Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics

NASA Astrophysics Data System (ADS)

Wehmeyer, Christoph; Noé, Frank

2018-06-01

Inspired by the success of deep learning techniques in the physical and chemical sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension reduction of molecular dynamics data. We can show that our time-lagged autoencoder reliably finds low-dimensional embeddings for high-dimensional feature spaces which capture the slow dynamics of the underlying stochastic processes—beyond the capabilities of linear dimension reduction techniques.

A sparse grid based method for generative dimensionality reduction of high-dimensional data

NASA Astrophysics Data System (ADS)

Bohn, Bastian; Garcke, Jochen; Griebel, Michael

2016-03-01

Generative dimensionality reduction methods play an important role in machine learning applications because they construct an explicit mapping from a low-dimensional space to the high-dimensional data space. We discuss a general framework to describe generative dimensionality reduction methods, where the main focus lies on a regularized principal manifold learning variant. Since most generative dimensionality reduction algorithms exploit the representer theorem for reproducing kernel Hilbert spaces, their computational costs grow at least quadratically in the number n of data. Instead, we introduce a grid-based discretization approach which automatically scales just linearly in n. To circumvent the curse of dimensionality of full tensor product grids, we use the concept of sparse grids. Furthermore, in real-world applications, some embedding directions are usually more important than others and it is reasonable to refine the underlying discretization space only in these directions. To this end, we employ a dimension-adaptive algorithm which is based on the ANOVA (analysis of variance) decomposition of a function. In particular, the reconstruction error is used to measure the quality of an embedding. As an application, the study of large simulation data from an engineering application in the automotive industry (car crash simulation) is performed.

Graph embedding and extensions: a general framework for dimensionality reduction.

PubMed

Yan, Shuicheng; Xu, Dong; Zhang, Benyu; Zhang, Hong-Jiang; Yang, Qiang; Lin, Stephen

2007-01-01

Over the past few decades, a large family of algorithms - supervised or unsupervised; stemming from statistics or geometry theory - has been designed to provide different solutions to the problem of dimensionality reduction. Despite the different motivations of these algorithms, we present in this paper a general formulation known as graph embedding to unify them within a common framework. In graph embedding, each algorithm can be considered as the direct graph embedding or its linear/kernel/tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set, with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided. Furthermore, the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms. By utilizing this framework as a tool, we propose a new supervised dimensionality reduction algorithm called Marginal Fisher Analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class, while the penalty graph connects the marginal points and characterizes the interclass separability. We show that MFA effectively overcomes the limitations of the traditional Linear Discriminant Analysis algorithm due to data distribution assumptions and available projection directions. Real face recognition experiments show the superiority of our proposed MFA in comparison to LDA, also for corresponding kernel and tensor extensions.

Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

NASA Technical Reports Server (NTRS)

Burns, John A.; Marrekchi, Hamadi

1993-01-01

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

Controls/CFD Interdisciplinary Research Software Generates Low-Order Linear Models for Control Design From Steady-State CFD Results

NASA Technical Reports Server (NTRS)

Melcher, Kevin J.

1997-01-01

The NASA Lewis Research Center is developing analytical methods and software tools to create a bridge between the controls and computational fluid dynamics (CFD) disciplines. Traditionally, control design engineers have used coarse nonlinear simulations to generate information for the design of new propulsion system controls. However, such traditional methods are not adequate for modeling the propulsion systems of complex, high-speed vehicles like the High Speed Civil Transport. To properly model the relevant flow physics of high-speed propulsion systems, one must use simulations based on CFD methods. Such CFD simulations have become useful tools for engineers that are designing propulsion system components. The analysis techniques and software being developed as part of this effort are an attempt to evolve CFD into a useful tool for control design as well. One major aspect of this research is the generation of linear models from steady-state CFD results. CFD simulations, often used during the design of high-speed inlets, yield high resolution operating point data. Under a NASA grant, the University of Akron has developed analytical techniques and software tools that use these data to generate linear models for control design. The resulting linear models have the same number of states as the original CFD simulation, so they are still very large and computationally cumbersome. Model reduction techniques have been successfully applied to reduce these large linear models by several orders of magnitude without significantly changing the dynamic response. The result is an accurate, easy to use, low-order linear model that takes less time to generate than those generated by traditional means. The development of methods for generating low-order linear models from steady-state CFD is most complete at the one-dimensional level, where software is available to generate models with different kinds of input and output variables. One-dimensional methods have been extended somewhat so that linear models can also be generated from two- and three-dimensional steady-state results. Standard techniques are adequate for reducing the order of one-dimensional CFD-based linear models. However, reduction of linear models based on two- and three-dimensional CFD results is complicated by very sparse, ill-conditioned matrices. Some novel approaches are being investigated to solve this problem.

A Fourier dimensionality reduction model for big data interferometric imaging

NASA Astrophysics Data System (ADS)

Vijay Kartik, S.; Carrillo, Rafael E.; Thiran, Jean-Philippe; Wiaux, Yves

2017-06-01

Data dimensionality reduction in radio interferometry can provide savings of computational resources for image reconstruction through reduced memory footprints and lighter computations per iteration, which is important for the scalability of imaging methods to the big data setting of the next-generation telescopes. This article sheds new light on dimensionality reduction from the perspective of the compressed sensing theory and studies its interplay with imaging algorithms designed in the context of convex optimization. We propose a post-gridding linear data embedding to the space spanned by the left singular vectors of the measurement operator, providing a dimensionality reduction below image size. This embedding preserves the null space of the measurement operator and hence its sampling properties are also preserved in light of the compressed sensing theory. We show that this can be approximated by first computing the dirty image and then applying a weighted subsampled discrete Fourier transform to obtain the final reduced data vector. This Fourier dimensionality reduction model ensures a fast implementation of the full measurement operator, essential for any iterative image reconstruction method. The proposed reduction also preserves the independent and identically distributed Gaussian properties of the original measurement noise. For convex optimization-based imaging algorithms, this is key to justify the use of the standard ℓ2-norm as the data fidelity term. Our simulations confirm that this dimensionality reduction approach can be leveraged by convex optimization algorithms with no loss in imaging quality relative to reconstructing the image from the complete visibility data set. Reconstruction results in simulation settings with no direction dependent effects or calibration errors show promising performance of the proposed dimensionality reduction. Further tests on real data are planned as an extension of the current work. matlab code implementing the proposed reduction method is available on GitHub.

Optimal linear and nonlinear feature extraction based on the minimization of the increased risk of misclassification. [Bayes theorem - statistical analysis/data processing

NASA Technical Reports Server (NTRS)

Defigueiredo, R. J. P.

1974-01-01

General classes of nonlinear and linear transformations were investigated for the reduction of the dimensionality of the classification (feature) space so that, for a prescribed dimension m of this space, the increase of the misclassification risk is minimized.

Feature extraction with deep neural networks by a generalized discriminant analysis.

PubMed

Stuhlsatz, André; Lippel, Jens; Zielke, Thomas

2012-04-01

We present an approach to feature extraction that is a generalization of the classical linear discriminant analysis (LDA) on the basis of deep neural networks (DNNs). As for LDA, discriminative features generated from independent Gaussian class conditionals are assumed. This modeling has the advantages that the intrinsic dimensionality of the feature space is bounded by the number of classes and that the optimal discriminant function is linear. Unfortunately, linear transformations are insufficient to extract optimal discriminative features from arbitrarily distributed raw measurements. The generalized discriminant analysis (GerDA) proposed in this paper uses nonlinear transformations that are learnt by DNNs in a semisupervised fashion. We show that the feature extraction based on our approach displays excellent performance on real-world recognition and detection tasks, such as handwritten digit recognition and face detection. In a series of experiments, we evaluate GerDA features with respect to dimensionality reduction, visualization, classification, and detection. Moreover, we show that GerDA DNNs can preprocess truly high-dimensional input data to low-dimensional representations that facilitate accurate predictions even if simple linear predictors or measures of similarity are used.

Shape component analysis: structure-preserving dimension reduction on biological shape spaces.

PubMed

Lee, Hao-Chih; Liao, Tao; Zhang, Yongjie Jessica; Yang, Ge

2016-03-01

Quantitative shape analysis is required by a wide range of biological studies across diverse scales, ranging from molecules to cells and organisms. In particular, high-throughput and systems-level studies of biological structures and functions have started to produce large volumes of complex high-dimensional shape data. Analysis and understanding of high-dimensional biological shape data require dimension-reduction techniques. We have developed a technique for non-linear dimension reduction of 2D and 3D biological shape representations on their Riemannian spaces. A key feature of this technique is that it preserves distances between different shapes in an embedded low-dimensional shape space. We demonstrate an application of this technique by combining it with non-linear mean-shift clustering on the Riemannian spaces for unsupervised clustering of shapes of cellular organelles and proteins. Source code and data for reproducing results of this article are freely available at https://github.com/ccdlcmu/shape_component_analysis_Matlab The implementation was made in MATLAB and supported on MS Windows, Linux and Mac OS. geyang@andrew.cmu.edu. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Nonlinear vs. linear biasing in Trp-cage folding simulations

NASA Astrophysics Data System (ADS)

Spiwok, Vojtěch; Oborský, Pavel; Pazúriková, Jana; Křenek, Aleš; Králová, Blanka

2015-03-01

Biased simulations have great potential for the study of slow processes, including protein folding. Atomic motions in molecules are nonlinear, which suggests that simulations with enhanced sampling of collective motions traced by nonlinear dimensionality reduction methods may perform better than linear ones. In this study, we compare an unbiased folding simulation of the Trp-cage miniprotein with metadynamics simulations using both linear (principle component analysis) and nonlinear (Isomap) low dimensional embeddings as collective variables. Folding of the mini-protein was successfully simulated in 200 ns simulation with linear biasing and non-linear motion biasing. The folded state was correctly predicted as the free energy minimum in both simulations. We found that the advantage of linear motion biasing is that it can sample a larger conformational space, whereas the advantage of nonlinear motion biasing lies in slightly better resolution of the resulting free energy surface. In terms of sampling efficiency, both methods are comparable.

Nonlinear vs. linear biasing in Trp-cage folding simulations.

PubMed

Spiwok, Vojtěch; Oborský, Pavel; Pazúriková, Jana; Křenek, Aleš; Králová, Blanka

2015-03-21

Biased simulations have great potential for the study of slow processes, including protein folding. Atomic motions in molecules are nonlinear, which suggests that simulations with enhanced sampling of collective motions traced by nonlinear dimensionality reduction methods may perform better than linear ones. In this study, we compare an unbiased folding simulation of the Trp-cage miniprotein with metadynamics simulations using both linear (principle component analysis) and nonlinear (Isomap) low dimensional embeddings as collective variables. Folding of the mini-protein was successfully simulated in 200 ns simulation with linear biasing and non-linear motion biasing. The folded state was correctly predicted as the free energy minimum in both simulations. We found that the advantage of linear motion biasing is that it can sample a larger conformational space, whereas the advantage of nonlinear motion biasing lies in slightly better resolution of the resulting free energy surface. In terms of sampling efficiency, both methods are comparable.

Reduction of respiratory ghosting motion artifacts in conventional two-dimensional multi-slice Cartesian turbo spin-echo: which k-space filling order is the best?

PubMed

Inoue, Yuuji; Yoneyama, Masami; Nakamura, Masanobu; Takemura, Atsushi

2018-06-01

The two-dimensional Cartesian turbo spin-echo (TSE) sequence is widely used in routine clinical studies, but it is sensitive to respiratory motion. We investigated the k-space orders in Cartesian TSE that can effectively reduce motion artifacts. The purpose of this study was to demonstrate the relationship between k-space order and degree of motion artifacts using a moving phantom. We compared the degree of motion artifacts between linear and asymmetric k-space orders. The actual spacing of ghost artifacts in the asymmetric order was doubled compared with that in the linear order in the free-breathing situation. The asymmetric order clearly showed less sensitivity to incomplete breath-hold at the latter half of the imaging period. Because of the actual number of partitions of the k-space and the temporal filling order, the asymmetric k-space order of Cartesian TSE was superior to the linear k-space order for reduction of ghosting motion artifacts.

Chaos and Robustness in a Single Family of Genetic Oscillatory Networks

PubMed Central

Fu, Daniel; Tan, Patrick; Kuznetsov, Alexey; Molkov, Yaroslav I.

2014-01-01

Genetic oscillatory networks can be mathematically modeled with delay differential equations (DDEs). Interpreting genetic networks with DDEs gives a more intuitive understanding from a biological standpoint. However, it presents a problem mathematically, for DDEs are by construction infinitely-dimensional and thus cannot be analyzed using methods common for systems of ordinary differential equations (ODEs). In our study, we address this problem by developing a method for reducing infinitely-dimensional DDEs to two- and three-dimensional systems of ODEs. We find that the three-dimensional reductions provide qualitative improvements over the two-dimensional reductions. We find that the reducibility of a DDE corresponds to its robustness. For non-robust DDEs that exhibit high-dimensional dynamics, we calculate analytic dimension lines to predict the dependence of the DDEs’ correlation dimension on parameters. From these lines, we deduce that the correlation dimension of non-robust DDEs grows linearly with the delay. On the other hand, for robust DDEs, we find that the period of oscillation grows linearly with delay. We find that DDEs with exclusively negative feedback are robust, whereas DDEs with feedback that changes its sign are not robust. We find that non-saturable degradation damps oscillations and narrows the range of parameter values for which oscillations exist. Finally, we deduce that natural genetic oscillators with highly-regular periods likely have solely negative feedback. PMID:24667178

Simple Procedure to Compute the Inductance of a Toroidal Ferrite Core from the Linear to the Saturation Regions

PubMed Central

Salas, Rosa Ana; Pleite, Jorge

2013-01-01

We propose a specific procedure to compute the inductance of a toroidal ferrite core as a function of the excitation current. The study includes the linear, intermediate and saturation regions. The procedure combines the use of Finite Element Analysis in 2D and experimental measurements. Through the two dimensional (2D) procedure we are able to achieve convergence, a reduction of computational cost and equivalent results to those computed by three dimensional (3D) simulations. The validation is carried out by comparing 2D, 3D and experimental results. PMID:28809283

Linear and nonlinear subspace analysis of hand movements during grasping.

PubMed

Cui, Phil Hengjun; Visell, Yon

2014-01-01

This study investigated nonlinear patterns of coordination, or synergies, underlying whole-hand grasping kinematics. Prior research has shed considerable light on roles played by such coordinated degrees-of-freedom (DOF), illuminating how motor control is facilitated by structural and functional specializations in the brain, peripheral nervous system, and musculoskeletal system. However, existing analyses suppose that the patterns of coordination can be captured by means of linear analyses, as linear combinations of nominally independent DOF. In contrast, hand kinematics is itself highly nonlinear in nature. To address this discrepancy, we sought to to determine whether nonlinear synergies might serve to more accurately and efficiently explain human grasping kinematics than is possible with linear analyses. We analyzed motion capture data acquired from the hands of individuals as they grasped an array of common objects, using four of the most widely used linear and nonlinear dimensionality reduction algorithms. We compared the results using a recently developed algorithm-agnostic quality measure, which enabled us to assess the quality of the dimensional reductions that resulted by assessing the extent to which local neighborhood information in the data was preserved. Although qualitative inspection of this data suggested that nonlinear correlations between kinematic variables were present, we found that linear modeling, in the form of Principle Components Analysis, could perform better than any of the nonlinear techniques we applied.

Nonlinear vs. linear biasing in Trp-cage folding simulations

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

Spiwok, Vojtěch, E-mail: spiwokv@vscht.cz; Oborský, Pavel; Králová, Blanka

2015-03-21

Biased simulations have great potential for the study of slow processes, including protein folding. Atomic motions in molecules are nonlinear, which suggests that simulations with enhanced sampling of collective motions traced by nonlinear dimensionality reduction methods may perform better than linear ones. In this study, we compare an unbiased folding simulation of the Trp-cage miniprotein with metadynamics simulations using both linear (principle component analysis) and nonlinear (Isomap) low dimensional embeddings as collective variables. Folding of the mini-protein was successfully simulated in 200 ns simulation with linear biasing and non-linear motion biasing. The folded state was correctly predicted as the free energymore » minimum in both simulations. We found that the advantage of linear motion biasing is that it can sample a larger conformational space, whereas the advantage of nonlinear motion biasing lies in slightly better resolution of the resulting free energy surface. In terms of sampling efficiency, both methods are comparable.« less

Complexity-reduced implementations of complete and null-space-based linear discriminant analysis.

PubMed

Lu, Gui-Fu; Zheng, Wenming

2013-10-01

Dimensionality reduction has become an important data preprocessing step in a lot of applications. Linear discriminant analysis (LDA) is one of the most well-known dimensionality reduction methods. However, the classical LDA cannot be used directly in the small sample size (SSS) problem where the within-class scatter matrix is singular. In the past, many generalized LDA methods has been reported to address the SSS problem. Among these methods, complete linear discriminant analysis (CLDA) and null-space-based LDA (NLDA) provide good performances. The existing implementations of CLDA are computationally expensive. In this paper, we propose a new and fast implementation of CLDA. Our proposed implementation of CLDA, which is the most efficient one, is equivalent to the existing implementations of CLDA in theory. Since CLDA is an extension of null-space-based LDA (NLDA), our implementation of CLDA also provides a fast implementation of NLDA. Experiments on some real-world data sets demonstrate the effectiveness of our proposed new CLDA and NLDA algorithms. Copyright © 2013 Elsevier Ltd. All rights reserved.

Dimensionality reduction based on distance preservation to local mean for symmetric positive definite matrices and its application in brain-computer interfaces

NASA Astrophysics Data System (ADS)

Davoudi, Alireza; Shiry Ghidary, Saeed; Sadatnejad, Khadijeh

2017-06-01

Objective. In this paper, we propose a nonlinear dimensionality reduction algorithm for the manifold of symmetric positive definite (SPD) matrices that considers the geometry of SPD matrices and provides a low-dimensional representation of the manifold with high class discrimination in a supervised or unsupervised manner. Approach. The proposed algorithm tries to preserve the local structure of the data by preserving distances to local means (DPLM) and also provides an implicit projection matrix. DPLM is linear in terms of the number of training samples. Main results. We performed several experiments on the multi-class dataset IIa from BCI competition IV and two other datasets from BCI competition III including datasets IIIa and IVa. The results show that our approach as dimensionality reduction technique—leads to superior results in comparison with other competitors in the related literature because of its robustness against outliers and the way it preserves the local geometry of the data. Significance. The experiments confirm that the combination of DPLM with filter geodesic minimum distance to mean as the classifier leads to superior performance compared with the state of the art on brain-computer interface competition IV dataset IIa. Also the statistical analysis shows that our dimensionality reduction method performs significantly better than its competitors.

Simulated bi-SQUID Arrays Performing Direction Finding

DTIC Science & Technology

2015-09-01

First, we applied the multiple signal classification ( MUSIC ) algorithm on linearly polarized signals. We included multiple signals in the output...both of the same frequency and different fre- quencies. Next, we explored a modified MUSIC algorithm called dimensionality reduction MUSIC (DR- MUSIC ... MUSIC algorithm is able to determine the AoA from the simulated SQUID data for linearly polarized signals. The MUSIC algorithm could accurately find

Modeling and control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Mingori, D. L.

1988-01-01

This monograph presents integrated modeling and controller design methods for flexible structures. The controllers, or compensators, developed are optimal in the linear-quadratic-Gaussian sense. The performance objectives, sensor and actuator locations and external disturbances influence both the construction of the model and the design of the finite dimensional compensator. The modeling and controller design procedures are carried out in parallel to ensure compatibility of these two aspects of the design problem. Model reduction techniques are introduced to keep both the model order and the controller order as small as possible. A linear distributed, or infinite dimensional, model is the theoretical basis for most of the text, but finite dimensional models arising from both lumped-mass and finite element approximations also play an important role. A central purpose of the approach here is to approximate an optimal infinite dimensional controller with an implementable finite dimensional compensator. Both convergence theory and numerical approximation methods are given. Simple examples are used to illustrate the theory.

Investigation of the Nicole model

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

Adam, C.; Sanchez-Guillen, J.; Vazquez, R.A.

2006-05-15

We study soliton solutions of the Nicole model - a non-linear four-dimensional field theory consisting of the CP{sup 1} Lagrangian density to the non-integer power (3/2) - using an ansatz within toroidal coordinates, which is indicated by the conformal symmetry of the static equations of motion. We calculate the soliton energies numerically and find that they grow linearly with the topological charge (Hopf index). Further we prove this behavior to hold exactly for the ansatz. On the other hand, for the full three-dimensional system without symmetry reduction we prove a sub-linear upper bound, analogously to the case of the Faddeev-Niemimore » model. It follows that symmetric solitons cannot be true minimizers of the energy for sufficiently large Hopf index, again in analogy to the Faddeev-Niemi model.« less

Locally linear embedding: dimension reduction of massive protostellar spectra

NASA Astrophysics Data System (ADS)

Ward, J. L.; Lumsden, S. L.

2016-09-01

We present the results of the application of locally linear embedding (LLE) to reduce the dimensionality of dereddened and continuum subtracted near-infrared spectra using a combination of models and real spectra of massive protostars selected from the Red MSX Source survey data base. A brief comparison is also made with two other dimension reduction techniques; principal component analysis (PCA) and Isomap using the same set of spectra as well as a more advanced form of LLE, Hessian locally linear embedding. We find that whilst LLE certainly has its limitations, it significantly outperforms both PCA and Isomap in classification of spectra based on the presence/absence of emission lines and provides a valuable tool for classification and analysis of large spectral data sets.

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.

Spillover, nonlinearity, and flexible structures

NASA Technical Reports Server (NTRS)

Bass, Robert W.; Zes, Dean

1991-01-01

Many systems whose evolution in time is governed by Partial Differential Equations (PDEs) are linearized around a known equilibrium before Computer Aided Control Engineering (CACE) is considered. In this case, there are infinitely many independent vibrational modes, and it is intuitively evident on physical grounds that infinitely many actuators would be needed in order to control all modes. A more precise, general formulation of this grave difficulty (spillover problem) is due to A.V. Balakrishnan. A possible route to circumvention of this difficulty lies in leaving the PDE in its original nonlinear form, and adding the essentially finite dimensional control action prior to linearization. One possibly applicable technique is the Liapunov Schmidt rigorous reduction of singular infinite dimensional implicit function problems to finite dimensional implicit function problems. Omitting details of Banach space rigor, the formalities of this approach are given.

A general soft label based linear discriminant analysis for semi-supervised dimensionality reduction.

PubMed

Zhao, Mingbo; Zhang, Zhao; Chow, Tommy W S; Li, Bing

2014-07-01

Dealing with high-dimensional data has always been a major problem in research of pattern recognition and machine learning, and Linear Discriminant Analysis (LDA) is one of the most popular methods for dimension reduction. However, it only uses labeled samples while neglecting unlabeled samples, which are abundant and can be easily obtained in the real world. In this paper, we propose a new dimension reduction method, called "SL-LDA", by using unlabeled samples to enhance the performance of LDA. The new method first propagates label information from the labeled set to the unlabeled set via a label propagation process, where the predicted labels of unlabeled samples, called "soft labels", can be obtained. It then incorporates the soft labels into the construction of scatter matrixes to find a transformed matrix for dimension reduction. In this way, the proposed method can preserve more discriminative information, which is preferable when solving the classification problem. We further propose an efficient approach for solving SL-LDA under a least squares framework, and a flexible method of SL-LDA (FSL-LDA) to better cope with datasets sampled from a nonlinear manifold. Extensive simulations are carried out on several datasets, and the results show the effectiveness of the proposed method. Copyright © 2014 Elsevier Ltd. All rights reserved.

Spectral Regression Discriminant Analysis for Hyperspectral Image Classification

NASA Astrophysics Data System (ADS)

Pan, Y.; Wu, J.; Huang, H.; Liu, J.

2012-08-01

Dimensionality reduction algorithms, which aim to select a small set of efficient and discriminant features, have attracted great attention for Hyperspectral Image Classification. The manifold learning methods are popular for dimensionality reduction, such as Locally Linear Embedding, Isomap, and Laplacian Eigenmap. However, a disadvantage of many manifold learning methods is that their computations usually involve eigen-decomposition of dense matrices which is expensive in both time and memory. In this paper, we introduce a new dimensionality reduction method, called Spectral Regression Discriminant Analysis (SRDA). SRDA casts the problem of learning an embedding function into a regression framework, which avoids eigen-decomposition of dense matrices. Also, with the regression based framework, different kinds of regularizes can be naturally incorporated into our algorithm which makes it more flexible. It can make efficient use of data points to discover the intrinsic discriminant structure in the data. Experimental results on Washington DC Mall and AVIRIS Indian Pines hyperspectral data sets demonstrate the effectiveness of the proposed method.

Deep linear autoencoder and patch clustering-based unified one-dimensional coding of image and video

NASA Astrophysics Data System (ADS)

Li, Honggui

2017-09-01

This paper proposes a unified one-dimensional (1-D) coding framework of image and video, which depends on deep learning neural network and image patch clustering. First, an improved K-means clustering algorithm for image patches is employed to obtain the compact inputs of deep artificial neural network. Second, for the purpose of best reconstructing original image patches, deep linear autoencoder (DLA), a linear version of the classical deep nonlinear autoencoder, is introduced to achieve the 1-D representation of image blocks. Under the circumstances of 1-D representation, DLA is capable of attaining zero reconstruction error, which is impossible for the classical nonlinear dimensionality reduction methods. Third, a unified 1-D coding infrastructure for image, intraframe, interframe, multiview video, three-dimensional (3-D) video, and multiview 3-D video is built by incorporating different categories of videos into the inputs of patch clustering algorithm. Finally, it is shown in the results of simulation experiments that the proposed methods can simultaneously gain higher compression ratio and peak signal-to-noise ratio than those of the state-of-the-art methods in the situation of low bitrate transmission.

Gravity from entanglement and RG flow in a top-down approach

NASA Astrophysics Data System (ADS)

Kwon, O.-Kab; Jang, Dongmin; Kim, Yoonbai; Tolla, D. D.

2018-05-01

The duality between a d-dimensional conformal field theory with relevant deformation and a gravity theory on an asymptotically AdS d+1 geometry, has become a suitable tool in the investigation of the emergence of gravity from quantum entanglement in field theory. Recently, we have tested the duality between the mass-deformed ABJM theory and asymptotically AdS4 gravity theory, which is obtained from the KK reduction of the 11-dimensional supergravity on the LLM geometry. In this paper, we extend the KK reduction procedure beyond the linear order and establish non-trivial KK maps between 4-dimensional fields and 11-dimensional fluctuations. We rely on this gauge/gravity duality to calculate the entanglement entropy by using the Ryu-Takayanagi holographic formula and the path integral method developed by Faulkner. We show that the entanglement entropies obtained using these two methods agree when the asymptotically AdS4 metric satisfies the linearized Einstein equation with nonvanishing energy-momentum tensor for two scalar fields. These scalar fields encode the information of the relevant deformation of the ABJM theory. This confirms that the asymptotic limit of LLM geometry is the emergent gravity of the quantum entanglement in the mass-deformed ABJM theory with a small mass parameter. We also comment on the issue of the relative entropy and the Fisher information in our setup.

Prediction of high-dimensional states subject to respiratory motion: a manifold learning approach

NASA Astrophysics Data System (ADS)

Liu, Wenyang; Sawant, Amit; Ruan, Dan

2016-07-01

The development of high-dimensional imaging systems in image-guided radiotherapy provides important pathways to the ultimate goal of real-time full volumetric motion monitoring. Effective motion management during radiation treatment usually requires prediction to account for system latency and extra signal/image processing time. It is challenging to predict high-dimensional respiratory motion due to the complexity of the motion pattern combined with the curse of dimensionality. Linear dimension reduction methods such as PCA have been used to construct a linear subspace from the high-dimensional data, followed by efficient predictions on the lower-dimensional subspace. In this study, we extend such rationale to a more general manifold and propose a framework for high-dimensional motion prediction with manifold learning, which allows one to learn more descriptive features compared to linear methods with comparable dimensions. Specifically, a kernel PCA is used to construct a proper low-dimensional feature manifold, where accurate and efficient prediction can be performed. A fixed-point iterative pre-image estimation method is used to recover the predicted value in the original state space. We evaluated and compared the proposed method with a PCA-based approach on level-set surfaces reconstructed from point clouds captured by a 3D photogrammetry system. The prediction accuracy was evaluated in terms of root-mean-squared-error. Our proposed method achieved consistent higher prediction accuracy (sub-millimeter) for both 200 ms and 600 ms lookahead lengths compared to the PCA-based approach, and the performance gain was statistically significant.

Consensus embedding: theory, algorithms and application to segmentation and classification of biomedical data

PubMed Central

2012-01-01

Background Dimensionality reduction (DR) enables the construction of a lower dimensional space (embedding) from a higher dimensional feature space while preserving object-class discriminability. However several popular DR approaches suffer from sensitivity to choice of parameters and/or presence of noise in the data. In this paper, we present a novel DR technique known as consensus embedding that aims to overcome these problems by generating and combining multiple low-dimensional embeddings, hence exploiting the variance among them in a manner similar to ensemble classifier schemes such as Bagging. We demonstrate theoretical properties of consensus embedding which show that it will result in a single stable embedding solution that preserves information more accurately as compared to any individual embedding (generated via DR schemes such as Principal Component Analysis, Graph Embedding, or Locally Linear Embedding). Intelligent sub-sampling (via mean-shift) and code parallelization are utilized to provide for an efficient implementation of the scheme. Results Applications of consensus embedding are shown in the context of classification and clustering as applied to: (1) image partitioning of white matter and gray matter on 10 different synthetic brain MRI images corrupted with 18 different combinations of noise and bias field inhomogeneity, (2) classification of 4 high-dimensional gene-expression datasets, (3) cancer detection (at a pixel-level) on 16 image slices obtained from 2 different high-resolution prostate MRI datasets. In over 200 different experiments concerning classification and segmentation of biomedical data, consensus embedding was found to consistently outperform both linear and non-linear DR methods within all applications considered. Conclusions We have presented a novel framework termed consensus embedding which leverages ensemble classification theory within dimensionality reduction, allowing for application to a wide range of high-dimensional biomedical data classification and segmentation problems. Our generalizable framework allows for improved representation and classification in the context of both imaging and non-imaging data. The algorithm offers a promising solution to problems that currently plague DR methods, and may allow for extension to other areas of biomedical data analysis. PMID:22316103

On the control canonical structure of a class of scalar input systems

NASA Technical Reports Server (NTRS)

Teglas, R.

1983-01-01

A discrete finite dimensional system, nonharmonic Fourier series and controllability, reduction to canonical form, and spectral synthesis are considered. The extent to which the eigenvalue associated with a controllable pair of a certain type may be modified via continuous linear state feedback is demonstrated.

Exact solutions to three-dimensional generalized nonlinear Schrödinger equations with varying potential and nonlinearities.

PubMed

Yan, Zhenya; Konotop, V V

2009-09-01

It is shown that using the similarity transformations, a set of three-dimensional p-q nonlinear Schrödinger (NLS) equations with inhomogeneous coefficients can be reduced to one-dimensional stationary NLS equation with constant or varying coefficients, thus allowing for obtaining exact localized and periodic wave solutions. In the suggested reduction the original coordinates in the (1+3) space are mapped into a set of one-parametric coordinate surfaces, whose parameter plays the role of the coordinate of the one-dimensional equation. We describe the algorithm of finding solutions and concentrate on power (linear and nonlinear) potentials presenting a number of case examples. Generalizations of the method are also discussed.

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

Multispectral x-ray CT: multivariate statistical analysis for efficient reconstruction

NASA Astrophysics Data System (ADS)

Kheirabadi, Mina; Mustafa, Wail; Lyksborg, Mark; Lund Olsen, Ulrik; Bjorholm Dahl, Anders

2017-10-01

Recent developments in multispectral X-ray detectors allow for an efficient identification of materials based on their chemical composition. This has a range of applications including security inspection, which is our motivation. In this paper, we analyze data from a tomographic setup employing the MultiX detector, that records projection data in 128 energy bins covering the range from 20 to 160 keV. Obtaining all information from this data requires reconstructing 128 tomograms, which is computationally expensive. Instead, we propose to reduce the dimensionality of projection data prior to reconstruction and reconstruct from the reduced data. We analyze three linear methods for dimensionality reduction using a dataset with 37 equally-spaced projection angles. Four bottles with different materials are recorded for which we are able to obtain similar discrimination of their content using a very reduced subset of tomograms compared to the 128 tomograms that would otherwise be needed without dimensionality reduction.

Assessment of Schrodinger Eigenmaps for target detection

NASA Astrophysics Data System (ADS)

Dorado Munoz, Leidy P.; Messinger, David W.; Czaja, Wojtek

2014-06-01

Non-linear dimensionality reduction methods have been widely applied to hyperspectral imagery due to its structure as the information can be represented in a lower dimension without losing information, and because the non-linear methods preserve the local geometry of the data while the dimension is reduced. One of these methods is Laplacian Eigenmaps (LE), which assumes that the data lies on a low dimensional manifold embedded in a high dimensional space. LE builds a nearest neighbor graph, computes its Laplacian and performs the eigendecomposition of the Laplacian. These eigenfunctions constitute a basis for the lower dimensional space in which the geometry of the manifold is preserved. In addition to the reduction problem, LE has been widely used in tasks such as segmentation, clustering, and classification. In this regard, a new Schrodinger Eigenmaps (SE) method was developed and presented as a semi-supervised classification scheme in order to improve the classification performance and take advantage of the labeled data. SE is an algorithm built upon LE, where the former Laplacian operator is replaced by the Schrodinger operator. The Schrodinger operator includes a potential term V, that, taking advantage of the additional information such as labeled data, allows clustering of similar points. In this paper, we explore the idea of using SE in target detection. In this way, we present a framework where the potential term V is defined as a barrier potential: a diagonal matrix encoding the spatial position of the target, and the detection performance is evaluated by using different targets and different hyperspectral scenes.

QUADRO: A SUPERVISED DIMENSION REDUCTION METHOD VIA RAYLEIGH QUOTIENT OPTIMIZATION.

PubMed

Fan, Jianqing; Ke, Zheng Tracy; Liu, Han; Xia, Lucy

We propose a novel Rayleigh quotient based sparse quadratic dimension reduction method-named QUADRO (Quadratic Dimension Reduction via Rayleigh Optimization)-for analyzing high-dimensional data. Unlike in the linear setting where Rayleigh quotient optimization coincides with classification, these two problems are very different under nonlinear settings. In this paper, we clarify this difference and show that Rayleigh quotient optimization may be of independent scientific interests. One major challenge of Rayleigh quotient optimization is that the variance of quadratic statistics involves all fourth cross-moments of predictors, which are infeasible to compute for high-dimensional applications and may accumulate too many stochastic errors. This issue is resolved by considering a family of elliptical models. Moreover, for heavy-tail distributions, robust estimates of mean vectors and covariance matrices are employed to guarantee uniform convergence in estimating non-polynomially many parameters, even though only the fourth moments are assumed. Methodologically, QUADRO is based on elliptical models which allow us to formulate the Rayleigh quotient maximization as a convex optimization problem. Computationally, we propose an efficient linearized augmented Lagrangian method to solve the constrained optimization problem. Theoretically, we provide explicit rates of convergence in terms of Rayleigh quotient under both Gaussian and general elliptical models. Thorough numerical results on both synthetic and real datasets are also provided to back up our theoretical results.

Model reduction of nonsquare linear MIMO systems using multipoint matrix continued-fraction expansions

NASA Technical Reports Server (NTRS)

Guo, Tong-Yi; Hwang, Chyi; Shieh, Leang-San

1994-01-01

This paper deals with the multipoint Cauer matrix continued-fraction expansion (MCFE) for model reduction of linear multi-input multi-output (MIMO) systems with various numbers of inputs and outputs. A salient feature of the proposed MCFE approach to model reduction of MIMO systems with square transfer matrices is its equivalence to the matrix Pade approximation approach. The Cauer second form of the ordinary MCFE for a square transfer function matrix is generalized in this paper to a multipoint and nonsquare-matrix version. An interesting connection of the multipoint Cauer MCFE method to the multipoint matrix Pade approximation method is established. Also, algorithms for obtaining the reduced-degree matrix-fraction descriptions and reduced-dimensional state-space models from a transfer function matrix via the multipoint Cauer MCFE algorithm are presented. Practical advantages of using the multipoint Cauer MCFE are discussed and a numerical example is provided to illustrate the algorithms.

The Equivalence of Information-Theoretic and Likelihood-Based Methods for Neural Dimensionality Reduction

PubMed Central

Williamson, Ross S.; Sahani, Maneesh; Pillow, Jonathan W.

2015-01-01

Stimulus dimensionality-reduction methods in neuroscience seek to identify a low-dimensional space of stimulus features that affect a neuron’s probability of spiking. One popular method, known as maximally informative dimensions (MID), uses an information-theoretic quantity known as “single-spike information” to identify this space. Here we examine MID from a model-based perspective. We show that MID is a maximum-likelihood estimator for the parameters of a linear-nonlinear-Poisson (LNP) model, and that the empirical single-spike information corresponds to the normalized log-likelihood under a Poisson model. This equivalence implies that MID does not necessarily find maximally informative stimulus dimensions when spiking is not well described as Poisson. We provide several examples to illustrate this shortcoming, and derive a lower bound on the information lost when spiking is Bernoulli in discrete time bins. To overcome this limitation, we introduce model-based dimensionality reduction methods for neurons with non-Poisson firing statistics, and show that they can be framed equivalently in likelihood-based or information-theoretic terms. Finally, we show how to overcome practical limitations on the number of stimulus dimensions that MID can estimate by constraining the form of the non-parametric nonlinearity in an LNP model. We illustrate these methods with simulations and data from primate visual cortex. PMID:25831448

Network embedding-based representation learning for single cell RNA-seq data.

PubMed

Li, Xiangyu; Chen, Weizheng; Chen, Yang; Zhang, Xuegong; Gu, Jin; Zhang, Michael Q

2017-11-02

Single cell RNA-seq (scRNA-seq) techniques can reveal valuable insights of cell-to-cell heterogeneities. Projection of high-dimensional data into a low-dimensional subspace is a powerful strategy in general for mining such big data. However, scRNA-seq suffers from higher noise and lower coverage than traditional bulk RNA-seq, hence bringing in new computational difficulties. One major challenge is how to deal with the frequent drop-out events. The events, usually caused by the stochastic burst effect in gene transcription and the technical failure of RNA transcript capture, often render traditional dimension reduction methods work inefficiently. To overcome this problem, we have developed a novel Single Cell Representation Learning (SCRL) method based on network embedding. This method can efficiently implement data-driven non-linear projection and incorporate prior biological knowledge (such as pathway information) to learn more meaningful low-dimensional representations for both cells and genes. Benchmark results show that SCRL outperforms other dimensional reduction methods on several recent scRNA-seq datasets. © The Author(s) 2017. Published by Oxford University Press on behalf of Nucleic Acids Research.

Visual analysis of mass cytometry data by hierarchical stochastic neighbour embedding reveals rare cell types.

PubMed

van Unen, Vincent; Höllt, Thomas; Pezzotti, Nicola; Li, Na; Reinders, Marcel J T; Eisemann, Elmar; Koning, Frits; Vilanova, Anna; Lelieveldt, Boudewijn P F

2017-11-23

Mass cytometry allows high-resolution dissection of the cellular composition of the immune system. However, the high-dimensionality, large size, and non-linear structure of the data poses considerable challenges for the data analysis. In particular, dimensionality reduction-based techniques like t-SNE offer single-cell resolution but are limited in the number of cells that can be analyzed. Here we introduce Hierarchical Stochastic Neighbor Embedding (HSNE) for the analysis of mass cytometry data sets. HSNE constructs a hierarchy of non-linear similarities that can be interactively explored with a stepwise increase in detail up to the single-cell level. We apply HSNE to a study on gastrointestinal disorders and three other available mass cytometry data sets. We find that HSNE efficiently replicates previous observations and identifies rare cell populations that were previously missed due to downsampling. Thus, HSNE removes the scalability limit of conventional t-SNE analysis, a feature that makes it highly suitable for the analysis of massive high-dimensional data sets.

Solution of two-body relativistic bound state equations with confining plus Coulomb interactions

NASA Technical Reports Server (NTRS)

Maung, Khin Maung; Kahana, David E.; Norbury, John W.

1992-01-01

Studies of meson spectroscopy have often employed a nonrelativistic Coulomb plus Linear Confining potential in position space. However, because the quarks in mesons move at an appreciable fraction of the speed of light, it is necessary to use a relativistic treatment of the bound state problem. Such a treatment is most easily carried out in momentum space. However, the position space Linear and Coulomb potentials lead to singular kernels in momentum space. Using a subtraction procedure we show how to remove these singularities exactly and thereby solve the Schroedinger equation in momentum space for all partial waves. Furthermore, we generalize the Linear and Coulomb potentials to relativistic kernels in four dimensional momentum space. Again we use a subtraction procedure to remove the relativistic singularities exactly for all partial waves. This enables us to solve three dimensional reductions of the Bethe-Salpeter equation. We solve six such equations for Coulomb plus Confining interactions for all partial waves.

Kernel PLS-SVC for Linear and Nonlinear Discrimination

NASA Technical Reports Server (NTRS)

Rosipal, Roman; Trejo, Leonard J.; Matthews, Bryan

2003-01-01

A new methodology for discrimination is proposed. This is based on kernel orthonormalized partial least squares (PLS) dimensionality reduction of the original data space followed by support vector machines for classification. Close connection of orthonormalized PLS and Fisher's approach to linear discrimination or equivalently with canonical correlation analysis is described. This gives preference to use orthonormalized PLS over principal component analysis. Good behavior of the proposed method is demonstrated on 13 different benchmark data sets and on the real world problem of the classification finger movement periods versus non-movement periods based on electroencephalogram.

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.

Reductions in finite-dimensional integrable systems and special points of classical r-matrices

NASA Astrophysics Data System (ADS)

Skrypnyk, T.

2016-12-01

For a given 𝔤 ⊗ 𝔤-valued non-skew-symmetric non-dynamical classical r-matrices r(u, v) with spectral parameters, we construct the general form of 𝔤-valued Lax matrices of finite-dimensional integrable systems satisfying linear r-matrix algebra. We show that the reduction in the corresponding finite-dimensional integrable systems is connected with "the special points" of the classical r-matrices in which they become degenerated. We also propose a systematic way of the construction of additional integrals of the Lax-integrable systems associated with the symmetries of the corresponding r-matrices. We consider examples of the Lax matrices and integrable systems that are obtained in the framework of the general scheme. Among them there are such physically important systems as generalized Gaudin systems in an external magnetic field, ultimate integrable generalization of Toda-type chains (including "modified" or "deformed" Toda chains), generalized integrable Jaynes-Cummings-Dicke models, integrable boson models generalizing Bose-Hubbard dimer models, etc.

The use of kernel local Fisher discriminant analysis for the channelization of the Hotelling model observer

NASA Astrophysics Data System (ADS)

Wen, Gezheng; Markey, Mia K.

2015-03-01

It is resource-intensive to conduct human studies for task-based assessment of medical image quality and system optimization. Thus, numerical model observers have been developed as a surrogate for human observers. The Hotelling observer (HO) is the optimal linear observer for signal-detection tasks, but the high dimensionality of imaging data results in a heavy computational burden. Channelization is often used to approximate the HO through a dimensionality reduction step, but how to produce channelized images without losing significant image information remains a key challenge. Kernel local Fisher discriminant analysis (KLFDA) uses kernel techniques to perform supervised dimensionality reduction, which finds an embedding transformation that maximizes betweenclass separability and preserves within-class local structure in the low-dimensional manifold. It is powerful for classification tasks, especially when the distribution of a class is multimodal. Such multimodality could be observed in many practical clinical tasks. For example, primary and metastatic lesions may both appear in medical imaging studies, but the distributions of their typical characteristics (e.g., size) may be very different. In this study, we propose to use KLFDA as a novel channelization method. The dimension of the embedded manifold (i.e., the result of KLFDA) is a counterpart to the number of channels in the state-of-art linear channelization. We present a simulation study to demonstrate the potential usefulness of KLFDA for building the channelized HOs (CHOs) and generating reliable decision statistics for clinical tasks. We show that the performance of the CHO with KLFDA channels is comparable to that of the benchmark CHOs.

Manifold Learning in MR spectroscopy using nonlinear dimensionality reduction and unsupervised clustering.

PubMed

Yang, Guang; Raschke, Felix; Barrick, Thomas R; Howe, Franklyn A

2015-09-01

To investigate whether nonlinear dimensionality reduction improves unsupervised classification of (1) H MRS brain tumor data compared with a linear method. In vivo single-voxel (1) H magnetic resonance spectroscopy (55 patients) and (1) H magnetic resonance spectroscopy imaging (MRSI) (29 patients) data were acquired from histopathologically diagnosed gliomas. Data reduction using Laplacian eigenmaps (LE) or independent component analysis (ICA) was followed by k-means clustering or agglomerative hierarchical clustering (AHC) for unsupervised learning to assess tumor grade and for tissue type segmentation of MRSI data. An accuracy of 93% in classification of glioma grade II and grade IV, with 100% accuracy in distinguishing tumor and normal spectra, was obtained by LE with unsupervised clustering, but not with the combination of k-means and ICA. With (1) H MRSI data, LE provided a more linear distribution of data for cluster analysis and better cluster stability than ICA. LE combined with k-means or AHC provided 91% accuracy for classifying tumor grade and 100% accuracy for identifying normal tissue voxels. Color-coded visualization of normal brain, tumor core, and infiltration regions was achieved with LE combined with AHC. The LE method is promising for unsupervised clustering to separate brain and tumor tissue with automated color-coding for visualization of (1) H MRSI data after cluster analysis. © 2014 Wiley Periodicals, Inc.

QUADRO: A SUPERVISED DIMENSION REDUCTION METHOD VIA RAYLEIGH QUOTIENT OPTIMIZATION

PubMed Central

Fan, Jianqing; Ke, Zheng Tracy; Liu, Han; Xia, Lucy

2016-01-01

We propose a novel Rayleigh quotient based sparse quadratic dimension reduction method—named QUADRO (Quadratic Dimension Reduction via Rayleigh Optimization)—for analyzing high-dimensional data. Unlike in the linear setting where Rayleigh quotient optimization coincides with classification, these two problems are very different under nonlinear settings. In this paper, we clarify this difference and show that Rayleigh quotient optimization may be of independent scientific interests. One major challenge of Rayleigh quotient optimization is that the variance of quadratic statistics involves all fourth cross-moments of predictors, which are infeasible to compute for high-dimensional applications and may accumulate too many stochastic errors. This issue is resolved by considering a family of elliptical models. Moreover, for heavy-tail distributions, robust estimates of mean vectors and covariance matrices are employed to guarantee uniform convergence in estimating non-polynomially many parameters, even though only the fourth moments are assumed. Methodologically, QUADRO is based on elliptical models which allow us to formulate the Rayleigh quotient maximization as a convex optimization problem. Computationally, we propose an efficient linearized augmented Lagrangian method to solve the constrained optimization problem. Theoretically, we provide explicit rates of convergence in terms of Rayleigh quotient under both Gaussian and general elliptical models. Thorough numerical results on both synthetic and real datasets are also provided to back up our theoretical results. PMID:26778864

A non-linear dimension reduction methodology for generating data-driven stochastic input models

NASA Astrophysics Data System (ADS)

Ganapathysubramanian, Baskar; Zabaras, Nicholas

2008-06-01

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem of manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space Rn. An isometric mapping F from M to a low-dimensional, compact, connected set A⊂Rd(d≪n) is constructed. Given only a finite set of samples of the data, the methodology uses arguments from graph theory and differential geometry to construct the isometric transformation F:M→A. Asymptotic convergence of the representation of M by A is shown. This mapping F serves as an accurate, low-dimensional, data-driven representation of the property variations. The reduced-order model of the material topology and thermal diffusivity variations is subsequently used as an input in the solution of stochastic partial differential equations that describe the evolution of dependant variables. A sparse grid collocation strategy (Smolyak algorithm) is utilized to solve these stochastic equations efficiently. We showcase the methodology by constructing low-dimensional input stochastic models to represent thermal diffusivity in two-phase microstructures. This model is used in analyzing the effect of topological variations of two-phase microstructures on the evolution of temperature in heat conduction processes.

A Numerical Study on the Screening of Blast-Induced Waves for Reducing Ground Vibration

NASA Astrophysics Data System (ADS)

Park, Dohyun; Jeon, Byungkyu; Jeon, Seokwon

2009-06-01

Blasting is often a necessary part of mining and construction operations, and is the most cost-effective way to break rock, but blasting generates both noise and ground vibration. In urban areas, noise and vibration have an environmental impact, and cause structural damage to nearby structures. Various wave-screening methods have been used for many years to reduce blast-induced ground vibration. However, these methods have not been quantitatively studied for their reduction effect of ground vibration. The present study focused on the quantitative assessment of the effectiveness in vibration reduction of line-drilling as a screening method using a numerical method. Two numerical methods were used to analyze the reduction effect toward ground vibration, namely, the “distinct element method” and the “non-linear hydrocode.” The distinct element method, by particle flow code in two dimensions (PFC 2D), was used for two-dimensional parametric analyses, and some cases of two-dimensional analyses were analyzed three-dimensionally using AUTODYN 3D, the program of the non-linear hydrocode. To analyze the screening effectiveness of line-drilling, parametric analyses were carried out under various conditions, with the spacing, diameter of drill holes, distance between the blasthole and line-drilling, and the number of rows of drill holes, including their arrangement, used as parameters. The screening effectiveness was assessed via a comparison of the vibration amplitude between cases both with and without screening. Also, the frequency distribution of ground motion of the two cases was investigated through fast Fourier transform (FFT), with the differences also examined. From our study, it was concluded that line-drilling as a screening method of blast-induced waves was considerably effective under certain design conditions. The design details for field application have also been proposed.

SpectralNET – an application for spectral graph analysis and visualization

PubMed Central

Forman, Joshua J; Clemons, Paul A; Schreiber, Stuart L; Haggarty, Stephen J

2005-01-01

Background Graph theory provides a computational framework for modeling a variety of datasets including those emerging from genomics, proteomics, and chemical genetics. Networks of genes, proteins, small molecules, or other objects of study can be represented as graphs of nodes (vertices) and interactions (edges) that can carry different weights. SpectralNET is a flexible application for analyzing and visualizing these biological and chemical networks. Results Available both as a standalone .NET executable and as an ASP.NET web application, SpectralNET was designed specifically with the analysis of graph-theoretic metrics in mind, a computational task not easily accessible using currently available applications. Users can choose either to upload a network for analysis using a variety of input formats, or to have SpectralNET generate an idealized random network for comparison to a real-world dataset. Whichever graph-generation method is used, SpectralNET displays detailed information about each connected component of the graph, including graphs of degree distribution, clustering coefficient by degree, and average distance by degree. In addition, extensive information about the selected vertex is shown, including degree, clustering coefficient, various distance metrics, and the corresponding components of the adjacency, Laplacian, and normalized Laplacian eigenvectors. SpectralNET also displays several graph visualizations, including a linear dimensionality reduction for uploaded datasets (Principal Components Analysis) and a non-linear dimensionality reduction that provides an elegant view of global graph structure (Laplacian eigenvectors). Conclusion SpectralNET provides an easily accessible means of analyzing graph-theoretic metrics for data modeling and dimensionality reduction. SpectralNET is publicly available as both a .NET application and an ASP.NET web application from . Source code is available upon request. PMID:16236170

SpectralNET--an application for spectral graph analysis and visualization.

PubMed

Forman, Joshua J; Clemons, Paul A; Schreiber, Stuart L; Haggarty, Stephen J

2005-10-19

Graph theory provides a computational framework for modeling a variety of datasets including those emerging from genomics, proteomics, and chemical genetics. Networks of genes, proteins, small molecules, or other objects of study can be represented as graphs of nodes (vertices) and interactions (edges) that can carry different weights. SpectralNET is a flexible application for analyzing and visualizing these biological and chemical networks. Available both as a standalone .NET executable and as an ASP.NET web application, SpectralNET was designed specifically with the analysis of graph-theoretic metrics in mind, a computational task not easily accessible using currently available applications. Users can choose either to upload a network for analysis using a variety of input formats, or to have SpectralNET generate an idealized random network for comparison to a real-world dataset. Whichever graph-generation method is used, SpectralNET displays detailed information about each connected component of the graph, including graphs of degree distribution, clustering coefficient by degree, and average distance by degree. In addition, extensive information about the selected vertex is shown, including degree, clustering coefficient, various distance metrics, and the corresponding components of the adjacency, Laplacian, and normalized Laplacian eigenvectors. SpectralNET also displays several graph visualizations, including a linear dimensionality reduction for uploaded datasets (Principal Components Analysis) and a non-linear dimensionality reduction that provides an elegant view of global graph structure (Laplacian eigenvectors). SpectralNET provides an easily accessible means of analyzing graph-theoretic metrics for data modeling and dimensionality reduction. SpectralNET is publicly available as both a .NET application and an ASP.NET web application from http://chembank.broad.harvard.edu/resources/. Source code is available upon request.

Manifold Learning by Preserving Distance Orders.

PubMed

Ataer-Cansizoglu, Esra; Akcakaya, Murat; Orhan, Umut; Erdogmus, Deniz

2014-03-01

Nonlinear dimensionality reduction is essential for the analysis and the interpretation of high dimensional data sets. In this manuscript, we propose a distance order preserving manifold learning algorithm that extends the basic mean-squared error cost function used mainly in multidimensional scaling (MDS)-based methods. We develop a constrained optimization problem by assuming explicit constraints on the order of distances in the low-dimensional space. In this optimization problem, as a generalization of MDS, instead of forcing a linear relationship between the distances in the high-dimensional original and low-dimensional projection space, we learn a non-decreasing relation approximated by radial basis functions. We compare the proposed method with existing manifold learning algorithms using synthetic datasets based on the commonly used residual variance and proposed percentage of violated distance orders metrics. We also perform experiments on a retinal image dataset used in Retinopathy of Prematurity (ROP) diagnosis.

Thermally induced rarefied gas flow in a three-dimensional enclosure with square cross-section

NASA Astrophysics Data System (ADS)

Zhu, Lianhua; Yang, Xiaofan; Guo, Zhaoli

2017-12-01

Rarefied gas flow in a three-dimensional enclosure induced by nonuniform temperature distribution is numerically investigated. The enclosure has a square channel-like geometry with alternatively heated closed ends and lateral walls with a linear temperature distribution. A recently proposed implicit discrete velocity method with a memory reduction technique is used to numerically simulate the problem based on the nonlinear Shakhov kinetic equation. The Knudsen number dependencies of the vortices pattern, slip velocity at the planar walls and edges, and heat transfer are investigated. The influences of the temperature ratio imposed at the ends of the enclosure and the geometric aspect ratio are also evaluated. The overall flow pattern shows similarities with those observed in two-dimensional configurations in literature. However, features due to the three-dimensionality are observed with vortices that are not identified in previous studies on similar two-dimensional enclosures at high Knudsen and small aspect ratios.

The staircase method: integrals for periodic reductions of integrable lattice equations

NASA Astrophysics Data System (ADS)

van der Kamp, Peter H.; Quispel, G. R. W.

2010-11-01

We show, in full generality, that the staircase method (Papageorgiou et al 1990 Phys. Lett. A 147 106-14, Quispel et al 1991 Physica A 173 243-66) provides integrals for mappings, and correspondences, obtained as traveling wave reductions of (systems of) integrable partial difference equations. We apply the staircase method to a variety of equations, including the Korteweg-De Vries equation, the five-point Bruschi-Calogero-Droghei equation, the quotient-difference (QD)-algorithm and the Boussinesq system. We show that, in all these cases, if the staircase method provides r integrals for an n-dimensional mapping, with 2r, then one can introduce q <= 2r variables, which reduce the dimension of the mapping from n to q. These dimension-reducing variables are obtained as joint invariants of k-symmetries of the mappings. Our results support the idea that often the staircase method provides sufficiently many integrals for the periodic reductions of integrable lattice equations to be completely integrable. We also study reductions on other quad-graphs than the regular {\\ Z}^2 lattice, and we prove linear growth of the multi-valuedness of iterates of high-dimensional correspondences obtained as reductions of the QD-algorithm.

Whitham modulation theory for the Kadomtsev- Petviashvili equation.

PubMed

Ablowitz, Mark J; Biondini, Gino; Wang, Qiao

2017-08-01

The genus-1 Kadomtsev-Petviashvili (KP)-Whitham system is derived for both variants of the KP equation; namely the KPI and KPII equations. The basic properties of the KP-Whitham system, including symmetries, exact reductions and its possible complete integrability, together with the appropriate generalization of the one-dimensional Riemann problem for the Korteweg-de Vries equation are discussed. Finally, the KP-Whitham system is used to study the linear stability properties of the genus-1 solutions of the KPI and KPII equations; it is shown that all genus-1 solutions of KPI are linearly unstable, while all genus-1 solutions of KPII are linearly stable within the context of Whitham theory.

Whitham modulation theory for the Kadomtsev- Petviashvili equation

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Biondini, Gino; Wang, Qiao

2017-08-01

The genus-1 Kadomtsev-Petviashvili (KP)-Whitham system is derived for both variants of the KP equation; namely the KPI and KPII equations. The basic properties of the KP-Whitham system, including symmetries, exact reductions and its possible complete integrability, together with the appropriate generalization of the one-dimensional Riemann problem for the Korteweg-de Vries equation are discussed. Finally, the KP-Whitham system is used to study the linear stability properties of the genus-1 solutions of the KPI and KPII equations; it is shown that all genus-1 solutions of KPI are linearly unstable, while all genus-1 solutions of KPII are linearly stable within the context of Whitham theory.

Quasi-one-dimensional arrangement of silver nanoparticles templated by cellulose microfibrils.

PubMed

Wu, Min; Kuga, Shigenori; Huang, Yong

2008-09-16

We demonstrate a simple, facile approach to the deposition of silver nanoparticles on the surface of cellulose microfibrils with a quasi-one-dimensional arrangement. The process involves the generation of aldehyde groups by oxidizing the surface of cellulose microfibrils and then the assembly of silver nanoparticles on the surface by means of the silver mirror reaction. The linear nature of the microfibrils and the relatively uniform surface chemical modification result in a uniform linear distribution of silver particles along the microfibrils. The effects of various reaction parameters, such as the reaction time for the reduction process and employed starting materials, have been investigated by transmission electron microscopy (TEM) and ultraviolet-visible spectroscopy. Additionally, the products were examined for their electric current-voltage characteristics, the results showing that these materials had an electric conductivity of approximately 5 S/cm, being different from either the oxidated cellulose or bulk silver materials by many orders of magnitude.

Analysis of Information Content in High-Spectral Resolution Sounders using Subset Selection Analysis

NASA Technical Reports Server (NTRS)

Velez-Reyes, Miguel; Joiner, Joanna

1998-01-01

In this paper, we summarize the results of the sensitivity analysis and data reduction carried out to determine the information content of AIRS and IASI channels. The analysis and data reduction was based on the use of subset selection techniques developed in the linear algebra and statistical community to study linear dependencies in high dimensional data sets. We applied the subset selection method to study dependency among channels by studying the dependency among their weighting functions. Also, we applied the technique to study the information provided by the different levels in which the atmosphere is discretized for retrievals and analysis. Results from the method correlate well with intuition in many respects and point out to possible modifications for band selection in sensor design and number and location of levels in the analysis process.

Local structure-based image decomposition for feature extraction with applications to face recognition.

PubMed

Qian, Jianjun; Yang, Jian; Xu, Yong

2013-09-01

This paper presents a robust but simple image feature extraction method, called image decomposition based on local structure (IDLS). It is assumed that in the local window of an image, the macro-pixel (patch) of the central pixel, and those of its neighbors, are locally linear. IDLS captures the local structural information by describing the relationship between the central macro-pixel and its neighbors. This relationship is represented with the linear representation coefficients determined using ridge regression. One image is actually decomposed into a series of sub-images (also called structure images) according to a local structure feature vector. All the structure images, after being down-sampled for dimensionality reduction, are concatenated into one super-vector. Fisher linear discriminant analysis is then used to provide a low-dimensional, compact, and discriminative representation for each super-vector. The proposed method is applied to face recognition and examined using our real-world face image database, NUST-RWFR, and five popular, publicly available, benchmark face image databases (AR, Extended Yale B, PIE, FERET, and LFW). Experimental results show the performance advantages of IDLS over state-of-the-art algorithms.

Nonlinearity-aware based dimensionality reduction and over-sampling for AD/MCI classification from MRI measures.

PubMed

Cao, Peng; Liu, Xiaoli; Yang, Jinzhu; Zhao, Dazhe; Huang, Min; Zhang, Jian; Zaiane, Osmar

2017-12-01

Alzheimer's disease (AD) has been not only a substantial financial burden to the health care system but also an emotional burden to patients and their families. Making accurate diagnosis of AD based on brain magnetic resonance imaging (MRI) is becoming more and more critical and emphasized at the earliest stages. However, the high dimensionality and imbalanced data issues are two major challenges in the study of computer aided AD diagnosis. The greatest limitations of existing dimensionality reduction and over-sampling methods are that they assume a linear relationship between the MRI features (predictor) and the disease status (response). To better capture the complicated but more flexible relationship, we propose a multi-kernel based dimensionality reduction and over-sampling approaches. We combined Marginal Fisher Analysis with ℓ 2,1 -norm based multi-kernel learning (MKMFA) to achieve the sparsity of region-of-interest (ROI), which leads to simultaneously selecting a subset of the relevant brain regions and learning a dimensionality transformation. Meanwhile, a multi-kernel over-sampling (MKOS) was developed to generate synthetic instances in the optimal kernel space induced by MKMFA, so as to compensate for the class imbalanced distribution. We comprehensively evaluate the proposed models for the diagnostic classification (binary class and multi-class classification) including all subjects from the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset. The experimental results not only demonstrate the proposed method has superior performance over multiple comparable methods, but also identifies relevant imaging biomarkers that are consistent with prior medical knowledge. Copyright © 2017 Elsevier Ltd. All rights reserved.

Vehicle Color Recognition with Vehicle-Color Saliency Detection and Dual-Orientational Dimensionality Reduction of CNN Deep Features

NASA Astrophysics Data System (ADS)

Zhang, Qiang; Li, Jiafeng; Zhuo, Li; Zhang, Hui; Li, Xiaoguang

2017-12-01

Color is one of the most stable attributes of vehicles and often used as a valuable cue in some important applications. Various complex environmental factors, such as illumination, weather, noise and etc., result in the visual characteristics of the vehicle color being obvious diversity. Vehicle color recognition in complex environments has been a challenging task. The state-of-the-arts methods roughly take the whole image for color recognition, but many parts of the images such as car windows; wheels and background contain no color information, which will have negative impact on the recognition accuracy. In this paper, a novel vehicle color recognition method using local vehicle-color saliency detection and dual-orientational dimensionality reduction of convolutional neural network (CNN) deep features has been proposed. The novelty of the proposed method includes two parts: (1) a local vehicle-color saliency detection method has been proposed to determine the vehicle color region of the vehicle image and exclude the influence of non-color regions on the recognition accuracy; (2) dual-orientational dimensionality reduction strategy has been designed to greatly reduce the dimensionality of deep features that are learnt from CNN, which will greatly mitigate the storage and computational burden of the subsequent processing, while improving the recognition accuracy. Furthermore, linear support vector machine is adopted as the classifier to train the dimensionality reduced features to obtain the recognition model. The experimental results on public dataset demonstrate that the proposed method can achieve superior recognition performance over the state-of-the-arts methods.

Incremental online learning in high dimensions.

PubMed

Vijayakumar, Sethu; D'Souza, Aaron; Schaal, Stefan

2005-12-01

Locally weighted projection regression (LWPR) is a new algorithm for incremental nonlinear function approximation in high-dimensional spaces with redundant and irrelevant input dimensions. At its core, it employs nonparametric regression with locally linear models. In order to stay computationally efficient and numerically robust, each local model performs the regression analysis with a small number of univariate regressions in selected directions in input space in the spirit of partial least squares regression. We discuss when and how local learning techniques can successfully work in high-dimensional spaces and review the various techniques for local dimensionality reduction before finally deriving the LWPR algorithm. The properties of LWPR are that it (1) learns rapidly with second-order learning methods based on incremental training, (2) uses statistically sound stochastic leave-one-out cross validation for learning without the need to memorize training data, (3) adjusts its weighting kernels based on only local information in order to minimize the danger of negative interference of incremental learning, (4) has a computational complexity that is linear in the number of inputs, and (5) can deal with a large number of-possibly redundant-inputs, as shown in various empirical evaluations with up to 90 dimensional data sets. For a probabilistic interpretation, predictive variance and confidence intervals are derived. To our knowledge, LWPR is the first truly incremental spatially localized learning method that can successfully and efficiently operate in very high-dimensional spaces.

Reduced-order model based feedback control of the modified Hasegawa-Wakatani model

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

Goumiri, I. R.; Rowley, C. W.; Ma, Z.

2013-04-15

In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modified Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in flow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then, a model-based feedback controller is designed for the reduced order model using linear quadratic regulators. Finally, a linear quadratic Gaussian controller which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHW equations to stabilizemore » the equilibrium and suppress the transition to drift-wave induced turbulence.« less

Reduced-Order Model Based Feedback Control For Modified Hasegawa-Wakatani Model

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

Goumiri, I. R.; Rowley, C. W.; Ma, Z.

2013-01-28

In this work, the development of model-based feedback control that stabilizes an unstable equilibrium is obtained for the Modi ed Hasegawa-Wakatani (MHW) equations, a classic model in plasma turbulence. First, a balanced truncation (a model reduction technique that has proven successful in ow control design problems) is applied to obtain a low dimensional model of the linearized MHW equation. Then a modelbased feedback controller is designed for the reduced order model using linear quadratic regulators (LQR). Finally, a linear quadratic gaussian (LQG) controller, which is more resistant to disturbances is deduced. The controller is applied on the non-reduced, nonlinear MHWmore » equations to stabilize the equilibrium and suppress the transition to drift-wave induced turbulence.« less

A fast efficient implicit scheme for the gasdynamic equations using a matrix reduction technique

NASA Technical Reports Server (NTRS)

Barth, T. J.; Steger, J. L.

1985-01-01

An efficient implicit finite-difference algorithm for the gasdynamic equations utilizing matrix reduction techniques is presented. A significant reduction in arithmetic operations is achieved without loss of the stability characteristics generality found in the Beam and Warming approximate factorization algorithm. Steady-state solutions to the conservative Euler equations in generalized coordinates are obtained for transonic flows and used to show that the method offers computational advantages over the conventional Beam and Warming scheme. Existing Beam and Warming codes can be retrofit with minimal effort. The theoretical extension of the matrix reduction technique to the full Navier-Stokes equations in Cartesian coordinates is presented in detail. Linear stability, using a Fourier stability analysis, is demonstrated and discussed for the one-dimensional Euler equations.

Identical phase oscillators with global sinusoidal coupling evolve by Mobius group action.

PubMed

Marvel, Seth A; Mirollo, Renato E; Strogatz, Steven H

2009-12-01

Systems of N identical phase oscillators with global sinusoidal coupling are known to display low-dimensional dynamics. Although this phenomenon was first observed about 20 years ago, its underlying cause has remained a puzzle. Here we expose the structure working behind the scenes of these systems by proving that the governing equations are generated by the action of the Mobius group, a three-parameter subgroup of fractional linear transformations that map the unit disk to itself. When there are no auxiliary state variables, the group action partitions the N-dimensional state space into three-dimensional invariant manifolds (the group orbits). The N-3 constants of motion associated with this foliation are the N-3 functionally independent cross ratios of the oscillator phases. No further reduction is possible, in general; numerical experiments on models of Josephson junction arrays suggest that the invariant manifolds often contain three-dimensional regions of neutrally stable chaos.

The high performance parallel algorithm for Unified Gas-Kinetic Scheme

NASA Astrophysics Data System (ADS)

Li, Shiyi; Li, Qibing; Fu, Song; Xu, Jinxiu

2016-11-01

A high performance parallel algorithm for UGKS is developed to simulate three-dimensional flows internal and external on arbitrary grid system. The physical domain and velocity domain are divided into different blocks and distributed according to the two-dimensional Cartesian topology with intra-communicators in physical domain for data exchange and other intra-communicators in velocity domain for sum reduction to moment integrals. Numerical results of three-dimensional cavity flow and flow past a sphere agree well with the results from the existing studies and validate the applicability of the algorithm. The scalability of the algorithm is tested both on small (1-16) and large (729-5832) scale processors. The tested speed-up ratio is near linear ashind thus the efficiency is around 1, which reveals the good scalability of the present algorithm.

Graph theory approach to the eigenvalue problem of large space structures

NASA Technical Reports Server (NTRS)

Reddy, A. S. S. R.; Bainum, P. M.

1981-01-01

Graph theory is used to obtain numerical solutions to eigenvalue problems of large space structures (LSS) characterized by a state vector of large dimensions. The LSS are considered as large, flexible systems requiring both orientation and surface shape control. Graphic interpretation of the determinant of a matrix is employed to reduce a higher dimensional matrix into combinations of smaller dimensional sub-matrices. The reduction is implemented by means of a Boolean equivalent of the original matrices formulated to obtain smaller dimensional equivalents of the original numerical matrix. Computation time becomes less and more accurate solutions are possible. An example is provided in the form of a free-free square plate. Linearized system equations and numerical values of a stiffness matrix are presented, featuring a state vector with 16 components.

Mathematical Techniques for Nonlinear System Theory.

DTIC Science & Technology

1981-09-01

This report deals with research results obtained in the following areas: (1) Finite-dimensional linear system theory by algebraic methods--linear...Infinite-dimensional linear systems--realization theory of infinite-dimensional linear systems; (3) Nonlinear system theory --basic properties of

A manifold learning approach to target detection in high-resolution hyperspectral imagery

NASA Astrophysics Data System (ADS)

Ziemann, Amanda K.

Imagery collected from airborne platforms and satellites provide an important medium for remotely analyzing the content in a scene. In particular, the ability to detect a specific material within a scene is of high importance to both civilian and defense applications. This may include identifying "targets" such as vehicles, buildings, or boats. Sensors that process hyperspectral images provide the high-dimensional spectral information necessary to perform such analyses. However, for a d-dimensional hyperspectral image, it is typical for the data to inherently occupy an m-dimensional space, with m << d. In the remote sensing community, this has led to a recent increase in the use of manifold learning, which aims to characterize the embedded lower-dimensional, non-linear manifold upon which the hyperspectral data inherently lie. Classic hyperspectral data models include statistical, linear subspace, and linear mixture models, but these can place restrictive assumptions on the distribution of the data; this is particularly true when implementing traditional target detection approaches, and the limitations of these models are well-documented. With manifold learning based approaches, the only assumption is that the data reside on an underlying manifold that can be discretely modeled by a graph. The research presented here focuses on the use of graph theory and manifold learning in hyperspectral imagery. Early work explored various graph-building techniques with application to the background model of the Topological Anomaly Detection (TAD) algorithm, which is a graph theory based approach to anomaly detection. This led towards a focus on target detection, and in the development of a specific graph-based model of the data and subsequent dimensionality reduction using manifold learning. An adaptive graph is built on the data, and then used to implement an adaptive version of locally linear embedding (LLE). We artificially induce a target manifold and incorporate it into the adaptive LLE transformation; the artificial target manifold helps to guide the separation of the target data from the background data in the new, lower-dimensional manifold coordinates. Then, target detection is performed in the manifold space.

Stability analysis of unsteady ablation fronts

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

Betti, R.; McCrory, R.L.; Verdon, C.P.

1993-08-01

The linear stability analysis of unsteady ablation fronts, is carried out for a semi-infinite uniform medium. For a laser accelerated target, it is shown that a properly selected modulation of the laser intensity can lead to the dynamic stabilization or growth-rate reduction of a large portion of the unstable spectrum. The theory is in qualitative agreement with the numerical results obtained by using the two-dimensional hydrodynamic code ORCHID.

Stability analysis of unsteady ablation fronts

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

Betti, R.; McCrory, R.L.; Verdon, C.P.

1993-11-08

The linear stability analysis of unsteady ablation fronts is carried out for a semi-infinite uniform medium. For a laser accelerated target, it is shown that a properly selected modulation of the laser intensity can lead to the dynamic stabilization or growth-rate reduction of a large portion of the unstable spectrum. The theory is in qualitative agreement with the numerical results obtained by using the two-dimensional hydrodynamic code ORCHID.

From 6D superconformal field theories to dynamic gauged linear sigma models

NASA Astrophysics Data System (ADS)

Apruzzi, Fabio; Hassler, Falk; Heckman, Jonathan J.; Melnikov, Ilarion V.

2017-09-01

Compactifications of six-dimensional (6D) superconformal field theories (SCFTs) on four- manifolds generate a large class of novel two-dimensional (2D) quantum field theories. We consider in detail the case of the rank-one simple non-Higgsable cluster 6D SCFTs. On the tensor branch of these theories, the gauge group is simple and there are no matter fields. For compactifications on suitably chosen Kähler surfaces, we present evidence that this provides a method to realize 2D SCFTs with N =(0 ,2 ) supersymmetry. In particular, we find that reduction on the tensor branch of the 6D SCFT yields a description of the same 2D fixed point that is described in the UV by a gauged linear sigma model (GLSM) in which the parameters are promoted to dynamical fields, that is, a "dynamic GLSM" (DGLSM). Consistency of the model requires the DGLSM to be coupled to additional non-Lagrangian sectors obtained from reduction of the antichiral two-form of the 6D theory. These extra sectors include both chiral and antichiral currents, as well as spacetime filling noncritical strings of the 6D theory. For each candidate 2D SCFT, we also extract the left- and right-moving central charges in terms of data of the 6D SCFT and the compactification manifold.

Application of Linear Discriminant Analysis in Dimensionality Reduction for Hand Motion Classification

NASA Astrophysics Data System (ADS)

Phinyomark, A.; Hu, H.; Phukpattaranont, P.; Limsakul, C.

2012-01-01

The classification of upper-limb movements based on surface electromyography (EMG) signals is an important issue in the control of assistive devices and rehabilitation systems. Increasing the number of EMG channels and features in order to increase the number of control commands can yield a high dimensional feature vector. To cope with the accuracy and computation problems associated with high dimensionality, it is commonplace to apply a processing step that transforms the data to a space of significantly lower dimensions with only a limited loss of useful information. Linear discriminant analysis (LDA) has been successfully applied as an EMG feature projection method. Recently, a number of extended LDA-based algorithms have been proposed, which are more competitive in terms of both classification accuracy and computational costs/times with classical LDA. This paper presents the findings of a comparative study of classical LDA and five extended LDA methods. From a quantitative comparison based on seven multi-feature sets, three extended LDA-based algorithms, consisting of uncorrelated LDA, orthogonal LDA and orthogonal fuzzy neighborhood discriminant analysis, produce better class separability when compared with a baseline system (without feature projection), principle component analysis (PCA), and classical LDA. Based on a 7-dimension time domain and time-scale feature vectors, these methods achieved respectively 95.2% and 93.2% classification accuracy by using a linear discriminant classifier.

Nonlinear dimensionality reduction of electroencephalogram (EEG) for Brain Computer interfaces.

PubMed

Teli, Mohammad Nayeem; Anderson, Charles

2009-01-01

Patterns in electroencephalogram (EEG) signals are analyzed for a Brain Computer Interface (BCI). An important aspect of this analysis is the work on transformations of high dimensional EEG data to low dimensional spaces in which we can classify the data according to mental tasks being performed. In this research we investigate how a Neural Network (NN) in an auto-encoder with bottleneck configuration can find such a transformation. We implemented two approximate second-order methods to optimize the weights of these networks, because the more common first-order methods are very slow to converge for networks like these with more than three layers of computational units. The resulting non-linear projections of time embedded EEG signals show interesting separations that are related to tasks. The bottleneck networks do indeed discover nonlinear transformations to low-dimensional spaces that capture much of the information present in EEG signals. However, the resulting low-dimensional representations do not improve classification rates beyond what is possible using Quadratic Discriminant Analysis (QDA) on the original time-lagged EEG.

TH-CD-207A-07: Prediction of High Dimensional State Subject to Respiratory Motion: A Manifold Learning Approach

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

Liu, W; Sawant, A; Ruan, D

Purpose: The development of high dimensional imaging systems (e.g. volumetric MRI, CBCT, photogrammetry systems) in image-guided radiotherapy provides important pathways to the ultimate goal of real-time volumetric/surface motion monitoring. This study aims to develop a prediction method for the high dimensional state subject to respiratory motion. Compared to conventional linear dimension reduction based approaches, our method utilizes manifold learning to construct a descriptive feature submanifold, where more efficient and accurate prediction can be performed. Methods: We developed a prediction framework for high-dimensional state subject to respiratory motion. The proposed method performs dimension reduction in a nonlinear setting to permit moremore » descriptive features compared to its linear counterparts (e.g., classic PCA). Specifically, a kernel PCA is used to construct a proper low-dimensional feature manifold, where low-dimensional prediction is performed. A fixed-point iterative pre-image estimation method is applied subsequently to recover the predicted value in the original state space. We evaluated and compared the proposed method with PCA-based method on 200 level-set surfaces reconstructed from surface point clouds captured by the VisionRT system. The prediction accuracy was evaluated with respect to root-mean-squared-error (RMSE) for both 200ms and 600ms lookahead lengths. Results: The proposed method outperformed PCA-based approach with statistically higher prediction accuracy. In one-dimensional feature subspace, our method achieved mean prediction accuracy of 0.86mm and 0.89mm for 200ms and 600ms lookahead lengths respectively, compared to 0.95mm and 1.04mm from PCA-based method. The paired t-tests further demonstrated the statistical significance of the superiority of our method, with p-values of 6.33e-3 and 5.78e-5, respectively. Conclusion: The proposed approach benefits from the descriptiveness of a nonlinear manifold and the prediction reliability in such low dimensional manifold. The fixed-point iterative approach turns out to work well practically for the pre-image recovery. Our approach is particularly suitable to facilitate managing respiratory motion in image-guide radiotherapy. This work is supported in part by NIH grant R01 CA169102-02.« less

Evolution of thermal stress and failure probability during reduction and re-oxidation of solid oxide fuel cell

NASA Astrophysics Data System (ADS)

Wang, Yu; Jiang, Wenchun; Luo, Yun; Zhang, Yucai; Tu, Shan-Tung

2017-12-01

The reduction and re-oxidation of anode have significant effects on the integrity of the solid oxide fuel cell (SOFC) sealed by the glass-ceramic (GC). The mechanical failure is mainly controlled by the stress distribution. Therefore, a three dimensional model of SOFC is established to investigate the stress evolution during the reduction and re-oxidation by finite element method (FEM) in this paper, and the failure probability is calculated using the Weibull method. The results demonstrate that the reduction of anode can decrease the thermal stresses and reduce the failure probability due to the volumetric contraction and porosity increasing. The re-oxidation can result in a remarkable increase of the thermal stresses, and the failure probabilities of anode, cathode, electrolyte and GC all increase to 1, which is mainly due to the large linear strain rather than the porosity decreasing. The cathode and electrolyte fail as soon as the linear strains are about 0.03% and 0.07%. Therefore, the re-oxidation should be controlled to ensure the integrity, and a lower re-oxidation temperature can decrease the stress and failure probability.

A non-linear dimension reduction methodology for generating data-driven stochastic input models

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

Ganapathysubramanian, Baskar; Zabaras, Nicholas

Stochastic analysis of random heterogeneous media (polycrystalline materials, porous media, functionally graded materials) provides information of significance only if realistic input models of the topology and property variations are used. This paper proposes a framework to construct such input stochastic models for the topology and thermal diffusivity variations in heterogeneous media using a data-driven strategy. Given a set of microstructure realizations (input samples) generated from given statistical information about the medium topology, the framework constructs a reduced-order stochastic representation of the thermal diffusivity. This problem of constructing a low-dimensional stochastic representation of property variations is analogous to the problem ofmore » manifold learning and parametric fitting of hyper-surfaces encountered in image processing and psychology. Denote by M the set of microstructures that satisfy the given experimental statistics. A non-linear dimension reduction strategy is utilized to map M to a low-dimensional region, A. We first show that M is a compact manifold embedded in a high-dimensional input space R{sup n}. An isometric mapping F from M to a low-dimensional, compact, connected set A is contained in R{sup d}(d<

Magnet pole shape design for reduction of thrust ripple of slotless permanent magnet linear synchronous motor with arc-shaped magnets considering end-effect based on analytical method

NASA Astrophysics Data System (ADS)

Shin, Kyung-Hun; Park, Hyung-Il; Kim, Kwan-Ho; Jang, Seok-Myeong; Choi, Jang-Young

2017-05-01

The shape of the magnet is essential to the performance of a slotless permanent magnet linear synchronous machine (PMLSM) because it is directly related to desirable machine performance. This paper presents a reduction in the thrust ripple of a PMLSM through the use of arc-shaped magnets based on electromagnetic field theory. The magnetic field solutions were obtained by considering end effect using a magnetic vector potential and two-dimensional Cartesian coordinate system. The analytical solution of each subdomain (PM, air-gap, coil, and end region) is derived, and the field solution is obtained by applying the boundary and interface conditions between the subdomains. In particular, an analytical method was derived for the instantaneous thrust and thrust ripple reduction of a PMLSM with arc-shaped magnets. In order to demonstrate the validity of the analytical results, the back electromotive force results of a finite element analysis and experiment on the manufactured prototype model were compared. The optimal point for thrust ripple minimization is suggested.

Reduced nonlinear prognostic model construction from high-dimensional data

NASA Astrophysics Data System (ADS)

Gavrilov, Andrey; Mukhin, Dmitry; Loskutov, Evgeny; Feigin, Alexander

2017-04-01

Construction of a data-driven model of evolution operator using universal approximating functions can only be statistically justified when the dimension of its phase space is small enough, especially in the case of short time series. At the same time in many applications real-measured data is high-dimensional, e.g. it is space-distributed and multivariate in climate science. Therefore it is necessary to use efficient dimensionality reduction methods which are also able to capture key dynamical properties of the system from observed data. To address this problem we present a Bayesian approach to an evolution operator construction which incorporates two key reduction steps. First, the data is decomposed into a set of certain empirical modes, such as standard empirical orthogonal functions or recently suggested nonlinear dynamical modes (NDMs) [1], and the reduced space of corresponding principal components (PCs) is obtained. Then, the model of evolution operator for PCs is constructed which maps a number of states in the past to the current state. The second step is to reduce this time-extended space in the past using appropriate decomposition methods. Such a reduction allows us to capture only the most significant spatio-temporal couplings. The functional form of the evolution operator includes separately linear, nonlinear (based on artificial neural networks) and stochastic terms. Explicit separation of the linear term from the nonlinear one allows us to more easily interpret degree of nonlinearity as well as to deal better with smooth PCs which can naturally occur in the decompositions like NDM, as they provide a time scale separation. Results of application of the proposed method to climate data are demonstrated and discussed. The study is supported by Government of Russian Federation (agreement #14.Z50.31.0033 with the Institute of Applied Physics of RAS). 1. Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. http://doi.org/10.1038/srep15510

Reduction by invariants and projection of linear representations of Lie algebras applied to the construction of nonlinear realizations

NASA Astrophysics Data System (ADS)

Campoamor-Stursberg, R.

2018-03-01

A procedure for the construction of nonlinear realizations of Lie algebras in the context of Vessiot-Guldberg-Lie algebras of first-order systems of ordinary differential equations (ODEs) is proposed. The method is based on the reduction of invariants and projection of lowest-dimensional (irreducible) representations of Lie algebras. Applications to the description of parameterized first-order systems of ODEs related by contraction of Lie algebras are given. In particular, the kinematical Lie algebras in (2 + 1)- and (3 + 1)-dimensions are realized simultaneously as Vessiot-Guldberg-Lie algebras of parameterized nonlinear systems in R3 and R4, respectively.

Multi-label classification of chronically ill patients with bag of words and supervised dimensionality reduction algorithms.

PubMed

Bromuri, Stefano; Zufferey, Damien; Hennebert, Jean; Schumacher, Michael

2014-10-01

This research is motivated by the issue of classifying illnesses of chronically ill patients for decision support in clinical settings. Our main objective is to propose multi-label classification of multivariate time series contained in medical records of chronically ill patients, by means of quantization methods, such as bag of words (BoW), and multi-label classification algorithms. Our second objective is to compare supervised dimensionality reduction techniques to state-of-the-art multi-label classification algorithms. The hypothesis is that kernel methods and locality preserving projections make such algorithms good candidates to study multi-label medical time series. We combine BoW and supervised dimensionality reduction algorithms to perform multi-label classification on health records of chronically ill patients. The considered algorithms are compared with state-of-the-art multi-label classifiers in two real world datasets. Portavita dataset contains 525 diabetes type 2 (DT2) patients, with co-morbidities of DT2 such as hypertension, dyslipidemia, and microvascular or macrovascular issues. MIMIC II dataset contains 2635 patients affected by thyroid disease, diabetes mellitus, lipoid metabolism disease, fluid electrolyte disease, hypertensive disease, thrombosis, hypotension, chronic obstructive pulmonary disease (COPD), liver disease and kidney disease. The algorithms are evaluated using multi-label evaluation metrics such as hamming loss, one error, coverage, ranking loss, and average precision. Non-linear dimensionality reduction approaches behave well on medical time series quantized using the BoW algorithm, with results comparable to state-of-the-art multi-label classification algorithms. Chaining the projected features has a positive impact on the performance of the algorithm with respect to pure binary relevance approaches. The evaluation highlights the feasibility of representing medical health records using the BoW for multi-label classification tasks. The study also highlights that dimensionality reduction algorithms based on kernel methods, locality preserving projections or both are good candidates to deal with multi-label classification tasks in medical time series with many missing values and high label density. Copyright © 2014 Elsevier Inc. All rights reserved.

Locally Linear Embedding of Local Orthogonal Least Squares Images for Face Recognition

NASA Astrophysics Data System (ADS)

Hafizhelmi Kamaru Zaman, Fadhlan

2018-03-01

Dimensionality reduction is very important in face recognition since it ensures that high-dimensionality data can be mapped to lower dimensional space without losing salient and integral facial information. Locally Linear Embedding (LLE) has been previously used to serve this purpose, however, the process of acquiring LLE features requires high computation and resources. To overcome this limitation, we propose a locally-applied Local Orthogonal Least Squares (LOLS) model can be used as initial feature extraction before the application of LLE. By construction of least squares regression under orthogonal constraints we can preserve more discriminant information in the local subspace of facial features while reducing the overall features into a more compact form that we called LOLS images. LLE can then be applied on the LOLS images to maps its representation into a global coordinate system of much lower dimensionality. Several experiments carried out using publicly available face datasets such as AR, ORL, YaleB, and FERET under Single Sample Per Person (SSPP) constraint demonstrates that our proposed method can reduce the time required to compute LLE features while delivering better accuracy when compared to when either LLE or OLS alone is used. Comparison against several other feature extraction methods and more recent feature-learning method such as state-of-the-art Convolutional Neural Networks (CNN) also reveal the superiority of the proposed method under SSPP constraint.

High-performance Cu nanoparticles/three-dimensional graphene/Ni foam hybrid for catalytic and sensing applications

NASA Astrophysics Data System (ADS)

Zhu, Long; Guo, Xinli; Liu, Yuanyuan; Chen, Zhongtao; Zhang, Weijie; Yin, Kuibo; Li, Long; Zhang, Yao; Wang, Zengmei; Sun, Litao; Zhao, Yuhong

2018-04-01

A novel hybrid of Cu nanoparticles/three-dimensional graphene/Ni foam (Cu NPs/3DGr/NiF) was prepared by chemical vapor deposition, followed by a galvanic displacement reaction in Ni- and Cu-ion-containing salt solution through a one-step reaction. The as-prepared Cu NPs/3DGr/NiF hybrid is uniform, stable, recyclable and exhibits an extraordinarily high catalytic efficiency for the reduction of 4-nitrophenol (4-NP) to 4-aminophenol (4-AP) with a reduction rate constant K = 0.056 15 s-1, required time ˜30 s and excellent sensing properties for the non-enzymatic amperometric hydrogen peroxide (H2O2) with a linear range ˜50 μM-9.65 mM, response time ˜3 s, detection limit ˜1 μM. The results indicate that the as-prepared Cu NPs/3DGr/NiF hybrid can be used to replace expensive noble metals in catalysis and sensing applications.

Computer simulations of electromagnetic cool ion beam instabilities. [in near earth space

NASA Technical Reports Server (NTRS)

Gary, S. P.; Madland, C. D.; Schriver, D.; Winske, D.

1986-01-01

Electromagnetic ion beam instabilities driven by cool ion beams at propagation parallel or antiparallel to a uniform magnetic field are studied using computer simulations. The elements of linear theory applicable to electromagnetic ion beam instabilities and the simulations derived from a one-dimensional hybrid computer code are described. The quasi-linear regime of the right-hand resonant ion beam instability, and the gyrophase bunching of the nonlinear regime of the right-hand resonant and nonresonant instabilities are examined. It is detected that in the quasi-linear regime the instability saturation is due to a reduction in the beam core relative drift speed and an increase in the perpendicular-to-parallel beam temperature; in the nonlinear regime the instabilities saturate when half the initial beam drift kinetic energy density is converted to fluctuating magnetic field energy density.

Principal component of explained variance: An efficient and optimal data dimension reduction framework for association studies.

PubMed

Turgeon, Maxime; Oualkacha, Karim; Ciampi, Antonio; Miftah, Hanane; Dehghan, Golsa; Zanke, Brent W; Benedet, Andréa L; Rosa-Neto, Pedro; Greenwood, Celia Mt; Labbe, Aurélie

2018-05-01

The genomics era has led to an increase in the dimensionality of data collected in the investigation of biological questions. In this context, dimension-reduction techniques can be used to summarise high-dimensional signals into low-dimensional ones, to further test for association with one or more covariates of interest. This paper revisits one such approach, previously known as principal component of heritability and renamed here as principal component of explained variance (PCEV). As its name suggests, the PCEV seeks a linear combination of outcomes in an optimal manner, by maximising the proportion of variance explained by one or several covariates of interest. By construction, this method optimises power; however, due to its computational complexity, it has unfortunately received little attention in the past. Here, we propose a general analytical PCEV framework that builds on the assets of the original method, i.e. conceptually simple and free of tuning parameters. Moreover, our framework extends the range of applications of the original procedure by providing a computationally simple strategy for high-dimensional outcomes, along with exact and asymptotic testing procedures that drastically reduce its computational cost. We investigate the merits of the PCEV using an extensive set of simulations. Furthermore, the use of the PCEV approach is illustrated using three examples taken from the fields of epigenetics and brain imaging.

Path Complexity in Virtual Water Maze Navigation: Differential Associations with Age, Sex, and Regional Brain Volume.

PubMed

Daugherty, Ana M; Yuan, Peng; Dahle, Cheryl L; Bender, Andrew R; Yang, Yiqin; Raz, Naftali

2015-09-01

Studies of human navigation in virtual maze environments have consistently linked advanced age with greater distance traveled between the start and the goal and longer duration of the search. Observations of search path geometry suggest that routes taken by older adults may be unnecessarily complex and that excessive path complexity may be an indicator of cognitive difficulties experienced by older navigators. In a sample of healthy adults, we quantify search path complexity in a virtual Morris water maze with a novel method based on fractal dimensionality. In a two-level hierarchical linear model, we estimated improvement in navigation performance across trials by a decline in route length, shortening of search time, and reduction in fractal dimensionality of the path. While replicating commonly reported age and sex differences in time and distance indices, a reduction in fractal dimension of the path accounted for improvement across trials, independent of age or sex. The volumes of brain regions associated with the establishment of cognitive maps (parahippocampal gyrus and hippocampus) were related to path dimensionality, but not to the total distance and time. Thus, fractal dimensionality of a navigational path may present a useful complementary method of quantifying performance in navigation. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Ermakov's Superintegrable Toy and Nonlocal Symmetries

NASA Astrophysics Data System (ADS)

Leach, P. G. L.; Karasu Kalkanli, A.; Nucci, M. C.; Andriopoulos, K.

2005-11-01

We investigate the symmetry properties of a pair of Ermakov equations. The system is superintegrable and yet possesses only three Lie point symmetries with the algebra sl(2, R). The number of point symmetries is insufficient and the algebra unsuitable for the complete specification of the system. We use the method of reduction of order to reduce the nonlinear fourth-order system to a third-order system comprising a linear second-order equation and a conservation law. We obtain the representation of the complete symmetry group from this system. Four of the required symmetries are nonlocal and the algebra is the direct sum of a one-dimensional Abelian algebra with the semidirect sum of a two-dimensional solvable algebra with a two-dimensional Abelian algebra. The problem illustrates the difficulties which can arise in very elementary systems. Our treatment demonstrates the existence of possible routes to overcome these problems in a systematic fashion.

Evaluation of linear classifiers on articles containing pharmacokinetic evidence of drug-drug interactions.

PubMed

Kolchinsky, A; Lourenço, A; Li, L; Rocha, L M

2013-01-01

Drug-drug interaction (DDI) is a major cause of morbidity and mortality. DDI research includes the study of different aspects of drug interactions, from in vitro pharmacology, which deals with drug interaction mechanisms, to pharmaco-epidemiology, which investigates the effects of DDI on drug efficacy and adverse drug reactions. Biomedical literature mining can aid both kinds of approaches by extracting relevant DDI signals from either the published literature or large clinical databases. However, though drug interaction is an ideal area for translational research, the inclusion of literature mining methodologies in DDI workflows is still very preliminary. One area that can benefit from literature mining is the automatic identification of a large number of potential DDIs, whose pharmacological mechanisms and clinical significance can then be studied via in vitro pharmacology and in populo pharmaco-epidemiology. We implemented a set of classifiers for identifying published articles relevant to experimental pharmacokinetic DDI evidence. These documents are important for identifying causal mechanisms behind putative drug-drug interactions, an important step in the extraction of large numbers of potential DDIs. We evaluate performance of several linear classifiers on PubMed abstracts, under different feature transformation and dimensionality reduction methods. In addition, we investigate the performance benefits of including various publicly-available named entity recognition features, as well as a set of internally-developed pharmacokinetic dictionaries. We found that several classifiers performed well in distinguishing relevant and irrelevant abstracts. We found that the combination of unigram and bigram textual features gave better performance than unigram features alone, and also that normalization transforms that adjusted for feature frequency and document length improved classification. For some classifiers, such as linear discriminant analysis (LDA), proper dimensionality reduction had a large impact on performance. Finally, the inclusion of NER features and dictionaries was found not to help classification.

Langevin and Fokker-Planck analyses of inhibited molecular passing processes controlling transport and reactivity in nanoporous materials

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

Wang, Chi-Jen; Ackerman, David M.; Slowing, Igor I.

2014-07-14

Inhibited passing of reactant and product molecules within the linear pores of nanoporous catalytic materials strongly reduces reactivity. The dependence of the passing propensity P on pore radius R is analyzed utilizing Langevin dynamics to account for solvent effects. We find that P~(R-R c) σ, where passing is sterically blocked for R≤R c, with σ below the transition state theory value. Deeper insight comes from analysis of the corresponding high-dimensional Fokker-Planck equation, which facilitates an effective small-P approximation, and dimensional reduction enabling utilization of conformal mapping ideas. We analyze passing for spherical molecules and also assess the effect of rotationalmore » degrees of freedom for elongated molecules.« less

Unsupervised nonlinear dimensionality reduction machine learning methods applied to multiparametric MRI in cerebral ischemia: preliminary results

NASA Astrophysics Data System (ADS)

Parekh, Vishwa S.; Jacobs, Jeremy R.; Jacobs, Michael A.

2014-03-01

The evaluation and treatment of acute cerebral ischemia requires a technique that can determine the total area of tissue at risk for infarction using diagnostic magnetic resonance imaging (MRI) sequences. Typical MRI data sets consist of T1- and T2-weighted imaging (T1WI, T2WI) along with advanced MRI parameters of diffusion-weighted imaging (DWI) and perfusion weighted imaging (PWI) methods. Each of these parameters has distinct radiological-pathological meaning. For example, DWI interrogates the movement of water in the tissue and PWI gives an estimate of the blood flow, both are critical measures during the evolution of stroke. In order to integrate these data and give an estimate of the tissue at risk or damaged; we have developed advanced machine learning methods based on unsupervised non-linear dimensionality reduction (NLDR) techniques. NLDR methods are a class of algorithms that uses mathematically defined manifolds for statistical sampling of multidimensional classes to generate a discrimination rule of guaranteed statistical accuracy and they can generate a two- or three-dimensional map, which represents the prominent structures of the data and provides an embedded image of meaningful low-dimensional structures hidden in their high-dimensional observations. In this manuscript, we develop NLDR methods on high dimensional MRI data sets of preclinical animals and clinical patients with stroke. On analyzing the performance of these methods, we observed that there was a high of similarity between multiparametric embedded images from NLDR methods and the ADC map and perfusion map. It was also observed that embedded scattergram of abnormal (infarcted or at risk) tissue can be visualized and provides a mechanism for automatic methods to delineate potential stroke volumes and early tissue at risk.

The Stability Region for Feedback Control of the Wake Behind Twin Oscillating Cylinders

NASA Astrophysics Data System (ADS)

Borggaard, Jeff; Gugercin, Serkan; Zietsman, Lizette

2016-11-01

Linear feedback control has the ability to stabilize vortex shedding behind twin cylinders where cylinder rotation is the actuation mechanism. Complete elimination of the wake is only possible for certain Reynolds numbers and cylinder spacing. This is related to the presence of asymmetric unstable modes in the linearized system. We investigate this region of parameter space using a number of closed-loop simulations that bound this region. We then consider the practical issue of designing feedback controls based on limited state measurements by building a nonlinear compensator using linear robust control theory with and incorporating the nonlinear terms in the compensator (e.g., using the extended Kalman filter). Interpolatory model reduction methods are applied to the large discretized, linearized Navier-Stokes system and used for computing the control laws and compensators. Preliminary closed-loop simulations of a three-dimensional version of this problem will also be presented. Supported in part by the National Science Foundation.

Sufficient Forecasting Using Factor Models

PubMed Central

Fan, Jianqing; Xue, Lingzhou; Yao, Jiawei

2017-01-01

We consider forecasting a single time series when there is a large number of predictors and a possible nonlinear effect. The dimensionality was first reduced via a high-dimensional (approximate) factor model implemented by the principal component analysis. Using the extracted factors, we develop a novel forecasting method called the sufficient forecasting, which provides a set of sufficient predictive indices, inferred from high-dimensional predictors, to deliver additional predictive power. The projected principal component analysis will be employed to enhance the accuracy of inferred factors when a semi-parametric (approximate) factor model is assumed. Our method is also applicable to cross-sectional sufficient regression using extracted factors. The connection between the sufficient forecasting and the deep learning architecture is explicitly stated. The sufficient forecasting correctly estimates projection indices of the underlying factors even in the presence of a nonparametric forecasting function. The proposed method extends the sufficient dimension reduction to high-dimensional regimes by condensing the cross-sectional information through factor models. We derive asymptotic properties for the estimate of the central subspace spanned by these projection directions as well as the estimates of the sufficient predictive indices. We further show that the natural method of running multiple regression of target on estimated factors yields a linear estimate that actually falls into this central subspace. Our method and theory allow the number of predictors to be larger than the number of observations. We finally demonstrate that the sufficient forecasting improves upon the linear forecasting in both simulation studies and an empirical study of forecasting macroeconomic variables. PMID:29731537

Application of machine learning techniques to analyse the effects of physical exercise in ventricular fibrillation.

PubMed

Caravaca, Juan; Soria-Olivas, Emilio; Bataller, Manuel; Serrano, Antonio J; Such-Miquel, Luis; Vila-Francés, Joan; Guerrero, Juan F

2014-02-01

This work presents the application of machine learning techniques to analyse the influence of physical exercise in the physiological properties of the heart, during ventricular fibrillation. To this end, different kinds of classifiers (linear and neural models) are used to classify between trained and sedentary rabbit hearts. The use of those classifiers in combination with a wrapper feature selection algorithm allows to extract knowledge about the most relevant features in the problem. The obtained results show that neural models outperform linear classifiers (better performance indices and a better dimensionality reduction). The most relevant features to describe the benefits of physical exercise are those related to myocardial heterogeneity, mean activation rate and activation complexity. © 2013 Published by Elsevier Ltd.

Visualization and Analyses of Jet Structures from a Cluster-Type Linear Aerospike Nozzle

NASA Astrophysics Data System (ADS)

Niimi, Tomohide; Mori, Hideo; Okabe, Kazuki; Masai, Yusuke; Taniguchi, Mashio

Aerospike nozzles have been expected as a candidate for an engine of reusable space shuttles to respond to growing demand for rocket-launching and its cost reduction. In this study, the flow field structure in any cross sections around the linear-type aerospike nozzle are visualized and analyzed, using laser induced fluorescence (LIF) of NO seeded in the carrier gas N2. Since the flow field structure is affected mainly by the pressure ratio (P/P), the linear-type aerospike nozzle is set inside the vacuum chamber to carry out the experiments in the wide range of pressure ratios from 75 to 250. Flow fields are visualized in several cross-sections, demonstrating the complicated three-dimensional flow field structures. Pressure sensitive paint (PSP) of PtTFPP bound by poly(TMSP) is also applied successfully to measurement of the complicated pressure distribution on the spike surface.

Nonparametric regression applied to quantitative structure-activity relationships

PubMed

Constans; Hirst

2000-03-01

Several nonparametric regressors have been applied to modeling quantitative structure-activity relationship (QSAR) data. The simplest regressor, the Nadaraya-Watson, was assessed in a genuine multivariate setting. Other regressors, the local linear and the shifted Nadaraya-Watson, were implemented within additive models--a computationally more expedient approach, better suited for low-density designs. Performances were benchmarked against the nonlinear method of smoothing splines. A linear reference point was provided by multilinear regression (MLR). Variable selection was explored using systematic combinations of different variables and combinations of principal components. For the data set examined, 47 inhibitors of dopamine beta-hydroxylase, the additive nonparametric regressors have greater predictive accuracy (as measured by the mean absolute error of the predictions or the Pearson correlation in cross-validation trails) than MLR. The use of principal components did not improve the performance of the nonparametric regressors over use of the original descriptors, since the original descriptors are not strongly correlated. It remains to be seen if the nonparametric regressors can be successfully coupled with better variable selection and dimensionality reduction in the context of high-dimensional QSARs.

Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.

PubMed

Talaei, Behzad; Jagannathan, Sarangapani; Singler, John

2018-04-01

This paper develops a near optimal boundary control method for distributed parameter systems governed by uncertain linear 1-D parabolic partial differential equations (PDE) by using approximate dynamic programming. A quadratic surface integral is proposed to express the optimal cost functional for the infinite-dimensional state space. Accordingly, the Hamilton-Jacobi-Bellman (HJB) equation is formulated in the infinite-dimensional domain without using any model reduction. Subsequently, a neural network identifier is developed to estimate the unknown spatially varying coefficient in PDE dynamics. Novel tuning law is proposed to guarantee the boundedness of identifier approximation error in the PDE domain. A radial basis network (RBN) is subsequently proposed to generate an approximate solution for the optimal surface kernel function online. The tuning law for near optimal RBN weights is created, such that the HJB equation error is minimized while the dynamics are identified and closed-loop system remains stable. Ultimate boundedness (UB) of the closed-loop system is verified by using the Lyapunov theory. The performance of the proposed controller is successfully confirmed by simulation on an unstable diffusion-reaction process.

Symmetries and integrability of a fourth-order Euler-Bernoulli beam equation

NASA Astrophysics Data System (ADS)

Bokhari, Ashfaque H.; Mahomed, F. M.; Zaman, F. D.

2010-05-01

The complete symmetry group classification of the fourth-order Euler-Bernoulli ordinary differential equation, where the elastic modulus and the area moment of inertia are constants and the applied load is a function of the normal displacement, is obtained. We perform the Lie and Noether symmetry analysis of this problem. In the Lie analysis, the principal Lie algebra which is one dimensional extends in four cases, viz. the linear, exponential, general power law, and a negative fractional power law. It is further shown that two cases arise in the Noether classification with respect to the standard Lagrangian. That is, the linear case for which the Noether algebra dimension is one less than the Lie algebra dimension as well as the negative fractional power law. In the latter case the Noether algebra is three dimensional and is isomorphic to the Lie algebra which is sl(2,R). This exceptional case, although admitting the nonsolvable algebra sl(2,R), remarkably allows for a two-parameter family of exact solutions via the Noether integrals. The Lie reduction gives a second-order ordinary differential equation which has nonlocal symmetry.

Low-rank separated representation surrogates of high-dimensional stochastic functions: Application in Bayesian inference

NASA Astrophysics Data System (ADS)

Validi, AbdoulAhad

2014-03-01

This study introduces a non-intrusive approach in the context of low-rank separated representation to construct a surrogate of high-dimensional stochastic functions, e.g., PDEs/ODEs, in order to decrease the computational cost of Markov Chain Monte Carlo simulations in Bayesian inference. The surrogate model is constructed via a regularized alternative least-square regression with Tikhonov regularization using a roughening matrix computing the gradient of the solution, in conjunction with a perturbation-based error indicator to detect optimal model complexities. The model approximates a vector of a continuous solution at discrete values of a physical variable. The required number of random realizations to achieve a successful approximation linearly depends on the function dimensionality. The computational cost of the model construction is quadratic in the number of random inputs, which potentially tackles the curse of dimensionality in high-dimensional stochastic functions. Furthermore, this vector-valued separated representation-based model, in comparison to the available scalar-valued case, leads to a significant reduction in the cost of approximation by an order of magnitude equal to the vector size. The performance of the method is studied through its application to three numerical examples including a 41-dimensional elliptic PDE and a 21-dimensional cavity flow.

Local Context Finder (LCF) reveals multidimensional relationships among mRNA expression profiles of Arabidopsis responding to pathogen infection

PubMed Central

Katagiri, Fumiaki; Glazebrook, Jane

2003-01-01

A major task in computational analysis of mRNA expression profiles is definition of relationships among profiles on the basis of similarities among them. This is generally achieved by pattern recognition in the distribution of data points representing each profile in a high-dimensional space. Some drawbacks of commonly used pattern recognition algorithms stem from their use of a globally linear space and/or limited degrees of freedom. A pattern recognition method called Local Context Finder (LCF) is described here. LCF uses nonlinear dimensionality reduction for pattern recognition. Then it builds a network of profiles based on the nonlinear dimensionality reduction results. LCF was used to analyze mRNA expression profiles of the plant host Arabidopsis interacting with the bacterial pathogen Pseudomonas syringae. In one case, LCF revealed two dimensions essential to explain the effects of the NahG transgene and the ndr1 mutation on resistant and susceptible responses. In another case, plant mutants deficient in responses to pathogen infection were classified on the basis of LCF analysis of their profiles. The classification by LCF was consistent with the results of biological characterization of the mutants. Thus, LCF is a powerful method for extracting information from expression profile data. PMID:12960373

A decentralized linear quadratic control design method for flexible structures

NASA Technical Reports Server (NTRS)

Su, Tzu-Jeng; Craig, Roy R., Jr.

1990-01-01

A decentralized suboptimal linear quadratic control design procedure which combines substructural synthesis, model reduction, decentralized control design, subcontroller synthesis, and controller reduction is proposed for the design of reduced-order controllers for flexible structures. The procedure starts with a definition of the continuum structure to be controlled. An evaluation model of finite dimension is obtained by the finite element method. Then, the finite element model is decomposed into several substructures by using a natural decomposition called substructuring decomposition. Each substructure, at this point, still has too large a dimension and must be reduced to a size that is Riccati-solvable. Model reduction of each substructure can be performed by using any existing model reduction method, e.g., modal truncation, balanced reduction, Krylov model reduction, or mixed-mode method. Then, based on the reduced substructure model, a subcontroller is designed by an LQ optimal control method for each substructure independently. After all subcontrollers are designed, a controller synthesis method called substructural controller synthesis is employed to synthesize all subcontrollers into a global controller. The assembling scheme used is the same as that employed for the structure matrices. Finally, a controller reduction scheme, called the equivalent impulse response energy controller (EIREC) reduction algorithm, is used to reduce the global controller to a reasonable size for implementation. The EIREC reduced controller preserves the impulse response energy of the full-order controller and has the property of matching low-frequency moments and low-frequency power moments. An advantage of the substructural controller synthesis method is that it relieves the computational burden associated with dimensionality. Besides that, the SCS design scheme is also a highly adaptable controller synthesis method for structures with varying configuration, or varying mass and stiffness properties.

A Multi Directional Perfect Reconstruction Filter Bank Designed with 2-D Eigenfilter Approach: Application to Ultrasound Speckle Reduction.

PubMed

Nagare, Mukund B; Patil, Bhushan D; Holambe, Raghunath S

2017-02-01

B-Mode ultrasound images are degraded by inherent noise called Speckle, which creates a considerable impact on image quality. This noise reduces the accuracy of image analysis and interpretation. Therefore, reduction of speckle noise is an essential task which improves the accuracy of the clinical diagnostics. In this paper, a Multi-directional perfect-reconstruction (PR) filter bank is proposed based on 2-D eigenfilter approach. The proposed method used for the design of two-dimensional (2-D) two-channel linear-phase FIR perfect-reconstruction filter bank. In this method, the fan shaped, diamond shaped and checkerboard shaped filters are designed. The quadratic measure of the error function between the passband and stopband of the filter has been used an objective function. First, the low-pass analysis filter is designed and then the PR condition has been expressed as a set of linear constraints on the corresponding synthesis low-pass filter. Subsequently, the corresponding synthesis filter is designed using the eigenfilter design method with linear constraints. The newly designed 2-D filters are used in translation invariant pyramidal directional filter bank (TIPDFB) for reduction of speckle noise in ultrasound images. The proposed 2-D filters give better symmetry, regularity and frequency selectivity of the filters in comparison to existing design methods. The proposed method is validated on synthetic and real ultrasound data which ensures improvement in the quality of ultrasound images and efficiently suppresses the speckle noise compared to existing methods.

A consensus embedding approach for segmentation of high resolution in vivo prostate magnetic resonance imagery

NASA Astrophysics Data System (ADS)

Viswanath, Satish; Rosen, Mark; Madabhushi, Anant

2008-03-01

Current techniques for localization of prostatic adenocarcinoma (CaP) via blinded trans-rectal ultrasound biopsy are associated with a high false negative detection rate. While high resolution endorectal in vivo Magnetic Resonance (MR) prostate imaging has been shown to have improved contrast and resolution for CaP detection over ultrasound, similarity in intensity characteristics between benign and cancerous regions on MR images contribute to a high false positive detection rate. In this paper, we present a novel unsupervised segmentation method that employs manifold learning via consensus schemes for detection of cancerous regions from high resolution 1.5 Tesla (T) endorectal in vivo prostate MRI. A significant contribution of this paper is a method to combine multiple weak, lower-dimensional representations of high dimensional feature data in a way analogous to classifier ensemble schemes, and hence create a stable and accurate reduced dimensional representation. After correcting for MR image intensity artifacts, such as bias field inhomogeneity and intensity non-standardness, our algorithm extracts over 350 3D texture features at every spatial location in the MR scene at multiple scales and orientations. Non-linear dimensionality reduction schemes such as Locally Linear Embedding (LLE) and Graph Embedding (GE) are employed to create multiple low dimensional data representations of this high dimensional texture feature space. Our novel consensus embedding method is used to average object adjacencies from within the multiple low dimensional projections so that class relationships are preserved. Unsupervised consensus clustering is then used to partition the objects in this consensus embedding space into distinct classes. Quantitative evaluation on 18 1.5 T prostate MR data against corresponding histology obtained from the multi-site ACRIN trials show a sensitivity of 92.65% and a specificity of 82.06%, which suggests that our method is successfully able to detect suspicious regions in the prostate.

Krylov-Subspace Recycling via the POD-Augmented Conjugate-Gradient Method

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

Carlberg, Kevin; Forstall, Virginia; Tuminaro, Ray

This paper presents a new Krylov-subspace-recycling method for efficiently solving sequences of linear systems of equations characterized by varying right-hand sides and symmetric-positive-definite matrices. As opposed to typical truncation strategies used in recycling such as deflation, we propose a truncation method inspired by goal-oriented proper orthogonal decomposition (POD) from model reduction. This idea is based on the observation that model reduction aims to compute a low-dimensional subspace that contains an accurate solution; as such, we expect the proposed method to generate a low-dimensional subspace that is well suited for computing solutions that can satisfy inexact tolerances. In particular, we proposemore » specific goal-oriented POD `ingredients' that align the optimality properties of POD with the objective of Krylov-subspace recycling. To compute solutions in the resulting 'augmented' POD subspace, we propose a hybrid direct/iterative three-stage method that leverages 1) the optimal ordering of POD basis vectors, and 2) well-conditioned reduced matrices. Numerical experiments performed on solid-mechanics problems highlight the benefits of the proposed method over existing approaches for Krylov-subspace recycling.« less

Krylov-Subspace Recycling via the POD-Augmented Conjugate-Gradient Method

DOE PAGES

Carlberg, Kevin; Forstall, Virginia; Tuminaro, Ray

2016-01-01

This paper presents a new Krylov-subspace-recycling method for efficiently solving sequences of linear systems of equations characterized by varying right-hand sides and symmetric-positive-definite matrices. As opposed to typical truncation strategies used in recycling such as deflation, we propose a truncation method inspired by goal-oriented proper orthogonal decomposition (POD) from model reduction. This idea is based on the observation that model reduction aims to compute a low-dimensional subspace that contains an accurate solution; as such, we expect the proposed method to generate a low-dimensional subspace that is well suited for computing solutions that can satisfy inexact tolerances. In particular, we proposemore » specific goal-oriented POD `ingredients' that align the optimality properties of POD with the objective of Krylov-subspace recycling. To compute solutions in the resulting 'augmented' POD subspace, we propose a hybrid direct/iterative three-stage method that leverages 1) the optimal ordering of POD basis vectors, and 2) well-conditioned reduced matrices. Numerical experiments performed on solid-mechanics problems highlight the benefits of the proposed method over existing approaches for Krylov-subspace recycling.« less

A Three-Dimensional Linearized Unsteady Euler Analysis for Turbomachinery Blade Rows

NASA Technical Reports Server (NTRS)

Montgomery, Matthew D.; Verdon, Joseph M.

1997-01-01

A three-dimensional, linearized, Euler analysis is being developed to provide an efficient unsteady aerodynamic analysis that can be used to predict the aeroelastic and aeroacoustic responses of axial-flow turbo-machinery blading.The field equations and boundary conditions needed to describe nonlinear and linearized inviscid unsteady flows through a blade row operating within a cylindrical annular duct are presented. A numerical model for linearized inviscid unsteady flows, which couples a near-field, implicit, wave-split, finite volume analysis to a far-field eigenanalysis, is also described. The linearized aerodynamic and numerical models have been implemented into a three-dimensional linearized unsteady flow code, called LINFLUX. This code has been applied to selected, benchmark, unsteady, subsonic flows to establish its accuracy and to demonstrate its current capabilities. The unsteady flows considered, have been chosen to allow convenient comparisons between the LINFLUX results and those of well-known, two-dimensional, unsteady flow codes. Detailed numerical results for a helical fan and a three-dimensional version of the 10th Standard Cascade indicate that important progress has been made towards the development of a reliable and useful, three-dimensional, prediction capability that can be used in aeroelastic and aeroacoustic design studies.

Low-Dimensional Feature Representation for Instrument Identification

NASA Astrophysics Data System (ADS)

Ihara, Mizuki; Maeda, Shin-Ichi; Ikeda, Kazushi; Ishii, Shin

For monophonic music instrument identification, various feature extraction and selection methods have been proposed. One of the issues toward instrument identification is that the same spectrum is not always observed even in the same instrument due to the difference of the recording condition. Therefore, it is important to find non-redundant instrument-specific features that maintain information essential for high-quality instrument identification to apply them to various instrumental music analyses. For such a dimensionality reduction method, the authors propose the utilization of linear projection methods: local Fisher discriminant analysis (LFDA) and LFDA combined with principal component analysis (PCA). After experimentally clarifying that raw power spectra are actually good for instrument classification, the authors reduced the feature dimensionality by LFDA or by PCA followed by LFDA (PCA-LFDA). The reduced features achieved reasonably high identification performance that was comparable or higher than those by the power spectra and those achieved by other existing studies. These results demonstrated that our LFDA and PCA-LFDA can successfully extract low-dimensional instrument features that maintain the characteristic information of the instruments.

Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA

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

Thimmisetty, Charanraj A.; Zhao, Wenju; Chen, Xiao

2017-10-18

Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even when gradient information can be computed efficiently. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this paper, we propose a novel Bayesian stochastic inversion methodology, which is characterized by a tight coupling between the gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). Thismore » approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated parameter space. In addition, non-Gaussian posterior distributions are estimated via an efficient LMCMC method on the projected low-dimensional feature space. We will demonstrate this computational framework by integrating and adapting our recent data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to a linear elasticity model.« less

Whitham modulation theory for (2  +  1)-dimensional equations of Kadomtsev–Petviashvili type

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Biondini, Gino; Rumanov, Igor

2018-05-01

Whitham modulation theory for certain two-dimensional evolution equations of Kadomtsev–Petviashvili (KP) type is presented. Three specific examples are considered in detail: the KP equation, the two-dimensional Benjamin–Ono (2DBO) equation and a modified KP (m2KP) equation. A unified derivation is also provided. In the case of the m2KP equation, the corresponding Whitham modulation system exhibits features different from the other two. The approach presented here does not require integrability of the original evolution equation. Indeed, while the KP equation is known to be a completely integrable equation, the 2DBO equation and the m2KP equation are not known to be integrable. In each of the cases considered, the Whitham modulation system obtained consists of five first-order quasilinear partial differential equations. The Riemann problem (i.e. the analogue of the Gurevich–Pitaevskii problem) for the one-dimensional reduction of the m2KP equation is studied. For the m2KP equation, the system of modulation equations is used to analyze the linear stability of traveling wave solutions.

Two-dimensional materials as catalysts for energy conversion

DOE PAGES

Siahrostami, Samira; Tsai, Charlie; Karamad, Mohammadreza; ...

2016-08-24

Although large efforts have been dedicated to studying two-dimensional materials for catalysis, a rationalization of the associated trends in their intrinsic activity has so far been elusive. In the present work we employ density functional theory to examine a variety of two-dimensional materials, including, carbon based materials, hexagonal boron nitride ( h-BN), transition metal dichalcogenides (e.g. MoS 2, MoSe 2) and layered oxides, to give an overview of the trends in adsorption energies. By examining key reaction intermediates relevant to the oxygen reduction, and oxygen evolution reactions we find that binding energies largely follow the linear scaling relationships observed formore » pure metals. Here, this observation is very important as it suggests that the same simplifying assumptions made to correlate descriptors with reaction rates in transition metal catalysts are also valid for the studied two-dimensional materials. By means of these scaling relations, for each reaction we also identify several promising candidates that are predicted to exhibit a comparable activity to the state-of-the-art catalysts.« less

An enhanced data visualization method for diesel engine malfunction classification using multi-sensor signals.

PubMed

Li, Yiqing; Wang, Yu; Zi, Yanyang; Zhang, Mingquan

2015-10-21

The various multi-sensor signal features from a diesel engine constitute a complex high-dimensional dataset. The non-linear dimensionality reduction method, t-distributed stochastic neighbor embedding (t-SNE), provides an effective way to implement data visualization for complex high-dimensional data. However, irrelevant features can deteriorate the performance of data visualization, and thus, should be eliminated a priori. This paper proposes a feature subset score based t-SNE (FSS-t-SNE) data visualization method to deal with the high-dimensional data that are collected from multi-sensor signals. In this method, the optimal feature subset is constructed by a feature subset score criterion. Then the high-dimensional data are visualized in 2-dimension space. According to the UCI dataset test, FSS-t-SNE can effectively improve the classification accuracy. An experiment was performed with a large power marine diesel engine to validate the proposed method for diesel engine malfunction classification. Multi-sensor signals were collected by a cylinder vibration sensor and a cylinder pressure sensor. Compared with other conventional data visualization methods, the proposed method shows good visualization performance and high classification accuracy in multi-malfunction classification of a diesel engine.

An Enhanced Data Visualization Method for Diesel Engine Malfunction Classification Using Multi-Sensor Signals

PubMed Central

Li, Yiqing; Wang, Yu; Zi, Yanyang; Zhang, Mingquan

2015-01-01

The various multi-sensor signal features from a diesel engine constitute a complex high-dimensional dataset. The non-linear dimensionality reduction method, t-distributed stochastic neighbor embedding (t-SNE), provides an effective way to implement data visualization for complex high-dimensional data. However, irrelevant features can deteriorate the performance of data visualization, and thus, should be eliminated a priori. This paper proposes a feature subset score based t-SNE (FSS-t-SNE) data visualization method to deal with the high-dimensional data that are collected from multi-sensor signals. In this method, the optimal feature subset is constructed by a feature subset score criterion. Then the high-dimensional data are visualized in 2-dimension space. According to the UCI dataset test, FSS-t-SNE can effectively improve the classification accuracy. An experiment was performed with a large power marine diesel engine to validate the proposed method for diesel engine malfunction classification. Multi-sensor signals were collected by a cylinder vibration sensor and a cylinder pressure sensor. Compared with other conventional data visualization methods, the proposed method shows good visualization performance and high classification accuracy in multi-malfunction classification of a diesel engine. PMID:26506347

Spectral embedding finds meaningful (relevant) structure in image and microarray data

PubMed Central

Higgs, Brandon W; Weller, Jennifer; Solka, Jeffrey L

2006-01-01

Background Accurate methods for extraction of meaningful patterns in high dimensional data have become increasingly important with the recent generation of data types containing measurements across thousands of variables. Principal components analysis (PCA) is a linear dimensionality reduction (DR) method that is unsupervised in that it relies only on the data; projections are calculated in Euclidean or a similar linear space and do not use tuning parameters for optimizing the fit to the data. However, relationships within sets of nonlinear data types, such as biological networks or images, are frequently mis-rendered into a low dimensional space by linear methods. Nonlinear methods, in contrast, attempt to model important aspects of the underlying data structure, often requiring parameter(s) fitting to the data type of interest. In many cases, the optimal parameter values vary when different classification algorithms are applied on the same rendered subspace, making the results of such methods highly dependent upon the type of classifier implemented. Results We present the results of applying the spectral method of Lafon, a nonlinear DR method based on the weighted graph Laplacian, that minimizes the requirements for such parameter optimization for two biological data types. We demonstrate that it is successful in determining implicit ordering of brain slice image data and in classifying separate species in microarray data, as compared to two conventional linear methods and three nonlinear methods (one of which is an alternative spectral method). This spectral implementation is shown to provide more meaningful information, by preserving important relationships, than the methods of DR presented for comparison. Tuning parameter fitting is simple and is a general, rather than data type or experiment specific approach, for the two datasets analyzed here. Tuning parameter optimization is minimized in the DR step to each subsequent classification method, enabling the possibility of valid cross-experiment comparisons. Conclusion Results from the spectral method presented here exhibit the desirable properties of preserving meaningful nonlinear relationships in lower dimensional space and requiring minimal parameter fitting, providing a useful algorithm for purposes of visualization and classification across diverse datasets, a common challenge in systems biology. PMID:16483359

Computing Finite-Time Lyapunov Exponents with Optimally Time Dependent Reduction

NASA Astrophysics Data System (ADS)

Babaee, Hessam; Farazmand, Mohammad; Sapsis, Themis; Haller, George

2016-11-01

We present a method to compute Finite-Time Lyapunov Exponents (FTLE) of a dynamical system using Optimally Time-Dependent (OTD) reduction recently introduced by H. Babaee and T. P. Sapsis. The OTD modes are a set of finite-dimensional, time-dependent, orthonormal basis {ui (x , t) } |i=1N that capture the directions associated with transient instabilities. The evolution equation of the OTD modes is derived from a minimization principle that optimally approximates the most unstable directions over finite times. To compute the FTLE, we evolve a single OTD mode along with the nonlinear dynamics. We approximate the FTLE from the reduced system obtained from projecting the instantaneous linearized dynamics onto the OTD mode. This results in a significant reduction in the computational cost compared to conventional methods for computing FTLE. We demonstrate the efficiency of our method for double Gyre and ABC flows. ARO project 66710-EG-YIP.

Nonlinear model-order reduction for compressible flow solvers using the Discrete Empirical Interpolation Method

NASA Astrophysics Data System (ADS)

Fosas de Pando, Miguel; Schmid, Peter J.; Sipp, Denis

2016-11-01

Nonlinear model reduction for large-scale flows is an essential component in many fluid applications such as flow control, optimization, parameter space exploration and statistical analysis. In this article, we generalize the POD-DEIM method, introduced by Chaturantabut & Sorensen [1], to address nonlocal nonlinearities in the equations without loss of performance or efficiency. The nonlinear terms are represented by nested DEIM-approximations using multiple expansion bases based on the Proper Orthogonal Decomposition. These extensions are imperative, for example, for applications of the POD-DEIM method to large-scale compressible flows. The efficient implementation of the presented model-reduction technique follows our earlier work [2] on linearized and adjoint analyses and takes advantage of the modular structure of our compressible flow solver. The efficacy of the nonlinear model-reduction technique is demonstrated to the flow around an airfoil and its acoustic footprint. We could obtain an accurate and robust low-dimensional model that captures the main features of the full flow.

Lie group classification of first-order delay ordinary differential equations

NASA Astrophysics Data System (ADS)

Dorodnitsyn, Vladimir A.; Kozlov, Roman; Meleshko, Sergey V.; Winternitz, Pavel

2018-05-01

A group classification of first-order delay ordinary differential equations (DODEs) accompanied by an equation for the delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs), which consists of linear DODEs and solution-independent delay relations, have infinite-dimensional symmetry algebras—as do nonlinear ones that are linearizable by an invertible transformation of variables. Genuinely nonlinear DODSs have symmetry algebras of dimension n, . It is shown how exact analytical solutions of invariant DODSs can be obtained using symmetry reduction.

Development of non-linear finite element computer code

NASA Technical Reports Server (NTRS)

Becker, E. B.; Miller, T.

1985-01-01

Recent work has shown that the use of separable symmetric functions of the principal stretches can adequately describe the response of certain propellant materials and, further, that a data reduction scheme gives a convenient way of obtaining the values of the functions from experimental data. Based on representation of the energy, a computational scheme was developed that allows finite element analysis of boundary value problems of arbitrary shape and loading. The computational procedure was implemental in a three-dimensional finite element code, TEXLESP-S, which is documented herein.

Linear discriminant analysis based on L1-norm maximization.

PubMed

Zhong, Fujin; Zhang, Jiashu

2013-08-01

Linear discriminant analysis (LDA) is a well-known dimensionality reduction technique, which is widely used for many purposes. However, conventional LDA is sensitive to outliers because its objective function is based on the distance criterion using L2-norm. This paper proposes a simple but effective robust LDA version based on L1-norm maximization, which learns a set of local optimal projection vectors by maximizing the ratio of the L1-norm-based between-class dispersion and the L1-norm-based within-class dispersion. The proposed method is theoretically proved to be feasible and robust to outliers while overcoming the singular problem of the within-class scatter matrix for conventional LDA. Experiments on artificial datasets, standard classification datasets and three popular image databases demonstrate the efficacy of the proposed method.

Correlation coefficient based supervised locally linear embedding for pulmonary nodule recognition.

PubMed

Wu, Panpan; Xia, Kewen; Yu, Hengyong

2016-11-01

Dimensionality reduction techniques are developed to suppress the negative effects of high dimensional feature space of lung CT images on classification performance in computer aided detection (CAD) systems for pulmonary nodule detection. An improved supervised locally linear embedding (SLLE) algorithm is proposed based on the concept of correlation coefficient. The Spearman's rank correlation coefficient is introduced to adjust the distance metric in the SLLE algorithm to ensure that more suitable neighborhood points could be identified, and thus to enhance the discriminating power of embedded data. The proposed Spearman's rank correlation coefficient based SLLE (SC(2)SLLE) is implemented and validated in our pilot CAD system using a clinical dataset collected from the publicly available lung image database consortium and image database resource initiative (LICD-IDRI). Particularly, a representative CAD system for solitary pulmonary nodule detection is designed and implemented. After a sequential medical image processing steps, 64 nodules and 140 non-nodules are extracted, and 34 representative features are calculated. The SC(2)SLLE, as well as SLLE and LLE algorithm, are applied to reduce the dimensionality. Several quantitative measurements are also used to evaluate and compare the performances. Using a 5-fold cross-validation methodology, the proposed algorithm achieves 87.65% accuracy, 79.23% sensitivity, 91.43% specificity, and 8.57% false positive rate, on average. Experimental results indicate that the proposed algorithm outperforms the original locally linear embedding and SLLE coupled with the support vector machine (SVM) classifier. Based on the preliminary results from a limited number of nodules in our dataset, this study demonstrates the great potential to improve the performance of a CAD system for nodule detection using the proposed SC(2)SLLE. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

A parametric study of transonic blade-vortex interaction noise

NASA Technical Reports Server (NTRS)

Lyrintzis, A. S.

1991-01-01

Several parameters of transonic blade-vortex interactions (BVI) are being studied and some ideas for noise reduction are introduced and tested using numerical simulation. The model used is the two-dimensional high frequency transonic small disturbance equation with regions of distributed vorticity (VTRAN2 code). The far-field noise signals are obtained by using the Kirchhoff method with extends the numerical 2-D near-field aerodynamic results to the linear acoustic 3-D far-field. The BVI noise mechanisms are explained and the effects of vortex type and strength, and angle of attack are studied. Particularly, airfoil shape modifications which lead to noise reduction are investigated. The results presented are expected to be helpful for better understanding of the nature of the BVI noise and better blade design.

Isotropic-resolution linear-array-based photoacoustic computed tomography through inverse Radon transform

NASA Astrophysics Data System (ADS)

Li, Guo; Xia, Jun; Li, Lei; Wang, Lidai; Wang, Lihong V.

2015-03-01

Linear transducer arrays are readily available for ultrasonic detection in photoacoustic computed tomography. They offer low cost, hand-held convenience, and conventional ultrasonic imaging. However, the elevational resolution of linear transducer arrays, which is usually determined by the weak focus of the cylindrical acoustic lens, is about one order of magnitude worse than the in-plane axial and lateral spatial resolutions. Therefore, conventional linear scanning along the elevational direction cannot provide high-quality three-dimensional photoacoustic images due to the anisotropic spatial resolutions. Here we propose an innovative method to achieve isotropic resolutions for three-dimensional photoacoustic images through combined linear and rotational scanning. In each scan step, we first elevationally scan the linear transducer array, and then rotate the linear transducer array along its center in small steps, and scan again until 180 degrees have been covered. To reconstruct isotropic three-dimensional images from the multiple-directional scanning dataset, we use the standard inverse Radon transform originating from X-ray CT. We acquired a three-dimensional microsphere phantom image through the inverse Radon transform method and compared it with a single-elevational-scan three-dimensional image. The comparison shows that our method improves the elevational resolution by up to one order of magnitude, approaching the in-plane lateral-direction resolution. In vivo rat images were also acquired.

A three-dimensional interpenetrating electrode of reduced graphene oxide for selective detection of dopamine.

PubMed

Yu, Xiaowen; Sheng, Kaixuan; Shi, Gaoquan

2014-09-21

Electrochemical detection of dopamine plays an important role in medical diagnosis. In this paper, we report a three-dimensional (3D) interpenetrating graphene electrode fabricated by electrochemical reduction of graphene oxide for selective detection of dopamine. This electrochemically reduced graphene oxide (ErGO) electrode was used directly without further functionalization or blending with other functional materials. This electrode can efficiently lower the oxidation potential of ascorbic acid; thus, it is able to selectively detect dopamine in the presence of ascorbic acid and uric acid. The ErGO-based biosensor exhibited a linear response towards dopamine in the concentration range of 0.1-10 μM with a low detection limit of 0.1 μM. Furthermore, this electrode has good reproducibility and environmental stability, and can be used to analyse real samples.

Fault diagnosis for analog circuits utilizing time-frequency features and improved VVRKFA

NASA Astrophysics Data System (ADS)

He, Wei; He, Yigang; Luo, Qiwu; Zhang, Chaolong

2018-04-01

This paper proposes a novel scheme for analog circuit fault diagnosis utilizing features extracted from the time-frequency representations of signals and an improved vector-valued regularized kernel function approximation (VVRKFA). First, the cross-wavelet transform is employed to yield the energy-phase distribution of the fault signals over the time and frequency domain. Since the distribution is high-dimensional, a supervised dimensionality reduction technique—the bilateral 2D linear discriminant analysis—is applied to build a concise feature set from the distributions. Finally, VVRKFA is utilized to locate the fault. In order to improve the classification performance, the quantum-behaved particle swarm optimization technique is employed to gradually tune the learning parameter of the VVRKFA classifier. The experimental results for the analog circuit faults classification have demonstrated that the proposed diagnosis scheme has an advantage over other approaches.

Polarization-dependent plasmonic photocurrents in two-dimensional electron systems

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

Popov, V. V., E-mail: popov-slava@yahoo.co.uk; Saratov State University, Saratov 410012; Saratov Scientific Center of the Russian Academy of Sciences, Saratov 410028

2016-06-27

Plasmonic polarization dependent photocurrents in a homogeneous two-dimensional electron system are studied. Those effects are completely different from the photon drag and electronic photogalvanic effects as well as from the plasmonic ratchet effect in a density modulated two-dimensional electron system. Linear and helicity-dependent contributions to the photocurrent are found. The linear contribution can be interpreted as caused by the longitudinal and transverse plasmon drag effect. The helicity-dependent contribution originates from the non-linear electron convection and changes its sign with reversing the plasmonic field helicity. It is shown that the helicity-dependent component of the photocurrent can exceed the linear one bymore » several orders of magnitude in high-mobility two-dimensional electron systems. The results open possibilities for all-electronic detection of the radiation polarization states by exciting the plasmonic photocurrents in two-dimensional electron systems.« less

Adaptive macro finite elements for the numerical solution of monodomain equations in cardiac electrophysiology.

PubMed

Heidenreich, Elvio A; Ferrero, José M; Doblaré, Manuel; Rodríguez, José F

2010-07-01

Many problems in biology and engineering are governed by anisotropic reaction-diffusion equations with a very rapidly varying reaction term. This usually implies the use of very fine meshes and small time steps in order to accurately capture the propagating wave while avoiding the appearance of spurious oscillations in the wave front. This work develops a family of macro finite elements amenable for solving anisotropic reaction-diffusion equations with stiff reactive terms. The developed elements are incorporated on a semi-implicit algorithm based on operator splitting that includes adaptive time stepping for handling the stiff reactive term. A linear system is solved on each time step to update the transmembrane potential, whereas the remaining ordinary differential equations are solved uncoupled. The method allows solving the linear system on a coarser mesh thanks to the static condensation of the internal degrees of freedom (DOF) of the macroelements while maintaining the accuracy of the finer mesh. The method and algorithm have been implemented in parallel. The accuracy of the method has been tested on two- and three-dimensional examples demonstrating excellent behavior when compared to standard linear elements. The better performance and scalability of different macro finite elements against standard finite elements have been demonstrated in the simulation of a human heart and a heterogeneous two-dimensional problem with reentrant activity. Results have shown a reduction of up to four times in computational cost for the macro finite elements with respect to equivalent (same number of DOF) standard linear finite elements as well as good scalability properties.

Study on longitudinal dispersion relation in one-dimensional relativistic plasma: Linear theory and Vlasov simulation

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

Zhang, H.; Wu, S. Z.; Zhou, C. T.

2013-09-15

The dispersion relation of one-dimensional longitudinal plasma waves in relativistic homogeneous plasmas is investigated with both linear theory and Vlasov simulation in this paper. From the Vlasov-Poisson equations, the linear dispersion relation is derived for the proper one-dimensional Jüttner distribution. Numerically obtained linear dispersion relation as well as an approximate formula for plasma wave frequency in the long wavelength limit is given. The dispersion of longitudinal wave is also simulated with a relativistic Vlasov code. The real and imaginary parts of dispersion relation are well studied by varying wave number and plasma temperature. Simulation results are in agreement with establishedmore » linear theory.« less

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

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.

A non-linear optimization programming model for air quality planning including co-benefits for GHG emissions.

PubMed

Turrini, Enrico; Carnevale, Claudio; Finzi, Giovanna; Volta, Marialuisa

2018-04-15

This paper introduces the MAQ (Multi-dimensional Air Quality) model aimed at defining cost-effective air quality plans at different scales (urban to national) and assessing the co-benefits for GHG emissions. The model implements and solves a non-linear multi-objective, multi-pollutant decision problem where the decision variables are the application levels of emission abatement measures allowing the reduction of energy consumption, end-of pipe technologies and fuel switch options. The objectives of the decision problem are the minimization of tropospheric secondary pollution exposure and of internal costs. The model assesses CO 2 equivalent emissions in order to support decision makers in the selection of win-win policies. The methodology is tested on Lombardy region, a heavily polluted area in northern Italy. Copyright © 2017 Elsevier B.V. All rights reserved.

Improved classification accuracy by feature extraction using genetic algorithms

NASA Astrophysics Data System (ADS)

Patriarche, Julia; Manduca, Armando; Erickson, Bradley J.

2003-05-01

A feature extraction algorithm has been developed for the purposes of improving classification accuracy. The algorithm uses a genetic algorithm / hill-climber hybrid to generate a set of linearly recombined features, which may be of reduced dimensionality compared with the original set. The genetic algorithm performs the global exploration, and a hill climber explores local neighborhoods. Hybridizing the genetic algorithm with a hill climber improves both the rate of convergence, and the final overall cost function value; it also reduces the sensitivity of the genetic algorithm to parameter selection. The genetic algorithm includes the operators: crossover, mutation, and deletion / reactivation - the last of these effects dimensionality reduction. The feature extractor is supervised, and is capable of deriving a separate feature space for each tissue (which are reintegrated during classification). A non-anatomical digital phantom was developed as a gold standard for testing purposes. In tests with the phantom, and with images of multiple sclerosis patients, classification with feature extractor derived features yielded lower error rates than using standard pulse sequences, and with features derived using principal components analysis. Using the multiple sclerosis patient data, the algorithm resulted in a mean 31% reduction in classification error of pure tissues.

Direct Linear Transformation Method for Three-Dimensional Cinematography

ERIC Educational Resources Information Center

Shapiro, Robert

1978-01-01

The ability of Direct Linear Transformation Method for three-dimensional cinematography to locate points in space was shown to meet the accuracy requirements associated with research on human movement. (JD)

Signal separation by nonlinear projections: The fetal electrocardiogram

NASA Astrophysics Data System (ADS)

Schreiber, Thomas; Kaplan, Daniel T.

1996-05-01

We apply a locally linear projection technique which has been developed for noise reduction in deterministically chaotic signals to extract the fetal component from scalar maternal electrocardiographic (ECG) recordings. Although we do not expect the maternal ECG to be deterministic chaotic, typical signals are effectively confined to a lower-dimensional manifold when embedded in delay space. The method is capable of extracting fetal heart rate even when the fetal component and the noise are of comparable amplitude. If the noise is small, more details of the fetal ECG, like P and T waves, can be recovered.

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.

ASTROP2-LE: A Mistuned Aeroelastic Analysis System Based on a Two Dimensional Linearized Euler Solver

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Srivastava, R.; Mehmed, Oral

2002-01-01

An aeroelastic analysis system for flutter and forced response analysis of turbomachines based on a two-dimensional linearized unsteady Euler solver has been developed. The ASTROP2 code, an aeroelastic stability analysis program for turbomachinery, was used as a basis for this development. The ASTROP2 code uses strip theory to couple a two dimensional aerodynamic model with a three dimensional structural model. The code was modified to include forced response capability. The formulation was also modified to include aeroelastic analysis with mistuning. A linearized unsteady Euler solver, LINFLX2D is added to model the unsteady aerodynamics in ASTROP2. By calculating the unsteady aerodynamic loads using LINFLX2D, it is possible to include the effects of transonic flow on flutter and forced response in the analysis. The stability is inferred from an eigenvalue analysis. The revised code, ASTROP2-LE for ASTROP2 code using Linearized Euler aerodynamics, is validated by comparing the predictions with those obtained using linear unsteady aerodynamic solutions.

Multi-Level Reduced Order Modeling Equipped with Probabilistic Error Bounds

NASA Astrophysics Data System (ADS)

Abdo, Mohammad Gamal Mohammad Mostafa

This thesis develops robust reduced order modeling (ROM) techniques to achieve the needed efficiency to render feasible the use of high fidelity tools for routine engineering analyses. Markedly different from the state-of-the-art ROM techniques, our work focuses only on techniques which can quantify the credibility of the reduction which can be measured with the reduction errors upper-bounded for the envisaged range of ROM model application. Our objective is two-fold. First, further developments of ROM techniques are proposed when conventional ROM techniques are too taxing to be computationally practical. This is achieved via a multi-level ROM methodology designed to take advantage of the multi-scale modeling strategy typically employed for computationally taxing models such as those associated with the modeling of nuclear reactor behavior. Second, the discrepancies between the original model and ROM model predictions over the full range of model application conditions are upper-bounded in a probabilistic sense with high probability. ROM techniques may be classified into two broad categories: surrogate construction techniques and dimensionality reduction techniques, with the latter being the primary focus of this work. We focus on dimensionality reduction, because it offers a rigorous approach by which reduction errors can be quantified via upper-bounds that are met in a probabilistic sense. Surrogate techniques typically rely on fitting a parametric model form to the original model at a number of training points, with the residual of the fit taken as a measure of the prediction accuracy of the surrogate. This approach, however, does not generally guarantee that the surrogate model predictions at points not included in the training process will be bound by the error estimated from the fitting residual. Dimensionality reduction techniques however employ a different philosophy to render the reduction, wherein randomized snapshots of the model variables, such as the model parameters, responses, or state variables, are projected onto lower dimensional subspaces, referred to as the "active subspaces", which are selected to capture a user-defined portion of the snapshots variations. Once determined, the ROM model application involves constraining the variables to the active subspaces. In doing so, the contribution from the variables discarded components can be estimated using a fundamental theorem from random matrix theory which has its roots in Dixon's theory, developed in 1983. This theory was initially presented for linear matrix operators. The thesis extends this theorem's results to allow reduction of general smooth nonlinear operators. The result is an approach by which the adequacy of a given active subspace determined using a given set of snapshots, generated either using the full high fidelity model, or other models with lower fidelity, can be assessed, which provides insight to the analyst on the type of snapshots required to reach a reduction that can satisfy user-defined preset tolerance limits on the reduction errors. Reactor physics calculations are employed as a test bed for the proposed developments. The focus will be on reducing the effective dimensionality of the various data streams such as the cross-section data and the neutron flux. The developed methods will be applied to representative assembly level calculations, where the size of the cross-section and flux spaces are typically large, as required by downstream core calculations, in order to capture the broad range of conditions expected during reactor operation. (Abstract shortened by ProQuest.).

Low-rank factorization of electron integral tensors and its application in electronic structure theory

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

Peng, Bo; Kowalski, Karol

In this letter, we introduce the reverse Cuthill-McKee (RCM) algorithm, which is often used for the bandwidth reduction of sparse tensors, to transform the two-electron integral tensors to their block diagonal forms. By further applying the pivoted Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates the low-rank factorization of the high-dimensional tensor contractions that are usually encountered in post-Hartree-Fock calculations. In this letter, we discuss the second-order Møller-Plesset (MP2) method and linear coupled- cluster model with doublesmore » (L-CCD) as two simple examples to demonstrate the efficiency of the RCM-CD technique in representing two-electron integrals in a compact form.« less

ACCELERATED FITTING OF STELLAR SPECTRA

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

Ting, Yuan-Sen; Conroy, Charlie; Rix, Hans-Walter

2016-07-20

Stellar spectra are often modeled and fitted by interpolating within a rectilinear grid of synthetic spectra to derive the stars’ labels: stellar parameters and elemental abundances. However, the number of synthetic spectra needed for a rectilinear grid grows exponentially with the label space dimensions, precluding the simultaneous and self-consistent fitting of more than a few elemental abundances. Shortcuts such as fitting subsets of labels separately can introduce unknown systematics and do not produce correct error covariances in the derived labels. In this paper we present a new approach—Convex Hull Adaptive Tessellation (chat)—which includes several new ideas for inexpensively generating amore » sufficient stellar synthetic library, using linear algebra and the concept of an adaptive, data-driven grid. A convex hull approximates the region where the data lie in the label space. A variety of tests with mock data sets demonstrate that chat can reduce the number of required synthetic model calculations by three orders of magnitude in an eight-dimensional label space. The reduction will be even larger for higher dimensional label spaces. In chat the computational effort increases only linearly with the number of labels that are fit simultaneously. Around each of these grid points in the label space an approximate synthetic spectrum can be generated through linear expansion using a set of “gradient spectra” that represent flux derivatives at every wavelength point with respect to all labels. These techniques provide new opportunities to fit the full stellar spectra from large surveys with 15–30 labels simultaneously.« less

Development, implementation and evaluation of a dedicated metal artefact reduction method for interventional flat-detector CT.

PubMed

Prell, D; Kalender, W A; Kyriakou, Y

2010-12-01

The purpose of this study was to develop, implement and evaluate a dedicated metal artefact reduction (MAR) method for flat-detector CT (FDCT). The algorithm uses the multidimensional raw data space to calculate surrogate attenuation values for the original metal traces in the raw data domain. The metal traces are detected automatically by a three-dimensional, threshold-based segmentation algorithm in an initial reconstructed image volume, based on twofold histogram information for calculating appropriate metal thresholds. These thresholds are combined with constrained morphological operations in the projection domain. A subsequent reconstruction of the modified raw data yields an artefact-reduced image volume that is further processed by a combining procedure that reinserts the missing metal information. For image quality assessment, measurements on semi-anthropomorphic phantoms containing metallic inserts were evaluated in terms of CT value accuracy, image noise and spatial resolution before and after correction. Measurements of the same phantoms without prostheses were used as ground truth for comparison. Cadaver measurements were performed on complex and realistic cases and to determine the influences of our correction method on the tissue surrounding the prostheses. The results showed a significant reduction of metal-induced streak artefacts (CT value differences were reduced to below 22 HU and image noise reduction of up to 200%). The cadaver measurements showed excellent results for imaging areas close to the implant and exceptional artefact suppression in these areas. Furthermore, measurements in the knee and spine regions confirmed the superiority of our method to standard one-dimensional, linear interpolation.

Wing download reduction using vortex trapping plates

NASA Technical Reports Server (NTRS)

Light, Jeffrey S.; Stremel, Paul M.; Bilanin, Alan J.

1994-01-01

A download reduction technique using spanwise plates on the upper and lower wing surfaces has been examined. Experimental and analytical techniques were used to determine the download reduction obtained using this technique. Simple two-dimensional wind tunnel testing confirmed the validity of the technique for reducing two-dimensional airfoil drag. Computations using a two-dimensional Navier-Stokes analysis provided insight into the mechanism causing the drag reduction. Finally, the download reduction technique was tested using a rotor and wing to determine the benefits for a semispan configuration representative of a tilt rotor aircraft.

Fukunaga-Koontz transform based dimensionality reduction for hyperspectral imagery

NASA Astrophysics Data System (ADS)

Ochilov, S.; Alam, M. S.; Bal, A.

2006-05-01

Fukunaga-Koontz Transform based technique offers some attractive properties for desired class oriented dimensionality reduction in hyperspectral imagery. In FKT, feature selection is performed by transforming into a new space where feature classes have complimentary eigenvectors. Dimensionality reduction technique based on these complimentary eigenvector analysis can be described under two classes, desired class and background clutter, such that each basis function best represent one class while carrying the least amount of information from the second class. By selecting a few eigenvectors which are most relevant to desired class, one can reduce the dimension of hyperspectral cube. Since the FKT based technique reduces data size, it provides significant advantages for near real time detection applications in hyperspectral imagery. Furthermore, the eigenvector selection approach significantly reduces computation burden via the dimensionality reduction processes. The performance of the proposed dimensionality reduction algorithm has been tested using real-world hyperspectral dataset.

Robust and efficient pharmacokinetic parameter non-linear least squares estimation for dynamic contrast enhanced MRI of the prostate.

PubMed

Kargar, Soudabeh; Borisch, Eric A; Froemming, Adam T; Kawashima, Akira; Mynderse, Lance A; Stinson, Eric G; Trzasko, Joshua D; Riederer, Stephen J

2018-05-01

To describe an efficient numerical optimization technique using non-linear least squares to estimate perfusion parameters for the Tofts and extended Tofts models from dynamic contrast enhanced (DCE) MRI data and apply the technique to prostate cancer. Parameters were estimated by fitting the two Tofts-based perfusion models to the acquired data via non-linear least squares. We apply Variable Projection (VP) to convert the fitting problem from a multi-dimensional to a one-dimensional line search to improve computational efficiency and robustness. Using simulation and DCE-MRI studies in twenty patients with suspected prostate cancer, the VP-based solver was compared against the traditional Levenberg-Marquardt (LM) strategy for accuracy, noise amplification, robustness to converge, and computation time. The simulation demonstrated that VP and LM were both accurate in that the medians closely matched assumed values across typical signal to noise ratio (SNR) levels for both Tofts models. VP and LM showed similar noise sensitivity. Studies using the patient data showed that the VP method reliably converged and matched results from LM with approximate 3× and 2× reductions in computation time for the standard (two-parameter) and extended (three-parameter) Tofts models. While LM failed to converge in 14% of the patient data, VP converged in the ideal 100%. The VP-based method for non-linear least squares estimation of perfusion parameters for prostate MRI is equivalent in accuracy and robustness to noise, while being more reliably (100%) convergent and computationally about 3× (TM) and 2× (ETM) faster than the LM-based method. Copyright © 2017 Elsevier Inc. All rights reserved.

An in vitro correlation of mechanical forces and metastatic capacity

NASA Astrophysics Data System (ADS)

Indra, Indrajyoti; Undyala, Vishnu; Kandow, Casey; Thirumurthi, Umadevi; Dembo, Micah; Beningo, Karen A.

2011-02-01

Mechanical forces have a major influence on cell migration and are predicted to significantly impact cancer metastasis, yet this idea is currently poorly defined. In this study we have asked if changes in traction stress and migratory properties correlate with the metastatic progression of tumor cells. For this purpose, four murine breast cancer cell lines derived from the same primary tumor, but possessing increasing metastatic capacity, were tested for adhesion strength, traction stress, focal adhesion organization and for differential migration rates in two-dimensional and three-dimensional environments. Using traction force microscopy (TFM), we were surprised to find an inverse relationship between traction stress and metastatic capacity, such that force production decreased as the metastatic capacity increased. Consistent with this observation, adhesion strength exhibited an identical profile to the traction data. A count of adhesions indicated a general reduction in the number as metastatic capacity increased but no difference in the maturation as determined by the ratio of nascent to mature adhesions. These changes correlated well with a reduction in active beta-1 integrin with increasing metastatic ability. Finally, in two dimensions, wound healing, migration and persistence were relatively low in the entire panel, maintaining a downward trend with increasing metastatic capacity. Why metastatic cells would migrate so poorly prompted us to ask if the loss of adhesive parameters in the most metastatic cells indicated a switch to a less adhesive mode of migration that would only be detected in a three-dimensional environment. Indeed, in three-dimensional migration assays, the most metastatic cells now showed the greatest linear speed. We conclude that traction stress, adhesion strength and rate of migration do indeed change as tumor cells progress in metastatic capacity and do so in a dimension-sensitive manner.

Three-dimensional modeling of flexible pavements : executive summary, August 2001.

DOT National Transportation Integrated Search

2001-08-01

A linear viscoelastic model has been incorporated into a three-dimensional finite element program for analysis of flexible pavements. Linear and quadratic versions of hexahedral elements and quadrilateral axisymmetrix elements are provided. Dynamic p...

Three dimensional modeling of flexible pavements : final report, March 2002.

DOT National Transportation Integrated Search

2001-08-01

A linear viscoelastic model has been incorporated into a three-dimensional finite element program for analysis of flexible pavements. Linear and quadratic versions of hexahedral elements and quadrilateral axisymmetrix elements are provided. Dynamic p...

Batch-mode Reinforcement Learning for improved hydro-environmental systems management

NASA Astrophysics Data System (ADS)

Castelletti, A.; Galelli, S.; Restelli, M.; Soncini-Sessa, R.

2010-12-01

Despite the great progresses made in the last decades, the optimal management of hydro-environmental systems still remains a very active and challenging research area. The combination of multiple, often conflicting interests, high non-linearities of the physical processes and the management objectives, strong uncertainties in the inputs, and high dimensional state makes the problem challenging and intriguing. Stochastic Dynamic Programming (SDP) is one of the most suitable methods for designing (Pareto) optimal management policies preserving the original problem complexity. However, it suffers from a dual curse, which, de facto, prevents its practical application to even reasonably complex water systems. (i) Computational requirement grows exponentially with state and control dimension (Bellman's curse of dimensionality), so that SDP can not be used with water systems where the state vector includes more than few (2-3) units. (ii) An explicit model of each system's component is required (curse of modelling) to anticipate the effects of the system transitions, i.e. any information included into the SDP framework can only be either a state variable described by a dynamic model or a stochastic disturbance, independent in time, with the associated pdf. Any exogenous information that could effectively improve the system operation cannot be explicitly considered in taking the management decision, unless a dynamic model is identified for each additional information, thus adding to the problem complexity through the curse of dimensionality (additional state variables). To mitigate this dual curse, the combined use of batch-mode Reinforcement Learning (bRL) and Dynamic Model Reduction (DMR) techniques is explored in this study. bRL overcomes the curse of modelling by replacing explicit modelling with an external simulator and/or historical observations. The curse of dimensionality is averted using a functional approximation of the SDP value function based on proper non-linear regressors. DMR reduces the complexity and the associated computational requirements of non-linear distributed process based models, making them suitable for being included into optimization schemes. Results from real world applications of the approach are also presented, including reservoir operation with both quality and quantity targets.

Linear dynamical modes as new variables for data-driven ENSO forecast

NASA Astrophysics Data System (ADS)

Gavrilov, Andrey; Seleznev, Aleksei; Mukhin, Dmitry; Loskutov, Evgeny; Feigin, Alexander; Kurths, Juergen

2018-05-01

A new data-driven model for analysis and prediction of spatially distributed time series is proposed. The model is based on a linear dynamical mode (LDM) decomposition of the observed data which is derived from a recently developed nonlinear dimensionality reduction approach. The key point of this approach is its ability to take into account simple dynamical properties of the observed system by means of revealing the system's dominant time scales. The LDMs are used as new variables for empirical construction of a nonlinear stochastic evolution operator. The method is applied to the sea surface temperature anomaly field in the tropical belt where the El Nino Southern Oscillation (ENSO) is the main mode of variability. The advantage of LDMs versus traditionally used empirical orthogonal function decomposition is demonstrated for this data. Specifically, it is shown that the new model has a competitive ENSO forecast skill in comparison with the other existing ENSO models.

Joint statistics of strongly correlated neurons via dimensionality reduction

NASA Astrophysics Data System (ADS)

Deniz, Taşkın; Rotter, Stefan

2017-06-01

The relative timing of action potentials in neurons recorded from local cortical networks often shows a non-trivial dependence, which is then quantified by cross-correlation functions. Theoretical models emphasize that such spike train correlations are an inevitable consequence of two neurons being part of the same network and sharing some synaptic input. For non-linear neuron models, however, explicit correlation functions are difficult to compute analytically, and perturbative methods work only for weak shared input. In order to treat strong correlations, we suggest here an alternative non-perturbative method. Specifically, we study the case of two leaky integrate-and-fire neurons with strong shared input. Correlation functions derived from simulated spike trains fit our theoretical predictions very accurately. Using our method, we computed the non-linear correlation transfer as well as correlation functions that are asymmetric due to inhomogeneous intrinsic parameters or unequal input.

Classification of hyperspectral imagery using MapReduce on a NVIDIA graphics processing unit (Conference Presentation)

NASA Astrophysics Data System (ADS)

Ramirez, Andres; Rahnemoonfar, Maryam

2017-04-01

A hyperspectral image provides multidimensional figure rich in data consisting of hundreds of spectral dimensions. Analyzing the spectral and spatial information of such image with linear and non-linear algorithms will result in high computational time. In order to overcome this problem, this research presents a system using a MapReduce-Graphics Processing Unit (GPU) model that can help analyzing a hyperspectral image through the usage of parallel hardware and a parallel programming model, which will be simpler to handle compared to other low-level parallel programming models. Additionally, Hadoop was used as an open-source version of the MapReduce parallel programming model. This research compared classification accuracy results and timing results between the Hadoop and GPU system and tested it against the following test cases: the CPU and GPU test case, a CPU test case and a test case where no dimensional reduction was applied.

Design of an ignition target for the laser megajoule, mitigating parametric instabilities

NASA Astrophysics Data System (ADS)

Laffite, S.; Loiseau, P.

2010-10-01

Laser plasma interaction (LPI) is a critical issue in ignition target design. Based on both scaling laws and two-dimensional calculations, this article describes how we can constrain a laser megajoule (LMJ) [J. Ebrardt and J. M. Chaput, J. Phys.: Conf. Ser. 112, 032005 (2008)] target design by mitigating LPI. An ignition indirect drive target has been designed for the 2/3 LMJ step. It requires 0.9 MJ and 260 TW of laser energy and power, to achieve a temperature of 300 eV in a rugby-shaped Hohlraum and give a yield of about 20 MJ. The study focuses on the analysis of linear gain for stimulated Raman and Brillouin scatterings. Enlarging the focal spot is an obvious way to reduce linear gains. We show that this reduction is nonlinear with the focal spot size. For relatively small focal spot area, linear gains are significantly reduced by enlarging the focal spot. However, there is no benefit in too large focal spots because of necessary larger laser entrance holes, which require more laser energy. Furthermore, this leads to the existence, for a given design, of a minimum value for linear gains for which we cannot go below.

Development of a linearized unsteady Euler analysis for turbomachinery blade rows

NASA Technical Reports Server (NTRS)

Verdon, Joseph M.; Montgomery, Matthew D.; Kousen, Kenneth A.

1995-01-01

A linearized unsteady aerodynamic analysis for axial-flow turbomachinery blading is described in this report. The linearization is based on the Euler equations of fluid motion and is motivated by the need for an efficient aerodynamic analysis that can be used in predicting the aeroelastic and aeroacoustic responses of blade rows. The field equations and surface conditions required for inviscid, nonlinear and linearized, unsteady aerodynamic analyses of three-dimensional flow through a single, blade row operating within a cylindrical duct, are derived. An existing numerical algorithm for determining time-accurate solutions of the nonlinear unsteady flow problem is described, and a numerical model, based upon this nonlinear flow solver, is formulated for the first-harmonic linear unsteady problem. The linearized aerodynamic and numerical models have been implemented into a first-harmonic unsteady flow code, called LINFLUX. At present this code applies only to two-dimensional flows, but an extension to three-dimensions is planned as future work. The three-dimensional aerodynamic and numerical formulations are described in this report. Numerical results for two-dimensional unsteady cascade flows, excited by prescribed blade motions and prescribed aerodynamic disturbances at inlet and exit, are also provided to illustrate the present capabilities of the LINFLUX analysis.

A Corresponding Lie Algebra of a Reductive homogeneous Group and Its Applications

NASA Astrophysics Data System (ADS)

Zhang, Yu-Feng; Wu, Li-Xin; Rui, Wen-Juan

2015-05-01

With the help of a Lie algebra of a reductive homogeneous space G/K, where G is a Lie group and K is a resulting isotropy group, we introduce a Lax pair for which an expanding (2+1)-dimensional integrable hierarchy is obtained by applying the binormial-residue representation (BRR) method, whose Hamiltonian structure is derived from the trace identity for deducing (2+1)-dimensional integrable hierarchies, which was proposed by Tu, et al. We further consider some reductions of the expanding integrable hierarchy obtained in the paper. The first reduction is just right the (2+1)-dimensional AKNS hierarchy, the second-type reduction reveals an integrable coupling of the (2+1)-dimensional AKNS equation (also called the Davey-Stewartson hierarchy), a kind of (2+1)-dimensional Schrödinger equation, which was once reobtained by Tu, Feng and Zhang. It is interesting that a new (2+1)-dimensional integrable nonlinear coupled equation is generated from the reduction of the part of the (2+1)-dimensional integrable coupling, which is further reduced to the standard (2+1)-dimensional diffusion equation along with a parameter. In addition, the well-known (1+1)-dimensional AKNS hierarchy, the (1+1)-dimensional nonlinear Schrödinger equation are all special cases of the (2+1)-dimensional expanding integrable hierarchy. Finally, we discuss a few discrete difference equations of the diffusion equation whose stabilities are analyzed by making use of the von Neumann condition and the Fourier method. Some numerical solutions of a special stationary initial value problem of the (2+1)-dimensional diffusion equation are obtained and the resulting convergence and estimation formula are investigated. Supported by the Innovation Team of Jiangsu Province hosted by China University of Mining and Technology (2014), the National Natural Science Foundation of China under Grant No. 11371361, the Fundamental Research Funds for the Central Universities (2013XK03), and the Natural Science Foundation of Shandong Province under Grant No. ZR2013AL016

Non-linear 3D evaluation of different oral implant-abutment connections.

PubMed

Streckbein, P; Streckbein, R G; Wilbrand, J F; Malik, C Y; Schaaf, H; Howaldt, H P; Flach, M

2012-12-01

Micro-gaps and osseous overload in the implant-abutment connection are the most common causes of peri-implant bone resorption and implant failure. These undesirable events can be visualized on standardized three-dimensional finite element models and by radiographic methods. The present study investigated the influence of 7 available implant systems (Ankylos, Astra, Bego, Brånemark, Camlog, Straumann, and Xive) with different implant-abutment connections on bone overload and the appearance of micro-gaps in vitro. The individual geometries of the implants were transferred to three-dimensional finite element models. In a non-linear analysis considering the pre-loading of the occlusion screw, friction between the implant and abutment, the influence of the cone angle on bone strain, and the appearance of micro-gaps were determined. Increased bone strains were correlated with small (< 15°) cone angles. Conical implant-abutment connections efficiently avoided micro-gaps but had a negative effect on peri-implant bone strain. Bone strain was reduced in implants with greater wall thickness (Ankylos) or a smaller cone angle (Bego). The results of our in silico study provide a solid basis for the reduction of peri-implant bone strain and micro-gaps in the implant-abutment connection to improve long-term stability.

One dimensional wavefront distortion sensor comprising a lens array system

DOEpatents

Neal, Daniel R.; Michie, Robert B.

1996-01-01

A 1-dimensional sensor for measuring wavefront distortion of a light beam as a function of time and spatial position includes a lens system which incorporates a linear array of lenses, and a detector system which incorporates a linear array of light detectors positioned from the lens system so that light passing through any of the lenses is focused on at least one of the light detectors. The 1-dimensional sensor determines the slope of the wavefront by location of the detectors illuminated by the light. The 1 dimensional sensor has much greater bandwidth that 2 dimensional systems.

Stable Direct Adaptive Control of Linear Infinite-dimensional Systems Using a Command Generator Tracker Approach

NASA Technical Reports Server (NTRS)

Balas, M. J.; Kaufman, H.; Wen, J.

1985-01-01

A command generator tracker approach to model following contol of linear distributed parameter systems (DPS) whose dynamics are described on infinite dimensional Hilbert spaces is presented. This method generates finite dimensional controllers capable of exponentially stable tracking of the reference trajectories when certain ideal trajectories are known to exist for the open loop DPS; we present conditions for the existence of these ideal trajectories. An adaptive version of this type of controller is also presented and shown to achieve (in some cases, asymptotically) stable finite dimensional control of the infinite dimensional DPS.

One dimensional wavefront distortion sensor comprising a lens array system

DOEpatents

Neal, D.R.; Michie, R.B.

1996-02-20

A 1-dimensional sensor for measuring wavefront distortion of a light beam as a function of time and spatial position includes a lens system which incorporates a linear array of lenses, and a detector system which incorporates a linear array of light detectors positioned from the lens system so that light passing through any of the lenses is focused on at least one of the light detectors. The 1-dimensional sensor determines the slope of the wavefront by location of the detectors illuminated by the light. The 1 dimensional sensor has much greater bandwidth that 2 dimensional systems. 8 figs.

Factor Analysis of Linear Type Traits and Their Relation with Longevity in Brazilian Holstein Cattle

PubMed Central

Kern, Elisandra Lurdes; Cobuci, Jaime Araújo; Costa, Cláudio Napolis; Pimentel, Concepta Margaret McManus

2014-01-01

In this study we aimed to evaluate the reduction in dimensionality of 20 linear type traits and more final score in 14,943 Holstein cows in Brazil using factor analysis, and indicate their relationship with longevity and 305 d first lactation milk production. Low partial correlations (−0.19 to 0.38), the medium to high Kaiser sampling mean (0.79) and the significance of the Bartlett sphericity test (p<0.001), indicated correlations between type traits and the suitability of these data for a factor analysis, after the elimination of seven traits. Two factors had autovalues greater than one. The first included width and height of posterior udder, udder texture, udder cleft, loin strength, bone quality and final score. The second included stature, top line, chest width, body depth, fore udder attachment, angularity and final score. The linear regression of the factors on several measures of longevity and 305 d milk production showed that selection considering only the first factor should lead to improvements in longevity and 305 milk production. PMID:25050015

Data-Adaptive Bias-Reduced Doubly Robust Estimation.

PubMed

Vermeulen, Karel; Vansteelandt, Stijn

2016-05-01

Doubly robust estimators have now been proposed for a variety of target parameters in the causal inference and missing data literature. These consistently estimate the parameter of interest under a semiparametric model when one of two nuisance working models is correctly specified, regardless of which. The recently proposed bias-reduced doubly robust estimation procedure aims to partially retain this robustness in more realistic settings where both working models are misspecified. These so-called bias-reduced doubly robust estimators make use of special (finite-dimensional) nuisance parameter estimators that are designed to locally minimize the squared asymptotic bias of the doubly robust estimator in certain directions of these finite-dimensional nuisance parameters under misspecification of both parametric working models. In this article, we extend this idea to incorporate the use of data-adaptive estimators (infinite-dimensional nuisance parameters), by exploiting the bias reduction estimation principle in the direction of only one nuisance parameter. We additionally provide an asymptotic linearity theorem which gives the influence function of the proposed doubly robust estimator under correct specification of a parametric nuisance working model for the missingness mechanism/propensity score but a possibly misspecified (finite- or infinite-dimensional) outcome working model. Simulation studies confirm the desirable finite-sample performance of the proposed estimators relative to a variety of other doubly robust estimators.

CyTOF workflow: differential discovery in high-throughput high-dimensional cytometry datasets

PubMed Central

Nowicka, Malgorzata; Krieg, Carsten; Weber, Lukas M.; Hartmann, Felix J.; Guglietta, Silvia; Becher, Burkhard; Levesque, Mitchell P.; Robinson, Mark D.

2017-01-01

High dimensional mass and flow cytometry (HDCyto) experiments have become a method of choice for high throughput interrogation and characterization of cell populations.Here, we present an R-based pipeline for differential analyses of HDCyto data, largely based on Bioconductor packages. We computationally define cell populations using FlowSOM clustering, and facilitate an optional but reproducible strategy for manual merging of algorithm-generated clusters. Our workflow offers different analysis paths, including association of cell type abundance with a phenotype or changes in signaling markers within specific subpopulations, or differential analyses of aggregated signals. Importantly, the differential analyses we show are based on regression frameworks where the HDCyto data is the response; thus, we are able to model arbitrary experimental designs, such as those with batch effects, paired designs and so on. In particular, we apply generalized linear mixed models to analyses of cell population abundance or cell-population-specific analyses of signaling markers, allowing overdispersion in cell count or aggregated signals across samples to be appropriately modeled. To support the formal statistical analyses, we encourage exploratory data analysis at every step, including quality control (e.g. multi-dimensional scaling plots), reporting of clustering results (dimensionality reduction, heatmaps with dendrograms) and differential analyses (e.g. plots of aggregated signals). PMID:28663787

Reduction of the two dimensional stationary Navier-Stokes problem to a sequence of Fredholm integral equations of the second kind

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.

1981-01-01

Present approaches to solving the stationary Navier-Stokes equations are of limited value; however, there does exist an equivalent representation of the problem that has significant potential in solving such problems. This is due to the fact that the equivalent representation consists of a sequence of Fredholm integral equations of the second kind, and the solving of this type of problem is very well developed. For the problem in this form, there is an excellent chance to also determine explicit error estimates, since bounded, rather than unbounded, linear operators are dealt with.

Dynamical behavior of susceptible-infected-recovered-susceptible epidemic model on weighted networks

NASA Astrophysics Data System (ADS)

Wu, Qingchu; Zhang, Fei

2018-02-01

We study susceptible-infected-recovered-susceptible epidemic model in weighted, regular, and random complex networks. We institute a pairwise-type mathematical model with a general transmission rate to evaluate the influence of the link-weight distribution on the spreading process. Furthermore, we develop a dimensionality reduction approach to derive the condition for the contagion outbreak. Finally, we analyze the influence of the heterogeneity of weight distribution on the outbreak condition for the scenario with a linear transmission rate. Our theoretical analysis is in agreement with stochastic simulations, showing that the heterogeneity of link-weight distribution can have a significant effect on the epidemic dynamics.

Discriminative components of data.

PubMed

Peltonen, Jaakko; Kaski, Samuel

2005-01-01

A simple probabilistic model is introduced to generalize classical linear discriminant analysis (LDA) in finding components that are informative of or relevant for data classes. The components maximize the predictability of the class distribution which is asymptotically equivalent to 1) maximizing mutual information with the classes, and 2) finding principal components in the so-called learning or Fisher metrics. The Fisher metric measures only distances that are relevant to the classes, that is, distances that cause changes in the class distribution. The components have applications in data exploration, visualization, and dimensionality reduction. In empirical experiments, the method outperformed, in addition to more classical methods, a Renyi entropy-based alternative while having essentially equivalent computational cost.

Multiview Locally Linear Embedding for Effective Medical Image Retrieval

PubMed Central

Shen, Hualei; Tao, Dacheng; Ma, Dianfu

2013-01-01

Content-based medical image retrieval continues to gain attention for its potential to assist radiological image interpretation and decision making. Many approaches have been proposed to improve the performance of medical image retrieval system, among which visual features such as SIFT, LBP, and intensity histogram play a critical role. Typically, these features are concatenated into a long vector to represent medical images, and thus traditional dimension reduction techniques such as locally linear embedding (LLE), principal component analysis (PCA), or laplacian eigenmaps (LE) can be employed to reduce the “curse of dimensionality”. Though these approaches show promising performance for medical image retrieval, the feature-concatenating method ignores the fact that different features have distinct physical meanings. In this paper, we propose a new method called multiview locally linear embedding (MLLE) for medical image retrieval. Following the patch alignment framework, MLLE preserves the geometric structure of the local patch in each feature space according to the LLE criterion. To explore complementary properties among a range of features, MLLE assigns different weights to local patches from different feature spaces. Finally, MLLE employs global coordinate alignment and alternating optimization techniques to learn a smooth low-dimensional embedding from different features. To justify the effectiveness of MLLE for medical image retrieval, we compare it with conventional spectral embedding methods. We conduct experiments on a subset of the IRMA medical image data set. Evaluation results show that MLLE outperforms state-of-the-art dimension reduction methods. PMID:24349277

Metric dimensional reduction at singularities with implications to Quantum Gravity

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

Stoica, Ovidiu Cristinel, E-mail: holotronix@gmail.com

2014-08-15

A series of old and recent theoretical observations suggests that the quantization of gravity would be feasible, and some problems of Quantum Field Theory would go away if, somehow, the spacetime would undergo a dimensional reduction at high energy scales. But an identification of the deep mechanism causing this dimensional reduction would still be desirable. The main contribution of this article is to show that dimensional reduction effects are due to General Relativity at singularities, and do not need to be postulated ad-hoc. Recent advances in understanding the geometry of singularities do not require modification of General Relativity, being justmore » non-singular extensions of its mathematics to the limit cases. They turn out to work fine for some known types of cosmological singularities (black holes and FLRW Big-Bang), allowing a choice of the fundamental geometric invariants and physical quantities which remain regular. The resulting equations are equivalent to the standard ones outside the singularities. One consequence of this mathematical approach to the singularities in General Relativity is a special, (geo)metric type of dimensional reduction: at singularities, the metric tensor becomes degenerate in certain spacetime directions, and some properties of the fields become independent of those directions. Effectively, it is like one or more dimensions of spacetime just vanish at singularities. This suggests that it is worth exploring the possibility that the geometry of singularities leads naturally to the spontaneous dimensional reduction needed by Quantum Gravity. - Highlights: • The singularities we introduce are described by finite geometric/physical objects. • Our singularities are accompanied by dimensional reduction effects. • They affect the metric, the measure, the topology, the gravitational DOF (Weyl = 0). • Effects proposed in other approaches to Quantum Gravity are obtained naturally. • The geometric dimensional reduction obtained opens new ways for Quantum Gravity.« 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 Few New 2+1-Dimensional Nonlinear Dynamics and the Representation of Riemann Curvature Tensors

NASA Astrophysics Data System (ADS)

Wang, Yan; Zhang, Yufeng; Zhang, Xiangzhi

2016-09-01

We first introduced a linear stationary equation with a quadratic operator in ∂x and ∂y, then a linear evolution equation is given by N-order polynomials of eigenfunctions. As applications, by taking N=2, we derived a (2+1)-dimensional generalized linear heat equation with two constant parameters associative with a symmetric space. When taking N=3, a pair of generalized Kadomtsev-Petviashvili equations with the same eigenvalues with the case of N=2 are generated. Similarly, a second-order flow associative with a homogeneous space is derived from the integrability condition of the two linear equations, which is a (2+1)-dimensional hyperbolic equation. When N=3, the third second flow associative with the homogeneous space is generated, which is a pair of new generalized Kadomtsev-Petviashvili equations. Finally, as an application of a Hermitian symmetric space, we established a pair of spectral problems to obtain a new (2+1)-dimensional generalized Schrödinger equation, which is expressed by the Riemann curvature tensors.

Fractal Dimensionality of Pore and Grain Volume of a Siliciclastic Marine Sand

NASA Astrophysics Data System (ADS)

Reed, A. H.; Pandey, R. B.; Lavoie, D. L.

Three-dimensional (3D) spatial distributions of pore and grain volumes were determined from high-resolution computer tomography (CT) images of resin-impregnated marine sands. Using a linear gradient extrapolation method, cubic three-dimensional samples were constructed from two-dimensional CT images. Image porosity (0.37) was found to be consistent with the estimate of porosity by water weight loss technique (0.36). Scaling of the pore volume (Vp) with the linear size (L), V~LD provides the fractal dimensionalities of the pore volume (D=2.74+/-0.02) and grain volume (D=2.90+/-0.02) typical for sedimentary materials.

Linear and volumetric dimensional changes of injection-molded PMMA denture base resins.

PubMed

El Bahra, Shadi; Ludwig, Klaus; Samran, Abdulaziz; Freitag-Wolf, Sandra; Kern, Matthias

2013-11-01

The aim of this study was to evaluate the linear and volumetric dimensional changes of six denture base resins processed by their corresponding injection-molding systems at 3 time intervals of water storage. Two heat-curing (SR Ivocap Hi Impact and Lucitone 199) and four auto-curing (IvoBase Hybrid, IvoBase Hi Impact, PalaXpress, and Futura Gen) acrylic resins were used with their specific injection-molding technique to fabricate 6 specimens of each material. Linear and volumetric dimensional changes were determined by means of a digital caliper and an electronic hydrostatic balance, respectively, after water storage of 1, 30, or 90 days. Means and standard deviations of linear and volumetric dimensional changes were calculated in percentage (%). Statistical analysis was done using Student's and Welch's t tests with Bonferroni-Holm correction for multiple comparisons (α=0.05). Statistically significant differences in linear dimensional changes between resins were demonstrated at all three time intervals of water immersion (p≤0.05), with exception of the following comparisons which showed no significant difference: IvoBase Hi Impact/SR Ivocap Hi Impact and PalaXpress/Lucitone 199 after 1 day, Futura Gen/PalaXpress and PalaXpress/Lucitone 199 after 30 days, and IvoBase Hybrid/IvoBase Hi Impact after 90 days. Also, statistically significant differences in volumetric dimensional changes between resins were found at all three time intervals of water immersion (p≤0.05), with exception of the comparison between PalaXpress and Futura Gen. Denture base resins (IvoBase Hybrid and IvoBase Hi Impact) processed by the new injection-molding system (IvoBase), revealed superior dimensional precision. Copyright © 2013 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Linear and non-linear infrared response of one-dimensional vibrational Holstein polarons in the anti-adiabatic limit: Optical and acoustical phonon models

NASA Astrophysics Data System (ADS)

Falvo, Cyril

2018-02-01

The theory of linear and non-linear infrared response of vibrational Holstein polarons in one-dimensional lattices is presented in order to identify the spectral signatures of self-trapping phenomena. Using a canonical transformation, the optical response is computed from the small polaron point of view which is valid in the anti-adiabatic limit. Two types of phonon baths are considered: optical phonons and acoustical phonons, and simple expressions are derived for the infrared response. It is shown that for the case of optical phonons, the linear response can directly probe the polaron density of states. The model is used to interpret the experimental spectrum of crystalline acetanilide in the C=O range. For the case of acoustical phonons, it is shown that two bound states can be observed in the two-dimensional infrared spectrum at low temperature. At high temperature, analysis of the time-dependence of the two-dimensional infrared spectrum indicates that bath mediated correlations slow down spectral diffusion. The model is used to interpret the experimental linear-spectroscopy of model α-helix and β-sheet polypeptides. This work shows that the Davydov Hamiltonian cannot explain the observations in the NH stretching range.

Comparative analysis of nonlinear dimensionality reduction techniques for breast MRI segmentation

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

Akhbardeh, Alireza; Jacobs, Michael A.; Russell H. Morgan Department of Radiology and Radiological Science, Johns Hopkins University School of Medicine, Baltimore, Maryland 21205

2012-04-15

Purpose: Visualization of anatomical structures using radiological imaging methods is an important tool in medicine to differentiate normal from pathological tissue and can generate large amounts of data for a radiologist to read. Integrating these large data sets is difficult and time-consuming. A new approach uses both supervised and unsupervised advanced machine learning techniques to visualize and segment radiological data. This study describes the application of a novel hybrid scheme, based on combining wavelet transform and nonlinear dimensionality reduction (NLDR) methods, to breast magnetic resonance imaging (MRI) data using three well-established NLDR techniques, namely, ISOMAP, local linear embedding (LLE), andmore » diffusion maps (DfM), to perform a comparative performance analysis. Methods: Twenty-five breast lesion subjects were scanned using a 3T scanner. MRI sequences used were T1-weighted, T2-weighted, diffusion-weighted imaging (DWI), and dynamic contrast-enhanced (DCE) imaging. The hybrid scheme consisted of two steps: preprocessing and postprocessing of the data. The preprocessing step was applied for B{sub 1} inhomogeneity correction, image registration, and wavelet-based image compression to match and denoise the data. In the postprocessing step, MRI parameters were considered data dimensions and the NLDR-based hybrid approach was applied to integrate the MRI parameters into a single image, termed the embedded image. This was achieved by mapping all pixel intensities from the higher dimension to a lower dimensional (embedded) space. For validation, the authors compared the hybrid NLDR with linear methods of principal component analysis (PCA) and multidimensional scaling (MDS) using synthetic data. For the clinical application, the authors used breast MRI data, comparison was performed using the postcontrast DCE MRI image and evaluating the congruence of the segmented lesions. Results: The NLDR-based hybrid approach was able to define and segment both synthetic and clinical data. In the synthetic data, the authors demonstrated the performance of the NLDR method compared with conventional linear DR methods. The NLDR approach enabled successful segmentation of the structures, whereas, in most cases, PCA and MDS failed. The NLDR approach was able to segment different breast tissue types with a high accuracy and the embedded image of the breast MRI data demonstrated fuzzy boundaries between the different types of breast tissue, i.e., fatty, glandular, and tissue with lesions (>86%). Conclusions: The proposed hybrid NLDR methods were able to segment clinical breast data with a high accuracy and construct an embedded image that visualized the contribution of different radiological parameters.« less

A fully 3D approach for metal artifact reduction in computed tomography.

PubMed

Kratz, Barbel; Weyers, Imke; Buzug, Thorsten M

2012-11-01

In computed tomography imaging metal objects in the region of interest introduce inconsistencies during data acquisition. Reconstructing these data leads to an image in spatial domain including star-shaped or stripe-like artifacts. In order to enhance the quality of the resulting image the influence of the metal objects can be reduced. Here, a metal artifact reduction (MAR) approach is proposed that is based on a recomputation of the inconsistent projection data using a fully three-dimensional Fourier-based interpolation. The success of the projection space restoration depends sensitively on a sensible continuation of neighboring structures into the recomputed area. Fortunately, structural information of the entire data is inherently included in the Fourier space of the data. This can be used for a reasonable recomputation of the inconsistent projection data. The key step of the proposed MAR strategy is the recomputation of the inconsistent projection data based on an interpolation using nonequispaced fast Fourier transforms (NFFT). The NFFT interpolation can be applied in arbitrary dimension. The approach overcomes the problem of adequate neighborhood definitions on irregular grids, since this is inherently given through the usage of higher dimensional Fourier transforms. Here, applications up to the third interpolation dimension are presented and validated. Furthermore, prior knowledge may be included by an appropriate damping of the transform during the interpolation step. This MAR method is applicable on each angular view of a detector row, on two-dimensional projection data as well as on three-dimensional projection data, e.g., a set of sequential acquisitions at different spatial positions, projection data of a spiral acquisition, or cone-beam projection data. Results of the novel MAR scheme based on one-, two-, and three-dimensional NFFT interpolations are presented. All results are compared in projection data space and spatial domain with the well-known one-dimensional linear interpolation strategy. In conclusion, it is recommended to include as much spatial information into the recomputation step as possible. This is realized by increasing the dimension of the NFFT. The resulting image quality can be enhanced considerably.

Spectral Target Detection using Schroedinger Eigenmaps

NASA Astrophysics Data System (ADS)

Dorado-Munoz, Leidy P.

Applications of optical remote sensing processes include environmental monitoring, military monitoring, meteorology, mapping, surveillance, etc. Many of these tasks include the detection of specific objects or materials, usually few or small, which are surrounded by other materials that clutter the scene and hide the relevant information. This target detection process has been boosted lately by the use of hyperspectral imagery (HSI) since its high spectral dimension provides more detailed spectral information that is desirable in data exploitation. Typical spectral target detectors rely on statistical or geometric models to characterize the spectral variability of the data. However, in many cases these parametric models do not fit well HSI data that impacts the detection performance. On the other hand, non-linear transformation methods, mainly based on manifold learning algorithms, have shown a potential use in HSI transformation, dimensionality reduction and classification. In target detection, non-linear transformation algorithms are used as preprocessing techniques that transform the data to a more suitable lower dimensional space, where the statistical or geometric detectors are applied. One of these non-linear manifold methods is the Schroedinger Eigenmaps (SE) algorithm that has been introduced as a technique for semi-supervised classification. The core tool of the SE algorithm is the Schroedinger operator that includes a potential term that encodes prior information about the materials present in a scene, and enables the embedding to be steered in some convenient directions in order to cluster similar pixels together. A completely novel target detection methodology based on SE algorithm is proposed for the first time in this thesis. The proposed methodology does not just include the transformation of the data to a lower dimensional space but also includes the definition of a detector that capitalizes on the theory behind SE. The fact that target pixels and those similar pixels are clustered in a predictable region of the low-dimensional representation is used to define a decision rule that allows one to identify target pixels over the rest of pixels in a given image. In addition, a knowledge propagation scheme is used to combine spectral and spatial information as a means to propagate the "potential constraints" to nearby points. The propagation scheme is introduced to reinforce weak connections and improve the separability between most of the target pixels and the background. Experiments using different HSI data sets are carried out in order to test the proposed methodology. The assessment is performed from a quantitative and qualitative point of view, and by comparing the SE-based methodology against two other detection methodologies that use linear/non-linear algorithms as transformations and the well-known Adaptive Coherence/Cosine Estimator (ACE) detector. Overall results show that the SE-based detector outperforms the other two detection methodologies, which indicates the usefulness of the SE transformation in spectral target detection problems.

Vestibular coriolis effect differences modeled with three-dimensional linear-angular interactions.

PubMed

Holly, Jan E

2004-01-01

The vestibular coriolis (or "cross-coupling") effect is traditionally explained by cross-coupled angular vectors, which, however, do not explain the differences in perceptual disturbance under different acceleration conditions. For example, during head roll tilt in a rotating chair, the magnitude of perceptual disturbance is affected by a number of factors, including acceleration or deceleration of the chair rotation or a zero-g environment. Therefore, it has been suggested that linear-angular interactions play a role. The present research investigated whether these perceptual differences and others involving linear coriolis accelerations could be explained under one common framework: the laws of motion in three dimensions, which include all linear-angular interactions among all six components of motion (three angular and three linear). The results show that the three-dimensional laws of motion predict the differences in perceptual disturbance. No special properties of the vestibular system or nervous system are required. In addition, simulations were performed with angular, linear, and tilt time constants inserted into the model, giving the same predictions. Three-dimensional graphics were used to highlight the manner in which linear-angular interaction causes perceptual disturbance, and a crucial component is the Stretch Factor, which measures the "unexpected" linear component.

A framework for optimal kernel-based manifold embedding of medical image data.

PubMed

Zimmer, Veronika A; Lekadir, Karim; Hoogendoorn, Corné; Frangi, Alejandro F; Piella, Gemma

2015-04-01

Kernel-based dimensionality reduction is a widely used technique in medical image analysis. To fully unravel the underlying nonlinear manifold the selection of an adequate kernel function and of its free parameters is critical. In practice, however, the kernel function is generally chosen as Gaussian or polynomial and such standard kernels might not always be optimal for a given image dataset or application. In this paper, we present a study on the effect of the kernel functions in nonlinear manifold embedding of medical image data. To this end, we first carry out a literature review on existing advanced kernels developed in the statistics, machine learning, and signal processing communities. In addition, we implement kernel-based formulations of well-known nonlinear dimensional reduction techniques such as Isomap and Locally Linear Embedding, thus obtaining a unified framework for manifold embedding using kernels. Subsequently, we present a method to automatically choose a kernel function and its associated parameters from a pool of kernel candidates, with the aim to generate the most optimal manifold embeddings. Furthermore, we show how the calculated selection measures can be extended to take into account the spatial relationships in images, or used to combine several kernels to further improve the embedding results. Experiments are then carried out on various synthetic and phantom datasets for numerical assessment of the methods. Furthermore, the workflow is applied to real data that include brain manifolds and multispectral images to demonstrate the importance of the kernel selection in the analysis of high-dimensional medical images. Copyright © 2014 Elsevier Ltd. All rights reserved.

Optical conductivity of three and two dimensional topological nodal-line semimetals

NASA Astrophysics Data System (ADS)

Barati, Shahin; Abedinpour, Saeed H.

2017-10-01

The peculiar shape of the Fermi surface of topological nodal-line semimetals at low carrier concentrations results in their unusual optical and transport properties. We analytically investigate the linear optical responses of three- and two-dimensional nodal-line semimetals using the Kubo formula. The optical conductivity of a three-dimensional nodal-line semimetal is anisotropic. Along the axial direction (i.e., the direction perpendicular to the nodal-ring plane), the Drude weight has a linear dependence on the chemical potential at both low and high carrier dopings. For the radial direction (i.e., the direction parallel to the nodal-ring plane), this dependence changes from linear into quadratic in the transition from low into high carrier concentration. The interband contribution into optical conductivity is also anisotropic. In particular, at large frequencies, it saturates to a constant value for the axial direction and linearly increases with frequency along the radial direction. In two-dimensional nodal-line semimetals, no interband optical transition could be induced and the only contribution to the optical conductivity arises from the intraband excitations. The corresponding Drude weight is independent of the carrier density at low carrier concentrations and linearly increases with chemical potential at high carrier doping.

Multidimensionally encoded magnetic resonance imaging.

PubMed

Lin, Fa-Hsuan

2013-07-01

Magnetic resonance imaging (MRI) typically achieves spatial encoding by measuring the projection of a q-dimensional object over q-dimensional spatial bases created by linear spatial encoding magnetic fields (SEMs). Recently, imaging strategies using nonlinear SEMs have demonstrated potential advantages for reconstructing images with higher spatiotemporal resolution and reducing peripheral nerve stimulation. In practice, nonlinear SEMs and linear SEMs can be used jointly to further improve the image reconstruction performance. Here, we propose the multidimensionally encoded (MDE) MRI to map a q-dimensional object onto a p-dimensional encoding space where p > q. MDE MRI is a theoretical framework linking imaging strategies using linear and nonlinear SEMs. Using a system of eight surface SEM coils with an eight-channel radiofrequency coil array, we demonstrate the five-dimensional MDE MRI for a two-dimensional object as a further generalization of PatLoc imaging and O-space imaging. We also present a method of optimizing spatial bases in MDE MRI. Results show that MDE MRI with a higher dimensional encoding space can reconstruct images more efficiently and with a smaller reconstruction error when the k-space sampling distribution and the number of samples are controlled. Copyright © 2012 Wiley Periodicals, Inc.

Reduction of time-resolved space-based CCD photometry developed for MOST Fabry Imaging data*

NASA Astrophysics Data System (ADS)

Reegen, P.; Kallinger, T.; Frast, D.; Gruberbauer, M.; Huber, D.; Matthews, J. M.; Punz, D.; Schraml, S.; Weiss, W. W.; Kuschnig, R.; Moffat, A. F. J.; Walker, G. A. H.; Guenther, D. B.; Rucinski, S. M.; Sasselov, D.

2006-04-01

The MOST (Microvariability and Oscillations of Stars) satellite obtains ultraprecise photometry from space with high sampling rates and duty cycles. Astronomical photometry or imaging missions in low Earth orbits, like MOST, are especially sensitive to scattered light from Earthshine, and all these missions have a common need to extract target information from voluminous data cubes. They consist of upwards of hundreds of thousands of two-dimensional CCD frames (or subrasters) containing from hundreds to millions of pixels each, where the target information, superposed on background and instrumental effects, is contained only in a subset of pixels (Fabry Images, defocused images, mini-spectra). We describe a novel reduction technique for such data cubes: resolving linear correlations of target and background pixel intensities. This step-wise multiple linear regression removes only those target variations which are also detected in the background. The advantage of regression analysis versus background subtraction is the appropriate scaling, taking into account that the amount of contamination may differ from pixel to pixel. The multivariate solution for all pairs of target/background pixels is minimally invasive of the raw photometry while being very effective in reducing contamination due to, e.g. stray light. The technique is tested and demonstrated with both simulated oscillation signals and real MOST photometry.

Reaction-Infiltration Instabilities in Fractured and Porous Rocks

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

Ladd, Anthony

In this project we are developing a multiscale analysis of the evolution of fracture permeability, using numerical simulations and linear stability analysis. Our simulations include fully three-dimensional simulations of the fracture topography, fluid flow, and reactant transport, two-dimensional simulations based on aperture models, and linear stability analysis.

A trace ratio maximization approach to multiple kernel-based dimensionality reduction.

PubMed

Jiang, Wenhao; Chung, Fu-lai

2014-01-01

Most dimensionality reduction techniques are based on one metric or one kernel, hence it is necessary to select an appropriate kernel for kernel-based dimensionality reduction. Multiple kernel learning for dimensionality reduction (MKL-DR) has been recently proposed to learn a kernel from a set of base kernels which are seen as different descriptions of data. As MKL-DR does not involve regularization, it might be ill-posed under some conditions and consequently its applications are hindered. This paper proposes a multiple kernel learning framework for dimensionality reduction based on regularized trace ratio, termed as MKL-TR. Our method aims at learning a transformation into a space of lower dimension and a corresponding kernel from the given base kernels among which some may not be suitable for the given data. The solutions for the proposed framework can be found based on trace ratio maximization. The experimental results demonstrate its effectiveness in benchmark datasets, which include text, image and sound datasets, for supervised, unsupervised as well as semi-supervised settings. Copyright © 2013 Elsevier Ltd. All rights reserved.

Charged black holes in compactified spacetimes

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

Karlovini, Max; Unge, Rikard von

2005-11-15

We construct and investigate a compactified version of the four-dimensional Reissner-Nordstroem-Taub-NUT solution, generalizing the compactified Schwarzschild black hole that has been previously studied by several workers. Our approach to compactification is based on dimensional reduction with respect to the stationary Killing vector, resulting in three-dimensional gravity coupled to a nonlinear sigma model. Knowing that the original noncompactified solution corresponds to a target space geodesic, the problem can be linearized much in the same way as in the case of no electric or Taub-NUT charge. An interesting feature of the solution family is that, for nonzero electric charge but vanishing Taub-NUTmore » charge, the solution has a curvature singularity on a torus that surrounds the event horizon, but this singularity is removed when the Taub-NUT charge is switched on. We also treat the Schwarzschild case in a more complete way than has been done previously. In particular, the asymptotic solution (the Levi-Civita solution with the height coordinate made periodic) has to our knowledge only been calculated up to a determination of the mass parameter. The periodic Levi-Civita solution contains three essential parameters, however, and the remaining two are explicitly calculated here.« less

Nitrogen-Doped Three Dimensional Graphene for Electrochemical Sensing.

PubMed

Yan, Jing; Chen, Ruwen; Liang, Qionglin; Li, Jinghong

2015-07-01

The rational assembly and doping of graphene play an crucial role in the improvement of electrochemical performance for analytical applications. Covalent assembly of graphene into ordered hierarchical structure provides an interconnected three dimensional conductive network and large specific area beneficial to electrolyte transfer on the electrode surface. Chemical doping with heteroatom is a powerful tool to intrinsically modify the electronic properties of graphene due to the increased free charge-carrier densities. By incorporating covalent assembly and nitrogen doping strategy, a novel nitrogen doped three dimensional reduced graphene oxide nanostructure (3D-N-RGO) was developed with synergetic enhancement in electrochemical behaviors. The as prepared 3D-N-RGO was further applied for catechol detection by differential pulse voltammetry. It exhibits much higher electrocatalytic activity towards catechol with increased peak current and decreased potential difference between the oxidation and reduction peaks. Owing to the improved electro-chemical properties, the response of the electrochemical sensor varies linearly with the catechol concentrations ranging from 5 µM to 100 µM with a detection limit of 2 µM (S/N = 3). This work is promising to open new possibilities in the study of novel graphene nanostructure and promote its potential electrochemical applications.

Scaling Properties of Dimensionality Reduction for Neural Populations and Network Models

PubMed Central

Cowley, Benjamin R.; Doiron, Brent; Kohn, Adam

2016-01-01

Recent studies have applied dimensionality reduction methods to understand how the multi-dimensional structure of neural population activity gives rise to brain function. It is unclear, however, how the results obtained from dimensionality reduction generalize to recordings with larger numbers of neurons and trials or how these results relate to the underlying network structure. We address these questions by applying factor analysis to recordings in the visual cortex of non-human primates and to spiking network models that self-generate irregular activity through a balance of excitation and inhibition. We compared the scaling trends of two key outputs of dimensionality reduction—shared dimensionality and percent shared variance—with neuron and trial count. We found that the scaling properties of networks with non-clustered and clustered connectivity differed, and that the in vivo recordings were more consistent with the clustered network. Furthermore, recordings from tens of neurons were sufficient to identify the dominant modes of shared variability that generalize to larger portions of the network. These findings can help guide the interpretation of dimensionality reduction outputs in regimes of limited neuron and trial sampling and help relate these outputs to the underlying network structure. PMID:27926936

Linearized compressible-flow theory for sonic flight speeds

NASA Technical Reports Server (NTRS)

Heaslet, Max A; Lomax, Harvard; Spreiter, John R

1950-01-01

The partial differential equation for the perturbation velocity potential is examined for free-stream Mach numbers close to and equal to one. It is found that, under the assumptions of linearized theory, solutions can be found consistent with the theory for lifting-surface problems both in stationary three-dimensional flow and in unsteady two-dimensional flow. Several examples are solved including a three dimensional swept-back wing and two dimensional harmonically-oscillating wing, both for a free stream Mach number equal to one. Momentum relations for the evaluation of wave and vortex drag are also discussed. (author)

Noncoherent parallel optical processor for discrete two-dimensional linear transformations.

PubMed

Glaser, I

1980-10-01

We describe a parallel optical processor, based on a lenslet array, that provides general linear two-dimensional transformations using noncoherent light. Such a processor could become useful in image- and signal-processing applications in which the throughput requirements cannot be adequately satisfied by state-of-the-art digital processors. Experimental results that illustrate the feasibility of the processor by demonstrating its use in parallel optical computation of the two-dimensional Walsh-Hadamard transformation are presented.

Globally maximizing, locally minimizing: unsupervised discriminant projection with applications to face and palm biometrics.

PubMed

Yang, Jian; Zhang, David; Yang, Jing-Yu; Niu, Ben

2007-04-01

This paper develops an unsupervised discriminant projection (UDP) technique for dimensionality reduction of high-dimensional data in small sample size cases. UDP can be seen as a linear approximation of a multimanifolds-based learning framework which takes into account both the local and nonlocal quantities. UDP characterizes the local scatter as well as the nonlocal scatter, seeking to find a projection that simultaneously maximizes the nonlocal scatter and minimizes the local scatter. This characteristic makes UDP more intuitive and more powerful than the most up-to-date method, Locality Preserving Projection (LPP), which considers only the local scatter for clustering or classification tasks. The proposed method is applied to face and palm biometrics and is examined using the Yale, FERET, and AR face image databases and the PolyU palmprint database. The experimental results show that UDP consistently outperforms LPP and PCA and outperforms LDA when the training sample size per class is small. This demonstrates that UDP is a good choice for real-world biometrics applications.

Simultaneous quantification of fluoxetine and norfluoxetine in colostrum and mature human milk using a 2-dimensional liquid chromatography-tandem mass spectrometry system.

PubMed

Lopes, Bianca Rebelo; Cassiano, Neila Maria; Carvalho, Daniela Miarelli; Moisés, Elaine Christine Dantas; Cass, Quezia Bezerra

2018-02-20

A two-dimensional liquid chromatography system coupled to triple quadrupole tandem mass spectrometer (2D LC-MS/MS) was employed for the determination of fluoxetine (FLU) and norfluoxetine (N-FLU) in colostrum and mature milk by direct sample injection. With a run time of 12 min representing a gain in throughput analysis, the validated methods furnished selectivity, extraction efficiency, accuracy, and precision in accordance with the criteria preconized by the European Medicines Agency guidelines. With a linear range of 3.00-150 ng/mL for FLU and 4.00-200 ng/mL for N-FLU they were applied to the analysis of colostrum and mature milk samples from nursing mothers. The paper discusses the differences and similarity of sample preparation for this two sample matrices. The herein reported methods are an advance in sample preparation procedures providing waste reduction and a sustainable approach. Copyright © 2017 Elsevier B.V. All rights reserved.

Improved dense trajectories for action recognition based on random projection and Fisher vectors

NASA Astrophysics Data System (ADS)

Ai, Shihui; Lu, Tongwei; Xiong, Yudian

2018-03-01

As an important application of intelligent monitoring system, the action recognition in video has become a very important research area of computer vision. In order to improve the accuracy rate of the action recognition in video with improved dense trajectories, one advanced vector method is introduced. Improved dense trajectories combine Fisher Vector with Random Projection. The method realizes the reduction of the characteristic trajectory though projecting the high-dimensional trajectory descriptor into the low-dimensional subspace based on defining and analyzing Gaussian mixture model by Random Projection. And a GMM-FV hybrid model is introduced to encode the trajectory feature vector and reduce dimension. The computational complexity is reduced by Random Projection which can drop Fisher coding vector. Finally, a Linear SVM is used to classifier to predict labels. We tested the algorithm in UCF101 dataset and KTH dataset. Compared with existed some others algorithm, the result showed that the method not only reduce the computational complexity but also improved the accuracy of action recognition.

The linear sizes tolerances and fits system modernization

NASA Astrophysics Data System (ADS)

Glukhov, V. I.; Grinevich, V. A.; Shalay, V. V.

2018-04-01

The study is carried out on the urgent topic for technical products quality providing in the tolerancing process of the component parts. The aim of the paper is to develop alternatives for improving the system linear sizes tolerances and dimensional fits in the international standard ISO 286-1. The tasks of the work are, firstly, to classify as linear sizes the elements additionally linear coordinating sizes that determine the detail elements location and, secondly, to justify the basic deviation of the tolerance interval for the element's linear size. The geometrical modeling method of real details elements, the analytical and experimental methods are used in the research. It is shown that the linear coordinates are the dimensional basis of the elements linear sizes. To standardize the accuracy of linear coordinating sizes in all accuracy classes, it is sufficient to select in the standardized tolerance system only one tolerance interval with symmetrical deviations: Js for internal dimensional elements (holes) and js for external elements (shafts). The main deviation of this coordinating tolerance is the average zero deviation, which coincides with the nominal value of the coordinating size. Other intervals of the tolerance system are remained for normalizing the accuracy of the elements linear sizes with a fundamental change in the basic deviation of all tolerance intervals is the maximum deviation corresponding to the limit of the element material: EI is the lower tolerance for the of the internal elements (holes) sizes and es is the upper tolerance deviation for the outer elements (shafts) sizes. It is the sizes of the material maximum that are involved in the of the dimensional elements mating of the shafts and holes and determine the fits type.

Lie symmetry analysis and reduction for exact solution of (2+1)-dimensional Bogoyavlensky-Konopelchenko equation by geometric approach

NASA Astrophysics Data System (ADS)

Ray, S. Saha

2018-04-01

In this paper, the symmetry analysis and similarity reduction of the (2+1)-dimensional Bogoyavlensky-Konopelchenko (B-K) equation are investigated by means of the geometric approach of an invariance group, which is equivalent to the classical Lie symmetry method. Using the extended Harrison and Estabrook’s differential forms approach, the infinitesimal generators for (2+1)-dimensional B-K equation are obtained. Firstly, the vector field associated with the Lie group of transformation is derived. Then the symmetry reduction and the corresponding explicit exact solution of (2+1)-dimensional B-K equation is obtained.

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Adamian, A.

1988-01-01

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

Low-dimensional manifold of actin polymerization dynamics

NASA Astrophysics Data System (ADS)

Floyd, Carlos; Jarzynski, Christopher; Papoian, Garegin

2017-12-01

Actin filaments are critical components of the eukaryotic cytoskeleton, playing important roles in a number of cellular functions, such as cell migration, organelle transport, and mechanosensation. They are helical polymers with a well-defined polarity, composed of globular subunits that bind nucleotides in one of three hydrolysis states (ATP, ADP-Pi, or ADP). Mean-field models of the dynamics of actin polymerization have succeeded in, among other things, determining the nucleotide profile of an average filament and resolving the mechanisms of accessory proteins. However, these models require numerical solution of a high-dimensional system of nonlinear ordinary differential equations. By truncating a set of recursion equations, the Brooks-Carlsson (BC) model reduces dimensionality to 11, but it still remains nonlinear and does not admit an analytical solution, hence, significantly hindering understanding of its resulting dynamics. In this work, by taking advantage of the fast timescales of the hydrolysis states of the filament tips, we propose two model reduction schemes: the quasi steady-state approximation model is five-dimensional and nonlinear, whereas the constant tip (CT) model is five-dimensional and linear, resulting from the approximation that the tip states are not dynamic variables. We provide an exact solution of the CT model and use it to shed light on the dynamical behaviors of the full BC model, highlighting the relative ordering of the timescales of various collective processes, and explaining some unusual dependence of the steady-state behavior on initial conditions.

Weyl and transverse diffeomorphism invariant spin-2 models in D=2+1

NASA Astrophysics Data System (ADS)

Dalmazi, Denis; dos Santos, A. L. R.; Ghosh, Subir; Mendonça, E. L.

2017-09-01

There are two covariant descriptions of massless spin-2 particles in D=3+1 via a symmetric rank-2 tensor: the linearized Einstein-Hilbert (LEH) theory and the Weyl plus transverse diffeomorphism (WTDIFF) invariant model. From the LEH theory one can obtain the linearized new massive gravity (NMG) in D=2+1 via Kaluza-Klein dimensional reduction followed by a dual master action. Here we show that a similar route takes us from the WTDIFF model to a linearized scalar-tensor NMG which belongs to a larger class of consistent spin-0 modifications of NMG. We also show that a traceless master action applied to a parity singlet furnishes two new spin-2 self-dual models. Moreover, we examine the singular replacement h_{μ ν } → h_{μ ν } - η _{μ ν }h/D and prove that it leads to consistent massive spin-2 models in D=2+1. They include linearized versions of unimodular topologically massive gravity (TMG) and unimodular NMG. Although the free part of those unimodular theories are Weyl invariant, we do not expect any improvement in the renormalizability. Both the linearized K-term (in NMG) and the linearized gravitational Chern-Simons term (in TMG) are invariant under longitudinal reparametrizations δ h_{μ ν } = partial _{μ }partial _{ν }ζ , which is not a symmetry of the WTDIFF Einstein-Hilbert term. Therefore, we still have one degree of freedom whose propagator behaves like 1/p^2 for large momentum.

Application of Linear and Non-Linear Harmonic Methods for Unsteady Transonic Flow

NASA Astrophysics Data System (ADS)

Gundevia, Rayomand

This thesis explores linear and non-linear computational methods for solving unsteady flow. The eventual goal is to apply these methods to two-dimensional and three-dimensional flutter predictions. In this study the quasi-one-dimensional nozzle is used as a framework for understanding these methods and their limitations. Subsonic and transonic cases are explored as the back-pressure is forced to oscillate with known amplitude and frequency. A steady harmonic approach is used to solve this unsteady problem for which perturbations are said to be small in comparison to the mean flow. The use of a linearized Euler equations (LEE) scheme is good at capturing the flow characteristics but is limited by accuracy to relatively small amplitude perturbations. The introduction of time-averaged second-order terms in the Non-Linear Harmonic (NLH) method means that a better approximation of the mean-valued solution, upon which the linearization is based, can be made. The nonlinear time-accurate Euler solutions are used for comparison and to establish the regimes of unsteadiness for which these schemes fails. The usefulness of the LEE and NLH methods lie in the gains in computational efficiency over the full equations.

Asymptotic and spectral analysis of the gyrokinetic-waterbag integro-differential operator in toroidal geometry

NASA Astrophysics Data System (ADS)

Besse, Nicolas; Coulette, David

2016-08-01

Achieving plasmas with good stability and confinement properties is a key research goal for magnetic fusion devices. The underlying equations are the Vlasov-Poisson and Vlasov-Maxwell (VPM) equations in three space variables, three velocity variables, and one time variable. Even in those somewhat academic cases where global equilibrium solutions are known, studying their stability requires the analysis of the spectral properties of the linearized operator, a daunting task. We have identified a model, for which not only equilibrium solutions can be constructed, but many of their stability properties are amenable to rigorous analysis. It uses a class of solution to the VPM equations (or to their gyrokinetic approximations) known as waterbag solutions which, in particular, are piecewise constant in phase-space. It also uses, not only the gyrokinetic approximation of fast cyclotronic motion around magnetic field lines, but also an asymptotic approximation regarding the magnetic-field-induced anisotropy: the spatial variation along the field lines is taken much slower than across them. Together, these assumptions result in a drastic reduction in the dimensionality of the linearized problem, which becomes a set of two nested one-dimensional problems: an integral equation in the poloidal variable, followed by a one-dimensional complex Schrödinger equation in the radial variable. We show here that the operator associated to the poloidal variable is meromorphic in the eigenparameter, the pulsation frequency. We also prove that, for all but a countable set of real pulsation frequencies, the operator is compact and thus behaves mostly as a finite-dimensional one. The numerical algorithms based on such ideas have been implemented in a companion paper [D. Coulette and N. Besse, "Numerical resolution of the global eigenvalue problem for gyrokinetic-waterbag model in toroidal geometry" (submitted)] and were found to be surprisingly close to those for the original gyrokinetic-Vlasov equations. The purpose of the present paper is to make these new ideas accessible to two readerships: applied mathematicians and plasma physicists.

Revisiting the Scale-Invariant, Two-Dimensional Linear Regression Method

ERIC Educational Resources Information Center

Patzer, A. Beate C.; Bauer, Hans; Chang, Christian; Bolte, Jan; Su¨lzle, Detlev

2018-01-01

The scale-invariant way to analyze two-dimensional experimental and theoretical data with statistical errors in both the independent and dependent variables is revisited by using what we call the triangular linear regression method. This is compared to the standard least-squares fit approach by applying it to typical simple sets of example data…

Mapping of power consumption and friction reduction in piezoelectrically-assisted ultrasonic lubrication

NASA Astrophysics Data System (ADS)

Dong, Sheng; Dapino, Marcelo J.

2015-04-01

Ultrasonic lubrication has been proven effective in reducing dynamic friction. This paper investigates the relationship between friction reduction, power consumption, linear velocity, and normal stress. A modified pin-on-disc tribometer was adopted as the experimental set-up, and a Labview system was utilized for signal generation and data acquisition. Friction reduction was quantified for 0.21 to 5.31 W of electric power, 50 to 200 mm/s of linear velocity, and 23 to 70 MPa of normal stress. Friction reduction near 100% can be achieved under certain conditions. Lower linear velocity and higher electric power result in greater friction reduction, while normal stress has little effect on friction reduction. Contour plots of friction reduction, power consumption, linear velocity, and normal stress were created. An efficiency coefficient was proposed to calculate power requirements for a certain friction reduction or reduced friction for a given electric power.

Assessment of metal artifact reduction methods in pelvic CT

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

Abdoli, Mehrsima; Mehranian, Abolfazl; Ailianou, Angeliki

2016-04-15

Purpose: Metal artifact reduction (MAR) produces images with improved quality potentially leading to confident and reliable clinical diagnosis and therapy planning. In this work, the authors evaluate the performance of five MAR techniques for the assessment of computed tomography images of patients with hip prostheses. Methods: Five MAR algorithms were evaluated using simulation and clinical studies. The algorithms included one-dimensional linear interpolation (LI) of the corrupted projection bins in the sinogram, two-dimensional interpolation (2D), a normalized metal artifact reduction (NMAR) technique, a metal deletion technique, and a maximum a posteriori completion (MAPC) approach. The algorithms were applied to ten simulatedmore » datasets as well as 30 clinical studies of patients with metallic hip implants. Qualitative evaluations were performed by two blinded experienced radiologists who ranked overall artifact severity and pelvic organ recognition for each algorithm by assigning scores from zero to five (zero indicating totally obscured organs with no structures identifiable and five indicating recognition with high confidence). Results: Simulation studies revealed that 2D, NMAR, and MAPC techniques performed almost equally well in all regions. LI falls behind the other approaches in terms of reducing dark streaking artifacts as well as preserving unaffected regions (p < 0.05). Visual assessment of clinical datasets revealed the superiority of NMAR and MAPC in the evaluated pelvic organs and in terms of overall image quality. Conclusions: Overall, all methods, except LI, performed equally well in artifact-free regions. Considering both clinical and simulation studies, 2D, NMAR, and MAPC seem to outperform the other techniques.« less

Regularized Embedded Multiple Kernel Dimensionality Reduction for Mine Signal Processing.

PubMed

Li, Shuang; Liu, Bing; Zhang, Chen

2016-01-01

Traditional multiple kernel dimensionality reduction models are generally based on graph embedding and manifold assumption. But such assumption might be invalid for some high-dimensional or sparse data due to the curse of dimensionality, which has a negative influence on the performance of multiple kernel learning. In addition, some models might be ill-posed if the rank of matrices in their objective functions was not high enough. To address these issues, we extend the traditional graph embedding framework and propose a novel regularized embedded multiple kernel dimensionality reduction method. Different from the conventional convex relaxation technique, the proposed algorithm directly takes advantage of a binary search and an alternative optimization scheme to obtain optimal solutions efficiently. The experimental results demonstrate the effectiveness of the proposed method for supervised, unsupervised, and semisupervised scenarios.

Optimal dimensionality reduction of complex dynamics: the chess game as diffusion on a free-energy landscape.

PubMed

Krivov, Sergei V

2011-07-01

Dimensionality reduction is ubiquitous in the analysis of complex dynamics. The conventional dimensionality reduction techniques, however, focus on reproducing the underlying configuration space, rather than the dynamics itself. The constructed low-dimensional space does not provide a complete and accurate description of the dynamics. Here I describe how to perform dimensionality reduction while preserving the essential properties of the dynamics. The approach is illustrated by analyzing the chess game--the archetype of complex dynamics. A variable that provides complete and accurate description of chess dynamics is constructed. The winning probability is predicted by describing the game as a random walk on the free-energy landscape associated with the variable. The approach suggests a possible way of obtaining a simple yet accurate description of many important complex phenomena. The analysis of the chess game shows that the approach can quantitatively describe the dynamics of processes where human decision-making plays a central role, e.g., financial and social dynamics.

Optimal dimensionality reduction of complex dynamics: The chess game as diffusion on a free-energy landscape

NASA Astrophysics Data System (ADS)

Krivov, Sergei V.

2011-07-01

Dimensionality reduction is ubiquitous in the analysis of complex dynamics. The conventional dimensionality reduction techniques, however, focus on reproducing the underlying configuration space, rather than the dynamics itself. The constructed low-dimensional space does not provide a complete and accurate description of the dynamics. Here I describe how to perform dimensionality reduction while preserving the essential properties of the dynamics. The approach is illustrated by analyzing the chess game—the archetype of complex dynamics. A variable that provides complete and accurate description of chess dynamics is constructed. The winning probability is predicted by describing the game as a random walk on the free-energy landscape associated with the variable. The approach suggests a possible way of obtaining a simple yet accurate description of many important complex phenomena. The analysis of the chess game shows that the approach can quantitatively describe the dynamics of processes where human decision-making plays a central role, e.g., financial and social dynamics.

Four-dimensional \\mathcal{N} = 2 supersymmetric theory with boundary as a two-dimensional complex Toda theory

NASA Astrophysics Data System (ADS)

Luo, Yuan; Tan, Meng-Chwan; Vasko, Petr; Zhao, Qin

2017-05-01

We perform a series of dimensional reductions of the 6d, \\mathcal{N} = (2, 0) SCFT on S 2 × Σ × I × S 1 down to 2d on Σ. The reductions are performed in three steps: (i) a reduction on S 1 (accompanied by a topological twist along Σ) leading to a supersymmetric Yang-Mills theory on S 2 × Σ × I, (ii) a further reduction on S 2 resulting in a complex Chern-Simons theory defined on Σ × I, with the real part of the complex Chern-Simons level being zero, and the imaginary part being proportional to the ratio of the radii of S 2 and S 1, and (iii) a final reduction to the boundary modes of complex Chern-Simons theory with the Nahm pole boundary condition at both ends of the interval I, which gives rise to a complex Toda CFT on the Riemann surface Σ. As the reduction of the 6d theory on Σ would give rise to an \\mathcal{N} = 2 supersymmetric theory on S 2 × I × S 1, our results imply a 4d-2d duality between four-dimensional \\mathcal{N} = 2 supersymmetric theory with boundary and two-dimensional complex Toda theory.

A dimensionally split Cartesian cut cell method for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Gokhale, Nandan; Nikiforakis, Nikos; Klein, Rupert

2018-07-01

We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a full description of its three-dimensional implementation in the dimensionally split framework of Klein et al. [1]. The convergence and stability of the method are proved for the one-dimensional linear advection equation, while its multi-dimensional numerical performance is investigated through the computation of solutions to a number of test problems for the linear advection and Euler equations. When compared to the cut cell flux of Klein et al., it was found that the new flux alleviates the problem of oscillatory boundary solutions produced by the former at higher Courant numbers, and also enables the computation of more accurate solutions near stagnation points. Being dimensionally split, the method is simple to implement and extends readily to multiple dimensions.

Gaussian processes with built-in dimensionality reduction: Applications to high-dimensional uncertainty propagation

NASA Astrophysics Data System (ADS)

Tripathy, Rohit; Bilionis, Ilias; Gonzalez, Marcial

2016-09-01

Uncertainty quantification (UQ) tasks, such as model calibration, uncertainty propagation, and optimization under uncertainty, typically require several thousand evaluations of the underlying computer codes. To cope with the cost of simulations, one replaces the real response surface with a cheap surrogate based, e.g., on polynomial chaos expansions, neural networks, support vector machines, or Gaussian processes (GP). However, the number of simulations required to learn a generic multivariate response grows exponentially as the input dimension increases. This curse of dimensionality can only be addressed, if the response exhibits some special structure that can be discovered and exploited. A wide range of physical responses exhibit a special structure known as an active subspace (AS). An AS is a linear manifold of the stochastic space characterized by maximal response variation. The idea is that one should first identify this low dimensional manifold, project the high-dimensional input onto it, and then link the projection to the output. If the dimensionality of the AS is low enough, then learning the link function is a much easier problem than the original problem of learning a high-dimensional function. The classic approach to discovering the AS requires gradient information, a fact that severely limits its applicability. Furthermore, and partly because of its reliance to gradients, it is not able to handle noisy observations. The latter is an essential trait if one wants to be able to propagate uncertainty through stochastic simulators, e.g., through molecular dynamics codes. In this work, we develop a probabilistic version of AS which is gradient-free and robust to observational noise. Our approach relies on a novel Gaussian process regression with built-in dimensionality reduction. In particular, the AS is represented as an orthogonal projection matrix that serves as yet another covariance function hyper-parameter to be estimated from the data. To train the model, we design a two-step maximum likelihood optimization procedure that ensures the orthogonality of the projection matrix by exploiting recent results on the Stiefel manifold, i.e., the manifold of matrices with orthogonal columns. The additional benefit of our probabilistic formulation, is that it allows us to select the dimensionality of the AS via the Bayesian information criterion. We validate our approach by showing that it can discover the right AS in synthetic examples without gradient information using both noiseless and noisy observations. We demonstrate that our method is able to discover the same AS as the classical approach in a challenging one-hundred-dimensional problem involving an elliptic stochastic partial differential equation with random conductivity. Finally, we use our approach to study the effect of geometric and material uncertainties in the propagation of solitary waves in a one dimensional granular system.

Gaussian processes with built-in dimensionality reduction: Applications to high-dimensional uncertainty propagation

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

Tripathy, Rohit, E-mail: rtripath@purdue.edu; Bilionis, Ilias, E-mail: ibilion@purdue.edu; Gonzalez, Marcial, E-mail: marcial-gonzalez@purdue.edu

2016-09-15

Uncertainty quantification (UQ) tasks, such as model calibration, uncertainty propagation, and optimization under uncertainty, typically require several thousand evaluations of the underlying computer codes. To cope with the cost of simulations, one replaces the real response surface with a cheap surrogate based, e.g., on polynomial chaos expansions, neural networks, support vector machines, or Gaussian processes (GP). However, the number of simulations required to learn a generic multivariate response grows exponentially as the input dimension increases. This curse of dimensionality can only be addressed, if the response exhibits some special structure that can be discovered and exploited. A wide range ofmore » physical responses exhibit a special structure known as an active subspace (AS). An AS is a linear manifold of the stochastic space characterized by maximal response variation. The idea is that one should first identify this low dimensional manifold, project the high-dimensional input onto it, and then link the projection to the output. If the dimensionality of the AS is low enough, then learning the link function is a much easier problem than the original problem of learning a high-dimensional function. The classic approach to discovering the AS requires gradient information, a fact that severely limits its applicability. Furthermore, and partly because of its reliance to gradients, it is not able to handle noisy observations. The latter is an essential trait if one wants to be able to propagate uncertainty through stochastic simulators, e.g., through molecular dynamics codes. In this work, we develop a probabilistic version of AS which is gradient-free and robust to observational noise. Our approach relies on a novel Gaussian process regression with built-in dimensionality reduction. In particular, the AS is represented as an orthogonal projection matrix that serves as yet another covariance function hyper-parameter to be estimated from the data. To train the model, we design a two-step maximum likelihood optimization procedure that ensures the orthogonality of the projection matrix by exploiting recent results on the Stiefel manifold, i.e., the manifold of matrices with orthogonal columns. The additional benefit of our probabilistic formulation, is that it allows us to select the dimensionality of the AS via the Bayesian information criterion. We validate our approach by showing that it can discover the right AS in synthetic examples without gradient information using both noiseless and noisy observations. We demonstrate that our method is able to discover the same AS as the classical approach in a challenging one-hundred-dimensional problem involving an elliptic stochastic partial differential equation with random conductivity. Finally, we use our approach to study the effect of geometric and material uncertainties in the propagation of solitary waves in a one dimensional granular system.« less

A meta-classifier for detecting prostate cancer by quantitative integration of in vivo magnetic resonance spectroscopy and magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Viswanath, Satish; Tiwari, Pallavi; Rosen, Mark; Madabhushi, Anant

2008-03-01

Recently, in vivo Magnetic Resonance Imaging (MRI) and Magnetic Resonance Spectroscopy (MRS) have emerged as promising new modalities to aid in prostate cancer (CaP) detection. MRI provides anatomic and structural information of the prostate while MRS provides functional data pertaining to biochemical concentrations of metabolites such as creatine, choline and citrate. We have previously presented a hierarchical clustering scheme for CaP detection on in vivo prostate MRS and have recently developed a computer-aided method for CaP detection on in vivo prostate MRI. In this paper we present a novel scheme to develop a meta-classifier to detect CaP in vivo via quantitative integration of multimodal prostate MRS and MRI by use of non-linear dimensionality reduction (NLDR) methods including spectral clustering and locally linear embedding (LLE). Quantitative integration of multimodal image data (MRI and PET) involves the concatenation of image intensities following image registration. However multimodal data integration is non-trivial when the individual modalities include spectral and image intensity data. We propose a data combination solution wherein we project the feature spaces (image intensities and spectral data) associated with each of the modalities into a lower dimensional embedding space via NLDR. NLDR methods preserve the relationships between the objects in the original high dimensional space when projecting them into the reduced low dimensional space. Since the original spectral and image intensity data are divorced from their original physical meaning in the reduced dimensional space, data at the same spatial location can be integrated by concatenating the respective embedding vectors. Unsupervised consensus clustering is then used to partition objects into different classes in the combined MRS and MRI embedding space. Quantitative results of our multimodal computer-aided diagnosis scheme on 16 sets of patient data obtained from the ACRIN trial, for which corresponding histological ground truth for spatial extent of CaP is known, show a marginally higher sensitivity, specificity, and positive predictive value compared to corresponding CAD results with the individual modalities.

Perfect commuting-operator strategies for linear system games

NASA Astrophysics Data System (ADS)

Cleve, Richard; Liu, Li; Slofstra, William

2017-01-01

Linear system games are a generalization of Mermin's magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional operator solutions of a certain set of non-commutative equations. We investigate linear system games in the commuting-operator model of entanglement, where Alice and Bob's measurement operators act on a joint Hilbert space, and Alice's operators must commute with Bob's operators. We show that perfect strategies in this model correspond to possibly infinite-dimensional operator solutions of the non-commutative equations. The proof is based around a finitely presented group associated with the linear system which arises from the non-commutative equations.

An approximation theory for the identification of linear thermoelastic systems

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Su, Chien-Hua Frank

1990-01-01

An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions. The approximation framework is based upon generic Galerkin approximation of the mild solutions, and convergence of solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme are discussed. Numerical results indicate how the approach might be used in a study of damping mechanisms in flexible structures.

Development of a Linearized Unsteady Euler Analysis with Application to Wake/Blade-Row Interactions

NASA Technical Reports Server (NTRS)

Verdon, Joseph M.; Montgomery, Matthew D.; Chuang, H. Andrew

1999-01-01

A three-dimensional, linearized, Euler analysis is being developed to provide a comprehensive and efficient unsteady aerodynamic analysis for predicting the aeroacoustic and aeroelastic responses of axial-flow turbomachinery blading. The mathematical models needed to describe nonlinear and linearized, inviscid, unsteady flows through a blade row operating within a cylindrical annular duct are presented in this report. A numerical model for linearized inviscid unsteady flows, which couples a near-field, implicit, wave-split, finite volume analysis to far-field eigen analyses, is also described. The linearized aerodynamic and numerical models have been implemented into the three-dimensional unsteady flow code, LINFLUX. This code is applied herein to predict unsteady subsonic flows driven by wake or vortical excitations. The intent is to validate the LINFLUX analysis via numerical results for simple benchmark unsteady flows and to demonstrate this analysis via application to a realistic wake/blade-row interaction. Detailed numerical results for a three-dimensional version of the 10th Standard Cascade and a fan exit guide vane indicate that LINFLUX is becoming a reliable and useful unsteady aerodynamic prediction capability that can be applied, in the future, to assess the three-dimensional flow physics important to blade-row, aeroacoustic and aeroelastic responses.

Exploiting symmetries in the modeling and analysis of tires

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Andersen, Carl M.; Tanner, John A.

1987-01-01

A simple and efficient computational strategy for reducing both the size of a tire model and the cost of the analysis of tires in the presence of symmetry-breaking conditions (unsymmetry in the tire material, geometry, or loading) is presented. The strategy is based on approximating the unsymmetric response of the tire with a linear combination of symmetric and antisymmetric global approximation vectors (or modes). Details are presented for the three main elements of the computational strategy, which include: use of special three-field mixed finite-element models, use of operator splitting, and substantial reduction in the number of degrees of freedom. The proposed computational stategy is applied to three quasi-symmetric problems of tires: linear analysis of anisotropic tires, through use of semianalytic finite elements, nonlinear analysis of anisotropic tires through use of two-dimensional shell finite elements, and nonlinear analysis of orthotropic tires subjected to unsymmetric loading. Three basic types of symmetry (and their combinations) exhibited by the tire response are identified.

Computational methods for optimal linear-quadratic compensators for infinite dimensional discrete-time systems

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.

Nonlinear dimensionality reduction methods for synthetic biology biobricks' visualization.

PubMed

Yang, Jiaoyun; Wang, Haipeng; Ding, Huitong; An, Ning; Alterovitz, Gil

2017-01-19

Visualizing data by dimensionality reduction is an important strategy in Bioinformatics, which could help to discover hidden data properties and detect data quality issues, e.g. data noise, inappropriately labeled data, etc. As crowdsourcing-based synthetic biology databases face similar data quality issues, we propose to visualize biobricks to tackle them. However, existing dimensionality reduction methods could not be directly applied on biobricks datasets. Hereby, we use normalized edit distance to enhance dimensionality reduction methods, including Isomap and Laplacian Eigenmaps. By extracting biobricks from synthetic biology database Registry of Standard Biological Parts, six combinations of various types of biobricks are tested. The visualization graphs illustrate discriminated biobricks and inappropriately labeled biobricks. Clustering algorithm K-means is adopted to quantify the reduction results. The average clustering accuracy for Isomap and Laplacian Eigenmaps are 0.857 and 0.844, respectively. Besides, Laplacian Eigenmaps is 5 times faster than Isomap, and its visualization graph is more concentrated to discriminate biobricks. By combining normalized edit distance with Isomap and Laplacian Eigenmaps, synthetic biology biobircks are successfully visualized in two dimensional space. Various types of biobricks could be discriminated and inappropriately labeled biobricks could be determined, which could help to assess crowdsourcing-based synthetic biology databases' quality, and make biobricks selection.

On the reduction of 4d $$ \\mathcal{N}=1 $$ theories on $$ {\\mathbb{S}}^2 $$

DOE PAGES

Gadde, Abhijit; Razamat, Shlomo S.; Willett, Brian

2015-11-24

Here, we discuss reductions of generalmore » $$ \\mathcal{N}=1 $$ four dimensional gauge theories on $$ {\\mathbb{S}}^2 $$. The effective two dimensional theory one obtains depends on the details of the coupling of the theory to background fields, which can be translated to a choice of R-symmetry. We argue that, for special choices of R-symmetry, the resulting two dimensional theory has a natural interpretation as an $$ \\mathcal{N}(0,2) $$ gauge theory. As an application of our general observations, we discuss reductions of $$ \\mathcal{N}=1 $$ and $$ \\mathcal{N}=2 $$ dualities and argue that they imply certain two dimensional dualities.« less

Linear stability theory and three-dimensional boundary layer transition

NASA Technical Reports Server (NTRS)

Spall, Robert E.; Malik, Mujeeb R.

1992-01-01

The viewgraphs and discussion of linear stability theory and three dimensional boundary layer transition are provided. The ability to predict, using analytical tools, the location of boundary layer transition over aircraft-type configurations is of great importance to designers interested in laminar flow control (LFC). The e(sup N) method has proven to be fairly effective in predicting, in a consistent manner, the location of the onset of transition for simple geometries in low disturbance environments. This method provides a correlation between the most amplified single normal mode and the experimental location of the onset of transition. Studies indicate that values of N between 8 and 10 correlate well with the onset of transition. For most previous calculations, the mean flows were restricted to two-dimensional or axisymmetric cases, or have employed simple three-dimensional mean flows (e.g., rotating disk, infinite swept wing, or tapered swept wing with straight isobars). Unfortunately, for flows over general wing configurations, and for nearly all flows over fuselage-type bodies at incidence, the analysis of fully three-dimensional flow fields is required. Results obtained for the linear stability of fully three-dimensional boundary layers formed over both wing and fuselage-type geometries, and for both high and low speed flows are discussed. When possible, transition estimates form the e(sup N) method are compared to experimentally determined locations. The stability calculations are made using a modified version of the linear stability code COSAL. Mean flows were computed using both Navier Stokes and boundary-layer codes.

A review on the multivariate statistical methods for dimensional reduction studies

NASA Astrophysics Data System (ADS)

Aik, Lim Eng; Kiang, Lam Chee; Mohamed, Zulkifley Bin; Hong, Tan Wei

2017-05-01

In this research study we have discussed multivariate statistical methods for dimensional reduction, which has been done by various researchers. The reduction of dimensionality is valuable to accelerate algorithm progression, as well as really may offer assistance with the last grouping/clustering precision. A lot of boisterous or even flawed info information regularly prompts a not exactly alluring algorithm progression. Expelling un-useful or dis-instructive information segments may for sure help the algorithm discover more broad grouping locales and principles and generally speaking accomplish better exhibitions on new data set.

The application of Green's theorem to the solution of boundary-value problems in linearized supersonic wing theory

NASA Technical Reports Server (NTRS)

Heaslet, Max A; Lomax, Harvard

1950-01-01

Following the introduction of the linearized partial differential equation for nonsteady three-dimensional compressible flow, general methods of solution are given for the two and three-dimensional steady-state and two-dimensional unsteady-state equations. It is also pointed out that, in the absence of thickness effects, linear theory yields solutions consistent with the assumptions made when applied to lifting-surface problems for swept-back plan forms at sonic speeds. The solutions of the particular equations are determined in all cases by means of Green's theorem, and thus depend on the use of Green's equivalent layer of sources, sinks, and doublets. Improper integrals in the supersonic theory are treated by means of Hadamard's "finite part" technique.

Entropy Analysis in Mixed Convection MHD flow of Nanofluid over a Non-linear Stretching Sheet

NASA Astrophysics Data System (ADS)

Matin, Meisam Habibi; Nobari, Mohammad Reza Heirani; Jahangiri, Pouyan

This article deals with a numerical study of entropy analysis in mixed convection MHD flow of nanofluid over a non-linear stretching sheet taking into account the effects of viscous dissipation and variable magnetic field. The nanofluid is made of such nano particles as SiO2 with pure water as a base fluid. To analyze the problem, at first the boundary layer equations are transformed into non-linear ordinary equations using a similarity transformation. The resultant equations are then solved numerically using the Keller-Box scheme based on the implicit finite-difference method. The effects of different non-dimensional governing parameters such as magnetic parameter, nanoparticles volume fraction, Nusselt, Richardson, Eckert, Hartman, Brinkman, Reynolds and entropy generation numbers are investigated in details. The results indicate that increasing the nano particles to the base fluids causes the reduction in shear forces and a decrease in stretching sheet heat transfer coefficient. Also, decreasing the magnetic parameter and increasing the Eckert number result in improves heat transfer rate. Furthermore, the surface acts as a strong source of irreversibility due to the higher entropy generation number near the surface.

Experimental Analyses of Flow Field Structures around Clustered Linear Aerospike Nozzles

NASA Astrophysics Data System (ADS)

Taniguchi, Mashio; Mori, Hideo; Nishihira, Ryutaro; Niimi, Tomohide

2005-05-01

An aerospike nozzle has been expected as a candidate for an engine of a reusable space shuttle to respond to growing demand for rocket-launching and its cost reduction. In this study, the flow field structures in any cross sections around clustered linear aerospike nozzles are visualized and analyzed, using laser induced fluorescence (LIF) of NO seeded in the carrier gas N2. Since flow field structures are affected mainly by pressure ratio (Ps/Pa, Ps: the source pressure in a reservoir, Pa: the ambient pressure in the vacuum chamber), the clustered linear aerospike nozzle is set inside a vacuum chamber to carry out the experiments in the wide range of pressure ratios from 75 to 200. Flow fields are visualized in several cross-sections, demonstrating the complicated three-dimensional flow field structures. Pressure sensitive paint (PSP) of PtTFPP bound by poly-IBM-co-TFEM is also applied to measurement of the complicated pressure distribution on the spike surface, and to verification of contribution of a truncation plane to the thrust. Finally, to examine the effect of the sidewalls attached to the aerospike nozzle, the flow fields around the nozzle with the sidewalls are compared with those without sidewalls.

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

PubMed Central

Brunton, Steven L.; Brunton, Bingni W.; Proctor, Joshua L.; Kutz, J. Nathan

2016-01-01

In 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. PMID:26919740

On the optimal systems of subalgebras for the equations of hydrodynamic stability analysis of smooth shear flows and their group-invariant solutions

NASA Astrophysics Data System (ADS)

Hau, Jan-Niklas; Oberlack, Martin; Chagelishvili, George

2017-04-01

We present a unifying solution framework for the linearized compressible equations for two-dimensional linearly sheared unbounded flows using the Lie symmetry analysis. The full set of symmetries that are admitted by the underlying system of equations is employed to systematically derive the one- and two-dimensional optimal systems of subalgebras, whose connected group reductions lead to three distinct invariant ansatz functions for the governing sets of partial differential equations (PDEs). The purpose of this analysis is threefold and explicitly we show that (i) there are three invariant solutions that stem from the optimal system. These include a general ansatz function with two free parameters, as well as the ansatz functions of the Kelvin mode and the modal approach. Specifically, the first approach unifies these well-known ansatz functions. By considering two limiting cases of the free parameters and related algebraic transformations, the general ansatz function is reduced to either of them. This fact also proves the existence of a link between the Kelvin mode and modal ansatz functions, as these appear to be the limiting cases of the general one. (ii) The Lie algebra associated with the Lie group admitted by the PDEs governing the compressible dynamics is a subalgebra associated with the group admitted by the equations governing the incompressible dynamics, which allows an additional (scaling) symmetry. Hence, any consequences drawn from the compressible case equally hold for the incompressible counterpart. (iii) In any of the systems of ordinary differential equations, derived by the three ansatz functions in the compressible case, the linearized potential vorticity is a conserved quantity that allows us to analyze vortex and wave mode perturbations separately.

Survival dimensionality reduction (SDR): development and clinical application of an innovative approach to detect epistasis in presence of right-censored data.

PubMed

Beretta, Lorenzo; Santaniello, Alessandro; van Riel, Piet L C M; Coenen, Marieke J H; Scorza, Raffaella

2010-08-06

Epistasis is recognized as a fundamental part of the genetic architecture of individuals. Several computational approaches have been developed to model gene-gene interactions in case-control studies, however, none of them is suitable for time-dependent analysis. Herein we introduce the Survival Dimensionality Reduction (SDR) algorithm, a non-parametric method specifically designed to detect epistasis in lifetime datasets. The algorithm requires neither specification about the underlying survival distribution nor about the underlying interaction model and proved satisfactorily powerful to detect a set of causative genes in synthetic epistatic lifetime datasets with a limited number of samples and high degree of right-censorship (up to 70%). The SDR method was then applied to a series of 386 Dutch patients with active rheumatoid arthritis that were treated with anti-TNF biological agents. Among a set of 39 candidate genes, none of which showed a detectable marginal effect on anti-TNF responses, the SDR algorithm did find that the rs1801274 SNP in the Fc gamma RIIa gene and the rs10954213 SNP in the IRF5 gene non-linearly interact to predict clinical remission after anti-TNF biologicals. Simulation studies and application in a real-world setting support the capability of the SDR algorithm to model epistatic interactions in candidate-genes studies in presence of right-censored data. http://sourceforge.net/projects/sdrproject/.

Stress optimization of leaf-spring crossed flexure pivots for an active Gurney flap mechanism

NASA Astrophysics Data System (ADS)

Freire Gómez, Jon; Booker, Julian D.; Mellor, Phil H.

2015-04-01

The EU's Green Rotorcraft programme is pursuing the development of a functional and airworthy Active Gurney Flap (AGF) for a full-scale helicopter rotor blade. Interest in the development of this `smart adaptive rotor blade' technology lies in its potential to provide a number of aerodynamic benefits, which would in turn translate into a reduction in fuel consumption and noise levels. The AGF mechanism selected employs leaf-spring crossed flexure pivots. These provide important advantages over bearings as they are not susceptible to seizing and do not require maintenance (i.e. lubrication or cleaning). A baseline design of this mechanism was successfully tested both in a fatigue rig and in a 2D wind tunnel environment at flight-representative deployment schedules. For full validation, a flight test would also be required. However, the severity of the in-flight loading conditions would likely compromise the mechanical integrity of the pivots' leaf-springs in their current form. This paper investigates the scope for stress reduction through three-dimensional shape optimization of the leaf-springs of a generic crossed flexure pivot. To this end, a procedure combining a linear strain energy formulation, a parametric leaf-spring profile definition and a series of optimization algorithms is employed. The resulting optimized leaf-springs are proven to be not only independent of the angular rotation at which the pivot operates, but also linearly scalable to leaf-springs of any length, minimum thickness and width. Validated using non-linear finite element analysis, the results show very significant stress reductions relative to pivots with constant cross section leaf-springs, of up to as much as 30% for the specific pivot configuration employed in the AGF mechanism. It is concluded that shape optimization offers great potential for reducing stress in crossed flexure pivots and, consequently, for extending their fatigue life and/or rotational range.

The Linear Parameters and the Decoupling Matrix for Linearly Coupled Motion in 6 Dimensional Phase Space

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

Parzen, George

It will be shown that starting from a coordinate system where the 6 phase space coordinates are linearly coupled, one can go to a new coordinate system, where the motion is uncoupled, by means of a linear transformation. The original coupled coordinates and the new uncoupled coordinates are related by a 6 x 6 matrix, R. R will be called the decoupling matrix. It will be shown that of the 36 elements of the 6 x 6 decoupling matrix R, only 12 elements are independent. This may be contrasted with the results for motion in 4- dimensional phase space, wheremore » R has 4 independent elements. A set of equations is given from which the 12 elements of R can be computed from the one period transfer matrix. This set of equations also allows the linear parameters, the β i,α i, i = 1, 3, for the uncoupled coordinates, to be computed from the one period transfer matrix. An alternative procedure for computing the linear parameters,β i,α i, i = 1, 3, and the 12 independent elements of the decoupling matrix R is also given which depends on computing the eigenvectors of the one period transfer matrix. These results can be used in a tracking program, where the one period transfer matrix can be computed by multiplying the transfer matrices of all the elements in a period, to compute the linear parameters α i and β i, i = 1, 3, and the elements of the decoupling matrix R. The procedure presented here for studying coupled motion in 6-dimensional phase space can also be applied to coupled motion in 4-dimensional phase space, where it may be a useful alternative procedure to the procedure presented by Edwards and Teng. In particular, it gives a simpler programing procedure for computing the beta functions and the emittances for coupled motion in 4-dimensional phase space.« less

The linear parameters and the decoupling matrix for linearly coupled motion in 6 dimensional phase space. Informal report

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

Parzen, G.

It will be shown that starting from a coordinate system where the 6 phase space coordinates are linearly coupled, one can go to a new coordinate system, where the motion is uncoupled, by means of a linear transformation. The original coupled coordinates and the new uncoupled coordinates are related by a 6 {times} 6 matrix, R. R will be called the decoupling matrix. It will be shown that of the 36 elements of the 6 {times} 6 decoupling matrix R, only 12 elements are independent. This may be contrasted with the results for motion in 4-dimensional phase space, where Rmore » has 4 independent elements. A set of equations is given from which the 12 elements of R can be computed from the one period transfer matrix. This set of equations also allows the linear parameters, {beta}{sub i}, {alpha}{sub i} = 1, 3, for the uncoupled coordinates, to be computed from the one period transfer matrix. An alternative procedure for computing the linear parameters, the {beta}{sub i}, {alpha}{sub i} i = 1, 3, and the 12 independent elements of the decoupling matrix R is also given which depends on computing the eigenvectors of the one period transfer matrix. These results can be used in a tracking program, where the one period transfer matrix can be computed by multiplying the transfer matrices of all the elements in a period, to compute the linear parameters {alpha}{sub i} and {beta}{sub i}, i = 1, 3, and the elements of the decoupling matrix R. The procedure presented here for studying coupled motion in 6-dimensional phase space can also be applied to coupled motion in 4-dimensional phase space, where it may be a useful alternative procedure to the procedure presented by Edwards and Teng. In particular, it gives a simpler programming procedure for computing the beta functions and the emittances for coupled motion in 4-dimensional phase space.« less

On the modeling of the bottom particles segregation with non-linear diffusion equations: application to the marine sand ripples

NASA Astrophysics Data System (ADS)

Tiguercha, Djlalli; Bennis, Anne-claire; Ezersky, Alexander

2015-04-01

The elliptical motion in surface waves causes an oscillating motion of the sand grains leading to the formation of ripple patterns on the bottom. Investigation how the grains with different properties are distributed inside the ripples is a difficult task because of the segration of particle. The work of Fernandez et al. (2003) was extended from one-dimensional to two-dimensional case. A new numerical model, based on these non-linear diffusion equations, was developed to simulate the grain distribution inside the marine sand ripples. The one and two-dimensional models are validated on several test cases where segregation appears. Starting from an homogeneous mixture of grains, the two-dimensional simulations demonstrate different segregation patterns: a) formation of zones with high concentration of light and heavy particles, b) formation of «cat's eye» patterns, c) appearance of inverse Brazil nut effect. Comparisons of numerical results with the new set of field data and wave flume experiments show that the two-dimensional non-linear diffusion equations allow us to reproduce qualitatively experimental results on particles segregation.

Tensor Train Neighborhood Preserving Embedding

NASA Astrophysics Data System (ADS)

Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin

2018-05-01

In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior trade-off in classification, computation, and dimensionality reduction in MNIST handwritten digits and Weizmann face datasets.

Kaluza-Klein cosmology from five-dimensional Lovelock-Cartan theory

NASA Astrophysics Data System (ADS)

Castillo-Felisola, Oscar; Corral, Cristóbal; del Pino, Simón; Ramírez, Francisca

2016-12-01

We study the Kaluza-Klein dimensional reduction of the Lovelock-Cartan theory in five-dimensional spacetime, with a compact dimension of S1 topology. We find cosmological solutions of the Friedmann-Robertson-Walker class in the reduced spacetime. The torsion and the fields arising from the dimensional reduction induce a nonvanishing energy-momentum tensor in four dimensions. We find solutions describing expanding, contracting, and bouncing universes. The model shows a dynamical compactification of the extra dimension in some regions of the parameter space.

Microwave imaging by three-dimensional Born linearization of electromagnetic scattering

NASA Astrophysics Data System (ADS)

Caorsi, S.; Gragnani, G. L.; Pastorino, M.

1990-11-01

An approach to microwave imaging is proposed that uses a three-dimensional vectorial form of the Born approximation to linearize the equation of electromagnetic scattering. The inverse scattering problem is numerically solved for three-dimensional geometries by means of the moment method. A pseudoinversion algorithm is adopted to overcome ill conditioning. Results show that the method is well suited for qualitative imaging purposes, while its capability for exactly reconstructing the complex dielectric permittivity is affected by the limitations inherent in the Born approximation and in ill conditioning.

Finite-dimensional linear approximations of solutions to general irregular nonlinear operator equations and equations with quadratic operators

NASA Astrophysics Data System (ADS)

Kokurin, M. Yu.

2010-11-01

A general scheme for improving approximate solutions to irregular nonlinear operator equations in Hilbert spaces is proposed and analyzed in the presence of errors. A modification of this scheme designed for equations with quadratic operators is also examined. The technique of universal linear approximations of irregular equations is combined with the projection onto finite-dimensional subspaces of a special form. It is shown that, for finite-dimensional quadratic problems, the proposed scheme provides information about the global geometric properties of the intersections of quadrics.

Recent Developments In Theory Of Balanced Linear Systems

NASA Technical Reports Server (NTRS)

Gawronski, Wodek

1994-01-01

Report presents theoretical study of some issues of controllability and observability of system represented by linear, time-invariant mathematical model of the form. x = Ax + Bu, y = Cx + Du, x(0) = xo where x is n-dimensional vector representing state of system; u is p-dimensional vector representing control input to system; y is q-dimensional vector representing output of system; n,p, and q are integers; x(0) is intial (zero-time) state vector; and set of matrices (A,B,C,D) said to constitute state-space representation of system.

Five-dimensional Myers-Perry black holes cannot be overspun in gedanken experiments

NASA Astrophysics Data System (ADS)

An, Jincheng; Shan, Jieru; Zhang, Hongbao; Zhao, Suting

2018-05-01

We apply the new version of a gedanken experiment designed recently by Sorce and Wald to overspin the five-dimensional Myers-Perry black holes. As a result, the extremal black holes cannot be overspun at the linear order. On the other hand, although the nearly extremal black holes could be overspun at the linear order, this process is shown to be prohibited by the quadratic order correction. Thus, no violation of the weak cosmic censorship conjecture occurs around the five-dimensional Myers-Perry black holes.

Sparse partial least squares regression for simultaneous dimension reduction and variable selection

PubMed Central

Chun, Hyonho; Keleş, Sündüz

2010-01-01

Partial least squares regression has been an alternative to ordinary least squares for handling multicollinearity in several areas of scientific research since the 1960s. It has recently gained much attention in the analysis of high dimensional genomic data. We show that known asymptotic consistency of the partial least squares estimator for a univariate response does not hold with the very large p and small n paradigm. We derive a similar result for a multivariate response regression with partial least squares. We then propose a sparse partial least squares formulation which aims simultaneously to achieve good predictive performance and variable selection by producing sparse linear combinations of the original predictors. We provide an efficient implementation of sparse partial least squares regression and compare it with well-known variable selection and dimension reduction approaches via simulation experiments. We illustrate the practical utility of sparse partial least squares regression in a joint analysis of gene expression and genomewide binding data. PMID:20107611

Finite element analysis of the end notched flexure specimen for measuring Mode II fracture toughness

NASA Technical Reports Server (NTRS)

Gillespie, J. W., Jr.; Carlsson, L. A.; Pipes, R. B.

1986-01-01

The paper presents a finite element analysis of the end-notched flexure (ENF) test specimen for Mode II interlaminar fracture testing of composite materials. Virtual crack closure and compliance techniques employed to calculate strain energy release rates from linear elastic two-dimensional analysis indicate that the ENF specimen is a pure Mode II fracture test within the constraints of small deflection theory. Furthermore, the ENF fracture specimen is shown to be relatively insensitive to process-induced cracks, offset from the laminate midplane. Frictional effects are investigated by including the contact problem in the finite element model. A parametric study investigating the influence of delamination length, span, thickness, and material properties assessed the accuracy of beam theory expressions for compliance and strain energy release rate, GII. Finite element results indicate that data reduction schemes based upon beam theory underestimate GII by approximately 20-40 percent for typical unidirectional graphite fiber composite test specimen geometries. Consequently, an improved data reduction scheme is proposed.

The effect of thermal reduction on the photoluminescence and electronic structures of graphene oxides.

PubMed

Chuang, C-H; Wang, Y-F; Shao, Y-C; Yeh, Y-C; Wang, D-Y; Chen, C-W; Chiou, J W; Ray, Sekhar C; Pong, W F; Zhang, L; Zhu, J F; Guo, J H

2014-04-10

Electronic structures of graphene oxide (GO) and hydro-thermally reduced graphene oxides (rGOs) processed at low temperatures (120-180°C) were studied using X-ray absorption near-edge structure (XANES), X-ray emission spectroscopy (XES) and resonant inelastic X-ray scattering (RIXS). C K-edge XANES spectra of rGOs reveal that thermal reduction restores C = C sp(2) bonds and removes some of the oxygen and hydroxyl groups of GO, which initiates the evolution of carbonaceous species. The combination of C K-edge XANES and Kα XES spectra shows that the overlapping π and π* orbitals in rGOs and GO are similar to that of highly ordered pyrolytic graphite (HOPG), which has no band-gap. C Kα RIXS spectra provide evidence that thermal reduction changes the density of states (DOSs) that is generated in the π-region and/or in the gap between the π and π* levels of the GO and rGOs. Two-dimensional C Kα RIXS mapping of the heavy reduction of rGOs further confirms that the residual oxygen and/or oxygen-containing functional groups modify the π and σ features, which are dispersed by the photon excitation energy. The dispersion behavior near the K point is approximately linear and differs from the parabolic-like dispersion observed in HOPG.

Semisupervised kernel marginal Fisher analysis for face recognition.

PubMed

Wang, Ziqiang; Sun, Xia; Sun, Lijun; Huang, Yuchun

2013-01-01

Dimensionality reduction is a key problem in face recognition due to the high-dimensionality of face image. To effectively cope with this problem, a novel dimensionality reduction algorithm called semisupervised kernel marginal Fisher analysis (SKMFA) for face recognition is proposed in this paper. SKMFA can make use of both labelled and unlabeled samples to learn the projection matrix for nonlinear dimensionality reduction. Meanwhile, it can successfully avoid the singularity problem by not calculating the matrix inverse. In addition, in order to make the nonlinear structure captured by the data-dependent kernel consistent with the intrinsic manifold structure, a manifold adaptive nonparameter kernel is incorporated into the learning process of SKMFA. Experimental results on three face image databases demonstrate the effectiveness of our proposed algorithm.

A Three-Dimensional Linearized Unsteady Euler Analysis for Turbomachinery Blade Rows

NASA Technical Reports Server (NTRS)

Montgomery, Matthew D.; Verdon, Joseph M.

1996-01-01

A three-dimensional, linearized, Euler analysis is being developed to provide an efficient unsteady aerodynamic analysis that can be used to predict the aeroelastic and aeroacoustic response characteristics of axial-flow turbomachinery blading. The field equations and boundary conditions needed to describe nonlinear and linearized inviscid unsteady flows through a blade row operating within a cylindrical annular duct are presented. In addition, a numerical model for linearized inviscid unsteady flow, which is based upon an existing nonlinear, implicit, wave-split, finite volume analysis, is described. These aerodynamic and numerical models have been implemented into an unsteady flow code, called LINFLUX. A preliminary version of the LINFLUX code is applied herein to selected, benchmark three-dimensional, subsonic, unsteady flows, to illustrate its current capabilities and to uncover existing problems and deficiencies. The numerical results indicate that good progress has been made toward developing a reliable and useful three-dimensional prediction capability. However, some problems, associated with the implementation of an unsteady displacement field and numerical errors near solid boundaries, still exist. Also, accurate far-field conditions must be incorporated into the FINFLUX analysis, so that this analysis can be applied to unsteady flows driven be external aerodynamic excitations.

Data-driven discovery of Koopman eigenfunctions using deep learning

NASA Astrophysics Data System (ADS)

Lusch, Bethany; Brunton, Steven L.; Kutz, J. Nathan

2017-11-01

Koopman operator theory transforms any autonomous non-linear dynamical system into an infinite-dimensional linear system. Since linear systems are well-understood, a mapping of non-linear dynamics to linear dynamics provides a powerful approach to understanding and controlling fluid flows. However, finding the correct change of variables remains an open challenge. We present a strategy to discover an approximate mapping using deep learning. Our neural networks find this change of variables, its inverse, and a finite-dimensional linear dynamical system defined on the new variables. Our method is completely data-driven and only requires measurements of the system, i.e. it does not require derivatives or knowledge of the governing equations. We find a minimal set of approximate Koopman eigenfunctions that are sufficient to reconstruct and advance the system to future states. We demonstrate the method on several dynamical systems.

Maxillary reaction patterns identified by three-dimensional analysis of casts from infants with unilateral cleft lip and palate.

PubMed

Neuschulz, J; Schaefer, I; Scheer, M; Christ, H; Braumann, B

2013-07-01

In order to visualize and quantify the direction and extent of morphological upper-jaw changes in infants with unilateral cleft lip and palate (UCLP) during early orthodontic treatment, a three-dimensional method of cast analysis for routine application was developed. In the present investigation, this method was used to identify reaction patterns associated with specific cleft forms. The study included a cast series reflecting the upper-jaw situations of 46 infants with complete (n=27) or incomplete (n=19) UCLP during week 1 and months 3, 6, and 12 of life. Three-dimensional datasets were acquired and visualized with scanning software (DigiModel®; OrthoProof, The Netherlands). Following interactive identification of landmarks on the digitized surface relief, a defined set of representative linear parameters were three-dimensionally measured. At the same time, the three-dimensional surfaces of one patient series were superimposed based on a defined reference plane. Morphometric differences were statistically analyzed. Thanks to the user-friendly software, all landmarks could be identified quickly and reproducibly, thus, allowing for simultaneous three-dimensional measurement of all defined parameters. The measured values revealed that significant morphometric differences were present in all three planes of space between the two patient groups. Patients with complete UCLP underwent significantly larger reductions in cleft width (p<0.001), and sagittal growth in the complete UCLP group exceeded sagittal growth in the incomplete UCLP group by almost 50% within the first year of life. Based on patients with incomplete versus complete UCLP, different reaction patterns were identified that depended not on apparent severities of malformation but on cleft forms.

LFSPMC: Linear feature selection program using the probability of misclassification

NASA Technical Reports Server (NTRS)

Guseman, L. F., Jr.; Marion, B. P.

1975-01-01

The computational procedure and associated computer program for a linear feature selection technique are presented. The technique assumes that: a finite number, m, of classes exists; each class is described by an n-dimensional multivariate normal density function of its measurement vectors; the mean vector and covariance matrix for each density function are known (or can be estimated); and the a priori probability for each class is known. The technique produces a single linear combination of the original measurements which minimizes the one-dimensional probability of misclassification defined by the transformed densities.

Robust L1-norm two-dimensional linear discriminant analysis.

PubMed

Li, Chun-Na; Shao, Yuan-Hai; Deng, Nai-Yang

2015-05-01

In this paper, we propose an L1-norm two-dimensional linear discriminant analysis (L1-2DLDA) with robust performance. Different from the conventional two-dimensional linear discriminant analysis with L2-norm (L2-2DLDA), where the optimization problem is transferred to a generalized eigenvalue problem, the optimization problem in our L1-2DLDA is solved by a simple justifiable iterative technique, and its convergence is guaranteed. Compared with L2-2DLDA, our L1-2DLDA is more robust to outliers and noises since the L1-norm is used. This is supported by our preliminary experiments on toy example and face datasets, which show the improvement of our L1-2DLDA over L2-2DLDA. Copyright © 2015 Elsevier Ltd. All rights reserved.

A two-stage linear discriminant analysis via QR-decomposition.

PubMed

Ye, Jieping; Li, Qi

2005-06-01

Linear Discriminant Analysis (LDA) is a well-known method for feature extraction and dimension reduction. It has been used widely in many applications involving high-dimensional data, such as image and text classification. An intrinsic limitation of classical LDA is the so-called singularity problems; that is, it fails when all scatter matrices are singular. Many LDA extensions were proposed in the past to overcome the singularity problems. Among these extensions, PCA+LDA, a two-stage method, received relatively more attention. In PCA+LDA, the LDA stage is preceded by an intermediate dimension reduction stage using Principal Component Analysis (PCA). Most previous LDA extensions are computationally expensive, and not scalable, due to the use of Singular Value Decomposition or Generalized Singular Value Decomposition. In this paper, we propose a two-stage LDA method, namely LDA/QR, which aims to overcome the singularity problems of classical LDA, while achieving efficiency and scalability simultaneously. The key difference between LDA/QR and PCA+LDA lies in the first stage, where LDA/QR applies QR decomposition to a small matrix involving the class centroids, while PCA+LDA applies PCA to the total scatter matrix involving all training data points. We further justify the proposed algorithm by showing the relationship among LDA/QR and previous LDA methods. Extensive experiments on face images and text documents are presented to show the effectiveness of the proposed algorithm.

A Two-Dimensional Linear Bicharacteristic Scheme for Electromagnetics

NASA Technical Reports Server (NTRS)

Beggs, John H.

2002-01-01

The upwind leapfrog or Linear Bicharacteristic Scheme (LBS) has previously been implemented and demonstrated on one-dimensional electromagnetic wave propagation problems. This memorandum extends the Linear Bicharacteristic Scheme for computational electromagnetics to model lossy dielectric and magnetic materials and perfect electrical conductors in two dimensions. This is accomplished by proper implementation of the LBS for homogeneous lossy dielectric and magnetic media and for perfect electrical conductors. Both the Transverse Electric and Transverse Magnetic polarizations are considered. Computational requirements and a Fourier analysis are also discussed. Heterogeneous media are modeled through implementation of surface boundary conditions and no special extrapolations or interpolations at dielectric material boundaries are required. Results are presented for two-dimensional model problems on uniform grids, and the Finite Difference Time Domain (FDTD) algorithm is chosen as a convenient reference algorithm for comparison. The results demonstrate that the two-dimensional explicit LBS is a dissipation-free, second-order accurate algorithm which uses a smaller stencil than the FDTD algorithm, yet it has less phase velocity error.

Visual exploration of high-dimensional data through subspace analysis and dynamic projections

DOE PAGES

Liu, S.; Wang, B.; Thiagarajan, J. J.; ...

2015-06-01

Here, we introduce a novel interactive framework for visualizing and exploring high-dimensional datasets based on subspace analysis and dynamic projections. We assume the high-dimensional dataset can be represented by a mixture of low-dimensional linear subspaces with mixed dimensions, and provide a method to reliably estimate the intrinsic dimension and linear basis of each subspace extracted from the subspace clustering. Subsequently, we use these bases to define unique 2D linear projections as viewpoints from which to visualize the data. To understand the relationships among the different projections and to discover hidden patterns, we connect these projections through dynamic projections that createmore » smooth animated transitions between pairs of projections. We introduce the view transition graph, which provides flexible navigation among these projections to facilitate an intuitive exploration. Finally, we provide detailed comparisons with related systems, and use real-world examples to demonstrate the novelty and usability of our proposed framework.« less

Visual Exploration of High-Dimensional Data through Subspace Analysis and Dynamic Projections

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

Liu, S.; Wang, B.; Thiagarajan, Jayaraman J.

2015-06-01

We introduce a novel interactive framework for visualizing and exploring high-dimensional datasets based on subspace analysis and dynamic projections. We assume the high-dimensional dataset can be represented by a mixture of low-dimensional linear subspaces with mixed dimensions, and provide a method to reliably estimate the intrinsic dimension and linear basis of each subspace extracted from the subspace clustering. Subsequently, we use these bases to define unique 2D linear projections as viewpoints from which to visualize the data. To understand the relationships among the different projections and to discover hidden patterns, we connect these projections through dynamic projections that create smoothmore » animated transitions between pairs of projections. We introduce the view transition graph, which provides flexible navigation among these projections to facilitate an intuitive exploration. Finally, we provide detailed comparisons with related systems, and use real-world examples to demonstrate the novelty and usability of our proposed framework.« less

Comparing and improving proper orthogonal decomposition (POD) to reduce the complexity of groundwater models

NASA Astrophysics Data System (ADS)

Gosses, Moritz; Nowak, Wolfgang; Wöhling, Thomas

2017-04-01

Physically-based modeling is a wide-spread tool in understanding and management of natural systems. With the high complexity of many such models and the huge amount of model runs necessary for parameter estimation and uncertainty analysis, overall run times can be prohibitively long even on modern computer systems. An encouraging strategy to tackle this problem are model reduction methods. In this contribution, we compare different proper orthogonal decomposition (POD, Siade et al. (2010)) methods and their potential applications to groundwater models. The POD method performs a singular value decomposition on system states as simulated by the complex (e.g., PDE-based) groundwater model taken at several time-steps, so-called snapshots. The singular vectors with the highest information content resulting from this decomposition are then used as a basis for projection of the system of model equations onto a subspace of much lower dimensionality than the original complex model, thereby greatly reducing complexity and accelerating run times. In its original form, this method is only applicable to linear problems. Many real-world groundwater models are non-linear, tough. These non-linearities are introduced either through model structure (unconfined aquifers) or boundary conditions (certain Cauchy boundaries, like rivers with variable connection to the groundwater table). To date, applications of POD focused on groundwater models simulating pumping tests in confined aquifers with constant head boundaries. In contrast, POD model reduction either greatly looses accuracy or does not significantly reduce model run time if the above-mentioned non-linearities are introduced. We have also found that variable Dirichlet boundaries are problematic for POD model reduction. An extension to the POD method, called POD-DEIM, has been developed for non-linear groundwater models by Stanko et al. (2016). This method uses spatial interpolation points to build the equation system in the reduced model space, thereby allowing the recalculation of system matrices at every time-step necessary for non-linear models while retaining the speed of the reduced model. This makes POD-DEIM applicable for groundwater models simulating unconfined aquifers. However, in our analysis, the method struggled to reproduce variable river boundaries accurately and gave no advantage for variable Dirichlet boundaries compared to the original POD method. We have developed another extension for POD that targets to address these remaining problems by performing a second POD operation on the model matrix on the left-hand side of the equation. The method aims to at least reproduce the accuracy of the other methods where they are applicable while outperforming them for setups with changing river boundaries or variable Dirichlet boundaries. We compared the new extension with original POD and POD-DEIM for different combinations of model structures and boundary conditions. The new method shows the potential of POD extensions for applications to non-linear groundwater systems and complex boundary conditions that go beyond the current, relatively limited range of applications. References: Siade, A. J., Putti, M., and Yeh, W. W.-G. (2010). Snapshot selection for groundwater model reduction using proper orthogonal decomposition. Water Resour. Res., 46(8):W08539. Stanko, Z. P., Boyce, S. E., and Yeh, W. W.-G. (2016). Nonlinear model reduction of unconfined groundwater flow using pod and deim. Advances in Water Resources, 97:130 - 143.

Score-level fusion of two-dimensional and three-dimensional palmprint for personal recognition systems

NASA Astrophysics Data System (ADS)

Chaa, Mourad; Boukezzoula, Naceur-Eddine; Attia, Abdelouahab

2017-01-01

Two types of scores extracted from two-dimensional (2-D) and three-dimensional (3-D) palmprint for personal recognition systems are merged, introducing a local image descriptor for 2-D palmprint-based recognition systems, named bank of binarized statistical image features (B-BSIF). The main idea of B-BSIF is that the extracted histograms from the binarized statistical image features (BSIF) code images (the results of applying the different BSIF descriptor size with the length 12) are concatenated into one to produce a large feature vector. 3-D palmprint contains the depth information of the palm surface. The self-quotient image (SQI) algorithm is applied for reconstructing illumination-invariant 3-D palmprint images. To extract discriminative Gabor features from SQI images, Gabor wavelets are defined and used. Indeed, the dimensionality reduction methods have shown their ability in biometrics systems. Given this, a principal component analysis (PCA)+linear discriminant analysis (LDA) technique is employed. For the matching process, the cosine Mahalanobis distance is applied. Extensive experiments were conducted on a 2-D and 3-D palmprint database with 10,400 range images from 260 individuals. Then, a comparison was made between the proposed algorithm and other existing methods in the literature. Results clearly show that the proposed framework provides a higher correct recognition rate. Furthermore, the best results were obtained by merging the score of B-BSIF descriptor with the score of the SQI+Gabor wavelets+PCA+LDA method, yielding an equal error rate of 0.00% and a recognition rate of rank-1=100.00%.

Offset-electrode profile acquisition strategy for electrical resistivity tomography

NASA Astrophysics Data System (ADS)

Robbins, Austin R.; Plattner, Alain

2018-04-01

We present an electrode layout strategy that allows electrical resistivity profiles to image the third dimension close to the profile plane. This "offset-electrode profile" approach involves laterally displacing electrodes away from the profile line in an alternating fashion and then inverting the resulting data using three-dimensional electrical resistivity tomography software. In our synthetic and field surveys, the offset-electrode method succeeds in revealing three-dimensional structures in the vicinity of the profile plane, which we could not achieve using three-dimensional inversions of linear profiles. We confirm and explain the limits of linear electrode profiles through a discussion of the three-dimensional sensitivity patterns: For a homogeneous starting model together with a linear electrode layout, all sensitivities remain symmetric with respect to the profile plane through each inversion step. This limitation can be overcome with offset-electrode layouts by breaking the symmetry pattern among the sensitivities. Thanks to freely available powerful three-dimensional resistivity tomography software and cheap modern computing power, the requirement for full three-dimensional calculations does not create a significant burden and renders the offset-electrode approach a cost-effective method. By offsetting the electrodes in an alternating pattern, as opposed to laying the profile out in a U-shape, we minimize shortening the profile length.

Prominent metallic surface conduction and the singular magnetic response of topological Dirac fermion in three-dimensional topological insulator Bi1.5Sb0.5Te1.7Se1.3.

PubMed

Dutta, Prithwish; Pariari, Arnab; Mandal, Prabhat

2017-07-07

We report semiconductor to metal-like crossover in the temperature dependence of resistivity (ρ) due to the switching of charge transport from bulk to surface channel in three-dimensional topological insulator Bi 1.5 Sb 0.5 Te 1.7 Se 1.3 . Unlike earlier studies, a much sharper drop in ρ(T) is observed below the crossover temperature due to the dominant surface conduction. Remarkably, the resistivity of the conducting surface channel follows a rarely observable T 2 dependence at low temperature, as predicted theoretically for a two-dimensional Fermi liquid system. The field dependence of magnetization shows a cusp-like paramagnetic peak in the susceptibility (χ) at zero field over the diamagnetic background. The peak is found to be robust against temperature and χ decays linearly with the field from its zero-field value. This unique behavior of the χ is associated with the spin-momentum locked topological surface state in Bi 1.5 Sb 0.5 Te 1.7 Se 1.3 . The reconstruction of the surface state with time is clearly reflected through the reduction of the peak height with the age of the sample.

Robust estimation for partially linear models with large-dimensional covariates

PubMed Central

Zhu, LiPing; Li, RunZe; Cui, HengJian

2014-01-01

We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon-cave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of o(n), where n is the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance. Comprehensive simulation studies are carried out and an application is presented to examine the finite-sample performance of the proposed procedures. PMID:24955087

Robust estimation for partially linear models with large-dimensional covariates.

PubMed

Zhu, LiPing; Li, RunZe; Cui, HengJian

2013-10-01

We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a noncon-cave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of [Formula: see text], where n is the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance. Comprehensive simulation studies are carried out and an application is presented to examine the finite-sample performance of the proposed procedures.

Chaotic oscillator containing memcapacitor and meminductor and its dimensionality reduction analysis.

PubMed

Yuan, Fang; Wang, Guangyi; Wang, Xiaowei

2017-03-01

In this paper, smooth curve models of meminductor and memcapacitor are designed, which are generalized from a memristor. Based on these models, a new five-dimensional chaotic oscillator that contains a meminductor and memcapacitor is proposed. By dimensionality reducing, this five-dimensional system can be transformed into a three-dimensional system. The main work of this paper is to give the comparisons between the five-dimensional system and its dimensionality reduction model. To investigate dynamics behaviors of the two systems, equilibrium points and stabilities are analyzed. And the bifurcation diagrams and Lyapunov exponent spectrums are used to explore their properties. In addition, digital signal processing technologies are used to realize this chaotic oscillator, and chaotic sequences are generated by the experimental device, which can be used in encryption applications.

Numerical simulation of Forchheimer flow to a partially penetrating well with a mixed-type boundary condition

NASA Astrophysics Data System (ADS)

Mathias, Simon A.; Wen, Zhang

2015-05-01

This article presents a numerical study to investigate the combined role of partial well penetration (PWP) and non-Darcy effects concerning the performance of groundwater production wells. A finite difference model is developed in MATLAB to solve the two-dimensional mixed-type boundary value problem associated with flow to a partially penetrating well within a cylindrical confined aquifer. Non-Darcy effects are incorporated using the Forchheimer equation. The model is verified by comparison to results from existing semi-analytical solutions concerning the same problem but assuming Darcy's law. A sensitivity analysis is presented to explore the problem of concern. For constant pressure production, Non-Darcy effects lead to a reduction in production rate, as compared to an equivalent problem solved using Darcy's law. For fully penetrating wells, this reduction in production rate becomes less significant with time. However, for partially penetrating wells, the reduction in production rate persists for much larger times. For constant production rate scenarios, the combined effect of PWP and non-Darcy flow takes the form of a constant additional drawdown term. An approximate solution for this loss term is obtained by performing linear regression on the modeling results.

GIXSGUI : a MATLAB toolbox for grazing-incidence X-ray scattering data visualization and reduction, and indexing of buried three-dimensional periodic nanostructured films

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

Jiang, Zhang

GIXSGUIis a MATLAB toolbox that offers both a graphical user interface and script-based access to visualize and process grazing-incidence X-ray scattering data from nanostructures on surfaces and in thin films. It provides routine surface scattering data reduction methods such as geometric correction, one-dimensional intensity linecut, two-dimensional intensity reshapingetc. Three-dimensional indexing is also implemented to determine the space group and lattice parameters of buried organized nanoscopic structures in supported thin films.

An accurate boundary element method for the exterior elastic scattering problem in two dimensions

NASA Astrophysics Data System (ADS)

Bao, Gang; Xu, Liwei; Yin, Tao

2017-11-01

This paper is concerned with a Galerkin boundary element method solving the two dimensional exterior elastic wave scattering problem. The original problem is first reduced to the so-called Burton-Miller [1] boundary integral formulation, and essential mathematical features of its variational form are discussed. In numerical implementations, a newly-derived and analytically accurate regularization formula [2] is employed for the numerical evaluation of hyper-singular boundary integral operator. A new computational approach is employed based on the series expansions of Hankel functions for the computation of weakly-singular boundary integral operators during the reduction of corresponding Galerkin equations into a discrete linear system. The effectiveness of proposed numerical methods is demonstrated using several numerical examples.

X-ray Raman scattering from molecules and solids in the framework of the Mahan-Nozières-De Dominicis model

NASA Astrophysics Data System (ADS)

Privalov, Timofei; Gel'mukhanov, Faris; Ågren, Hans

2001-10-01

We have developed a formulation of resonant x-ray Raman scattering of molecules and solids based on the Mahan-Nozières-De Dominicis model. A key step in the formulation is given by a reduction of the Keldysh-Dyson equations for the Green's function to a set of linear algebraic equations. This gave way for a tractable scheme that can be used to analyze the resonant x-ray scattering in the whole time domain. The formalism is used to investigate the role of core-hole relaxation, interference, band filling, detuning, and size of the scattering target. Numerical applications are performed with a one-dimensional tight-binding model.

Design and cost analysis of rapid aquifer restoration systems using flow simulation and quadratic programming.

USGS Publications Warehouse

Lefkoff, L.J.; Gorelick, S.M.

1986-01-01

Detailed two-dimensional flow simulation of a complex ground-water system is combined with quadratic and linear programming to evaluate design alternatives for rapid aquifer restoration. Results show how treatment and pumping costs depend dynamically on the type of treatment process, and capacity of pumping and injection wells, and the number of wells. The design for an inexpensive treatment process minimizes pumping costs, while an expensive process results in the minimization of treatment costs. Substantial reductions in pumping costs occur with increases in injection capacity or in the number of wells. Treatment costs are reduced by expansions in pumping capacity or injecion capacity. The analysis identifies maximum pumping and injection capacities.-from Authors

Optimization Design of Minimum Total Resistance Hull Form Based on CFD Method

NASA Astrophysics Data System (ADS)

Zhang, Bao-ji; Zhang, Sheng-long; Zhang, Hui

2018-06-01

In order to reduce the resistance and improve the hydrodynamic performance of a ship, two hull form design methods are proposed based on the potential flow theory and viscous flow theory. The flow fields are meshed using body-fitted mesh and structured grids. The parameters of the hull modification function are the design variables. A three-dimensional modeling method is used to alter the geometry. The Non-Linear Programming (NLP) method is utilized to optimize a David Taylor Model Basin (DTMB) model 5415 ship under the constraints, including the displacement constraint. The optimization results show an effective reduction of the resistance. The two hull form design methods developed in this study can provide technical support and theoretical basis for designing green ships.

Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations.

PubMed

Fu, Wei; Nijhoff, Frank W

2017-07-01

A unified framework is presented for the solution structure of three-dimensional discrete integrable systems, including the lattice AKP, BKP and CKP equations. This is done through the so-called direct linearizing transform, which establishes a general class of integral transforms between solutions. As a particular application, novel soliton-type solutions for the lattice CKP equation are obtained.

Statistical Signal Models and Algorithms for Image Analysis

DTIC Science & Technology

1984-10-25

In this report, two-dimensional stochastic linear models are used in developing algorithms for image analysis such as classification, segmentation, and object detection in images characterized by textured backgrounds. These models generate two-dimensional random processes as outputs to which statistical inference procedures can naturally be applied. A common thread throughout our algorithms is the interpretation of the inference procedures in terms of linear prediction

Unsteady transonic flows - Introduction, current trends, applications

NASA Technical Reports Server (NTRS)

Yates, E. C., Jr.

1985-01-01

The computational treatment of unsteady transonic flows is discussed, reviewing the historical development and current techniques. The fundamental physical principles are outlined; the governing equations are introduced; three-dimensional linearized and two-dimensional linear-perturbation theories in frequency domain are described in detail; and consideration is given to frequency-domain FEMs and time-domain finite-difference and integral-equation methods. Extensive graphs and diagrams are included.

A coarse-grid projection method for accelerating incompressible flow computations

NASA Astrophysics Data System (ADS)

San, Omer; Staples, Anne E.

2013-01-01

We present a coarse-grid projection (CGP) method for accelerating incompressible flow computations, which is applicable to methods involving Poisson equations as incompressibility constraints. The CGP methodology is a modular approach that facilitates data transfer with simple interpolations and uses black-box solvers for the Poisson and advection-diffusion equations in the flow solver. After solving the Poisson equation on a coarsened grid, an interpolation scheme is used to obtain the fine data for subsequent time stepping on the full grid. A particular version of the method is applied here to the vorticity-stream function, primitive variable, and vorticity-velocity formulations of incompressible Navier-Stokes equations. We compute several benchmark flow problems on two-dimensional Cartesian and non-Cartesian grids, as well as a three-dimensional flow problem. The method is found to accelerate these computations while retaining a level of accuracy close to that of the fine resolution field, which is significantly better than the accuracy obtained for a similar computation performed solely using a coarse grid. A linear acceleration rate is obtained for all the cases we consider due to the linear-cost elliptic Poisson solver used, with reduction factors in computational time between 2 and 42. The computational savings are larger when a suboptimal Poisson solver is used. We also find that the computational savings increase with increasing distortion ratio on non-Cartesian grids, making the CGP method a useful tool for accelerating generalized curvilinear incompressible flow solvers.

Two component-three dimensional catalysis

DOEpatents

Schwartz, Michael; White, James H.; Sammells, Anthony F.

2002-01-01

This invention relates to catalytic reactor membranes having a gas-impermeable membrane for transport of oxygen anions. The membrane has an oxidation surface and a reduction surface. The membrane is coated on its oxidation surface with an adherent catalyst layer and is optionally coated on its reduction surface with a catalyst that promotes reduction of an oxygen-containing species (e.g., O.sub.2, NO.sub.2, SO.sub.2, etc.) to generate oxygen anions on the membrane. The reactor has an oxidation zone and a reduction zone separated by the membrane. A component of an oxygen containing gas in the reduction zone is reduced at the membrane and a reduced species in a reactant gas in the oxidation zone of the reactor is oxidized. The reactor optionally contains a three-dimensional catalyst in the oxidation zone. The adherent catalyst layer and the three-dimensional catalyst are selected to promote a desired oxidation reaction, particularly a partial oxidation of a hydrocarbon.

Variable importance in nonlinear kernels (VINK): classification of digitized histopathology.

PubMed

Ginsburg, Shoshana; Ali, Sahirzeeshan; Lee, George; Basavanhally, Ajay; Madabhushi, Anant

2013-01-01

Quantitative histomorphometry is the process of modeling appearance of disease morphology on digitized histopathology images via image-based features (e.g., texture, graphs). Due to the curse of dimensionality, building classifiers with large numbers of features requires feature selection (which may require a large training set) or dimensionality reduction (DR). DR methods map the original high-dimensional features in terms of eigenvectors and eigenvalues, which limits the potential for feature transparency or interpretability. Although methods exist for variable selection and ranking on embeddings obtained via linear DR schemes (e.g., principal components analysis (PCA)), similar methods do not yet exist for nonlinear DR (NLDR) methods. In this work we present a simple yet elegant method for approximating the mapping between the data in the original feature space and the transformed data in the kernel PCA (KPCA) embedding space; this mapping provides the basis for quantification of variable importance in nonlinear kernels (VINK). We show how VINK can be implemented in conjunction with the popular Isomap and Laplacian eigenmap algorithms. VINK is evaluated in the contexts of three different problems in digital pathology: (1) predicting five year PSA failure following radical prostatectomy, (2) predicting Oncotype DX recurrence risk scores for ER+ breast cancers, and (3) distinguishing good and poor outcome p16+ oropharyngeal tumors. We demonstrate that subsets of features identified by VINK provide similar or better classification or regression performance compared to the original high dimensional feature sets.

Assessment of placental volume and vascularization at 11-14 weeks of gestation in a Taiwanese population using three-dimensional power Doppler ultrasound.

PubMed

Wang, Hsing-I; Yang, Ming-Jie; Wang, Peng-Hui; Wu, Yi-Cheng; Chen, Chih-Yao

2014-12-01

The placental volume and vascular indices are crucial in helping doctors to evaluate early fetal growth and development. Inadequate placental volume or vascularity might indicate poor fetal growth or gestational complications. This study aimed to evaluate the placental volume and vascular indices during the period of 11-14 weeks of gestation in a Taiwanese population. From June 2006 to September 2009, three-dimensional power Doppler ultrasound was performed in 222 normal pregnancies from 11-14 weeks of gestation. Power Doppler ultrasound was applied to the placenta and the placental volume was obtained by a rotational technique (VOCAL). The three-dimensional power histogram was used to assess the placental vascular indices, including the mean gray value, the vascularization index, the flow index, and the vascularization flow index. The placental vascular indices were then plotted against gestational age (GA) and placental volume. Our results showed that the linear regression equation for placental volume using gestational week as the independent variable was placental volume = 18.852 × GA - 180.89 (r = 0.481, p < 0.05). All the placental vascular indices showed a constant distribution throughout the period 11-14 weeks of gestation. A tendency for a reduction in the placental mean gray value with gestational week was observed, but without statistical significance. All the placental vascular indices estimated by three-dimensional power Doppler ultrasonography showed a constant distribution throughout gestation. Copyright © 2014. Published by Elsevier Taiwan.

Reduced order surrogate modelling (ROSM) of high dimensional deterministic simulations

NASA Astrophysics Data System (ADS)

Mitry, Mina

Often, computationally expensive engineering simulations can prohibit the engineering design process. As a result, designers may turn to a less computationally demanding approximate, or surrogate, model to facilitate their design process. However, owing to the the curse of dimensionality, classical surrogate models become too computationally expensive for high dimensional data. To address this limitation of classical methods, we develop linear and non-linear Reduced Order Surrogate Modelling (ROSM) techniques. Two algorithms are presented, which are based on a combination of linear/kernel principal component analysis and radial basis functions. These algorithms are applied to subsonic and transonic aerodynamic data, as well as a model for a chemical spill in a channel. The results of this thesis show that ROSM can provide a significant computational benefit over classical surrogate modelling, sometimes at the expense of a minor loss in accuracy.

A new randomized Kaczmarz based kernel canonical correlation analysis algorithm with applications to information retrieval.

PubMed

Cai, Jia; Tang, Yi

2018-02-01

Canonical correlation analysis (CCA) is a powerful statistical tool for detecting the linear relationship between two sets of multivariate variables. Kernel generalization of it, namely, kernel CCA is proposed to describe nonlinear relationship between two variables. Although kernel CCA can achieve dimensionality reduction results for high-dimensional data feature selection problem, it also yields the so called over-fitting phenomenon. In this paper, we consider a new kernel CCA algorithm via randomized Kaczmarz method. The main contributions of the paper are: (1) A new kernel CCA algorithm is developed, (2) theoretical convergence of the proposed algorithm is addressed by means of scaled condition number, (3) a lower bound which addresses the minimum number of iterations is presented. We test on both synthetic dataset and several real-world datasets in cross-language document retrieval and content-based image retrieval to demonstrate the effectiveness of the proposed algorithm. Numerical results imply the performance and efficiency of the new algorithm, which is competitive with several state-of-the-art kernel CCA methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

Functionalized graphene oxide for clinical glucose biosensing in urine and serum samples

PubMed Central

Veerapandian, Murugan; Seo, Yeong-Tai; Shin, Hyunkyung; Yun, Kyusik; Lee, Min-Ho

2012-01-01

A novel clinical glucose biosensor fabricated using functionalized metalloid-polymer (silver-silica coated with polyethylene glycol) hybrid nanoparticles on the surface of a graphene oxide nanosheet is reported. The cyclic voltammetric response of glucose oxidase modification on the surface of a functionalized graphene oxide electrode showed a surface-confined reaction and an effective redox potential near zero volts, with a wide linearity of 0.1–20 mM and a sensitivity of 7.66 μA mM−1 cm−2. The functionalized graphene oxide electrode showed a better electrocatalytic response toward oxidation of H2O2 and reduction of oxygen. The practical applicability of the functionalized graphene oxide electrode was demonstrated by measuring the peak current against multiple urine and serum samples from diabetic patients. This new hybrid nanoarchitecture combining a three-dimensional metalloid-polymer hybrid and two-dimensional graphene oxide provided a thin solid laminate on the electrode surface. The easy fabrication process and retention of bioactive immobilized enzymes on the functionalized graphene oxide electrode could potentially be extended to detection of other biomolecules, and have broad applications in electrochemical biosensing. PMID:23269871

Functionalized graphene oxide for clinical glucose biosensing in urine and serum samples.

PubMed

Veerapandian, Murugan; Seo, Yeong-Tai; Shin, Hyunkyung; Yun, Kyusik; Lee, Min-Ho

2012-01-01

A novel clinical glucose biosensor fabricated using functionalized metalloid-polymer (silver-silica coated with polyethylene glycol) hybrid nanoparticles on the surface of a graphene oxide nanosheet is reported. The cyclic voltammetric response of glucose oxidase modification on the surface of a functionalized graphene oxide electrode showed a surface-confined reaction and an effective redox potential near zero volts, with a wide linearity of 0.1-20 mM and a sensitivity of 7.66 μA mM(-1) cm(-2). The functionalized graphene oxide electrode showed a better electrocatalytic response toward oxidation of H(2)O(2) and reduction of oxygen. The practical applicability of the functionalized graphene oxide electrode was demonstrated by measuring the peak current against multiple urine and serum samples from diabetic patients. This new hybrid nanoarchitecture combining a three-dimensional metalloid-polymer hybrid and two-dimensional graphene oxide provided a thin solid laminate on the electrode surface. The easy fabrication process and retention of bioactive immobilized enzymes on the functionalized graphene oxide electrode could potentially be extended to detection of other biomolecules, and have broad applications in electrochemical biosensing.

Protein Sub-Nuclear Localization Based on Effective Fusion Representations and Dimension Reduction Algorithm LDA.

PubMed

Wang, Shunfang; Liu, Shuhui

2015-12-19

An effective representation of a protein sequence plays a crucial role in protein sub-nuclear localization. The existing representations, such as dipeptide composition (DipC), pseudo-amino acid composition (PseAAC) and position specific scoring matrix (PSSM), are insufficient to represent protein sequence due to their single perspectives. Thus, this paper proposes two fusion feature representations of DipPSSM and PseAAPSSM to integrate PSSM with DipC and PseAAC, respectively. When constructing each fusion representation, we introduce the balance factors to value the importance of its components. The optimal values of the balance factors are sought by genetic algorithm. Due to the high dimensionality of the proposed representations, linear discriminant analysis (LDA) is used to find its important low dimensional structure, which is essential for classification and location prediction. The numerical experiments on two public datasets with KNN classifier and cross-validation tests showed that in terms of the common indexes of sensitivity, specificity, accuracy and MCC, the proposed fusing representations outperform the traditional representations in protein sub-nuclear localization, and the representation treated by LDA outperforms the untreated one.

SPReM: Sparse Projection Regression Model For High-dimensional Linear Regression *

PubMed Central

Sun, Qiang; Zhu, Hongtu; Liu, Yufeng; Ibrahim, Joseph G.

2014-01-01

The aim of this paper is to develop a sparse projection regression modeling (SPReM) framework to perform multivariate regression modeling with a large number of responses and a multivariate covariate of interest. We propose two novel heritability ratios to simultaneously perform dimension reduction, response selection, estimation, and testing, while explicitly accounting for correlations among multivariate responses. Our SPReM is devised to specifically address the low statistical power issue of many standard statistical approaches, such as the Hotelling’s T2 test statistic or a mass univariate analysis, for high-dimensional data. We formulate the estimation problem of SPREM as a novel sparse unit rank projection (SURP) problem and propose a fast optimization algorithm for SURP. Furthermore, we extend SURP to the sparse multi-rank projection (SMURP) by adopting a sequential SURP approximation. Theoretically, we have systematically investigated the convergence properties of SURP and the convergence rate of SURP estimates. Our simulation results and real data analysis have shown that SPReM out-performs other state-of-the-art methods. PMID:26527844

SLLE for predicting membrane protein types.

PubMed

Wang, Meng; Yang, Jie; Xu, Zhi-Jie; Chou, Kuo-Chen

2005-01-07

Introduction of the concept of pseudo amino acid composition (PROTEINS: Structure, Function, and Genetics 43 (2001) 246; Erratum: ibid. 44 (2001) 60) has made it possible to incorporate a considerable amount of sequence-order effects by representing a protein sample in terms of a set of discrete numbers, and hence can significantly enhance the prediction quality of membrane protein type. As a continuous effort along such a line, the Supervised Locally Linear Embedding (SLLE) technique for nonlinear dimensionality reduction is introduced (Science 22 (2000) 2323). The advantage of using SLLE is that it can reduce the operational space by extracting the essential features from the high-dimensional pseudo amino acid composition space, and that the cluster-tolerant capacity can be increased accordingly. As a consequence by combining these two approaches, high success rates have been observed during the tests of self-consistency, jackknife and independent data set, respectively, by using the simplest nearest neighbour classifier. The current approach represents a new strategy to deal with the problems of protein attribute prediction, and hence may become a useful vehicle in the area of bioinformatics and proteomics.

On nonlinear evolution of low-frequency Alfvén waves in weakly-expanding solar wind plasmas

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

Nariyuki, Y.

A multi-dimensional nonlinear evolution equation for Alfvén waves in weakly-expanding solar wind plasmas is derived by using the reductive perturbation method. The expansion of solar wind plasma parcels is modeled by an expanding box model, which includes the accelerating expansion. It is shown that the resultant equation agrees with the Wentzel-Kramers-Brillouin prediction of the low-frequency Alfvén waves in the linear limit. In the cold and one-dimensional limit, a modified derivative nonlinear Schrodinger equation is obtained. Direct numerical simulations are carried out to discuss the effect of the expansion on the modulational instability of monochromatic Alfvén waves and the propagation ofmore » Alfvén solitons. By using the instantaneous frequency, it is quantitatively shown that as far as the expansion rate is much smaller than wave frequencies, effects of the expansion are almost adiabatic. It is also confirmed that while shapes of Alfvén solitons temporally change due to the expansion, some of them can stably propagate after their collision in weakly-expanding plasmas.« less

Protein Sub-Nuclear Localization Based on Effective Fusion Representations and Dimension Reduction Algorithm LDA

PubMed Central

Wang, Shunfang; Liu, Shuhui

2015-01-01

An effective representation of a protein sequence plays a crucial role in protein sub-nuclear localization. The existing representations, such as dipeptide composition (DipC), pseudo-amino acid composition (PseAAC) and position specific scoring matrix (PSSM), are insufficient to represent protein sequence due to their single perspectives. Thus, this paper proposes two fusion feature representations of DipPSSM and PseAAPSSM to integrate PSSM with DipC and PseAAC, respectively. When constructing each fusion representation, we introduce the balance factors to value the importance of its components. The optimal values of the balance factors are sought by genetic algorithm. Due to the high dimensionality of the proposed representations, linear discriminant analysis (LDA) is used to find its important low dimensional structure, which is essential for classification and location prediction. The numerical experiments on two public datasets with KNN classifier and cross-validation tests showed that in terms of the common indexes of sensitivity, specificity, accuracy and MCC, the proposed fusing representations outperform the traditional representations in protein sub-nuclear localization, and the representation treated by LDA outperforms the untreated one. PMID:26703574

A spectral-finite difference solution of the Navier-Stokes equations in three dimensions

NASA Astrophysics Data System (ADS)

Alfonsi, Giancarlo; Passoni, Giuseppe; Pancaldo, Lea; Zampaglione, Domenico

1998-07-01

A new computational code for the numerical integration of the three-dimensional Navier-Stokes equations in their non-dimensional velocity-pressure formulation is presented. The system of non-linear partial differential equations governing the time-dependent flow of a viscous incompressible fluid in a channel is managed by means of a mixed spectral-finite difference method, in which different numerical techniques are applied: Fourier decomposition is used along the homogeneous directions, second-order Crank-Nicolson algorithms are employed for the spatial derivatives in the direction orthogonal to the solid walls and a fourth-order Runge-Kutta procedure is implemented for both the calculation of the convective term and the time advancement. The pressure problem, cast in the Helmholtz form, is solved with the use of a cyclic reduction procedure. No-slip boundary conditions are used at the walls of the channel and cyclic conditions are imposed at the other boundaries of the computing domain.Results are provided for different values of the Reynolds number at several time steps of integration and are compared with results obtained by other authors.

Application of diffusion maps to identify human factors of self-reported anomalies in aviation.

PubMed

Andrzejczak, Chris; Karwowski, Waldemar; Mikusinski, Piotr

2012-01-01

A study investigating what factors are present leading to pilots submitting voluntary anomaly reports regarding their flight performance was conducted. Diffusion Maps (DM) were selected as the method of choice for performing dimensionality reduction on text records for this study. Diffusion Maps have seen successful use in other domains such as image classification and pattern recognition. High-dimensionality data in the form of narrative text reports from the NASA Aviation Safety Reporting System (ASRS) were clustered and categorized by way of dimensionality reduction. Supervised analyses were performed to create a baseline document clustering system. Dimensionality reduction techniques identified concepts or keywords within records, and allowed the creation of a framework for an unsupervised document classification system. Results from the unsupervised clustering algorithm performed similarly to the supervised methods outlined in the study. The dimensionality reduction was performed on 100 of the most commonly occurring words within 126,000 text records describing commercial aviation incidents. This study demonstrates that unsupervised machine clustering and organization of incident reports is possible based on unbiased inputs. Findings from this study reinforced traditional views on what factors contribute to civil aviation anomalies, however, new associations between previously unrelated factors and conditions were also found.

Three dimensional radiative flow of magnetite-nanofluid with homogeneous-heterogeneous reactions

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Rashid, Madiha; Alsaedi, Ahmed

2018-03-01

Present communication deals with the effects of homogeneous-heterogeneous reactions in flow of nanofluid by non-linear stretching sheet. Water based nanofluid containing magnetite nanoparticles is considered. Non-linear radiation and non-uniform heat sink/source effects are examined. Non-linear differential systems are computed by Optimal homotopy analysis method (OHAM). Convergent solutions of nonlinear systems are established. The optimal data of auxiliary variables is obtained. Impact of several non-dimensional parameters for velocity components, temperature and concentration fields are examined. Graphs are plotted for analysis of surface drag force and heat transfer rate.

Research on parallel load sharing principle of piezoelectric six-dimensional heavy force/torque sensor

NASA Astrophysics Data System (ADS)

Liu, Wei; Li, Ying-jun; Jia, Zhen-yuan; Zhang, Jun; Qian, Min

2011-01-01

In working process of huge heavy-load manipulators, such as the free forging machine, hydraulic die-forging press, forging manipulator, heavy grasping manipulator, large displacement manipulator, measurement of six-dimensional heavy force/torque and real-time force feedback of the operation interface are basis to realize coordinate operation control and force compliance control. It is also an effective way to raise the control accuracy and achieve highly efficient manufacturing. Facing to solve dynamic measurement problem on six-dimensional time-varying heavy load in extremely manufacturing process, the novel principle of parallel load sharing on six-dimensional heavy force/torque is put forward. The measuring principle of six-dimensional force sensor is analyzed, and the spatial model is built and decoupled. The load sharing ratios are analyzed and calculated in vertical and horizontal directions. The mapping relationship between six-dimensional heavy force/torque value to be measured and output force value is built. The finite element model of parallel piezoelectric six-dimensional heavy force/torque sensor is set up, and its static characteristics are analyzed by ANSYS software. The main parameters, which affect load sharing ratio, are analyzed. The experiments for load sharing with different diameters of parallel axis are designed. The results show that the six-dimensional heavy force/torque sensor has good linearity. Non-linearity errors are less than 1%. The parallel axis makes good effect of load sharing. The larger the diameter is, the better the load sharing effect is. The results of experiments are in accordance with the FEM analysis. The sensor has advantages of large measuring range, good linearity, high inherent frequency, and high rigidity. It can be widely used in extreme environments for real-time accurate measurement of six-dimensional time-varying huge loads on manipulators.

Reconfigurable Analog PDE computation for Baseband and RFComputation

DTIC Science & Technology

2017-03-01

waveguiding PDEs. One-dimensional ladder topologies enable linear delays, linear-phase analog filters , as well as analog beamforming, potentially at RF...performance. This discussion focuses on ODE / PDE analog computation available in SoC FPAA structures. One such computation is a ladder filter (Fig...Implementation of a one-dimensional ladder filter for computing inductor (L) and capacitor (C) lines. These components can be implemented in CABs or as

A non-linear piezoelectric actuator calibration using N-dimensional Lissajous figure

NASA Astrophysics Data System (ADS)

Albertazzi, A.; Viotti, M. R.; Veiga, C. L. N.; Fantin, A. V.

2016-08-01

Piezoelectric translators (PZTs) are very often used as phase shifters in interferometry. However, they typically present a non-linear behavior and strong hysteresis. The use of an additional resistive or capacitive sensor make possible to linearize the response of the PZT by feedback control. This approach works well, but makes the device more complex and expensive. A less expensive approach uses a non-linear calibration. In this paper, the authors used data from at least five interferograms to form N-dimensional Lissajous figures to establish the actual relationship between the applied voltages and the resulting phase shifts [1]. N-dimensional Lissajous figures are formed when N sinusoidal signals are combined in an N-dimensional space, where one signal is assigned to each axis. It can be verified that the resulting Ndimensional ellipsis lays in a 2D plane. By fitting an ellipsis equation to the resulting 2D ellipsis it is possible to accurately compute the resulting phase value for each interferogram. In this paper, the relationship between the resulting phase shift and the applied voltage is simultaneously established for a set of 12 increments by a fourth degree polynomial. The results in speckle interferometry show that, after two or three interactions, the calibration error is usually smaller than 1°.

Computational process to study the wave propagation In a non-linear medium by quasi- linearization

NASA Astrophysics Data System (ADS)

Sharath Babu, K.; Venkata Brammam, J.; Baby Rani, CH

2018-03-01

Two objects having distinct velocities come into contact an impact can occur. The impact study i.e., in the displacement of the objects after the impact, the impact force is function of time‘t’ which is behaves similar to compression force. The impact tenure is very short so impulses must be generated subsequently high stresses are generated. In this work we are examined the wave propagation inside the object after collision and measured the object non-linear behavior in the one-dimensional case. Wave transmission is studied by means of material acoustic parameter value. The objective of this paper is to present a computational study of propagating pulsation and harmonic waves in nonlinear media using quasi-linearization and subsequently utilized the central difference scheme. This study gives focus on longitudinal, one- dimensional wave propagation. In the finite difference scheme Non-linear system is reduced to a linear system by applying quasi-linearization method. The computed results exhibit good agreement on par with the selected non-liner wave propagation.

Determination of target detection limits in hyperspectral data using band selection and dimensionality reduction

NASA Astrophysics Data System (ADS)

Gross, W.; Boehler, J.; Twizer, K.; Kedem, B.; Lenz, A.; Kneubuehler, M.; Wellig, P.; Oechslin, R.; Schilling, H.; Rotman, S.; Middelmann, W.

2016-10-01

Hyperspectral remote sensing data can be used for civil and military applications to robustly detect and classify target objects. High spectral resolution of hyperspectral data can compensate for the comparatively low spatial resolution, which allows for detection and classification of small targets, even below image resolution. Hyperspectral data sets are prone to considerable spectral redundancy, affecting and limiting data processing and algorithm performance. As a consequence, data reduction strategies become increasingly important, especially in view of near-real-time data analysis. The goal of this paper is to analyze different strategies for hyperspectral band selection algorithms and their effect on subpixel classification for different target and background materials. Airborne hyperspectral data is used in combination with linear target simulation procedures to create a representative amount of target-to-background ratios for evaluation of detection limits. Data from two different airborne hyperspectral sensors, AISA Eagle and Hawk, are used to evaluate transferability of band selection when using different sensors. The same target objects were recorded to compare the calculated detection limits. To determine subpixel classification results, pure pixels from the target materials are extracted and used to simulate mixed pixels with selected background materials. Target signatures are linearly combined with different background materials in varying ratios. The commonly used classification algorithms Adaptive Coherence Estimator (ACE) is used to compare the detection limit for the original data with several band selection and data reduction strategies. The evaluation of the classification results is done by assuming a fixed false alarm ratio and calculating the mean target-to-background ratio of correctly detected pixels. The results allow drawing conclusions about specific band combinations for certain target and background combinations. Additionally, generally useful wavelength ranges are determined and the optimal amount of principal components is analyzed.

Reduced basis ANOVA methods for partial differential equations with high-dimensional random inputs

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

Liao, Qifeng, E-mail: liaoqf@shanghaitech.edu.cn; Lin, Guang, E-mail: guanglin@purdue.edu

2016-07-15

In this paper we present a reduced basis ANOVA approach for partial deferential equations (PDEs) with random inputs. The ANOVA method combined with stochastic collocation methods provides model reduction in high-dimensional parameter space through decomposing high-dimensional inputs into unions of low-dimensional inputs. In this work, to further reduce the computational cost, we investigate spatial low-rank structures in the ANOVA-collocation method, and develop efficient spatial model reduction techniques using hierarchically generated reduced bases. We present a general mathematical framework of the methodology, validate its accuracy and demonstrate its efficiency with numerical experiments.

Approximating high-dimensional dynamics by barycentric coordinates with linear programming

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

Hirata, Yoshito, E-mail: yoshito@sat.t.u-tokyo.ac.jp; Aihara, Kazuyuki; Suzuki, Hideyuki

The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics ofmore » the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.« less

Approximating high-dimensional dynamics by barycentric coordinates with linear programming.

PubMed

Hirata, Yoshito; Shiro, Masanori; Takahashi, Nozomu; Aihara, Kazuyuki; Suzuki, Hideyuki; Mas, Paloma

2015-01-01

The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.

Survival dimensionality reduction (SDR): development and clinical application of an innovative approach to detect epistasis in presence of right-censored data

PubMed Central

2010-01-01

Background Epistasis is recognized as a fundamental part of the genetic architecture of individuals. Several computational approaches have been developed to model gene-gene interactions in case-control studies, however, none of them is suitable for time-dependent analysis. Herein we introduce the Survival Dimensionality Reduction (SDR) algorithm, a non-parametric method specifically designed to detect epistasis in lifetime datasets. Results The algorithm requires neither specification about the underlying survival distribution nor about the underlying interaction model and proved satisfactorily powerful to detect a set of causative genes in synthetic epistatic lifetime datasets with a limited number of samples and high degree of right-censorship (up to 70%). The SDR method was then applied to a series of 386 Dutch patients with active rheumatoid arthritis that were treated with anti-TNF biological agents. Among a set of 39 candidate genes, none of which showed a detectable marginal effect on anti-TNF responses, the SDR algorithm did find that the rs1801274 SNP in the FcγRIIa gene and the rs10954213 SNP in the IRF5 gene non-linearly interact to predict clinical remission after anti-TNF biologicals. Conclusions Simulation studies and application in a real-world setting support the capability of the SDR algorithm to model epistatic interactions in candidate-genes studies in presence of right-censored data. Availability: http://sourceforge.net/projects/sdrproject/ PMID:20691091

A novel phase assignment protocol and driving system for a high-density focused ultrasound array.

PubMed

Caulfield, R Erich; Yin, Xiangtao; Juste, Jose; Hynynen, Kullervo

2007-04-01

Currently, most phased-array systems intended for therapy are one-dimensional (1-D) and use between 5 and 200 elements, with a few two-dimensional (2-D) systems using several hundred elements. The move toward lambda/2 interelement spacing, which provides complete 3-D beam steering, would require a large number of closely spaced elements (0.15 mm to 3 mm). A solution to the resulting problem of cost and cable assembly size, which this study examines, is to quantize the phases available at the array input. By connecting elements with similar phases to a single wire, a significant reduction in the number of incoming lines can be achieved while maintaining focusing and beam steering capability. This study has explored the feasibility of such an approach using computer simulations and experiments with a test circuit driving a 100-element linear array. Simulation results demonstrated that adequate focusing can be obtained with only four phase signals without large increases in the grating lobes or the dimensions of the focus. Experiments showed that the method can be implemented in practice, and adequate focusing can be achieved with four phase signals with a reduction of 20% in the peak pressure amplitude squared when compared with the infinite-phase resolution case. Results indicate that the use of this technique would make it possible to drive more than 10,000 elements with 33 input lines. The implementation of this method could have a large impact on ultrasound therapy and diagnostic devices.

Three-dimensional modeling of flexible pavements : research implementation plan.

DOT National Transportation Integrated Search

2006-02-14

Many of the asphalt pavement analysis programs are based on linear elastic models. A linear viscoelastic models : would be superior to linear elastic models for analyzing the response of asphalt concrete pavements to loads. There : is a need to devel...

Comparison of 3-Dimensional Shoulder Complex Kinematics in Individuals With and Without Shoulder Pain, Part 2: Glenohumeral Joint

PubMed Central

LAWRENCE, REBEKAH L.; BRAMAN, JONATHAN P.; STAKER, JUSTIN L.; LAPRADE, ROBERT F.; LUDEWIG, PAULA M.

2015-01-01

STUDY DESIGN Cross-sectional. OBJECTIVES To compare differences in glenohumeral joint angular motion and linear translations between symptomatic and asymptomatic individuals during shoulder motion performed in 3 planes of humerothoracic elevation. BACKGROUND Numerous clinical theories have linked abnormal glenohumeral kinematics, including decreased glenohumeral external rotation and increased superior translation, to individuals with shoulder pain and impingement diagnoses. However, relatively few studies have investigated glenohumeral joint angular motion and linear translations in this population. METHODS Transcortical bone pins were inserted into the scapula and humerus of 12 a symptomatic and 10 symptomatic participants for direct bone-fixed tracking using electromagnetic sensors. Glenohumeral joint angular positions and linear translations were calculated during active shoulder flexion, abduction, and scapular plane abduction. RESULTS Differences between groups in angular positions were limited to glenohumeral elevation, coinciding with a reduction in scapulothoracic upward rotation. Symptomatic participants demonstrated 1.4 mm more anterior glenohumeral translation between 90° and 120° of shoulder flexion and an average of 1 mm more inferior glenohumeral translation throughout shoulder abduction. CONCLUSION Differences in glenohumeral kinematics exist between symptomatic and a symptomatic individuals. The clinical implications of these differences are not yet understood, and more research is needed to understand the relationship between abnormal kinematics, shoulder pain, and pathoanatomy. PMID:25103132

Deep Independence Network Analysis of Structural Brain Imaging: Application to Schizophrenia

PubMed Central

Castro, Eduardo; Hjelm, R. Devon; Plis, Sergey M.; Dinh, Laurent; Turner, Jessica A.; Calhoun, Vince D.

2016-01-01

Linear independent component analysis (ICA) is a standard signal processing technique that has been extensively used on neuroimaging data to detect brain networks with coherent brain activity (functional MRI) or covarying structural patterns (structural MRI). However, its formulation assumes that the measured brain signals are generated by a linear mixture of the underlying brain networks and this assumption limits its ability to detect the inherent nonlinear nature of brain interactions. In this paper, we introduce nonlinear independent component estimation (NICE) to structural MRI data to detect abnormal patterns of gray matter concentration in schizophrenia patients. For this biomedical application, we further addressed the issue of model regularization of nonlinear ICA by performing dimensionality reduction prior to NICE, together with an appropriate control of the complexity of the model and the usage of a proper approximation of the probability distribution functions of the estimated components. We show that our results are consistent with previous findings in the literature, but we also demonstrate that the incorporation of nonlinear associations in the data enables the detection of spatial patterns that are not identified by linear ICA. Specifically, we show networks including basal ganglia, cerebellum and thalamus that show significant differences in patients versus controls, some of which show distinct nonlinear patterns. PMID:26891483

Employment of CB models for non-linear dynamic analysis

NASA Technical Reports Server (NTRS)

Klein, M. R. M.; Deloo, P.; Fournier-Sicre, A.

1990-01-01

The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.

Asymptotic and spectral analysis of the gyrokinetic-waterbag integro-differential operator in toroidal geometry

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

Besse, Nicolas, E-mail: Nicolas.Besse@oca.eu; Institut Jean Lamour, UMR CNRS/UL 7198, Université de Lorraine, BP 70239 54506 Vandoeuvre-lès-Nancy Cedex; Coulette, David, E-mail: David.Coulette@ipcms.unistra.fr

2016-08-15

Achieving plasmas with good stability and confinement properties is a key research goal for magnetic fusion devices. The underlying equations are the Vlasov–Poisson and Vlasov–Maxwell (VPM) equations in three space variables, three velocity variables, and one time variable. Even in those somewhat academic cases where global equilibrium solutions are known, studying their stability requires the analysis of the spectral properties of the linearized operator, a daunting task. We have identified a model, for which not only equilibrium solutions can be constructed, but many of their stability properties are amenable to rigorous analysis. It uses a class of solution to themore » VPM equations (or to their gyrokinetic approximations) known as waterbag solutions which, in particular, are piecewise constant in phase-space. It also uses, not only the gyrokinetic approximation of fast cyclotronic motion around magnetic field lines, but also an asymptotic approximation regarding the magnetic-field-induced anisotropy: the spatial variation along the field lines is taken much slower than across them. Together, these assumptions result in a drastic reduction in the dimensionality of the linearized problem, which becomes a set of two nested one-dimensional problems: an integral equation in the poloidal variable, followed by a one-dimensional complex Schrödinger equation in the radial variable. We show here that the operator associated to the poloidal variable is meromorphic in the eigenparameter, the pulsation frequency. We also prove that, for all but a countable set of real pulsation frequencies, the operator is compact and thus behaves mostly as a finite-dimensional one. The numerical algorithms based on such ideas have been implemented in a companion paper [D. Coulette and N. Besse, “Numerical resolution of the global eigenvalue problem for gyrokinetic-waterbag model in toroidal geometry” (submitted)] and were found to be surprisingly close to those for the original gyrokinetic-Vlasov equations. The purpose of the present paper is to make these new ideas accessible to two readerships: applied mathematicians and plasma physicists.« less

Small amplitude two dimensional electrostatic excitations in a magnetized dusty plasma with q-distributed electrons

NASA Astrophysics Data System (ADS)

Khan, Shahab Ullah; Adnan, Muhammad; Qamar, Anisa; Mahmood, Shahzad

2016-07-01

The propagation of linear and nonlinear electrostatic waves is investigated in magnetized dusty plasma with stationary negatively or positively charged dust, cold mobile ions and non-extensive electrons. Two normal modes are predicted in the linear regime, whose characteristics are investigated parametrically, focusing on the effect of electrons non-extensivity, dust charge polarity, concentration of dust and magnetic field strength. Using the reductive perturbation technique, a Zakharov-Kuznetsov (ZK) type equation is derived which governs the dynamics of small-amplitude solitary waves in magnetized dusty plasma. The properties of the solitary wave structures are analyzed numerically with the system parameters i.e. electrons non-extensivity, concentration of dust, polarity of dust and magnetic field strength. Following Allen and Rowlands (J. Plasma Phys. 53:63, 1995), we have shown that the pulse soliton solution of the ZK equation is unstable, and have analytically traced the dependence of the instability growth rate on the nonextensive parameter q for electrons, dust charge polarity and magnetic field strength. The results should be useful for understanding the nonlinear propagation of DIA solitary waves in laboratory and space plasmas.

Data analytics using canonical correlation analysis and Monte Carlo simulation

NASA Astrophysics Data System (ADS)

Rickman, Jeffrey M.; Wang, Yan; Rollett, Anthony D.; Harmer, Martin P.; Compson, Charles

2017-07-01

A canonical correlation analysis is a generic parametric model used in the statistical analysis of data involving interrelated or interdependent input and output variables. It is especially useful in data analytics as a dimensional reduction strategy that simplifies a complex, multidimensional parameter space by identifying a relatively few combinations of variables that are maximally correlated. One shortcoming of the canonical correlation analysis, however, is that it provides only a linear combination of variables that maximizes these correlations. With this in mind, we describe here a versatile, Monte-Carlo based methodology that is useful in identifying non-linear functions of the variables that lead to strong input/output correlations. We demonstrate that our approach leads to a substantial enhancement of correlations, as illustrated by two experimental applications of substantial interest to the materials science community, namely: (1) determining the interdependence of processing and microstructural variables associated with doped polycrystalline aluminas, and (2) relating microstructural decriptors to the electrical and optoelectronic properties of thin-film solar cells based on CuInSe2 absorbers. Finally, we describe how this approach facilitates experimental planning and process control.

Fractional representation theory - Robustness results with applications to finite dimensional control of a class of linear distributed systems

NASA Technical Reports Server (NTRS)

Nett, C. N.; Jacobson, C. A.; Balas, M. J.

1983-01-01

This paper reviews and extends the fractional representation theory. In particular, new and powerful robustness results are presented. This new theory is utilized to develop a preliminary design methodology for finite dimensional control of a class of linear evolution equations on a Banach space. The design is for stability in an input-output sense, but particular attention is paid to internal stability as well.

Self-diffusion in a stochastically heated two-dimensional dusty plasma

NASA Astrophysics Data System (ADS)

Sheridan, T. E.

2016-09-01

Diffusion in a two-dimensional dusty plasma liquid (i.e., a Yukawa liquid) is studied experimentally. The dusty plasma liquid is heated stochastically by a surrounding three-dimensional toroidal dusty plasma gas which acts as a thermal reservoir. The measured dust velocity distribution functions are isotropic Maxwellians, giving a well-defined kinetic temperature. The mean-square displacement for dust particles is found to increase linearly with time, indicating normal diffusion. The measured diffusion coefficients increase approximately linearly with temperature. The effective collision rate is dominated by collective dust-dust interactions rather than neutral gas drag, and is comparable to the dusty-plasma frequency.

A mechanism for hot-spot generation in a reactive two-dimensional sheared viscous layer

NASA Astrophysics Data System (ADS)

Timms, Robert; Purvis, Richard; Curtis, John P.

2018-05-01

A two-dimensional model for the non-uniform melting of a thin sheared viscous layer is developed. An asymptotic solution is presented for both a non-reactive and a reactive material. It is shown that the melt front is linearly stable to small perturbations in the non-reactive case, but becomes linearly unstable upon introduction of an Arrhenius source term to model the chemical reaction. Results demonstrate that non-uniform melting acts as a mechanism to generate hot spots that are found to be sufficient to reduce the time to ignition when compared with the corresponding one-dimensional model of melting.

Ultrahigh-Dimensional Multiclass Linear Discriminant Analysis by Pairwise Sure Independence Screening

PubMed Central

Pan, Rui; Wang, Hansheng; Li, Runze

2016-01-01

This paper is concerned with the problem of feature screening for multi-class linear discriminant analysis under ultrahigh dimensional setting. We allow the number of classes to be relatively large. As a result, the total number of relevant features is larger than usual. This makes the related classification problem much more challenging than the conventional one, where the number of classes is small (very often two). To solve the problem, we propose a novel pairwise sure independence screening method for linear discriminant analysis with an ultrahigh dimensional predictor. The proposed procedure is directly applicable to the situation with many classes. We further prove that the proposed method is screening consistent. Simulation studies are conducted to assess the finite sample performance of the new procedure. We also demonstrate the proposed methodology via an empirical analysis of a real life example on handwritten Chinese character recognition. PMID:28127109

Genetic Algorithm-Based Model Order Reduction of Aeroservoelastic Systems with Consistant States

NASA Technical Reports Server (NTRS)

Zhu, Jin; Wang, Yi; Pant, Kapil; Suh, Peter M.; Brenner, Martin J.

2017-01-01

This paper presents a model order reduction framework to construct linear parameter-varying reduced-order models of flexible aircraft for aeroservoelasticity analysis and control synthesis in broad two-dimensional flight parameter space. Genetic algorithms are used to automatically determine physical states for reduction and to generate reduced-order models at grid points within parameter space while minimizing the trial-and-error process. In addition, balanced truncation for unstable systems is used in conjunction with the congruence transformation technique to achieve locally optimal realization and weak fulfillment of state consistency across the entire parameter space. Therefore, aeroservoelasticity reduced-order models at any flight condition can be obtained simply through model interpolation. The methodology is applied to the pitch-plant model of the X-56A Multi-Use Technology Testbed currently being tested at NASA Armstrong Flight Research Center for flutter suppression and gust load alleviation. The present studies indicate that the reduced-order model with more than 12× reduction in the number of states relative to the original model is able to accurately predict system response among all input-output channels. The genetic-algorithm-guided approach exceeds manual and empirical state selection in terms of efficiency and accuracy. The interpolated aeroservoelasticity reduced order models exhibit smooth pole transition and continuously varying gains along a set of prescribed flight conditions, which verifies consistent state representation obtained by congruence transformation. The present model order reduction framework can be used by control engineers for robust aeroservoelasticity controller synthesis and novel vehicle design.

An improved input shaping design for an efficient sway control of a nonlinear 3D overhead crane with friction

NASA Astrophysics Data System (ADS)

Maghsoudi, Mohammad Javad; Mohamed, Z.; Sudin, S.; Buyamin, S.; Jaafar, H. I.; Ahmad, S. M.

2017-08-01

This paper proposes an improved input shaping scheme for an efficient sway control of a nonlinear three dimensional (3D) overhead crane with friction using the particle swarm optimization (PSO) algorithm. Using this approach, a higher payload sway reduction is obtained as the input shaper is designed based on a complete nonlinear model, as compared to the analytical-based input shaping scheme derived using a linear second order model. Zero Vibration (ZV) and Distributed Zero Vibration (DZV) shapers are designed using both analytical and PSO approaches for sway control of rail and trolley movements. To test the effectiveness of the proposed approach, MATLAB simulations and experiments on a laboratory 3D overhead crane are performed under various conditions involving different cable lengths and sway frequencies. Their performances are studied based on a maximum residual of payload sway and Integrated Absolute Error (IAE) values which indicate total payload sway of the crane. With experiments, the superiority of the proposed approach over the analytical-based is shown by 30-50% reductions of the IAE values for rail and trolley movements, for both ZV and DZV shapers. In addition, simulations results show higher sway reductions with the proposed approach. It is revealed that the proposed PSO-based input shaping design provides higher payload sway reductions of a 3D overhead crane with friction as compared to the commonly designed input shapers.

The Effect of Thermal Reduction on the Photoluminescence and Electronic Structures of Graphene Oxides

PubMed Central

Chuang, C.-H.; Wang, Y.-F.; Shao, Y.-C.; Yeh, Y.-C.; Wang, D.-Y.; Chen, C.-W.; Chiou, J. W.; Ray, Sekhar C.; Pong, W. F.; Zhang, L.; Zhu, J. F.; Guo, J. H.

2014-01-01

Electronic structures of graphene oxide (GO) and hydro-thermally reduced graphene oxides (rGOs) processed at low temperatures (120–180°C) were studied using X-ray absorption near-edge structure (XANES), X-ray emission spectroscopy (XES) and resonant inelastic X-ray scattering (RIXS). C K-edge XANES spectra of rGOs reveal that thermal reduction restores C = C sp2 bonds and removes some of the oxygen and hydroxyl groups of GO, which initiates the evolution of carbonaceous species. The combination of C K-edge XANES and Kα XES spectra shows that the overlapping π and π* orbitals in rGOs and GO are similar to that of highly ordered pyrolytic graphite (HOPG), which has no band-gap. C Kα RIXS spectra provide evidence that thermal reduction changes the density of states (DOSs) that is generated in the π-region and/or in the gap between the π and π* levels of the GO and rGOs. Two-dimensional C Kα RIXS mapping of the heavy reduction of rGOs further confirms that the residual oxygen and/or oxygen-containing functional groups modify the π and σ features, which are dispersed by the photon excitation energy. The dispersion behavior near the K point is approximately linear and differs from the parabolic-like dispersion observed in HOPG. PMID:24717290

A Glimpse in the Third Dimension for Electrical Resistivity Profiles

NASA Astrophysics Data System (ADS)

Robbins, A. R.; Plattner, A.

2017-12-01

We present an electrode layout strategy designed to enhance the popular two-dimensional electrical resistivity profile. Offsetting electrodes from the traditional linear layout and using 3-D inversion software allows for mapping the three-dimensional electrical resistivity close to the profile plane. We established a series of synthetic tests using simulated data generated from chosen resistivity distributions with a three-dimensional target feature. All inversions and simulations were conducted using freely-available ERT software, BERT and E4D. Synthetic results demonstrate the effectiveness of the offset electrode approach, whereas the linear layout failed to resolve the three-dimensional character of our subsurface feature. A field survey using trench backfill as a known resistivity contrast confirmed our synthetic tests. As we show, 3-D inversions of linear layouts for starting models without previously known structure are futile ventures because they generate symmetric resistivity solutions with respect to the profile plane. This is a consequence of the layout's inherent symmetrical sensitivity patterns. An offset electrode layout is not subject to the same limitation, as the collective measurements do not share a common sensitivity symmetry. For practitioners, this approach presents a low-cost improvement of a traditional geophysical method which is simple to use yet may provide critical information about the three dimensional structure of the subsurface close to the profile.

Linear Dimensional Stability of Irreversible Hydrocolloid Materials Over Time.

PubMed

Garrofé, Analía B; Ferrari, Beatriz A; Picca, Mariana; Kaplan, Andrea E

2015-12-01

The aim of this study was to evaluate the linear dimensional stability of different irreversible hydrocolloid materials over time. A metal mold was designed with custom trays made of thermoplastic sheets (Sabilex, sheets 0.125 mm thick). Perforations were made in order to improve retention of the material. Five impressions were taken with each of the following: Kromopan 100 (LASCOD) [AlKr], which has dimensional stability of 100 hours, and Phase Plus (ZHERMACK) [AlPh], which has dimensional stability of 48 hours. Standardized digital photographs were taken at different time intervals (0, 15, 30, 45, 60, 120 minutes; 12, 24 and 96 hours), using an "ad-hoc" device. The images were analyzed with software (UTHSCSA Image Tool) by measuring the distance between intersection of the lines previously made at the top of the mold. The results were analyzed by ANOVA for repeated measures. Initial and final values were (mean and standard deviation): AlKr: 16.44 (0.22) and 16.34 (0.11), AlPh: 16.40 (0.06) and 16.18 (0.06). Statistical evaluation showed significant effect of material and time factors. Under the conditions in this study, time significantly affects the linear dimensional stability of irreversible hydrocolloid materials. Sociedad Argentina de Investigación Odontológica.

Optimal sensor placement for control of a supersonic mixed-compression inlet with variable geometry

NASA Astrophysics Data System (ADS)

Moore, Kenneth Thomas

A method of using fluid dynamics models for the generation of models that are useable for control design and analysis is investigated. The problem considered is the control of the normal shock location in the VDC inlet, which is a mixed-compression, supersonic, variable-geometry inlet of a jet engine. A quasi-one-dimensional set of fluid equations incorporating bleed and moving walls is developed. An object-oriented environment is developed for simulation of flow systems under closed-loop control. A public interface between the controller and fluid classes is defined. A linear model representing the dynamics of the VDC inlet is developed from the finite difference equations, and its eigenstructure is analyzed. The order of this model is reduced using the square root balanced model reduction method to produce a reduced-order linear model that is suitable for control design and analysis tasks. A modification to this method that improves the accuracy of the reduced-order linear model for the purpose of sensor placement is presented and analyzed. The reduced-order linear model is used to develop a sensor placement method that quantifies as a function of the sensor location the ability of a sensor to provide information on the variable of interest for control. This method is used to develop a sensor placement metric for the VDC inlet. The reduced-order linear model is also used to design a closed loop control system to control the shock position in the VDC inlet. The object-oriented simulation code is used to simulate the nonlinear fluid equations under closed-loop control.

Prediction of siRNA potency using sparse logistic regression.

PubMed

Hu, Wei; Hu, John

2014-06-01

RNA interference (RNAi) can modulate gene expression at post-transcriptional as well as transcriptional levels. Short interfering RNA (siRNA) serves as a trigger for the RNAi gene inhibition mechanism, and therefore is a crucial intermediate step in RNAi. There have been extensive studies to identify the sequence characteristics of potent siRNAs. One such study built a linear model using LASSO (Least Absolute Shrinkage and Selection Operator) to measure the contribution of each siRNA sequence feature. This model is simple and interpretable, but it requires a large number of nonzero weights. We have introduced a novel technique, sparse logistic regression, to build a linear model using single-position specific nucleotide compositions which has the same prediction accuracy of the linear model based on LASSO. The weights in our new model share the same general trend as those in the previous model, but have only 25 nonzero weights out of a total 84 weights, a 54% reduction compared to the previous model. Contrary to the linear model based on LASSO, our model suggests that only a few positions are influential on the efficacy of the siRNA, which are the 5' and 3' ends and the seed region of siRNA sequences. We also employed sparse logistic regression to build a linear model using dual-position specific nucleotide compositions, a task LASSO is not able to accomplish well due to its high dimensional nature. Our results demonstrate the superiority of sparse logistic regression as a technique for both feature selection and regression over LASSO in the context of siRNA design.

Nonlinear dimensionality reduction of CT histogram based feature space for predicting recurrence-free survival in non-small-cell lung cancer

NASA Astrophysics Data System (ADS)

Kawata, Y.; Niki, N.; Ohmatsu, H.; Aokage, K.; Kusumoto, M.; Tsuchida, T.; Eguchi, K.; Kaneko, M.

2015-03-01

Advantages of CT scanners with high resolution have allowed the improved detection of lung cancers. In the recent release of positive results from the National Lung Screening Trial (NLST) in the US showing that CT screening does in fact have a positive impact on the reduction of lung cancer related mortality. While this study does show the efficacy of CT based screening, physicians often face the problems of deciding appropriate management strategies for maximizing patient survival and for preserving lung function. Several key manifold-learning approaches efficiently reveal intrinsic low-dimensional structures latent in high-dimensional data spaces. This study was performed to investigate whether the dimensionality reduction can identify embedded structures from the CT histogram feature of non-small-cell lung cancer (NSCLC) space to improve the performance in predicting the likelihood of RFS for patients with NSCLC.

TPSLVM: a dimensionality reduction algorithm based on thin plate splines.

PubMed

Jiang, Xinwei; Gao, Junbin; Wang, Tianjiang; Shi, Daming

2014-10-01

Dimensionality reduction (DR) has been considered as one of the most significant tools for data analysis. One type of DR algorithms is based on latent variable models (LVM). LVM-based models can handle the preimage problem easily. In this paper we propose a new LVM-based DR model, named thin plate spline latent variable model (TPSLVM). Compared to the well-known Gaussian process latent variable model (GPLVM), our proposed TPSLVM is more powerful especially when the dimensionality of the latent space is low. Also, TPSLVM is robust to shift and rotation. This paper investigates two extensions of TPSLVM, i.e., the back-constrained TPSLVM (BC-TPSLVM) and TPSLVM with dynamics (TPSLVM-DM) as well as their combination BC-TPSLVM-DM. Experimental results show that TPSLVM and its extensions provide better data visualization and more efficient dimensionality reduction compared to PCA, GPLVM, ISOMAP, etc.

Origin of nonsaturating linear magnetoresistivity

NASA Astrophysics Data System (ADS)

Kisslinger, Ferdinand; Ott, Christian; Weber, Heiko B.

2017-01-01

The observation of nonsaturating classical linear magnetoresistivity has been an enigmatic phenomenon in solid-state physics. We present a study of a two-dimensional ohmic conductor, including local Hall effect and a self-consistent consideration of the environment. An equivalent-circuit scheme delivers a simple and convincing argument why the magnetoresistivity is linear in strong magnetic field, provided that current and biasing electric field are misaligned by a nonlocal mechanism. A finite-element model of a two-dimensional conductor is suited to display the situations that create such deviating currents. Besides edge effects next to electrodes, charge carrier density fluctuations are efficiently generating this effect. However, mobility fluctuations that have frequently been related to linear magnetoresistivity are barely relevant. Despite its rare observation, linear magnetoresitivity is rather the rule than the exception in a regime of low charge carrier densities, misaligned current pathways and strong magnetic field.

Effects of upstream-biased third-order space correction terms on multidimensional Crowley advection schemes

NASA Technical Reports Server (NTRS)

Schlesinger, R. E.

1985-01-01

The impact of upstream-biased corrections for third-order spatial truncation error on the stability and phase error of the two-dimensional Crowley combined advective scheme with the cross-space term included is analyzed, putting primary emphasis on phase error reduction. The various versions of the Crowley scheme are formally defined, and their stability and phase error characteristics are intercompared using a linear Fourier component analysis patterned after Fromm (1968, 1969). The performances of the schemes under prototype simulation conditions are tested using time-dependent numerical experiments which advect an initially cone-shaped passive scalar distribution in each of three steady nondivergent flows. One such flow is solid rotation, while the other two are diagonal uniform flow and a strongly deformational vortex.

Causality networks from multivariate time series and application to epilepsy.

PubMed

Siggiridou, Elsa; Koutlis, Christos; Tsimpiris, Alkiviadis; Kimiskidis, Vasilios K; Kugiumtzis, Dimitris

2015-08-01

Granger causality and variants of this concept allow the study of complex dynamical systems as networks constructed from multivariate time series. In this work, a large number of Granger causality measures used to form causality networks from multivariate time series are assessed. For this, realizations on high dimensional coupled dynamical systems are considered and the performance of the Granger causality measures is evaluated, seeking for the measures that form networks closest to the true network of the dynamical system. In particular, the comparison focuses on Granger causality measures that reduce the state space dimension when many variables are observed. Further, the linear and nonlinear Granger causality measures of dimension reduction are compared to a standard Granger causality measure on electroencephalographic (EEG) recordings containing episodes of epileptiform discharges.

On the precision of quasi steady state assumptions in stochastic dynamics

NASA Astrophysics Data System (ADS)

Agarwal, Animesh; Adams, Rhys; Castellani, Gastone C.; Shouval, Harel Z.

2012-07-01

Many biochemical networks have complex multidimensional dynamics and there is a long history of methods that have been used for dimensionality reduction for such reaction networks. Usually a deterministic mass action approach is used; however, in small volumes, there are significant fluctuations from the mean which the mass action approach cannot capture. In such cases stochastic simulation methods should be used. In this paper, we evaluate the applicability of one such dimensionality reduction method, the quasi-steady state approximation (QSSA) [L. Menten and M. Michaelis, "Die kinetik der invertinwirkung," Biochem. Z 49, 333369 (1913)] for dimensionality reduction in case of stochastic dynamics. First, the applicability of QSSA approach is evaluated for a canonical system of enzyme reactions. Application of QSSA to such a reaction system in a deterministic setting leads to Michaelis-Menten reduced kinetics which can be used to derive the equilibrium concentrations of the reaction species. In the case of stochastic simulations, however, the steady state is characterized by fluctuations around the mean equilibrium concentration. Our analysis shows that a QSSA based approach for dimensionality reduction captures well the mean of the distribution as obtained from a full dimensional simulation but fails to accurately capture the distribution around that mean. Moreover, the QSSA approximation is not unique. We have then extended the analysis to a simple bistable biochemical network model proposed to account for the stability of synaptic efficacies; the substrate of learning and memory [J. E. Lisman, "A mechanism of memory storage insensitive to molecular turnover: A bistable autophosphorylating kinase," Proc. Natl. Acad. Sci. U.S.A. 82, 3055-3057 (1985)], 10.1073/pnas.82.9.3055. Our analysis shows that a QSSA based dimensionality reduction method results in errors as big as two orders of magnitude in predicting the residence times in the two stable states.

N-Dimensional LLL Reduction Algorithm with Pivoted Reflection

PubMed Central

Deng, Zhongliang; Zhu, Di

2018-01-01

The Lenstra-Lenstra-Lovász (LLL) lattice reduction algorithm and many of its variants have been widely used by cryptography, multiple-input-multiple-output (MIMO) communication systems and carrier phase positioning in global navigation satellite system (GNSS) to solve the integer least squares (ILS) problem. In this paper, we propose an n-dimensional LLL reduction algorithm (n-LLL), expanding the Lovász condition in LLL algorithm to n-dimensional space in order to obtain a further reduced basis. We also introduce pivoted Householder reflection into the algorithm to optimize the reduction time. For an m-order positive definite matrix, analysis shows that the n-LLL reduction algorithm will converge within finite steps and always produce better results than the original LLL reduction algorithm with n > 2. The simulations clearly prove that n-LLL is better than the original LLL in reducing the condition number of an ill-conditioned input matrix with 39% improvement on average for typical cases, which can significantly reduce the searching space for solving ILS problem. The simulation results also show that the pivoted reflection has significantly declined the number of swaps in the algorithm by 57%, making n-LLL a more practical reduction algorithm. PMID:29351224

Structural Properties and Estimation of Delay Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Kwong, R. H. S.

1975-01-01

Two areas in the theory of delay systems were studied: structural properties and their applications to feedback control, and optimal linear and nonlinear estimation. The concepts of controllability, stabilizability, observability, and detectability were investigated. The property of pointwise degeneracy of linear time-invariant delay systems is considered. Necessary and sufficient conditions for three dimensional linear systems to be made pointwise degenerate by delay feedback were obtained, while sufficient conditions for this to be possible are given for higher dimensional linear systems. These results were applied to obtain solvability conditions for the minimum time output zeroing control problem by delay feedback. A representation theorem is given for conditional moment functionals of general nonlinear stochastic delay systems, and stochastic differential equations are derived for conditional moment functionals satisfying certain smoothness properties.

Theory of bimolecular reactions in a solution with linear traps: Application to the problem of target search on DNA.

PubMed

Turkin, Alexander; van Oijen, Antoine M; Turkin, Anatoliy A

2015-01-01

One-dimensional sliding along DNA as a means to accelerate protein target search is a well-known phenomenon occurring in various biological systems. Using a biomimetic approach, we have recently demonstrated the practical use of DNA-sliding peptides to speed up bimolecular reactions more than an order of magnitude by allowing the reactants to associate not only in the solution by three-dimensional (3D) diffusion, but also on DNA via one-dimensional (1D) diffusion [A. Turkin et al., Chem. Sci. (2015)]. Here we present a mean-field kinetic model of a bimolecular reaction in a solution with linear extended sinks (e.g., DNA) that can intermittently trap molecules present in a solution. The model consists of chemical rate equations for mean concentrations of reacting species. Our model demonstrates that addition of linear traps to the solution can significantly accelerate reactant association. We show that at optimum concentrations of linear traps the 1D reaction pathway dominates in the kinetics of the bimolecular reaction; i.e., these 1D traps function as an assembly line of the reaction product. Moreover, we show that the association reaction on linear sinks between trapped reactants exhibits a nonclassical third-order behavior. Predictions of the model agree well with our experimental observations. Our model provides a general description of bimolecular reactions that are controlled by a combined 3D+1D mechanism and can be used to quantitatively describe both naturally occurring as well as biomimetic biochemical systems that reduce the dimensionality of search.

Linear Transceiver Design for Interference Alignment: Complexity and Computation

DTIC Science & Technology

2010-07-01

restriction on the choice of beamforming vector of node b. Thus, for any fixed transmit node b in H , there are multiple restriction sets, each...signal space can be chosen. The receive nodes in H can achieve interference alignment if and only if these restricted sets of one-dimensional signal...total number of restriction sets is at most linear in the number of edges in H and each restriction set contains at most two one-dimensional

Handy elementary algebraic properties of the geometry of entanglement

NASA Astrophysics Data System (ADS)

Blair, Howard A.; Alsing, Paul M.

2013-05-01

The space of separable states of a quantum system is a hyperbolic surface in a high dimensional linear space, which we call the separation surface, within the exponentially high dimensional linear space containing the quantum states of an n component multipartite quantum system. A vector in the linear space is representable as an n-dimensional hypermatrix with respect to bases of the component linear spaces. A vector will be on the separation surface iff every determinant of every 2-dimensional, 2-by-2 submatrix of the hypermatrix vanishes. This highly rigid constraint can be tested merely in time asymptotically proportional to d, where d is the dimension of the state space of the system due to the extreme interdependence of the 2-by-2 submatrices. The constraint on 2-by-2 determinants entails an elementary closed formformula for a parametric characterization of the entire separation surface with d-1 parameters in the char- acterization. The state of a factor of a partially separable state can be calculated in time asymptotically proportional to the dimension of the state space of the component. If all components of the system have approximately the same dimension, the time complexity of calculating a component state as a function of the parameters is asymptotically pro- portional to the time required to sort the basis. Metric-based entanglement measures of pure states are characterized in terms of the separation hypersurface.

Drag reduction by a linear viscosity profile.

PubMed

De Angelis, Elisabetta; Casciola, Carlo M; L'vov, Victor S; Pomyalov, Anna; Procaccia, Itamar; Tiberkevich, Vasil

2004-11-01

Drag reduction by polymers in turbulent flows raises an apparent contradiction: the stretching of the polymers must increase the viscosity, so why is the drag reduced? A recent theory proposed that drag reduction, in agreement with experiments, is consistent with the effective viscosity growing linearly with the distance from the wall. With this self-consistent solution the reduction in the Reynolds stress overwhelms the increase in viscous drag. In this Rapid Communication we show, using direct numerical simulations, that a linear viscosity profile indeed reduces the drag in agreement with the theory and in close correspondence with direct simulations of the FENE-P model at the same flow conditions.

Preprocessing of 2-Dimensional Gel Electrophoresis Images Applied to Proteomic Analysis: A Review.

PubMed

Goez, Manuel Mauricio; Torres-Madroñero, Maria Constanza; Röthlisberger, Sarah; Delgado-Trejos, Edilson

2018-02-01

Various methods and specialized software programs are available for processing two-dimensional gel electrophoresis (2-DGE) images. However, due to the anomalies present in these images, a reliable, automated, and highly reproducible system for 2-DGE image analysis has still not been achieved. The most common anomalies found in 2-DGE images include vertical and horizontal streaking, fuzzy spots, and background noise, which greatly complicate computational analysis. In this paper, we review the preprocessing techniques applied to 2-DGE images for noise reduction, intensity normalization, and background correction. We also present a quantitative comparison of non-linear filtering techniques applied to synthetic gel images, through analyzing the performance of the filters under specific conditions. Synthetic proteins were modeled into a two-dimensional Gaussian distribution with adjustable parameters for changing the size, intensity, and degradation. Three types of noise were added to the images: Gaussian, Rayleigh, and exponential, with signal-to-noise ratios (SNRs) ranging 8-20 decibels (dB). We compared the performance of wavelet, contourlet, total variation (TV), and wavelet-total variation (WTTV) techniques using parameters SNR and spot efficiency. In terms of spot efficiency, contourlet and TV were more sensitive to noise than wavelet and WTTV. Wavelet worked the best for images with SNR ranging 10-20 dB, whereas WTTV performed better with high noise levels. Wavelet also presented the best performance with any level of Gaussian noise and low levels (20-14 dB) of Rayleigh and exponential noise in terms of SNR. Finally, the performance of the non-linear filtering techniques was evaluated using a real 2-DGE image with previously identified proteins marked. Wavelet achieved the best detection rate for the real image. Copyright © 2018 Beijing Institute of Genomics, Chinese Academy of Sciences and Genetics Society of China. Production and hosting by Elsevier B.V. All rights reserved.

Methodology to reduce 6D patient positional shifts into a 3D linear shift and its verification in frameless stereotactic radiotherapy

NASA Astrophysics Data System (ADS)

Sarkar, Biplab; Ray, Jyotirmoy; Ganesh, Tharmarnadar; Manikandan, Arjunan; Munshi, Anusheel; Rathinamuthu, Sasikumar; Kaur, Harpreet; Anbazhagan, Satheeshkumar; Giri, Upendra K.; Roy, Soumya; Jassal, Kanan; Kalyan Mohanti, Bidhu

2018-04-01

The aim of this article is to derive and verify a mathematical formulation for the reduction of the six-dimensional (6D) positional inaccuracies of patients (lateral, longitudinal, vertical, pitch, roll and yaw) to three-dimensional (3D) linear shifts. The formulation was mathematically and experimentally tested and verified for 169 stereotactic radiotherapy patients. The mathematical verification involves the comparison of any (one) of the calculated rotational coordinates with the corresponding value from the 6D shifts obtained by cone beam computed tomography (CBCT). The experimental verification involves three sets of measurements using an ArcCHECK phantom, when (i) the phantom was not moved (neutral position: 0MES), (ii) the position of the phantom shifted by 6D shifts obtained from CBCT (6DMES) from neutral position and (iii) the phantom shifted from its neutral position by 3D shifts reduced from 6D shifts (3DMES). Dose volume histogram and statistical comparisons were made between ≤ft< TPSCAL{\\text -}0MES \\right> and ≤ft< 3DMES{\\text -6DMES} \\right> . The mathematical verification was performed by a comparison of the calculated and measured yaw (γ°) rotation values, which gave a straight line, Y  =  1X with a goodness of fit as R 2  =  0.9982. The verification, based on measurements, gave a planning target volume receiving 100% of the dose (V100%) as 99.1  ±  1.9%, 96.3  ±  1.8%, 74.3  ±  1.9% and 72.6  ±  2.8% for the calculated treatment planning system values TPSCAL, 0MES, 3DMES and 6DMES, respectively. The statistical significance (p-values: paired sample t-test) of V100% were found to be 0.03 for the paired sample ≤ft< 3DMES{\\text -6DMES} \\right> and 0.01 for ≤ft< 0MES{\\text -TPSCAL} \\right> . In this paper, a mathematical method to reduce 6D shifts to 3D shifts is presented. The mathematical method is verified by using well-matched values between the measured and calculated γ°. Measurements done on the ArcCHECK phantom also proved that the proposed methodology is correct. The post-correction of the table position condition introduces a minimal spatial dose delivery error in the frameless stereotactic system, using a 6D motion enabled robotic couch. This formulation enables the reduction of 6D positional inaccuracies to 3D linear shifts, and hence allows the treatment of patients with frameless stereotactic radiosurgery by using only a 3D linear motion enabled couch.

Methodology to reduce 6D patient positional shifts into a 3D linear shift and its verification in frameless stereotactic radiotherapy.

PubMed

Sarkar, Biplab; Ray, Jyotirmoy; Ganesh, Tharmarnadar; Manikandan, Arjunan; Munshi, Anusheel; Rathinamuthu, Sasikumar; Kaur, Harpreet; Anbazhagan, Satheeshkumar; Giri, Upendra K; Roy, Soumya; Jassal, Kanan; Mohanti, Bidhu Kalyan

2018-03-22

The aim of this article is to derive and verify a mathematical formulation for the reduction of the six-dimensional (6D) positional inaccuracies of patients (lateral, longitudinal, vertical, pitch, roll and yaw) to three-dimensional (3D) linear shifts. The formulation was mathematically and experimentally tested and verified for 169 stereotactic radiotherapy patients. The mathematical verification involves the comparison of any (one) of the calculated rotational coordinates with the corresponding value from the 6D shifts obtained by cone beam computed tomography (CBCT). The experimental verification involves three sets of measurements using an ArcCHECK phantom, when (i) the phantom was not moved (neutral position: 0MES), (ii) the position of the phantom shifted by 6D shifts obtained from CBCT (6DMES) from neutral position and (iii) the phantom shifted from its neutral position by 3D shifts reduced from 6D shifts (3DMES). Dose volume histogram and statistical comparisons were made between [Formula: see text] and [Formula: see text]. The mathematical verification was performed by a comparison of the calculated and measured yaw (γ°) rotation values, which gave a straight line, Y  =  1X with a goodness of fit as R 2   =  0.9982. The verification, based on measurements, gave a planning target volume receiving 100% of the dose (V100%) as 99.1  ±  1.9%, 96.3  ±  1.8%, 74.3  ±  1.9% and 72.6  ±  2.8% for the calculated treatment planning system values TPSCAL, 0MES, 3DMES and 6DMES, respectively. The statistical significance (p-values: paired sample t-test) of V100% were found to be 0.03 for the paired sample [Formula: see text] and 0.01 for [Formula: see text]. In this paper, a mathematical method to reduce 6D shifts to 3D shifts is presented. The mathematical method is verified by using well-matched values between the measured and calculated γ°. Measurements done on the ArcCHECK phantom also proved that the proposed methodology is correct. The post-correction of the table position condition introduces a minimal spatial dose delivery error in the frameless stereotactic system, using a 6D motion enabled robotic couch. This formulation enables the reduction of 6D positional inaccuracies to 3D linear shifts, and hence allows the treatment of patients with frameless stereotactic radiosurgery by using only a 3D linear motion enabled couch.

Cell mechanics, structure, and function are regulated by the stiffness of the three-dimensional microenvironment.

PubMed

Chen, J; Irianto, J; Inamdar, S; Pravincumar, P; Lee, D A; Bader, D L; Knight, M M

2012-09-19

This study adopts a combined computational and experimental approach to determine the mechanical, structural, and metabolic properties of isolated chondrocytes cultured within three-dimensional hydrogels. A series of linear elastic and hyperelastic finite-element models demonstrated that chondrocytes cultured for 24 h in gels for which the relaxation modulus is <5 kPa exhibit a cellular Young's modulus of ∼5 kPa. This is notably greater than that reported for isolated chondrocytes in suspension. The increase in cell modulus occurs over a 24-h period and is associated with an increase in the organization of the cortical actin cytoskeleton, which is known to regulate cell mechanics. However, there was a reduction in chromatin condensation, suggesting that changes in the nucleus mechanics may not be involved. Comparison of cells in 1% and 3% agarose showed that cells in the stiffer gels rapidly develop a higher Young's modulus of ∼20 kPa, sixfold greater than that observed in the softer gels. This was associated with higher levels of actin organization and chromatin condensation, but only after 24 h in culture. Further studies revealed that cells in stiffer gels synthesize less extracellular matrix over a 28-day culture period. Hence, this study demonstrates that the properties of the three-dimensional microenvironment regulate the mechanical, structural, and metabolic properties of living cells. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Laser-driven magnetized liner inertial fusion

DOE PAGES

Davies, J. R.

2017-06-05

A laser-driven, magnetized liner inertial fusion (MagLIF) experiment is designed in this paper for the OMEGA Laser System by scaling down the Z point design to provide the first experimental data on MagLIF scaling. OMEGA delivers roughly 1000× less energy than Z, so target linear dimensions are reduced by factors of ~10. Magneto-inertial fusion electrical discharge system could provide an axial magnetic field of 10 T. Two-dimensional hydrocode modeling indicates that a single OMEGA beam can preheat the fuel to a mean temperature of ~200 eV, limited by mix caused by heat flow into the wall. One-dimensional magnetohydrodynamic (MHD) modelingmore » is used to determine the pulse duration and fuel density that optimize neutron yield at a fuel convergence ratio of roughly 25 or less, matching the Z point design, for a range of shell thicknesses. A relatively thinner shell, giving a higher implosion velocity, is required to give adequate fuel heating on OMEGA compared to Z because of the increase in thermal losses in smaller targets. Two-dimensional MHD modeling of the point design gives roughly a 50% reduction in compressed density, temperature, and magnetic field from 1-D because of end losses. Finally, scaling up the OMEGA point design to the MJ laser energy available on the National Ignition Facility gives a 500-fold increase in neutron yield in 1-D modeling.« less

Laser-driven magnetized liner inertial fusion

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

Davies, J. R.

A laser-driven, magnetized liner inertial fusion (MagLIF) experiment is designed in this paper for the OMEGA Laser System by scaling down the Z point design to provide the first experimental data on MagLIF scaling. OMEGA delivers roughly 1000× less energy than Z, so target linear dimensions are reduced by factors of ~10. Magneto-inertial fusion electrical discharge system could provide an axial magnetic field of 10 T. Two-dimensional hydrocode modeling indicates that a single OMEGA beam can preheat the fuel to a mean temperature of ~200 eV, limited by mix caused by heat flow into the wall. One-dimensional magnetohydrodynamic (MHD) modelingmore » is used to determine the pulse duration and fuel density that optimize neutron yield at a fuel convergence ratio of roughly 25 or less, matching the Z point design, for a range of shell thicknesses. A relatively thinner shell, giving a higher implosion velocity, is required to give adequate fuel heating on OMEGA compared to Z because of the increase in thermal losses in smaller targets. Two-dimensional MHD modeling of the point design gives roughly a 50% reduction in compressed density, temperature, and magnetic field from 1-D because of end losses. Finally, scaling up the OMEGA point design to the MJ laser energy available on the National Ignition Facility gives a 500-fold increase in neutron yield in 1-D modeling.« less

A reduction for spiking integrate-and-fire network dynamics ranging from homogeneity to synchrony.

PubMed

Zhang, J W; Rangan, A V

2015-04-01

In this paper we provide a general methodology for systematically reducing the dynamics of a class of integrate-and-fire networks down to an augmented 4-dimensional system of ordinary-differential-equations. The class of integrate-and-fire networks we focus on are homogeneously-structured, strongly coupled, and fluctuation-driven. Our reduction succeeds where most current firing-rate and population-dynamics models fail because we account for the emergence of 'multiple-firing-events' involving the semi-synchronous firing of many neurons. These multiple-firing-events are largely responsible for the fluctuations generated by the network and, as a result, our reduction faithfully describes many dynamic regimes ranging from homogeneous to synchronous. Our reduction is based on first principles, and provides an analyzable link between the integrate-and-fire network parameters and the relatively low-dimensional dynamics underlying the 4-dimensional augmented ODE.

Classifying bilinear differential equations by linear superposition principle

NASA Astrophysics Data System (ADS)

Zhang, Lijun; Khalique, Chaudry Masood; Ma, Wen-Xiu

2016-09-01

In this paper, we investigate the linear superposition principle of exponential traveling waves to construct a sub-class of N-wave solutions of Hirota bilinear equations. A necessary and sufficient condition for Hirota bilinear equations possessing this specific sub-class of N-wave solutions is presented. We apply this result to find N-wave solutions to the (2+1)-dimensional KP equation, a (3+1)-dimensional generalized Kadomtsev-Petviashvili (KP) equation, a (3+1)-dimensional generalized BKP equation and the (2+1)-dimensional BKP equation. The inverse question, i.e., constructing Hirota Bilinear equations possessing N-wave solutions, is considered and a refined 3-step algorithm is proposed. As examples, we construct two very general kinds of Hirota bilinear equations of order 4 possessing N-wave solutions among which one satisfies dispersion relation and another does not satisfy dispersion relation.

Kolmogorov-Kraichnan Scaling in the Inverse Energy Cascade of Two-Dimensional Plasma Turbulence

NASA Astrophysics Data System (ADS)

Antar, G. Y.

2003-08-01

Turbulence in plasmas that are magnetically confined, such as tokamaks or linear devices, is two dimensional or at least quasi two dimensional due to the strong magnetic field, which leads to extreme elongation of the fluctuations, if any, in the direction parallel to the magnetic field. These plasmas are also compressible fluid flows obeying the compressible Navier-Stokes equations. This Letter presents the first comprehensive scaling of the structure functions of the density and velocity fields up to 10th order in the PISCES linear plasma device and up to 6th order in the Mega-Ampère Spherical Tokamak (MAST). In the two devices, it is found that the scaling of the turbulent fields is in good agreement with the prediction of the Kolmogorov-Kraichnan theory for two-dimensional turbulence in the energy cascade subrange.

Lie algebras and linear differential equations.

NASA Technical Reports Server (NTRS)

Brockett, R. W.; Rahimi, A.

1972-01-01

Certain symmetry properties possessed by the solutions of linear differential equations are examined. For this purpose, some basic ideas from the theory of finite dimensional linear systems are used together with the work of Wei and Norman on the use of Lie algebraic methods in differential equation theory.

Understanding decay resistance, dimensional stability and strength changes in heat treated and acetylated wood

Treesearch

Roger M. Rowell; Rebecca E. Ibach; James McSweeny; Thomas Nilsson

2009-01-01

Reductions in hygroscopicity, increased dimensional stability and decay resistance of heat-treated wood depend on decomposition of a large portion of the hemicelluloses in the wood cell wall. In theory, these hemicelluloses are converted to small organic molecules, water and volatile furan-type intermediates that can polymerize in the cell wall. Reductions in...

An in vitro investigation into the physical properties of irreversible hydrocolloid alternatives.

PubMed

Patel, Rishi D; Kattadiyil, Mathew T; Goodacre, Charles J; Winer, Myron S

2010-11-01

A number of manufacturers have introduced new products that are marketed as alternatives to irreversible hydrocolloid impression materials. However, there is a paucity of laboratory and clinical research on these products compared to traditional irreversible hydrocolloid. The purpose of this study was to evaluate the detail reproduction, gypsum compatibility, and linear dimensional change of 3 recently introduced impression materials designed as alternatives to irreversible hydrocolloid. The tested materials were Position Penta Quick, Silgimix, and AlgiNot. An irreversible hydrocolloid impression material, Jeltrate Plus Antimicrobial, served as the control. The parameters of detail reproduction, gypsum compatibility, and linear dimensional change were tested in accordance with ANSI/ADA Specifications No. 18 and 19. The gypsum compatibility was tested using a type III stone (Microstone Golden) and a type IV stone (Die-Keen Green). The data were analyzed using the Kruskal-Wallis rank test and the Mann-Whitney U test (α=.05). The test materials demonstrated significantly (P<.001) better detail reproduction than the control material. Silgimix exhibited the best compatibility with Microstone, whereas AlgiNot and Position Penta Quick exhibited the best gypsum compatibility with Die-Keen. An incompatibility was observed over time between the Jeltrate control material and the Microstone gypsum material. For linear dimensional change, the mean dimension of the control material most closely approximated the distance between the lines on the test die, but it exhibited the greatest variability in measurements. All of the test materials exhibited linear dimensional change within the ADA's accepted limit of 1.0%. The 3 new impression materials exhibited better detail reproduction and less variability in linear dimensional change than the irreversible hydrocolloid control. Gypsum compatibility varied with the brand of gypsum used, with an incompatibility identified between the control material (Jeltrate Plus Antimicrobial) and Microstone related to surface changes observed over time. Copyright © 2010 The Editorial Council of the Journal of Prosthetic Dentistry. Published by Mosby, Inc. All rights reserved.

Aeroelastic loads prediction for an arrow wing. Task 3: Evaluation of the Boeing three-dimensional leading-edge vortex code

NASA Technical Reports Server (NTRS)

Manro, M. E.

1983-01-01

Two separated flow computer programs and a semiempirical method for incorporating the experimentally measured separated flow effects into a linear aeroelastic analysis were evaluated. The three dimensional leading edge vortex (LEV) code is evaluated. This code is an improved panel method for three dimensional inviscid flow over a wing with leading edge vortex separation. The governing equations are the linear flow differential equation with nonlinear boundary conditions. The solution is iterative; the position as well as the strength of the vortex is determined. Cases for both full and partial span vortices were executed. The predicted pressures are good and adequately reflect changes in configuration.

New infinite-dimensional hidden symmetries for heterotic string theory

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

Gao Yajun

The symmetry structures of two-dimensional heterotic string theory are studied further. A (2d+n)x(2d+n) matrix complex H-potential is constructed and the field equations are extended into a complex matrix formulation. A pair of Hauser-Ernst-type linear systems are established. Based on these linear systems, explicit formulations of new hidden symmetry transformations for the considered theory are given and then these symmetry transformations are verified to constitute infinite-dimensional Lie algebras: the semidirect product of the Kac-Moody o(d,d+n-circumflex) and Virasoro algebras (without center charges). These results demonstrate that the heterotic string theory under consideration possesses more and richer symmetry structures than previously expected.

Transition scenario and transition control of the flow over a semi-infinite square leading-edge plate

NASA Astrophysics Data System (ADS)

Huang, Yadong; Zhou, Benmou; Tang, Zhaolie; Zhang, Fei

2017-07-01

In recent investigations of the flow over a square leading-edge flat plate, elliptic instability and transient growth of perturbations are proposed to explain the turbulent transition mechanism of the separating and reattaching flow reported in early experimental visualizations. An original transition scenario as well as a transition control method is presented by a detailed numerical study in this paper. The transient growth of perturbations in the separation bubble induces the primary instability that causes the 2D unsteady flow consisting of Kelvin-Helmholtz (KH) vortices. The pairing instability of the KH vortices induces the subharmonic secondary instability, and then resonance transition occurs. The streamwise Lorentz force as the control input is applied in the recirculation region where the separation bubble generates. The maximum energy amplification magnitude of perturbations takes a linear attenuation with the interaction number; thus, the primary instability is reduced under control. The interaction number represents the strength of the streamwise Lorentz force relative to the inertial force of the fluid. The reduced primary instability is not strong enough to induce the secondary instability, so the flow is globally stable under control. Three-dimensional direct numerical simulation confirms the results of the linear stability analysis. Although the growth rate of the convectively unstable secondary instability is limited by the flow field scale, the feedback loop of the energy transfer promotes the resonance transition. However, as the separation bubble scale is reduced and the feedback loop is broken by the streamwise Lorentz force, the three-dimensional transition is suppressed and a skin-friction drag reduction is achieved.

Recovery of sparse translation-invariant signals with continuous basis pursuit

PubMed Central

Ekanadham, Chaitanya; Tranchina, Daniel; Simoncelli, Eero

2013-01-01

We consider the problem of decomposing a signal into a linear combination of features, each a continuously translated version of one of a small set of elementary features. Although these constituents are drawn from a continuous family, most current signal decomposition methods rely on a finite dictionary of discrete examples selected from this family (e.g., shifted copies of a set of basic waveforms), and apply sparse optimization methods to select and solve for the relevant coefficients. Here, we generate a dictionary that includes auxiliary interpolation functions that approximate translates of features via adjustment of their coefficients. We formulate a constrained convex optimization problem, in which the full set of dictionary coefficients represents a linear approximation of the signal, the auxiliary coefficients are constrained so as to only represent translated features, and sparsity is imposed on the primary coefficients using an L1 penalty. The basis pursuit denoising (BP) method may be seen as a special case, in which the auxiliary interpolation functions are omitted, and we thus refer to our methodology as continuous basis pursuit (CBP). We develop two implementations of CBP for a one-dimensional translation-invariant source, one using a first-order Taylor approximation, and another using a form of trigonometric spline. We examine the tradeoff between sparsity and signal reconstruction accuracy in these methods, demonstrating empirically that trigonometric CBP substantially outperforms Taylor CBP, which in turn offers substantial gains over ordinary BP. In addition, the CBP bases can generally achieve equally good or better approximations with much coarser sampling than BP, leading to a reduction in dictionary dimensionality. PMID:24352562

Maxillary distraction osteogenesis in the adolescent cleft patient: three-dimensional computed tomography analysis of linear and volumetric changes over five years.

PubMed

Chen, Philip Kuo-Ting; Por, Yong-Chen; Liou, Eric Jein-Wein; Chang, Frank Chun-Shin

2011-07-01

To assess the results of maxillary distraction osteogenesis with the Rigid External Distraction System using three-dimensional computed tomography scan volume-rendered images with respect to stability and facial growth at three time frames: preoperative (T0), 1-year postoperative (T1), and 5-years postoperative (T2). Retrospective analysis. Tertiary. A total of 12 patients with severe cleft maxillary hypoplasia were treated between June 30, 1997, and July 15, 1998. The mean age at surgery was 11 years 1 month. Le Fort I maxillary distraction osteogenesis. Distraction was started 2 to 5 days postsurgery at a rate of 1 mm per day. The consolidation period was 3 months. No face mask was used. A paired t test was used for statistical analysis. Overjet, ANB, and SNA and maxillary, pterygoid, and mandibular volumes. From T0 to T1, there were statistically significant increments of overjet, ANB, and SNA and maxillary, pterygoid, and mandibular volumes. The T1 to T2 period demonstrated a reduction of overjet (30.07%) and ANB (54.42%). The maxilla showed a stable SNA and a small but statistically significant advancement of the ANS point. There was a significant increase in the mandibular volume. However, there was no significant change in the maxillary and pterygoid volumes. Maxillary distraction osteogenesis demonstrated linear and volumetric maxillary growth during the distraction phase without clinically significant continued growth thereafter. Overcorrection is required to take into account recurrence of midface retrusion over the long term.

Optimal Wavelength Selection on Hyperspectral Data with Fused Lasso for Biomass Estimation of Tropical Rain Forest

NASA Astrophysics Data System (ADS)

Takayama, T.; Iwasaki, A.

2016-06-01

Above-ground biomass prediction of tropical rain forest using remote sensing data is of paramount importance to continuous large-area forest monitoring. Hyperspectral data can provide rich spectral information for the biomass prediction; however, the prediction accuracy is affected by a small-sample-size problem, which widely exists as overfitting in using high dimensional data where the number of training samples is smaller than the dimensionality of the samples due to limitation of require time, cost, and human resources for field surveys. A common approach to addressing this problem is reducing the dimensionality of dataset. Also, acquired hyperspectral data usually have low signal-to-noise ratio due to a narrow bandwidth and local or global shifts of peaks due to instrumental instability or small differences in considering practical measurement conditions. In this work, we propose a methodology based on fused lasso regression that select optimal bands for the biomass prediction model with encouraging sparsity and grouping, which solves the small-sample-size problem by the dimensionality reduction from the sparsity and the noise and peak shift problem by the grouping. The prediction model provided higher accuracy with root-mean-square error (RMSE) of 66.16 t/ha in the cross-validation than other methods; multiple linear analysis, partial least squares regression, and lasso regression. Furthermore, fusion of spectral and spatial information derived from texture index increased the prediction accuracy with RMSE of 62.62 t/ha. This analysis proves efficiency of fused lasso and image texture in biomass estimation of tropical forests.

Numerical calculations of two dimensional, unsteady transonic flows with circulation

NASA Technical Reports Server (NTRS)

Beam, R. M.; Warming, R. F.

1974-01-01

The feasibility of obtaining two-dimensional, unsteady transonic aerodynamic data by numerically integrating the Euler equations is investigated. An explicit, third-order-accurate, noncentered, finite-difference scheme is used to compute unsteady flows about airfoils. Solutions for lifting and nonlifting airfoils are presented and compared with subsonic linear theory. The applicability and efficiency of the numerical indicial function method are outlined. Numerically computed subsonic and transonic oscillatory aerodynamic coefficients are presented and compared with those obtained from subsonic linear theory and transonic wind-tunnel data.

Estimating contrast transfer function and associated parameters by constrained non-linear optimization.

PubMed

Yang, C; Jiang, W; Chen, D-H; Adiga, U; Ng, E G; Chiu, W

2009-03-01

The three-dimensional reconstruction of macromolecules from two-dimensional single-particle electron images requires determination and correction of the contrast transfer function (CTF) and envelope function. A computational algorithm based on constrained non-linear optimization is developed to estimate the essential parameters in the CTF and envelope function model simultaneously and automatically. The application of this estimation method is demonstrated with focal series images of amorphous carbon film as well as images of ice-embedded icosahedral virus particles suspended across holes.

Cross Flow Effects on Glaze Ice Roughness Formation

NASA Technical Reports Server (NTRS)

Tsao, Jen-Ching

2004-01-01

The present study examines the impact of large-scale cross flow on the creation of ice roughness elements on the leading edge of a swept wing under glaze icing conditions. A three-dimensional triple-deck structure is developed to describe the local interaction of a 3 D air boundary layer with ice sheets and liquid films. A linear stability analysis is presented here. It is found that, as the sweep angle increases, the local icing instabilities enhance and the most linearly unstable modes are strictly three dimensional.

Linear instability in the wake of an elliptic wing

NASA Astrophysics Data System (ADS)

He, Wei; Tendero, Juan Ángel; Paredes, Pedro; Theofilis, Vassilis

2017-12-01

Linear global instability analysis has been performed in the wake of a low aspect ratio three-dimensional wing of elliptic cross section, constructed with appropriately scaled Eppler E387 airfoils. The flow field over the airfoil and in its wake has been computed by full three-dimensional direct numerical simulation at a chord Reynolds number of Rec=1750 and two angles of attack, {AoA}=0° and 5°. Point-vortex methods have been employed to predict the inviscid counterpart of this flow. The spatial BiGlobal eigenvalue problem governing linear small-amplitude perturbations superposed upon the viscous three-dimensional wake has been solved at several axial locations, and results were used to initialize linear PSE-3D analyses without any simplifying assumptions regarding the form of the trailing vortex system, other than weak dependence of all flow quantities on the axial spatial direction. Two classes of linearly unstable perturbations were identified, namely stronger-amplified symmetric modes and weaker-amplified antisymmetric disturbances, both peaking at the vortex sheet which connects the trailing vortices. The amplitude functions of both classes of modes were documented, and their characteristics were compared with those delivered by local linear stability analysis in the wake near the symmetry plane and in the vicinity of the vortex core. While all linear instability analysis approaches employed have delivered qualitatively consistent predictions, only PSE-3D is free from assumptions regarding the underlying base flow and should thus be employed to obtain quantitative information on amplification rates and amplitude functions in this class of configurations.

Reconstruction of three-dimensional ultrasound images based on cyclic Savitzky-Golay filters

NASA Astrophysics Data System (ADS)

Toonkum, Pollakrit; Suwanwela, Nijasri C.; Chinrungrueng, Chedsada

2011-01-01

We present a new algorithm for reconstructing a three-dimensional (3-D) ultrasound image from a series of two-dimensional B-scan ultrasound slices acquired in the mechanical linear scanning framework. Unlike most existing 3-D ultrasound reconstruction algorithms, which have been developed and evaluated in the freehand scanning framework, the new algorithm has been designed to capitalize the regularity pattern of the mechanical linear scanning, where all the B-scan slices are precisely parallel and evenly spaced. The new reconstruction algorithm, referred to as the cyclic Savitzky-Golay (CSG) reconstruction filter, is an improvement on the original Savitzky-Golay filter in two respects: First, it is extended to accept a 3-D array of data as the filter input instead of a one-dimensional data sequence. Second, it incorporates the cyclic indicator function in its least-squares objective function so that the CSG algorithm can simultaneously perform both smoothing and interpolating tasks. The performance of the CSG reconstruction filter compared to that of most existing reconstruction algorithms in generating a 3-D synthetic test image and a clinical 3-D carotid artery bifurcation in the mechanical linear scanning framework are also reported.

Discrimination of stroke-related mild cognitive impairment and vascular dementia using EEG signal analysis.

PubMed

Al-Qazzaz, Noor Kamal; Ali, Sawal Hamid Bin Mohd; Ahmad, Siti Anom; Islam, Mohd Shabiul; Escudero, Javier

2018-01-01

Stroke survivors are more prone to developing cognitive impairment and dementia. Dementia detection is a challenge for supporting personalized healthcare. This study analyzes the electroencephalogram (EEG) background activity of 5 vascular dementia (VaD) patients, 15 stroke-related patients with mild cognitive impairment (MCI), and 15 control healthy subjects during a working memory (WM) task. The objective of this study is twofold. First, it aims to enhance the discrimination of VaD, stroke-related MCI patients, and control subjects using fuzzy neighborhood preserving analysis with QR-decomposition (FNPAQR); second, it aims to extract and investigate the spectral features that characterize the post-stroke dementia patients compared to the control subjects. Nineteen channels were recorded and analyzed using the independent component analysis and wavelet analysis (ICA-WT) denoising technique. Using ANOVA, linear spectral power including relative powers (RP) and power ratio were calculated to test whether the EEG dominant frequencies were slowed down in VaD and stroke-related MCI patients. Non-linear features including permutation entropy (PerEn) and fractal dimension (FD) were used to test the degree of irregularity and complexity, which was significantly lower in patients with VaD and stroke-related MCI than that in control subjects (ANOVA; p ˂ 0.05). This study is the first to use fuzzy neighborhood preserving analysis with QR-decomposition (FNPAQR) dimensionality reduction technique with EEG background activity of dementia patients. The impairment of post-stroke patients was detected using support vector machine (SVM) and k-nearest neighbors (kNN) classifiers. A comparative study has been performed to check the effectiveness of using FNPAQR dimensionality reduction technique with the SVM and kNN classifiers. FNPAQR with SVM and kNN obtained 91.48 and 89.63% accuracy, respectively, whereas without using the FNPAQR exhibited 70 and 67.78% accuracy for SVM and kNN, respectively, in classifying VaD, stroke-related MCI, and control patients, respectively. Therefore, EEG could be a reliable index for inspecting concise markers that are sensitive to VaD and stroke-related MCI patients compared to control healthy subjects.

Fractional exclusion and braid statistics in one dimension: a study via dimensional reduction of Chern-Simons theory

NASA Astrophysics Data System (ADS)

Ye, Fei; Marchetti, P. A.; Su, Z. B.; Yu, L.

2017-09-01

The relation between braid and exclusion statistics is examined in one-dimensional systems, within the framework of Chern-Simons statistical transmutation in gauge invariant form with an appropriate dimensional reduction. If the matter action is anomalous, as for chiral fermions, a relation between braid and exclusion statistics can be established explicitly for both mutual and nonmutual cases. However, if it is not anomalous, the exclusion statistics of emergent low energy excitations is not necessarily connected to the braid statistics of the physical charged fields of the system. Finally, we also discuss the bosonization of one-dimensional anyonic systems through T-duality. Dedicated to the memory of Mario Tonin.

Global invariants of paths and curves for the group of all linear similarities in the two-dimensional Euclidean space

NASA Astrophysics Data System (ADS)

Khadjiev, Djavvat; Ören, Idri˙s; Pekşen, Ömer

Let E2 be the 2-dimensional Euclidean space, LSim(2) be the group of all linear similarities of E2 and LSim+(2) be the group of all orientation-preserving linear similarities of E2. The present paper is devoted to solutions of problems of global G-equivalence of paths and curves in E2 for the groups G = LSim(2),LSim+(2). Complete systems of global G-invariants of a path and a curve in E2 are obtained. Existence and uniqueness theorems are given. Evident forms of a path and a curve with the given global invariants are obtained.

Diffusion maps for high-dimensional single-cell analysis of differentiation data.

PubMed

Haghverdi, Laleh; Buettner, Florian; Theis, Fabian J

2015-09-15

Single-cell technologies have recently gained popularity in cellular differentiation studies regarding their ability to resolve potential heterogeneities in cell populations. Analyzing such high-dimensional single-cell data has its own statistical and computational challenges. Popular multivariate approaches are based on data normalization, followed by dimension reduction and clustering to identify subgroups. However, in the case of cellular differentiation, we would not expect clear clusters to be present but instead expect the cells to follow continuous branching lineages. Here, we propose the use of diffusion maps to deal with the problem of defining differentiation trajectories. We adapt this method to single-cell data by adequate choice of kernel width and inclusion of uncertainties or missing measurement values, which enables the establishment of a pseudotemporal ordering of single cells in a high-dimensional gene expression space. We expect this output to reflect cell differentiation trajectories, where the data originates from intrinsic diffusion-like dynamics. Starting from a pluripotent stage, cells move smoothly within the transcriptional landscape towards more differentiated states with some stochasticity along their path. We demonstrate the robustness of our method with respect to extrinsic noise (e.g. measurement noise) and sampling density heterogeneities on simulated toy data as well as two single-cell quantitative polymerase chain reaction datasets (i.e. mouse haematopoietic stem cells and mouse embryonic stem cells) and an RNA-Seq data of human pre-implantation embryos. We show that diffusion maps perform considerably better than Principal Component Analysis and are advantageous over other techniques for non-linear dimension reduction such as t-distributed Stochastic Neighbour Embedding for preserving the global structures and pseudotemporal ordering of cells. The Matlab implementation of diffusion maps for single-cell data is available at https://www.helmholtz-muenchen.de/icb/single-cell-diffusion-map. fbuettner.phys@gmail.com, fabian.theis@helmholtz-muenchen.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.

Linear optical response of carbon nanotubes under axial magnetic field

NASA Astrophysics Data System (ADS)

Moradian, Rostam; Chegel, Raad; Behzad, Somayeh

2010-04-01

We considered single walled carbon naotubes (SWCNTs) as real three dimensional (3D) systems in a cylindrical coordinate. The optical matrix elements and linear susceptibility, χ(ω), in the tight binding approximation in terms of one-dimensional wave vector, kz and subband index, l are calculated. In an external axial magnetic field optical frequency dependence of linear susceptibility are investigated. We found that axial magnetic field has two effects on the imaginary part of the linear susceptibility spectrum, in agreement with experimental results. The first effect is broadening and the second, splitting. Also we found that for all metallic zigzag and armchair SWCNTs, the axial magnetic field leads to the creation of a peak with energy less than 1.5 eV, contrary to what is observed in the absence of a magnetic field.

A characterization of positive linear maps and criteria of entanglement for quantum states

NASA Astrophysics Data System (ADS)

Hou, Jinchuan

2010-09-01

Let H and K be (finite- or infinite-dimensional) complex Hilbert spaces. A characterization of positive completely bounded normal linear maps from {\\mathcal B}(H) into {\\mathcal B}(K) is given, which particularly gives a characterization of positive elementary operators including all positive linear maps between matrix algebras. This characterization is then applied to give a representation of quantum channels (operations) between infinite-dimensional systems. A necessary and sufficient criterion of separability is given which shows that a state ρ on HotimesK is separable if and only if (ΦotimesI)ρ >= 0 for all positive finite-rank elementary operators Φ. Examples of NCP and indecomposable positive linear maps are given and are used to recognize some entangled states that cannot be recognized by the PPT criterion and the realignment criterion.

A geometric approach to non-linear correlations with intrinsic scatter

NASA Astrophysics Data System (ADS)

Pihajoki, Pauli

2017-12-01

We propose a new mathematical model for n - k-dimensional non-linear correlations with intrinsic scatter in n-dimensional data. The model is based on Riemannian geometry and is naturally symmetric with respect to the measured variables and invariant under coordinate transformations. We combine the model with a Bayesian approach for estimating the parameters of the correlation relation and the intrinsic scatter. A side benefit of the approach is that censored and truncated data sets and independent, arbitrary measurement errors can be incorporated. We also derive analytic likelihoods for the typical astrophysical use case of linear relations in n-dimensional Euclidean space. We pay particular attention to the case of linear regression in two dimensions and compare our results to existing methods. Finally, we apply our methodology to the well-known MBH-σ correlation between the mass of a supermassive black hole in the centre of a galactic bulge and the corresponding bulge velocity dispersion. The main result of our analysis is that the most likely slope of this correlation is ∼6 for the data sets used, rather than the values in the range of ∼4-5 typically quoted in the literature for these data.

Comparative Analysis of Haar and Daubechies Wavelet for Hyper Spectral Image Classification

NASA Astrophysics Data System (ADS)

Sharif, I.; Khare, S.

2014-11-01

With the number of channels in the hundreds instead of in the tens Hyper spectral imagery possesses much richer spectral information than multispectral imagery. The increased dimensionality of such Hyper spectral data provides a challenge to the current technique for analyzing data. Conventional classification methods may not be useful without dimension reduction pre-processing. So dimension reduction has become a significant part of Hyper spectral image processing. This paper presents a comparative analysis of the efficacy of Haar and Daubechies wavelets for dimensionality reduction in achieving image classification. Spectral data reduction using Wavelet Decomposition could be useful because it preserves the distinction among spectral signatures. Daubechies wavelets optimally capture the polynomial trends while Haar wavelet is discontinuous and resembles a step function. The performance of these wavelets are compared in terms of classification accuracy and time complexity. This paper shows that wavelet reduction has more separate classes and yields better or comparable classification accuracy. In the context of the dimensionality reduction algorithm, it is found that the performance of classification of Daubechies wavelets is better as compared to Haar wavelet while Daubechies takes more time compare to Haar wavelet. The experimental results demonstrate the classification system consistently provides over 84% classification accuracy.

The structure of mode-locking regions of piecewise-linear continuous maps: II. Skew sawtooth maps

NASA Astrophysics Data System (ADS)

Simpson, D. J. W.

2018-05-01

In two-parameter bifurcation diagrams of piecewise-linear continuous maps on , mode-locking regions typically have points of zero width known as shrinking points. Near any shrinking point, but outside the associated mode-locking region, a significant proportion of parameter space can be usefully partitioned into a two-dimensional array of annular sectors. The purpose of this paper is to show that in these sectors the dynamics is well-approximated by a three-parameter family of skew sawtooth circle maps, where the relationship between the skew sawtooth maps and the N-dimensional map is fixed within each sector. The skew sawtooth maps are continuous, degree-one, and piecewise-linear, with two different slopes. They approximate the stable dynamics of the N-dimensional map with an error that goes to zero with the distance from the shrinking point. The results explain the complicated radial pattern of periodic, quasi-periodic, and chaotic dynamics that occurs near shrinking points.

Linear Scaling of the Exciton Binding Energy versus the Band Gap of Two-Dimensional Materials

NASA Astrophysics Data System (ADS)

Choi, Jin-Ho; Cui, Ping; Lan, Haiping; Zhang, Zhenyu

2015-08-01

The exciton is one of the most crucial physical entities in the performance of optoelectronic and photonic devices, and widely varying exciton binding energies have been reported in different classes of materials. Using first-principles calculations within the G W -Bethe-Salpeter equation approach, here we investigate the excitonic properties of two recently discovered layered materials: phosphorene and graphene fluoride. We first confirm large exciton binding energies of, respectively, 0.85 and 2.03 eV in these systems. Next, by comparing these systems with several other representative two-dimensional materials, we discover a striking linear relationship between the exciton binding energy and the band gap and interpret the existence of the linear scaling law within a simple hydrogenic picture. The broad applicability of this novel scaling law is further demonstrated by using strained graphene fluoride. These findings are expected to stimulate related studies in higher and lower dimensions, potentially resulting in a deeper understanding of excitonic effects in materials of all dimensionalities.

Dynamic analysis of geometrically non-linear three-dimensional beams under moving mass

NASA Astrophysics Data System (ADS)

Zupan, E.; Zupan, D.

2018-01-01

In this paper, we present a coupled dynamic analysis of a moving particle on a deformable three-dimensional frame. The presented numerical model is capable of considering arbitrary curved and twisted initial geometry of the beam and takes into account geometric non-linearity of the structure. Coupled with dynamic equations of the structure, the equations of moving particle are solved. The moving particle represents the dynamic load and varies the mass distribution of the structure and at the same time its path is adapting due to deformability of the structure. A coupled geometrically non-linear behaviour of beam and particle is studied. The equation of motion of the particle is added to the system of the beam dynamic equations and an additional unknown representing the coordinate of the curvilinear path of the particle is introduced. The specially designed finite-element formulation of the three-dimensional beam based on the weak form of consistency conditions is employed where only the boundary conditions are affected by the contact forces.

Theory of the Lattice Boltzmann Equation: Symmetry properties of Discrete Velocity Sets

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Luo, Li-Shi

2007-01-01

In the lattice Boltzmann equation, continuous particle velocity space is replaced by a finite dimensional discrete set. The number of linearly independent velocity moments in a lattice Boltzmann model cannot exceed the number of discrete velocities. Thus, finite dimensionality introduces linear dependencies among the moments that do not exist in the exact continuous theory. Given a discrete velocity set, it is important to know to exactly what order moments are free of these dependencies. Elementary group theory is applied to the solution of this problem. It is found that by decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group, it becomes relatively straightforward to assess the behavior of moments in the theory. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing some new higher dimensional models are suggested.

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

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

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at; Tuffaha, Amjad, E-mail: atufaha@aus.edu

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solutionmore » of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.« less

Higher-dimensional Bianchi type-VIh cosmologies

NASA Astrophysics Data System (ADS)

Lorenz-Petzold, D.

1985-09-01

The higher-dimensional perfect fluid equations of a generalization of the (1 + 3)-dimensional Bianchi type-VIh space-time are discussed. Bianchi type-V and Bianchi type-III space-times are also included as special cases. It is shown that the Chodos-Detweiler (1980) mechanism of cosmological dimensional-reduction is possible in these cases.

A Recurrent Probabilistic Neural Network with Dimensionality Reduction Based on Time-series Discriminant Component Analysis.

PubMed

Hayashi, Hideaki; Shibanoki, Taro; Shima, Keisuke; Kurita, Yuichi; Tsuji, Toshio

2015-12-01

This paper proposes a probabilistic neural network (NN) developed on the basis of time-series discriminant component analysis (TSDCA) that can be used to classify high-dimensional time-series patterns. TSDCA involves the compression of high-dimensional time series into a lower dimensional space using a set of orthogonal transformations and the calculation of posterior probabilities based on a continuous-density hidden Markov model with a Gaussian mixture model expressed in the reduced-dimensional space. The analysis can be incorporated into an NN, which is named a time-series discriminant component network (TSDCN), so that parameters of dimensionality reduction and classification can be obtained simultaneously as network coefficients according to a backpropagation through time-based learning algorithm with the Lagrange multiplier method. The TSDCN is considered to enable high-accuracy classification of high-dimensional time-series patterns and to reduce the computation time taken for network training. The validity of the TSDCN is demonstrated for high-dimensional artificial data and electroencephalogram signals in the experiments conducted during the study.

Linearization instability for generic gravity in AdS spacetime

NASA Astrophysics Data System (ADS)

Altas, Emel; Tekin, Bayram

2018-01-01

In general relativity, perturbation theory about a background solution fails if the background spacetime has a Killing symmetry and a compact spacelike Cauchy surface. This failure, dubbed as linearization instability, shows itself as non-integrability of the perturbative infinitesimal deformation to a finite deformation of the background. Namely, the linearized field equations have spurious solutions which cannot be obtained from the linearization of exact solutions. In practice, one can show the failure of the linear perturbation theory by showing that a certain quadratic (integral) constraint on the linearized solutions is not satisfied. For non-compact Cauchy surfaces, the situation is different and for example, Minkowski space having a non-compact Cauchy surface, is linearization stable. Here we study, the linearization instability in generic metric theories of gravity where Einstein's theory is modified with additional curvature terms. We show that, unlike the case of general relativity, for modified theories even in the non-compact Cauchy surface cases, there are some theories which show linearization instability about their anti-de Sitter backgrounds. Recent D dimensional critical and three dimensional chiral gravity theories are two such examples. This observation sheds light on the paradoxical behavior of vanishing conserved charges (mass, angular momenta) for non-vacuum solutions, such as black holes, in these theories.

Localized contourlet features in vehicle make and model recognition

NASA Astrophysics Data System (ADS)

Zafar, I.; Edirisinghe, E. A.; Acar, B. S.

2009-02-01

Automatic vehicle Make and Model Recognition (MMR) systems provide useful performance enhancements to vehicle recognitions systems that are solely based on Automatic Number Plate Recognition (ANPR) systems. Several vehicle MMR systems have been proposed in literature. In parallel to this, the usefulness of multi-resolution based feature analysis techniques leading to efficient object classification algorithms have received close attention from the research community. To this effect, Contourlet transforms that can provide an efficient directional multi-resolution image representation has recently been introduced. Already an attempt has been made in literature to use Curvelet/Contourlet transforms in vehicle MMR. In this paper we propose a novel localized feature detection method in Contourlet transform domain that is capable of increasing the classification rates up to 4%, as compared to the previously proposed Contourlet based vehicle MMR approach in which the features are non-localized and thus results in sub-optimal classification. Further we show that the proposed algorithm can achieve the increased classification accuracy of 96% at significantly lower computational complexity due to the use of Two Dimensional Linear Discriminant Analysis (2DLDA) for dimensionality reduction by preserving the features with high between-class variance and low inter-class variance.

Two-dimensional inorganic-organic perovskite hexagonal nanosheets: growth and mechanism

NASA Astrophysics Data System (ADS)

Shakya, Suman; Prakash, G. Vijaya

2015-03-01

In this era of novel technological materials, inorganic-organic (IO) materials has emerged as new class of materials for their application in photonic materials, miniaturized sensors, optoelectronic devices, non-linear optical apparatus by exploiting the properties of both constituents in a single entity. Here we present the formation and growth mechanism of two dimensional Inorganic-organic (IO) perovskite structures from anisotropically grown PbO hexagonal nanosheets, in three steps: Fabrication of hexagonal PbO nanosheets by the versatile bottom-up electrochemical deposition technique, iodinization of PbO into PbI2, followed by conversion of PbI2 into IO hybrid by the intercalation of organic moiety. A systematic and detailed structural study reveals that PbO nanosheet formation is more likely to result from an oriented attachment mechanism, in which the sheets formed by the reduction in surface area that happens during aggregation of small nanoparticle that each has a net dipole moment, which tends to form a self-assembled structure. Intercalation of organic moiety into the PbI2 layers yielded a selfassembled quantum-wells system of one of the IO hybrid, i.e. (C6H9C2H4NH3)2PbI4 (CHPI), sustaining the hexagonal shape.

Application of the adjoint optimisation of shock control bump for ONERA-M6 wing

NASA Astrophysics Data System (ADS)

Nejati, A.; Mazaheri, K.

2017-11-01

This article is devoted to the numerical investigation of the shock wave/boundary layer interaction (SWBLI) as the main factor influencing the aerodynamic performance of transonic bumped airfoils and wings. The numerical analysis is conducted for the ONERA-M6 wing through a shock control bump (SCB) shape optimisation process using the adjoint optimisation method. SWBLI is analyzed for both clean and bumped airfoils and wings, and it is shown how the modified wave structure originating from upstream of the SCB reduces the wave drag, by improving the boundary layer velocity profile downstream of the shock wave. The numerical simulation of the turbulent viscous flow and a gradient-based adjoint algorithm are used to find the optimum location and shape of the SCB for the ONERA-M6 airfoil and wing. Two different geometrical models are introduced for the 3D SCB, one with linear variations, and another with periodic variations. Both configurations result in drag reduction and improvement in the aerodynamic efficiency, but the periodic model is more effective. Although the three-dimensional flow structure involves much more complexities, the overall results are shown to be similar to the two-dimensional case.

Econo-ESA in semantic text similarity.

PubMed

Rahutomo, Faisal; Aritsugi, Masayoshi

2014-01-01

Explicit semantic analysis (ESA) utilizes an immense Wikipedia index matrix in its interpreter part. This part of the analysis multiplies a large matrix by a term vector to produce a high-dimensional concept vector. A similarity measurement between two texts is performed between two concept vectors with numerous dimensions. The cost is expensive in both interpretation and similarity measurement steps. This paper proposes an economic scheme of ESA, named econo-ESA. We investigate two aspects of this proposal: dimensional reduction and experiments with various data. We use eight recycling test collections in semantic text similarity. The experimental results show that both the dimensional reduction and test collection characteristics can influence the results. They also show that an appropriate concept reduction of econo-ESA can decrease the cost with minor differences in the results from the original ESA.

Hybrid approach combining chemometrics and likelihood ratio framework for reporting the evidential value of spectra.

PubMed

Martyna, Agnieszka; Zadora, Grzegorz; Neocleous, Tereza; Michalska, Aleksandra; Dean, Nema

2016-08-10

Many chemometric tools are invaluable and have proven effective in data mining and substantial dimensionality reduction of highly multivariate data. This becomes vital for interpreting various physicochemical data due to rapid development of advanced analytical techniques, delivering much information in a single measurement run. This concerns especially spectra, which are frequently used as the subject of comparative analysis in e.g. forensic sciences. In the presented study the microtraces collected from the scenarios of hit-and-run accidents were analysed. Plastic containers and automotive plastics (e.g. bumpers, headlamp lenses) were subjected to Fourier transform infrared spectrometry and car paints were analysed using Raman spectroscopy. In the forensic context analytical results must be interpreted and reported according to the standards of the interpretation schemes acknowledged in forensic sciences using the likelihood ratio approach. However, for proper construction of LR models for highly multivariate data, such as spectra, chemometric tools must be employed for substantial data compression. Conversion from classical feature representation to distance representation was proposed for revealing hidden data peculiarities and linear discriminant analysis was further applied for minimising the within-sample variability while maximising the between-sample variability. Both techniques enabled substantial reduction of data dimensionality. Univariate and multivariate likelihood ratio models were proposed for such data. It was shown that the combination of chemometric tools and the likelihood ratio approach is capable of solving the comparison problem of highly multivariate and correlated data after proper extraction of the most relevant features and variance information hidden in the data structure. Copyright © 2016 Elsevier B.V. All rights reserved.

A purely Lagrangian method for computing linearly-perturbed flows in spherical geometry

NASA Astrophysics Data System (ADS)

Jaouen, Stéphane

2007-07-01

In many physical applications, one wishes to control the development of multi-dimensional instabilities around a one-dimensional (1D) complex flow. For predicting the growth rates of these perturbations, a general numerical approach is viable which consists in solving simultaneously the one-dimensional equations and their linearized form for three-dimensional perturbations. In Clarisse et al. [J.-M. Clarisse, S. Jaouen, P.-A. Raviart, A Godunov-type method in Lagrangian coordinates for computing linearly-perturbed planar-symmetric flows of gas dynamics, J. Comp. Phys. 198 (2004) 80-105], a class of Godunov-type schemes for planar-symmetric flows of gas dynamics has been proposed. Pursuing this effort, we extend these results to spherically symmetric flows. A new method to derive the Lagrangian perturbation equations, based on the canonical form of systems of conservation laws with zero entropy flux [B. Després, Lagrangian systems of conservation laws. Invariance properties of Lagrangian systems of conservation laws, approximate Riemann solvers and the entropy condition, Numer. Math. 89 (2001) 99-134; B. Després, C. Mazeran, Lagrangian gas dynamics in two dimensions and Lagrangian systems, Arch. Rational Mech. Anal. 178 (2005) 327-372] is also described. It leads to many advantages. First of all, many physical problems we are interested in enter this formalism (gas dynamics, two-temperature plasma equations, ideal magnetohydrodynamics, etc.) whatever is the geometry. Secondly, a class of numerical entropic schemes is available for the basic flow [11]. Last, linearizing and devising numerical schemes for the perturbed flow is straightforward. The numerical capabilities of these methods are illustrated on three test cases of increasing difficulties and we show that - due to its simplicity and its low computational cost - the Linear Perturbations Code (LPC) is a powerful tool to understand and predict the development of hydrodynamic instabilities in the linear regime.

Digital Image Restoration Under a Regression Model - The Unconstrained, Linear Equality and Inequality Constrained Approaches

DTIC Science & Technology

1974-01-01

REGRESSION MODEL - THE UNCONSTRAINED, LINEAR EQUALITY AND INEQUALITY CONSTRAINED APPROACHES January 1974 Nelson Delfino d’Avila Mascarenha;? Image...Report 520 DIGITAL IMAGE RESTORATION UNDER A REGRESSION MODEL THE UNCONSTRAINED, LINEAR EQUALITY AND INEQUALITY CONSTRAINED APPROACHES January...a two- dimensional form adequately describes the linear model . A dis- cretization is performed by using quadrature methods. By trans

Dusty plasma (Yukawa) rings

NASA Astrophysics Data System (ADS)

Sheridan, T. E.; Gallagher, James C.

2016-11-01

One-dimensional and quasi-one-dimensional strongly coupled dusty plasma rings have been created experimentally. Longitudinal (acoustic) and transverse (optical) dispersion relations for the one-ring are measured and found to be in excellent agreement with the theory for an unbounded straight chain of particles interacting through a Yukawa (i.e., screened Coulomb or Debye-Hückel) potential. These rings provide a new experimental system to directly study one-dimensional and quasi-one-dimensional linear and nonlinear phenomena.

Higher-order gravity in higher dimensions: geometrical origins of four-dimensional cosmology?

NASA Astrophysics Data System (ADS)

Troisi, Antonio

2017-03-01

Determining the cosmological field equations is still very much debated and led to a wide discussion around different theoretical proposals. A suitable conceptual scheme could be represented by gravity models that naturally generalize Einstein theory like higher-order gravity theories and higher-dimensional ones. Both of these two different approaches allow one to define, at the effective level, Einstein field equations equipped with source-like energy-momentum tensors of geometrical origin. In this paper, the possibility is discussed to develop a five-dimensional fourth-order gravity model whose lower-dimensional reduction could provide an interpretation of cosmological four-dimensional matter-energy components. We describe the basic concepts of the model, the complete field equations formalism and the 5-D to 4-D reduction procedure. Five-dimensional f( R) field equations turn out to be equivalent, on the four-dimensional hypersurfaces orthogonal to the extra coordinate, to an Einstein-like cosmological model with three matter-energy tensors related with higher derivative and higher-dimensional counter-terms. By considering the gravity model with f(R)=f_0R^n the possibility is investigated to obtain five-dimensional power law solutions. The effective four-dimensional picture and the behaviour of the geometrically induced sources are finally outlined in correspondence to simple cases of such higher-dimensional solutions.

Three-dimensional instabilities of natural convection between two differentially heated vertical plates: Linear and nonlinear complementary approaches

NASA Astrophysics Data System (ADS)

Gao, Zhenlan; Podvin, Berengere; Sergent, Anne; Xin, Shihe; Chergui, Jalel

2018-05-01

The transition to the chaos of the air flow between two vertical plates maintained at different temperatures is studied in the Boussinesq approximation. After the first bifurcation at critical Rayleigh number Rac, the flow consists of two-dimensional (2D) corotating rolls. The stability of the 2D rolls is examined, confronting linear predictions with nonlinear integration. In all cases the 2D rolls are destabilized in the spanwise direction. Efficient linear stability analysis based on an Arnoldi method shows competition between two eigenmodes, corresponding to different spanwise wavelengths and different types of roll distortion. Nonlinear integration shows that the lower-wave-number mode is always dominant. A partial route to chaos is established through the nonlinear simulations. The flow becomes temporally chaotic for Ra =1.05 Rac , but remains characterized by the spatial patterns identified by linear stability analysis. This highlights the complementary role of linear stability analysis and nonlinear simulation.

A numerical algorithm for optimal feedback gains in high dimensional linear quadratic regulator problems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Ito, K.

1991-01-01

A hybrid method for computing the feedback gains in linear quadratic regulator problem is proposed. The method, which combines use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite-dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantages of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed, and numerical evidence of the efficacy of these ideas is presented.

More on cosmological gravitational waves and their memories

NASA Astrophysics Data System (ADS)

Chu, Yi-Zen

2017-10-01

We extend recent theoretical results on the propagation of linear gravitational waves (GWs), including their associated memories, in spatially flat Friedmann-Lemaître-Robertson-Walker universes, for all spacetime dimensions higher than 3. By specializing to a cosmology driven by a perfect fluid with a constant equation-of-state w, conformal re-scaling, dimension-reduction and Nariai’s ansatz may then be exploited to obtain analytic expressions for the graviton and photon Green’s functions, allowing their causal structure to be elucidated. When 0 < w ≤slant 1 , the gauge-invariant scalar mode admits wave solutions, and like its tensor counterpart, likely contributes to the tidal squeezing and stretching of the space around a GW detector. In addition, scalar GWs in 4D radiation dominated universes—like tensor GWs in 4D matter dominated ones—appear to yield a tail signal that does not decay with increasing spatial distance from the source. We then solve electromagnetism in the same cosmologies, and point out a tail-induced electric memory effect. Finally, in even dimensional Minkowski backgrounds higher than 2, we make a brief but explicit comparison between the linear GW memory generated by point masses scattering off each other on unbound trajectories and the linear Yang-Mills memory generated by color point charges doing the same—and point out how there is a ‘double copy’ relation between the two.

Magnetic susceptibility, artifact volume in MRI, and tensile properties of swaged Zr-Ag composites for biomedical applications.

PubMed

Imai, Haruki; Tanaka, Yoji; Nomura, Naoyuki; Doi, Hisashi; Tsutsumi, Yusuke; Ono, Takashi; Hanawa, Takao

2017-02-01

Zr-Ag composites were fabricated to decrease the magnetic susceptibility by compensating for the magnetic susceptibility of their components. The Zr-Ag composites with a different Zr-Ag ratio were swaged, and their magnetic susceptibility, artifact volume, and mechanical properties were evaluated by magnetic balance, three-dimensional (3-D) artifact rendering, and a tensile test, respectively. These properties were correlated with the volume fraction of Ag using the linear rule of mixture. We successfully obtained the swaged Zr-Ag composites up to the reduction ratio of 96% for Zr-4, 16, 36, 64Ag and 86% for Zr-81Ag. However, the volume fraction of Ag after swaging tended to be lower than that before swaging, especially for Ag-rich Zr-Ag composites. The magnetic susceptibility of the composites linearly decreased with the increasing volume fraction of Ag. No artifact could be estimated with the Ag volume fraction in the range from 93.7% to 95.4% in three conditions. Young's modulus, ultimate tensile strength (UTS), and 0.2% yield strength of Zr-Ag composites showed slightly lower values compared to the estimated values using a linear rule of mixture. The decrease in magnetic susceptibility of Zr and Ag by alloying or combining would contribute to the decrease of the Ag fraction, leading to the improvement of mechanical properties. Copyright © 2016 Elsevier Ltd. All rights reserved.

Global optimization for quantum dynamics of few-fermion systems

NASA Astrophysics Data System (ADS)

Li, Xikun; Pecak, Daniel; Sowiński, Tomasz; Sherson, Jacob; Nielsen, Anne E. B.

2018-03-01

Quantum state preparation is vital to quantum computation and quantum information processing tasks. In adiabatic state preparation, the target state is theoretically obtained with nearly perfect fidelity if the control parameter is tuned slowly enough. As this, however, leads to slow dynamics, it is often desirable to be able to carry out processes more rapidly. In this work, we employ two global optimization methods to estimate the quantum speed limit for few-fermion systems confined in a one-dimensional harmonic trap. Such systems can be produced experimentally in a well-controlled manner. We determine the optimized control fields and achieve a reduction in the ramping time of more than a factor of four compared to linear ramping. We also investigate how robust the fidelity is to small variations of the control fields away from the optimized shapes.

Position specific interaction dependent scoring technique for virtual screening based on weighted protein--ligand interaction fingerprint profiles.

PubMed

Nandigam, Ravi K; Kim, Sangtae; Singh, Juswinder; Chuaqui, Claudio

2009-05-01

The desire to exploit structural information to aid structure based design and virtual screening led to the development of the interaction fingerprint for analyzing, mining, and filtering the binding patterns underlying the complex 3D data. In this paper we introduce a new approach, weighted SIFt (or w-SIFt), extending the concept of SIFt to capture the relative importance of different binding interactions. The methodology presented here for determining the weights in w-SIFt involves utilizing a dimensionality reduction technique for eliminating linear redundancies in the data followed by a stochastic optimization. We find that the relative weights of the fingerprint bits provide insight into what interactions are critical in determining inhibitor potency. Moreover, the weighted interaction fingerprint can serve as an interpretable position dependent scoring function for ligand protein interactions.

Wake Management Strategies for Reduction of Turbomachinery Fan Noise

NASA Technical Reports Server (NTRS)

Waitz, Ian A.

1998-01-01

The primary objective of our work was to evaluate and test several wake management schemes for the reduction of turbomachinery fan noise. Throughout the course of this work we relied on several tools. These include 1) Two-dimensional steady boundary-layer and wake analyses using MISES (a thin-shear layer Navier-Stokes code), 2) Two-dimensional unsteady wake-stator interaction simulations using UNSFLO, 3) Three-dimensional, steady Navier-Stokes rotor simulations using NEWT, 4) Internal blade passage design using quasi-one-dimensional passage flow models developed at MIT, 5) Acoustic modeling using LINSUB, 6) Acoustic modeling using VO72, 7) Experiments in a low-speed cascade wind-tunnel, and 8) ADP fan rig tests in the MIT Blowdown Compressor.

Perturbations of linear delay differential equations at the verge of instability.

PubMed

Lingala, N; Namachchivaya, N Sri

2016-06-01

The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e., a pair of roots of the characteristic equation lies on the imaginary axis of the complex plane and all other roots have negative real parts. It is shown that when small noise perturbations are present, the probability distribution of the dynamics can be approximated by the probability distribution of a certain one-dimensional stochastic differential equation (SDE) without delay. This is advantageous because equations without delay are easier to simulate and one-dimensional SDEs are analytically tractable. When the perturbations are also linear, it is shown that the stability depends on a specific complex number. The theory is applied to study oscillators with delayed feedback. Some errors in other articles that use multiscale approach are pointed out.

Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices

DOE PAGES

Chong, C.; Kevrekidis, P. G.; Ablowitz, M. J.; ...

2016-01-25

We explore linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in a hexagonal packing configuration is analyzed. Upon identifying the dispersion relation of the underlying linear problem, the resulting diffraction properties are considered. Analysis both via a heuristic argument for the linear propagation of a wave packet and via asymptotic analysis leading to the derivation of a Dirac system suggests the occurrence of conical diffraction. This analysis is valid for strong precompression, i.e., near the linear regime. Formore » weak precompression, conical wave propagation is still possible, but the resulting expanding circular wave front is of a nonoscillatory nature, resulting from the complex interplay among the discreteness, nonlinearity, and geometry of the packing. Lastly, the transition between these two types of propagation is explored.« less

System and method for investigating sub-surface features and 3D imaging of non-linear property, compressional velocity VP, shear velocity VS and velocity ratio VP/VS of a rock formation

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

Vu, Cung Khac; Skelt, Christopher; Nihei, Kurt

A system and a method for generating a three-dimensional image of a rock formation, compressional velocity VP, shear velocity VS and velocity ratio VP/VS of a rock formation are provided. A first acoustic signal includes a first plurality of pulses. A second acoustic signal from a second source includes a second plurality of pulses. A detected signal returning to the borehole includes a signal generated by a non-linear mixing process from the first and second acoustic signals in a non-linear mixing zone within an intersection volume. The received signal is processed to extract the signal over noise and/or signals resultingmore » from linear interaction and the three dimensional image of is generated.« less

Linear response approach to active Brownian particles in time-varying activity fields

NASA Astrophysics Data System (ADS)

Merlitz, Holger; Vuijk, Hidde D.; Brader, Joseph; Sharma, Abhinav; Sommer, Jens-Uwe

2018-05-01

In a theoretical and simulation study, active Brownian particles (ABPs) in three-dimensional bulk systems are exposed to time-varying sinusoidal activity waves that are running through the system. A linear response (Green-Kubo) formalism is applied to derive fully analytical expressions for the torque-free polarization profiles of non-interacting particles. The activity waves induce fluxes that strongly depend on the particle size and may be employed to de-mix mixtures of ABPs or to drive the particles into selected areas of the system. Three-dimensional Langevin dynamics simulations are carried out to verify the accuracy of the linear response formalism, which is shown to work best when the particles are small (i.e., highly Brownian) or operating at low activity levels.

Finite-dimensional integrable systems: A collection of research problems

NASA Astrophysics Data System (ADS)

Bolsinov, A. V.; Izosimov, A. M.; Tsonev, D. M.

2017-05-01

This article suggests a series of problems related to various algebraic and geometric aspects of integrability. They reflect some recent developments in the theory of finite-dimensional integrable systems such as bi-Poisson linear algebra, Jordan-Kronecker invariants of finite dimensional Lie algebras, the interplay between singularities of Lagrangian fibrations and compatible Poisson brackets, and new techniques in projective geometry.

Supercomputer algorithms for efficient linear octree encoding of three-dimensional brain images.

PubMed

Berger, S B; Reis, D J

1995-02-01

We designed and implemented algorithms for three-dimensional (3-D) reconstruction of brain images from serial sections using two important supercomputer architectures, vector and parallel. These architectures were represented by the Cray YMP and Connection Machine CM-2, respectively. The programs operated on linear octree representations of the brain data sets, and achieved 500-800 times acceleration when compared with a conventional laboratory workstation. As the need for higher resolution data sets increases, supercomputer algorithms may offer a means of performing 3-D reconstruction well above current experimental limits.

Separation of Arylenevinylene Macrocycles with a Surface-Confined Two-Dimensional Covalent Organic Framework.

PubMed

Liu, Chunhua; Park, Eunsol; Jin, Yinghua; Liu, Jie; Yu, Yanxia; Zhang, Wei; Lei, Shengbin; Hu, Wenping

2018-05-31

A two-dimensional surface covalent organic framework, prepared by a surface-confined synthesis using 4,4'-azodianiline and benzene-1,3,5-tricarbaldehyde as the precursors, was used as a host network to effectively immobilize arylenevinylene macrocycles (AVMs). Thus AVMs could be separated from their linear polymer analogues, which are the common side-products in the cyclooligomerization process. Scanning tunneling microscopy investigations revealed efficient removal of linear polymers by a simple surface binding and solvent washing process. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

The three-dimensional evolution of a plane mixing layer. Part 1: The Kelvin-Helmholtz roll-up

NASA Technical Reports Server (NTRS)

Rogers, Michael M.; Moser, Robert D.

1991-01-01

The Kelvin Helmholtz roll up of three dimensional, temporally evolving, plane mixing layers were simulated numerically. All simulations were begun from a few low wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity profile. The spanwise disturbance wavelength was taken to be less than or equal to the streamwise wavelength associated with the Kelvin Helmholtz roll up. A standard set of clean structures develop in most of the simulations. The spanwise vorticity rolls up into a corrugated spanwise roller, with vortex stretching creating strong spanwise vorticity in a cup shaped region at the vends of the roller. Predominantly streamwise rib vortices develop in the braid region between the rollers. For sufficiently strong initial three dimensional disturbances, these ribs collapse into compact axisymmetric vortices. The rib vortex lines connect to neighboring ribs and are kinked in the opposite direction of the roller vortex lines. Because of this, these two sets of vortex lines remain distinct. For certain initial conditions, persistent ribs do not develop. In such cases the development of significant three dimensionality is delayed. When the initial three dimensional disturbance energy is about equal to, or less than, the two dimensional fundamental disturbance energy, the evolution of the three dimensional disturbance is nearly linear (with respect to the mean and the two dimensional disturbances), at least until the first Kelvin Helmholtz roll up is completed.

Valuation of financial models with non-linear state spaces

NASA Astrophysics Data System (ADS)

Webber, Nick

2001-02-01

A common assumption in valuation models for derivative securities is that the underlying state variables take values in a linear state space. We discuss numerical implementation issues in an interest rate model with a simple non-linear state space, formulating and comparing Monte Carlo, finite difference and lattice numerical solution methods. We conclude that, at least in low dimensional spaces, non-linear interest rate models may be viable.

Simplifying the representation of complex free-energy landscapes using sketch-map

PubMed Central

Ceriotti, Michele; Tribello, Gareth A.; Parrinello, Michele

2011-01-01

A new scheme, sketch-map, for obtaining a low-dimensional representation of the region of phase space explored during an enhanced dynamics simulation is proposed. We show evidence, from an examination of the distribution of pairwise distances between frames, that some features of the free-energy surface are inherently high-dimensional. This makes dimensionality reduction problematic because the data does not satisfy the assumptions made in conventional manifold learning algorithms We therefore propose that when dimensionality reduction is performed on trajectory data one should think of the resultant embedding as a quickly sketched set of directions rather than a road map. In other words, the embedding tells one about the connectivity between states but does not provide the vectors that correspond to the slow degrees of freedom. This realization informs the development of sketch-map, which endeavors to reproduce the proximity information from the high-dimensionality description in a space of lower dimensionality even when a faithful embedding is not possible. PMID:21730167

Physical aspects of heat generation/absorption in the second grade fluid flow due to Riga plate: Application of Cattaneo-Christov approach

NASA Astrophysics Data System (ADS)

Anjum, Aisha; Mir, N. A.; Farooq, M.; Javed, M.; Ahmad, S.; Malik, M. Y.; Alshomrani, A. S.

2018-06-01

The present article concentrates on thermal stratification in the flow of second grade fluid past a Riga plate with linear stretching towards a stagnation region. Heat transfer phenomenon is disclosed with heat generation/absorption. Riga plate is known as electromagnetic actuator which comprises of permanent magnets and alternating electrodes placed on a plane surface. Cattaneo-Christov heat flux model is implemented to analyze the features of heat transfer. This new heat flux model is the generalization of classical Fourier's law with the contribution of thermal relaxation time. For the first time heat generation/absorption effect is computed with non-Fourier's law of heat conduction (i.e., Cattaneo-Christov heat flux model). Transformations are used to obtain the governing non-linear ordinary differential equations. Approximate convergent solutions are developed for the non-dimensionalized governing problems. Physical features of velocity and temperature distributions are graphically analyzed corresponding to various parameters in 2D and 3D. It is noted that velocity field enhances with an increment of modified Hartman number while it reduces with increasing variable thickness parameter. Increment in modified heat generation parameter results in reduction of temperature field.

Restoration of dimensional reduction in the random-field Ising model at five dimensions

NASA Astrophysics Data System (ADS)

Fytas, Nikolaos G.; Martín-Mayor, Víctor; Picco, Marco; Sourlas, Nicolas

2017-04-01

The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in D dimensions are identical to those of the pure Ising ferromagnet in D -2 dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at D =5 . We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions 3 ≤D <6 to their values in the pure Ising model at D -2 dimensions, and we provide a clear verification of the Rushbrooke equality at all studied dimensions.

Restoration of dimensional reduction in the random-field Ising model at five dimensions.

PubMed

Fytas, Nikolaos G; Martín-Mayor, Víctor; Picco, Marco; Sourlas, Nicolas

2017-04-01

The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in D dimensions are identical to those of the pure Ising ferromagnet in D-2 dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at D=5. We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions 3≤D<6 to their values in the pure Ising model at D-2 dimensions, and we provide a clear verification of the Rushbrooke equality at all studied dimensions.

Dimensional reduction for a SIR type model

NASA Astrophysics Data System (ADS)

Cahyono, Edi; Soeharyadi, Yudi; Mukhsar

2018-03-01

Epidemic phenomena are often modeled in the form of dynamical systems. Such model has also been used to model spread of rumor, spread of extreme ideology, and dissemination of knowledge. Among the simplest is SIR (susceptible, infected and recovered) model, a model that consists of three compartments, and hence three variables. The variables are functions of time which represent the number of subpopulations, namely suspect, infected and recovery. The sum of the three is assumed to be constant. Hence, the model is actually two dimensional which sits in three-dimensional ambient space. This paper deals with the reduction of a SIR type model into two variables in two-dimensional ambient space to understand the geometry and dynamics better. The dynamics is studied, and the phase portrait is presented. The two dimensional model preserves the equilibrium and the stability. The model has been applied for knowledge dissemination, which has been the interest of knowledge management.

DeDaL: Cytoscape 3 app for producing and morphing data-driven and structure-driven network layouts.

PubMed

Czerwinska, Urszula; Calzone, Laurence; Barillot, Emmanuel; Zinovyev, Andrei

2015-08-14

Visualization and analysis of molecular profiling data together with biological networks are able to provide new mechanistic insights into biological functions. Currently, it is possible to visualize high-throughput data on top of pre-defined network layouts, but they are not always adapted to a given data analysis task. A network layout based simultaneously on the network structure and the associated multidimensional data might be advantageous for data visualization and analysis in some cases. We developed a Cytoscape app, which allows constructing biological network layouts based on the data from molecular profiles imported as values of node attributes. DeDaL is a Cytoscape 3 app, which uses linear and non-linear algorithms of dimension reduction to produce data-driven network layouts based on multidimensional data (typically gene expression). DeDaL implements several data pre-processing and layout post-processing steps such as continuous morphing between two arbitrary network layouts and aligning one network layout with respect to another one by rotating and mirroring. The combination of all these functionalities facilitates the creation of insightful network layouts representing both structural network features and correlation patterns in multivariate data. We demonstrate the added value of applying DeDaL in several practical applications, including an example of a large protein-protein interaction network. DeDaL is a convenient tool for applying data dimensionality reduction methods and for designing insightful data displays based on data-driven layouts of biological networks, built within Cytoscape environment. DeDaL is freely available for downloading at http://bioinfo-out.curie.fr/projects/dedal/.

Applying the J-optimal channelized quadratic observer to SPECT myocardial perfusion defect detection

NASA Astrophysics Data System (ADS)

Kupinski, Meredith K.; Clarkson, Eric; Ghaly, Michael; Frey, Eric C.

2016-03-01

To evaluate performance on a perfusion defect detection task from 540 image pairs of myocardial perfusion SPECT image data we apply the J-optimal channelized quadratic observer (J-CQO). We compare AUC values of the linear Hotelling observer and J-CQO when the defect location is fixed and when it occurs in one of two locations. As expected, when the location is fixed a single channels maximizes AUC; location variability requires multiple channels to maximize the AUC. The AUC is estimated from both the projection data and reconstructed images. J-CQO is quadratic since it uses the first- and second- order statistics of the image data from both classes. The linear data reduction by the channels is described by an L x M channel matrix and in prior work we introduced an iterative gradient-based method for calculating the channel matrix. The dimensionality reduction from M measurements to L channels yields better estimates of these sample statistics from smaller sample sizes, and since the channelized covariance matrix is L x L instead of M x M, the matrix inverse is easier to compute. The novelty of our approach is the use of Jeffrey's divergence (J) as the figure of merit (FOM) for optimizing the channel matrix. We previously showed that the J-optimal channels are also the optimum channels for the AUC and the Bhattacharyya distance when the channel outputs are Gaussian distributed with equal means. This work evaluates the use of J as a surrogate FOM (SFOM) for AUC when these statistical conditions are not satisfied.

Imaging of downward-looking linear array SAR using three-dimensional spatial smoothing MUSIC algorithm

NASA Astrophysics Data System (ADS)

Zhang, Siqian; Kuang, Gangyao

2014-10-01

In this paper, a novel three-dimensional imaging algorithm of downward-looking linear array SAR is presented. To improve the resolution, multiple signal classification (MUSIC) algorithm has been used. However, since the scattering centers are always correlated in real SAR system, the estimated covariance matrix becomes singular. To address the problem, a three-dimensional spatial smoothing method is proposed in this paper to restore the singular covariance matrix to a full-rank one. The three-dimensional signal matrix can be divided into a set of orthogonal three-dimensional subspaces. The main idea of the method is based on extracting the array correlation matrix as the average of all correlation matrices from the subspaces. In addition, the spectral height of the peaks contains no information with regard to the scattering intensity of the different scattering centers, thus it is difficulty to reconstruct the backscattering information. The least square strategy is used to estimate the amplitude of the scattering center in this paper. The above results of the theoretical analysis are verified by 3-D scene simulations and experiments on real data.

Asymmetries and three-dimensional features of vestibular cross-coupled stimuli illuminated through modeling

PubMed Central

Holly, Jan E.; Masood, M. Arjumand; Bhandari, Chiran S.

2017-01-01

Head movements during sustained rotation can cause angular cross-coupling which leads to tumbling illusions. Even though angular vectors predict equal magnitude illusions for head movements in opposite directions, the magnitudes of the illusions are often surprisingly asymmetric, such as during leftward versus rightward yaw while horizontal in a centrifuge. This paper presents a comprehensive investigation of the angular-linear stimulus combinations from eight different published papers in which asymmetries were found. Interactions between all angular and linear vectors, including gravity, are taken into account to model the three-dimensional consequences of the stimuli. Three main results followed. First, for every pair of head yaw movements, an asymmetry was found in the stimulus itself when considered in a fully three-dimensional manner, and the direction of the asymmetry matched the subjectively reported magnitude asymmetry. Second, for pitch and roll head movements for which motion sickness was measured, the stimulus was found symmetric in every case except one, and motion sickness generally aligned with other factors such as the existence of a head rest. Third, three-dimensional modeling predicted subjective inconsistency in the direction of perceived rotation when linear and angular components were oppositely-directed, and predicted surplus illusory rotation in the direction of head movement. PMID:27814310

Optimum Particle Size for Gold-Catalyzed CO Oxidation

PubMed Central

2018-01-01

The structure sensitivity of gold-catalyzed CO oxidation is presented by analyzing in detail the dependence of CO oxidation rate on particle size. Clusters with less than 14 gold atoms adopt a planar structure, whereas larger ones adopt a three-dimensional structure. The CO and O2 adsorption properties depend strongly on particle structure and size. All of the reaction barriers relevant to CO oxidation display linear scaling relationships with CO and O2 binding strengths as main reactivity descriptors. Planar and three-dimensional gold clusters exhibit different linear scaling relationship due to different surface topologies and different coordination numbers of the surface atoms. On the basis of these linear scaling relationships, first-principles microkinetics simulations were conducted to determine CO oxidation rates and possible rate-determining step of Au particles. Planar Au9 and three-dimensional Au79 clusters present the highest CO oxidation rates for planar and three-dimensional clusters, respectively. The planar Au9 cluster is much more active than the optimum Au79 cluster. A common feature of optimum CO oxidation performance is the intermediate binding strengths of CO and O2, resulting in intermediate coverages of CO, O2, and O. Both these optimum particles present lower performance than maximum Sabatier performance, indicating that there is sufficient room for improvement of gold catalysts for CO oxidation. PMID:29707098

The Stark Effect in Linear Potentials

ERIC Educational Resources Information Center

Robinett, R. W.

2010-01-01

We examine the Stark effect (the second-order shifts in the energy spectrum due to an external constant force) for two one-dimensional model quantum mechanical systems described by linear potentials, the so-called quantum bouncer (defined by V(z) = Fz for z greater than 0 and V(z) = [infinity] for z less than 0) and the symmetric linear potential…

Linear Equating for the NEAT Design: Parameter Substitution Models and Chained Linear Relationship Models

ERIC Educational Resources Information Center

Kane, Michael T.; Mroch, Andrew A.; Suh, Youngsuk; Ripkey, Douglas R.

2009-01-01

This paper analyzes five linear equating models for the "nonequivalent groups with anchor test" (NEAT) design with internal anchors (i.e., the anchor test is part of the full test). The analysis employs a two-dimensional framework. The first dimension contrasts two general approaches to developing the equating relationship. Under a "parameter…

Sparse representation of multi parametric DCE-MRI features using K-SVD for classifying gene expression based breast cancer recurrence risk

NASA Astrophysics Data System (ADS)

Mahrooghy, Majid; Ashraf, Ahmed B.; Daye, Dania; Mies, Carolyn; Rosen, Mark; Feldman, Michael; Kontos, Despina

2014-03-01

We evaluate the prognostic value of sparse representation-based features by applying the K-SVD algorithm on multiparametric kinetic, textural, and morphologic features in breast dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). K-SVD is an iterative dimensionality reduction method that optimally reduces the initial feature space by updating the dictionary columns jointly with the sparse representation coefficients. Therefore, by using K-SVD, we not only provide sparse representation of the features and condense the information in a few coefficients but also we reduce the dimensionality. The extracted K-SVD features are evaluated by a machine learning algorithm including a logistic regression classifier for the task of classifying high versus low breast cancer recurrence risk as determined by a validated gene expression assay. The features are evaluated using ROC curve analysis and leave one-out cross validation for different sparse representation and dimensionality reduction numbers. Optimal sparse representation is obtained when the number of dictionary elements is 4 (K=4) and maximum non-zero coefficients is 2 (L=2). We compare K-SVD with ANOVA based feature selection for the same prognostic features. The ROC results show that the AUC of the K-SVD based (K=4, L=2), the ANOVA based, and the original features (i.e., no dimensionality reduction) are 0.78, 0.71. and 0.68, respectively. From the results, it can be inferred that by using sparse representation of the originally extracted multi-parametric, high-dimensional data, we can condense the information on a few coefficients with the highest predictive value. In addition, the dimensionality reduction introduced by K-SVD can prevent models from over-fitting.

Mapping the conformational free energy of aspartic acid in the gas phase and in aqueous solution.

PubMed

Comitani, Federico; Rossi, Kevin; Ceriotti, Michele; Sanz, M Eugenia; Molteni, Carla

2017-04-14

The conformational free energy landscape of aspartic acid, a proteogenic amino acid involved in a wide variety of biological functions, was investigated as an example of the complexity that multiple rotatable bonds produce even in relatively simple molecules. To efficiently explore such a landscape, this molecule was studied in the neutral and zwitterionic forms, in the gas phase and in water solution, by means of molecular dynamics and the enhanced sampling method metadynamics with classical force-fields. Multi-dimensional free energy landscapes were reduced to bi-dimensional maps through the non-linear dimensionality reduction algorithm sketch-map to identify the energetically stable conformers and their interconnection paths. Quantum chemical calculations were then performed on the minimum free energy structures. Our procedure returned the low energy conformations observed experimentally in the gas phase with rotational spectroscopy [M. E. Sanz et al., Phys. Chem. Chem. Phys. 12, 3573 (2010)]. Moreover, it provided information on higher energy conformers not accessible to experiments and on the conformers in water. The comparison between different force-fields and quantum chemical data highlighted the importance of the underlying potential energy surface to accurately capture energy rankings. The combination of force-field based metadynamics, sketch-map analysis, and quantum chemical calculations was able to produce an exhaustive conformational exploration in a range of significant free energies that complements the experimental data. Similar protocols can be applied to larger peptides with complex conformational landscapes and would greatly benefit from the next generation of accurate force-fields.

Mapping the conformational free energy of aspartic acid in the gas phase and in aqueous solution

NASA Astrophysics Data System (ADS)

Comitani, Federico; Rossi, Kevin; Ceriotti, Michele; Sanz, M. Eugenia; Molteni, Carla

2017-04-01

The conformational free energy landscape of aspartic acid, a proteogenic amino acid involved in a wide variety of biological functions, was investigated as an example of the complexity that multiple rotatable bonds produce even in relatively simple molecules. To efficiently explore such a landscape, this molecule was studied in the neutral and zwitterionic forms, in the gas phase and in water solution, by means of molecular dynamics and the enhanced sampling method metadynamics with classical force-fields. Multi-dimensional free energy landscapes were reduced to bi-dimensional maps through the non-linear dimensionality reduction algorithm sketch-map to identify the energetically stable conformers and their interconnection paths. Quantum chemical calculations were then performed on the minimum free energy structures. Our procedure returned the low energy conformations observed experimentally in the gas phase with rotational spectroscopy [M. E. Sanz et al., Phys. Chem. Chem. Phys. 12, 3573 (2010)]. Moreover, it provided information on higher energy conformers not accessible to experiments and on the conformers in water. The comparison between different force-fields and quantum chemical data highlighted the importance of the underlying potential energy surface to accurately capture energy rankings. The combination of force-field based metadynamics, sketch-map analysis, and quantum chemical calculations was able to produce an exhaustive conformational exploration in a range of significant free energies that complements the experimental data. Similar protocols can be applied to larger peptides with complex conformational landscapes and would greatly benefit from the next generation of accurate force-fields.

Simulation Methods for Poisson Processes in Nonstationary Systems.

DTIC Science & Technology

1978-08-01

for simulation of nonhomogeneous Poisson processes is stated with log-linear rate function. The method is based on an identity relating the...and relatively efficient new method for simulation of one-dimensional and two-dimensional nonhomogeneous Poisson processes is described. The method is

High-Dimensional Quantum Information Processing with Linear Optics

NASA Astrophysics Data System (ADS)

Fitzpatrick, Casey A.

Quantum information processing (QIP) is an interdisciplinary field concerned with the development of computers and information processing systems that utilize quantum mechanical properties of nature to carry out their function. QIP systems have become vastly more practical since the turn of the century. Today, QIP applications span imaging, cryptographic security, computation, and simulation (quantum systems that mimic other quantum systems). Many important strategies improve quantum versions of classical information system hardware, such as single photon detectors and quantum repeaters. Another more abstract strategy engineers high-dimensional quantum state spaces, so that each successful event carries more information than traditional two-level systems allow. Photonic states in particular bring the added advantages of weak environmental coupling and data transmission near the speed of light, allowing for simpler control and lower system design complexity. In this dissertation, numerous novel, scalable designs for practical high-dimensional linear-optical QIP systems are presented. First, a correlated photon imaging scheme using orbital angular momentum (OAM) states to detect rotational symmetries in objects using measurements, as well as building images out of those interactions is reported. Then, a statistical detection method using chains of OAM superpositions distributed according to the Fibonacci sequence is established and expanded upon. It is shown that the approach gives rise to schemes for sorting, detecting, and generating the recursively defined high-dimensional states on which some quantum cryptographic protocols depend. Finally, an ongoing study based on a generalization of the standard optical multiport for applications in quantum computation and simulation is reported upon. The architecture allows photons to reverse momentum inside the device. This in turn enables realistic implementation of controllable linear-optical scattering vertices for carrying out quantum walks on arbitrary graph structures, a powerful tool for any quantum computer. It is shown that the novel architecture provides new, efficient capabilities for the optical quantum simulation of Hamiltonians and topologically protected states. Further, these simulations use exponentially fewer resources than feedforward techniques, scale linearly to higher-dimensional systems, and use only linear optics, thus offering a concrete experimentally achievable implementation of graphical models of discrete-time quantum systems.

Modeling and Analysis of Micro-Spacecraft Attitude Sensing with Gyrowheel.

PubMed

Liu, Xiaokun; Zhao, Hui; Yao, Yu; He, Fenghua

2016-08-19

This paper proposes two kinds of approaches of angular rate sensing for micro-spacecraft with a gyrowheel (GW), which can combine attitude sensing with attitude control into one single device to achieve a compact micro-spacecraft design. In this implementation, during the three-dimensional attitude control torques being produced, two-dimensional spacecraft angular rates can be sensed from the signals of the GW sensors, such as the currents of the torque coils, the tilt angles of the rotor, the motor rotation, etc. This paper focuses on the problems of the angular rate sensing with the GW at large tilt angles of the rotor. For this purpose, a novel real-time linearization approach based on Lyapunov's linearization theory is proposed, and a GW linearized measurement model at arbitrary tilt angles of the rotor is derived. Furthermore, by representing the two-dimensional rotor tilt angles and tilt control torques as complex quantities and separating the twice periodic terms about the motor spin speed, the linearized measurement model at smaller tilt angles of the rotor is given and simplified. According to the respective characteristics, the application schemes of the two measurement models are analyzed from the engineering perspective. Finally, the simulation results are presented to demonstrate the effectiveness of the proposed strategy.

Modeling and Analysis of Micro-Spacecraft Attitude Sensing with Gyrowheel

PubMed Central

Liu, Xiaokun; Zhao, Hui; Yao, Yu; He, Fenghua

2016-01-01

This paper proposes two kinds of approaches of angular rate sensing for micro-spacecraft with a gyrowheel (GW), which can combine attitude sensing with attitude control into one single device to achieve a compact micro-spacecraft design. In this implementation, during the three-dimensional attitude control torques being produced, two-dimensional spacecraft angular rates can be sensed from the signals of the GW sensors, such as the currents of the torque coils, the tilt angles of the rotor, the motor rotation, etc. This paper focuses on the problems of the angular rate sensing with the GW at large tilt angles of the rotor. For this purpose, a novel real-time linearization approach based on Lyapunov’s linearization theory is proposed, and a GW linearized measurement model at arbitrary tilt angles of the rotor is derived. Furthermore, by representing the two-dimensional rotor tilt angles and tilt control torques as complex quantities and separating the twice periodic terms about the motor spin speed, the linearized measurement model at smaller tilt angles of the rotor is given and simplified. According to the respective characteristics, the application schemes of the two measurement models are analyzed from the engineering perspective. Finally, the simulation results are presented to demonstrate the effectiveness of the proposed strategy. PMID:27548178

Complexity of free energy landscapes of peptides revealed by nonlinear principal component analysis.

PubMed

Nguyen, Phuong H

2006-12-01

Employing the recently developed hierarchical nonlinear principal component analysis (NLPCA) method of Saegusa et al. (Neurocomputing 2004;61:57-70 and IEICE Trans Inf Syst 2005;E88-D:2242-2248), the complexities of the free energy landscapes of several peptides, including triglycine, hexaalanine, and the C-terminal beta-hairpin of protein G, were studied. First, the performance of this NLPCA method was compared with the standard linear principal component analysis (PCA). In particular, we compared two methods according to (1) the ability of the dimensionality reduction and (2) the efficient representation of peptide conformations in low-dimensional spaces spanned by the first few principal components. The study revealed that NLPCA reduces the dimensionality of the considered systems much better, than did PCA. For example, in order to get the similar error, which is due to representation of the original data of beta-hairpin in low dimensional space, one needs 4 and 21 principal components of NLPCA and PCA, respectively. Second, by representing the free energy landscapes of the considered systems as a function of the first two principal components obtained from PCA, we obtained the relatively well-structured free energy landscapes. In contrast, the free energy landscapes of NLPCA are much more complicated, exhibiting many states which are hidden in the PCA maps, especially in the unfolded regions. Furthermore, the study also showed that many states in the PCA maps are mixed up by several peptide conformations, while those of the NLPCA maps are more pure. This finding suggests that the NLPCA should be used to capture the essential features of the systems. (c) 2006 Wiley-Liss, Inc.

Analysis of Ninety Degree Flexure Tests for Characterization of Composite Transverse Tensile Strength

NASA Technical Reports Server (NTRS)

OBrien, T. Kevin; Krueger, Ronald

2001-01-01

Finite element (FE) analysis was performed on 3-point and 4-point bending test configurations of ninety degree oriented glass-epoxy and graphite-epoxy composite beams to identify deviations from beam theory predictions. Both linear and geometric non-linear analyses were performed using the ABAQUS finite element code. The 3-point and 4-point bending specimens were first modeled with two-dimensional elements. Three-dimensional finite element models were then performed for selected 4-point bending configurations to study the stress distribution across the width of the specimens and compare the results to the stresses computed from two-dimensional plane strain and plane stress analyses and the stresses from beam theory. Stresses for all configurations were analyzed at load levels corresponding to the measured transverse tensile strength of the material.

Density-matrix renormalization group method for the conductance of one-dimensional correlated systems using the Kubo formula

NASA Astrophysics Data System (ADS)

Bischoff, Jan-Moritz; Jeckelmann, Eric

2017-11-01

We improve the density-matrix renormalization group (DMRG) evaluation of the Kubo formula for the zero-temperature linear conductance of one-dimensional correlated systems. The dynamical DMRG is used to compute the linear response of a finite system to an applied ac source-drain voltage; then the low-frequency finite-system response is extrapolated to the thermodynamic limit to obtain the dc conductance of an infinite system. The method is demonstrated on the one-dimensional spinless fermion model at half filling. Our method is able to replicate several predictions of the Luttinger liquid theory such as the renormalization of the conductance in a homogeneous conductor, the universal effects of a single barrier, and the resonant tunneling through a double barrier.

An exact solution of the van der Waals interaction between two ground-state hydrogen atoms

NASA Astrophysics Data System (ADS)

Koga, Toshikatsu; Matsumoto, Shinya

1985-06-01

A momentum space treatment shows that perturbation equations for the H(1s)-H(1s) van der Waals interaction can be exactly solved in their Schrödinger forms without invoking any variational methods. Using the Fock transformation, which projects the momentum vector of an electron from the three-dimensional hyperplane onto the four-dimensional hypersphere, we solve the third order integral-type perturbation equation with respect to the reciprocal of the internuclear distance R. An exact third order wave function is found as a linear combination of infinite number of four-dimensional spherical harmonics. The result allows us to evaluate the exact dispersion energy E6R-6, which is completely determined by the first three coefficients of the above linear combination.

Singularities of interference of three waves with different polarization states.

PubMed

Kurzynowski, Piotr; Woźniak, Władysław A; Zdunek, Marzena; Borwińska, Monika

2012-11-19

We presented the interference setup which can produce interesting two-dimensional patterns in polarization state of the resulting light wave emerging from the setup. The main element of our setup is the Wollaston prism which gives two plane, linearly polarized waves (eigenwaves of both Wollaston's wedges) with linearly changed phase difference between them (along the x-axis). The third wave coming from the second arm of proposed polarization interferometer is linearly or circularly polarized with linearly changed phase difference along the y-axis. The interference of three plane waves with different polarization states (LLL - linear-linear-linear or LLC - linear-linear-circular) and variable change difference produce two-dimensional light polarization and phase distributions with some characteristic points and lines which can be claimed to constitute singularities of different types. The aim of this article is to find all kind of these phase and polarization singularities as well as their classification. We postulated in our theoretical simulations and verified in our experiments different kinds of polarization singularities, depending on which polarization parameter was considered (the azimuth and ellipticity angles or the diagonal and phase angles). We also observed the phase singularities as well as the isolated zero intensity points which resulted from the polarization singularities when the proper analyzer was used at the end of the setup. The classification of all these singularities as well as their relationships were analyzed and described.

Waves on the Free Surface Described by Linearized Equations of Hydrodynamics with Localized Right-Hand Sides

NASA Astrophysics Data System (ADS)

Dobrokhotov, S. Yu.; Nazaikinskii, V. E.

2018-01-01

A linearized system of equations of hydrodynamics with time-dependent spatially localized right-hand side placed both on the free surface (and on the bottom of the basin) and also in the layer of the liquid is considered in a layer of variable depth with a given basic plane-parallel flow. A method of constructing asymptotic solutions of this problem is suggested; it consists of two stages: (1) a reduction of the three-dimensional problem to a two-dimensional inhomogeneous pseudodifferential equation on the nonperturbed free surface of the liquid, (2) a representation of the localized right-hand side in the form of a Maslov canonical operator on a special Lagrangian manifold and the subsequent application of a generalization to evolution problems of an approach, which was recently suggested in the paper [A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, and M. Rouleux, Dokl. Ross. Akad. Nauk 475 (6), 624-628 (2017); Engl. transl.: Dokl. Math. 96 (1), 406-410 (2017)], to solving stationary problems with localized right-hand sides and its combination with "nonstandard" characteristics. A method of calculation (generalizing long-standing results of Dobrokhotov and Zhevandrov) of an analog of the Kelvin wedge and the wave fields inside the wedge and in its neighborhood is suggested, which uses the consideration that this method is the projection to the extended configuration space of a Lagrangian manifold formed by the trajectories of the Hamiltonian vector field issuing from the intersection of the set of zeros of the extended Hamiltonian of the problem with conormal bundle to the graph of the vector function defining the trajectory of motion of an equivalent source on the surface of the liquid.

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.

Application of Hyperspectral Techniques to Monitoring and Management of Invasive Plant Species Infestation

DTIC Science & Technology

2008-01-01

the sensor is a data cloud in multi- dimensional space with each band generating an axis of dimension. When the data cloud is viewed in two or three...endmember of interest is not a true endmember in the data space . A ) B) Figure 8: Linear mixture models. A ) two- dimensional ...multi- dimensional space . A classifier is a computer algorithm that takes

Finite-dimensional Liouville integrable Hamiltonian systems generated from Lax pairs of a bi-Hamiltonian soliton hierarchy by symmetry constraints

NASA Astrophysics Data System (ADS)

Manukure, Solomon

2018-04-01

We construct finite-dimensional Hamiltonian systems by means of symmetry constraints from the Lax pairs and adjoint Lax pairs of a bi-Hamiltonian hierarchy of soliton equations associated with the 3-dimensional special linear Lie algebra, and discuss the Liouville integrability of these systems based on the existence of sufficiently many integrals of motion.

Abel's Theorem Simplifies Reduction of Order

ERIC Educational Resources Information Center

Green, William R.

2011-01-01

We give an alternative to the standard method of reduction or order, in which one uses one solution of a homogeneous, linear, second order differential equation to find a second, linearly independent solution. Our method, based on Abel's Theorem, is shorter, less complex and extends to higher order equations.

Manifold Embedding and Semantic Segmentation for Intraoperative Guidance With Hyperspectral Brain Imaging.

PubMed

Ravi, Daniele; Fabelo, Himar; Callic, Gustavo Marrero; Yang, Guang-Zhong

2017-09-01

Recent advances in hyperspectral imaging have made it a promising solution for intra-operative tissue characterization, with the advantages of being non-contact, non-ionizing, and non-invasive. Working with hyperspectral images in vivo, however, is not straightforward as the high dimensionality of the data makes real-time processing challenging. In this paper, a novel dimensionality reduction scheme and a new processing pipeline are introduced to obtain a detailed tumor classification map for intra-operative margin definition during brain surgery. However, existing approaches to dimensionality reduction based on manifold embedding can be time consuming and may not guarantee a consistent result, thus hindering final tissue classification. The proposed framework aims to overcome these problems through a process divided into two steps: dimensionality reduction based on an extension of the T-distributed stochastic neighbor approach is first performed and then a semantic segmentation technique is applied to the embedded results by using a Semantic Texton Forest for tissue classification. Detailed in vivo validation of the proposed method has been performed to demonstrate the potential clinical value of the system.

Dimensionality reduction in epidemic spreading models

NASA Astrophysics Data System (ADS)

Frasca, M.; Rizzo, A.; Gallo, L.; Fortuna, L.; Porfiri, M.

2015-09-01

Complex dynamical systems often exhibit collective dynamics that are well described by a reduced set of key variables in a low-dimensional space. Such a low-dimensional description offers a privileged perspective to understand the system behavior across temporal and spatial scales. In this work, we propose a data-driven approach to establish low-dimensional representations of large epidemic datasets by using a dimensionality reduction algorithm based on isometric features mapping (ISOMAP). We demonstrate our approach on synthetic data for epidemic spreading in a population of mobile individuals. We find that ISOMAP is successful in embedding high-dimensional data into a low-dimensional manifold, whose topological features are associated with the epidemic outbreak. Across a range of simulation parameters and model instances, we observe that epidemic outbreaks are embedded into a family of closed curves in a three-dimensional space, in which neighboring points pertain to instants that are close in time. The orientation of each curve is unique to a specific outbreak, and the coordinates correlate with the number of infected individuals. A low-dimensional description of epidemic spreading is expected to improve our understanding of the role of individual response on the outbreak dynamics, inform the selection of meaningful global observables, and, possibly, aid in the design of control and quarantine procedures.

Shape design sensitivity analysis and optimization of three dimensional elastic solids using geometric modeling and automatic regridding. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Yao, Tse-Min; Choi, Kyung K.

1987-01-01

An automatic regridding method and a three dimensional shape design parameterization technique were constructed and integrated into a unified theory of shape design sensitivity analysis. An algorithm was developed for general shape design sensitivity analysis of three dimensional eleastic solids. Numerical implementation of this shape design sensitivity analysis method was carried out using the finite element code ANSYS. The unified theory of shape design sensitivity analysis uses the material derivative of continuum mechanics with a design velocity field that represents shape change effects over the structural design. Automatic regridding methods were developed by generating a domain velocity field with boundary displacement method. Shape design parameterization for three dimensional surface design problems was illustrated using a Bezier surface with boundary perturbations that depend linearly on the perturbation of design parameters. A linearization method of optimization, LINRM, was used to obtain optimum shapes. Three examples from different engineering disciplines were investigated to demonstrate the accuracy and versatility of this shape design sensitivity analysis method.

The relationship between facial 3-D morphometry and the perception of attractiveness in children.

PubMed

Ferrario, V F; Sforza, C; Poggio, C E; Colombo, A; Tartaglia, G

1997-01-01

The aim of this investigation was to determine whether attractive children differ in their three-dimensional facial characteristics from nonattractive children of the same age, race, and sex. The facial characteristics of 36 boys and 44 girls aged 8 to 9 years were investigated. Frontal and profile photographs were analyzed independently by 21 judges, and, for each view, four groups were obtained: attractive boys, nonattractive boys, attractive girls, and nonattractive girls. For each child, the three-dimensional coordinates of 16 standardized soft tissue facial landmarks were automatically collected using an infrared system and used to calculate several three-dimensional angles, linear distances, and linear distance ratios. Mean values were computed in the eight groups, and attractive and nonattractive children were compared within sex and view. Most children received a different esthetic evaluation in the separate frontal and profile assessments; concordance in both attractive and nonattractive groups was only 50%. Moreover, three-dimensional facial morphometry was not able to separate attractive and nonattractive children.

A plasma source driven predator-prey like mechanism as a potential cause of spiraling intermittencies in linear plasma devices

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

Reiser, D.; Ohno, N.; Tanaka, H.

2014-03-15

Three-dimensional global drift fluid simulations are carried out to analyze coherent plasma structures appearing in the NAGDIS-II linear device (nagoya divertor plasma Simulator-II). The numerical simulations reproduce several features of the intermittent spiraling structures observed, for instance, statistical properties, rotation frequency, and the frequency of plasma expulsion. The detailed inspection of the three-dimensional plasma dynamics allows to identify the key mechanism behind the formation of these intermittent events. The resistive coupling between electron pressure and parallel electric field in the plasma source region gives rise to a quasilinear predator-prey like dynamics where the axisymmetric mode represents the prey and themore » spiraling structure with low azimuthal mode number represents the predator. This interpretation is confirmed by a reduced one-dimensional quasilinear model derived on the basis of the findings in the full three-dimensional simulations. The dominant dynamics reveals certain similarities to the classical Lotka-Volterra cycle.« less

A Two-Dimensional Linear Bicharacteristic FDTD Method

NASA Technical Reports Server (NTRS)

Beggs, John H.

2002-01-01

The linear bicharacteristic scheme (LBS) was originally developed to improve unsteady solutions in computational acoustics and aeroacoustics. The LBS has previously been extended to treat lossy materials for one-dimensional problems. It is a classical leapfrog algorithm, but is combined with upwind bias in the spatial derivatives. This approach preserves the time-reversibility of the leapfrog algorithm, which results in no dissipation, and it permits more flexibility by the ability to adopt a characteristic based method. The use of characteristic variables allows the LBS to include the Perfectly Matched Layer boundary condition with no added storage or complexity. The LBS offers a central storage approach with lower dispersion than the Yee algorithm, plus it generalizes much easier to nonuniform grids. It has previously been applied to two and three-dimensional free-space electromagnetic propagation and scattering problems. This paper extends the LBS to the two-dimensional case. Results are presented for point source radiation problems, and the FDTD algorithm is chosen as a convenient reference for comparison.

Controller Synthesis for Periodically Forced Chaotic Systems

NASA Astrophysics Data System (ADS)

Basso, Michele; Genesio, Roberto; Giovanardi, Lorenzo

Delayed feedback controllers are an appealing tool for stabilization of periodic orbits in chaotic systems. Despite their conceptual simplicity, specific and reliable design procedures are difficult to obtain, partly also because of their inherent infinite-dimensional structure. This chapter considers the use of finite dimensional linear time invariant controllers for stabilization of periodic solutions in a general class of sinusoidally forced nonlinear systems. For such controllers — which can be interpreted as rational approximations of the delayed ones — we provide a computationally attractive synthesis technique based on Linear Matrix Inequalities (LMIs), by mixing results concerning absolute stability of nonlinear systems and robustness of uncertain linear systems. The resulting controllers prove to be effective for chaos suppression in electronic circuits and systems, as shown by two different application examples.

FeynArts model file for MSSM transition counterterms from DREG to DRED

NASA Astrophysics Data System (ADS)

Stöckinger, Dominik; Varšo, Philipp

2012-02-01

The FeynArts model file MSSMdreg2dred implements MSSM transition counterterms which can convert one-loop Green functions from dimensional regularization to dimensional reduction. They correspond to a slight extension of the well-known Martin/Vaughn counterterms, specialized to the MSSM, and can serve also as supersymmetry-restoring counterterms. The paper provides full analytic results for the counterterms and gives one- and two-loop usage examples. The model file can simplify combining MS¯-parton distribution functions with supersymmetric renormalization or avoiding the renormalization of ɛ-scalars in dimensional reduction. Program summaryProgram title:MSSMdreg2dred.mod Catalogue identifier: AEKR_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKR_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: LGPL-License [1] No. of lines in distributed program, including test data, etc.: 7600 No. of bytes in distributed program, including test data, etc.: 197 629 Distribution format: tar.gz Programming language: Mathematica, FeynArts Computer: Any, capable of running Mathematica and FeynArts Operating system: Any, with running Mathematica, FeynArts installation Classification: 4.4, 5, 11.1 Subprograms used: Cat Id Title Reference ADOW_v1_0 FeynArts CPC 140 (2001) 418 Nature of problem: The computation of one-loop Feynman diagrams in the minimal supersymmetric standard model (MSSM) requires regularization. Two schemes, dimensional regularization and dimensional reduction are both common but have different pros and cons. In order to combine the advantages of both schemes one would like to easily convert existing results from one scheme into the other. Solution method: Finite counterterms are constructed which correspond precisely to the one-loop scheme differences for the MSSM. They are provided as a FeynArts [2] model file. Using this model file together with FeynArts, the (ultra-violet) regularization of any MSSM one-loop Green function is switched automatically from dimensional regularization to dimensional reduction. In particular the counterterms serve as supersymmetry-restoring counterterms for dimensional regularization. Restrictions: The counterterms are restricted to the one-loop level and the MSSM. Running time: A few seconds to generate typical Feynman graphs with FeynArts.

Pythagoras's theorem on a two-dimensional lattice from a `natural' Dirac operator and Connes's distance formula

NASA Astrophysics Data System (ADS)

Dai, Jian; Song, Xing-Chang

2001-07-01

One of the key ingredients of Connes's noncommutative geometry is a generalized Dirac operator which induces a metric (Connes's distance) on the pure state space. We generalize such a Dirac operator devised by Dimakis et al, whose Connes distance recovers the linear distance on an one-dimensional lattice, to the two-dimensional case. This Dirac operator has the local eigenvalue property and induces a Euclidean distance on this two-dimensional lattice, which is referred to as `natural'. This kind of Dirac operator can be easily generalized into any higher-dimensional lattices.

Linear and nonlinear pattern selection in Rayleigh-Benard stability problems

NASA Technical Reports Server (NTRS)

Davis, Sanford S.

1993-01-01

A new algorithm is introduced to compute finite-amplitude states using primitive variables for Rayleigh-Benard convection on relatively coarse meshes. The algorithm is based on a finite-difference matrix-splitting approach that separates all physical and dimensional effects into one-dimensional subsets. The nonlinear pattern selection process for steady convection in an air-filled square cavity with insulated side walls is investigated for Rayleigh numbers up to 20,000. The internalization of disturbances that evolve into coherent patterns is investigated and transient solutions from linear perturbation theory are compared with and contrasted to the full numerical simulations.

Defects in regular nanosystems and interference spectra at reemission of electromagnetic field attosecond pulses

NASA Astrophysics Data System (ADS)

Matveev, V. I.; Makarov, D. N.

2017-01-01

The effect of defects in nanostructured targets on interference spectra at the reemission of attosecond electromagnetic pulses has been considered. General expressions have been obtained for calculations of spectral distributions for one-, two-, and three-dimensional multiatomic nanosystems consisting of identical complex atoms with defects such as bends, vacancies, and breaks. Changes in interference spectra by a linear chain with several removed atoms (chain with breaks) and by a linear chain with a bend have been calculated as examples allowing a simple analytical representation. Generalization to two- and three-dimensional nanosystems has been developed.

Stable long-time semiclassical description of zero-point energy in high-dimensional molecular systems.

PubMed

Garashchuk, Sophya; Rassolov, Vitaly A

2008-07-14

Semiclassical implementation of the quantum trajectory formalism [J. Chem. Phys. 120, 1181 (2004)] is further developed to give a stable long-time description of zero-point energy in anharmonic systems of high dimensionality. The method is based on a numerically cheap linearized quantum force approach; stabilizing terms compensating for the linearization errors are added into the time-evolution equations for the classical and nonclassical components of the momentum operator. The wave function normalization and energy are rigorously conserved. Numerical tests are performed for model systems of up to 40 degrees of freedom.

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 feedback control infinite dimensional parabolic evolution systems: Approximation techniques

NASA Technical Reports Server (NTRS)

Banks, H. T.; Wang, C.

1989-01-01

A general approximation framework is discussed for computation of optimal feedback controls in linear quadratic regular problems for nonautonomous parabolic distributed parameter systems. This is done in the context of a theoretical framework using general evolution systems in infinite dimensional Hilbert spaces. Conditions are discussed for preservation under approximation of stabilizability and detectability hypotheses on the infinite dimensional system. The special case of periodic systems is also treated.

Special Holonomy and Two-Dimensional Supersymmetric Sigma-Models

NASA Astrophysics Data System (ADS)

Stojevic, Vid

2006-11-01

Two-dimensional sigma-models describing superstrings propagating on manifolds of special holonomy are characterized by symmetries related to covariantly constant forms that these manifolds hold, which are generally non-linear and close in a field dependent sense. The thesis explores various aspects of the special holonomy symmetries.

A reconstruction algorithm for three-dimensional object-space data using spatial-spectral multiplexing

NASA Astrophysics Data System (ADS)

Wu, Zhejun; Kudenov, Michael W.

2017-05-01

This paper presents a reconstruction algorithm for the Spatial-Spectral Multiplexing (SSM) optical system. The goal of this algorithm is to recover the three-dimensional spatial and spectral information of a scene, given that a one-dimensional spectrometer array is used to sample the pupil of the spatial-spectral modulator. The challenge of the reconstruction is that the non-parametric representation of the three-dimensional spatial and spectral object requires a large number of variables, thus leading to an underdetermined linear system that is hard to uniquely recover. We propose to reparameterize the spectrum using B-spline functions to reduce the number of unknown variables. Our reconstruction algorithm then solves the improved linear system via a least- square optimization of such B-spline coefficients with additional spatial smoothness regularization. The ground truth object and the optical model for the measurement matrix are simulated with both spatial and spectral assumptions according to a realistic field of view. In order to test the robustness of the algorithm, we add Poisson noise to the measurement and test on both two-dimensional and three-dimensional spatial and spectral scenes. Our analysis shows that the root mean square error of the recovered results can be achieved within 5.15%.

Semi-implicit finite difference methods for three-dimensional shallow water flow

USGS Publications Warehouse

Casulli, Vincenzo; Cheng, Ralph T.

1992-01-01

A semi-implicit finite difference method for the numerical solution of three-dimensional shallow water flows is presented and discussed. The governing equations are the primitive three-dimensional turbulent mean flow equations where the pressure distribution in the vertical has been assumed to be hydrostatic. In the method of solution a minimal degree of implicitness has been adopted in such a fashion that the resulting algorithm is stable and gives a maximal computational efficiency at a minimal computational cost. At each time step the numerical method requires the solution of one large linear system which can be formally decomposed into a set of small three-diagonal systems coupled with one five-diagonal system. All these linear systems are symmetric and positive definite. Thus the existence and uniquencess of the numerical solution are assured. When only one vertical layer is specified, this method reduces as a special case to a semi-implicit scheme for solving the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm has been shown to be fast, accurate and mass-conservative and can also be applied to simulate flooding and drying of tidal mud-flats in conjunction with three-dimensional flows. Furthermore, the resulting algorithm is fully vectorizable for an efficient implementation on modern vector computers.

Image Processing Research

DTIC Science & Technology

1975-09-30

systems a linear model results in an object f being mappad into an image _ by a point spread function matrix H. Thus with noise j +Hf +n (1) The simplest... linear models for imaging systems are given by space invariant point spread functions (SIPSF) in which case H is block circulant. If the linear model is...Ij,...,k-IM1 is a set of two dimensional indices each distinct and prior to k. Modeling Procedare: To derive the linear predictor (block LP of figure

Sampling-free Bayesian inversion with adaptive hierarchical tensor representations

NASA Astrophysics Data System (ADS)

Eigel, Martin; Marschall, Manuel; Schneider, Reinhold

2018-03-01

A sampling-free approach to Bayesian inversion with an explicit polynomial representation of the parameter densities is developed, based on an affine-parametric representation of a linear forward model. This becomes feasible due to the complete treatment in function spaces, which requires an efficient model reduction technique for numerical computations. The advocated perspective yields the crucial benefit that error bounds can be derived for all occuring approximations, leading to provable convergence subject to the discretization parameters. Moreover, it enables a fully adaptive a posteriori control with automatic problem-dependent adjustments of the employed discretizations. The method is discussed in the context of modern hierarchical tensor representations, which are used for the evaluation of a random PDE (the forward model) and the subsequent high-dimensional quadrature of the log-likelihood, alleviating the ‘curse of dimensionality’. Numerical experiments demonstrate the performance and confirm the theoretical results.

Domain decomposition methods for systems of conservation laws: Spectral collocation approximations

NASA Technical Reports Server (NTRS)

Quarteroni, Alfio

1989-01-01

Hyperbolic systems of conversation laws are considered which are discretized in space by spectral collocation methods and advanced in time by finite difference schemes. At any time-level a domain deposition method based on an iteration by subdomain procedure was introduced yielding at each step a sequence of independent subproblems (one for each subdomain) that can be solved simultaneously. The method is set for a general nonlinear problem in several space variables. The convergence analysis, however, is carried out only for a linear one-dimensional system with continuous solutions. A precise form of the error reduction factor at each iteration is derived. Although the method is applied here to the case of spectral collocation approximation only, the idea is fairly general and can be used in a different context as well. For instance, its application to space discretization by finite differences is straight forward.

3D theory of a high-gain free-electron laser based on a transverse gradient undulator

NASA Astrophysics Data System (ADS)

Baxevanis, Panagiotis; Ding, Yuantao; Huang, Zhirong; Ruth, Ronald

2014-02-01

The performance of a free-electron laser (FEL) depends significantly on the various parameters of the driving electron beam. In particular, a large energy spread in the beam results in a substantial reduction of the FEL gain, an effect which is especially relevant when one considers FELs driven by plasma accelerators or ultimate storage rings. For such cases, one possible solution is to use a transverse gradient undulator (TGU). In this concept, the energy spread problem is mitigated by properly dispersing the electron beam and introducing a linear, transverse field dependence in the undulator. This paper presents a self-consistent theoretical analysis of a TGU-based, high-gain FEL which takes into account three-dimensional (3D) effects, including beam size variations along the undulator. The results of our theory compare favorably with simulation and are used in fast optimization studies of various x-ray FEL configurations.

On the correct implementation of Fermi-Dirac statistics and electron trapping in nonlinear electrostatic plane wave propagation in collisionless plasmas

NASA Astrophysics Data System (ADS)

Schamel, Hans; Eliasson, Bengt

2016-05-01

Quantum statistics and electron trapping have a decisive influence on the propagation characteristics of coherent stationary electrostatic waves. The description of these strictly nonlinear structures, which are of electron hole type and violate linear Vlasov theory due to the particle trapping at any excitation amplitude, is obtained by a correct reduction of the three-dimensional Fermi-Dirac distribution function to one dimension and by a proper incorporation of trapping. For small but finite amplitudes, the holes become of cnoidal wave type and the electron density is shown to be described by a ϕ ( x ) 1 / 2 rather than a ϕ ( x ) expansion, where ϕ ( x ) is the electrostatic potential. The general coefficients are presented for a degenerate plasma as well as the quantum statistical analogue to these steady state coherent structures, including the shape of ϕ ( x ) and the nonlinear dispersion relation, which describes their phase velocity.

Mesoporous gold sponges: electric charge-assisted seed mediated synthesis and application as surface-enhanced Raman scattering substrates

NASA Astrophysics Data System (ADS)

Yi, Zao; Luo, Jiangshan; Tan, Xiulan; Yi, Yong; Yao, Weitang; Kang, Xiaoli; Ye, Xin; Zhu, Wenkun; Duan, Tao; Yi, Yougen; Tang, Yongjian

2015-11-01

Mesoporous gold sponges were prepared using 4-dimethylaminopyridine (DMAP)-stabilized Au seeds. This is a general process, which involves a simple template-free method, room temperature reduction of HAuCl4·4H2O with hydroxylamine. The formation process of mesoporous gold sponges could be accounted for the electrostatic interaction (the small Au nanoparticles (~3 nm) and the positively charged DMAP-stabilized Au seeds) and Ostwald ripening process. The mesoporous gold sponges had appeared to undergo electrostatic adsorption initially, sequentially linear aggregation, welding and Ostwald ripening, then, they randomly cross link into self-supporting, three-dimensional networks with time. The mesoporous gold sponges exhibit higher surface area than the literature. In addition, application of the spongelike networks as an active material for surface-enhanced Raman scattering has been investigated by employing 4-aminothiophenol (4-ATP) molecules as a probe.

On the strength of random fiber networks

NASA Astrophysics Data System (ADS)

Deogekar, S.; Picu, R. C.

2018-07-01

Damage accumulation and failure in random fiber networks is of importance in a variety of applications, from design of synthetic materials, such as paper and non-wovens, to accidental tearing of biological tissues. In this work we study these processes using three-dimensional models of athermal fiber networks, focusing attention on the modes of failure and on the relationship between network strength and network structural parameters. We consider network failure at small and large strains associated with the rupture of inter-fiber bonds. It is observed that the strength increases linearly with the network volume fraction and with the bond strength, while the stretch at peak stress is inversely related to these two parameters. A small fraction of the bonds rupture before peak stress and this fraction increases with increasing failure stretch. Rendering the bond strength stochastic causes a reduction of the network strength. However, heterogeneity retards damage localization and increases the stretch at peak stress, therefore promoting ductility.

Asymmetry and irregularity border as discrimination factor between melanocytic lesions

NASA Astrophysics Data System (ADS)

Sbrissa, David; Pratavieira, Sebastião.; Salvio, Ana Gabriela; Kurachi, Cristina; Bagnato, Vanderlei Salvadori; Costa, Luciano Da Fontoura; Travieso, Gonzalo

2015-06-01

Image processing tools have been widely used in systems supporting medical diagnosis. The use of mobile devices for the diagnosis of melanoma can assist doctors and improve their diagnosis of a melanocytic lesion. This study proposes a method of image analysis for melanoma discrimination from other types of melanocytic lesions, such as regular and atypical nevi. The process is based on extracting features related with asymmetry and border irregularity. It were collected 104 images, from medical database of two years. The images were obtained with standard digital cameras without lighting and scale control. Metrics relating to the characteristics of shape, asymmetry and curvature of the contour were extracted from segmented images. Linear Discriminant Analysis was performed for dimensionality reduction and data visualization. Segmentation results showed good efficiency in the process, with approximately 88:5% accuracy. Validation results presents sensibility and specificity 85% and 70% for melanoma detection, respectively.

Data-based adjoint and H2 optimal control of the Ginzburg-Landau equation

NASA Astrophysics Data System (ADS)

Banks, Michael; Bodony, Daniel

2017-11-01

Equation-free, reduced-order methods of control are desirable when the governing system of interest is of very high dimension or the control is to be applied to a physical experiment. Two-phase flow optimal control problems, our target application, fit these criteria. Dynamic Mode Decomposition (DMD) is a data-driven method for model reduction that can be used to resolve the dynamics of very high dimensional systems and project the dynamics onto a smaller, more manageable basis. We evaluate the effectiveness of DMD-based forward and adjoint operator estimation when applied to H2 optimal control approaches applied to the linear and nonlinear Ginzburg-Landau equation. Perspectives on applying the data-driven adjoint to two phase flow control will be given. Office of Naval Research (ONR) as part of the Multidisciplinary University Research Initiatives (MURI) Program, under Grant Number N00014-16-1-2617.

Mesoporous gold sponges: electric charge-assisted seed mediated synthesis and application as surface-enhanced Raman scattering substrates

PubMed Central

Yi, Zao; Luo, Jiangshan; Tan, Xiulan; Yi, Yong; Yao, Weitang; Kang, Xiaoli; Ye, Xin; Zhu, Wenkun; Duan, Tao; Yi, Yougen; Tang, Yongjian

2015-01-01

Mesoporous gold sponges were prepared using 4-dimethylaminopyridine (DMAP)-stabilized Au seeds. This is a general process, which involves a simple template-free method, room temperature reduction of HAuCl4·4H2O with hydroxylamine. The formation process of mesoporous gold sponges could be accounted for the electrostatic interaction (the small Au nanoparticles (~3 nm) and the positively charged DMAP-stabilized Au seeds) and Ostwald ripening process. The mesoporous gold sponges had appeared to undergo electrostatic adsorption initially, sequentially linear aggregation, welding and Ostwald ripening, then, they randomly cross link into self-supporting, three-dimensional networks with time. The mesoporous gold sponges exhibit higher surface area than the literature. In addition, application of the spongelike networks as an active material for surface-enhanced Raman scattering has been investigated by employing 4-aminothiophenol (4-ATP) molecules as a probe. PMID:26538365

Black holes and stars in Horndeski theory

NASA Astrophysics Data System (ADS)

Babichev, Eugeny; Charmousis, Christos; Lehébel, Antoine

2016-08-01

We review black hole and star solutions for Horndeski theory. For non-shift symmetric theories, black holes involve a Kaluza-Klein reduction of higher dimensional Lovelock solutions. On the other hand, for shift symmetric theories of Horndeski and beyond Horndeski, black holes involve two classes of solutions: those that include, at the level of the action, a linear coupling to the Gauss-Bonnet term and those that involve time dependence in the galileon field. We analyze the latter class in detail for a specific subclass of Horndeski theory, discussing the general solution of a static and spherically symmetric spacetime. We then discuss stability issues, slowly rotating solutions as well as black holes coupled to matter. The latter case involves a conformally coupled scalar field as well as an electromagnetic field and the (primary) hair black holes thus obtained. We review and discuss the recent results on neutron stars in Horndeski theories.

Discovering biclusters in gene expression data based on high-dimensional linear geometries

PubMed Central

Gan, Xiangchao; Liew, Alan Wee-Chung; Yan, Hong

2008-01-01

Background In DNA microarray experiments, discovering groups of genes that share similar transcriptional characteristics is instrumental in functional annotation, tissue classification and motif identification. However, in many situations a subset of genes only exhibits consistent pattern over a subset of conditions. Conventional clustering algorithms that deal with the entire row or column in an expression matrix would therefore fail to detect these useful patterns in the data. Recently, biclustering has been proposed to detect a subset of genes exhibiting consistent pattern over a subset of conditions. However, most existing biclustering algorithms are based on searching for sub-matrices within a data matrix by optimizing certain heuristically defined merit functions. Moreover, most of these algorithms can only detect a restricted set of bicluster patterns. Results In this paper, we present a novel geometric perspective for the biclustering problem. The biclustering process is interpreted as the detection of linear geometries in a high dimensional data space. Such a new perspective views biclusters with different patterns as hyperplanes in a high dimensional space, and allows us to handle different types of linear patterns simultaneously by matching a specific set of linear geometries. This geometric viewpoint also inspires us to propose a generic bicluster pattern, i.e. the linear coherent model that unifies the seemingly incompatible additive and multiplicative bicluster models. As a particular realization of our framework, we have implemented a Hough transform-based hyperplane detection algorithm. The experimental results on human lymphoma gene expression dataset show that our algorithm can find biologically significant subsets of genes. Conclusion We have proposed a novel geometric interpretation of the biclustering problem. We have shown that many common types of bicluster are just different spatial arrangements of hyperplanes in a high dimensional data space. An implementation of the geometric framework using the Fast Hough transform for hyperplane detection can be used to discover biologically significant subsets of genes under subsets of conditions for microarray data analysis. PMID:18433477

Reaction of facial soft tissues to treatment with a Herbst appliance.

PubMed

Meyer-Marcotty, P; Kochel, J; Richter, U; Richter, F; Stellzig-Eisenhauer, Angelika

2012-04-01

The objective of this prospective longitudinal study was to investigate the reaction of facial soft tissues to treatment with a Herbst appliance. We aimed to quantify three-dimensionally (3D) the isolated effect of the Herbst appliance and volume changes in the lip profile. The 3D data of the facial soft tissues of 34 patients with skeletal Class II (17 female and 17 male, mean age 13.5 ± 1.8 years) were prepared in a standardized manner immediately before (T1) and after (T2) treatment with a Herbst appliance. Anthropometric evaluation was carried out in sagittal and vertical dimensions. To quantify volume changes, pretherapeutic and posttherapeutic images were superimposed three-dimensionally and the difference volumes calculated. Following testing for normal distribution, a statistical analysis was carried out using the paired t test. We observed ventral development of the soft tissues of the lower jaw with flattening of the profile curvature and anterior displacement of the sublabial region in a total of 27 patients. Anterior facial height was lengthened and the facial depth at the lower jaw increased. The largest percentage changes were noted in the lip profile, with a reduction in the red margin of the upper lip and an increase in lower lip height. We also observed a reduction of the sublabial fold in conjunction with a simultaneous increase in volume. The influence of the Herbst appliance on the facial soft tissues is expected to result in a positive treatment outcome, particularly in patients with a convex profile, a retrusive lower lip, and a marked sublabial fold. We observed a broad clinical spectrum of individual reactions in the facial soft tissues. It is, thus, not possible to detect a linear relationship between the Herbst treatment and soft tissue changes, making soft tissue changes difficult to predict.

Background field removal technique using regularization enabled sophisticated harmonic artifact reduction for phase data with varying kernel sizes.

PubMed

Kan, Hirohito; Kasai, Harumasa; Arai, Nobuyuki; Kunitomo, Hiroshi; Hirose, Yasujiro; Shibamoto, Yuta

2016-09-01

An effective background field removal technique is desired for more accurate quantitative susceptibility mapping (QSM) prior to dipole inversion. The aim of this study was to evaluate the accuracy of regularization enabled sophisticated harmonic artifact reduction for phase data with varying spherical kernel sizes (REV-SHARP) method using a three-dimensional head phantom and human brain data. The proposed REV-SHARP method used the spherical mean value operation and Tikhonov regularization in the deconvolution process, with varying 2-14mm kernel sizes. The kernel sizes were gradually reduced, similar to the SHARP with varying spherical kernel (VSHARP) method. We determined the relative errors and relationships between the true local field and estimated local field in REV-SHARP, VSHARP, projection onto dipole fields (PDF), and regularization enabled SHARP (RESHARP). Human experiment was also conducted using REV-SHARP, VSHARP, PDF, and RESHARP. The relative errors in the numerical phantom study were 0.386, 0.448, 0.838, and 0.452 for REV-SHARP, VSHARP, PDF, and RESHARP. REV-SHARP result exhibited the highest correlation between the true local field and estimated local field. The linear regression slopes were 1.005, 1.124, 0.988, and 0.536 for REV-SHARP, VSHARP, PDF, and RESHARP in regions of interest on the three-dimensional head phantom. In human experiments, no obvious errors due to artifacts were present in REV-SHARP. The proposed REV-SHARP is a new method combined with variable spherical kernel size and Tikhonov regularization. This technique might make it possible to be more accurate backgroud field removal and help to achive better accuracy of QSM. Copyright © 2016 Elsevier Inc. All rights reserved.

Integrability and Poisson Structures of Three Dimensional Dynamical Systems and Equations of Hydrodynamic Type

NASA Astrophysics Data System (ADS)

Gumral, Hasan

Poisson structure of completely integrable 3 dimensional dynamical systems can be defined in terms of an integrable 1-form. We take advantage of this fact and use the theory of foliations in discussing the geometrical structure underlying complete and partial integrability. We show that the Halphen system can be formulated in terms of a flat SL(2,R)-valued connection and belongs to a non-trivial Godbillon-Vey class. On the other hand, for the Euler top and a special case of 3-species Lotka-Volterra equations which are contained in the Halphen system as limiting cases, this structure degenerates into the form of globally integrable bi-Hamiltonian structures. The globally integrable bi-Hamiltonian case is a linear and the sl_2 structure is a quadratic unfolding of an integrable 1-form in 3 + 1 dimensions. We complete the discussion of the Hamiltonian structure of 2-component equations of hydrodynamic type by presenting the Hamiltonian operators for Euler's equation and a continuum limit of Toda lattice. We present further infinite sequences of conserved quantities for shallow water equations and show that their generalizations by Kodama admit bi-Hamiltonian structure. We present a simple way of constructing the second Hamiltonian operators for N-component equations admitting some scaling properties. The Kodama reduction of the dispersionless-Boussinesq equations and the Lax reduction of the Benney moment equations are shown to be equivalent by a symmetry transformation. They can be cast into the form of a triplet of conservation laws which enable us to recognize a non-trivial scaling symmetry. The resulting bi-Hamiltonian structure generates three infinite sequences of conserved densities.

Three-dimensional shape measurement and calibration for fringe projection by considering unequal height of the projector and the camera

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

Zhu Feipeng; Shi Hongjian; Bai Pengxiang

In fringe projection, the CCD camera and the projector are often placed at equal height. In this paper, we will study the calibration of an unequal arrangement of the CCD camera and the projector. The principle of fringe projection with two-dimensional digital image correlation to acquire the profile of object surface is described in detail. By formula derivation and experiment, the linear relationship between the out-of-plane calibration coefficient and the y coordinate is clearly found. To acquire the three-dimensional (3D) information of an object correctly, this paper presents an effective calibration method with linear least-squares fitting, which is very simplemore » in principle and calibration. Experiments are implemented to validate the availability and reliability of the calibration method.« less

Improved finite element methodology for integrated thermal structural analysis

NASA Technical Reports Server (NTRS)

Dechaumphai, P.; Thornton, E. A.

1982-01-01

An integrated thermal-structural finite element approach for efficient coupling of thermal and structural analysis is presented. New thermal finite elements which yield exact nodal and element temperatures for one dimensional linear steady state heat transfer problems are developed. A nodeless variable formulation is used to establish improved thermal finite elements for one dimensional nonlinear transient and two dimensional linear transient heat transfer problems. The thermal finite elements provide detailed temperature distributions without using additional element nodes and permit a common discretization with lower order congruent structural finite elements. The accuracy of the integrated approach is evaluated by comparisons with analytical solutions and conventional finite element thermal structural analyses for a number of academic and more realistic problems. Results indicate that the approach provides a significant improvement in the accuracy and efficiency of thermal stress analysis for structures with complex temperature distributions.

Thermal conductivity of disordered two-dimensional binary alloys.

PubMed

Zhou, Yang; Guo, Zhi-Xin; Cao, Hai-Yuan; Chen, Shi-You; Xiang, Hong-Jun; Gong, Xin-Gao

2016-10-20

Using non-equilibrium molecular dynamics simulations, we have studied the effect of disorder on the thermal conductivity of two-dimensional (2D) C 1-x N x alloys. We find that the thermal conductivity not only depends on the substitution concentration of nitrogen, but also strongly depends on the disorder distribution. A general linear relationship is revealed between the thermal conductivity and the participation ratio of phonons in 2D alloys. Localization mode analysis further indicates that the thermal conductivity variation in the ordered alloys can be attributed to the number of inequivalent atoms. As for the disordered alloys, we find that the thermal conductivity variation can be described by a simple linear formula with the disorder degree and the substitution concentration. The present study suggests some general guidance for phonon manipulation and thermal engineering in low dimensional alloys.

Upon Generating (2+1)-dimensional Dynamical Systems

NASA Astrophysics Data System (ADS)

Zhang, Yufeng; Bai, Yang; Wu, Lixin

2016-06-01

Under the framework of the Adler-Gel'fand-Dikii(AGD) scheme, we first propose two Hamiltonian operator pairs over a noncommutative ring so that we construct a new dynamical system in 2+1 dimensions, then we get a generalized special Novikov-Veselov (NV) equation via the Manakov triple. Then with the aid of a special symmetric Lie algebra of a reductive homogeneous group G, we adopt the Tu-Andrushkiw-Huang (TAH) scheme to generate a new integrable (2+1)-dimensional dynamical system and its Hamiltonian structure, which can reduce to the well-known (2+1)-dimensional Davey-Stewartson (DS) hierarchy. Finally, we extend the binormial residue representation (briefly BRR) scheme to the super higher dimensional integrable hierarchies with the help of a super subalgebra of the super Lie algebra sl(2/1), which is also a kind of symmetric Lie algebra of the reductive homogeneous group G. As applications, we obtain a super 2+1 dimensional MKdV hierarchy which can be reduced to a super 2+1 dimensional generalized AKNS equation. Finally, we compare the advantages and the shortcomings for the three schemes to generate integrable dynamical systems.

Quinone 1 e – and 2 e – /2 H + Reduction Potentials: Identification and Analysis of Deviations from Systematic Scaling Relationships

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

Huynh, Mioy T.; Anson, Colin W.; Cavell, Andrew C.

Quinones participate in diverse electron transfer and proton-coupled electron transfer processes in chemistry and biology. An experimental study of common quinones reveals a non-linear correlation between the 1 e – and 2 e –/2 H + reduction potentials. This unexpected observation prompted a computational study of 128 different quinones, probing their 1 e – reduction potentials, pKa values, and 2 e –/2 H + reduction potentials. The density functional theory calculations reveal an approximately linear correlation between these three properties and an effective Hammett constant associated with the quinone substituent(s). However, deviations from this linear scaling relationship are evident formore » quinones that feature halogen substituents, charged substituents, intramolecular hydrogen bonding in the hydroquinone, and/or sterically bulky substituents. These results, particularly the different substituent effects on the 1 e – versus 2 e – /2 H + reduction potentials, have important implications for designing quinones with tailored redox properties.« less

ADER schemes for scalar non-linear hyperbolic conservation laws with source terms in three-space dimensions

NASA Astrophysics Data System (ADS)

Toro, E. F.; Titarev, V. A.

2005-01-01

In this paper we develop non-linear ADER schemes for time-dependent scalar linear and non-linear conservation laws in one-, two- and three-space dimensions. Numerical results of schemes of up to fifth order of accuracy in both time and space illustrate that the designed order of accuracy is achieved in all space dimensions for a fixed Courant number and essentially non-oscillatory results are obtained for solutions with discontinuities. We also present preliminary results for two-dimensional non-linear systems.

Wall effects in wind tunnels

NASA Technical Reports Server (NTRS)

Chevallier, J. P.; Vaucheret, X.

1986-01-01

A synthesis of current trends in the reduction and computation of wall effects is presented. Some of the points discussed include: (1) for the two-dimensional, transonic tests, various control techniques of boundary conditions are used with adaptive walls offering high precision in determining reference conditions and residual corrections. A reduction in the boundary layer effects of the lateral walls is obtained at T2; (2) for the three-dimensional tests, the methods for the reduction of wall effects are still seldom applied due to a lesser need and to their complexity; (3) the supports holding the model of the probes have to be taken into account in the estimation of perturbatory effects.

Wideband radar cross section reduction using two-dimensional phase gradient metasurfaces

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

Li, Yongfeng; Qu, Shaobo; Wang, Jiafu

2014-06-02

Phase gradient metasurface (PGMs) are artificial surfaces that can provide pre-defined in-plane wave-vectors to manipulate the directions of refracted/reflected waves. In this Letter, we propose to achieve wideband radar cross section (RCS) reduction using two-dimensional (2D) PGMs. A 2D PGM was designed using a square combination of 49 split-ring sub-unit cells. The PGM can provide additional wave-vectors along the two in-plane directions simultaneously, leading to either surface wave conversion, deflected reflection, or diffuse reflection. Both the simulation and experiment results verified the wide-band, polarization-independent, high-efficiency RCS reduction induced by the 2D PGM.

Self-force on a point charge and linear source in the space of a screw dislocation

NASA Astrophysics Data System (ADS)

Azevedo, Sérgio; Moraes, Fernando

2000-03-01

Using a description of defect in solids in terms of three-dimensional gravity, we determine the eletrostatic self-force acting on a point teste charge and a linear source in the presence of a screw dislocation.

Target oriented dimensionality reduction of hyperspectral data by Kernel Fukunaga-Koontz Transform

NASA Astrophysics Data System (ADS)

Binol, Hamidullah; Ochilov, Shuhrat; Alam, Mohammad S.; Bal, Abdullah

2017-02-01

Principal component analysis (PCA) is a popular technique in remote sensing for dimensionality reduction. While PCA is suitable for data compression, it is not necessarily an optimal technique for feature extraction, particularly when the features are exploited in supervised learning applications (Cheriyadat and Bruce, 2003) [1]. Preserving features belonging to the target is very crucial to the performance of target detection/recognition techniques. Fukunaga-Koontz Transform (FKT) based supervised band reduction technique can be used to provide this requirement. FKT achieves feature selection by transforming into a new space in where feature classes have complimentary eigenvectors. Analysis of these eigenvectors under two classes, target and background clutter, can be utilized for target oriented band reduction since each basis functions best represent target class while carrying least information of the background class. By selecting few eigenvectors which are the most relevant to the target class, dimension of hyperspectral data can be reduced and thus, it presents significant advantages for near real time target detection applications. The nonlinear properties of the data can be extracted by kernel approach which provides better target features. Thus, we propose constructing kernel FKT (KFKT) to present target oriented band reduction. The performance of the proposed KFKT based target oriented dimensionality reduction algorithm has been tested employing two real-world hyperspectral data and results have been reported consequently.

Symmetry reduction and exact solutions of two higher-dimensional nonlinear evolution equations.

PubMed

Gu, Yongyi; Qi, Jianming

2017-01-01

In this paper, symmetries and symmetry reduction of two higher-dimensional nonlinear evolution equations (NLEEs) are obtained by Lie group method. These NLEEs play an important role in nonlinear sciences. We derive exact solutions to these NLEEs via the [Formula: see text]-expansion method and complex method. Five types of explicit function solutions are constructed, which are rational, exponential, trigonometric, hyperbolic and elliptic function solutions of the variables in the considered equations.

Participatory three dimensional mapping for the preparation of landslide disaster risk reduction program

NASA Astrophysics Data System (ADS)

Kusratmoko, Eko; Wibowo, Adi; Cholid, Sofyan; Pin, Tjiong Giok

2017-07-01

This paper presents the results of applications of participatory three dimensional mapping (P3DM) method for fqcilitating the people of Cibanteng' village to compile a landslide disaster risk reduction program. Physical factors, as high rainfall, topography, geology and land use, and coupled with the condition of demographic and social-economic factors, make up the Cibanteng region highly susceptible to landslides. During the years 2013-2014 has happened 2 times landslides which caused economic losses, as a result of damage to homes and farmland. Participatory mapping is one part of the activities of community-based disaster risk reduction (CBDRR)), because of the involvement of local communities is a prerequisite for sustainable disaster risk reduction. In this activity, participatory mapping method are done in two ways, namely participatory two-dimensional mapping (P2DM) with a focus on mapping of disaster areas and participatory three-dimensional mapping (P3DM) with a focus on the entire territory of the village. Based on the results P3DM, the ability of the communities in understanding the village environment spatially well-tested and honed, so as to facilitate the preparation of the CBDRR programs. Furthermore, the P3DM method can be applied to another disaster areas, due to it becomes a medium of effective dialogue between all levels of involved communities.

Exploring the effects of dimensionality reduction in deep networks for force estimation in robotic-assisted surgery

NASA Astrophysics Data System (ADS)

Aviles, Angelica I.; Alsaleh, Samar; Sobrevilla, Pilar; Casals, Alicia

2016-03-01

Robotic-Assisted Surgery approach overcomes the limitations of the traditional laparoscopic and open surgeries. However, one of its major limitations is the lack of force feedback. Since there is no direct interaction between the surgeon and the tissue, there is no way of knowing how much force the surgeon is applying which can result in irreversible injuries. The use of force sensors is not practical since they impose different constraints. Thus, we make use of a neuro-visual approach to estimate the applied forces, in which the 3D shape recovery together with the geometry of motion are used as input to a deep network based on LSTM-RNN architecture. When deep networks are used in real time, pre-processing of data is a key factor to reduce complexity and improve the network performance. A common pre-processing step is dimensionality reduction which attempts to eliminate redundant and insignificant information by selecting a subset of relevant features to use in model construction. In this work, we show the effects of dimensionality reduction in a real-time application: estimating the applied force in Robotic-Assisted Surgeries. According to the results, we demonstrated positive effects of doing dimensionality reduction on deep networks including: faster training, improved network performance, and overfitting prevention. We also show a significant accuracy improvement, ranging from about 33% to 86%, over existing approaches related to force estimation.

Visualizing phylogenetic tree landscapes.

PubMed

Wilgenbusch, James C; Huang, Wen; Gallivan, Kyle A

2017-02-02

Genomic-scale sequence alignments are increasingly used to infer phylogenies in order to better understand the processes and patterns of evolution. Different partitions within these new alignments (e.g., genes, codon positions, and structural features) often favor hundreds if not thousands of competing phylogenies. Summarizing and comparing phylogenies obtained from multi-source data sets using current consensus tree methods discards valuable information and can disguise potential methodological problems. Discovery of efficient and accurate dimensionality reduction methods used to display at once in 2- or 3- dimensions the relationship among these competing phylogenies will help practitioners diagnose the limits of current evolutionary models and potential problems with phylogenetic reconstruction methods when analyzing large multi-source data sets. We introduce several dimensionality reduction methods to visualize in 2- and 3-dimensions the relationship among competing phylogenies obtained from gene partitions found in three mid- to large-size mitochondrial genome alignments. We test the performance of these dimensionality reduction methods by applying several goodness-of-fit measures. The intrinsic dimensionality of each data set is also estimated to determine whether projections in 2- and 3-dimensions can be expected to reveal meaningful relationships among trees from different data partitions. Several new approaches to aid in the comparison of different phylogenetic landscapes are presented. Curvilinear Components Analysis (CCA) and a stochastic gradient decent (SGD) optimization method give the best representation of the original tree-to-tree distance matrix for each of the three- mitochondrial genome alignments and greatly outperformed the method currently used to visualize tree landscapes. The CCA + SGD method converged at least as fast as previously applied methods for visualizing tree landscapes. We demonstrate for all three mtDNA alignments that 3D projections significantly increase the fit between the tree-to-tree distances and can facilitate the interpretation of the relationship among phylogenetic trees. We demonstrate that the choice of dimensionality reduction method can significantly influence the spatial relationship among a large set of competing phylogenetic trees. We highlight the importance of selecting a dimensionality reduction method to visualize large multi-locus phylogenetic landscapes and demonstrate that 3D projections of mitochondrial tree landscapes better capture the relationship among the trees being compared.

Reduction of multi-dimensional laboratory data to a two-dimensional plot: a novel technique for the identification of laboratory error.

PubMed

Kazmierczak, Steven C; Leen, Todd K; Erdogmus, Deniz; Carreira-Perpinan, Miguel A

2007-01-01

The clinical laboratory generates large amounts of patient-specific data. Detection of errors that arise during pre-analytical, analytical, and post-analytical processes is difficult. We performed a pilot study, utilizing a multidimensional data reduction technique, to assess the utility of this method for identifying errors in laboratory data. We evaluated 13,670 individual patient records collected over a 2-month period from hospital inpatients and outpatients. We utilized those patient records that contained a complete set of 14 different biochemical analytes. We used two-dimensional generative topographic mapping to project the 14-dimensional record to a two-dimensional space. The use of a two-dimensional generative topographic mapping technique to plot multi-analyte patient data as a two-dimensional graph allows for the rapid identification of potentially anomalous data. Although we performed a retrospective analysis, this technique has the benefit of being able to assess laboratory-generated data in real time, allowing for the rapid identification and correction of anomalous data before they are released to the physician. In addition, serial laboratory multi-analyte data for an individual patient can also be plotted as a two-dimensional plot. This tool might also be useful for assessing patient wellbeing and prognosis.

Euclidean sections of protein conformation space and their implications in dimensionality reduction

PubMed Central

Duan, Mojie; Li, Minghai; Han, Li; Huo, Shuanghong

2014-01-01

Dimensionality reduction is widely used in searching for the intrinsic reaction coordinates for protein conformational changes. We find the dimensionality–reduction methods using the pairwise root–mean–square deviation as the local distance metric face a challenge. We use Isomap as an example to illustrate the problem. We believe that there is an implied assumption for the dimensionality–reduction approaches that aim to preserve the geometric relations between the objects: both the original space and the reduced space have the same kind of geometry, such as Euclidean geometry vs. Euclidean geometry or spherical geometry vs. spherical geometry. When the protein free energy landscape is mapped onto a 2D plane or 3D space, the reduced space is Euclidean, thus the original space should also be Euclidean. For a protein with N atoms, its conformation space is a subset of the 3N-dimensional Euclidean space R3N. We formally define the protein conformation space as the quotient space of R3N by the equivalence relation of rigid motions. Whether the quotient space is Euclidean or not depends on how it is parameterized. When the pairwise root–mean–square deviation is employed as the local distance metric, implicit representations are used for the protein conformation space, leading to no direct correspondence to a Euclidean set. We have demonstrated that an explicit Euclidean-based representation of protein conformation space and the local distance metric associated to it improve the quality of dimensionality reduction in the tetra-peptide and β–hairpin systems. PMID:24913095

Interpretable dimensionality reduction of single cell transcriptome data with deep generative models.

PubMed

Ding, Jiarui; Condon, Anne; Shah, Sohrab P

2018-05-21

Single-cell RNA-sequencing has great potential to discover cell types, identify cell states, trace development lineages, and reconstruct the spatial organization of cells. However, dimension reduction to interpret structure in single-cell sequencing data remains a challenge. Existing algorithms are either not able to uncover the clustering structures in the data or lose global information such as groups of clusters that are close to each other. We present a robust statistical model, scvis, to capture and visualize the low-dimensional structures in single-cell gene expression data. Simulation results demonstrate that low-dimensional representations learned by scvis preserve both the local and global neighbor structures in the data. In addition, scvis is robust to the number of data points and learns a probabilistic parametric mapping function to add new data points to an existing embedding. We then use scvis to analyze four single-cell RNA-sequencing datasets, exemplifying interpretable two-dimensional representations of the high-dimensional single-cell RNA-sequencing data.

Modeling of matter-wave solitons in a nonlinear inductor-capacitor network through a Gross-Pitaevskii equation with time-dependent linear potential

NASA Astrophysics Data System (ADS)

Kengne, E.; Lakhssassi, A.; Liu, W. M.

2017-08-01

A lossless nonlinear L C transmission network is considered. With the use of the reductive perturbation method in the semidiscrete limit, we show that the dynamics of matter-wave solitons in the network can be modeled by a one-dimensional Gross-Pitaevskii (GP) equation with a time-dependent linear potential in the presence of a chemical potential. An explicit expression for the growth rate of a purely growing modulational instability (MI) is presented and analyzed. We find that the potential parameter of the GP equation of the system does not affect the different regions of the MI. Neglecting the chemical potential in the GP equation, we derive exact analytical solutions which describe the propagation of both bright and dark solitary waves on continuous-wave (cw) backgrounds. Using the found exact analytical solutions of the GP equation, we investigate numerically the transmission of both bright and dark solitary voltage signals in the network. Our numerical studies show that the amplitude of a bright solitary voltage signal and the depth of a dark solitary voltage signal as well as their width, their motion, and their behavior depend on (i) the propagation frequencies, (ii) the potential parameter, and (iii) the amplitude of the cw background. The GP equation derived in this paper with a time-dependent linear potential opens up different ideas that may be of considerable theoretical interest for the management of matter-wave solitons in nonlinear L C transmission networks.

Research on fast algorithm of small UAV navigation in non-linear matrix reductionism method

NASA Astrophysics Data System (ADS)

Zhang, Xiao; Fang, Jiancheng; Sheng, Wei; Cao, Juanjuan

2008-10-01

The low Reynolds numbers of small UAV will result in unfavorable aerodynamic conditions to support controlled flight. And as operated near ground, the small UAV will be affected seriously by low-frequency interference caused by atmospheric disturbance. Therefore, the GNC system needs high frequency of attitude estimation and control to realize the steady of the UAV. In company with the dimensional of small UAV dwindling away, its GNC system is more and more taken embedded designing technology to reach the purpose of compactness, light weight and low power consumption. At the same time, the operational capability of GNC system also gets limit in a certain extent. Therefore, a kind of high speed navigation algorithm design becomes the imminence demand of GNC system. Aiming at such requirement, a kind of non-linearity matrix reduction approach is adopted in this paper to create a new high speed navigation algorithm which holds the radius of meridian circle and prime vertical circle as constant and linearizes the position matrix calculation formulae of navigation equation. Compared with normal navigation algorithm, this high speed navigation algorithm decreases 17.3% operand. Within small UAV"s mission radius (20km), the accuracy of position error is less than 0.13m. The results of semi-physical experiments and small UAV's auto pilot testing proved that this algorithm can realize high frequency attitude estimation and control. It will avoid low-frequency interference caused by atmospheric disturbance properly.

A characterization of linearly repetitive cut and project sets

NASA Astrophysics Data System (ADS)

Haynes, Alan; Koivusalo, Henna; Walton, James

2018-02-01

For the development of a mathematical theory which can be used to rigorously investigate physical properties of quasicrystals, it is necessary to understand regularity of patterns in special classes of aperiodic point sets in Euclidean space. In one dimension, prototypical mathematical models for quasicrystals are provided by Sturmian sequences and by point sets generated by substitution rules. Regularity properties of such sets are well understood, thanks mostly to well known results by Morse and Hedlund, and physicists have used this understanding to study one dimensional random Schrödinger operators and lattice gas models. A key fact which plays an important role in these problems is the existence of a subadditive ergodic theorem, which is guaranteed when the corresponding point set is linearly repetitive. In this paper we extend the one-dimensional model to cut and project sets, which generalize Sturmian sequences in higher dimensions, and which are frequently used in mathematical and physical literature as models for higher dimensional quasicrystals. By using a combination of algebraic, geometric, and dynamical techniques, together with input from higher dimensional Diophantine approximation, we give a complete characterization of all linearly repetitive cut and project sets with cubical windows. We also prove that these are precisely the collection of such sets which satisfy subadditive ergodic theorems. The results are explicit enough to allow us to apply them to known classical models, and to construct linearly repetitive cut and project sets in all pairs of dimensions and codimensions in which they exist. Research supported by EPSRC grants EP/L001462, EP/J00149X, EP/M023540. HK also gratefully acknowledges the support of the Osk. Huttunen foundation.

Internal Kinematics of the Tongue Following Volume Reduction

PubMed Central

SHCHERBATYY, VOLODYMYR; PERKINS, JONATHAN A.; LIU, ZI-JUN

2008-01-01

This study was undertaken to determine the functional consequences following tongue volume reduction on tongue internal kinematics during mastication and neuromuscular stimulation in a pig model. Six ultrasonic-crystals were implanted into the tongue body in a wedge-shaped configuration which allows recording distance changes in the bilateral length (LENG) and posterior thickness (THICK), as well as anterior (AW), posterior dorsal (PDW), and ventral (PVW) widths in 12 Yucatan-minipigs. Six animals received a uniform mid-sagittal tongue volume reduction surgery (reduction), and the other six had identical incisions without tissue removal (sham). The initial-distances among each crystal-pairs were recorded before, and immediately after surgery to calculate the dimensional losses. Referring to the initial-distance there were 3−66% and 1−4% tongue dimensional losses by the reduction and sham surgeries, respectively. The largest deformation in sham animals during mastication was in AW, significantly larger than LENG, PDW, PVW, and THICK (P < 0.01−0.001). In reduction animals, however, these deformational changes significantly diminished and enhanced in the anterior and posterior tongue, respectively (P < 0.05−0.001). In both groups, neuromuscular stimulation produced deformational ranges that were 2−4 times smaller than those occurred during chewing. Furthermore, reduction animals showed significantly decreased ranges of deformation in PVW, LENG, and THICK (P < 0.05−0.01). These results indicate that tongue volume reduction alters the tongue internal kinematics, and the dimensional losses in the anterior tongue caused by volume reduction can be compensated by increased deformations in the posterior tongue during mastication. This compensatory effect, however, diminishes during stimulation of the hypoglossal nerve and individual tongue muscles. PMID:18484603

Perceptual disturbances predicted in zero-g through three-dimensional modeling.

PubMed

Holly, Jan E

2003-01-01

Perceptual disturbances in zero-g and 1-g differ. For example, the vestibular coriolis (or "cross-coupled") effect is weaker in zero-g. In 1-g, blindfolded subjects rotating on-axis experience perceptual disturbances upon head tilt, but the effects diminish in zero-g. Head tilts during centrifugation in zero-g and 1-g are investigated here by means of three-dimensional modeling, using a model that was previously used to explain the zero-g reduction of the on-axis vestibular coriolis effect. The model's foundation comprises the laws of physics, including linear-angular interactions in three dimensions. Addressed is the question: In zero-g, will the vestibular coriolis effect be as weak during centrifugation as during on-axis rotation? Centrifugation in 1-g was simulated first, with the subject supine, head toward center. The most noticeable result concerned direction of head yaw. For clockwise centrifuge rotation, greater perceptual effects arose in simulations during yaw counterclockwise (as viewed from the top of the head) than for yaw clockwise. Centrifugation in zero-g was then simulated with the same "supine" orientation. The result: In zero-g the simulated vestibular coriolis effect was greater during centrifugation than during on-axis rotation. In addition, clockwise-counterclockwise differences did not appear in zero-g, in contrast to the differences that appear in 1-g.

Three-dimensional simulations of thin ferro-fluid films and drops in magnetic fields

NASA Astrophysics Data System (ADS)

Conroy, Devin; Wray, Alex; Matar, Omar

2016-11-01

We consider the interfacial dynamics of a thin, ferrofluidic film flowing down an inclined substrate, under the action of a magnetic field, bounded above by an inviscid gas. The fluid is assumed to be weakly-conducting. Its dynamics are governed by a coupled system of the steady Maxwell's, the Navier-Stokes, and continuity equations. The magnetisation of the film is a function of the magnetic field, and is prescribed by a Langevin function. We make use of a long-wave reduction in order to solve for the dynamics of the pressure, velocity, and magnetic fields inside the film. The potential in the gas phase is solved with the use of Fourier Transforms. Imposition of appropriate interfacial conditions allows for the construction of an evolution equation for the interfacial shape, via use of the kinematic condition, and the magnetic field. We consider the three-dimensional evolution of the film to spawise perturbations by solving the non-linear equations numerically. The constant flux configuration is considered, which corresponds to a thin film and drop flowing down an incline, and a parametric study is performed to understand the effect of a magnetic field on the stability and structure of the formed drops. EPSRC UK platform Grant MACIPh (EP/L020564/1) and programme Grant MEMPHIS (EP/K003976/1).

Tuning the Electronic, Optical, and Magnetic Properties of Monolayer GaSe with a Vertical Electric Field

NASA Astrophysics Data System (ADS)

Ke, Congming; Wu, Yaping; Guo, Guang-Yu; Lin, Wei; Wu, Zhiming; Zhou, Changjie; Kang, Junyong

2018-04-01

Inspired by two-dimensional material with their unique physical properties and innovative device applications, here we report a design framework on monolayer GaSe, an important member of the two-dimensional material family, in an effort to tune the electronic, optical, and magnetic properties through a vertical electric field. A transition from indirect to direct band gap in monolayer GaSe is found with an electric field of 0.09 V /Å . The giant Stark effect results in a reduction of the band gap with a Stark coefficient of 3.54 Å. Optical and dielectric properties of monolayer GaSe are dependent on the vertical electric field. A large regulation range for polarization E ∥c ^ is found for the static dielectric constant. The optical anisotropy with the dipole transition from E ∥c ^ to E ⊥c ^ is achieved. Induced by the spin-orbit coupling, spin-splitting energy at the valence band maximum increases linearly with the electric field. The effective mass of holes is highly susceptible to the vertical electric field. Switchable spin-polarization features in spin texture of monolayer GaSe are predicted. The tunable electronic, optical, and magnetic properties of monolayer GaSe hold great promise for applications in both the optoelectronic and spintronic devices.

Calculating vibrational spectra with sum of product basis functions without storing full-dimensional vectors or matrices.

PubMed

Leclerc, Arnaud; Carrington, Tucker

2014-05-07

We propose an iterative method for computing vibrational spectra that significantly reduces the memory cost of calculations. It uses a direct product primitive basis, but does not require storing vectors with as many components as there are product basis functions. Wavefunctions are represented in a basis each of whose functions is a sum of products (SOP) and the factorizable structure of the Hamiltonian is exploited. If the factors of the SOP basis functions are properly chosen, wavefunctions are linear combinations of a small number of SOP basis functions. The SOP basis functions are generated using a shifted block power method. The factors are refined with a rank reduction algorithm to cap the number of terms in a SOP basis function. The ideas are tested on a 20-D model Hamiltonian and a realistic CH3CN (12 dimensional) potential. For the 20-D problem, to use a standard direct product iterative approach one would need to store vectors with about 10(20) components and would hence require about 8 × 10(11) GB. With the approach of this paper only 1 GB of memory is necessary. Results for CH3CN agree well with those of a previous calculation on the same potential.

The discovery of structural form

PubMed Central

Kemp, Charles; Tenenbaum, Joshua B.

2008-01-01

Algorithms for finding structure in data have become increasingly important both as tools for scientific data analysis and as models of human learning, yet they suffer from a critical limitation. Scientists discover qualitatively new forms of structure in observed data: For instance, Linnaeus recognized the hierarchical organization of biological species, and Mendeleev recognized the periodic structure of the chemical elements. Analogous insights play a pivotal role in cognitive development: Children discover that object category labels can be organized into hierarchies, friendship networks are organized into cliques, and comparative relations (e.g., “bigger than” or “better than”) respect a transitive order. Standard algorithms, however, can only learn structures of a single form that must be specified in advance: For instance, algorithms for hierarchical clustering create tree structures, whereas algorithms for dimensionality-reduction create low-dimensional spaces. Here, we present a computational model that learns structures of many different forms and that discovers which form is best for a given dataset. The model makes probabilistic inferences over a space of graph grammars representing trees, linear orders, multidimensional spaces, rings, dominance hierarchies, cliques, and other forms and successfully discovers the underlying structure of a variety of physical, biological, and social domains. Our approach brings structure learning methods closer to human abilities and may lead to a deeper computational understanding of cognitive development. PMID:18669663

A data-driven approach for modeling post-fire debris-flow volumes and their uncertainty

USGS Publications Warehouse

Friedel, Michael J.

2011-01-01

This study demonstrates the novel application of genetic programming to evolve nonlinear post-fire debris-flow volume equations from variables associated with a data-driven conceptual model of the western United States. The search space is constrained using a multi-component objective function that simultaneously minimizes root-mean squared and unit errors for the evolution of fittest equations. An optimization technique is then used to estimate the limits of nonlinear prediction uncertainty associated with the debris-flow equations. In contrast to a published multiple linear regression three-variable equation, linking basin area with slopes greater or equal to 30 percent, burn severity characterized as area burned moderate plus high, and total storm rainfall, the data-driven approach discovers many nonlinear and several dimensionally consistent equations that are unbiased and have less prediction uncertainty. Of the nonlinear equations, the best performance (lowest prediction uncertainty) is achieved when using three variables: average basin slope, total burned area, and total storm rainfall. Further reduction in uncertainty is possible for the nonlinear equations when dimensional consistency is not a priority and by subsequently applying a gradient solver to the fittest solutions. The data-driven modeling approach can be applied to nonlinear multivariate problems in all fields of study.

Three New (2+1)-dimensional Integrable Systems and Some Related Darboux Transformations

NASA Astrophysics Data System (ADS)

Guo, Xiu-Rong

2016-06-01

We introduce two operator commutators by using different-degree loop algebras of the Lie algebra A1, then under the framework of zero curvature equations we generate two (2+1)-dimensional integrable hierarchies, including the (2+1)-dimensional shallow water wave (SWW) hierarchy and the (2+1)-dimensional Kaup-Newell (KN) hierarchy. Through reduction of the (2+1)-dimensional hierarchies, we get a (2+1)-dimensional SWW equation and a (2+1)-dimensional KN equation. Furthermore, we obtain two Darboux transformations of the (2+1)-dimensional SWW equation. Similarly, the Darboux transformations of the (2+1)-dimensional KN equation could be deduced. Finally, with the help of the spatial spectral matrix of SWW hierarchy, we generate a (2+1) heat equation and a (2+1) nonlinear generalized SWW system containing inverse operators with respect to the variables x and y by using a reduction spectral problem from the self-dual Yang-Mills equations. Supported by the National Natural Science Foundation of China under Grant No. 11371361, the Shandong Provincial Natural Science Foundation of China under Grant Nos. ZR2012AQ011, ZR2013AL016, ZR2015EM042, National Social Science Foundation of China under Grant No. 13BJY026, the Development of Science and Technology Project under Grant No. 2015NS1048 and A Project of Shandong Province Higher Educational Science and Technology Program under Grant No. J14LI58

Physics and control of wall turbulence for drag reduction.

PubMed

Kim, John

2011-04-13

Turbulence physics responsible for high skin-friction drag in turbulent boundary layers is first reviewed. A self-sustaining process of near-wall turbulence structures is then discussed from the perspective of controlling this process for the purpose of skin-friction drag reduction. After recognizing that key parts of this self-sustaining process are linear, a linear systems approach to boundary-layer control is discussed. It is shown that singular-value decomposition analysis of the linear system allows us to examine different approaches to boundary-layer control without carrying out the expensive nonlinear simulations. Results from the linear analysis are consistent with those observed in full nonlinear simulations, thus demonstrating the validity of the linear analysis. Finally, fundamental performance limit expected of optimal control input is discussed.

Linear stability analysis of the three-dimensional thermally-driven ocean circulation: application to interdecadal oscillations

NASA Astrophysics Data System (ADS)

Huck, Thierry; Vallis, Geoffrey K.

2001-08-01

What can we learn from performing a linear stability analysis of the large-scale ocean circulation? Can we predict from the basic state the occurrence of interdecadal oscillations, such as might be found in a forward integration of the full equations of motion? If so, do the structure and period of the linearly unstable modes resemble those found in a forward integration? We pursue here a preliminary study of these questions for a case in idealized geometry, in which the full nonlinear behavior can also be explored through forward integrations. Specifically, we perform a three-dimensional linear stability analysis of the thermally-driven circulation of the planetary geostrophic equations. We examine the resulting eigenvalues and eigenfunctions, comparing them with the structure of the interdecadal oscillations found in the fully nonlinear model in various parameter regimes. We obtain a steady state by running the time-dependent, nonlinear model to equilibrium using restoring boundary conditions on surface temperature. If the surface heat fluxes are then diagnosed, and these values applied as constant flux boundary conditions, the nonlinear model switches into a state of perpetual, finite amplitude, interdecadal oscillations. We construct a linearized version of the model by empirically evaluating the tangent linear matrix at the steady state, under both restoring and constant-flux boundary conditions. An eigen-analysis shows there are no unstable eigenmodes of the linearized model with restoring conditions. In contrast, under constant flux conditions, we find a single unstable eigenmode that shows a striking resemblance to the fully-developed oscillations in terms of three-dimensional structure, period and growth rate. The mode may be damped through either surface restoring boundary conditions or sufficiently large horizontal tracer diffusion. The success of this simple numerical method in idealized geometry suggests applications in the study of the stability of the ocean circulation in more realistic configurations, and the possibility of predicting potential oceanic modes, even weakly damped, that might be excited by stochastic atmospheric forcing or mesoscale ocean eddies.

Reduction of Large Dynamical Systems by Minimization of Evolution Rate

NASA Technical Reports Server (NTRS)

Girimaji, Sharath S.

1999-01-01

Reduction of a large system of equations to a lower-dimensional system of similar dynamics is investigated. For dynamical systems with disparate timescales, a criterion for determining redundant dimensions and a general reduction method based on the minimization of evolution rate are proposed.

Sample Dimensionality Effects on d' and Proportion of Correct Responses in Discrimination Testing.

PubMed

Bloom, David J; Lee, Soo-Yeun

2016-09-01

Products in the food and beverage industry have varying levels of dimensionality ranging from pure water to multicomponent food products, which can modify sensory perception and possibly influence discrimination testing results. The objectives of the study were to determine the impact of (1) sample dimensionality and (2) complex formulation changes on the d' and proportion of correct response of the 3-AFC and triangle methods. Two experiments were conducted using 47 prescreened subjects who performed either triangle or 3-AFC test procedures. In Experiment I, subjects performed 3-AFC and triangle tests using model solutions with different levels of dimensionality. Samples increased in dimensionality from 1-dimensional sucrose in water solution to 3-dimensional sucrose, citric acid, and flavor in water solution. In Experiment II, subjects performed 3-AFC and triangle tests using 3-dimensional solutions. Sample pairs differed in all 3 dimensions simultaneously to represent complex formulation changes. Two forms of complexity were compared: dilution, where all dimensions decreased in the same ratio, and compensation, where a dimension was increased to compensate for a reduction in another. The proportion of correct responses decreased for both methods when the dimensionality was increased from 1- to 2-dimensional samples. No reduction in correct responses was observed from 2- to 3-dimensional samples. No significant differences in d' were demonstrated between the 2 methods when samples with complex formulation changes were tested. Results reveal an impact on proportion of correct responses due to sample dimensionality and should be explored further using a wide range of sample formulations. © 2016 Institute of Food Technologists®

Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction

NASA Astrophysics Data System (ADS)

Cui, Tiangang; Marzouk, Youssef; Willcox, Karen

2016-06-01

Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or noisy data, the state variation and parameter dependence of the forward model, and correlations in the prior collectively provide useful structure that can be exploited for dimension reduction in this setting-both in the parameter space of the inverse problem and in the state space of the forward model. To this end, we show how to jointly construct low-dimensional subspaces of the parameter space and the state space in order to accelerate the Bayesian solution of the inverse problem. As a byproduct of state dimension reduction, we also show how to identify low-dimensional subspaces of the data in problems with high-dimensional observations. These subspaces enable approximation of the posterior as a product of two factors: (i) a projection of the posterior onto a low-dimensional parameter subspace, wherein the original likelihood is replaced by an approximation involving a reduced model; and (ii) the marginal prior distribution on the high-dimensional complement of the parameter subspace. We present and compare several strategies for constructing these subspaces using only a limited number of forward and adjoint model simulations. The resulting posterior approximations can rapidly be characterized using standard sampling techniques, e.g., Markov chain Monte Carlo. Two numerical examples demonstrate the accuracy and efficiency of our approach: inversion of an integral equation in atmospheric remote sensing, where the data dimension is very high; and the inference of a heterogeneous transmissivity field in a groundwater system, which involves a partial differential equation forward model with high dimensional state and parameters.

Nonlinear dimensionality reduction of data lying on the multicluster manifold.

PubMed

Meng, Deyu; Leung, Yee; Fung, Tung; Xu, Zongben

2008-08-01

A new method, which is called decomposition-composition (D-C) method, is proposed for the nonlinear dimensionality reduction (NLDR) of data lying on the multicluster manifold. The main idea is first to decompose a given data set into clusters and independently calculate the low-dimensional embeddings of each cluster by the decomposition procedure. Based on the intercluster connections, the embeddings of all clusters are then composed into their proper positions and orientations by the composition procedure. Different from other NLDR methods for multicluster data, which consider associatively the intracluster and intercluster information, the D-C method capitalizes on the separate employment of the intracluster neighborhood structures and the intercluster topologies for effective dimensionality reduction. This, on one hand, isometrically preserves the rigid-body shapes of the clusters in the embedding process and, on the other hand, guarantees the proper locations and orientations of all clusters. The theoretical arguments are supported by a series of experiments performed on the synthetic and real-life data sets. In addition, the computational complexity of the proposed method is analyzed, and its efficiency is theoretically analyzed and experimentally demonstrated. Related strategies for automatic parameter selection are also examined.

Multivariate generalized multifactor dimensionality reduction to detect gene-gene interactions

PubMed Central

2013-01-01

Background Recently, one of the greatest challenges in genome-wide association studies is to detect gene-gene and/or gene-environment interactions for common complex human diseases. Ritchie et al. (2001) proposed multifactor dimensionality reduction (MDR) method for interaction analysis. MDR is a combinatorial approach to reduce multi-locus genotypes into high-risk and low-risk groups. Although MDR has been widely used for case-control studies with binary phenotypes, several extensions have been proposed. One of these methods, a generalized MDR (GMDR) proposed by Lou et al. (2007), allows adjusting for covariates and applying to both dichotomous and continuous phenotypes. GMDR uses the residual score of a generalized linear model of phenotypes to assign either high-risk or low-risk group, while MDR uses the ratio of cases to controls. Methods In this study, we propose multivariate GMDR, an extension of GMDR for multivariate phenotypes. Jointly analysing correlated multivariate phenotypes may have more power to detect susceptible genes and gene-gene interactions. We construct generalized estimating equations (GEE) with multivariate phenotypes to extend generalized linear models. Using the score vectors from GEE we discriminate high-risk from low-risk groups. We applied the multivariate GMDR method to the blood pressure data of the 7,546 subjects from the Korean Association Resource study: systolic blood pressure (SBP) and diastolic blood pressure (DBP). We compare the results of multivariate GMDR for SBP and DBP to the results from separate univariate GMDR for SBP and DBP, respectively. We also applied the multivariate GMDR method to the repeatedly measured hypertension status from 5,466 subjects and compared its result with those of univariate GMDR at each time point. Results Results from the univariate GMDR and multivariate GMDR in two-locus model with both blood pressures and hypertension phenotypes indicate best combinations of SNPs whose interaction has significant association with risk for high blood pressures or hypertension. Although the test balanced accuracy (BA) of multivariate analysis was not always greater than that of univariate analysis, the multivariate BAs were more stable with smaller standard deviations. Conclusions In this study, we have developed multivariate GMDR method using GEE approach. It is useful to use multivariate GMDR with correlated multiple phenotypes of interests. PMID:24565370

Clustering and Dimensionality Reduction to Discover Interesting Patterns in Binary Data

NASA Astrophysics Data System (ADS)

Palumbo, Francesco; D'Enza, Alfonso Iodice

The attention towards binary data coding increased consistently in the last decade due to several reasons. The analysis of binary data characterizes several fields of application, such as market basket analysis, DNA microarray data, image mining, text mining and web-clickstream mining. The paper illustrates two different approaches exploiting a profitable combination of clustering and dimensionality reduction for the identification of non-trivial association structures in binary data. An application in the Association Rules framework supports the theory with the empirical evidence.

Laser speckle reduction due to spatial and angular diversity introduced by fast scanning micromirror.

PubMed

Akram, M Nadeem; Tong, Zhaomin; Ouyang, Guangmin; Chen, Xuyuan; Kartashov, Vladimir

2010-06-10

We utilize spatial and angular diversity to achieve speckle reduction in laser illumination. Both free-space and imaging geometry configurations are considered. A fast two-dimensional scanning micromirror is employed to steer the laser beam. A simple experimental setup is built to demonstrate the application of our technique in a two-dimensional laser picture projection. Experimental results show that the speckle contrast factor can be reduced down to 5% within the integration time of the detector.

Argyres–Douglas theories, S 1 reductions, and topological symmetries

DOE PAGES

Buican, Matthew; Nishinaka, Takahiro

2015-12-21

In a recent paper, we proposed closed-form expressions for the superconformal indices of the (A(1), A(2n-3)) and(A(1), D-2n) Argyres-Douglas (AD) superconformal field theories (SCFTs) in the Schur limit. Following up on our results, we turn our attention to the small S-1 regime of these indices. As expected on general grounds, our study reproduces the S-3 partition functions of the resulting dimensionally reduced theories. However, we show that in all cases-with the exception of the reduction of the (A(1), D-4) SCFTcertain imaginary partners of real mass terms are turned on in the corresponding mirror theories. We interpret these deformations as Rmore » symmetry mixing with the topological symmetries of the direct S-1 reductions. Moreover, we argue that these shifts occur in any of our theories whose four-dimensional N = 2 superconformal U(1)(R) symmetry does not obey an SU(2) quantization condition. We then use our R symmetry map to find the fourdimensional ancestors of certain three-dimensional operators. Somewhat surprisingly, this picture turns out to imply that the scaling dimensions of many of the chiral operators of the four-dimensional theory are encoded in accidental symmetries of the three-dimensional theory. We also comment on the implications of our work on the space of general N = 2 SCFTs.« less

Argyres–Douglas theories, S 1 reductions, and topological symmetries

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

Buican, Matthew; Nishinaka, Takahiro

In a recent paper, we proposed closed-form expressions for the superconformal indices of the (A(1), A(2n-3)) and(A(1), D-2n) Argyres-Douglas (AD) superconformal field theories (SCFTs) in the Schur limit. Following up on our results, we turn our attention to the small S-1 regime of these indices. As expected on general grounds, our study reproduces the S-3 partition functions of the resulting dimensionally reduced theories. However, we show that in all cases-with the exception of the reduction of the (A(1), D-4) SCFTcertain imaginary partners of real mass terms are turned on in the corresponding mirror theories. We interpret these deformations as Rmore » symmetry mixing with the topological symmetries of the direct S-1 reductions. Moreover, we argue that these shifts occur in any of our theories whose four-dimensional N = 2 superconformal U(1)(R) symmetry does not obey an SU(2) quantization condition. We then use our R symmetry map to find the fourdimensional ancestors of certain three-dimensional operators. Somewhat surprisingly, this picture turns out to imply that the scaling dimensions of many of the chiral operators of the four-dimensional theory are encoded in accidental symmetries of the three-dimensional theory. We also comment on the implications of our work on the space of general N = 2 SCFTs.« less

Features in chemical kinetics. I. Signatures of self-emerging dimensional reduction from a general format of the evolution law

NASA Astrophysics Data System (ADS)

Nicolini, Paolo; Frezzato, Diego

2013-06-01

Simplification of chemical kinetics description through dimensional reduction is particularly important to achieve an accurate numerical treatment of complex reacting systems, especially when stiff kinetics are considered and a comprehensive picture of the evolving system is required. To this aim several tools have been proposed in the past decades, such as sensitivity analysis, lumping approaches, and exploitation of time scales separation. In addition, there are methods based on the existence of the so-called slow manifolds, which are hyper-surfaces of lower dimension than the one of the whole phase-space and in whose neighborhood the slow evolution occurs after an initial fast transient. On the other hand, all tools contain to some extent a degree of subjectivity which seems to be irremovable. With reference to macroscopic and spatially homogeneous reacting systems under isothermal conditions, in this work we shall adopt a phenomenological approach to let self-emerge the dimensional reduction from the mathematical structure of the evolution law. By transforming the original system of polynomial differential equations, which describes the chemical evolution, into a universal quadratic format, and making a direct inspection of the high-order time-derivatives of the new dynamic variables, we then formulate a conjecture which leads to the concept of an "attractiveness" region in the phase-space where a well-defined state-dependent rate function ω has the simple evolution dot{ω }= - ω ^2 along any trajectory up to the stationary state. This constitutes, by itself, a drastic dimensional reduction from a system of N-dimensional equations (being N the number of chemical species) to a one-dimensional and universal evolution law for such a characteristic rate. Step-by-step numerical inspections on model kinetic schemes are presented. In the companion paper [P. Nicolini and D. Frezzato, J. Chem. Phys. 138, 234102 (2013)], 10.1063/1.4809593 this outcome will be naturally related to the appearance (and hence, to the definition) of the slow manifolds.

Low-resistance gateless high electron mobility transistors using three-dimensional inverted pyramidal AlGaN/GaN surfaces

NASA Astrophysics Data System (ADS)

So, Hongyun; Senesky, Debbie G.

2016-01-01

In this letter, three-dimensional gateless AlGaN/GaN high electron mobility transistors (HEMTs) were demonstrated with 54% reduction in electrical resistance and 73% increase in surface area compared with conventional gateless HEMTs on planar substrates. Inverted pyramidal AlGaN/GaN surfaces were microfabricated using potassium hydroxide etched silicon with exposed (111) surfaces and metal-organic chemical vapor deposition of coherent AlGaN/GaN thin films. In addition, electrical characterization of the devices showed that a combination of series and parallel connections of the highly conductive two-dimensional electron gas along the pyramidal geometry resulted in a significant reduction in electrical resistance at both room and high temperatures (up to 300 °C). This three-dimensional HEMT architecture can be leveraged to realize low-power and reliable power electronics, as well as harsh environment sensors with increased surface area.