporal restricted Boltzmann machines and suggest a novel temporal autoencoding training procedure. When tested on a dynamic multi-variate benchmark dataset this method outperformed existing models of this class. Learning features on a large dataset of natural movies allowed us to model spatio-temporal receptive fields for single neurons. They resemble temporally smooth transformations of previously obtained static receptive fields and are thus consistent with existing theories. A neuronal spike response model demonstrates how the dynamic receptive field facilitates temporal and population sparseness. We discuss the potential mechanisms and benefits of a spatially and temporally sparse representation of natural visual input. Copyright © 2013 The Authors. Published by Elsevier B.V. All rights reserved.

Hidden acoustic information revealed by intentional nonlinearity

NASA Astrophysics Data System (ADS)

Dowling, David R.

2017-11-01

Acoustic waves are omnipresent in modern life and are well described by the linearized equations of fluid dynamics. Once generated, acoustic waves carry and collect information about their source and the environment through which they propagate, respectively, and this information may be retrieved by analyzing recordings of these waves. Because of this, acoustics is the primary means for observation, surveillance, reconnaissance, and remote sensing in otherwise opaque environments, such as the Earth's oceans and crust, and the interior of the human body. For such information-retrieval tasks, acoustic fields are nearly always interrogated within their recorded frequency range or bandwidth. However, this frequency-range restriction is not general; acoustic fields may also carry (hidden) information at frequencies outside their bandwidth. Although such a claim may seem counter intuitive, hidden acoustic-field information can be revealed by re-introducing a marquee trait of fluid dynamics: nonlinearity. In particular, an intentional quadratic nonlinearity - a form of intra-signal heterodyning - can be used to obtain acoustic field information at frequencies outside a recorded acoustic field's bandwidth. This quadratic nonlinearity enables a variety of acoustic remote sensing applications that were long thought to be impossible. In particular, it allows the detrimental effects of sparse recordings and random scattering to be suppressed when the original acoustic field has sufficient bandwidth. In this presentation, the topic is developed heuristically, with a just brief exposition of the relevant mathematics. Hidden acoustic field information is then revealed from simulated and measured acoustic fields in simple and complicated acoustic environments involving frequencies from a few Hertz to more than 100 kHz, and propagation distances from tens of centimeters to hundreds of kilometers. Sponsored by ONR, NAVSEA, and NSF.

Statistical prediction with Kanerva's sparse distributed memory

NASA Technical Reports Server (NTRS)

Rogers, David

1989-01-01

A new viewpoint of the processing performed by Kanerva's sparse distributed memory (SDM) is presented. In conditions of near- or over-capacity, where the associative-memory behavior of the model breaks down, the processing performed by the model can be interpreted as that of a statistical predictor. Mathematical results are presented which serve as the framework for a new statistical viewpoint of sparse distributed memory and for which the standard formulation of SDM is a special case. This viewpoint suggests possible enhancements to the SDM model, including a procedure for improving the predictiveness of the system based on Holland's work with genetic algorithms, and a method for improving the capacity of SDM even when used as an associative memory.

Large-scale linear rankSVM.

PubMed

Lee, Ching-Pei; Lin, Chih-Jen

2014-04-01

Linear rankSVM is one of the widely used methods for learning to rank. Although its performance may be inferior to nonlinear methods such as kernel rankSVM and gradient boosting decision trees, linear rankSVM is useful to quickly produce a baseline model. Furthermore, following its recent development for classification, linear rankSVM may give competitive performance for large and sparse data. A great deal of works have studied linear rankSVM. The focus is on the computational efficiency when the number of preference pairs is large. In this letter, we systematically study existing works, discuss their advantages and disadvantages, and propose an efficient algorithm. We discuss different implementation issues and extensions with detailed experiments. Finally, we develop a robust linear rankSVM tool for public use.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Spotz, William F.

PyTrilinos is a set of Python interfaces to compiled Trilinos packages. This collection supports serial and parallel dense linear algebra, serial and parallel sparse linear algebra, direct and iterative linear solution techniques, algebraic and multilevel preconditioners, nonlinear solvers and continuation algorithms, eigensolvers and partitioning algorithms. Also included are a variety of related utility functions and classes, including distributed I/O, coloring algorithms and matrix generation. PyTrilinos vector objects are compatible with the popular NumPy Python package. As a Python front end to compiled libraries, PyTrilinos takes advantage of the flexibility and ease of use of Python, and the efficiency of themore » underlying C++, C and Fortran numerical kernels. This paper covers recent, previously unpublished advances in the PyTrilinos package.« less

Elastic-Waveform Inversion with Compressive Sensing for Sparse Seismic Data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Youzuo; Huang, Lianjie

2015-01-28

Accurate velocity models of compressional- and shear-waves are essential for geothermal reservoir characterization and microseismic imaging. Elastic-waveform inversion of multi-component seismic data can provide high-resolution inversion results of subsurface geophysical properties. However, the method requires seismic data acquired using dense source and receiver arrays. In practice, seismic sources and/or geophones are often sparsely distributed on the surface and/or in a borehole, such as 3D vertical seismic profiling (VSP) surveys. We develop a novel elastic-waveform inversion method with compressive sensing for inversion of sparse seismic data. We employ an alternating-minimization algorithm to solve the optimization problem of our new waveform inversionmore » method. We validate our new method using synthetic VSP data for a geophysical model built using geologic features found at the Raft River enhanced-geothermal-system (EGS) field. We apply our method to synthetic VSP data with a sparse source array and compare the results with those obtained with a dense source array. Our numerical results demonstrate that the velocity models produced with our new method using a sparse source array are almost as accurate as those obtained using a dense source array.« less

An extended harmonic balance method based on incremental nonlinear control parameters

NASA Astrophysics Data System (ADS)

Khodaparast, Hamed Haddad; Madinei, Hadi; Friswell, Michael I.; Adhikari, Sondipon; Coggon, Simon; Cooper, Jonathan E.

2017-02-01

A new formulation for calculating the steady-state responses of multiple-degree-of-freedom (MDOF) non-linear dynamic systems due to harmonic excitation is developed. This is aimed at solving multi-dimensional nonlinear systems using linear equations. Nonlinearity is parameterised by a set of 'non-linear control parameters' such that the dynamic system is effectively linear for zero values of these parameters and nonlinearity increases with increasing values of these parameters. Two sets of linear equations which are formed from a first-order truncated Taylor series expansion are developed. The first set of linear equations provides the summation of sensitivities of linear system responses with respect to non-linear control parameters and the second set are recursive equations that use the previous responses to update the sensitivities. The obtained sensitivities of steady-state responses are then used to calculate the steady state responses of non-linear dynamic systems in an iterative process. The application and verification of the method are illustrated using a non-linear Micro-Electro-Mechanical System (MEMS) subject to a base harmonic excitation. The non-linear control parameters in these examples are the DC voltages that are applied to the electrodes of the MEMS devices.

On the benefit of DMT modulation in nonlinear VLC systems.

PubMed

Qian, Hua; Cai, Sunzeng; Yao, Saijie; Zhou, Ting; Yang, Yang; Wang, Xudong

2015-02-09

In a visible light communication (VLC) system, the nonlinear characteristic of the light emitting diode (LED) in transmitter is a limiting factor of system performance. Modern modulation signals with large peak-to-power-ratio (PAPR) suffers uneven distortion. The nonlinear response directly impacts the intensity modulation and direct detection VLC system with pulse-amplitude modulation (PAM). The amplitude of the PAM signal is distorted unevenly and large signal is vulnerable to noise. Orthogonal linear transformations, such as discrete multi-tone (DMT) modulation, can spread the nonlinear effects evenly to each data symbol, thus perform better than PAM signals. In this paper, we provide theoretical analysis on the benefit of DMT modulation in nonlinear VLC system. We show that the DMT modulation is a better choice than the PAM modulation for the VLC system as the DMT modulation is more robust against nonlinearity. We also show that the post-distortion nonlinear elimination method, which is applied at the receiver, can be a reliable solution to the nonlinear VLC system. Simulation results show that the post-distortion greatly improves the system performance for the DMT modulation.

Complex nonlinear dynamics in the limit of weak coupling of a system of microcantilevers connected by a geometrically nonlinear tunable nanomembrane.

PubMed

Jeong, Bongwon; Cho, Hanna; Keum, Hohyun; Kim, Seok; Michael McFarland, D; Bergman, Lawrence A; King, William P; Vakakis, Alexander F

2014-11-21

Intentional utilization of geometric nonlinearity in micro/nanomechanical resonators provides a breakthrough to overcome the narrow bandwidth limitation of linear dynamic systems. In past works, implementation of intentional geometric nonlinearity to an otherwise linear nano/micromechanical resonator has been successfully achieved by local modification of the system through nonlinear attachments of nanoscale size, such as nanotubes and nanowires. However, the conventional fabrication method involving manual integration of nanoscale components produced a low yield rate in these systems. In the present work, we employed a transfer-printing assembly technique to reliably integrate a silicon nanomembrane as a nonlinear coupling component onto a linear dynamic system with two discrete microcantilevers. The dynamics of the developed system was modeled analytically and investigated experimentally as the coupling strength was finely tuned via FIB post-processing. The transition from the linear to the nonlinear dynamic regime with gradual change in the coupling strength was experimentally studied. In addition, we observed for the weakly coupled system that oscillation was asynchronous in the vicinity of the resonance, thus exhibiting a nonlinear complex mode. We conjectured that the emergence of this nonlinear complex mode could be attributed to the nonlinear damping arising from the attached nanomembrane.

Track monitoring from the dynamic response of a passing train: A sparse approach

NASA Astrophysics Data System (ADS)

Lederman, George; Chen, Siheng; Garrett, James H.; Kovačević, Jelena; Noh, Hae Young; Bielak, Jacobo

2017-06-01

Collecting vibration data from revenue service trains could be a low-cost way to more frequently monitor railroad tracks, yet operational variability makes robust analysis a challenge. We propose a novel analysis technique for track monitoring that exploits the sparsity inherent in train-vibration data. This sparsity is based on the observation that large vertical train vibrations typically involve the excitation of the train's fundamental mode due to track joints, switchgear, or other discrete hardware. Rather than try to model the entire rail profile, in this study we examine a sparse approach to solving an inverse problem where (1) the roughness is constrained to a discrete and limited set of "bumps"; and (2) the train system is idealized as a simple damped oscillator that models the train's vibration in the fundamental mode. We use an expectation maximization (EM) approach to iteratively solve for the track profile and the train system properties, using orthogonal matching pursuit (OMP) to find the sparse approximation within each step. By enforcing sparsity, the inverse problem is well posed and the train's position can be found relative to the sparse bumps, thus reducing the uncertainty in the GPS data. We validate the sparse approach on two sections of track monitored from an operational train over a 16 month period of time, one where track changes did not occur during this period and another where changes did occur. We show that this approach can not only detect when track changes occur, but also offers insight into the type of such changes.

Review: The state-of-art of sparse channel models and their applicability to performance assessment of radioactive waste repositories in fractured crystalline formations

NASA Astrophysics Data System (ADS)

Figueiredo, Bruno; Tsang, Chin-Fu; Niemi, Auli; Lindgren, Georg

2016-11-01

Laboratory and field experiments done on fractured rock show that flow and solute transport often occur along flow channels. `Sparse channels' refers to the case where these channels are characterised by flow in long flow paths separated from each other by large spacings relative to the size of flow domain. A literature study is presented that brings together information useful to assess whether a sparse-channel network concept is an appropriate representation of the flow system in tight fractured rock of low transmissivity, such as that around a nuclear waste repository in deep crystalline rocks. A number of observations are made in this review. First, conventional fracture network models may lead to inaccurate results for flow and solute transport in tight fractured rocks. Secondly, a flow dimension of 1, as determined by the analysis of pressure data in well testing, may be indicative of channelised flow, but such interpretation is not unique or definitive. Thirdly, in sparse channels, the percolation may be more influenced by the fracture shape than the fracture size and orientation but further studies are needed. Fourthly, the migration of radionuclides from a waste canister in a repository to the biosphere may be strongly influenced by the type of model used (e.g. discrete fracture network, channel model). Fifthly, the determination of appropriateness of representing an in situ flow system by a sparse-channel network model needs parameters usually neglected in site characterisation, such as the density of channels or fracture intersections.

Design of a nonlinear torsional vibration absorber

NASA Astrophysics Data System (ADS)

Tahir, Ammaar Bin

Tuned mass dampers (TMD) utilizing linear spring mechanisms to mitigate destructive vibrations are commonly used in practice. A TMD is usually tuned for a specific resonant frequency or an operating frequency of a system. Recently, nonlinear vibration absorbers attracted attention of researchers due to some potential advantages they possess over the TMDs. The nonlinear vibration absorber, or the nonlinear energy sink (NES), has an advantage of being effective over a broad range of excitation frequencies, which makes it more suitable for systems with several resonant frequencies, or for a system with varying excitation frequency. Vibration dissipation mechanism in an NES is passive and ensures that there is no energy backflow to the primary system. In this study, an experimental setup of a rotational system has been designed for validation of the concept of nonlinear torsional vibration absorber with geometrically induced cubic stiffness nonlinearity. Dimensions of the primary system have been optimized so as to get the first natural frequency of the system to be fairly low. This was done in order to excite the dynamic system for torsional vibration response by the available motor. Experiments have been performed to obtain the modal parameters of the system. Based on the obtained modal parameters, the design optimization of the nonlinear torsional vibration absorber was carried out using an equivalent 2-DOF modal model. The optimality criterion was chosen to be maximization of energy dissipation in the nonlinear absorber attached to the equivalent 2-DOF system. The optimized design parameters of the nonlinear absorber were tested on the original 5-DOF system numerically. A comparison was made between the performance of linear and nonlinear absorbers using the numerical models. The comparison showed the superiority of the nonlinear absorber over its linear counterpart for the given set of primary system parameters as the vibration energy dissipation in the former is larger than that in the latter. A nonlinear absorber design has been proposed comprising of thin beams as elastic elements. The geometric configuration of the proposed design has been shown to provide cubic stiffness nonlinearity in torsion. The values of design variables, namely the strength of nonlinearity alpha and torsional stiffness kalpha, were obtained by optimizing dimensions and material properties of the beams for a maximum vibration energy dissipation in the nonlinear absorber. A parametric study has also been conducted to analyze the effect of the magnitude of excitation provided to the system on the performance of a nonlinear absorber. It has been shown that the nonlinear absorber turns out to be more effective in terms of energy dissipation as compared to a linear absorber with an increase in the excitation level applied to the system.

In-Storage Embedded Accelerator for Sparse Pattern Processing

DTIC Science & Technology

2016-09-13

computation . As a result, a very small processor could be used and still make full use of storage device bandwidth. When the host software sends...Rean Griffith, Anthony D. Joseph, Randy Katz, Andy Konwinski, Gunho Lee et al. "A view of cloud computing ."Communications of the ACM 53, no. 4 (2010...Laboratory, * MIT Computer Science & Artificial Intelligence Laboratory Abstract— We present a novel system architecture for sparse pattern

Spatial nonlinearities: Cascading effects in the earth system

USGS Publications Warehouse

Peters, Debra P.C.; Pielke, R.A.; Bestelmeyer, B.T.; Allen, Craig D.; Munson-McGee, Stuart; Havstad, K. M.; Canadell, Josep G.; Pataki, Diane E.; Pitelka, Louis F.

2006-01-01

Nonlinear behavior is prevalent in all aspects of the Earth System, including ecological responses to global change (Gallagher and Appenzeller 1999; Steffen et al. 2004). Nonlinear behavior refers to a large, discontinuous change in response to a small change in a driving variable (Rial et al. 2004). In contrast to linear systems where responses are smooth, well-behaved, continuous functions, nonlinear systems often undergo sharp or discontinuous transitions resulting from the crossing of thresholds. These nonlinear responses can result in surprising behavior that makes forecasting difficult (Kaplan and Glass 1995). Given that many system dynamics are nonlinear, it is imperative that conceptual and quantitative tools be developed to increase our understanding of the processes leading to nonlinear behavior in order to determine if forecasting can be improved under future environmental changes (Clark et al. 2001).

Computer Sciences and Data Systems, volume 1

NASA Technical Reports Server (NTRS)

1987-01-01

Topics addressed include: software engineering; university grants; institutes; concurrent processing; sparse distributed memory; distributed operating systems; intelligent data management processes; expert system for image analysis; fault tolerant software; and architecture research.

Analysis of large power systems

NASA Technical Reports Server (NTRS)

Dommel, H. W.

1975-01-01

Computer-oriented power systems analysis procedures in the electric utilities are surveyed. The growth of electric power systems is discussed along with the solution of sparse network equations, power flow, and stability studies.

Towards Real-Time Maneuver Detection: Automatic State and Dynamics Estimation with the Adaptive Optimal Control Based Estimator

NASA Astrophysics Data System (ADS)

Lubey, D.; Scheeres, D.

Tracking objects in Earth orbit is fraught with complications. This is due to the large population of orbiting spacecraft and debris that continues to grow, passive (i.e. no direct communication) and data-sparse observations, and the presence of maneuvers and dynamics mismodeling. Accurate orbit determination in this environment requires an algorithm to capture both a system's state and its state dynamics in order to account for mismodelings. Previous studies by the authors yielded an algorithm called the Optimal Control Based Estimator (OCBE) - an algorithm that simultaneously estimates a system's state and optimal control policies that represent dynamic mismodeling in the system for an arbitrary orbit-observer setup. The stochastic properties of these estimated controls are then used to determine the presence of mismodelings (maneuver detection), as well as characterize and reconstruct the mismodelings. The purpose of this paper is to develop the OCBE into an accurate real-time orbit tracking and maneuver detection algorithm by automating the algorithm and removing its linear assumptions. This results in a nonlinear adaptive estimator. In its original form the OCBE had a parameter called the assumed dynamic uncertainty, which is selected by the user with each new measurement to reflect the level of dynamic mismodeling in the system. This human-in-the-loop approach precludes real-time application to orbit tracking problems due to their complexity. This paper focuses on the Adaptive OCBE, a version of the estimator where the assumed dynamic uncertainty is chosen automatically with each new measurement using maneuver detection results to ensure that state uncertainties are properly adjusted to account for all dynamic mismodelings. The paper also focuses on a nonlinear implementation of the estimator. Originally, the OCBE was derived from a nonlinear cost function then linearized about a nominal trajectory, which is assumed to be ballistic (i.e. the nominal optimal control policy is zero for all times). In this paper, we relax this assumption on the nominal trajectory in order to allow for controlled nominal trajectories. This allows the estimator to be iterated to obtain a more accurate nonlinear solution for both the state and control estimates. Beyond these developments to the estimator, this paper also introduces a modified distance metric for maneuver detection. The original metric used in the OCBE only accounted for the estimated control and its uncertainty. This new metric accounts for measurement deviation and a priori state deviations, such that it accounts for all three major forms of uncertainty in orbit determination. This allows the user to understand the contributions of each source of uncertainty toward the total system mismodeling so that the user can properly account for them. Together these developments create an accurate orbit determination algorithm that is automated, robust to mismodeling, and capable of detecting and reconstructing the presence of mismodeling. These qualities make this algorithm a good foundation from which to approach the problem of real-time maneuver detection and reconstruction for Space Situational Awareness applications. This is further strengthened by the algorithm's general formulation that allows it to be applied to problems with an arbitrary target and observer.

Artificial neural network does better spatiotemporal compressive sampling

NASA Astrophysics Data System (ADS)

Lee, Soo-Young; Hsu, Charles; Szu, Harold

2012-06-01

Spatiotemporal sparseness is generated naturally by human visual system based on artificial neural network modeling of associative memory. Sparseness means nothing more and nothing less than the compressive sensing achieves merely the information concentration. To concentrate the information, one uses the spatial correlation or spatial FFT or DWT or the best of all adaptive wavelet transform (cf. NUS, Shen Shawei). However, higher dimensional spatiotemporal information concentration, the mathematics can not do as flexible as a living human sensory system. The reason is obviously for survival reasons. The rest of the story is given in the paper.

Optimal sparse approximation with integrate and fire neurons.

PubMed

Shapero, Samuel; Zhu, Mengchen; Hasler, Jennifer; Rozell, Christopher

2014-08-01

Sparse approximation is a hypothesized coding strategy where a population of sensory neurons (e.g. V1) encodes a stimulus using as few active neurons as possible. We present the Spiking LCA (locally competitive algorithm), a rate encoded Spiking Neural Network (SNN) of integrate and fire neurons that calculate sparse approximations. The Spiking LCA is designed to be equivalent to the nonspiking LCA, an analog dynamical system that converges on a ℓ(1)-norm sparse approximations exponentially. We show that the firing rate of the Spiking LCA converges on the same solution as the analog LCA, with an error inversely proportional to the sampling time. We simulate in NEURON a network of 128 neuron pairs that encode 8 × 8 pixel image patches, demonstrating that the network converges to nearly optimal encodings within 20 ms of biological time. We also show that when using more biophysically realistic parameters in the neurons, the gain function encourages additional ℓ(0)-norm sparsity in the encoding, relative both to ideal neurons and digital solvers.

Assisted navigation based on shared-control, using discrete and sparse human-machine interfaces.

PubMed

Lopes, Ana C; Nunes, Urbano; Vaz, Luis; Vaz, Luís

2010-01-01

This paper presents a shared-control approach for Assistive Mobile Robots (AMR), which depends on the user's ability to navigate a semi-autonomous powered wheelchair, using a sparse and discrete human-machine interface (HMI). This system is primarily intended to help users with severe motor disabilities that prevent them to use standard human-machine interfaces. Scanning interfaces and Brain Computer Interfaces (BCI), characterized to provide a small set of commands issued sparsely, are possible HMIs. This shared-control approach is intended to be applied in an Assisted Navigation Training Framework (ANTF) that is used to train users' ability in steering a powered wheelchair in an appropriate manner, given the restrictions imposed by their limited motor capabilities. A shared-controller based on user characterization, is proposed. This controller is able to share the information provided by the local motion planning level with the commands issued sparsely by the user. Simulation results of the proposed shared-control method, are presented.

A Hyperspherical Adaptive Sparse-Grid Method for High-Dimensional Discontinuity Detection

DOE PAGES

Zhang, Guannan; Webster, Clayton G.; Gunzburger, Max D.; ...

2015-06-24

This study proposes and analyzes a hyperspherical adaptive hierarchical sparse-grid method for detecting jump discontinuities of functions in high-dimensional spaces. The method is motivated by the theoretical and computational inefficiencies of well-known adaptive sparse-grid methods for discontinuity detection. Our novel approach constructs a function representation of the discontinuity hypersurface of an N-dimensional discontinuous quantity of interest, by virtue of a hyperspherical transformation. Then, a sparse-grid approximation of the transformed function is built in the hyperspherical coordinate system, whose value at each point is estimated by solving a one-dimensional discontinuity detection problem. Due to the smoothness of the hypersurface, the newmore » technique can identify jump discontinuities with significantly reduced computational cost, compared to existing methods. In addition, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. Rigorous complexity analyses of the new method are provided as are several numerical examples that illustrate the effectiveness of the approach.« less

A hyper-spherical adaptive sparse-grid method for high-dimensional discontinuity detection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Guannan; Webster, Clayton G.; Gunzburger, Max D.

This work proposes and analyzes a hyper-spherical adaptive hierarchical sparse-grid method for detecting jump discontinuities of functions in high-dimensional spaces is proposed. The method is motivated by the theoretical and computational inefficiencies of well-known adaptive sparse-grid methods for discontinuity detection. Our novel approach constructs a function representation of the discontinuity hyper-surface of an N-dimensional dis- continuous quantity of interest, by virtue of a hyper-spherical transformation. Then, a sparse-grid approximation of the transformed function is built in the hyper-spherical coordinate system, whose value at each point is estimated by solving a one-dimensional discontinuity detection problem. Due to the smoothness of themore » hyper-surface, the new technique can identify jump discontinuities with significantly reduced computational cost, compared to existing methods. Moreover, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. Rigorous error estimates and complexity analyses of the new method are provided as are several numerical examples that illustrate the effectiveness of the approach.« less

Sparse dictionary learning for resting-state fMRI analysis

NASA Astrophysics Data System (ADS)

Lee, Kangjoo; Han, Paul Kyu; Ye, Jong Chul

2011-09-01

Recently, there has been increased interest in the usage of neuroimaging techniques to investigate what happens in the brain at rest. Functional imaging studies have revealed that the default-mode network activity is disrupted in Alzheimer's disease (AD). However, there is no consensus, as yet, on the choice of analysis method for the application of resting-state analysis for disease classification. This paper proposes a novel compressed sensing based resting-state fMRI analysis tool called Sparse-SPM. As the brain's functional systems has shown to have features of complex networks according to graph theoretical analysis, we apply a graph model to represent a sparse combination of information flows in complex network perspectives. In particular, a new concept of spatially adaptive design matrix has been proposed by implementing sparse dictionary learning based on sparsity. The proposed approach shows better performance compared to other conventional methods, such as independent component analysis (ICA) and seed-based approach, in classifying the AD patients from normal using resting-state analysis.

Systematic sparse matrix error control for linear scaling electronic structure calculations.

PubMed

Rubensson, Emanuel H; Sałek, Paweł

2005-11-30

Efficient truncation criteria used in multiatom blocked sparse matrix operations for ab initio calculations are proposed. As system size increases, so does the need to stay on top of errors and still achieve high performance. A variant of a blocked sparse matrix algebra to achieve strict error control with good performance is proposed. The presented idea is that the condition to drop a certain submatrix should depend not only on the magnitude of that particular submatrix, but also on which other submatrices that are dropped. The decision to remove a certain submatrix is based on the contribution the removal would cause to the error in the chosen norm. We study the effect of an accumulated truncation error in iterative algorithms like trace correcting density matrix purification. One way to reduce the initial exponential growth of this error is presented. The presented error control for a sparse blocked matrix toolbox allows for achieving optimal performance by performing only necessary operations needed to maintain the requested level of accuracy. Copyright 2005 Wiley Periodicals, Inc.

Resonance-Based Time-Frequency Manifold for Feature Extraction of Ship-Radiated Noise.

PubMed

Yan, Jiaquan; Sun, Haixin; Chen, Hailan; Junejo, Naveed Ur Rehman; Cheng, En

2018-03-22

In this paper, a novel time-frequency signature using resonance-based sparse signal decomposition (RSSD), phase space reconstruction (PSR), time-frequency distribution (TFD) and manifold learning is proposed for feature extraction of ship-radiated noise, which is called resonance-based time-frequency manifold (RTFM). This is suitable for analyzing signals with oscillatory, non-stationary and non-linear characteristics in a situation of serious noise pollution. Unlike the traditional methods which are sensitive to noise and just consider one side of oscillatory, non-stationary and non-linear characteristics, the proposed RTFM can provide the intact feature signature of all these characteristics in the form of a time-frequency signature by the following steps: first, RSSD is employed on the raw signal to extract the high-oscillatory component and abandon the low-oscillatory component. Second, PSR is performed on the high-oscillatory component to map the one-dimensional signal to the high-dimensional phase space. Third, TFD is employed to reveal non-stationary information in the phase space. Finally, manifold learning is applied to the TFDs to fetch the intrinsic non-linear manifold. A proportional addition of the top two RTFMs is adopted to produce the improved RTFM signature. All of the case studies are validated on real audio recordings of ship-radiated noise. Case studies of ship-radiated noise on different datasets and various degrees of noise pollution manifest the effectiveness and robustness of the proposed method.

Resonance-Based Time-Frequency Manifold for Feature Extraction of Ship-Radiated Noise

PubMed Central

Yan, Jiaquan; Sun, Haixin; Chen, Hailan; Junejo, Naveed Ur Rehman; Cheng, En

2018-01-01

In this paper, a novel time-frequency signature using resonance-based sparse signal decomposition (RSSD), phase space reconstruction (PSR), time-frequency distribution (TFD) and manifold learning is proposed for feature extraction of ship-radiated noise, which is called resonance-based time-frequency manifold (RTFM). This is suitable for analyzing signals with oscillatory, non-stationary and non-linear characteristics in a situation of serious noise pollution. Unlike the traditional methods which are sensitive to noise and just consider one side of oscillatory, non-stationary and non-linear characteristics, the proposed RTFM can provide the intact feature signature of all these characteristics in the form of a time-frequency signature by the following steps: first, RSSD is employed on the raw signal to extract the high-oscillatory component and abandon the low-oscillatory component. Second, PSR is performed on the high-oscillatory component to map the one-dimensional signal to the high-dimensional phase space. Third, TFD is employed to reveal non-stationary information in the phase space. Finally, manifold learning is applied to the TFDs to fetch the intrinsic non-linear manifold. A proportional addition of the top two RTFMs is adopted to produce the improved RTFM signature. All of the case studies are validated on real audio recordings of ship-radiated noise. Case studies of ship-radiated noise on different datasets and various degrees of noise pollution manifest the effectiveness and robustness of the proposed method. PMID:29565288

Hybrid time-frequency domain equalization for LED nonlinearity mitigation in OFDM-based VLC systems.

PubMed

Li, Jianfeng; Huang, Zhitong; Liu, Xiaoshuang; Ji, Yuefeng

2015-01-12

A novel hybrid time-frequency domain equalization scheme is proposed and experimentally demonstrated to mitigate the white light emitting diode (LED) nonlinearity in visible light communication (VLC) systems based on orthogonal frequency division multiplexing (OFDM). We handle the linear and nonlinear distortion separately in a nonlinear OFDM system. The linear part is equalized in frequency domain and the nonlinear part is compensated by an adaptive nonlinear time domain equalizer (N-TDE). The experimental results show that with only a small number of parameters the nonlinear equalizer can efficiently mitigate the LED nonlinearity. With the N-TDE the modulation index (MI) and BER performance can be significantly enhanced.

Efficient ICCG on a shared memory multiprocessor

NASA Technical Reports Server (NTRS)

Hammond, Steven W.; Schreiber, Robert

1989-01-01

Different approaches are discussed for exploiting parallelism in the ICCG (Incomplete Cholesky Conjugate Gradient) method for solving large sparse symmetric positive definite systems of equations on a shared memory parallel computer. Techniques for efficiently solving triangular systems and computing sparse matrix-vector products are explored. Three methods for scheduling the tasks in solving triangular systems are implemented on the Sequent Balance 21000. Sample problems that are representative of a large class of problems solved using iterative methods are used. We show that a static analysis to determine data dependences in the triangular solve can greatly improve its parallel efficiency. We also show that ignoring symmetry and storing the whole matrix can reduce solution time substantially.

Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

NASA Astrophysics Data System (ADS)

Stevanović Hedrih, K.

2008-02-01

This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of "an open a spiral form" of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task

Applied Nonlinear Dynamics and Stochastic Systems Near The Millenium. Proceedings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kadtke, J.B.; Bulsara, A.

These proceedings represent papers presented at the Applied Nonlinear Dynamics and Stochastic Systems conference held in San Diego, California in July 1997. The conference emphasized the applications of nonlinear dynamical systems theory in fields as diverse as neuroscience and biomedical engineering, fluid dynamics, chaos control, nonlinear signal/image processing, stochastic resonance, devices and nonlinear dynamics in socio{minus}economic systems. There were 56 papers presented at the conference and 5 have been abstracted for the Energy Science and Technology database.(AIP)

Improving EEG-Based Driver Fatigue Classification Using Sparse-Deep Belief Networks.

PubMed

Chai, Rifai; Ling, Sai Ho; San, Phyo Phyo; Naik, Ganesh R; Nguyen, Tuan N; Tran, Yvonne; Craig, Ashley; Nguyen, Hung T

2017-01-01

This paper presents an improvement of classification performance for electroencephalography (EEG)-based driver fatigue classification between fatigue and alert states with the data collected from 43 participants. The system employs autoregressive (AR) modeling as the features extraction algorithm, and sparse-deep belief networks (sparse-DBN) as the classification algorithm. Compared to other classifiers, sparse-DBN is a semi supervised learning method which combines unsupervised learning for modeling features in the pre-training layer and supervised learning for classification in the following layer. The sparsity in sparse-DBN is achieved with a regularization term that penalizes a deviation of the expected activation of hidden units from a fixed low-level prevents the network from overfitting and is able to learn low-level structures as well as high-level structures. For comparison, the artificial neural networks (ANN), Bayesian neural networks (BNN), and original deep belief networks (DBN) classifiers are used. The classification results show that using AR feature extractor and DBN classifiers, the classification performance achieves an improved classification performance with a of sensitivity of 90.8%, a specificity of 90.4%, an accuracy of 90.6%, and an area under the receiver operating curve (AUROC) of 0.94 compared to ANN (sensitivity at 80.8%, specificity at 77.8%, accuracy at 79.3% with AUC-ROC of 0.83) and BNN classifiers (sensitivity at 84.3%, specificity at 83%, accuracy at 83.6% with AUROC of 0.87). Using the sparse-DBN classifier, the classification performance improved further with sensitivity of 93.9%, a specificity of 92.3%, and an accuracy of 93.1% with AUROC of 0.96. Overall, the sparse-DBN classifier improved accuracy by 13.8, 9.5, and 2.5% over ANN, BNN, and DBN classifiers, respectively.

Improving EEG-Based Driver Fatigue Classification Using Sparse-Deep Belief Networks

PubMed Central

Chai, Rifai; Ling, Sai Ho; San, Phyo Phyo; Naik, Ganesh R.; Nguyen, Tuan N.; Tran, Yvonne; Craig, Ashley; Nguyen, Hung T.

2017-01-01

This paper presents an improvement of classification performance for electroencephalography (EEG)-based driver fatigue classification between fatigue and alert states with the data collected from 43 participants. The system employs autoregressive (AR) modeling as the features extraction algorithm, and sparse-deep belief networks (sparse-DBN) as the classification algorithm. Compared to other classifiers, sparse-DBN is a semi supervised learning method which combines unsupervised learning for modeling features in the pre-training layer and supervised learning for classification in the following layer. The sparsity in sparse-DBN is achieved with a regularization term that penalizes a deviation of the expected activation of hidden units from a fixed low-level prevents the network from overfitting and is able to learn low-level structures as well as high-level structures. For comparison, the artificial neural networks (ANN), Bayesian neural networks (BNN), and original deep belief networks (DBN) classifiers are used. The classification results show that using AR feature extractor and DBN classifiers, the classification performance achieves an improved classification performance with a of sensitivity of 90.8%, a specificity of 90.4%, an accuracy of 90.6%, and an area under the receiver operating curve (AUROC) of 0.94 compared to ANN (sensitivity at 80.8%, specificity at 77.8%, accuracy at 79.3% with AUC-ROC of 0.83) and BNN classifiers (sensitivity at 84.3%, specificity at 83%, accuracy at 83.6% with AUROC of 0.87). Using the sparse-DBN classifier, the classification performance improved further with sensitivity of 93.9%, a specificity of 92.3%, and an accuracy of 93.1% with AUROC of 0.96. Overall, the sparse-DBN classifier improved accuracy by 13.8, 9.5, and 2.5% over ANN, BNN, and DBN classifiers, respectively. PMID:28326009

Asymptotic Stability of Interconnected Passive Non-Linear Systems

NASA Technical Reports Server (NTRS)

Isidori, A.; Joshi, S. M.; Kelkar, A. G.

1999-01-01

This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.

Influence of unbalance on the nonlinear dynamical response and stability of flexible rotor-bearing systems

NASA Technical Reports Server (NTRS)

Gunter, E. J.; Humphris, R. R.; Springer, H.

1983-01-01

In this paper, some of the effects of unbalance on the nonlinear response and stability of flexible rotor-bearing systems is presented from both a theoretical and experimental standpoint. In a linear system, operating above its stability threshold, the amplitude of motion grows exponentially with time and the orbits become unbounded. In an actual system, this is not necessarily the case. The actual amplitudes of motion may be bounded due to various nonlinear effects in the system. These nonlinear effects cause limit cycles of motion. Nonlinear effects are inherent in fluid film bearings and seals. Other contributors to nonlinear effects are shafts, couplings and foundations. In addition to affecting the threshold of stability, the nonlinear effects can cause jump phenomena to occur at not only the critical speeds, but also at stability onset or restabilization speeds.

Fast sparsely synchronized brain rhythms in a scale-free neural network.

PubMed

Kim, Sang-Yoon; Lim, Woochang

2015-08-01

We consider a directed version of the Barabási-Albert scale-free network model with symmetric preferential attachment with the same in- and out-degrees and study the emergence of sparsely synchronized rhythms for a fixed attachment degree in an inhibitory population of fast-spiking Izhikevich interneurons. Fast sparsely synchronized rhythms with stochastic and intermittent neuronal discharges are found to appear for large values of J (synaptic inhibition strength) and D (noise intensity). For an intensive study we fix J at a sufficiently large value and investigate the population states by increasing D. For small D, full synchronization with the same population-rhythm frequency fp and mean firing rate (MFR) fi of individual neurons occurs, while for large D partial synchronization with fp>〈fi〉 (〈fi〉: ensemble-averaged MFR) appears due to intermittent discharge of individual neurons; in particular, the case of fp>4〈fi〉 is referred to as sparse synchronization. For the case of partial and sparse synchronization, MFRs of individual neurons vary depending on their degrees. As D passes a critical value D* (which is determined by employing an order parameter), a transition to unsynchronization occurs due to the destructive role of noise to spoil the pacing between sparse spikes. For D

Nonreciprocity in the dynamics of coupled oscillators with nonlinearity, asymmetry, and scale hierarchy

NASA Astrophysics Data System (ADS)

Moore, Keegan J.; Bunyan, Jonathan; Tawfick, Sameh; Gendelman, Oleg V.; Li, Shuangbao; Leamy, Michael; Vakakis, Alexander F.

2018-01-01

In linear time-invariant dynamical and acoustical systems, reciprocity holds by the Onsager-Casimir principle of microscopic reversibility, and this can be broken only by odd external biases, nonlinearities, or time-dependent properties. A concept is proposed in this work for breaking dynamic reciprocity based on irreversible nonlinear energy transfers from large to small scales in a system with nonlinear hierarchical internal structure, asymmetry, and intentional strong stiffness nonlinearity. The resulting nonreciprocal large-to-small scale energy transfers mimic analogous nonlinear energy transfer cascades that occur in nature (e.g., in turbulent flows), and are caused by the strong frequency-energy dependence of the essentially nonlinear small-scale components of the system considered. The theoretical part of this work is mainly based on action-angle transformations, followed by direct numerical simulations of the resulting system of nonlinear coupled oscillators. The experimental part considers a system with two scales—a linear large-scale oscillator coupled to a small scale by a nonlinear spring—and validates the theoretical findings demonstrating nonreciprocal large-to-small scale energy transfer. The proposed study promotes a paradigm for designing nonreciprocal acoustic materials harnessing strong nonlinearity, which in a future application will be implemented in designing lattices incorporating nonlinear hierarchical internal structures, asymmetry, and scale mixing.

Piecewise multivariate modelling of sequential metabolic profiling data.

PubMed

Rantalainen, Mattias; Cloarec, Olivier; Ebbels, Timothy M D; Lundstedt, Torbjörn; Nicholson, Jeremy K; Holmes, Elaine; Trygg, Johan

2008-02-19

Modelling the time-related behaviour of biological systems is essential for understanding their dynamic responses to perturbations. In metabolic profiling studies, the sampling rate and number of sampling points are often restricted due to experimental and biological constraints. A supervised multivariate modelling approach with the objective to model the time-related variation in the data for short and sparsely sampled time-series is described. A set of piecewise Orthogonal Projections to Latent Structures (OPLS) models are estimated, describing changes between successive time points. The individual OPLS models are linear, but the piecewise combination of several models accommodates modelling and prediction of changes which are non-linear with respect to the time course. We demonstrate the method on both simulated and metabolic profiling data, illustrating how time related changes are successfully modelled and predicted. The proposed method is effective for modelling and prediction of short and multivariate time series data. A key advantage of the method is model transparency, allowing easy interpretation of time-related variation in the data. The method provides a competitive complement to commonly applied multivariate methods such as OPLS and Principal Component Analysis (PCA) for modelling and analysis of short time-series data.

Parametric model of servo-hydraulic actuator coupled with a nonlinear system: Experimental validation

NASA Astrophysics Data System (ADS)

Maghareh, Amin; Silva, Christian E.; Dyke, Shirley J.

2018-05-01

Hydraulic actuators play a key role in experimental structural dynamics. In a previous study, a physics-based model for a servo-hydraulic actuator coupled with a nonlinear physical system was developed. Later, this dynamical model was transformed into controllable canonical form for position tracking control purposes. For this study, a nonlinear device is designed and fabricated to exhibit various nonlinear force-displacement profiles depending on the initial condition and the type of materials used as replaceable coupons. Using this nonlinear system, the controllable canonical dynamical model is experimentally validated for a servo-hydraulic actuator coupled with a nonlinear physical system.

Whole-body PET parametric imaging employing direct 4D nested reconstruction and a generalized non-linear Patlak model

NASA Astrophysics Data System (ADS)

Karakatsanis, Nicolas A.; Rahmim, Arman

2014-03-01

Graphical analysis is employed in the research setting to provide quantitative estimation of PET tracer kinetics from dynamic images at a single bed. Recently, we proposed a multi-bed dynamic acquisition framework enabling clinically feasible whole-body parametric PET imaging by employing post-reconstruction parameter estimation. In addition, by incorporating linear Patlak modeling within the system matrix, we enabled direct 4D reconstruction in order to effectively circumvent noise amplification in dynamic whole-body imaging. However, direct 4D Patlak reconstruction exhibits a relatively slow convergence due to the presence of non-sparse spatial correlations in temporal kinetic analysis. In addition, the standard Patlak model does not account for reversible uptake, thus underestimating the influx rate Ki. We have developed a novel whole-body PET parametric reconstruction framework in the STIR platform, a widely employed open-source reconstruction toolkit, a) enabling accelerated convergence of direct 4D multi-bed reconstruction, by employing a nested algorithm to decouple the temporal parameter estimation from the spatial image update process, and b) enhancing the quantitative performance particularly in regions with reversible uptake, by pursuing a non-linear generalized Patlak 4D nested reconstruction algorithm. A set of published kinetic parameters and the XCAT phantom were employed for the simulation of dynamic multi-bed acquisitions. Quantitative analysis on the Ki images demonstrated considerable acceleration in the convergence of the nested 4D whole-body Patlak algorithm. In addition, our simulated and patient whole-body data in the postreconstruction domain indicated the quantitative benefits of our extended generalized Patlak 4D nested reconstruction for tumor diagnosis and treatment response monitoring.

Optimization of sparse synthetic transmit aperture imaging with coded excitation and frequency division.

PubMed

Behar, Vera; Adam, Dan

2005-12-01

An effective aperture approach is used for optimization of a sparse synthetic transmit aperture (STA) imaging system with coded excitation and frequency division. A new two-stage algorithm is proposed for optimization of both the positions of the transmit elements and the weights of the receive elements. In order to increase the signal-to-noise ratio in a synthetic aperture system, temporal encoding of the excitation signals is employed. When comparing the excitation by linear frequency modulation (LFM) signals and phase shift key modulation (PSKM) signals, the analysis shows that chirps are better for excitation, since at the output of a compression filter the sidelobes generated are much smaller than those produced by the binary PSKM signals. Here, an implementation of a fast STA imaging is studied by spatial encoding with frequency division of the LFM signals. The proposed system employs a 64-element array with only four active elements used during transmit. The two-dimensional point spread function (PSF) produced by such a sparse STA system is compared to the PSF produced by an equivalent phased array system, using the Field II simulation program. The analysis demonstrates the superiority of the new sparse STA imaging system while using coded excitation and frequency division. Compared to a conventional phased array imaging system, this system acquires images of equivalent quality 60 times faster, when the transmit elements are fired in pairs consecutively and the power level used during transmit is very low. The fastest acquisition time is achieved when all transmit elements are fired simultaneously, which improves detectability, but at the cost of a slight degradation of the axial resolution. In real-time implementation, however, it must be borne in mind that the frame rate of a STA imaging system depends not only on the acquisition time of the data but also on the processing time needed for image reconstruction. Comparing to phased array imaging, a significant increase in the frame rate of a STA imaging system is possible if and only if an equivalent time efficient algorithm is used for image reconstruction.

The effect of system nonlinearities on system noise statistics

NASA Technical Reports Server (NTRS)

Robinson, L. H., Jr.

1971-01-01

The effects are studied of nonlinearities in a baseline communications system on the system noise amplitude statistics. So that a meaningful identification of system nonlinearities can be made, the baseline system is assumed to transmit a single biphase-modulated signal through a relay satellite to the receiving equipment. The significant nonlinearities thus identified include square-law or product devices (e.g., in the carrier reference recovery loops in the receivers), bandpass limiters, and traveling wave tube amplifiers.

A robust real-time surface reconstruction method on point clouds captured from a 3D surface photogrammetry system.

PubMed

Liu, Wenyang; Cheung, Yam; Sawant, Amit; Ruan, Dan

2016-05-01

To develop a robust and real-time surface reconstruction method on point clouds captured from a 3D surface photogrammetry system. The authors have developed a robust and fast surface reconstruction method on point clouds acquired by the photogrammetry system, without explicitly solving the partial differential equation required by a typical variational approach. Taking advantage of the overcomplete nature of the acquired point clouds, their method solves and propagates a sparse linear relationship from the point cloud manifold to the surface manifold, assuming both manifolds share similar local geometry. With relatively consistent point cloud acquisitions, the authors propose a sparse regression (SR) model to directly approximate the target point cloud as a sparse linear combination from the training set, assuming that the point correspondences built by the iterative closest point (ICP) is reasonably accurate and have residual errors following a Gaussian distribution. To accommodate changing noise levels and/or presence of inconsistent occlusions during the acquisition, the authors further propose a modified sparse regression (MSR) model to model the potentially large and sparse error built by ICP with a Laplacian prior. The authors evaluated the proposed method on both clinical point clouds acquired under consistent acquisition conditions and on point clouds with inconsistent occlusions. The authors quantitatively evaluated the reconstruction performance with respect to root-mean-squared-error, by comparing its reconstruction results against that from the variational method. On clinical point clouds, both the SR and MSR models have achieved sub-millimeter reconstruction accuracy and reduced the reconstruction time by two orders of magnitude to a subsecond reconstruction time. On point clouds with inconsistent occlusions, the MSR model has demonstrated its advantage in achieving consistent and robust performance despite the introduced occlusions. The authors have developed a fast and robust surface reconstruction method on point clouds captured from a 3D surface photogrammetry system, with demonstrated sub-millimeter reconstruction accuracy and subsecond reconstruction time. It is suitable for real-time motion tracking in radiotherapy, with clear surface structures for better quantifications.

A robust real-time surface reconstruction method on point clouds captured from a 3D surface photogrammetry system

PubMed Central

Liu, Wenyang; Cheung, Yam; Sawant, Amit; Ruan, Dan

2016-01-01

Purpose: To develop a robust and real-time surface reconstruction method on point clouds captured from a 3D surface photogrammetry system. Methods: The authors have developed a robust and fast surface reconstruction method on point clouds acquired by the photogrammetry system, without explicitly solving the partial differential equation required by a typical variational approach. Taking advantage of the overcomplete nature of the acquired point clouds, their method solves and propagates a sparse linear relationship from the point cloud manifold to the surface manifold, assuming both manifolds share similar local geometry. With relatively consistent point cloud acquisitions, the authors propose a sparse regression (SR) model to directly approximate the target point cloud as a sparse linear combination from the training set, assuming that the point correspondences built by the iterative closest point (ICP) is reasonably accurate and have residual errors following a Gaussian distribution. To accommodate changing noise levels and/or presence of inconsistent occlusions during the acquisition, the authors further propose a modified sparse regression (MSR) model to model the potentially large and sparse error built by ICP with a Laplacian prior. The authors evaluated the proposed method on both clinical point clouds acquired under consistent acquisition conditions and on point clouds with inconsistent occlusions. The authors quantitatively evaluated the reconstruction performance with respect to root-mean-squared-error, by comparing its reconstruction results against that from the variational method. Results: On clinical point clouds, both the SR and MSR models have achieved sub-millimeter reconstruction accuracy and reduced the reconstruction time by two orders of magnitude to a subsecond reconstruction time. On point clouds with inconsistent occlusions, the MSR model has demonstrated its advantage in achieving consistent and robust performance despite the introduced occlusions. Conclusions: The authors have developed a fast and robust surface reconstruction method on point clouds captured from a 3D surface photogrammetry system, with demonstrated sub-millimeter reconstruction accuracy and subsecond reconstruction time. It is suitable for real-time motion tracking in radiotherapy, with clear surface structures for better quantifications. PMID:27147347

Nonlinear versus Ordinary Adaptive Control of Continuous Stirred-Tank Reactor

PubMed Central

Dostal, Petr

2015-01-01

Unfortunately, the major group of the systems in industry has nonlinear behavior and control of such processes with conventional control approaches with fixed parameters causes problems and suboptimal or unstable control results. An adaptive control is one way to how we can cope with nonlinearity of the system. This contribution compares classic adaptive control and its modification with Wiener system. This configuration divides nonlinear controller into the dynamic linear part and the static nonlinear part. The dynamic linear part is constructed with the use of polynomial synthesis together with the pole-placement method and the spectral factorization. The static nonlinear part uses static analysis of the controlled plant for introducing the mathematical nonlinear description of the relation between the controlled output and the change of the control input. Proposed controller is tested by the simulations on the mathematical model of the continuous stirred-tank reactor with cooling in the jacket as a typical nonlinear system. PMID:26346878

An approximation theory for the identification of nonlinear distributed parameter systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Reich, Simeon; Rosen, I. G.

1988-01-01

An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

Investigation of a Nonlinear Control System

NASA Technical Reports Server (NTRS)

Flugge-Lotz, I; Taylor, C F; Lindberg, H E

1958-01-01

A discontinuous variation of coefficients of the differential equation describing the linear control system before nonlinear elements are added is studied in detail. The nonlinear feedback is applied to a second-order system. Simulation techniques are used to study performance of the nonlinear control system and to compare it with the linear system for a wide variety of inputs. A detailed quantitative study of the influence of relay delays and of a transport delay is presented.

Linear and nonlinear schemes applied to pitch control of wind turbines.

PubMed

Geng, Hua; Yang, Geng

2014-01-01

Linear controllers have been employed in industrial applications for many years, but sometimes they are noneffective on the system with nonlinear characteristics. This paper discusses the structure, performance, implementation cost, advantages, and disadvantages of different linear and nonlinear schemes applied to the pitch control of the wind energy conversion systems (WECSs). The linear controller has the simplest structure and is easily understood by the engineers and thus is widely accepted by the industry. In contrast, nonlinear schemes are more complicated, but they can provide better performance. Although nonlinear algorithms can be implemented in a powerful digital processor nowadays, they need time to be accepted by the industry and their reliability needs to be verified in the commercial products. More information about the system nonlinear feature is helpful to simplify the controller design. However, nonlinear schemes independent of the system model are more robust to the uncertainties or deviations of the system parameters.

Application of a sparse representation method using K-SVD to data compression of experimental ambient vibration data for SHM

NASA Astrophysics Data System (ADS)

Noh, Hae Young; Kiremidjian, Anne S.

2011-04-01

This paper introduces a data compression method using the K-SVD algorithm and its application to experimental ambient vibration data for structural health monitoring purposes. Because many damage diagnosis algorithms that use system identification require vibration measurements of multiple locations, it is necessary to transmit long threads of data. In wireless sensor networks for structural health monitoring, however, data transmission is often a major source of battery consumption. Therefore, reducing the amount of data to transmit can significantly lengthen the battery life and reduce maintenance cost. The K-SVD algorithm was originally developed in information theory for sparse signal representation. This algorithm creates an optimal over-complete set of bases, referred to as a dictionary, using singular value decomposition (SVD) and represents the data as sparse linear combinations of these bases using the orthogonal matching pursuit (OMP) algorithm. Since ambient vibration data are stationary, we can segment them and represent each segment sparsely. Then only the dictionary and the sparse vectors of the coefficients need to be transmitted wirelessly for restoration of the original data. We applied this method to ambient vibration data measured from a four-story steel moment resisting frame. The results show that the method can compress the data efficiently and restore the data with very little error.

Reducing computational costs in large scale 3D EIT by using a sparse Jacobian matrix with block-wise CGLS reconstruction.

PubMed

Yang, C L; Wei, H Y; Adler, A; Soleimani, M

2013-06-01

Electrical impedance tomography (EIT) is a fast and cost-effective technique to provide a tomographic conductivity image of a subject from boundary current-voltage data. This paper proposes a time and memory efficient method for solving a large scale 3D EIT inverse problem using a parallel conjugate gradient (CG) algorithm. The 3D EIT system with a large number of measurement data can produce a large size of Jacobian matrix; this could cause difficulties in computer storage and the inversion process. One of challenges in 3D EIT is to decrease the reconstruction time and memory usage, at the same time retaining the image quality. Firstly, a sparse matrix reduction technique is proposed using thresholding to set very small values of the Jacobian matrix to zero. By adjusting the Jacobian matrix into a sparse format, the element with zeros would be eliminated, which results in a saving of memory requirement. Secondly, a block-wise CG method for parallel reconstruction has been developed. The proposed method has been tested using simulated data as well as experimental test samples. Sparse Jacobian with a block-wise CG enables the large scale EIT problem to be solved efficiently. Image quality measures are presented to quantify the effect of sparse matrix reduction in reconstruction results.

Compressive sampling by artificial neural networks for video

NASA Astrophysics Data System (ADS)

Szu, Harold; Hsu, Charles; Jenkins, Jeffrey; Reinhardt, Kitt

2011-06-01

We describe a smart surveillance strategy for handling novelty changes. Current sensors seem to keep all, redundant or not. The Human Visual System's Hubel-Wiesel (wavelet) edge detection mechanism pays attention to changes in movement, which naturally produce organized sparseness because a stagnant edge is not reported to the brain's visual cortex by retinal neurons. Sparseness is defined as an ordered set of ones (movement or not) relative to zeros that could be pseudo-orthogonal among themselves; then suited for fault tolerant storage and retrieval by means of Associative Memory (AM). The firing is sparse at the change locations. Unlike purely random sparse masks adopted in medical Compressive Sensing, these organized ones have an additional benefit of using the image changes to make retrievable graphical indexes. We coined this organized sparseness as Compressive Sampling; sensing but skipping over redundancy without altering the original image. Thus, we turn illustrate with video the survival tactics which animals that roam the Earth use daily. They acquire nothing but the space-time changes that are important to satisfy specific prey-predator relationships. We have noticed a similarity between the mathematical Compressive Sensing and this biological mechanism used for survival. We have designed a hardware implementation of the Human Visual System's Compressive Sampling scheme. To speed up further, our mixedsignal circuit design of frame differencing is built in on-chip processing hardware. A CMOS trans-conductance amplifier is designed here to generate a linear current output using a pair of differential input voltages from 2 photon detectors for change detection---one for the previous value and the other the subsequent value, ("write" synaptic weight by Hebbian outer products; "read" by inner product & pt. NL threshold) to localize and track the threat targets.

The interplay of intrinsic and extrinsic bounded noises in biomolecular networks.

PubMed

Caravagna, Giulio; Mauri, Giancarlo; d'Onofrio, Alberto

2013-01-01

After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a biomolecular network. The influence of intrinsic and extrinsic noises on biomolecular networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on: (i) the Michaelis-Menten approximation of noisy enzymatic reactions, which we show to be applicable also in co-presence of both intrinsic and extrinsic noise, (ii) a model of enzymatic futile cycle and (iii) a genetic toggle switch. In (ii) and (iii) we show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possible functional role of bounded noises.

Human motion tracking by temporal-spatial local gaussian process experts.

PubMed

Zhao, Xu; Fu, Yun; Liu, Yuncai

2011-04-01

Human pose estimation via motion tracking systems can be considered as a regression problem within a discriminative framework. It is always a challenging task to model the mapping from observation space to state space because of the high-dimensional characteristic in the multimodal conditional distribution. In order to build the mapping, existing techniques usually involve a large set of training samples in the learning process which are limited in their capability to deal with multimodality. We propose, in this work, a novel online sparse Gaussian Process (GP) regression model to recover 3-D human motion in monocular videos. Particularly, we investigate the fact that for a given test input, its output is mainly determined by the training samples potentially residing in its local neighborhood and defined in the unified input-output space. This leads to a local mixture GP experts system composed of different local GP experts, each of which dominates a mapping behavior with the specific covariance function adapting to a local region. To handle the multimodality, we combine both temporal and spatial information therefore to obtain two categories of local experts. The temporal and spatial experts are integrated into a seamless hybrid system, which is automatically self-initialized and robust for visual tracking of nonlinear human motion. Learning and inference are extremely efficient as all the local experts are defined online within very small neighborhoods. Extensive experiments on two real-world databases, HumanEva and PEAR, demonstrate the effectiveness of our proposed model, which significantly improve the performance of existing models.

Coupling nonlinear optical waves to photoreactive and phase-separating soft matter: Current status and perspectives

NASA Astrophysics Data System (ADS)

Biria, Saeid; Morim, Derek R.; An Tsao, Fu; Saravanamuttu, Kalaichelvi; Hosein, Ian D.

2017-10-01

Nonlinear optics and polymer systems are distinct fields that have been studied for decades. These two fields intersect with the observation of nonlinear wave propagation in photoreactive polymer systems. This has led to studies on the nonlinear dynamics of transmitted light in polymer media, particularly for optical self-trapping and optical modulation instability. The irreversibility of polymerization leads to permanent capture of nonlinear optical patterns in the polymer structure, which is a new synthetic route to complex structured soft materials. Over time more intricate polymer systems are employed, whereby nonlinear optical dynamics can couple to nonlinear chemical dynamics, opening opportunities for self-organization. This paper discusses the work to date on nonlinear optical pattern formation processes in polymers. A brief overview of nonlinear optical phenomenon is provided to set the stage for understanding their effects. We review the accomplishments of the field on studying nonlinear waveform propagation in photopolymerizable systems, then discuss our most recent progress in coupling nonlinear optical pattern formation to polymer blends and phase separation. To this end, perspectives on future directions and areas of sustained inquiry are provided. This review highlights the significant opportunity in exploiting nonlinear optical pattern formation in soft matter for the discovery of new light-directed and light-stimulated materials phenomenon, and in turn, soft matter provides a platform by which new nonlinear optical phenomenon may be discovered.

Localization and identification of structural nonlinearities using cascaded optimization and neural networks

NASA Astrophysics Data System (ADS)

Koyuncu, A.; Cigeroglu, E.; Özgüven, H. N.

2017-10-01

In this study, a new approach is proposed for identification of structural nonlinearities by employing cascaded optimization and neural networks. Linear finite element model of the system and frequency response functions measured at arbitrary locations of the system are used in this approach. Using the finite element model, a training data set is created, which appropriately spans the possible nonlinear configurations space of the system. A classification neural network trained on these data sets then localizes and determines the types of all nonlinearities associated with the nonlinear degrees of freedom in the system. A new training data set spanning the parametric space associated with the determined nonlinearities is created to facilitate parametric identification. Utilizing this data set, initially, a feed forward regression neural network is trained, which parametrically identifies the classified nonlinearities. Then, the results obtained are further improved by carrying out an optimization which uses network identified values as starting points. Unlike identification methods available in literature, the proposed approach does not require data collection from the degrees of freedoms where nonlinear elements are attached, and furthermore, it is sufficiently accurate even in the presence of measurement noise. The application of the proposed approach is demonstrated on an example system with nonlinear elements and on a real life experimental setup with a local nonlinearity.

Synthesizing spatiotemporally sparse smartphone sensor data for bridge modal identification

NASA Astrophysics Data System (ADS)

Ozer, Ekin; Feng, Maria Q.

2016-08-01

Smartphones as vibration measurement instruments form a large-scale, citizen-induced, and mobile wireless sensor network (WSN) for system identification and structural health monitoring (SHM) applications. Crowdsourcing-based SHM is possible with a decentralized system granting citizens with operational responsibility and control. Yet, citizen initiatives introduce device mobility, drastically changing SHM results due to uncertainties in the time and the space domains. This paper proposes a modal identification strategy that fuses spatiotemporally sparse SHM data collected by smartphone-based WSNs. Multichannel data sampled with the time and the space independence is used to compose the modal identification parameters such as frequencies and mode shapes. Structural response time history can be gathered by smartphone accelerometers and converted into Fourier spectra by the processor units. Timestamp, data length, energy to power conversion address temporal variation, whereas spatial uncertainties are reduced by geolocation services or determining node identity via QR code labels. Then, parameters collected from each distributed network component can be extended to global behavior to deduce modal parameters without the need of a centralized and synchronous data acquisition system. The proposed method is tested on a pedestrian bridge and compared with a conventional reference monitoring system. The results show that the spatiotemporally sparse mobile WSN data can be used to infer modal parameters despite non-overlapping sensor operation schedule.

Adaptive non-predictor control of lower triangular uncertain nonlinear systems with an unknown time-varying delay in the input

NASA Astrophysics Data System (ADS)

Koo, Min-Sung; Choi, Ho-Lim

2018-01-01

In this paper, we consider a control problem for a class of uncertain nonlinear systems in which there exists an unknown time-varying delay in the input and lower triangular nonlinearities. Usually, in the existing results, input delays have been coupled with feedforward (or upper triangular) nonlinearities; in other words, the combination of lower triangular nonlinearities and input delay has been rare. Motivated by the existing controller for input-delayed chain of integrators with nonlinearity, we show that the control of input-delayed nonlinear systems with two particular types of lower triangular nonlinearities can be done. As a control solution, we propose a newly designed feedback controller whose main features are its dynamic gain and non-predictor approach. Three examples are given for illustration.

Model-based nonlinear control of hydraulic servo systems: Challenges, developments and perspectives

NASA Astrophysics Data System (ADS)

Yao, Jianyong

2018-06-01

Hydraulic servo system plays a significant role in industries, and usually acts as a core point in control and power transmission. Although linear theory-based control methods have been well established, advanced controller design methods for hydraulic servo system to achieve high performance is still an unending pursuit along with the development of modern industry. Essential nonlinearity is a unique feature and makes model-based nonlinear control more attractive, due to benefit from prior knowledge of the servo valve controlled hydraulic system. In this paper, a discussion for challenges in model-based nonlinear control, latest developments and brief perspectives of hydraulic servo systems are presented: Modelling uncertainty in hydraulic system is a major challenge, which includes parametric uncertainty and time-varying disturbance; some specific requirements also arise ad hoc difficulties such as nonlinear friction during low velocity tracking, severe disturbance, periodic disturbance, etc.; to handle various challenges, nonlinear solutions including parameter adaptation, nonlinear robust control, state and disturbance observation, backstepping design and so on, are proposed and integrated, theoretical analysis and lots of applications reveal their powerful capability to solve pertinent problems; and at the end, some perspectives and associated research topics (measurement noise, constraints, inner valve dynamics, input nonlinearity, etc.) in nonlinear hydraulic servo control are briefly explored and discussed.

Structured functional additive regression in reproducing kernel Hilbert spaces.

PubMed

Zhu, Hongxiao; Yao, Fang; Zhang, Hao Helen

2014-06-01

Functional additive models (FAMs) provide a flexible yet simple framework for regressions involving functional predictors. The utilization of data-driven basis in an additive rather than linear structure naturally extends the classical functional linear model. However, the critical issue of selecting nonlinear additive components has been less studied. In this work, we propose a new regularization framework for the structure estimation in the context of Reproducing Kernel Hilbert Spaces. The proposed approach takes advantage of the functional principal components which greatly facilitates the implementation and the theoretical analysis. The selection and estimation are achieved by penalized least squares using a penalty which encourages the sparse structure of the additive components. Theoretical properties such as the rate of convergence are investigated. The empirical performance is demonstrated through simulation studies and a real data application.

On the photonic implementation of universal quantum gates, bell states preparation circuit and quantum LDPC encoders and decoders based on directional couplers and HNLF.

PubMed

Djordjevic, Ivan B

2010-04-12

The Bell states preparation circuit is a basic circuit required in quantum teleportation. We describe how to implement it in all-fiber technology. The basic building blocks for its implementation are directional couplers and highly nonlinear optical fiber (HNLF). Because the quantum information processing is based on delicate superposition states, it is sensitive to quantum errors. In order to enable fault-tolerant quantum computing the use of quantum error correction is unavoidable. We show how to implement in all-fiber technology encoders and decoders for sparse-graph quantum codes, and provide an illustrative example to demonstrate this implementation. We also show that arbitrary set of universal quantum gates can be implemented based on directional couplers and HNLFs.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dayman, Ken J; Ade, Brian J; Weber, Charles F

High-dimensional, nonlinear function estimation using large datasets is a current area of interest in the machine learning community, and applications may be found throughout the analytical sciences, where ever-growing datasets are making more information available to the analyst. In this paper, we leverage the existing relevance vector machine, a sparse Bayesian version of the well-studied support vector machine, and expand the method to include integrated feature selection and automatic function shaping. These innovations produce an algorithm that is able to distinguish variables that are useful for making predictions of a response from variables that are unrelated or confusing. We testmore » the technology using synthetic data, conduct initial performance studies, and develop a model capable of making position-independent predictions of the coreaveraged burnup using a single specimen drawn randomly from a nuclear reactor core.« less

Efficient Parallel Algorithms for Landscape Evolution Modelling

NASA Astrophysics Data System (ADS)

Moresi, L. N.; Mather, B.; Beucher, R.

2017-12-01

Landscape erosion and the deposition of sediments by river systems are strongly controlled bytopography, rainfall patterns, and the susceptibility of the basement to the action ofrunning water. It is well understood that each of these processes depends on the other, for example:topography results from active tectonic processes; deformation, metamorphosis andexhumation alter the competence of the basement; rainfall patterns depend on topography;uplift and subsidence in response to tectonic stress can be amplified by erosionand sediment deposition. We typically gain understanding of such coupled systems through forward models which capture theessential interactions of the various components and attempt parameterise those parts of the individual systemthat are unresolvable at the scale of the interaction. Here we address the problem of predicting erosion and deposition rates at a continental scalewith a resolution of tens to hundreds of metres in a dynamic, Lagrangian framework. This isa typical requirement for a code to interface with a mantle / lithosphere dynamics model anddemands an efficient, unstructured, parallel implementation. We address this through a very general algorithm that treats all parts of the landscape evolution equationsin sparse-matrix form including those for stream-flow accumulation, dam-filling and catchment determination. This givesus considerable flexibility in developing unstructured, parallel code, and in creating a modular packagethat can be configured by users to work at different temporal and spatial scales, but is also has potential advantagesin treating the non-linear parts of the problem in a general manner.

Optical Modeling of the Alignment and Test of the NASA James Webb Space Telescope

NASA Technical Reports Server (NTRS)

Howard, Joseph M.; Hayden, Bill; Keski-Kuha, Ritva; Feinberg, Lee

2007-01-01

Optical modeling challenges of the ground alignment plan and optical test and verification of the NASA James Webb Space Telescope are discussed. Issues such as back-out of the gravity sag of light-weighted mirrors, as well as the use of a sparse-aperture auto-collimating flat system are discussed. A walk-through of the interferometer based alignment procedure is summarized, and sensitivities from the sparse aperture wavefront test are included as examples.'

Sparse polynomial space approach to dissipative quantum systems: application to the sub-ohmic spin-boson model.

PubMed

Alvermann, A; Fehske, H

2009-04-17

We propose a general numerical approach to open quantum systems with a coupling to bath degrees of freedom. The technique combines the methodology of polynomial expansions of spectral functions with the sparse grid concept from interpolation theory. Thereby we construct a Hilbert space of moderate dimension to represent the bath degrees of freedom, which allows us to perform highly accurate and efficient calculations of static, spectral, and dynamic quantities using standard exact diagonalization algorithms. The strength of the approach is demonstrated for the phase transition, critical behavior, and dissipative spin dynamics in the spin-boson model.

Computational efficiency improvements for image colorization

NASA Astrophysics Data System (ADS)

Yu, Chao; Sharma, Gaurav; Aly, Hussein

2013-03-01

We propose an efficient algorithm for colorization of greyscale images. As in prior work, colorization is posed as an optimization problem: a user specifies the color for a few scribbles drawn on the greyscale image and the color image is obtained by propagating color information from the scribbles to surrounding regions, while maximizing the local smoothness of colors. In this formulation, colorization is obtained by solving a large sparse linear system, which normally requires substantial computation and memory resources. Our algorithm improves the computational performance through three innovations over prior colorization implementations. First, the linear system is solved iteratively without explicitly constructing the sparse matrix, which significantly reduces the required memory. Second, we formulate each iteration in terms of integral images obtained by dynamic programming, reducing repetitive computation. Third, we use a coarseto- fine framework, where a lower resolution subsampled image is first colorized and this low resolution color image is upsampled to initialize the colorization process for the fine level. The improvements we develop provide significant speedup and memory savings compared to the conventional approach of solving the linear system directly using off-the-shelf sparse solvers, and allow us to colorize images with typical sizes encountered in realistic applications on typical commodity computing platforms.

A new modal superposition method for nonlinear vibration analysis of structures using hybrid mode shapes

NASA Astrophysics Data System (ADS)

Ferhatoglu, Erhan; Cigeroglu, Ender; Özgüven, H. Nevzat

2018-07-01

In this paper, a new modal superposition method based on a hybrid mode shape concept is developed for the determination of steady state vibration response of nonlinear structures. The method is developed specifically for systems having nonlinearities where the stiffness of the system may take different limiting values. Stiffness variation of these nonlinear systems enables one to define different linear systems corresponding to each value of the limiting equivalent stiffness. Moreover, the response of the nonlinear system is bounded by the confinement of these linear systems. In this study, a modal superposition method utilizing novel hybrid mode shapes which are defined as linear combinations of the modal vectors of the limiting linear systems is proposed to determine periodic response of nonlinear systems. In this method the response of the nonlinear system is written in terms of hybrid modes instead of the modes of the underlying linear system. This provides decrease of the number of modes that should be retained for an accurate solution, which in turn reduces the number of nonlinear equations to be solved. In this way, computational time for response calculation is directly curtailed. In the solution, the equations of motion are converted to a set of nonlinear algebraic equations by using describing function approach, and the numerical solution is obtained by using Newton's method with arc-length continuation. The method developed is applied on two different systems: a lumped parameter model and a finite element model. Several case studies are performed and the accuracy and computational efficiency of the proposed modal superposition method with hybrid mode shapes are compared with those of the classical modal superposition method which utilizes the mode shapes of the underlying linear system.

FINAL REPORT (MILESTONE DATE 9/30/11) FOR SUBCONTRACT NO. B594099 NUMERICAL METHODS FOR LARGE-SCALE DATA FACTORIZATION

DOE Office of Scientific and Technical Information (OSTI.GOV)

De Sterck, H

2011-10-18

The following work has been performed by PI Hans De Sterck and graduate student Manda Winlaw for the required tasks 1-5 (as listed in the Statement of Work). Graduate student Manda Winlaw has visited LLNL January 31-March 11, 2011 and May 23-August 19, 2010, working with Van Henson and Mike O'Hara on non-negative matrix factorizations (NMF). She has investigated the dense subgraph clustering algorithm from 'Finding Dense Subgraphs for Sparse Undirected, Directed, and Bipartite Graphs' by Chen and Saad, testing this method on several term-document matrices and adapting it to cluster based on the rank of the subgraphs instead ofmore » the density. Manda Winlaw was awarded a first prize in the annual LLNL summer student poster competition for a poster on her NMF research. PI Hans De Sterck has developed a new adaptive algebraic multigrid algorithm for computing a few dominant or minimal singular triplets of sparse rectangular matrices. This work builds on adaptive algebraic multigrid methods that were further developed by the PI and collaborators (including Sanders and Henson) for Markov chains. The method also combines and extends existing multigrid algorithms for the symmetric eigenproblem. The PI has visited LLNL February 22-25, 2011, and has given a CASC seminar 'Algebraic Multigrid for the Singular Value Problem' on this work on February 23, 2011. During his visit, he has discussed this work and related topics with Van Henson, Geoffrey Sanders, Panayot Vassilevski, and others. He has tested the algorithm on PDE matrices and on a term-document matrix, with promising initial results. Manda Winlaw has also started to work, with O'Hara, on estimating probability distributions over undirected graph edges. The goal is to estimate probabilistic models from sets of undirected graph edges for the purpose of prediction, anomaly detection and support to supervised learning. Graduate student Manda Winlaw is writing a paper on the results obtained with O'Hara which will be submitted some time later in 2011 to a data mining conference. PI Hans De Sterck has developed a new optimization algorithm for canonical tensor approximation, formulating an extension of the nonlinear GMRES method to optimization problems. Numerical results for tensors with up to 8 modes show that this new method is efficient for sparse and dense tensors. He has written a paper on this which has been submitted to the SIAM Journal on Scientific Computing. PI Hans De Sterck has further developed his new optimization algorithm for canonical tensor approximation, formulating an extension in terms of steepest-descent preconditioning, which makes the approach generally applicable for nonlinear optimization. He has written a paper on this extension which has been submitted to Numerical Linear Algebra with Applications.« less

A study of machine learning regression methods for major elemental analysis of rocks using laser-induced breakdown spectroscopy

NASA Astrophysics Data System (ADS)

Boucher, Thomas F.; Ozanne, Marie V.; Carmosino, Marco L.; Dyar, M. Darby; Mahadevan, Sridhar; Breves, Elly A.; Lepore, Kate H.; Clegg, Samuel M.

2015-05-01

The ChemCam instrument on the Mars Curiosity rover is generating thousands of LIBS spectra and bringing interest in this technique to public attention. The key to interpreting Mars or any other types of LIBS data are calibrations that relate laboratory standards to unknowns examined in other settings and enable predictions of chemical composition. Here, LIBS spectral data are analyzed using linear regression methods including partial least squares (PLS-1 and PLS-2), principal component regression (PCR), least absolute shrinkage and selection operator (lasso), elastic net, and linear support vector regression (SVR-Lin). These were compared against results from nonlinear regression methods including kernel principal component regression (K-PCR), polynomial kernel support vector regression (SVR-Py) and k-nearest neighbor (kNN) regression to discern the most effective models for interpreting chemical abundances from LIBS spectra of geological samples. The results were evaluated for 100 samples analyzed with 50 laser pulses at each of five locations averaged together. Wilcoxon signed-rank tests were employed to evaluate the statistical significance of differences among the nine models using their predicted residual sum of squares (PRESS) to make comparisons. For MgO, SiO2, Fe2O3, CaO, and MnO, the sparse models outperform all the others except for linear SVR, while for Na2O, K2O, TiO2, and P2O5, the sparse methods produce inferior results, likely because their emission lines in this energy range have lower transition probabilities. The strong performance of the sparse methods in this study suggests that use of dimensionality-reduction techniques as a preprocessing step may improve the performance of the linear models. Nonlinear methods tend to overfit the data and predict less accurately, while the linear methods proved to be more generalizable with better predictive performance. These results are attributed to the high dimensionality of the data (6144 channels) relative to the small number of samples studied. The best-performing models were SVR-Lin for SiO2, MgO, Fe2O3, and Na2O, lasso for Al2O3, elastic net for MnO, and PLS-1 for CaO, TiO2, and K2O. Although these differences in model performance between methods were identified, most of the models produce comparable results when p ≤ 0.05 and all techniques except kNN produced statistically-indistinguishable results. It is likely that a combination of models could be used together to yield a lower total error of prediction, depending on the requirements of the user.

Nonlinear dynamics and control of a vibrating rectangular plate

NASA Technical Reports Server (NTRS)

Shebalin, J. V.

1983-01-01

The von Karman equations of nonlinear elasticity are solved for the case of a vibrating rectangular plate by meams of a Fourier spectral transform method. The amplification of a particular Fourier mode by nonlinear transfer of energy is demonstrated for this conservative system. The multi-mode system is reduced to a minimal (two mode) system, retaining the qualitative features of the multi-mode system. The effect of a modal control law on the dynamics of this minimal nonlinear elastic system is examined.

Optimization-Based Robust Nonlinear Control

DTIC Science & Technology

2006-08-01

ABSTRACT New control algorithms were developed for robust stabilization of nonlinear dynamical systems . Novel, linear matrix inequality-based synthesis...was to further advance optimization-based robust nonlinear control design, for general nonlinear systems (especially in discrete time ), for linear...Teel, IEEE Transactions on Control Systems Technology, vol. 14, no. 3, p. 398-407, May 2006. 3. "A unified framework for input-to-state stability in

Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method.

PubMed

He, Xiaowei; Liang, Jimin; Wang, Xiaorui; Yu, Jingjing; Qu, Xiaochao; Wang, Xiaodong; Hou, Yanbin; Chen, Duofang; Liu, Fang; Tian, Jie

2010-11-22

In this paper, we present an incomplete variables truncated conjugate gradient (IVTCG) method for bioluminescence tomography (BLT). Considering the sparse characteristic of the light source and insufficient surface measurement in the BLT scenarios, we combine a sparseness-inducing (ℓ1 norm) regularization term with a quadratic error term in the IVTCG-based framework for solving the inverse problem. By limiting the number of variables updated at each iterative and combining a variable splitting strategy to find the search direction more efficiently, it obtains fast and stable source reconstruction, even without a priori information of the permissible source region and multispectral measurements. Numerical experiments on a mouse atlas validate the effectiveness of the method. In vivo mouse experimental results further indicate its potential for a practical BLT system.

Finite difference method accelerated with sparse solvers for structural analysis of the metal-organic complexes

NASA Astrophysics Data System (ADS)

Guda, A. A.; Guda, S. A.; Soldatov, M. A.; Lomachenko, K. A.; Bugaev, A. L.; Lamberti, C.; Gawelda, W.; Bressler, C.; Smolentsev, G.; Soldatov, A. V.; Joly, Y.

2016-05-01

Finite difference method (FDM) implemented in the FDMNES software [Phys. Rev. B, 2001, 63, 125120] was revised. Thorough analysis shows, that the calculated diagonal in the FDM matrix consists of about 96% zero elements. Thus a sparse solver would be more suitable for the problem instead of traditional Gaussian elimination for the diagonal neighbourhood. We have tried several iterative sparse solvers and the direct one MUMPS solver with METIS ordering turned out to be the best. Compared to the Gaussian solver present method is up to 40 times faster and allows XANES simulations for complex systems already on personal computers. We show applicability of the software for metal-organic [Fe(bpy)3]2+ complex both for low spin and high spin states populated after laser excitation.

Automatic segmentation of brain MRI in high-dimensional local and non-local feature space based on sparse representation.

PubMed

Khalilzadeh, Mohammad Mahdi; Fatemizadeh, Emad; Behnam, Hamid

2013-06-01

Automatic extraction of the varying regions of magnetic resonance images is required as a prior step in a diagnostic intelligent system. The sparsest representation and high-dimensional feature are provided based on learned dictionary. The classification is done by employing the technique that computes the reconstruction error locally and non-locally of each pixel. The acquired results from the real and simulated images are superior to the best MRI segmentation method with regard to the stability advantages. In addition, it is segmented exactly through a formula taken from the distance and sparse factors. Also, it is done automatically taking sparse factor in unsupervised clustering methods whose results have been improved. Copyright © 2013 Elsevier Inc. All rights reserved.

Sustainability science: accounting for nonlinear dynamics in policy and social-ecological systems

EPA Science Inventory

Resilience is an emergent property of complex systems. Understanding resilience is critical for sustainability science, as linked social-ecological systems and the policy process that governs them are characterized by non-linear dynamics. Non-linear dynamics in these systems mean...

Dynamics of cochlear nonlinearity: Automatic gain control or instantaneous damping?

PubMed

Altoè, Alessandro; Charaziak, Karolina K; Shera, Christopher A

2017-12-01

Measurements of basilar-membrane (BM) motion show that the compressive nonlinearity of cochlear mechanical responses is not an instantaneous phenomenon. For this reason, the cochlear amplifier has been thought to incorporate an automatic gain control (AGC) mechanism characterized by a finite reaction time. This paper studies the effect of instantaneous nonlinear damping on the responses of oscillatory systems. The principal results are that (i) instantaneous nonlinear damping produces a noninstantaneous gain control that differs markedly from typical AGC strategies; (ii) the kinetics of compressive nonlinearity implied by the finite reaction time of an AGC system appear inconsistent with the nonlinear dynamics measured on the gerbil basilar membrane; and (iii) conversely, those nonlinear dynamics can be reproduced using an harmonic oscillator with instantaneous nonlinear damping. Furthermore, existing cochlear models that include instantaneous gain-control mechanisms capture the principal kinetics of BM nonlinearity. Thus, an AGC system with finite reaction time appears neither necessary nor sufficient to explain nonlinear gain control in the cochlea.

Chirped solitary pulses for a nonic nonlinear Schrödinger equation on a continuous-wave background

NASA Astrophysics Data System (ADS)

Triki, Houria; Porsezian, K.; Choudhuri, Amitava; Dinda, P. Tchofo

2016-06-01

A class of derivative nonlinear Schrödinger equation with cubic-quintic-septic-nonic nonlinear terms describing the propagation of ultrashort optical pulses through a nonlinear medium with higher-order Kerr responses is investigated. An intensity-dependent chirp ansatz is adopted for solving the two coupled amplitude-phase nonlinear equations of the propagating wave. We find that the dynamics of field amplitude in this system is governed by a first-order nonlinear ordinary differential equation with a tenth-degree nonlinear term. We demonstrate that this system allows the propagation of a very rich variety of solitary waves (kink, dark, bright, and gray solitary pulses) which do not coexist in the conventional nonlinear systems that have appeared so far in the literature. The stability of the solitary wave solution under some violation on the parametric conditions is investigated. Moreover, we show that, unlike conventional systems, the nonlinear Schrödinger equation considered here meets the special requirements for the propagation of a chirped solitary wave on a continuous-wave background, involving a balance among group velocity dispersion, self-steepening, and higher-order nonlinearities of different nature.

Nonlinear normal modes in electrodynamic systems: A nonperturbative approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kudrin, A. V., E-mail: kud@rf.unn.ru; Kudrina, O. A.; Petrov, E. Yu.

2016-06-15

We consider electromagnetic nonlinear normal modes in cylindrical cavity resonators filled with a nonlinear nondispersive medium. The key feature of the analysis is that exact analytic solutions of the nonlinear field equations are employed to study the mode properties in detail. Based on such a nonperturbative approach, we rigorously prove that the total energy of free nonlinear oscillations in a distributed conservative system, such as that considered in our work, can exactly coincide with the sum of energies of the normal modes of the system. This fact implies that the energy orthogonality property, which has so far been known tomore » hold only for linear oscillations and fields, can also be observed in a nonlinear oscillatory system.« less

Linear and non-linear dynamic models of a geared rotor-bearing system

NASA Technical Reports Server (NTRS)

Kahraman, Ahmet; Singh, Rajendra

1990-01-01

A three degree of freedom non-linear model of a geared rotor-bearing system with gear backlash and radial clearances in rolling element bearings is proposed here. This reduced order model can be used to describe the transverse-torsional motion of the system. It is justified by comparing the eigen solutions yielded by corresponding linear model with the finite element method results. Nature of nonlinearities in bearings is examined and two approximate nonlinear stiffness functions are proposed. These approximate bearing models are verified by comparing their frequency responses with the results given by the exact form of nonlinearity. The proposed nonlinear dynamic model of the geared rotor-bearing system can be used to investigate the dynamic behavior and chaos.

Integrable pair-transition-coupled nonlinear Schrödinger equations.

PubMed

Ling, Liming; Zhao, Li-Chen

2015-08-01

We study integrable coupled nonlinear Schrödinger equations with pair particle transition between components. Based on exact solutions of the coupled model with attractive or repulsive interaction, we predict that some new dynamics of nonlinear excitations can exist, such as the striking transition dynamics of breathers, new excitation patterns for rogue waves, topological kink excitations, and other new stable excitation structures. In particular, we find that nonlinear wave solutions of this coupled system can be written as a linear superposition of solutions for the simplest scalar nonlinear Schrödinger equation. Possibilities to observe them are discussed in a cigar-shaped Bose-Einstein condensate with two hyperfine states. The results would enrich our knowledge on nonlinear excitations in many coupled nonlinear systems with transition coupling effects, such as multimode nonlinear fibers, coupled waveguides, and a multicomponent Bose-Einstein condensate system.

An oscillating wave energy converter with nonlinear snap-through Power-Take-Off systems in regular waves

NASA Astrophysics Data System (ADS)

Zhang, Xian-tao; Yang, Jian-min; Xiao, Long-fei

2016-07-01

Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off (PTO) system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.

Robust nonlinear variable selective control for networked systems

NASA Astrophysics Data System (ADS)

Rahmani, Behrooz

2016-10-01

This paper is concerned with the networked control of a class of uncertain nonlinear systems. In this way, Takagi-Sugeno (T-S) fuzzy modelling is used to extend the previously proposed variable selective control (VSC) methodology to nonlinear systems. This extension is based upon the decomposition of the nonlinear system to a set of fuzzy-blended locally linearised subsystems and further application of the VSC methodology to each subsystem. To increase the applicability of the T-S approach for uncertain nonlinear networked control systems, this study considers the asynchronous premise variables in the plant and the controller, and then introduces a robust stability analysis and control synthesis. The resulting optimal switching-fuzzy controller provides a minimum guaranteed cost on an H2 performance index. Simulation studies on three nonlinear benchmark problems demonstrate the effectiveness of the proposed method.

Robust Pedestrian Tracking and Recognition from FLIR Video: A Unified Approach via Sparse Coding

PubMed Central

Li, Xin; Guo, Rui; Chen, Chao

2014-01-01

Sparse coding is an emerging method that has been successfully applied to both robust object tracking and recognition in the vision literature. In this paper, we propose to explore a sparse coding-based approach toward joint object tracking-and-recognition and explore its potential in the analysis of forward-looking infrared (FLIR) video to support nighttime machine vision systems. A key technical contribution of this work is to unify existing sparse coding-based approaches toward tracking and recognition under the same framework, so that they can benefit from each other in a closed-loop. On the one hand, tracking the same object through temporal frames allows us to achieve improved recognition performance through dynamical updating of template/dictionary and combining multiple recognition results; on the other hand, the recognition of individual objects facilitates the tracking of multiple objects (i.e., walking pedestrians), especially in the presence of occlusion within a crowded environment. We report experimental results on both the CASIAPedestrian Database and our own collected FLIR video database to demonstrate the effectiveness of the proposed joint tracking-and-recognition approach. PMID:24961216

Exact recovery of sparse multiple measurement vectors by [Formula: see text]-minimization.

PubMed

Wang, Changlong; Peng, Jigen

2018-01-01

The joint sparse recovery problem is a generalization of the single measurement vector problem widely studied in compressed sensing. It aims to recover a set of jointly sparse vectors, i.e., those that have nonzero entries concentrated at a common location. Meanwhile [Formula: see text]-minimization subject to matrixes is widely used in a large number of algorithms designed for this problem, i.e., [Formula: see text]-minimization [Formula: see text] Therefore the main contribution in this paper is two theoretical results about this technique. The first one is proving that in every multiple system of linear equations there exists a constant [Formula: see text] such that the original unique sparse solution also can be recovered from a minimization in [Formula: see text] quasi-norm subject to matrixes whenever [Formula: see text]. The other one is showing an analytic expression of such [Formula: see text]. Finally, we display the results of one example to confirm the validity of our conclusions, and we use some numerical experiments to show that we increase the efficiency of these algorithms designed for [Formula: see text]-minimization by using our results.

The HTM Spatial Pooler-A Neocortical Algorithm for Online Sparse Distributed Coding.

PubMed

Cui, Yuwei; Ahmad, Subutai; Hawkins, Jeff

2017-01-01

Hierarchical temporal memory (HTM) provides a theoretical framework that models several key computational principles of the neocortex. In this paper, we analyze an important component of HTM, the HTM spatial pooler (SP). The SP models how neurons learn feedforward connections and form efficient representations of the input. It converts arbitrary binary input patterns into sparse distributed representations (SDRs) using a combination of competitive Hebbian learning rules and homeostatic excitability control. We describe a number of key properties of the SP, including fast adaptation to changing input statistics, improved noise robustness through learning, efficient use of cells, and robustness to cell death. In order to quantify these properties we develop a set of metrics that can be directly computed from the SP outputs. We show how the properties are met using these metrics and targeted artificial simulations. We then demonstrate the value of the SP in a complete end-to-end real-world HTM system. We discuss the relationship with neuroscience and previous studies of sparse coding. The HTM spatial pooler represents a neurally inspired algorithm for learning sparse representations from noisy data streams in an online fashion.

Nonlinear stability and control study of highly maneuverable high performance aircraft, phase 2

NASA Technical Reports Server (NTRS)

Mohler, R. R.

1992-01-01

Research leading to the development of new nonlinear methodologies for the adaptive control and stability analysis of high angle of attack aircraft such as the F-18 is discussed. The emphasis has been on nonlinear adaptive control, but associated model development, system identification, stability analysis, and simulation were studied in some detail as well. Studies indicated that nonlinear adaptive control can outperform linear adaptive control for rapid maneuvers with large changes in angle of attack. Included here are studies on nonlinear model algorithmic controller design and an analysis of nonlinear system stability using robust stability analysis for linear systems.

Automatic Management of Parallel and Distributed System Resources

NASA Technical Reports Server (NTRS)

Yan, Jerry; Ngai, Tin Fook; Lundstrom, Stephen F.

1990-01-01

Viewgraphs on automatic management of parallel and distributed system resources are presented. Topics covered include: parallel applications; intelligent management of multiprocessing systems; performance evaluation of parallel architecture; dynamic concurrent programs; compiler-directed system approach; lattice gaseous cellular automata; and sparse matrix Cholesky factorization.

Leaderless consensus for the fractional-order nonlinear multi-agent systems under directed interaction topology

NASA Astrophysics Data System (ADS)

Bai, Jing; Wen, Guoguang; Rahmani, Ahmed

2018-04-01

Leaderless consensus for the fractional-order nonlinear multi-agent systems is investigated in this paper. At the first part, a control protocol is proposed to achieve leaderless consensus for the nonlinear single-integrator multi-agent systems. At the second part, based on sliding mode estimator, a control protocol is given to solve leaderless consensus for the the nonlinear single-integrator multi-agent systems. It shows that the control protocol can improve the systems' convergence speed. At the third part, a control protocol is designed to accomplish leaderless consensus for the nonlinear double-integrator multi-agent systems. To judge the systems' stability in this paper, two classic continuous Lyapunov candidate functions are chosen. Finally, several worked out examples under directed interaction topology are given to prove above results.

JDINAC: joint density-based non-parametric differential interaction network analysis and classification using high-dimensional sparse omics data.

PubMed

Ji, Jiadong; He, Di; Feng, Yang; He, Yong; Xue, Fuzhong; Xie, Lei

2017-10-01

A complex disease is usually driven by a number of genes interwoven into networks, rather than a single gene product. Network comparison or differential network analysis has become an important means of revealing the underlying mechanism of pathogenesis and identifying clinical biomarkers for disease classification. Most studies, however, are limited to network correlations that mainly capture the linear relationship among genes, or rely on the assumption of a parametric probability distribution of gene measurements. They are restrictive in real application. We propose a new Joint density based non-parametric Differential Interaction Network Analysis and Classification (JDINAC) method to identify differential interaction patterns of network activation between two groups. At the same time, JDINAC uses the network biomarkers to build a classification model. The novelty of JDINAC lies in its potential to capture non-linear relations between molecular interactions using high-dimensional sparse data as well as to adjust confounding factors, without the need of the assumption of a parametric probability distribution of gene measurements. Simulation studies demonstrate that JDINAC provides more accurate differential network estimation and lower classification error than that achieved by other state-of-the-art methods. We apply JDINAC to a Breast Invasive Carcinoma dataset, which includes 114 patients who have both tumor and matched normal samples. The hub genes and differential interaction patterns identified were consistent with existing experimental studies. Furthermore, JDINAC discriminated the tumor and normal sample with high accuracy by virtue of the identified biomarkers. JDINAC provides a general framework for feature selection and classification using high-dimensional sparse omics data. R scripts available at https://github.com/jijiadong/JDINAC. lxie@iscb.org. Supplementary data are available at Bioinformatics online. © The Author (2017). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ahlfeld, R., E-mail: r.ahlfeld14@imperial.ac.uk; Belkouchi, B.; Montomoli, F.

2016-09-01

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrixmore » is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10 different input distributions or histograms.« less

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

NASA Astrophysics Data System (ADS)

Ahlfeld, R.; Belkouchi, B.; Montomoli, F.

2016-09-01

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrix is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10 different input distributions or histograms.

Short-Time Nonlinear Effects in the Exciton-Polariton System

NASA Astrophysics Data System (ADS)

Guevara, Cristi D.; Shipman, Stephen P.

2018-04-01

In the exciton-polariton system, a linear dispersive photon field is coupled to a nonlinear exciton field. Short-time analysis of the lossless system shows that, when the photon field is excited, the time required for that field to exhibit nonlinear effects is longer than the time required for the nonlinear Schrödinger equation, in which the photon field itself is nonlinear. When the initial condition is scaled by ɛ ^α , it is found that the relative error committed by omitting the nonlinear term in the exciton-polariton system remains within ɛ for all times up to t=Cɛ ^β , where β =(1-α (p-1))/(p+2). This is in contrast to β =1-α (p-1) for the nonlinear Schrödinger equation. The result is proved for solutions in H^s(R^n) for s>n/2. Numerical computations indicate that the results are sharp and also hold in L^2(R^n).

Equivalent reduced model technique development for nonlinear system dynamic response

NASA Astrophysics Data System (ADS)

Thibault, Louis; Avitabile, Peter; Foley, Jason; Wolfson, Janet

2013-04-01

The dynamic response of structural systems commonly involves nonlinear effects. Often times, structural systems are made up of several components, whose individual behavior is essentially linear compared to the total assembled system. However, the assembly of linear components using highly nonlinear connection elements or contact regions causes the entire system to become nonlinear. Conventional transient nonlinear integration of the equations of motion can be extremely computationally intensive, especially when the finite element models describing the components are very large and detailed. In this work, the equivalent reduced model technique (ERMT) is developed to address complicated nonlinear contact problems. ERMT utilizes a highly accurate model reduction scheme, the System equivalent reduction expansion process (SEREP). Extremely reduced order models that provide dynamic characteristics of linear components, which are interconnected with highly nonlinear connection elements, are formulated with SEREP for the dynamic response evaluation using direct integration techniques. The full-space solution will be compared to the response obtained using drastically reduced models to make evident the usefulness of the technique for a variety of analytical cases.

Digital nonlinearity compensation in high-capacity optical communication systems considering signal spectral broadening effect.

PubMed

Xu, Tianhua; Karanov, Boris; Shevchenko, Nikita A; Lavery, Domaniç; Liga, Gabriele; Killey, Robert I; Bayvel, Polina

2017-10-11

Nyquist-spaced transmission and digital signal processing have proved effective in maximising the spectral efficiency and reach of optical communication systems. In these systems, Kerr nonlinearity determines the performance limits, and leads to spectral broadening of the signals propagating in the fibre. Although digital nonlinearity compensation was validated to be promising for mitigating Kerr nonlinearities, the impact of spectral broadening on nonlinearity compensation has never been quantified. In this paper, the performance of multi-channel digital back-propagation (MC-DBP) for compensating fibre nonlinearities in Nyquist-spaced optical communication systems is investigated, when the effect of signal spectral broadening is considered. It is found that accounting for the spectral broadening effect is crucial for achieving the best performance of DBP in both single-channel and multi-channel communication systems, independent of modulation formats used. For multi-channel systems, the degradation of DBP performance due to neglecting the spectral broadening effect in the compensation is more significant for outer channels. Our work also quantified the minimum bandwidths of optical receivers and signal processing devices to ensure the optimal compensation of deterministic nonlinear distortions.

A Sparse Reconstruction Approach for Identifying Gene Regulatory Networks Using Steady-State Experiment Data

PubMed Central

Zhang, Wanhong; Zhou, Tong

2015-01-01

Motivation Identifying gene regulatory networks (GRNs) which consist of a large number of interacting units has become a problem of paramount importance in systems biology. Situations exist extensively in which causal interacting relationships among these units are required to be reconstructed from measured expression data and other a priori information. Though numerous classical methods have been developed to unravel the interactions of GRNs, these methods either have higher computing complexities or have lower estimation accuracies. Note that great similarities exist between identification of genes that directly regulate a specific gene and a sparse vector reconstruction, which often relates to the determination of the number, location and magnitude of nonzero entries of an unknown vector by solving an underdetermined system of linear equations y = Φx. Based on these similarities, we propose a novel framework of sparse reconstruction to identify the structure of a GRN, so as to increase accuracy of causal regulation estimations, as well as to reduce their computational complexity. Results In this paper, a sparse reconstruction framework is proposed on basis of steady-state experiment data to identify GRN structure. Different from traditional methods, this approach is adopted which is well suitable for a large-scale underdetermined problem in inferring a sparse vector. We investigate how to combine the noisy steady-state experiment data and a sparse reconstruction algorithm to identify causal relationships. Efficiency of this method is tested by an artificial linear network, a mitogen-activated protein kinase (MAPK) pathway network and the in silico networks of the DREAM challenges. The performance of the suggested approach is compared with two state-of-the-art algorithms, the widely adopted total least-squares (TLS) method and those available results on the DREAM project. Actual results show that, with a lower computational cost, the proposed method can significantly enhance estimation accuracy and greatly reduce false positive and negative errors. Furthermore, numerical calculations demonstrate that the proposed algorithm may have faster convergence speed and smaller fluctuation than other methods when either estimate error or estimate bias is considered. PMID:26207991

General implementation of arbitrary nonlinear quadrature phase gates

NASA Astrophysics Data System (ADS)

Marek, Petr; Filip, Radim; Ogawa, Hisashi; Sakaguchi, Atsushi; Takeda, Shuntaro; Yoshikawa, Jun-ichi; Furusawa, Akira

2018-02-01

We propose general methodology of deterministic single-mode quantum interaction nonlinearly modifying single quadrature variable of a continuous-variable system. The methodology is based on linear coupling of the system to ancillary systems subsequently measured by quadrature detectors. The nonlinear interaction is obtained by using the data from the quadrature detection for dynamical manipulation of the coupling parameters. This measurement-induced methodology enables direct realization of arbitrary nonlinear quadrature interactions without the need to construct them from the lowest-order gates. Such nonlinear interactions are crucial for more practical and efficient manipulation of continuous quadrature variables as well as qubits encoded in continuous-variable systems.

Gradient-based optimization with B-splines on sparse grids for solving forward-dynamics simulations of three-dimensional, continuum-mechanical musculoskeletal system models.

PubMed

Valentin, J; Sprenger, M; Pflüger, D; Röhrle, O

2018-05-01

Investigating the interplay between muscular activity and motion is the basis to improve our understanding of healthy or diseased musculoskeletal systems. To be able to analyze the musculoskeletal systems, computational models are used. Albeit some severe modeling assumptions, almost all existing musculoskeletal system simulations appeal to multibody simulation frameworks. Although continuum-mechanical musculoskeletal system models can compensate for some of these limitations, they are essentially not considered because of their computational complexity and cost. The proposed framework is the first activation-driven musculoskeletal system model, in which the exerted skeletal muscle forces are computed using 3-dimensional, continuum-mechanical skeletal muscle models and in which muscle activations are determined based on a constraint optimization problem. Numerical feasibility is achieved by computing sparse grid surrogates with hierarchical B-splines, and adaptive sparse grid refinement further reduces the computational effort. The choice of B-splines allows the use of all existing gradient-based optimization techniques without further numerical approximation. This paper demonstrates that the resulting surrogates have low relative errors (less than 0.76%) and can be used within forward simulations that are subject to constraint optimization. To demonstrate this, we set up several different test scenarios in which an upper limb model consisting of the elbow joint, the biceps and triceps brachii, and an external load is subjected to different optimization criteria. Even though this novel method has only been demonstrated for a 2-muscle system, it can easily be extended to musculoskeletal systems with 3 or more muscles. Copyright © 2018 John Wiley & Sons, Ltd.

Nonlinear dynamics near resonances of a rotor-active magnetic bearings system with 16-pole legs and time varying stiffness

NASA Astrophysics Data System (ADS)

Wu, R. Q.; Zhang, W.; Yao, M. H.

2018-02-01

In this paper, we analyze the complicated nonlinear dynamics of rotor-active magnetic bearings (rotor-AMB) with 16-pole legs and the time varying stiffness. The magnetic force with 16-pole legs is obtained by applying the electromagnetic theory. The governing equation of motion for rotor-active magnetic bearings is derived by using the Newton's second law. The resulting dimensionless equation of motion for the rotor-AMB system is expressed as a two-degree-of-freedom nonlinear system including the parametric excitation, quadratic and cubic nonlinearities. The averaged equation of the rotor-AMB system is obtained by using the method of multiple scales when the primary parametric resonance and 1/2 subharmonic resonance are taken into account. From the frequency-response curves, it is found that there exist the phenomena of the soft-spring type nonlinearity and the hardening-spring type nonlinearity in the rotor-AMB system. The effects of different parameters on the nonlinear dynamic behaviors of the rotor-AMB system are investigated. The numerical results indicate that the periodic, quasi-periodic and chaotic motions occur alternately in the rotor-AMB system.

Nonlinear analysis of a rotor-bearing system using describing functions

NASA Astrophysics Data System (ADS)

Maraini, Daniel; Nataraj, C.

2018-04-01

This paper presents a technique for modelling the nonlinear behavior of a rotor-bearing system with Hertzian contact, clearance, and rotating unbalance. The rotor-bearing system is separated into linear and nonlinear components, and the nonlinear bearing force is replaced with an equivalent describing function gain. The describing function captures the relationship between the amplitude of the fundamental input to the nonlinearity and the fundamental output. The frequency response is constructed for various values of the clearance parameter, and the results show the presence of a jump resonance in bearings with both clearance and preload. Nonlinear hardening type behavior is observed in the case with clearance and softening behavior is observed for the case with preload. Numerical integration is also carried out on the nonlinear equations of motion showing strong agreement with the approximate solution. This work could easily be extended to include additional nonlinearities that arise from defects, providing a powerful diagnostic tool.

Solutions of the cylindrical nonlinear Maxwell equations.

PubMed

Xiong, Hao; Si, Liu-Gang; Ding, Chunling; Lü, Xin-You; Yang, Xiaoxue; Wu, Ying

2012-01-01

Cylindrical nonlinear optics is a burgeoning research area which describes cylindrical electromagnetic wave propagation in nonlinear media. Finding new exact solutions for different types of nonlinearity and inhomogeneity to describe cylindrical electromagnetic wave propagation is of great interest and meaningful for theory and application. This paper gives exact solutions for the cylindrical nonlinear Maxwell equations and presents an interesting connection between the exact solutions for different cylindrical nonlinear Maxwell equations. We also provide some examples and discussion to show the application of the results we obtained. Our results provide the basis for solving complex systems of nonlinearity and inhomogeneity with simple systems.

Efficient Implementation of an Optimal Interpolator for Large Spatial Data Sets

NASA Technical Reports Server (NTRS)

Memarsadeghi, Nargess; Mount, David M.

2007-01-01

Scattered data interpolation is a problem of interest in numerous areas such as electronic imaging, smooth surface modeling, and computational geometry. Our motivation arises from applications in geology and mining, which often involve large scattered data sets and a demand for high accuracy. The method of choice is ordinary kriging. This is because it is a best unbiased estimator. Unfortunately, this interpolant is computationally very expensive to compute exactly. For n scattered data points, computing the value of a single interpolant involves solving a dense linear system of size roughly n x n. This is infeasible for large n. In practice, kriging is solved approximately by local approaches that are based on considering only a relatively small'number of points that lie close to the query point. There are many problems with this local approach, however. The first is that determining the proper neighborhood size is tricky, and is usually solved by ad hoc methods such as selecting a fixed number of nearest neighbors or all the points lying within a fixed radius. Such fixed neighborhood sizes may not work well for all query points, depending on local density of the point distribution. Local methods also suffer from the problem that the resulting interpolant is not continuous. Meyer showed that while kriging produces smooth continues surfaces, it has zero order continuity along its borders. Thus, at interface boundaries where the neighborhood changes, the interpolant behaves discontinuously. Therefore, it is important to consider and solve the global system for each interpolant. However, solving such large dense systems for each query point is impractical. Recently a more principled approach to approximating kriging has been proposed based on a technique called covariance tapering. The problems arise from the fact that the covariance functions that are used in kriging have global support. Our implementations combine, utilize, and enhance a number of different approaches that have been introduced in literature for solving large linear systems for interpolation of scattered data points. For very large systems, exact methods such as Gaussian elimination are impractical since they require 0(n(exp 3)) time and 0(n(exp 2)) storage. As Billings et al. suggested, we use an iterative approach. In particular, we use the SYMMLQ method, for solving the large but sparse ordinary kriging systems that result from tapering. The main technical issue that need to be overcome in our algorithmic solution is that the points' covariance matrix for kriging should be symmetric positive definite. The goal of tapering is to obtain a sparse approximate representation of the covariance matrix while maintaining its positive definiteness. Furrer et al. used tapering to obtain a sparse linear system of the form Ax = b, where A is the tapered symmetric positive definite covariance matrix. Thus, Cholesky factorization could be used to solve their linear systems. They implemented an efficient sparse Cholesky decomposition method. They also showed if these tapers are used for a limited class of covariance models, the solution of the system converges to the solution of the original system. Matrix A in the ordinary kriging system, while symmetric, is not positive definite. Thus, their approach is not applicable to the ordinary kriging system. Therefore, we use tapering only to obtain a sparse linear system. Then, we use SYMMLQ to solve the ordinary kriging system. We show that solving large kriging systems becomes practical via tapering and iterative methods, and results in lower estimation errors compared to traditional local approaches, and significant memory savings compared to the original global system. We also developed a more efficient variant of the sparse SYMMLQ method for large ordinary kriging systems. This approach adaptively finds the correct local neighborhood for each query point in the interpolation process.

Investigation on the Nonlinear Control System of High-Pressure Common Rail (HPCR) System in a Diesel Engine

NASA Astrophysics Data System (ADS)

Cai, Le; Mao, Xiaobing; Ma, Zhexuan

2018-02-01

This study first constructed the nonlinear mathematical model of the high-pressure common rail (HPCR) system in the diesel engine. Then, the nonlinear state transformation was performed using the flow’s calculation and the standard state space equation was acquired. Based on sliding-mode variable structure control (SMVSC) theory, a sliding-mode controller for nonlinear systems was designed for achieving the control of common rail pressure and the diesel engine’s rotational speed. Finally, on the simulation platform of MATLAB, the designed nonlinear HPCR system was simulated. The simulation results demonstrate that sliding-mode variable structure control algorithm shows favorable control performances and overcome the shortcomings of traditional PID control in overshoot, parameter adjustment, system precision, adjustment time and ascending time.

Exact modelling of the optical bistability in ferroelectics via two-wave mixing: A system with full nonlinearity

NASA Astrophysics Data System (ADS)

Khushaini, Muhammad Asif A.; Ibrahim, Abdel-Baset M. A.; Choudhury, P. K.

2018-05-01

In this paper, we provide a complete mathematical model of the phenomenon of optical bistability (OB) resulting from the degenerate two-wave mixing (TWM) process of laser beams interacting with a single nonlinear layer of ferroelectric material. Starting with the electromagnetic wave equation for optical wave propagating in nonlinear media, a nonlinear coupled wave (CW) system with both self-phase modulation (SPM) and cross-phase modulation (XPM) sources of nonlinearity are derived. The complete CW system with full nonlinearity is solved numerically and a comparison between both the cases of with and without SPM at various combinations of design parameters is given. Furthermore, to provide a reliable theoretical model for the OB via TWM process, the results obtained theoretically are compared with the available experimental data. We found that the nonlinear system without SPM fails to predict the bistable response at lower combinations of the input parameters. However, at relatively higher values, the solution without SPM shows a reduction in the switching contrast and period in the OB response. A comparison with the experimental results shows better agreement with the system with full nonlinearity.

Signal processing using sparse derivatives with applications to chromatograms and ECG

NASA Astrophysics Data System (ADS)

Ning, Xiaoran

In this thesis, we investigate the sparsity exist in the derivative domain. Particularly, we focus on the type of signals which posses up to Mth (M > 0) order sparse derivatives. Efforts are put on formulating proper penalty functions and optimization problems to capture properties related to sparse derivatives, searching for fast, computationally efficient solvers. Also the effectiveness of these algorithms are applied to two real world applications. In the first application, we provide an algorithm which jointly addresses the problems of chromatogram baseline correction and noise reduction. The series of chromatogram peaks are modeled as sparse with sparse derivatives, and the baseline is modeled as a low-pass signal. A convex optimization problem is formulated so as to encapsulate these non-parametric models. To account for the positivity of chromatogram peaks, an asymmetric penalty function is also utilized with symmetric penalty functions. A robust, computationally efficient, iterative algorithm is developed that is guaranteed to converge to the unique optimal solution. The approach, termed Baseline Estimation And Denoising with Sparsity (BEADS), is evaluated and compared with two state-of-the-art methods using both simulated and real chromatogram data. Promising result is obtained. In the second application, a novel Electrocardiography (ECG) enhancement algorithm is designed also based on sparse derivatives. In the real medical environment, ECG signals are often contaminated by various kinds of noise or artifacts, for example, morphological changes due to motion artifact, non-stationary noise due to muscular contraction (EMG), etc. Some of these contaminations severely affect the usefulness of ECG signals, especially when computer aided algorithms are utilized. By solving the proposed convex l1 optimization problem, artifacts are reduced by modeling the clean ECG signal as a sum of two signals whose second and third-order derivatives (differences) are sparse respectively. At the end, the algorithm is applied to a QRS detection system and validated using the MIT-BIH Arrhythmia database (109452 anotations), resulting a sensitivity of Se = 99.87%$ and a positive prediction of +P = 99.88%.

Reinforcement-learning-based dual-control methodology for complex nonlinear discrete-time systems with application to spark engine EGR operation.

PubMed

Shih, Peter; Kaul, Brian C; Jagannathan, S; Drallmeier, James A

2008-08-01

A novel reinforcement-learning-based dual-control methodology adaptive neural network (NN) controller is developed to deliver a desired tracking performance for a class of complex feedback nonlinear discrete-time systems, which consists of a second-order nonlinear discrete-time system in nonstrict feedback form and an affine nonlinear discrete-time system, in the presence of bounded and unknown disturbances. For example, the exhaust gas recirculation (EGR) operation of a spark ignition (SI) engine is modeled by using such a complex nonlinear discrete-time system. A dual-controller approach is undertaken where primary adaptive critic NN controller is designed for the nonstrict feedback nonlinear discrete-time system whereas the secondary one for the affine nonlinear discrete-time system but the controllers together offer the desired performance. The primary adaptive critic NN controller includes an NN observer for estimating the states and output, an NN critic, and two action NNs for generating virtual control and actual control inputs for the nonstrict feedback nonlinear discrete-time system, whereas an additional critic NN and an action NN are included for the affine nonlinear discrete-time system by assuming the state availability. All NN weights adapt online towards minimization of a certain performance index, utilizing gradient-descent-based rule. Using Lyapunov theory, the uniformly ultimate boundedness (UUB) of the closed-loop tracking error, weight estimates, and observer estimates are shown. The adaptive critic NN controller performance is evaluated on an SI engine operating with high EGR levels where the controller objective is to reduce cyclic dispersion in heat release while minimizing fuel intake. Simulation and experimental results indicate that engine out emissions drop significantly at 20% EGR due to reduction in dispersion in heat release thus verifying the dual-control approach.

An experimental study of nonlinear dynamic system identification

NASA Technical Reports Server (NTRS)

Stry, Greselda I.; Mook, D. Joseph

1990-01-01

A technique for robust identification of nonlinear dynamic systems is developed and illustrated using both simulations and analog experiments. The technique is based on the Minimum Model Error optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature of the current work is the ability to identify nonlinear dynamic systems without prior assumptions regarding the form of the nonlinearities, in constrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length.

A methodology for designing robust multivariable nonlinear control systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Grunberg, D. B.

1986-01-01

A new methodology is described for the design of nonlinear dynamic controllers for nonlinear multivariable systems providing guarantees of closed-loop stability, performance, and robustness. The methodology is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate inverse operator for the plant. A major feature of the methodology is a unification of both the state-space and input-output formulations. In addition, new results on stability theory, nonlinear state estimation, and optimal nonlinear regulator theory are presented, including the guaranteed global properties of the extended Kalman filter and optimal nonlinear regulators.

Controllable nonlinearity in a dual-coupling optomechanical system under a weak-coupling regime

NASA Astrophysics Data System (ADS)

Zhu, Gui-Lei; Lü, Xin-You; Wan, Liang-Liang; Yin, Tai-Shuang; Bin, Qian; Wu, Ying

2018-03-01

Strong quantum nonlinearity gives rise to many interesting quantum effects and has wide applications in quantum physics. Here we investigate the quantum nonlinear effect of an optomechanical system (OMS) consisting of both linear and quadratic coupling. Interestingly, a controllable optomechanical nonlinearity is obtained by applying a driving laser into the cavity. This controllable optomechanical nonlinearity can be enhanced into a strong coupling regime, even if the system is initially in the weak-coupling regime. Moreover, the system dissipation can be suppressed effectively, which allows the appearance of phonon sideband and photon blockade effects in the weak-coupling regime. This work may inspire the exploration of a dual-coupling optomechanical system as well as its applications in modern quantum science.

Controllability in nonlinear systems

NASA Technical Reports Server (NTRS)

Hirschorn, R. M.

1975-01-01

An explicit expression for the reachable set is obtained for a class of nonlinear systems. This class is described by a chain condition on the Lie algebra of vector fields associated with each nonlinear system. These ideas are used to obtain a generalization of a controllability result for linear systems in the case where multiplicative controls are present.

A Teaching and Learning Sequence about the Interplay of Chance and Determinism in Nonlinear Systems

ERIC Educational Resources Information Center

Stavrou, D.; Duit, R.; Komorek, M.

2008-01-01

A teaching and learning sequence aimed at introducing upper secondary school students to the interplay between chance and determinism in nonlinear systems is presented. Three experiments concerning nonlinear systems (deterministic chaos, self-organization and fractals) and one experiment concerning linear systems are introduced. Thirty upper…

Reservoir Computing Beyond Memory-Nonlinearity Trade-off.

PubMed

Inubushi, Masanobu; Yoshimura, Kazuyuki

2017-08-31

Reservoir computing is a brain-inspired machine learning framework that employs a signal-driven dynamical system, in particular harnessing common-signal-induced synchronization which is a widely observed nonlinear phenomenon. Basic understanding of a working principle in reservoir computing can be expected to shed light on how information is stored and processed in nonlinear dynamical systems, potentially leading to progress in a broad range of nonlinear sciences. As a first step toward this goal, from the viewpoint of nonlinear physics and information theory, we study the memory-nonlinearity trade-off uncovered by Dambre et al. (2012). Focusing on a variational equation, we clarify a dynamical mechanism behind the trade-off, which illustrates why nonlinear dynamics degrades memory stored in dynamical system in general. Moreover, based on the trade-off, we propose a mixture reservoir endowed with both linear and nonlinear dynamics and show that it improves the performance of information processing. Interestingly, for some tasks, significant improvements are observed by adding a few linear dynamics to the nonlinear dynamical system. By employing the echo state network model, the effect of the mixture reservoir is numerically verified for a simple function approximation task and for more complex tasks.

The influence of and the identification of nonlinearity in flexible structures

NASA Technical Reports Server (NTRS)

Zavodney, Lawrence D.

1988-01-01

Several models were built at NASA Langley and used to demonstrate the following nonlinear behavior: internal resonance in a free response, principal parametric resonance and subcritical instability in a cantilever beam-lumped mass structure, combination resonance in a parametrically excited flexible beam, autoparametric interaction in a two-degree-of-freedom system, instability of the linear solution, saturation of the excited mode, subharmonic bifurcation, and chaotic responses. A video tape documenting these phenomena was made. An attempt to identify a simple structure consisting of two light-weight beams and two lumped masses using the Eigensystem Realization Algorithm showed the inherent difficulty of using a linear based theory to identify a particular nonlinearity. Preliminary results show the technique requires novel interpretation, and hence may not be useful for structural modes that are coupled by a guadratic nonlinearity. A literature survey was also completed on recent work in parametrically excited nonlinear system. In summary, nonlinear systems may possess unique behaviors that require nonlinear identification techniques based on an understanding of how nonlinearity affects the dynamic response of structures. In this was, the unique behaviors of nonlinear systems may be properly identified. Moreover, more accutate quantifiable estimates can be made once the qualitative model has been determined.

Nonlinear stability research on the hydraulic system of double-side rolling shear.

PubMed

Wang, Jun; Huang, Qingxue; An, Gaocheng; Qi, Qisong; Sun, Binyu

2015-10-01

This paper researches the stability of the nonlinear system taking the hydraulic system of double-side rolling shear as an example. The hydraulic system of double-side rolling shear uses unsymmetrical electro-hydraulic proportional servo valve to control the cylinder with single piston rod, which can make best use of the space and reduce reversing shock. It is a typical nonlinear structure. The nonlinear state-space equations of the unsymmetrical valve controlling cylinder system are built first, and the second Lyapunov method is used to evaluate its stability. Second, the software AMEsim is applied to simulate the nonlinear system, and the results indicate that the system is stable. At last, the experimental results show that the system unsymmetrical valve controlling the cylinder with single piston rod is stable and conforms to what is deduced by theoretical analysis and simulation. The construction and application of Lyapunov function not only provide the theoretical basis for using of unsymmetrical valve controlling cylinder with single piston rod but also develop a new thought for nonlinear stability evaluation.

Nonlinear stability research on the hydraulic system of double-side rolling shear

NASA Astrophysics Data System (ADS)

Wang, Jun; Huang, Qingxue; An, Gaocheng; Qi, Qisong; Sun, Binyu

2015-10-01

This paper researches the stability of the nonlinear system taking the hydraulic system of double-side rolling shear as an example. The hydraulic system of double-side rolling shear uses unsymmetrical electro-hydraulic proportional servo valve to control the cylinder with single piston rod, which can make best use of the space and reduce reversing shock. It is a typical nonlinear structure. The nonlinear state-space equations of the unsymmetrical valve controlling cylinder system are built first, and the second Lyapunov method is used to evaluate its stability. Second, the software AMEsim is applied to simulate the nonlinear system, and the results indicate that the system is stable. At last, the experimental results show that the system unsymmetrical valve controlling the cylinder with single piston rod is stable and conforms to what is deduced by theoretical analysis and simulation. The construction and application of Lyapunov function not only provide the theoretical basis for using of unsymmetrical valve controlling cylinder with single piston rod but also develop a new thought for nonlinear stability evaluation.

Nonlinear vibration of a coupled high- Tc superconducting levitation system

NASA Astrophysics Data System (ADS)

Sugiura, T.; Inoue, T.; Ura, H.

2004-10-01

High- Tc superconducting levitation can be applied to electro-mechanical systems, such as flywheel energy storage and linear-drive transportation. Such a system can be modeled as a magnetically coupled system of many permanent magnets and high- Tc superconducting bulks. It is a multi-degree-of-freedom dynamical system coupled by nonlinear interaction between levitated magnets and superconducting bulks. This nonlinearly coupled system, with small damping due to no contact support, can easily show complicated phenomena of nonlinear dynamics. In mechanical design, it is important to evaluate this nonlinear dynamics, though it has not been well studied so far. This research deals with forced vibration of a coupled superconducting levitation system. As a simple modeling of a coupled system, a permanent magnet levitated above a superconducting bulk is placed between two fixed permanent magnets without contact. Frequency response of the levitated magnet under excitation of one of the fixed magnets was examined theoretically. The results show typical nonlinear vibration, such as jump, hysteresis, and parametric resonance, which were confirmed in our numerical analyses and experiments.

Nonlinear model updating applied to the IMAC XXXII Round Robin benchmark system

NASA Astrophysics Data System (ADS)

Kurt, Mehmet; Moore, Keegan J.; Eriten, Melih; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.

2017-05-01

We consider the application of a new nonlinear model updating strategy to a computational benchmark system. The approach relies on analyzing system response time series in the frequency-energy domain by constructing both Hamiltonian and forced and damped frequency-energy plots (FEPs). The system parameters are then characterized and updated by matching the backbone branches of the FEPs with the frequency-energy wavelet transforms of experimental and/or computational time series. The main advantage of this method is that no nonlinearity model is assumed a priori, and the system model is updated solely based on simulation and/or experimental measured time series. By matching the frequency-energy plots of the benchmark system and its reduced-order model, we show that we are able to retrieve the global strongly nonlinear dynamics in the frequency and energy ranges of interest, identify bifurcations, characterize local nonlinearities, and accurately reconstruct time series. We apply the proposed methodology to a benchmark problem, which was posed to the system identification community prior to the IMAC XXXII (2014) and XXXIII (2015) Conferences as a "Round Robin Exercise on Nonlinear System Identification". We show that we are able to identify the parameters of the non-linear element in the problem with a priori knowledge about its position.

Algorithms for solving large sparse systems of simultaneous linear equations on vector processors

NASA Technical Reports Server (NTRS)

David, R. E.

1984-01-01

Very efficient algorithms for solving large sparse systems of simultaneous linear equations have been developed for serial processing computers. These involve a reordering of matrix rows and columns in order to obtain a near triangular pattern of nonzero elements. Then an LU factorization is developed to represent the matrix inverse in terms of a sequence of elementary Gaussian eliminations, or pivots. In this paper it is shown how these algorithms are adapted for efficient implementation on vector processors. Results obtained on the CYBER 200 Model 205 are presented for a series of large test problems which show the comparative advantages of the triangularization and vector processing algorithms.

Robust approximation-free prescribed performance control for nonlinear systems and its application

NASA Astrophysics Data System (ADS)

Sun, Ruisheng; Na, Jing; Zhu, Bin

2018-02-01

This paper presents a robust prescribed performance control approach and its application to nonlinear tail-controlled missile systems with unknown dynamics and uncertainties. The idea of prescribed performance function (PPF) is incorporated into the control design, such that both the steady-state and transient control performance can be strictly guaranteed. Unlike conventional PPF-based control methods, we further tailor a recently proposed systematic control design procedure (i.e. approximation-free control) using the transformed tracking error dynamics, which provides a proportional-like control action. Hence, the function approximators (e.g. neural networks, fuzzy systems) that are widely used to address the unknown nonlinearities in the nonlinear control designs are not needed. The proposed control design leads to a robust yet simplified function approximation-free control for nonlinear systems. The closed-loop system stability and the control error convergence are all rigorously proved. Finally, comparative simulations are conducted based on nonlinear missile systems to validate the improved response and the robustness of the proposed control method.

Modeling actual evapotranspiration with routine meteorological variables in the data-scarce region of the Tibetan Plateau: Comparisons and implications

NASA Astrophysics Data System (ADS)

Ma, Ning; Zhang, Yinsheng; Xu, Chong-Yu; Szilagyi, Jozsef

2015-08-01

Quantitative estimation of actual evapotranspiration (ETa) by in situ measurements and mathematical modeling is a fundamental task for physical understanding of ETa as well as the feedback mechanisms between land and the ambient atmosphere. However, the ETa information in the Tibetan Plateau (TP) has been greatly impeded by the extremely sparse ground observation network in the region. Approaches for estimating ETa solely from routine meteorological variables are therefore important for investigating spatiotemporal variations of ETa in the data-scarce region of the TP. Motivated by this need, the complementary relationship (CR) and Penman-Monteith approaches were evaluated against in situ measurements of ETa on a daily basis in an alpine steppe region of the TP. The former includes the Nonlinear Complementary Relationship (Nonlinear-CR) as well as the Complementary Relationship Areal Evapotranspiration (CRAE) models, while the latter involves the Katerji-Perrier and the Todorovic models. Results indicate that the Nonlinear-CR, CRAE, and Katerji-Perrier models are all capable of efficiently simulating daily ETa, provided their parameter values were appropriately calibrated. The Katerji-Perrier model performed best since its site-specific parameters take the soil water status into account. The Nonlinear-CR model also performed well with the advantage of not requiring the user to choose between a symmetric and asymmetric CR. The CRAE model, even with a relatively low Nash-Sutcliffe efficiency (NSE) value, is also an acceptable approach in this data-scarce region as it does not need information of wind speed and ground surface conditions. In contrast, application of the Todorovic model was found to be inappropriate in the dry regions of the TP due to its significant overestimation of ETa as it neglects the effect of water stress on the bulk surface resistance. Sensitivity analysis of the parameter values demonstrated the relative importance of each parameter in the corresponding model. Overall, the Nonlinear-CR model is recommended in the absence of measured ETa for local calibration of the model parameter values.

High resolution depth reconstruction from monocular images and sparse point clouds using deep convolutional neural network

NASA Astrophysics Data System (ADS)

Dimitrievski, Martin; Goossens, Bart; Veelaert, Peter; Philips, Wilfried

2017-09-01

Understanding the 3D structure of the environment is advantageous for many tasks in the field of robotics and autonomous vehicles. From the robot's point of view, 3D perception is often formulated as a depth image reconstruction problem. In the literature, dense depth images are often recovered deterministically from stereo image disparities. Other systems use an expensive LiDAR sensor to produce accurate, but semi-sparse depth images. With the advent of deep learning there have also been attempts to estimate depth by only using monocular images. In this paper we combine the best of the two worlds, focusing on a combination of monocular images and low cost LiDAR point clouds. We explore the idea that very sparse depth information accurately captures the global scene structure while variations in image patches can be used to reconstruct local depth to a high resolution. The main contribution of this paper is a supervised learning depth reconstruction system based on a deep convolutional neural network. The network is trained on RGB image patches reinforced with sparse depth information and the output is a depth estimate for each pixel. Using image and point cloud data from the KITTI vision dataset we are able to learn a correspondence between local RGB information and local depth, while at the same time preserving the global scene structure. Our results are evaluated on sequences from the KITTI dataset and our own recordings using a low cost camera and LiDAR setup.

Discriminative spatial-frequency-temporal feature extraction and classification of motor imagery EEG: An sparse regression and Weighted Naïve Bayesian Classifier-based approach.

PubMed

Miao, Minmin; Zeng, Hong; Wang, Aimin; Zhao, Changsen; Liu, Feixiang

2017-02-15

Common spatial pattern (CSP) is most widely used in motor imagery based brain-computer interface (BCI) systems. In conventional CSP algorithm, pairs of the eigenvectors corresponding to both extreme eigenvalues are selected to construct the optimal spatial filter. In addition, an appropriate selection of subject-specific time segments and frequency bands plays an important role in its successful application. This study proposes to optimize spatial-frequency-temporal patterns for discriminative feature extraction. Spatial optimization is implemented by channel selection and finding discriminative spatial filters adaptively on each time-frequency segment. A novel Discernibility of Feature Sets (DFS) criteria is designed for spatial filter optimization. Besides, discriminative features located in multiple time-frequency segments are selected automatically by the proposed sparse time-frequency segment common spatial pattern (STFSCSP) method which exploits sparse regression for significant features selection. Finally, a weight determined by the sparse coefficient is assigned for each selected CSP feature and we propose a Weighted Naïve Bayesian Classifier (WNBC) for classification. Experimental results on two public EEG datasets demonstrate that optimizing spatial-frequency-temporal patterns in a data-driven manner for discriminative feature extraction greatly improves the classification performance. The proposed method gives significantly better classification accuracies in comparison with several competing methods in the literature. The proposed approach is a promising candidate for future BCI systems. Copyright © 2016 Elsevier B.V. All rights reserved.

Fast iterative image reconstruction using sparse matrix factorization with GPU acceleration

NASA Astrophysics Data System (ADS)

Zhou, Jian; Qi, Jinyi

2011-03-01

Statistically based iterative approaches for image reconstruction have gained much attention in medical imaging. An accurate system matrix that defines the mapping from the image space to the data space is the key to high-resolution image reconstruction. However, an accurate system matrix is often associated with high computational cost and huge storage requirement. Here we present a method to address this problem by using sparse matrix factorization and parallel computing on a graphic processing unit (GPU).We factor the accurate system matrix into three sparse matrices: a sinogram blurring matrix, a geometric projection matrix, and an image blurring matrix. The sinogram blurring matrix models the detector response. The geometric projection matrix is based on a simple line integral model. The image blurring matrix is to compensate for the line-of-response (LOR) degradation due to the simplified geometric projection matrix. The geometric projection matrix is precomputed, while the sinogram and image blurring matrices are estimated by minimizing the difference between the factored system matrix and the original system matrix. The resulting factored system matrix has much less number of nonzero elements than the original system matrix and thus substantially reduces the storage and computation cost. The smaller size also allows an efficient implement of the forward and back projectors on GPUs, which have limited amount of memory. Our simulation studies show that the proposed method can dramatically reduce the computation cost of high-resolution iterative image reconstruction. The proposed technique is applicable to image reconstruction for different imaging modalities, including x-ray CT, PET, and SPECT.

Tunneling induced absorption with competing Nonlinearities.

PubMed

Peng, Yandong; Yang, Aihong; Xu, Yan; Wang, Peng; Yu, Yang; Guo, Hongju; Ren, Tingqi

2016-12-13

We investigate tunneling induced nonlinear absorption phenomena in a coupled quantum-dot system. Resonant tunneling causes constructive interference in the nonlinear absorption that leads to an increase of more than an order of magnitude over the maximum absorption in a coupled quantum dot system without tunneling. Resonant tunneling also leads to a narrowing of the linewidth of the absorption peak to a sublinewidth level. Analytical expressions show that the enhanced nonlinear absorption is largely due to the fifth-order nonlinear term. Competition between third- and fifth-order nonlinearities leads to an anomalous dispersion of the total susceptibility.

Nanopore Current Oscillations: Nonlinear Dynamics on the Nanoscale.

PubMed

Hyland, Brittany; Siwy, Zuzanna S; Martens, Craig C

2015-05-21

In this Letter, we describe theoretical modeling of an experimentally realized nanoscale system that exhibits the general universal behavior of a nonlinear dynamical system. In particular, we consider the description of voltage-induced current fluctuations through a single nanopore from the perspective of nonlinear dynamics. We briefly review the experimental system and its behavior observed and then present a simple phenomenological nonlinear model that reproduces the qualitative behavior of the experimental data. The model consists of a two-dimensional deterministic nonlinear bistable oscillator experiencing both dissipation and random noise. The multidimensionality of the model and the interplay between deterministic and stochastic forces are both required to obtain a qualitatively accurate description of the physical system.

Deformable segmentation via sparse representation and dictionary learning.

PubMed

Zhang, Shaoting; Zhan, Yiqiang; Metaxas, Dimitris N

2012-10-01

"Shape" and "appearance", the two pillars of a deformable model, complement each other in object segmentation. In many medical imaging applications, while the low-level appearance information is weak or mis-leading, shape priors play a more important role to guide a correct segmentation, thanks to the strong shape characteristics of biological structures. Recently a novel shape prior modeling method has been proposed based on sparse learning theory. Instead of learning a generative shape model, shape priors are incorporated on-the-fly through the sparse shape composition (SSC). SSC is robust to non-Gaussian errors and still preserves individual shape characteristics even when such characteristics is not statistically significant. Although it seems straightforward to incorporate SSC into a deformable segmentation framework as shape priors, the large-scale sparse optimization of SSC has low runtime efficiency, which cannot satisfy clinical requirements. In this paper, we design two strategies to decrease the computational complexity of SSC, making a robust, accurate and efficient deformable segmentation system. (1) When the shape repository contains a large number of instances, which is often the case in 2D problems, K-SVD is used to learn a more compact but still informative shape dictionary. (2) If the derived shape instance has a large number of vertices, which often appears in 3D problems, an affinity propagation method is used to partition the surface into small sub-regions, on which the sparse shape composition is performed locally. Both strategies dramatically decrease the scale of the sparse optimization problem and hence speed up the algorithm. Our method is applied on a diverse set of biomedical image analysis problems. Compared to the original SSC, these two newly-proposed modules not only significant reduce the computational complexity, but also improve the overall accuracy. Copyright © 2012 Elsevier B.V. All rights reserved.

Nonlinear aeroservoelastic analysis of a controlled multiple-actuated-wing model with free-play

NASA Astrophysics Data System (ADS)

Huang, Rui; Hu, Haiyan; Zhao, Yonghui

2013-10-01

In this paper, the effects of structural nonlinearity due to free-play in both leading-edge and trailing-edge outboard control surfaces on the linear flutter control system are analyzed for an aeroelastic model of three-dimensional multiple-actuated-wing. The free-play nonlinearities in the control surfaces are modeled theoretically by using the fictitious mass approach. The nonlinear aeroelastic equations of the presented model can be divided into nine sub-linear modal-based aeroelastic equations according to the different combinations of deflections of the leading-edge and trailing-edge outboard control surfaces. The nonlinear aeroelastic responses can be computed based on these sub-linear aeroelastic systems. To demonstrate the effects of nonlinearity on the linear flutter control system, a single-input and single-output controller and a multi-input and multi-output controller are designed based on the unconstrained optimization techniques. The numerical results indicate that the free-play nonlinearity can lead to either limit cycle oscillations or divergent motions when the linear control system is implemented.

Command Filtering-Based Fuzzy Control for Nonlinear Systems With Saturation Input.

PubMed

Yu, Jinpeng; Shi, Peng; Dong, Wenjie; Lin, Chong

2017-09-01

In this paper, command filtering-based fuzzy control is designed for uncertain multi-input multioutput (MIMO) nonlinear systems with saturation nonlinearity input. First, the command filtering method is employed to deal with the explosion of complexity caused by the derivative of virtual controllers. Then, fuzzy logic systems are utilized to approximate the nonlinear functions of MIMO systems. Furthermore, error compensation mechanism is introduced to overcome the drawback of the dynamics surface approach. The developed method will guarantee all signals of the systems are bounded. The effectiveness and advantages of the theoretic result are obtained by a simulation example.

Fuel-optimal low-thrust formation reconfiguration via Radau pseudospectral method

NASA Astrophysics Data System (ADS)

Li, Jing

2016-07-01

This paper investigates fuel-optimal low-thrust formation reconfiguration near circular orbit. Based on the Clohessy-Wiltshire equations, first-order necessary optimality conditions are derived from the Pontryagin's maximum principle. The fuel-optimal impulsive solution is utilized to divide the low-thrust trajectory into thrust and coast arcs. By introducing the switching times as optimization variables, the fuel-optimal low-thrust formation reconfiguration is posed as a nonlinear programming problem (NLP) via direct transcription using multiple-phase Radau pseudospectral method (RPM), which is then solved by a sparse nonlinear optimization software SNOPT. To facilitate optimality verification and, if necessary, further refinement of the optimized solution of the NLP, formulas for mass costate estimation and initial costates scaling are presented. Numerical examples are given to show the application of the proposed optimization method. To fix the problem, generic fuel-optimal low-thrust formation reconfiguration can be simplified as reconfiguration without any initial and terminal coast arcs, whose optimal solutions can be efficiently obtained from the multiple-phase RPM at the cost of a slight fuel increment. Finally, influence of the specific impulse and maximum thrust magnitude on the fuel-optimal low-thrust formation reconfiguration is analyzed. Numerical results shown the links and differences between the fuel-optimal impulsive and low-thrust solutions.

An efficient distribution method for nonlinear transport problems in stochastic porous media

NASA Astrophysics Data System (ADS)

Ibrahima, F.; Tchelepi, H.; Meyer, D. W.

2015-12-01

Because geophysical data are inexorably sparse and incomplete, stochastic treatments of simulated responses are convenient to explore possible scenarios and assess risks in subsurface problems. In particular, understanding how uncertainties propagate in porous media with nonlinear two-phase flow is essential, yet challenging, in reservoir simulation and hydrology. We give a computationally efficient and numerically accurate method to estimate the one-point probability density (PDF) and cumulative distribution functions (CDF) of the water saturation for the stochastic Buckley-Leverett problem when the probability distributions of the permeability and porosity fields are available. The method draws inspiration from the streamline approach and expresses the distributions of interest essentially in terms of an analytically derived mapping and the distribution of the time of flight. In a large class of applications the latter can be estimated at low computational costs (even via conventional Monte Carlo). Once the water saturation distribution is determined, any one-point statistics thereof can be obtained, especially its average and standard deviation. Moreover, rarely available in other approaches, yet crucial information such as the probability of rare events and saturation quantiles (e.g. P10, P50 and P90) can be derived from the method. We provide various examples and comparisons with Monte Carlo simulations to illustrate the performance of the method.

A hierarchy for modeling high speed propulsion systems

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Deabreu, Alex

1991-01-01

General research efforts on reduced order propulsion models for control systems design are overviewed. Methods for modeling high speed propulsion systems are discussed including internal flow propulsion systems that do not contain rotating machinery such as inlets, ramjets, and scramjets. The discussion is separated into four sections: (1) computational fluid dynamics model for the entire nonlinear system or high order nonlinear models; (2) high order linearized model derived from fundamental physics; (3) low order linear models obtained from other high order models; and (4) low order nonlinear models. Included are special considerations on any relevant control system designs. The methods discussed are for the quasi-one dimensional Euler equations of gasdynamic flow. The essential nonlinear features represented are large amplitude nonlinear waves, moving normal shocks, hammershocks, subsonic combustion via heat addition, temperature dependent gases, detonation, and thermal choking.

Global Optimal Trajectory in Chaos and NP-Hardness

NASA Astrophysics Data System (ADS)

Latorre, Vittorio; Gao, David Yang

This paper presents an unconventional theory and method for solving general nonlinear dynamical systems. Instead of the direct iterative methods, the discretized nonlinear system is first formulated as a global optimization problem via the least squares method. A newly developed canonical duality theory shows that this nonconvex minimization problem can be solved deterministically in polynomial time if a global optimality condition is satisfied. The so-called pseudo-chaos produced by linear iterative methods are mainly due to the intrinsic numerical error accumulations. Otherwise, the global optimization problem could be NP-hard and the nonlinear system can be really chaotic. A conjecture is proposed, which reveals the connection between chaos in nonlinear dynamics and NP-hardness in computer science. The methodology and the conjecture are verified by applications to the well-known logistic equation, a forced memristive circuit and the Lorenz system. Computational results show that the canonical duality theory can be used to identify chaotic systems and to obtain realistic global optimal solutions in nonlinear dynamical systems. The method and results presented in this paper should bring some new insights into nonlinear dynamical systems and NP-hardness in computational complexity theory.

Robust energy harvesting from walking vibrations by means of nonlinear cantilever beams

NASA Astrophysics Data System (ADS)

Kluger, Jocelyn M.; Sapsis, Themistoklis P.; Slocum, Alexander H.

2015-04-01

In the present work we examine how mechanical nonlinearity can be appropriately utilized to achieve strong robustness of performance in an energy harvesting setting. More specifically, for energy harvesting applications, a great challenge is the uncertain character of the excitation. The combination of this uncertainty with the narrow range of good performance for linear oscillators creates the need for more robust designs that adapt to a wider range of excitation signals. A typical application of this kind is energy harvesting from walking vibrations. Depending on the particular characteristics of the person that walks as well as on the pace of walking, the excitation signal obtains completely different forms. In the present work we study a nonlinear spring mechanism that is composed of a cantilever wrapping around a curved surface as it deflects. While for the free cantilever, the force acting on the free tip depends linearly on the tip displacement, the utilization of a contact surface with the appropriate distribution of curvature leads to essentially nonlinear dependence between the tip displacement and the acting force. The studied nonlinear mechanism has favorable mechanical properties such as low frictional losses, minimal moving parts, and a rugged design that can withstand excessive loads. Through numerical simulations we illustrate that by utilizing this essentially nonlinear element in a 2 degrees-of-freedom (DOF) system, we obtain strongly nonlinear energy transfers between the modes of the system. We illustrate that this nonlinear behavior is associated with strong robustness over three radically different excitation signals that correspond to different walking paces. To validate the strong robustness properties of the 2DOF nonlinear system, we perform a direct parameter optimization for 1DOF and 2DOF linear systems as well as for a class of 1DOF and 2DOF systems with nonlinear springs similar to that of the cubic spring that are physically realized by the cantilever-surface mechanism. The optimization results show that the 2DOF nonlinear system presents the best average performance when the excitation signals have three possible forms. Moreover, we observe that while for the linear systems the optimal performance is obtained for small values of the electromagnetic damping, for the 2DOF nonlinear system optimal performance is achieved for large values of damping. This feature is of particular importance for the system's robustness to parasitic damping.

Fractional analysis for nonlinear electrical transmission line and nonlinear Schroedinger equations with incomplete sub-equation

NASA Astrophysics Data System (ADS)

Fendzi-Donfack, Emmanuel; Nguenang, Jean Pierre; Nana, Laurent

2018-02-01

We use the fractional complex transform with the modified Riemann-Liouville derivative operator to establish the exact and generalized solutions of two fractional partial differential equations. We determine the solutions of fractional nonlinear electrical transmission lines (NETL) and the perturbed nonlinear Schroedinger (NLS) equation with the Kerr law nonlinearity term. The solutions are obtained for the parameters in the range (0<α≤1) of the derivative operator and we found the traditional solutions for the limiting case of α =1. We show that according to the modified Riemann-Liouville derivative, the solutions found can describe physical systems with memory effect, transient effects in electrical systems and nonlinear transmission lines, and other systems such as optical fiber.

Structured functional additive regression in reproducing kernel Hilbert spaces

PubMed Central

Zhu, Hongxiao; Yao, Fang; Zhang, Hao Helen

2013-01-01

Summary Functional additive models (FAMs) provide a flexible yet simple framework for regressions involving functional predictors. The utilization of data-driven basis in an additive rather than linear structure naturally extends the classical functional linear model. However, the critical issue of selecting nonlinear additive components has been less studied. In this work, we propose a new regularization framework for the structure estimation in the context of Reproducing Kernel Hilbert Spaces. The proposed approach takes advantage of the functional principal components which greatly facilitates the implementation and the theoretical analysis. The selection and estimation are achieved by penalized least squares using a penalty which encourages the sparse structure of the additive components. Theoretical properties such as the rate of convergence are investigated. The empirical performance is demonstrated through simulation studies and a real data application. PMID:25013362

A Steady-State Kalman Predictor-Based Filtering Strategy for Non-Overlapping Sub-Band Spectral Estimation

PubMed Central

Li, Zenghui; Xu, Bin; Yang, Jian; Song, Jianshe

2015-01-01

This paper focuses on suppressing spectral overlap for sub-band spectral estimation, with which we can greatly decrease the computational complexity of existing spectral estimation algorithms, such as nonlinear least squares spectral analysis and non-quadratic regularized sparse representation. Firstly, our study shows that the nominal ability of the high-order analysis filter to suppress spectral overlap is greatly weakened when filtering a finite-length sequence, because many meaningless zeros are used as samples in convolution operations. Next, an extrapolation-based filtering strategy is proposed to produce a series of estimates as the substitutions of the zeros and to recover the suppression ability. Meanwhile, a steady-state Kalman predictor is applied to perform a linearly-optimal extrapolation. Finally, several typical methods for spectral analysis are applied to demonstrate the effectiveness of the proposed strategy. PMID:25609038

Functional interaction-based nonlinear models with application to multiplatform genomics data.

PubMed

Davenport, Clemontina A; Maity, Arnab; Baladandayuthapani, Veerabhadran

2018-05-07

Functional regression allows for a scalar response to be dependent on a functional predictor; however, not much work has been done when a scalar exposure that interacts with the functional covariate is introduced. In this paper, we present 2 functional regression models that account for this interaction and propose 2 novel estimation procedures for the parameters in these models. These estimation methods allow for a noisy and/or sparsely observed functional covariate and are easily extended to generalized exponential family responses. We compute standard errors of our estimators, which allows for further statistical inference and hypothesis testing. We compare the performance of the proposed estimators to each other and to one found in the literature via simulation and demonstrate our methods using a real data example. Copyright © 2018 John Wiley & Sons, Ltd.

Gravity and count probabilities in an expanding universe

NASA Technical Reports Server (NTRS)

Bouchet, Francois R.; Hernquist, Lars

1992-01-01

The time evolution of nonlinear clustering on large scales in cold dark matter, hot dark matter, and white noise models of the universe is investigated using N-body simulations performed with a tree code. Count probabilities in cubic cells are determined as functions of the cell size and the clustering state (redshift), and comparisons are made with various theoretical models. We isolate the features that appear to be the result of gravitational instability, those that depend on the initial conditions, and those that are likely a consequence of numerical limitations. More specifically, we study the development of skewness, kurtosis, and the fifth moment in relation to variance, the dependence of the void probability on time as well as on sparseness of sampling, and the overall shape of the count probability distribution. Implications of our results for theoretical and observational studies are discussed.

Database development of land use characteristics along major U.S. highways

DOT National Transportation Integrated Search

2000-06-01

Information about land use by and adjacent to transportation systems is essential to : understanding the environmental impacts of transportation systems. Nevertheless, such data : are presently sparse and incomplete, especially at the national scale....

Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity

NASA Astrophysics Data System (ADS)

Jeevarekha, A.; Paul Asir, M.; Philominathan, P.

2016-06-01

This paper addresses the problem of sharing common nonlinearity among nonautonomous and autonomous oscillators. By choosing a suitable common nonlinear element with the driving point characteristics capable of bringing out chaotic motion in a combined system, we obtain identical chaotic states. The dynamics of the coupled system is explored through numerical and experimental studies. Employing the concept of common nonlinearity, a simple chaotic communication system is modeled and its performance is verified through Multisim simulation.

Extension of a nonlinear systems theory to general-frequency unsteady transonic aerodynamic responses

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1993-01-01

A methodology for modeling nonlinear unsteady aerodynamic responses, for subsequent use in aeroservoelastic analysis and design, using the Volterra-Wiener theory of nonlinear systems is presented. The methodology is extended to predict nonlinear unsteady aerodynamic responses of arbitrary frequency. The Volterra-Wiener theory uses multidimensional convolution integrals to predict the response of nonlinear systems to arbitrary inputs. The CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code is used to generate linear and nonlinear unit impulse responses that correspond to each of the integrals for a rectangular wing with a NACA 0012 section with pitch and plunge degrees of freedom. The computed kernels then are used to predict linear and nonlinear unsteady aerodynamic responses via convolution and compared to responses obtained using the CAP-TSD code directly. The results indicate that the approach can be used to predict linear unsteady aerodynamic responses exactly for any input amplitude or frequency at a significant cost savings. Convolution of the nonlinear terms results in nonlinear unsteady aerodynamic responses that compare reasonably well with those computed using the CAP-TSD code directly but at significant computational cost savings.

Generating giant and tunable nonlinearity in a macroscopic mechanical resonator from a single chemical bond

NASA Astrophysics Data System (ADS)

Huang, Pu; Zhou, Jingwei; Zhang, Liang; Hou, Dong; Lin, Shaochun; Deng, Wen; Meng, Chao; Duan, Changkui; Ju, Chenyong; Zheng, Xiao; Xue, Fei; Du, Jiangfeng

2016-05-01

Nonlinearity in macroscopic mechanical systems may lead to abundant phenomena for fundamental studies and potential applications. However, it is difficult to generate nonlinearity due to the fact that macroscopic mechanical systems follow Hooke's law and respond linearly to external force, unless strong drive is used. Here we propose and experimentally realize high cubic nonlinear response in a macroscopic mechanical system by exploring the anharmonicity in chemical bonding interactions. We demonstrate the high tunability of nonlinear response by precisely controlling the chemical bonding interaction, and realize, at the single-bond limit, a cubic elastic constant of 1 × 1020 N m-3. This enables us to observe the resonator's vibrational bi-states transitions driven by the weak Brownian thermal noise at 6 K. This method can be flexibly applied to a variety of mechanical systems to improve nonlinear responses, and can be used, with further improvements, to explore macroscopic quantum mechanics.

Adaptive Neural Networks Prescribed Performance Control Design for Switched Interconnected Uncertain Nonlinear Systems.

PubMed

Li, Yongming; Tong, Shaocheng

2017-06-28

In this paper, an adaptive neural networks (NNs)-based decentralized control scheme with the prescribed performance is proposed for uncertain switched nonstrict-feedback interconnected nonlinear systems. It is assumed that nonlinear interconnected terms and nonlinear functions of the concerned systems are unknown, and also the switching signals are unknown and arbitrary. A linear state estimator is constructed to solve the problem of unmeasured states. The NNs are employed to approximate unknown interconnected terms and nonlinear functions. A new output feedback decentralized control scheme is developed by using the adaptive backstepping design technique. The control design problem of nonlinear interconnected switched systems with unknown switching signals can be solved by the proposed scheme, and only a tuning parameter is needed for each subsystem. The proposed scheme can ensure that all variables of the control systems are semi-globally uniformly ultimately bounded and the tracking errors converge to a small residual set with the prescribed performance bound. The effectiveness of the proposed control approach is verified by some simulation results.

Integrable nonlinear Schrödinger system on a lattice with three structural elements in the unit cell

NASA Astrophysics Data System (ADS)

Vakhnenko, Oleksiy O.

2018-05-01

Developing the idea of increasing the number of structural elements in the unit cell of a quasi-one-dimensional lattice as applied to the semi-discrete integrable systems of nonlinear Schrödinger type, we construct the zero-curvature representation for the general integrable nonlinear system on a lattice with three structural elements in the unit cell. The integrability of the obtained general system permits to find explicitly a number of local conservation laws responsible for the main features of system dynamics and in particular for the so-called natural constraints separating the field variables into the basic and the concomitant ones. Thus, considering the reduction to the semi-discrete integrable system of nonlinear Schrödinger type, we revealed the essentially nontrivial impact of concomitant fields on the Poisson structure and on the whole Hamiltonian formulation of system dynamics caused by the nonzero background values of these fields. On the other hand, the zero-curvature representation of a general nonlinear system serves as an indispensable key to the dressing procedure of system integration based upon the Darboux transformation of the auxiliary linear problem and the implicit Bäcklund transformation of field variables. Due to the symmetries inherent to the six-component semi-discrete integrable nonlinear Schrödinger system with attractive-type nonlinearities, the Darboux-Bäcklund dressing scheme is shown to be simplified considerably, giving rise to the appropriately parameterized multi-component soliton solution consisting of six basic and four concomitant components.

Study report on guidelines and test procedures for investigating stability of nonlinear cardiovascular control system models

NASA Technical Reports Server (NTRS)

Fitzjerrell, D. G.

1974-01-01

A general study of the stability of nonlinear as compared to linear control systems is presented. The analysis is general and, therefore, applies to other types of nonlinear biological control systems as well as the cardiovascular control system models. Both inherent and numerical stability are discussed for corresponding analytical and graphic methods and numerical methods.

The Recommendations for Linear Measurement Techniques on the Measurements of Nonlinear System Parameters of a Joint.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, Scott A; Catalfamo, Simone; Brake, Matthew R. W.

2017-01-01

In the study of the dynamics of nonlinear systems, experimental measurements often convolute the response of the nonlinearity of interest and the effects of the experimental setup. To reduce the influence of the experimental setup on the deduction of the parameters of the nonlinearity, the response of a mechanical joint is investigated under various experimental setups. These experiments first focus on quantifying how support structures and measurement techniques affect the natural frequency and damping of a linear system. The results indicate that support structures created from bungees have negligible influence on the system in terms of frequency and damping ratiomore » variations. The study then focuses on the effects of the excitation technique on the response for a linear system. The findings suggest that thinner stingers should not be used, because under the high force requirements the stinger bending modes are excited adding unwanted torsional coupling. The optimal configuration for testing the linear system is then applied to a nonlinear system in order to assess the robustness of the test configuration. Finally, recommendations are made for conducting experiments on nonlinear systems using conventional/linear testing techniques.« less

Parameter and Structure Inference for Nonlinear Dynamical Systems

NASA Technical Reports Server (NTRS)

Morris, Robin D.; Smelyanskiy, Vadim N.; Millonas, Mark

2006-01-01

A great many systems can be modeled in the non-linear dynamical systems framework, as x = f(x) + xi(t), where f() is the potential function for the system, and xi is the excitation noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications.

A sparse matrix-vector multiplication based algorithm for accurate density matrix computations on systems of millions of atoms

NASA Astrophysics Data System (ADS)

Ghale, Purnima; Johnson, Harley T.

2018-06-01

We present an efficient sparse matrix-vector (SpMV) based method to compute the density matrix P from a given Hamiltonian in electronic structure computations. Our method is a hybrid approach based on Chebyshev-Jackson approximation theory and matrix purification methods like the second order spectral projection purification (SP2). Recent methods to compute the density matrix scale as O(N) in the number of floating point operations but are accompanied by large memory and communication overhead, and they are based on iterative use of the sparse matrix-matrix multiplication kernel (SpGEMM), which is known to be computationally irregular. In addition to irregularity in the sparse Hamiltonian H, the nonzero structure of intermediate estimates of P depends on products of H and evolves over the course of computation. On the other hand, an expansion of the density matrix P in terms of Chebyshev polynomials is straightforward and SpMV based; however, the resulting density matrix may not satisfy the required constraints exactly. In this paper, we analyze the strengths and weaknesses of the Chebyshev-Jackson polynomials and the second order spectral projection purification (SP2) method, and propose to combine them so that the accurate density matrix can be computed using the SpMV computational kernel only, and without having to store the density matrix P. Our method accomplishes these objectives by using the Chebyshev polynomial estimate as the initial guess for SP2, which is followed by using sparse matrix-vector multiplications (SpMVs) to replicate the behavior of the SP2 algorithm for purification. We demonstrate the method on a tight-binding model system of an oxide material containing more than 3 million atoms. In addition, we also present the predicted behavior of our method when applied to near-metallic Hamiltonians with a wide energy spectrum.

Neural Network Control of a Magnetically Suspended Rotor System

NASA Technical Reports Server (NTRS)

Choi, Benjamin; Brown, Gerald; Johnson, Dexter

1997-01-01

Abstract Magnetic bearings offer significant advantages because of their noncontact operation, which can reduce maintenance. Higher speeds, no friction, no lubrication, weight reduction, precise position control, and active damping make them far superior to conventional contact bearings. However, there are technical barriers that limit the application of this technology in industry. One of them is the need for a nonlinear controller that can overcome the system nonlinearity and uncertainty inherent in magnetic bearings. This paper discusses the use of a neural network as a nonlinear controller that circumvents system nonlinearity. A neural network controller was well trained and successfully demonstrated on a small magnetic bearing rig. This work demonstrated the feasibility of using a neural network to control nonlinear magnetic bearings and systems with unknown dynamics.

Quasi-Linear Parameter Varying Representation of General Aircraft Dynamics Over Non-Trim Region

NASA Technical Reports Server (NTRS)

Shin, Jong-Yeob

2007-01-01

For applying linear parameter varying (LPV) control synthesis and analysis to a nonlinear system, it is required that a nonlinear system be represented in the form of an LPV model. In this paper, a new representation method is developed to construct an LPV model from a nonlinear mathematical model without the restriction that an operating point must be in the neighborhood of equilibrium points. An LPV model constructed by the new method preserves local stabilities of the original nonlinear system at "frozen" scheduling parameters and also represents the original nonlinear dynamics of a system over a non-trim region. An LPV model of the motion of FASER (Free-flying Aircraft for Subscale Experimental Research) is constructed by the new method.

Object-Oriented Design for Sparse Direct Solvers

NASA Technical Reports Server (NTRS)

Dobrian, Florin; Kumfert, Gary; Pothen, Alex

1999-01-01

We discuss the object-oriented design of a software package for solving sparse, symmetric systems of equations (positive definite and indefinite) by direct methods. At the highest layers, we decouple data structure classes from algorithmic classes for flexibility. We describe the important structural and algorithmic classes in our design, and discuss the trade-offs we made for high performance. The kernels at the lower layers were optimized by hand. Our results show no performance loss from our object-oriented design, while providing flexibility, case of use, and extensibility over solvers using procedural design.

Using Chebyshev polynomials and approximate inverse triangular factorizations for preconditioning the conjugate gradient method

NASA Astrophysics Data System (ADS)

Kaporin, I. E.

2012-02-01

In order to precondition a sparse symmetric positive definite matrix, its approximate inverse is examined, which is represented as the product of two sparse mutually adjoint triangular matrices. In this way, the solution of the corresponding system of linear algebraic equations (SLAE) by applying the preconditioned conjugate gradient method (CGM) is reduced to performing only elementary vector operations and calculating sparse matrix-vector products. A method for constructing the above preconditioner is described and analyzed. The triangular factor has a fixed sparsity pattern and is optimal in the sense that the preconditioned matrix has a minimum K-condition number. The use of polynomial preconditioning based on Chebyshev polynomials makes it possible to considerably reduce the amount of scalar product operations (at the cost of an insignificant increase in the total number of arithmetic operations). The possibility of an efficient massively parallel implementation of the resulting method for solving SLAEs is discussed. For a sequential version of this method, the results obtained by solving 56 test problems from the Florida sparse matrix collection (which are large-scale and ill-conditioned) are presented. These results show that the method is highly reliable and has low computational costs.

Energy Balanced Strategies for Maximizing the Lifetime of Sparsely Deployed Underwater Acoustic Sensor Networks

PubMed Central

Luo, Hanjiang; Guo, Zhongwen; Wu, Kaishun; Hong, Feng; Feng, Yuan

2009-01-01

Underwater acoustic sensor networks (UWA-SNs) are envisioned to perform monitoring tasks over the large portion of the world covered by oceans. Due to economics and the large area of the ocean, UWA-SNs are mainly sparsely deployed networks nowadays. The limited battery resources is a big challenge for the deployment of such long-term sensor networks. Unbalanced battery energy consumption will lead to early energy depletion of nodes, which partitions the whole networks and impairs the integrity of the monitoring datasets or even results in the collapse of the entire networks. On the contrary, balanced energy dissipation of nodes can prolong the lifetime of such networks. In this paper, we focus on the energy balance dissipation problem of two types of sparsely deployed UWA-SNs: underwater moored monitoring systems and sparsely deployed two-dimensional UWA-SNs. We first analyze the reasons of unbalanced energy consumption in such networks, then we propose two energy balanced strategies to maximize the lifetime of networks both in shallow and deep water. Finally, we evaluate our methods by simulations and the results show that the two strategies can achieve balanced energy consumption per node while at the same time prolong the networks lifetime. PMID:22399970

Reconstruction of finite-valued sparse signals

NASA Astrophysics Data System (ADS)

Keiper, Sandra; Kutyniok, Gitta; Lee, Dae Gwan; Pfander, Götz

2017-08-01

The need of reconstructing discrete-valued sparse signals from few measurements, that is solving an undetermined system of linear equations, appears frequently in science and engineering. Those signals appear, for example, in error correcting codes as well as massive Multiple-Input Multiple-Output (MIMO) channel and wideband spectrum sensing. A particular example is given by wireless communications, where the transmitted signals are sequences of bits, i.e., with entries in f0; 1g. Whereas classical compressed sensing algorithms do not incorporate the additional knowledge of the discrete nature of the signal, classical lattice decoding approaches do not utilize sparsity constraints. In this talk, we present an approach that incorporates a discrete values prior into basis pursuit. In particular, we address finite-valued sparse signals, i.e., sparse signals with entries in a finite alphabet. We will introduce an equivalent null space characterization and show that phase transition takes place earlier than when using the classical basis pursuit approach. We will further discuss robustness of the algorithm and show that the nonnegative case is very different from the bipolar one. One of our findings is that the positioning of the zero in the alphabet - i.e., whether it is a boundary element or not - is crucial.

Tunneling induced absorption with competing Nonlinearities

PubMed Central

Peng, Yandong; Yang, Aihong; Xu, Yan; Wang, Peng; Yu, Yang; Guo, Hongju; Ren, Tingqi

2016-01-01

We investigate tunneling induced nonlinear absorption phenomena in a coupled quantum-dot system. Resonant tunneling causes constructive interference in the nonlinear absorption that leads to an increase of more than an order of magnitude over the maximum absorption in a coupled quantum dot system without tunneling. Resonant tunneling also leads to a narrowing of the linewidth of the absorption peak to a sublinewidth level. Analytical expressions show that the enhanced nonlinear absorption is largely due to the fifth-order nonlinear term. Competition between third- and fifth-order nonlinearities leads to an anomalous dispersion of the total susceptibility. PMID:27958303

Special class of nonlinear damping models in flexible space structures

NASA Technical Reports Server (NTRS)

Hu, Anren; Singh, Ramendra P.; Taylor, Lawrence W.

1991-01-01

A special class of nonlinear damping models is investigated in which the damping force is proportional to the product of positive integer or the fractional power of the absolute values of displacement and velocity. For a one-degree-of-freedom system, the classical Krylov-Bogoliubov 'averaging' method is used, whereas for a distributed system, both an ad hoc perturbation technique and the finite difference method are employed to study the effects of nonlinear damping. The results are compared with linear viscous damping models. The amplitude decrement of free vibration for a single mode system with nonlinear models depends not only on the damping ratio but also on the initial amplitude, the time to measure the response, the frequency of the system, and the powers of displacement and velocity. For the distributed system, the action of nonlinear damping is found to reduce the energy of the system and to pass energy to lower modes.

Adaptive Fuzzy Output-Constrained Fault-Tolerant Control of Nonlinear Stochastic Large-Scale Systems With Actuator Faults.

PubMed

Li, Yongming; Ma, Zhiyao; Tong, Shaocheng

2017-09-01

The problem of adaptive fuzzy output-constrained tracking fault-tolerant control (FTC) is investigated for the large-scale stochastic nonlinear systems of pure-feedback form. The nonlinear systems considered in this paper possess the unstructured uncertainties, unknown interconnected terms and unknown nonaffine nonlinear faults. The fuzzy logic systems are employed to identify the unknown lumped nonlinear functions so that the problems of structured uncertainties can be solved. An adaptive fuzzy state observer is designed to solve the nonmeasurable state problem. By combining the barrier Lyapunov function theory, adaptive decentralized and stochastic control principles, a novel fuzzy adaptive output-constrained FTC approach is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.

Nonlinear low-frequency electrostatic wave dynamics in a two-dimensional quantum plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Samiran, E-mail: sran_g@yahoo.com; Chakrabarti, Nikhil, E-mail: nikhil.chakrabarti@saha.ac.in

2016-08-15

The problem of two-dimensional arbitrary amplitude low-frequency electrostatic oscillation in a quasi-neutral quantum plasma is solved exactly by elementary means. In such quantum plasmas we have treated electrons quantum mechanically and ions classically. The exact analytical solution of the nonlinear system exhibits the formation of dark and black solitons. Numerical simulation also predicts the possible periodic solution of the nonlinear system. Nonlinear analysis reveals that the system does have a bifurcation at a critical Mach number that depends on the angle of propagation of the wave. The small-amplitude limit leads to the formation of weakly nonlinear Kadomstev–Petviashvili solitons.

Adaptive nearly optimal control for a class of continuous-time nonaffine nonlinear systems with inequality constraints.

PubMed

Fan, Quan-Yong; Yang, Guang-Hong

2017-01-01

The state inequality constraints have been hardly considered in the literature on solving the nonlinear optimal control problem based the adaptive dynamic programming (ADP) method. In this paper, an actor-critic (AC) algorithm is developed to solve the optimal control problem with a discounted cost function for a class of state-constrained nonaffine nonlinear systems. To overcome the difficulties resulting from the inequality constraints and the nonaffine nonlinearities of the controlled systems, a novel transformation technique with redesigned slack functions and a pre-compensator method are introduced to convert the constrained optimal control problem into an unconstrained one for affine nonlinear systems. Then, based on the policy iteration (PI) algorithm, an online AC scheme is proposed to learn the nearly optimal control policy for the obtained affine nonlinear dynamics. Using the information of the nonlinear model, novel adaptive update laws are designed to guarantee the convergence of the neural network (NN) weights and the stability of the affine nonlinear dynamics without the requirement for the probing signal. Finally, the effectiveness of the proposed method is validated by simulation studies. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Automated reverse engineering of nonlinear dynamical systems

PubMed Central

Bongard, Josh; Lipson, Hod

2007-01-01

Complex nonlinear dynamics arise in many fields of science and engineering, but uncovering the underlying differential equations directly from observations poses a challenging task. The ability to symbolically model complex networked systems is key to understanding them, an open problem in many disciplines. Here we introduce for the first time a method that can automatically generate symbolic equations for a nonlinear coupled dynamical system directly from time series data. This method is applicable to any system that can be described using sets of ordinary nonlinear differential equations, and assumes that the (possibly noisy) time series of all variables are observable. Previous automated symbolic modeling approaches of coupled physical systems produced linear models or required a nonlinear model to be provided manually. The advance presented here is made possible by allowing the method to model each (possibly coupled) variable separately, intelligently perturbing and destabilizing the system to extract its less observable characteristics, and automatically simplifying the equations during modeling. We demonstrate this method on four simulated and two real systems spanning mechanics, ecology, and systems biology. Unlike numerical models, symbolic models have explanatory value, suggesting that automated “reverse engineering” approaches for model-free symbolic nonlinear system identification may play an increasing role in our ability to understand progressively more complex systems in the future. PMID:17553966

Automated reverse engineering of nonlinear dynamical systems.

PubMed

Bongard, Josh; Lipson, Hod

2007-06-12

Complex nonlinear dynamics arise in many fields of science and engineering, but uncovering the underlying differential equations directly from observations poses a challenging task. The ability to symbolically model complex networked systems is key to understanding them, an open problem in many disciplines. Here we introduce for the first time a method that can automatically generate symbolic equations for a nonlinear coupled dynamical system directly from time series data. This method is applicable to any system that can be described using sets of ordinary nonlinear differential equations, and assumes that the (possibly noisy) time series of all variables are observable. Previous automated symbolic modeling approaches of coupled physical systems produced linear models or required a nonlinear model to be provided manually. The advance presented here is made possible by allowing the method to model each (possibly coupled) variable separately, intelligently perturbing and destabilizing the system to extract its less observable characteristics, and automatically simplifying the equations during modeling. We demonstrate this method on four simulated and two real systems spanning mechanics, ecology, and systems biology. Unlike numerical models, symbolic models have explanatory value, suggesting that automated "reverse engineering" approaches for model-free symbolic nonlinear system identification may play an increasing role in our ability to understand progressively more complex systems in the future.

Determination of nonlinear nanomechanical resonator-qubit coupling coefficient in a hybrid quantum system.

PubMed

Geng, Qi; Zhu, Ka-Di

2016-07-10

We have theoretically investigated a hybrid system that is composed of a traditional optomechanical component and an additional charge qubit (Cooper pair box) that induces a new nonlinear interaction. It is shown that the peak in optomechanically induced transparency has been split by the new nonlinear interaction, and the width of the splitting is proportional to the coupling coefficient of this nonlinear interaction. This may give a way to measure the nanomechanical oscillator-qubit coupling coefficient in hybrid quantum systems.

Irrationality and Quasiperiodicity in Driven Nonlinear Systems

NASA Astrophysics Data System (ADS)

Cubero, David; Casado-Pascual, Jesús; Renzoni, Ferruccio

2014-05-01

We analyze the relationship between irrationality and quasiperiodicity in nonlinear driven systems. To that purpose, we consider a nonlinear system whose steady-state response is very sensitive to the periodic or quasiperiodic character of the input signal. In the infinite time limit, an input signal consisting of two incommensurate frequencies will be recognized by the system as quasiperiodic. We show that this is, in general, not true in the case of finite interaction times. An irrational ratio of the driving frequencies of the input signal is not sufficient for it to be recognized by the nonlinear system as quasiperiodic, resulting in observations which may differ by several orders of magnitude from the expected quasiperiodic behavior. Thus, the system response depends on the nature of the irrational ratio, as well as the observation time. We derive a condition for the input signal to be identified by the system as quasiperiodic. Such a condition also takes into account the sub-Fourier response of the nonlinear system.

General purpose nonlinear system solver based on Newton-Krylov method.

DOE Office of Scientific and Technical Information (OSTI.GOV)

2013-12-01

KINSOL is part of a software family called SUNDIALS: SUite of Nonlinear and Differential/Algebraic equation Solvers [1]. KINSOL is a general-purpose nonlinear system solver based on Newton-Krylov and fixed-point solver technologies [2].

Observers for a class of systems with nonlinearities satisfying an incremental quadratic inequality

NASA Technical Reports Server (NTRS)

Acikmese, Ahmet Behcet; Martin, Corless

2004-01-01

We consider the problem of state estimation from nonlinear time-varying system whose nonlinearities satisfy an incremental quadratic inequality. Observers are presented which guarantee that the state estimation error exponentially converges to zero.

Sparse matrix-vector multiplication on network-on-chip

NASA Astrophysics Data System (ADS)

Sun, C.-C.; Götze, J.; Jheng, H.-Y.; Ruan, S.-J.

2010-12-01

In this paper, we present an idea for performing matrix-vector multiplication by using Network-on-Chip (NoC) architecture. In traditional IC design on-chip communications have been designed with dedicated point-to-point interconnections. Therefore, regular local data transfer is the major concept of many parallel implementations. However, when dealing with the parallel implementation of sparse matrix-vector multiplication (SMVM), which is the main step of all iterative algorithms for solving systems of linear equation, the required data transfers depend on the sparsity structure of the matrix and can be extremely irregular. Using the NoC architecture makes it possible to deal with arbitrary structure of the data transfers; i.e. with the irregular structure of the sparse matrices. So far, we have already implemented the proposed SMVM-NoC architecture with the size 4×4 and 5×5 in IEEE 754 single float point precision using FPGA.

Finite-time H∞ filtering for non-linear stochastic systems

NASA Astrophysics Data System (ADS)

Hou, Mingzhe; Deng, Zongquan; Duan, Guangren

2016-09-01

This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.

Distributed Adaptive Neural Control for Stochastic Nonlinear Multiagent Systems.

PubMed

Wang, Fang; Chen, Bing; Lin, Chong; Li, Xuehua

2016-11-14

In this paper, a consensus tracking problem of nonlinear multiagent systems is investigated under a directed communication topology. All the followers are modeled by stochastic nonlinear systems in nonstrict feedback form, where nonlinearities and stochastic disturbance terms are totally unknown. Based on the structural characteristic of neural networks (in Lemma 4), a novel distributed adaptive neural control scheme is put forward. The raised control method not only effectively handles unknown nonlinearities in nonstrict feedback systems, but also copes with the interactions among agents and coupling terms. Based on the stochastic Lyapunov functional method, it is indicated that all the signals of the closed-loop system are bounded in probability and all followers' outputs are convergent to a neighborhood of the output of leader. At last, the efficiency of the control method is testified by a numerical example.

Efficient techniques for forced response involving linear modal components interconnected by discrete nonlinear connection elements

NASA Astrophysics Data System (ADS)

Avitabile, Peter; O'Callahan, John

2009-01-01

Generally, response analysis of systems containing discrete nonlinear connection elements such as typical mounting connections require the physical finite element system matrices to be used in a direct integration algorithm to compute the nonlinear response analysis solution. Due to the large size of these physical matrices, forced nonlinear response analysis requires significant computational resources. Usually, the individual components of the system are analyzed and tested as separate components and their individual behavior may essentially be linear when compared to the total assembled system. However, the joining of these linear subsystems using highly nonlinear connection elements causes the entire system to become nonlinear. It would be advantageous if these linear modal subsystems could be utilized in the forced nonlinear response analysis since much effort has usually been expended in fine tuning and adjusting the analytical models to reflect the tested subsystem configuration. Several more efficient techniques have been developed to address this class of problem. Three of these techniques given as: equivalent reduced model technique (ERMT);modal modification response technique (MMRT); andcomponent element method (CEM); are presented in this paper and are compared to traditional methods.

How do neurons work together? Lessons from auditory cortex.

PubMed

Harris, Kenneth D; Bartho, Peter; Chadderton, Paul; Curto, Carina; de la Rocha, Jaime; Hollender, Liad; Itskov, Vladimir; Luczak, Artur; Marguet, Stephan L; Renart, Alfonso; Sakata, Shuzo

2011-01-01

Recordings of single neurons have yielded great insights into the way acoustic stimuli are represented in auditory cortex. However, any one neuron functions as part of a population whose combined activity underlies cortical information processing. Here we review some results obtained by recording simultaneously from auditory cortical populations and individual morphologically identified neurons, in urethane-anesthetized and unanesthetized passively listening rats. Auditory cortical populations produced structured activity patterns both in response to acoustic stimuli, and spontaneously without sensory input. Population spike time patterns were broadly conserved across multiple sensory stimuli and spontaneous events, exhibiting a generally conserved sequential organization lasting approximately 100 ms. Both spontaneous and evoked events exhibited sparse, spatially localized activity in layer 2/3 pyramidal cells, and densely distributed activity in larger layer 5 pyramidal cells and putative interneurons. Laminar propagation differed however, with spontaneous activity spreading upward from deep layers and slowly across columns, but sensory responses initiating in presumptive thalamorecipient layers, spreading rapidly across columns. In both unanesthetized and urethanized rats, global activity fluctuated between "desynchronized" state characterized by low amplitude, high-frequency local field potentials and a "synchronized" state of larger, lower-frequency waves. Computational studies suggested that responses could be predicted by a simple dynamical system model fitted to the spontaneous activity immediately preceding stimulus presentation. Fitting this model to the data yielded a nonlinear self-exciting system model in synchronized states and an approximately linear system in desynchronized states. We comment on the significance of these results for auditory cortical processing of acoustic and non-acoustic information. © 2010 Elsevier B.V. All rights reserved.

Modeling hydrologic and geomorphic hazards across post-fire landscapes using a self-organizing map approach

USGS Publications Warehouse

Friedel, Michael J.

2011-01-01

Few studies attempt to model the range of possible post-fire hydrologic and geomorphic hazards because of the sparseness of data and the coupled, nonlinear, spatial, and temporal relationships among landscape variables. In this study, a type of unsupervised artificial neural network, called a self-organized map (SOM), is trained using data from 540 burned basins in the western United States. The sparsely populated data set includes variables from independent numerical landscape categories (climate, land surface form, geologic texture, and post-fire condition), independent landscape classes (bedrock geology and state), and dependent initiation processes (runoff, landslide, and runoff and landslide combination) and responses (debris flows, floods, and no events). Pattern analysis of the SOM-based component planes is used to identify and interpret relations among the variables. Application of the Davies-Bouldin criteria following k-means clustering of the SOM neurons identified eight conceptual regional models for focusing future research and empirical model development. A split-sample validation on 60 independent basins (not included in the training) indicates that simultaneous predictions of initiation process and response types are at least 78% accurate. As climate shifts from wet to dry conditions, forecasts across the burned landscape reveal a decreasing trend in the total number of debris flow, flood, and runoff events with considerable variability among individual basins. These findings suggest the SOM may be useful in forecasting real-time post-fire hazards, and long-term post-recovery processes and effects of climate change scenarios.

Machine Learning Techniques for Global Sensitivity Analysis in Climate Models

NASA Astrophysics Data System (ADS)

Safta, C.; Sargsyan, K.; Ricciuto, D. M.

2017-12-01

Climate models studies are not only challenged by the compute intensive nature of these models but also by the high-dimensionality of the input parameter space. In our previous work with the land model components (Sargsyan et al., 2014) we identified subsets of 10 to 20 parameters relevant for each QoI via Bayesian compressive sensing and variance-based decomposition. Nevertheless the algorithms were challenged by the nonlinear input-output dependencies for some of the relevant QoIs. In this work we will explore a combination of techniques to extract relevant parameters for each QoI and subsequently construct surrogate models with quantified uncertainty necessary to future developments, e.g. model calibration and prediction studies. In the first step, we will compare the skill of machine-learning models (e.g. neural networks, support vector machine) to identify the optimal number of classes in selected QoIs and construct robust multi-class classifiers that will partition the parameter space in regions with smooth input-output dependencies. These classifiers will be coupled with techniques aimed at building sparse and/or low-rank surrogate models tailored to each class. Specifically we will explore and compare sparse learning techniques with low-rank tensor decompositions. These models will be used to identify parameters that are important for each QoI. Surrogate accuracy requirements are higher for subsequent model calibration studies and we will ascertain the performance of this workflow for multi-site ALM simulation ensembles.

Fast implementation for compressive recovery of highly accelerated cardiac cine MRI using the balanced sparse model.

PubMed

Ting, Samuel T; Ahmad, Rizwan; Jin, Ning; Craft, Jason; Serafim da Silveira, Juliana; Xue, Hui; Simonetti, Orlando P

2017-04-01

Sparsity-promoting regularizers can enable stable recovery of highly undersampled magnetic resonance imaging (MRI), promising to improve the clinical utility of challenging applications. However, lengthy computation time limits the clinical use of these methods, especially for dynamic MRI with its large corpus of spatiotemporal data. Here, we present a holistic framework that utilizes the balanced sparse model for compressive sensing and parallel computing to reduce the computation time of cardiac MRI recovery methods. We propose a fast, iterative soft-thresholding method to solve the resulting ℓ1-regularized least squares problem. In addition, our approach utilizes a parallel computing environment that is fully integrated with the MRI acquisition software. The methodology is applied to two formulations of the multichannel MRI problem: image-based recovery and k-space-based recovery. Using measured MRI data, we show that, for a 224 × 144 image series with 48 frames, the proposed k-space-based approach achieves a mean reconstruction time of 2.35 min, a 24-fold improvement compared a reconstruction time of 55.5 min for the nonlinear conjugate gradient method, and the proposed image-based approach achieves a mean reconstruction time of 13.8 s. Our approach can be utilized to achieve fast reconstruction of large MRI datasets, thereby increasing the clinical utility of reconstruction techniques based on compressed sensing. Magn Reson Med 77:1505-1515, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Low photon count based digital holography for quadratic phase cryptography.

PubMed

Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Ryle, James P; Healy, John J; Lee, Byung-Geun; Sheridan, John T

2017-07-15

Recently, the vulnerability of the linear canonical transform-based double random phase encryption system to attack has been demonstrated. To alleviate this, we present for the first time, to the best of our knowledge, a method for securing a two-dimensional scene using a quadratic phase encoding system operating in the photon-counted imaging (PCI) regime. Position-phase-shifting digital holography is applied to record the photon-limited encrypted complex samples. The reconstruction of the complex wavefront involves four sparse (undersampled) dataset intensity measurements (interferograms) at two different positions. Computer simulations validate that the photon-limited sparse-encrypted data has adequate information to authenticate the original data set. Finally, security analysis, employing iterative phase retrieval attacks, has been performed.

The Kepler DB: a database management system for arrays, sparse arrays, and binary data

NASA Astrophysics Data System (ADS)

McCauliff, Sean; Cote, Miles T.; Girouard, Forrest R.; Middour, Christopher; Klaus, Todd C.; Wohler, Bill

2010-07-01

The Kepler Science Operations Center stores pixel values on approximately six million pixels collected every 30 minutes, as well as data products that are generated as a result of running the Kepler science processing pipeline. The Kepler Database management system (Kepler DB)was created to act as the repository of this information. After one year of flight usage, Kepler DB is managing 3 TiB of data and is expected to grow to over 10 TiB over the course of the mission. Kepler DB is a non-relational, transactional database where data are represented as one-dimensional arrays, sparse arrays or binary large objects. We will discuss Kepler DB's APIs, implementation, usage and deployment at the Kepler Science Operations Center.

The Kepler DB, a Database Management System for Arrays, Sparse Arrays and Binary Data

NASA Technical Reports Server (NTRS)

McCauliff, Sean; Cote, Miles T.; Girouard, Forrest R.; Middour, Christopher; Klaus, Todd C.; Wohler, Bill

2010-01-01

The Kepler Science Operations Center stores pixel values on approximately six million pixels collected every 30-minutes, as well as data products that are generated as a result of running the Kepler science processing pipeline. The Kepler Database (Kepler DB) management system was created to act as the repository of this information. After one year of ight usage, Kepler DB is managing 3 TiB of data and is expected to grow to over 10 TiB over the course of the mission. Kepler DB is a non-relational, transactional database where data are represented as one dimensional arrays, sparse arrays or binary large objects. We will discuss Kepler DB's APIs, implementation, usage and deployment at the Kepler Science Operations Center.

Sliding mode control for a two-joint coupling nonlinear system based on extended state observer.

PubMed

Zhao, Ling; Cheng, Haiyan; Wang, Tao

2018-02-01

A two-joint coupling nonlinear system driven by pneumatic artificial muscles is introduced in this paper. A sliding mode controller with extended state observer is proposed to cope with nonlinearities and disturbances for the two-joint coupling nonlinear system. In addition, convergence of the extended state observer is presented and stability analysis of the closed-loop system is also demonstrated with the sliding mode controller. Lastly, some experiments are carried out to show the reality effectiveness of the proposed method. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Finite-time synchronization for second-order nonlinear multi-agent system via pinning exponent sliding mode control.

PubMed

Hou, Huazhou; Zhang, Qingling

2016-11-01

In this paper we investigate the finite-time synchronization for second-order multi-agent system via pinning exponent sliding mode control. Firstly, for the nonlinear multi-agent system, differential mean value theorem is employed to transfer the nonlinear system into linear system, then, by pinning only one node in the system with novel exponent sliding mode control, we can achieve synchronization in finite time. Secondly, considering the 3-DOF helicopter system with nonlinear dynamics and disturbances, the novel exponent sliding mode control protocol is applied to only one node to achieve the synchronization. Finally, the simulation results show the effectiveness and the advantages of the proposed method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Volterra-series-based nonlinear system modeling and its engineering applications: A state-of-the-art review

NASA Astrophysics Data System (ADS)

Cheng, C. M.; Peng, Z. K.; Zhang, W. M.; Meng, G.

2017-03-01

Nonlinear problems have drawn great interest and extensive attention from engineers, physicists and mathematicians and many other scientists because most real systems are inherently nonlinear in nature. To model and analyze nonlinear systems, many mathematical theories and methods have been developed, including Volterra series. In this paper, the basic definition of the Volterra series is recapitulated, together with some frequency domain concepts which are derived from the Volterra series, including the general frequency response function (GFRF), the nonlinear output frequency response function (NOFRF), output frequency response function (OFRF) and associated frequency response function (AFRF). The relationship between the Volterra series and other nonlinear system models and nonlinear problem solving methods are discussed, including the Taylor series, Wiener series, NARMAX model, Hammerstein model, Wiener model, Wiener-Hammerstein model, harmonic balance method, perturbation method and Adomian decomposition. The challenging problems and their state of arts in the series convergence study and the kernel identification study are comprehensively introduced. In addition, a detailed review is then given on the applications of Volterra series in mechanical engineering, aeroelasticity problem, control engineering, electronic and electrical engineering.

Lp-stability (1 less than or equal to p less than or equal to infinity) of multivariable nonlinear time-varying feedback systems that are open-loop unstable. [noting unstable convolution subsystem forward control and time varying nonlinear feedback

NASA Technical Reports Server (NTRS)

Callier, F. M.; Desoer, C. A.

1973-01-01

A class of multivariable, nonlinear time-varying feedback systems with an unstable convolution subsystem as feedforward and a time-varying nonlinear gain as feedback was considered. The impulse response of the convolution subsystem is the sum of a finite number of increasing exponentials multiplied by nonnegative powers of the time t, a term that is absolutely integrable and an infinite series of delayed impulses. The main result is a theorem. It essentially states that if the unstable convolution subsystem can be stabilized by a constant feedback gain F and if incremental gain of the difference between the nonlinear gain function and F is sufficiently small, then the nonlinear system is L(p)-stable for any p between one and infinity. Furthermore, the solutions of the nonlinear system depend continuously on the inputs in any L(p)-norm. The fixed point theorem is crucial in deriving the above theorem.

A deep belief network with PLSR for nonlinear system modeling.

PubMed

Qiao, Junfei; Wang, Gongming; Li, Wenjing; Li, Xiaoli

2018-08-01

Nonlinear system modeling plays an important role in practical engineering, and deep learning-based deep belief network (DBN) is now popular in nonlinear system modeling and identification because of the strong learning ability. However, the existing weights optimization for DBN is based on gradient, which always leads to a local optimum and a poor training result. In this paper, a DBN with partial least square regression (PLSR-DBN) is proposed for nonlinear system modeling, which focuses on the problem of weights optimization for DBN using PLSR. Firstly, unsupervised contrastive divergence (CD) algorithm is used in weights initialization. Secondly, initial weights derived from CD algorithm are optimized through layer-by-layer PLSR modeling from top layer to bottom layer. Instead of gradient method, PLSR-DBN can determine the optimal weights using several PLSR models, so that a better performance of PLSR-DBN is achieved. Then, the analysis of convergence is theoretically given to guarantee the effectiveness of the proposed PLSR-DBN model. Finally, the proposed PLSR-DBN is tested on two benchmark nonlinear systems and an actual wastewater treatment system as well as a handwritten digit recognition (nonlinear mapping and modeling) with high-dimension input data. The experiment results show that the proposed PLSR-DBN has better performances of time and accuracy on nonlinear system modeling than that of other methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

PRESS-based EFOR algorithm for the dynamic parametrical modeling of nonlinear MDOF systems

NASA Astrophysics Data System (ADS)

Liu, Haopeng; Zhu, Yunpeng; Luo, Zhong; Han, Qingkai

2017-09-01

In response to the identification problem concerning multi-degree of freedom (MDOF) nonlinear systems, this study presents the extended forward orthogonal regression (EFOR) based on predicted residual sums of squares (PRESS) to construct a nonlinear dynamic parametrical model. The proposed parametrical model is based on the non-linear autoregressive with exogenous inputs (NARX) model and aims to explicitly reveal the physical design parameters of the system. The PRESS-based EFOR algorithm is proposed to identify such a model for MDOF systems. By using the algorithm, we built a common-structured model based on the fundamental concept of evaluating its generalization capability through cross-validation. The resulting model aims to prevent over-fitting with poor generalization performance caused by the average error reduction ratio (AERR)-based EFOR algorithm. Then, a functional relationship is established between the coefficients of the terms and the design parameters of the unified model. Moreover, a 5-DOF nonlinear system is taken as a case to illustrate the modeling of the proposed algorithm. Finally, a dynamic parametrical model of a cantilever beam is constructed from experimental data. Results indicate that the dynamic parametrical model of nonlinear systems, which depends on the PRESS-based EFOR, can accurately predict the output response, thus providing a theoretical basis for the optimal design of modeling methods for MDOF nonlinear systems.

Simulation and measurement of nonlinear behavior in a high-power test cell.

PubMed

Harvey, Gerald; Gachagan, Anthony

2011-04-01

High-power ultrasound has many diverse uses in process applications in industries ranging from food to pharmaceutical. Because cavitation is frequently a desirable effect within many high-power, low-frequency systems, these systems are commonly expected to feature highly nonlinear acoustic propagation because of the high input levels employed. This generation of harmonics significantly alters the field profile compared with that of a linear system, making accurate field modeling difficult. However, when the short propagation distances involved are considered, it is not unreasonable to assume that these systems may remain largely linear until the onset of cavitation, in terms of classical acoustic propagation. The purpose of this paper is to investigate the possible nonlinear effects within such systems before the onset of cavitation. A theoretical description of nonlinear propagation will be presented and the merits of common analytical models will be discussed. Following this, a numerical model of nonlinearity will be outlined and the advantages it presents for representing nonlinear effects in bounded fields will be discussed. Next, the driving equipment and transducers will be evaluated for linearity to disengage any effects from those formed in the transmission load. Finally, the linearity of the system will be measured using an acoustic hydrophone and compared with finite element analysis to confirm that nonlinear effects are not prevalent in such systems at the onset of cavitation. © 2011 IEEE

Multigrid approaches to non-linear diffusion problems on unstructured meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.

Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials

PubMed Central

Khan, Rahmat Ali; Tajadodi, Haleh; Johnston, Sarah Jane

2014-01-01

In this paper we propose the Bernstein polynomials to achieve the numerical solutions of nonlinear fractional-order chaotic system known by fractional-order Brusselator system. We use operational matrices of fractional integration and multiplication of Bernstein polynomials, which turns the nonlinear fractional-order Brusselator system to a system of algebraic equations. Two illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques. PMID:25485293

Nonlinear modes of snap-through motions of a shallow arch

NASA Astrophysics Data System (ADS)

Breslavsky, I.; Avramov, K. V.; Mikhlin, Yu.; Kochurov, R.

2008-03-01

Nonlinear modes of snap-through motions of a shallow arch are analyzed. Dynamics of shallow arch is modeled by a two-degree-of-freedom system. Two nonlinear modes of this discrete system are treated. The methods of Ince algebraization and Hill determinants are used to study stability of nonlinear modes. The analytical results are compared with the data of the numerical simulations.

Sparse Matrices in MATLAB: Design and Implementation

NASA Technical Reports Server (NTRS)

Gilbert, John R.; Moler, Cleve; Schreiber, Robert

1992-01-01

The matrix computation language and environment MATLAB is extended to include sparse matrix storage and operations. The only change to the outward appearance of the MATLAB language is a pair of commands to create full or sparse matrices. Nearly all the operations of MATLAB now apply equally to full or sparse matrices, without any explicit action by the user. The sparse data structure represents a matrix in space proportional to the number of nonzero entries, and most of the operations compute sparse results in time proportional to the number of arithmetic operations on nonzeros.

NIMROD: a program for inference via a normal approximation of the posterior in models with random effects based on ordinary differential equations.

PubMed

Prague, Mélanie; Commenges, Daniel; Guedj, Jérémie; Drylewicz, Julia; Thiébaut, Rodolphe

2013-08-01

Models based on ordinary differential equations (ODE) are widespread tools for describing dynamical systems. In biomedical sciences, data from each subject can be sparse making difficult to precisely estimate individual parameters by standard non-linear regression but information can often be gained from between-subjects variability. This makes natural the use of mixed-effects models to estimate population parameters. Although the maximum likelihood approach is a valuable option, identifiability issues favour Bayesian approaches which can incorporate prior knowledge in a flexible way. However, the combination of difficulties coming from the ODE system and from the presence of random effects raises a major numerical challenge. Computations can be simplified by making a normal approximation of the posterior to find the maximum of the posterior distribution (MAP). Here we present the NIMROD program (normal approximation inference in models with random effects based on ordinary differential equations) devoted to the MAP estimation in ODE models. We describe the specific implemented features such as convergence criteria and an approximation of the leave-one-out cross-validation to assess the model quality of fit. In pharmacokinetics models, first, we evaluate the properties of this algorithm and compare it with FOCE and MCMC algorithms in simulations. Then, we illustrate NIMROD use on Amprenavir pharmacokinetics data from the PUZZLE clinical trial in HIV infected patients. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Identification of limit cycles in multi-nonlinearity, multiple path systems

NASA Technical Reports Server (NTRS)

Mitchell, J. R.; Barron, O. L.

1979-01-01

A method of analysis which identifies limit cycles in autonomous systems with multiple nonlinearities and multiple forward paths is presented. The FORTRAN code for implementing the Harmonic Balance Algorithm is reported. The FORTRAN code is used to identify limit cycles in multiple path and nonlinearity systems while retaining the effects of several harmonic components.

Robust model predictive control for constrained continuous-time nonlinear systems

NASA Astrophysics Data System (ADS)

Sun, Tairen; Pan, Yongping; Zhang, Jun; Yu, Haoyong

2018-02-01

In this paper, a robust model predictive control (MPC) is designed for a class of constrained continuous-time nonlinear systems with bounded additive disturbances. The robust MPC consists of a nonlinear feedback control and a continuous-time model-based dual-mode MPC. The nonlinear feedback control guarantees the actual trajectory being contained in a tube centred at the nominal trajectory. The dual-mode MPC is designed to ensure asymptotic convergence of the nominal trajectory to zero. This paper extends current results on discrete-time model-based tube MPC and linear system model-based tube MPC to continuous-time nonlinear model-based tube MPC. The feasibility and robustness of the proposed robust MPC have been demonstrated by theoretical analysis and applications to a cart-damper springer system and a one-link robot manipulator.

[Analysis of vegetation spatial and temporal variations in Qinghai Province based on remote sensing].

PubMed

Wang, Li-wen; Wei, Ya-xing; Niu, Zheng

2008-06-01

1 km MODIS NDVI time series data combining with decision tree classification, supervised classification and unsupervised classification was used to classify land cover type of Qinghai Province into 14 classes. In our classification system, sparse grassland and sparse shrub were emphasized, and their spatial distribution locations were labeled. From digital elevation model (DEM) of Qinghai Province, five elevation belts were achieved, and we utilized geographic information system (GIS) software to analyze vegetation cover variation on different elevation belts. Our research result shows that vegetation cover in Qinghai Province has been improved in recent five years. Vegetation cover area increases from 370047 km2 in 2001 to 374576 km2 in 2006, and vegetation cover rate increases by 0.63%. Among five grade elevation belts, vegetation cover ratio of high mountain belt is the highest (67.92%). The area of middle density grassland in high mountain belt is the largest, of which area is 94 003 km2. Increased area of dense grassland in high mountain belt is the greatest (1280 km2). During five years, the biggest variation is the conversion from sparse grassland to middle density grassland in high mountain belt, of which area is 15931 km2.

A Vehicle Active Safety Model: Vehicle Speed Control Based on Driver Vigilance Detection Using Wearable EEG and Sparse Representation.

PubMed

Zhang, Zutao; Luo, Dianyuan; Rasim, Yagubov; Li, Yanjun; Meng, Guanjun; Xu, Jian; Wang, Chunbai

2016-02-19

In this paper, we present a vehicle active safety model for vehicle speed control based on driver vigilance detection using low-cost, comfortable, wearable electroencephalographic (EEG) sensors and sparse representation. The proposed system consists of three main steps, namely wireless wearable EEG collection, driver vigilance detection, and vehicle speed control strategy. First of all, a homemade low-cost comfortable wearable brain-computer interface (BCI) system with eight channels is designed for collecting the driver's EEG signal. Second, wavelet de-noising and down-sample algorithms are utilized to enhance the quality of EEG data, and Fast Fourier Transformation (FFT) is adopted to extract the EEG power spectrum density (PSD). In this step, sparse representation classification combined with k-singular value decomposition (KSVD) is firstly introduced in PSD to estimate the driver's vigilance level. Finally, a novel safety strategy of vehicle speed control, which controls the electronic throttle opening and automatic braking after driver fatigue detection using the above method, is presented to avoid serious collisions and traffic accidents. The simulation and practical testing results demonstrate the feasibility of the vehicle active safety model.

Multimode waveguide speckle patterns for compressive sensing.

PubMed

Valley, George C; Sefler, George A; Justin Shaw, T

2016-06-01

Compressive sensing (CS) of sparse gigahertz-band RF signals using microwave photonics may achieve better performances with smaller size, weight, and power than electronic CS or conventional Nyquist rate sampling. The critical element in a CS system is the device that produces the CS measurement matrix (MM). We show that passive speckle patterns in multimode waveguides potentially provide excellent MMs for CS. We measure and calculate the MM for a multimode fiber and perform simulations using this MM in a CS system. We show that the speckle MM exhibits the sharp phase transition and coherence properties needed for CS and that these properties are similar to those of a sub-Gaussian MM with the same mean and standard deviation. We calculate the MM for a multimode planar waveguide and find dimensions of the planar guide that give a speckle MM with a performance similar to that of the multimode fiber. The CS simulations show that all measured and calculated speckle MMs exhibit a robust performance with equal amplitude signals that are sparse in time, in frequency, and in wavelets (Haar wavelet transform). The planar waveguide results indicate a path to a microwave photonic integrated circuit for measuring sparse gigahertz-band RF signals using CS.

Task-based data-acquisition optimization for sparse image reconstruction systems

NASA Astrophysics Data System (ADS)

Chen, Yujia; Lou, Yang; Kupinski, Matthew A.; Anastasio, Mark A.

2017-03-01

Conventional wisdom dictates that imaging hardware should be optimized by use of an ideal observer (IO) that exploits full statistical knowledge of the class of objects to be imaged, without consideration of the reconstruction method to be employed. However, accurate and tractable models of the complete object statistics are often difficult to determine in practice. Moreover, in imaging systems that employ compressive sensing concepts, imaging hardware and (sparse) image reconstruction are innately coupled technologies. We have previously proposed a sparsity-driven ideal observer (SDIO) that can be employed to optimize hardware by use of a stochastic object model that describes object sparsity. The SDIO and sparse reconstruction method can therefore be "matched" in the sense that they both utilize the same statistical information regarding the class of objects to be imaged. To efficiently compute SDIO performance, the posterior distribution is estimated by use of computational tools developed recently for variational Bayesian inference. Subsequently, the SDIO test statistic can be computed semi-analytically. The advantages of employing the SDIO instead of a Hotelling observer are systematically demonstrated in case studies in which magnetic resonance imaging (MRI) data acquisition schemes are optimized for signal detection tasks.

Regression-based adaptive sparse polynomial dimensional decomposition for sensitivity analysis

NASA Astrophysics Data System (ADS)

Tang, Kunkun; Congedo, Pietro; Abgrall, Remi

2014-11-01

Polynomial dimensional decomposition (PDD) is employed in this work for global sensitivity analysis and uncertainty quantification of stochastic systems subject to a large number of random input variables. Due to the intimate structure between PDD and Analysis-of-Variance, PDD is able to provide simpler and more direct evaluation of the Sobol' sensitivity indices, when compared to polynomial chaos (PC). Unfortunately, the number of PDD terms grows exponentially with respect to the size of the input random vector, which makes the computational cost of the standard method unaffordable for real engineering applications. In order to address this problem of curse of dimensionality, this work proposes a variance-based adaptive strategy aiming to build a cheap meta-model by sparse-PDD with PDD coefficients computed by regression. During this adaptive procedure, the model representation by PDD only contains few terms, so that the cost to resolve repeatedly the linear system of the least-square regression problem is negligible. The size of the final sparse-PDD representation is much smaller than the full PDD, since only significant terms are eventually retained. Consequently, a much less number of calls to the deterministic model is required to compute the final PDD coefficients.

A Vehicle Active Safety Model: Vehicle Speed Control Based on Driver Vigilance Detection Using Wearable EEG and Sparse Representation

PubMed Central

Zhang, Zutao; Luo, Dianyuan; Rasim, Yagubov; Li, Yanjun; Meng, Guanjun; Xu, Jian; Wang, Chunbai

2016-01-01

In this paper, we present a vehicle active safety model for vehicle speed control based on driver vigilance detection using low-cost, comfortable, wearable electroencephalographic (EEG) sensors and sparse representation. The proposed system consists of three main steps, namely wireless wearable EEG collection, driver vigilance detection, and vehicle speed control strategy. First of all, a homemade low-cost comfortable wearable brain-computer interface (BCI) system with eight channels is designed for collecting the driver’s EEG signal. Second, wavelet de-noising and down-sample algorithms are utilized to enhance the quality of EEG data, and Fast Fourier Transformation (FFT) is adopted to extract the EEG power spectrum density (PSD). In this step, sparse representation classification combined with k-singular value decomposition (KSVD) is firstly introduced in PSD to estimate the driver’s vigilance level . Finally, a novel safety strategy of vehicle speed control, which controls the electronic throttle opening and automatic braking after driver fatigue detection using the above method, is presented to avoid serious collisions and traffic accidents. The simulation and practical testing results demonstrate the feasibility of the vehicle active safety model. PMID:26907278

An embedded system for face classification in infrared video using sparse representation

NASA Astrophysics Data System (ADS)

Saavedra M., Antonio; Pezoa, Jorge E.; Zarkesh-Ha, Payman; Figueroa, Miguel

2017-09-01

We propose a platform for robust face recognition in Infrared (IR) images using Compressive Sensing (CS). In line with CS theory, the classification problem is solved using a sparse representation framework, where test images are modeled by means of a linear combination of the training set. Because the training set constitutes an over-complete dictionary, we identify new images by finding their sparsest representation based on the training set, using standard l1-minimization algorithms. Unlike conventional face-recognition algorithms, we feature extraction is performed using random projections with a precomputed binary matrix, as proposed in the CS literature. This random sampling reduces the effects of noise and occlusions such as facial hair, eyeglasses, and disguises, which are notoriously challenging in IR images. Thus, the performance of our framework is robust to these noise and occlusion factors, achieving an average accuracy of approximately 90% when the UCHThermalFace database is used for training and testing purposes. We implemented our framework on a high-performance embedded digital system, where the computation of the sparse representation of IR images was performed by a dedicated hardware using a deeply pipelined architecture on an Field-Programmable Gate Array (FPGA).

DOE Office of Scientific and Technical Information (OSTI.GOV)

Okumura, Teppei; Seljak, Uroš; Desjacques, Vincent, E-mail: teppei@ewha.ac.kr, E-mail: useljak@berkeley.edu, E-mail: dvince@physik.uzh.ch

It was recently shown that the power spectrum in redshift space can be written as a sum of cross-power spectra between number weighted velocity moments, of which the lowest are density and momentum density. We investigate numerically the properties of these power spectra for simulated galaxies and dark matter halos and compare them to the dark matter power spectra, generalizing the concept of the bias in density-density power spectra. Because all of the quantities are number weighted this approach is well defined even for sparse systems such as massive halos. This contrasts to the previous approaches to RSD where velocitymore » correlations have been explored, but velocity field is a poorly defined concept for sparse systems. We find that the number density weighting leads to a strong scale dependence of the bias terms for momentum density auto-correlation and cross-correlation with density. This trend becomes more significant for the more biased halos and leads to an enhancement of RSD power relative to the linear theory. Fingers-of-god effects, which in this formalism come from the correlations of the higher order moments beyond the momentum density, lead to smoothing of the power spectrum and can reduce this enhancement of power from the scale dependent bias, but are relatively small for halos with no small scale velocity dispersion. In comparison, for a more realistic galaxy sample with satellites the small scale velocity dispersion generated by satellite motions inside the halos leads to a larger power suppression on small scales, but this depends on the satellite fraction and on the details of how the satellites are distributed inside the halo. We investigate several statistics such as the two-dimensional power spectrum P(k,μ), where μ is the angle between the Fourier mode and line of sight, its multipole moments, its powers of μ{sup 2}, and configuration space statistics. Overall we find that the nonlinear effects in realistic galaxy samples such as luminous red galaxies affect the redshift space clustering on very large scales: for example, the quadrupole moment is affected by 10% for k < 0.1hMpc{sup −1}, which means that these effects need to be understood if we want to extract cosmological information from the redshift space distortions.« less

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kutz, J Nathan

2016-01-01

In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.ork, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.

A variable-frequency structural health monitoring system based on omnidirectional shear horizontal wave piezoelectric transducers

NASA Astrophysics Data System (ADS)

Huan, Qiang; Miao, Hongchen; Li, Faxin

2018-02-01

Structural health monitoring (SHM) is of great importance for engineering structures as it may detect the early degradation and thus avoid life and financial loss. Guided wave based inspection is very useful in SHM due to its capability for long distance and wide range monitoring. The fundamental shear horizontal (SH0) wave based method should be most promising since SH0 is the unique non-dispersive wave mode in plate-like structures. In this work, a sparse array SHM system based on omnidirectional SH wave piezoelectric transducers (OSH-PT) was proposed and the multi data fusion method was used for defect inspection in a 2 mm thick aluminum plate. Firstly, the performances of three types OSH-PTs was comprehensively compared and the thickness-poled d15 mode OSH-PT used in this work was demonstrated obviously superior to the other two. Then, the signal processing method and imaging algorithm for this SHM system was presented. Finally, experiments were carried out to examine the performance of the proposed SHM system in defect localization and imaging. Results indicated that this SHM system can locate a through hole as small as 0.12λ (4 mm) in diameter (where λ is the wavelength corresponding to the central operation frequency) under frequencies from 90 to 150 kHz. It can also locate multiple defects accurately based on the baseline subtraction method. Obviously, this SHM system can detect larger areas with sparse sensors because of the adopted single mode, non-dispersive and low frequency SH0 wave which can propagate long distance with small attenuation. Considering its good performances, simple data processing and sparse array, this SH0 wave-based SHM system is expected to greatly promote the applications of guided wave inspection.

Plastic and Large-Deflection Analysis of Nonlinear Structures

NASA Technical Reports Server (NTRS)

Thomson, R. G.; Hayduk, R. J.; Robinson, M. P.; Durling, B. J.; Pifko, A.; Levine, H. S.; Armen, H. J.; Levy, A.; Ogilvie, P.

1982-01-01

Plastic and Large Deflection Analysis of Nonlinear Structures (PLANS) system is collection of five computer programs for finite-element static-plastic and large deflection analysis of variety of nonlinear structures. System considers bending and membrane stresses, general three-dimensional bodies, and laminated composites.

Nonlinear modal resonances in low-gravity slosh-spacecraft systems

NASA Technical Reports Server (NTRS)

Peterson, Lee D.

1991-01-01

Nonlinear models of low gravity slosh, when coupled to spacecraft vibrations, predict intense nonlinear eigenfrequency shifts at zero gravity. These nonlinear frequency shifts are due to internal quadratic and cubic resonances between fluid slosh modes and spacecraft vibration modes. Their existence has been verified experimentally, and they cannot be correctly modeled by approximate, uncoupled nonlinear models, such as pendulum mechanical analogs. These predictions mean that linear slosh assumptions for spacecraft vibration models can be invalid, and may lead to degraded control system stability and performance. However, a complete nonlinear modal analysis will predict the correct dynamic behavior. This paper presents the analytical basis for these results, and discusses the effect of internal resonances on the nonlinear coupled response at zero gravity.

Evaluating the use of transfers for improving demand responsive systems adopting zoning strategies.

DOT National Transportation Integrated Search

2011-08-01

Due to widely dispersed population density over large and sparsely suburban/rural areas, : conventional fixed route transit services hardly satisfy the travel needs of their residents. As an : alternative, demand responsive transit (DRT) systems have...

Chaos, patterns, coherent structures, and turbulence: Reflections on nonlinear science.

PubMed

Ecke, Robert E

2015-09-01

The paradigms of nonlinear science were succinctly articulated over 25 years ago as deterministic chaos, pattern formation, coherent structures, and adaptation/evolution/learning. For chaos, the main unifying concept was universal routes to chaos in general nonlinear dynamical systems, built upon a framework of bifurcation theory. Pattern formation focused on spatially extended nonlinear systems, taking advantage of symmetry properties to develop highly quantitative amplitude equations of the Ginzburg-Landau type to describe early nonlinear phenomena in the vicinity of critical points. Solitons, mathematically precise localized nonlinear wave states, were generalized to a larger and less precise class of coherent structures such as, for example, concentrated regions of vorticity from laboratory wake flows to the Jovian Great Red Spot. The combination of these three ideas was hoped to provide the tools and concepts for the understanding and characterization of the strongly nonlinear problem of fluid turbulence. Although this early promise has been largely unfulfilled, steady progress has been made using the approaches of nonlinear science. I provide a series of examples of bifurcations and chaos, of one-dimensional and two-dimensional pattern formation, and of turbulence to illustrate both the progress and limitations of the nonlinear science approach. As experimental and computational methods continue to improve, the promise of nonlinear science to elucidate fluid turbulence continues to advance in a steady manner, indicative of the grand challenge nature of strongly nonlinear multi-scale dynamical systems.

Learning Sparse Feature Representations using Probabilistic Quadtrees and Deep Belief Nets

DTIC Science & Technology

2015-04-24

Feature Representations usingProbabilistic Quadtrees and Deep Belief Nets Learning sparse feature representations is a useful instru- ment for solving an...novel framework for the classifi cation of handwritten digits that learns sparse representations using probabilistic quadtrees and Deep Belief Nets... Learning Sparse Feature Representations usingProbabilistic Quadtrees and Deep Belief Nets Report Title Learning sparse feature representations is a useful

Reconstructing Mammalian Sleep Dynamics with Data Assimilation

PubMed Central

Sedigh-Sarvestani, Madineh; Schiff, Steven J.; Gluckman, Bruce J.

2012-01-01

Data assimilation is a valuable tool in the study of any complex system, where measurements are incomplete, uncertain, or both. It enables the user to take advantage of all available information including experimental measurements and short-term model forecasts of a system. Although data assimilation has been used to study other biological systems, the study of the sleep-wake regulatory network has yet to benefit from this toolset. We present a data assimilation framework based on the unscented Kalman filter (UKF) for combining sparse measurements together with a relatively high-dimensional nonlinear computational model to estimate the state of a model of the sleep-wake regulatory system. We demonstrate with simulation studies that a few noisy variables can be used to accurately reconstruct the remaining hidden variables. We introduce a metric for ranking relative partial observability of computational models, within the UKF framework, that allows us to choose the optimal variables for measurement and also provides a methodology for optimizing framework parameters such as UKF covariance inflation. In addition, we demonstrate a parameter estimation method that allows us to track non-stationary model parameters and accommodate slow dynamics not included in the UKF filter model. Finally, we show that we can even use observed discretized sleep-state, which is not one of the model variables, to reconstruct model state and estimate unknown parameters. Sleep is implicated in many neurological disorders from epilepsy to schizophrenia, but simultaneous observation of the many brain components that regulate this behavior is difficult. We anticipate that this data assimilation framework will enable better understanding of the detailed interactions governing sleep and wake behavior and provide for better, more targeted, therapies. PMID:23209396