Surface electromyography based muscle fatigue detection using high-resolution time-frequency methods and machine learning algorithms.

PubMed

Karthick, P A; Ghosh, Diptasree Maitra; Ramakrishnan, S

2018-02-01

Surface electromyography (sEMG) based muscle fatigue research is widely preferred in sports science and occupational/rehabilitation studies due to its noninvasiveness. However, these signals are complex, multicomponent and highly nonstationary with large inter-subject variations, particularly during dynamic contractions. Hence, time-frequency based machine learning methodologies can improve the design of automated system for these signals. In this work, the analysis based on high-resolution time-frequency methods, namely, Stockwell transform (S-transform), B-distribution (BD) and extended modified B-distribution (EMBD) are proposed to differentiate the dynamic muscle nonfatigue and fatigue conditions. The nonfatigue and fatigue segments of sEMG signals recorded from the biceps brachii of 52 healthy volunteers are preprocessed and subjected to S-transform, BD and EMBD. Twelve features are extracted from each method and prominent features are selected using genetic algorithm (GA) and binary particle swarm optimization (BPSO). Five machine learning algorithms, namely, naïve Bayes, support vector machine (SVM) of polynomial and radial basis kernel, random forest and rotation forests are used for the classification. The results show that all the proposed time-frequency distributions (TFDs) are able to show the nonstationary variations of sEMG signals. Most of the features exhibit statistically significant difference in the muscle fatigue and nonfatigue conditions. The maximum number of features (66%) is reduced by GA and BPSO for EMBD and BD-TFD respectively. The combination of EMBD- polynomial kernel based SVM is found to be most accurate (91% accuracy) in classifying the conditions with the features selected using GA. The proposed methods are found to be capable of handling the nonstationary and multicomponent variations of sEMG signals recorded in dynamic fatiguing contractions. Particularly, the combination of EMBD- polynomial kernel based SVM could be used to detect the dynamic muscle fatigue conditions. Copyright © 2017 Elsevier B.V. All rights reserved.

A 3D Ginibre Point Field

NASA Astrophysics Data System (ADS)

Kargin, Vladislav

2018-06-01

We introduce a family of three-dimensional random point fields using the concept of the quaternion determinant. The kernel of each field is an n-dimensional orthogonal projection on a linear space of quaternionic polynomials. We find explicit formulas for the basis of the orthogonal quaternion polynomials and for the kernel of the projection. For number of particles n → ∞, we calculate the scaling limits of the point field in the bulk and at the center of coordinates. We compare our construction with the previously introduced Fermi-sphere point field process.

Flood susceptibility mapping using a novel ensemble weights-of-evidence and support vector machine models in GIS

NASA Astrophysics Data System (ADS)

Tehrany, Mahyat Shafapour; Pradhan, Biswajeet; Jebur, Mustafa Neamah

2014-05-01

Flood is one of the most devastating natural disasters that occur frequently in Terengganu, Malaysia. Recently, ensemble based techniques are getting extremely popular in flood modeling. In this paper, weights-of-evidence (WoE) model was utilized first, to assess the impact of classes of each conditioning factor on flooding through bivariate statistical analysis (BSA). Then, these factors were reclassified using the acquired weights and entered into the support vector machine (SVM) model to evaluate the correlation between flood occurrence and each conditioning factor. Through this integration, the weak point of WoE can be solved and the performance of the SVM will be enhanced. The spatial database included flood inventory, slope, stream power index (SPI), topographic wetness index (TWI), altitude, curvature, distance from the river, geology, rainfall, land use/cover (LULC), and soil type. Four kernel types of SVM (linear kernel (LN), polynomial kernel (PL), radial basis function kernel (RBF), and sigmoid kernel (SIG)) were used to investigate the performance of each kernel type. The efficiency of the new ensemble WoE and SVM method was tested using area under curve (AUC) which measured the prediction and success rates. The validation results proved the strength and efficiency of the ensemble method over the individual methods. The best results were obtained from RBF kernel when compared with the other kernel types. Success rate and prediction rate for ensemble WoE and RBF-SVM method were 96.48% and 95.67% respectively. The proposed ensemble flood susceptibility mapping method could assist researchers and local governments in flood mitigation strategies.

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.

CS-AMPPred: An Updated SVM Model for Antimicrobial Activity Prediction in Cysteine-Stabilized Peptides

PubMed Central

Porto, William F.; Pires, Állan S.; Franco, Octavio L.

2012-01-01

The antimicrobial peptides (AMP) have been proposed as an alternative to control resistant pathogens. However, due to multifunctional properties of several AMP classes, until now there has been no way to perform efficient AMP identification, except through in vitro and in vivo tests. Nevertheless, an indication of activity can be provided by prediction methods. In order to contribute to the AMP prediction field, the CS-AMPPred (Cysteine-Stabilized Antimicrobial Peptides Predictor) is presented here, consisting of an updated version of the Support Vector Machine (SVM) model for antimicrobial activity prediction in cysteine-stabilized peptides. The CS-AMPPred is based on five sequence descriptors: indexes of (i) α-helix and (ii) loop formation; and averages of (iii) net charge, (iv) hydrophobicity and (v) flexibility. CS-AMPPred was based on 310 cysteine-stabilized AMPs and 310 sequences extracted from PDB. The polynomial kernel achieves the best accuracy on 5-fold cross validation (85.81%), while the radial and linear kernels achieve 84.19%. Testing in a blind data set, the polynomial and radial kernels achieve an accuracy of 90.00%, while the linear model achieves 89.33%. The three models reach higher accuracies than previously described methods. A standalone version of CS-AMPPred is available for download at and runs on any Linux machine. PMID:23240023

Milne problem for non-absorbing medium with extremely anisotropic scattering kernel in the case of specular and diffuse reflecting boundaries

NASA Astrophysics Data System (ADS)

Güleçyüz, M. Ç.; Şenyiğit, M.; Ersoy, A.

2018-01-01

The Milne problem is studied in one speed neutron transport theory using the linearly anisotropic scattering kernel which combines forward and backward scatterings (extremely anisotropic scattering) for a non-absorbing medium with specular and diffuse reflection boundary conditions. In order to calculate the extrapolated endpoint for the Milne problem, Legendre polynomial approximation (PN method) is applied and numerical results are tabulated for selected cases as a function of different degrees of anisotropic scattering. Finally, some results are discussed and compared with the existing results in literature.

A Linear Kernel for Co-Path/Cycle Packing

NASA Astrophysics Data System (ADS)

Chen, Zhi-Zhong; Fellows, Michael; Fu, Bin; Jiang, Haitao; Liu, Yang; Wang, Lusheng; Zhu, Binhai

Bounded-Degree Vertex Deletion is a fundamental problem in graph theory that has new applications in computational biology. In this paper, we address a special case of Bounded-Degree Vertex Deletion, the Co-Path/Cycle Packing problem, which asks to delete as few vertices as possible such that the graph of the remaining (residual) vertices is composed of disjoint paths and simple cycles. The problem falls into the well-known class of 'node-deletion problems with hereditary properties', is hence NP-complete and unlikely to admit a polynomial time approximation algorithm with approximation factor smaller than 2. In the framework of parameterized complexity, we present a kernelization algorithm that produces a kernel with at most 37k vertices, improving on the super-linear kernel of Fellows et al.'s general theorem for Bounded-Degree Vertex Deletion. Using this kernel,and the method of bounded search trees, we devise an FPT algorithm that runs in time O *(3.24 k ). On the negative side, we show that the problem is APX-hard and unlikely to have a kernel smaller than 2k by a reduction from Vertex Cover.

A comparison of different chemometrics approaches for the robust classification of electronic nose data.

PubMed

Gromski, Piotr S; Correa, Elon; Vaughan, Andrew A; Wedge, David C; Turner, Michael L; Goodacre, Royston

2014-11-01

Accurate detection of certain chemical vapours is important, as these may be diagnostic for the presence of weapons, drugs of misuse or disease. In order to achieve this, chemical sensors could be deployed remotely. However, the readout from such sensors is a multivariate pattern, and this needs to be interpreted robustly using powerful supervised learning methods. Therefore, in this study, we compared the classification accuracy of four pattern recognition algorithms which include linear discriminant analysis (LDA), partial least squares-discriminant analysis (PLS-DA), random forests (RF) and support vector machines (SVM) which employed four different kernels. For this purpose, we have used electronic nose (e-nose) sensor data (Wedge et al., Sensors Actuators B Chem 143:365-372, 2009). In order to allow direct comparison between our four different algorithms, we employed two model validation procedures based on either 10-fold cross-validation or bootstrapping. The results show that LDA (91.56% accuracy) and SVM with a polynomial kernel (91.66% accuracy) were very effective at analysing these e-nose data. These two models gave superior prediction accuracy, sensitivity and specificity in comparison to the other techniques employed. With respect to the e-nose sensor data studied here, our findings recommend that SVM with a polynomial kernel should be favoured as a classification method over the other statistical models that we assessed. SVM with non-linear kernels have the advantage that they can be used for classifying non-linear as well as linear mapping from analytical data space to multi-group classifications and would thus be a suitable algorithm for the analysis of most e-nose sensor data.

[Study on application of SVM in prediction of coronary heart disease].

PubMed

Zhu, Yue; Wu, Jianghua; Fang, Ying

2013-12-01

Base on the data of blood pressure, plasma lipid, Glu and UA by physical test, Support Vector Machine (SVM) was applied to identify coronary heart disease (CHD) in patients and non-CHD individuals in south China population for guide of further prevention and treatment of the disease. Firstly, the SVM classifier was built using radial basis kernel function, liner kernel function and polynomial kernel function, respectively. Secondly, the SVM penalty factor C and kernel parameter sigma were optimized by particle swarm optimization (PSO) and then employed to diagnose and predict the CHD. By comparison with those from artificial neural network with the back propagation (BP) model, linear discriminant analysis, logistic regression method and non-optimized SVM, the overall results of our calculation demonstrated that the classification performance of optimized RBF-SVM model could be superior to other classifier algorithm with higher accuracy rate, sensitivity and specificity, which were 94.51%, 92.31% and 96.67%, respectively. So, it is well concluded that SVM could be used as a valid method for assisting diagnosis of CHD.

A Unified Methodology for Computing Accurate Quaternion Color Moments and Moment Invariants.

PubMed

Karakasis, Evangelos G; Papakostas, George A; Koulouriotis, Dimitrios E; Tourassis, Vassilios D

2014-02-01

In this paper, a general framework for computing accurate quaternion color moments and their corresponding invariants is proposed. The proposed unified scheme arose by studying the characteristics of different orthogonal polynomials. These polynomials are used as kernels in order to form moments, the invariants of which can easily be derived. The resulted scheme permits the usage of any polynomial-like kernel in a unified and consistent way. The resulted moments and moment invariants demonstrate robustness to noisy conditions and high discriminative power. Additionally, in the case of continuous moments, accurate computations take place to avoid approximation errors. Based on this general methodology, the quaternion Tchebichef, Krawtchouk, Dual Hahn, Legendre, orthogonal Fourier-Mellin, pseudo Zernike and Zernike color moments, and their corresponding invariants are introduced. A selected paradigm presents the reconstruction capability of each moment family, whereas proper classification scenarios evaluate the performance of color moment invariants.

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

Sevast'yanov, E A; Sadekova, E Kh

The Bulgarian mathematicians Sendov, Popov, and Boyanov have well-known results on the asymptotic behaviour of the least deviations of 2{pi}-periodic functions in the classes H{sup {omega}} from trigonometric polynomials in the Hausdorff metric. However, the asymptotics they give are not adequate to detect a difference in, for example, the rate of approximation of functions f whose moduli of continuity {omega}(f;{delta}) differ by factors of the form (log(1/{delta})){sup {beta}}. Furthermore, a more detailed determination of the asymptotic behaviour by traditional methods becomes very difficult. This paper develops an approach based on using trigonometric snakes as approximating polynomials. The snakes of ordermore » n inscribed in the Minkowski {delta}-neighbourhood of the graph of the approximated function f provide, in a number of cases, the best approximation for f (for the appropriate choice of {delta}). The choice of {delta} depends on n and f and is based on constructing polynomial kernels adjusted to the Hausdorff metric and polynomials with special oscillatory properties. Bibliography: 19 titles.« less

Kernelization

NASA Astrophysics Data System (ADS)

Fomin, Fedor V.

Preprocessing (data reduction or kernelization) as a strategy of coping with hard problems is universally used in almost every implementation. The history of preprocessing, like applying reduction rules simplifying truth functions, can be traced back to the 1950's [6]. A natural question in this regard is how to measure the quality of preprocessing rules proposed for a specific problem. For a long time the mathematical analysis of polynomial time preprocessing algorithms was neglected. The basic reason for this anomaly was that if we start with an instance I of an NP-hard problem and can show that in polynomial time we can replace this with an equivalent instance I' with |I'| < |I| then that would imply P=NP in classical complexity.

A sparse matrix-vector multiplication based algorithm for accurate density matrix computations on systems of millions of atoms

NASA Astrophysics Data System (ADS)

Ghale, Purnima; Johnson, Harley T.

2018-06-01

We present an efficient sparse matrix-vector (SpMV) based method to compute the density matrix P from a given Hamiltonian in electronic structure computations. Our method is a hybrid approach based on Chebyshev-Jackson approximation theory and matrix purification methods like the second order spectral projection purification (SP2). Recent methods to compute the density matrix scale as O(N) in the number of floating point operations but are accompanied by large memory and communication overhead, and they are based on iterative use of the sparse matrix-matrix multiplication kernel (SpGEMM), which is known to be computationally irregular. In addition to irregularity in the sparse Hamiltonian H, the nonzero structure of intermediate estimates of P depends on products of H and evolves over the course of computation. On the other hand, an expansion of the density matrix P in terms of Chebyshev polynomials is straightforward and SpMV based; however, the resulting density matrix may not satisfy the required constraints exactly. In this paper, we analyze the strengths and weaknesses of the Chebyshev-Jackson polynomials and the second order spectral projection purification (SP2) method, and propose to combine them so that the accurate density matrix can be computed using the SpMV computational kernel only, and without having to store the density matrix P. Our method accomplishes these objectives by using the Chebyshev polynomial estimate as the initial guess for SP2, which is followed by using sparse matrix-vector multiplications (SpMVs) to replicate the behavior of the SP2 algorithm for purification. We demonstrate the method on a tight-binding model system of an oxide material containing more than 3 million atoms. In addition, we also present the predicted behavior of our method when applied to near-metallic Hamiltonians with a wide energy spectrum.

Reactive Collisions and Final State Analysis in Hypersonic Flight Regime

DTIC Science & Technology

2016-09-13

Kelvin.[7] The gas-phase, surface reactions and energy transfer at these tempera- tures are essentially uncharacterized and the experimental methodologies...high temperatures (1000 to 20000 K) and compared with results from experimentally derived thermodynamics quantities from the NASA CEA (NASA Chemical...with a reproducing kernel Hilbert space (RKHS) method[13] combined with Legendre polynomials; (2) quasi classical trajectory (QCT) calculations to study

Construction of phylogenetic trees by kernel-based comparative analysis of metabolic networks.

PubMed

Oh, S June; Joung, Je-Gun; Chang, Jeong-Ho; Zhang, Byoung-Tak

2006-06-06

To infer the tree of life requires knowledge of the common characteristics of each species descended from a common ancestor as the measuring criteria and a method to calculate the distance between the resulting values of each measure. Conventional phylogenetic analysis based on genomic sequences provides information about the genetic relationships between different organisms. In contrast, comparative analysis of metabolic pathways in different organisms can yield insights into their functional relationships under different physiological conditions. However, evaluating the similarities or differences between metabolic networks is a computationally challenging problem, and systematic methods of doing this are desirable. Here we introduce a graph-kernel method for computing the similarity between metabolic networks in polynomial time, and use it to profile metabolic pathways and to construct phylogenetic trees. To compare the structures of metabolic networks in organisms, we adopted the exponential graph kernel, which is a kernel-based approach with a labeled graph that includes a label matrix and an adjacency matrix. To construct the phylogenetic trees, we used an unweighted pair-group method with arithmetic mean, i.e., a hierarchical clustering algorithm. We applied the kernel-based network profiling method in a comparative analysis of nine carbohydrate metabolic networks from 81 biological species encompassing Archaea, Eukaryota, and Eubacteria. The resulting phylogenetic hierarchies generally support the tripartite scheme of three domains rather than the two domains of prokaryotes and eukaryotes. By combining the kernel machines with metabolic information, the method infers the context of biosphere development that covers physiological events required for adaptation by genetic reconstruction. The results show that one may obtain a global view of the tree of life by comparing the metabolic pathway structures using meta-level information rather than sequence information. This method may yield further information about biological evolution, such as the history of horizontal transfer of each gene, by studying the detailed structure of the phylogenetic tree constructed by the kernel-based method.

Least square regularized regression in sum space.

PubMed

Xu, Yong-Li; Chen, Di-Rong; Li, Han-Xiong; Liu, Lu

2013-04-01

This paper proposes a least square regularized regression algorithm in sum space of reproducing kernel Hilbert spaces (RKHSs) for nonflat function approximation, and obtains the solution of the algorithm by solving a system of linear equations. This algorithm can approximate the low- and high-frequency component of the target function with large and small scale kernels, respectively. The convergence and learning rate are analyzed. We measure the complexity of the sum space by its covering number and demonstrate that the covering number can be bounded by the product of the covering numbers of basic RKHSs. For sum space of RKHSs with Gaussian kernels, by choosing appropriate parameters, we tradeoff the sample error and regularization error, and obtain a polynomial learning rate, which is better than that in any single RKHS. The utility of this method is illustrated with two simulated data sets and five real-life databases.

Knot invariants from Virasoro related representation and pretzel knots

DOE PAGES

Galakhov, D.; Melnikov, D.; Mironov, A.; ...

2015-08-06

In this study, we remind the method to calculate colored Jones polynomials for the plat representations of knot diagrams from the knowledge of modular transformation (monodromies) of Virasoro conformal blocks with insertions of degenerate fields. As an illustration we use a rich family of pretzel knots, lying on a surface of arbitrary genus g, which was recently analyzed by the evolution method. Further generalizations can be to generic Virasoro modular transformations, provided by integral kernels, which can lead to the Hikami invariants.

An SVM model with hybrid kernels for hydrological time series

NASA Astrophysics Data System (ADS)

Wang, C.; Wang, H.; Zhao, X.; Xie, Q.

2017-12-01

Support Vector Machine (SVM) models have been widely applied to the forecast of climate/weather and its impact on other environmental variables such as hydrologic response to climate/weather. When using SVM, the choice of the kernel function plays the key role. Conventional SVM models mostly use one single type of kernel function, e.g., radial basis kernel function. Provided that there are several featured kernel functions available, each having its own advantages and drawbacks, a combination of these kernel functions may give more flexibility and robustness to SVM approach, making it suitable for a wide range of application scenarios. This paper presents such a linear combination of radial basis kernel and polynomial kernel for the forecast of monthly flowrate in two gaging stations using SVM approach. The results indicate significant improvement in the accuracy of predicted series compared to the approach with either individual kernel function, thus demonstrating the feasibility and advantages of such hybrid kernel approach for SVM applications.

A shortest-path graph kernel for estimating gene product semantic similarity.

PubMed

Alvarez, Marco A; Qi, Xiaojun; Yan, Changhui

2011-07-29

Existing methods for calculating semantic similarity between gene products using the Gene Ontology (GO) often rely on external resources, which are not part of the ontology. Consequently, changes in these external resources like biased term distribution caused by shifting of hot research topics, will affect the calculation of semantic similarity. One way to avoid this problem is to use semantic methods that are "intrinsic" to the ontology, i.e. independent of external knowledge. We present a shortest-path graph kernel (spgk) method that relies exclusively on the GO and its structure. In spgk, a gene product is represented by an induced subgraph of the GO, which consists of all the GO terms annotating it. Then a shortest-path graph kernel is used to compute the similarity between two graphs. In a comprehensive evaluation using a benchmark dataset, spgk compares favorably with other methods that depend on external resources. Compared with simUI, a method that is also intrinsic to GO, spgk achieves slightly better results on the benchmark dataset. Statistical tests show that the improvement is significant when the resolution and EC similarity correlation coefficient are used to measure the performance, but is insignificant when the Pfam similarity correlation coefficient is used. Spgk uses a graph kernel method in polynomial time to exploit the structure of the GO to calculate semantic similarity between gene products. It provides an alternative to both methods that use external resources and "intrinsic" methods with comparable performance.

On Convergence Aspects of Spheroidal Monogenics

NASA Astrophysics Data System (ADS)

Georgiev, S.; Morais, J.

2011-09-01

Orthogonal polynomials have found wide applications in mathematical physics, numerical analysis, and other fields. Accordingly there is an enormous amount of variety of such polynomials and relations that describe their properties. The paper's main results are the discussion of approximation properties for monogenic functions over prolate spheroids in R3 in terms of orthogonal monogenic polynomials and their interdependences. Certain results are stated without proof for now. The motivation for the present study stems from the fact that these polynomials play an important role in the calculation of the Bergman kernel and Green's monogenic functions in a spheroid. Once these functions are known, it is possible to solve both basic boundary value and conformal mapping problems. Interestingly, most of the used methods have a n-dimensional counterpart and can be extended to arbitrary ellipsoids. But such a procedure would make the further study of the underlying ellipsoidal monogenics somewhat laborious, and for this reason we shall not discuss these general cases here. To the best of our knowledge, this does not appear to have been done in literature before.

Pyrcca: Regularized Kernel Canonical Correlation Analysis in Python and Its Applications to Neuroimaging.

PubMed

Bilenko, Natalia Y; Gallant, Jack L

2016-01-01

In this article we introduce Pyrcca, an open-source Python package for performing canonical correlation analysis (CCA). CCA is a multivariate analysis method for identifying relationships between sets of variables. Pyrcca supports CCA with or without regularization, and with or without linear, polynomial, or Gaussian kernelization. We first use an abstract example to describe Pyrcca functionality. We then demonstrate how Pyrcca can be used to analyze neuroimaging data. Specifically, we use Pyrcca to implement cross-subject comparison in a natural movie functional magnetic resonance imaging (fMRI) experiment by finding a data-driven set of functional response patterns that are similar across individuals. We validate this cross-subject comparison method in Pyrcca by predicting responses to novel natural movies across subjects. Finally, we show how Pyrcca can reveal retinotopic organization in brain responses to natural movies without the need for an explicit model.

Pyrcca: Regularized Kernel Canonical Correlation Analysis in Python and Its Applications to Neuroimaging

PubMed Central

Bilenko, Natalia Y.; Gallant, Jack L.

2016-01-01

In this article we introduce Pyrcca, an open-source Python package for performing canonical correlation analysis (CCA). CCA is a multivariate analysis method for identifying relationships between sets of variables. Pyrcca supports CCA with or without regularization, and with or without linear, polynomial, or Gaussian kernelization. We first use an abstract example to describe Pyrcca functionality. We then demonstrate how Pyrcca can be used to analyze neuroimaging data. Specifically, we use Pyrcca to implement cross-subject comparison in a natural movie functional magnetic resonance imaging (fMRI) experiment by finding a data-driven set of functional response patterns that are similar across individuals. We validate this cross-subject comparison method in Pyrcca by predicting responses to novel natural movies across subjects. Finally, we show how Pyrcca can reveal retinotopic organization in brain responses to natural movies without the need for an explicit model. PMID:27920675

Image preprocessing study on KPCA-based face recognition

NASA Astrophysics Data System (ADS)

Li, Xuan; Li, Dehua

2015-12-01

Face recognition as an important biometric identification method, with its friendly, natural, convenient advantages, has obtained more and more attention. This paper intends to research a face recognition system including face detection, feature extraction and face recognition, mainly through researching on related theory and the key technology of various preprocessing methods in face detection process, using KPCA method, focuses on the different recognition results in different preprocessing methods. In this paper, we choose YCbCr color space for skin segmentation and choose integral projection for face location. We use erosion and dilation of the opening and closing operation and illumination compensation method to preprocess face images, and then use the face recognition method based on kernel principal component analysis method for analysis and research, and the experiments were carried out using the typical face database. The algorithms experiment on MATLAB platform. Experimental results show that integration of the kernel method based on PCA algorithm under certain conditions make the extracted features represent the original image information better for using nonlinear feature extraction method, which can obtain higher recognition rate. In the image preprocessing stage, we found that images under various operations may appear different results, so as to obtain different recognition rate in recognition stage. At the same time, in the process of the kernel principal component analysis, the value of the power of the polynomial function can affect the recognition result.

A robust nonparametric framework for reconstruction of stochastic differential equation models

NASA Astrophysics Data System (ADS)

Rajabzadeh, Yalda; Rezaie, Amir Hossein; Amindavar, Hamidreza

2016-05-01

In this paper, we employ a nonparametric framework to robustly estimate the functional forms of drift and diffusion terms from discrete stationary time series. The proposed method significantly improves the accuracy of the parameter estimation. In this framework, drift and diffusion coefficients are modeled through orthogonal Legendre polynomials. We employ the least squares regression approach along with the Euler-Maruyama approximation method to learn coefficients of stochastic model. Next, a numerical discrete construction of mean squared prediction error (MSPE) is established to calculate the order of Legendre polynomials in drift and diffusion terms. We show numerically that the new method is robust against the variation in sample size and sampling rate. The performance of our method in comparison with the kernel-based regression (KBR) method is demonstrated through simulation and real data. In case of real dataset, we test our method for discriminating healthy electroencephalogram (EEG) signals from epilepsy ones. We also demonstrate the efficiency of the method through prediction in the financial data. In both simulation and real data, our algorithm outperforms the KBR method.

Bi-cubic interpolation for shift-free pan-sharpening

NASA Astrophysics Data System (ADS)

Aiazzi, Bruno; Baronti, Stefano; Selva, Massimo; Alparone, Luciano

2013-12-01

Most of pan-sharpening techniques require the re-sampling of the multi-spectral (MS) image for matching the size of the panchromatic (Pan) image, before the geometric details of Pan are injected into the MS image. This operation is usually performed in a separable fashion by means of symmetric digital low-pass filtering kernels with odd lengths that utilize piecewise local polynomials, typically implementing linear or cubic interpolation functions. Conversely, constant, i.e. nearest-neighbour, and quadratic kernels, implementing zero and two degree polynomials, respectively, introduce shifts in the magnified images, that are sub-pixel in the case of interpolation by an even factor, as it is the most usual case. However, in standard satellite systems, the point spread functions (PSF) of the MS and Pan instruments are centered in the middle of each pixel. Hence, commercial MS and Pan data products, whose scale ratio is an even number, are relatively shifted by an odd number of half pixels. Filters of even lengths may be exploited to compensate the half-pixel shifts between the MS and Pan sampling grids. In this paper, it is shown that separable polynomial interpolations of odd degrees are feasible with linear-phase kernels of even lengths. The major benefit is that bi-cubic interpolation, which is known to represent the best trade-off between performances and computational complexity, can be applied to commercial MS + Pan datasets, without the need of performing a further half-pixel registration after interpolation, to align the expanded MS with the Pan image.

Discrimination of raw and processed Dipsacus asperoides by near infrared spectroscopy combined with least squares-support vector machine and random forests

NASA Astrophysics Data System (ADS)

Xin, Ni; Gu, Xiao-Feng; Wu, Hao; Hu, Yu-Zhu; Yang, Zhong-Lin

2012-04-01

Most herbal medicines could be processed to fulfill the different requirements of therapy. The purpose of this study was to discriminate between raw and processed Dipsacus asperoides, a common traditional Chinese medicine, based on their near infrared (NIR) spectra. Least squares-support vector machine (LS-SVM) and random forests (RF) were employed for full-spectrum classification. Three types of kernels, including linear kernel, polynomial kernel and radial basis function kernel (RBF), were checked for optimization of LS-SVM model. For comparison, a linear discriminant analysis (LDA) model was performed for classification, and the successive projections algorithm (SPA) was executed prior to building an LDA model to choose an appropriate subset of wavelengths. The three methods were applied to a dataset containing 40 raw herbs and 40 corresponding processed herbs. We ran 50 runs of 10-fold cross validation to evaluate the model's efficiency. The performance of the LS-SVM with RBF kernel (RBF LS-SVM) was better than the other two kernels. The RF, RBF LS-SVM and SPA-LDA successfully classified all test samples. The mean error rates for the 50 runs of 10-fold cross validation were 1.35% for RBF LS-SVM, 2.87% for RF, and 2.50% for SPA-LDA. The best classification results were obtained by using LS-SVM with RBF kernel, while RF was fast in the training and making predictions.

Sepsis mortality prediction with the Quotient Basis Kernel.

PubMed

Ribas Ripoll, Vicent J; Vellido, Alfredo; Romero, Enrique; Ruiz-Rodríguez, Juan Carlos

2014-05-01

This paper presents an algorithm to assess the risk of death in patients with sepsis. Sepsis is a common clinical syndrome in the intensive care unit (ICU) that can lead to severe sepsis, a severe state of septic shock or multi-organ failure. The proposed algorithm may be implemented as part of a clinical decision support system that can be used in combination with the scores deployed in the ICU to improve the accuracy, sensitivity and specificity of mortality prediction for patients with sepsis. In this paper, we used the Simplified Acute Physiology Score (SAPS) for ICU patients and the Sequential Organ Failure Assessment (SOFA) to build our kernels and algorithms. In the proposed method, we embed the available data in a suitable feature space and use algorithms based on linear algebra, geometry and statistics for inference. We present a simplified version of the Fisher kernel (practical Fisher kernel for multinomial distributions), as well as a novel kernel that we named the Quotient Basis Kernel (QBK). These kernels are used as the basis for mortality prediction using soft-margin support vector machines. The two new kernels presented are compared against other generative kernels based on the Jensen-Shannon metric (centred, exponential and inverse) and other widely used kernels (linear, polynomial and Gaussian). Clinical relevance is also evaluated by comparing these results with logistic regression and the standard clinical prediction method based on the initial SAPS score. As described in this paper, we tested the new methods via cross-validation with a cohort of 400 test patients. The results obtained using our methods compare favourably with those obtained using alternative kernels (80.18% accuracy for the QBK) and the standard clinical prediction method, which are based on the basal SAPS score or logistic regression (71.32% and 71.55%, respectively). The QBK presented a sensitivity and specificity of 79.34% and 83.24%, which outperformed the other kernels analysed, logistic regression and the standard clinical prediction method based on the basal SAPS score. Several scoring systems for patients with sepsis have been introduced and developed over the last 30 years. They allow for the assessment of the severity of disease and provide an estimate of in-hospital mortality. Physiology-based scoring systems are applied to critically ill patients and have a number of advantages over diagnosis-based systems. Severity score systems are often used to stratify critically ill patients for possible inclusion in clinical trials. In this paper, we present an effective algorithm that combines both scoring methodologies for the assessment of death in patients with sepsis that can be used to improve the sensitivity and specificity of the currently available methods. Copyright © 2014 Elsevier B.V. All rights reserved.

Effect of finite sample size on feature selection and classification: a simulation study.

PubMed

Way, Ted W; Sahiner, Berkman; Hadjiiski, Lubomir M; Chan, Heang-Ping

2010-02-01

The small number of samples available for training and testing is often the limiting factor in finding the most effective features and designing an optimal computer-aided diagnosis (CAD) system. Training on a limited set of samples introduces bias and variance in the performance of a CAD system relative to that trained with an infinite sample size. In this work, the authors conducted a simulation study to evaluate the performances of various combinations of classifiers and feature selection techniques and their dependence on the class distribution, dimensionality, and the training sample size. The understanding of these relationships will facilitate development of effective CAD systems under the constraint of limited available samples. Three feature selection techniques, the stepwise feature selection (SFS), sequential floating forward search (SFFS), and principal component analysis (PCA), and two commonly used classifiers, Fisher's linear discriminant analysis (LDA) and support vector machine (SVM), were investigated. Samples were drawn from multidimensional feature spaces of multivariate Gaussian distributions with equal or unequal covariance matrices and unequal means, and with equal covariance matrices and unequal means estimated from a clinical data set. Classifier performance was quantified by the area under the receiver operating characteristic curve Az. The mean Az values obtained by resubstitution and hold-out methods were evaluated for training sample sizes ranging from 15 to 100 per class. The number of simulated features available for selection was chosen to be 50, 100, and 200. It was found that the relative performance of the different combinations of classifier and feature selection method depends on the feature space distributions, the dimensionality, and the available training sample sizes. The LDA and SVM with radial kernel performed similarly for most of the conditions evaluated in this study, although the SVM classifier showed a slightly higher hold-out performance than LDA for some conditions and vice versa for other conditions. PCA was comparable to or better than SFS and SFFS for LDA at small samples sizes, but inferior for SVM with polynomial kernel. For the class distributions simulated from clinical data, PCA did not show advantages over the other two feature selection methods. Under this condition, the SVM with radial kernel performed better than the LDA when few training samples were available, while LDA performed better when a large number of training samples were available. None of the investigated feature selection-classifier combinations provided consistently superior performance under the studied conditions for different sample sizes and feature space distributions. In general, the SFFS method was comparable to the SFS method while PCA may have an advantage for Gaussian feature spaces with unequal covariance matrices. The performance of the SVM with radial kernel was better than, or comparable to, that of the SVM with polynomial kernel under most conditions studied.

An Efficient numerical method to calculate the conductivity tensor for disordered topological matter

NASA Astrophysics Data System (ADS)

Garcia, Jose H.; Covaci, Lucian; Rappoport, Tatiana G.

2015-03-01

We propose a new efficient numerical approach to calculate the conductivity tensor in solids. We use a real-space implementation of the Kubo formalism where both diagonal and off-diagonal conductivities are treated in the same footing. We adopt a formulation of the Kubo theory that is known as Bastin formula and expand the Green's functions involved in terms of Chebyshev polynomials using the kernel polynomial method. Within this method, all the computational effort is on the calculation of the expansion coefficients. It also has the advantage of obtaining both conductivities in a single calculation step and for various values of temperature and chemical potential, capturing the topology of the band-structure. Our numerical technique is very general and is suitable for the calculation of transport properties of disordered systems. We analyze how the method's accuracy varies with the number of moments used in the expansion and illustrate our approach by calculating the transverse conductivity of different topological systems. T.G.R, J.H.G and L.C. acknowledge Brazilian agencies CNPq, FAPERJ and INCT de Nanoestruturas de Carbono, Flemish Science Foundation for financial support.

Noninvasive prostate cancer screening based on serum surface-enhanced Raman spectroscopy and support vector machine

NASA Astrophysics Data System (ADS)

Li, Shaoxin; Zhang, Yanjiao; Xu, Junfa; Li, Linfang; Zeng, Qiuyao; Lin, Lin; Guo, Zhouyi; Liu, Zhiming; Xiong, Honglian; Liu, Songhao

2014-09-01

This study aims to present a noninvasive prostate cancer screening methods using serum surface-enhanced Raman scattering (SERS) and support vector machine (SVM) techniques through peripheral blood sample. SERS measurements are performed using serum samples from 93 prostate cancer patients and 68 healthy volunteers by silver nanoparticles. Three types of kernel functions including linear, polynomial, and Gaussian radial basis function (RBF) are employed to build SVM diagnostic models for classifying measured SERS spectra. For comparably evaluating the performance of SVM classification models, the standard multivariate statistic analysis method of principal component analysis (PCA) is also applied to classify the same datasets. The study results show that for the RBF kernel SVM diagnostic model, the diagnostic accuracy of 98.1% is acquired, which is superior to the results of 91.3% obtained from PCA methods. The receiver operating characteristic curve of diagnostic models further confirm above research results. This study demonstrates that label-free serum SERS analysis technique combined with SVM diagnostic algorithm has great potential for noninvasive prostate cancer screening.

Predictive analysis of beer quality by correlating sensory evaluation with higher alcohol and ester production using multivariate statistics methods.

PubMed

Dong, Jian-Jun; Li, Qing-Liang; Yin, Hua; Zhong, Cheng; Hao, Jun-Guang; Yang, Pan-Fei; Tian, Yu-Hong; Jia, Shi-Ru

2014-10-15

Sensory evaluation is regarded as a necessary procedure to ensure a reproducible quality of beer. Meanwhile, high-throughput analytical methods provide a powerful tool to analyse various flavour compounds, such as higher alcohol and ester. In this study, the relationship between flavour compounds and sensory evaluation was established by non-linear models such as partial least squares (PLS), genetic algorithm back-propagation neural network (GA-BP), support vector machine (SVM). It was shown that SVM with a Radial Basis Function (RBF) had a better performance of prediction accuracy for both calibration set (94.3%) and validation set (96.2%) than other models. Relatively lower prediction abilities were observed for GA-BP (52.1%) and PLS (31.7%). In addition, the kernel function of SVM played an essential role of model training when the prediction accuracy of SVM with polynomial kernel function was 32.9%. As a powerful multivariate statistics method, SVM holds great potential to assess beer quality. Copyright © 2014 Elsevier Ltd. All rights reserved.

Analytic Evolution of Singular Distribution Amplitudes in QCD

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

Tandogan Kunkel, Asli

2014-08-01

Distribution amplitudes (DAs) are the basic functions that contain information about the quark momentum. DAs are necessary to describe hard exclusive processes in quantum chromodynamics. We describe a method of analytic evolution of DAs that have singularities such as nonzero values at the end points of the support region, jumps at some points inside the support region and cusps. We illustrate the method by applying it to the evolution of a at (constant) DA, antisymmetric at DA, and then use the method for evolution of the two-photon generalized distribution amplitude. Our approach to DA evolution has advantages over the standardmore » method of expansion in Gegenbauer polynomials [1, 2] and over a straightforward iteration of an initial distribution with evolution kernel. Expansion in Gegenbauer polynomials requires an infinite number of terms in order to accurately reproduce functions in the vicinity of singular points. Straightforward iteration of an initial distribution produces logarithmically divergent terms at each iteration. In our method the logarithmic singularities are summed from the start, which immediately produces a continuous curve. Afterwards, in order to get precise results, only one or two iterations are needed.« less

Detection of subjects and brain regions related to Alzheimer's disease using 3D MRI scans based on eigenbrain and machine learning

PubMed Central

Zhang, Yudong; Dong, Zhengchao; Phillips, Preetha; Wang, Shuihua; Ji, Genlin; Yang, Jiquan; Yuan, Ti-Fei

2015-01-01

Purpose: Early diagnosis or detection of Alzheimer's disease (AD) from the normal elder control (NC) is very important. However, the computer-aided diagnosis (CAD) was not widely used, and the classification performance did not reach the standard of practical use. We proposed a novel CAD system for MR brain images based on eigenbrains and machine learning with two goals: accurate detection of both AD subjects and AD-related brain regions. Method: First, we used maximum inter-class variance (ICV) to select key slices from 3D volumetric data. Second, we generated an eigenbrain set for each subject. Third, the most important eigenbrain (MIE) was obtained by Welch's t-test (WTT). Finally, kernel support-vector-machines with different kernels that were trained by particle swarm optimization, were used to make an accurate prediction of AD subjects. Coefficients of MIE with values higher than 0.98 quantile were highlighted to obtain the discriminant regions that distinguish AD from NC. Results: The experiments showed that the proposed method can predict AD subjects with a competitive performance with existing methods, especially the accuracy of the polynomial kernel (92.36 ± 0.94) was better than the linear kernel of 91.47 ± 1.02 and the radial basis function (RBF) kernel of 86.71 ± 1.93. The proposed eigenbrain-based CAD system detected 30 AD-related brain regions (Anterior Cingulate, Caudate Nucleus, Cerebellum, Cingulate Gyrus, Claustrum, Inferior Frontal Gyrus, Inferior Parietal Lobule, Insula, Lateral Ventricle, Lentiform Nucleus, Lingual Gyrus, Medial Frontal Gyrus, Middle Frontal Gyrus, Middle Occipital Gyrus, Middle Temporal Gyrus, Paracentral Lobule, Parahippocampal Gyrus, Postcentral Gyrus, Posterial Cingulate, Precentral Gyrus, Precuneus, Subcallosal Gyrus, Sub-Gyral, Superior Frontal Gyrus, Superior Parietal Lobule, Superior Temporal Gyrus, Supramarginal Gyrus, Thalamus, Transverse Temporal Gyrus, and Uncus). The results were coherent with existing literatures. Conclusion: The eigenbrain method was effective in AD subject prediction and discriminant brain-region detection in MRI scanning. PMID:26082713

Optimal approximation of harmonic growth clusters by orthogonal polynomials

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

Teodorescu, Razvan

2008-01-01

Interface dynamics in two-dimensional systems with a maximal number of conservation laws gives an accurate theoreticaI model for many physical processes, from the hydrodynamics of immiscible, viscous flows (zero surface-tension limit of Hele-Shaw flows), to the granular dynamics of hard spheres, and even diffusion-limited aggregation. Although a complete solution for the continuum case exists, efficient approximations of the boundary evolution are very useful due to their practical applications. In this article, the approximation scheme based on orthogonal polynomials with a deformed Gaussian kernel is discussed, as well as relations to potential theory.

Oscillatory singular integrals and harmonic analysis on nilpotent groups

PubMed Central

Ricci, F.; Stein, E. M.

1986-01-01

Several related classes of operators on nilpotent Lie groups are considered. These operators involve the following features: (i) oscillatory factors that are exponentials of imaginary polynomials, (ii) convolutions with singular kernels supported on lower-dimensional submanifolds, (iii) validity in the general context not requiring the existence of dilations that are automorphisms. PMID:16593640

Protein Kinase Classification with 2866 Hidden Markov Models and One Support Vector Machine

NASA Technical Reports Server (NTRS)

Weber, Ryan; New, Michael H.; Fonda, Mark (Technical Monitor)

2002-01-01

The main application considered in this paper is predicting true kinases from randomly permuted kinases that share the same length and amino acid distributions as the true kinases. Numerous methods already exist for this classification task, such as HMMs, motif-matchers, and sequence comparison algorithms. We build on some of these efforts by creating a vector from the output of thousands of structurally based HMMs, created offline with Pfam-A seed alignments using SAM-T99, which then must be combined into an overall classification for the protein. Then we use a Support Vector Machine for classifying this large ensemble Pfam-Vector, with a polynomial and chisquared kernel. In particular, the chi-squared kernel SVM performs better than the HMMs and better than the BLAST pairwise comparisons, when predicting true from false kinases in some respects, but no one algorithm is best for all purposes or in all instances so we consider the particular strengths and weaknesses of each.

SVM-Based Synthetic Fingerprint Discrimination Algorithm and Quantitative Optimization Strategy

PubMed Central

Chen, Suhang; Chang, Sheng; Huang, Qijun; He, Jin; Wang, Hao; Huang, Qiangui

2014-01-01

Synthetic fingerprints are a potential threat to automatic fingerprint identification systems (AFISs). In this paper, we propose an algorithm to discriminate synthetic fingerprints from real ones. First, four typical characteristic factors—the ridge distance features, global gray features, frequency feature and Harris Corner feature—are extracted. Then, a support vector machine (SVM) is used to distinguish synthetic fingerprints from real fingerprints. The experiments demonstrate that this method can achieve a recognition accuracy rate of over 98% for two discrete synthetic fingerprint databases as well as a mixed database. Furthermore, a performance factor that can evaluate the SVM's accuracy and efficiency is presented, and a quantitative optimization strategy is established for the first time. After the optimization of our synthetic fingerprint discrimination task, the polynomial kernel with a training sample proportion of 5% is the optimized value when the minimum accuracy requirement is 95%. The radial basis function (RBF) kernel with a training sample proportion of 15% is a more suitable choice when the minimum accuracy requirement is 98%. PMID:25347063

Mesh-free based variational level set evolution for breast region segmentation and abnormality detection using mammograms.

PubMed

Kashyap, Kanchan L; Bajpai, Manish K; Khanna, Pritee; Giakos, George

2018-01-01

Automatic segmentation of abnormal region is a crucial task in computer-aided detection system using mammograms. In this work, an automatic abnormality detection algorithm using mammographic images is proposed. In the preprocessing step, partial differential equation-based variational level set method is used for breast region extraction. The evolution of the level set method is done by applying mesh-free-based radial basis function (RBF). The limitation of mesh-based approach is removed by using mesh-free-based RBF method. The evolution of variational level set function is also done by mesh-based finite difference method for comparison purpose. Unsharp masking and median filtering is used for mammogram enhancement. Suspicious abnormal regions are segmented by applying fuzzy c-means clustering. Texture features are extracted from the segmented suspicious regions by computing local binary pattern and dominated rotated local binary pattern (DRLBP). Finally, suspicious regions are classified as normal or abnormal regions by means of support vector machine with linear, multilayer perceptron, radial basis, and polynomial kernel function. The algorithm is validated on 322 sample mammograms of mammographic image analysis society (MIAS) and 500 mammograms from digital database for screening mammography (DDSM) datasets. Proficiency of the algorithm is quantified by using sensitivity, specificity, and accuracy. The highest sensitivity, specificity, and accuracy of 93.96%, 95.01%, and 94.48%, respectively, are obtained on MIAS dataset using DRLBP feature with RBF kernel function. Whereas, the highest 92.31% sensitivity, 98.45% specificity, and 96.21% accuracy are achieved on DDSM dataset using DRLBP feature with RBF kernel function. Copyright © 2017 John Wiley & Sons, Ltd.

Crossover ensembles of random matrices and skew-orthogonal polynomials

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

Kumar, Santosh, E-mail: skumar.physics@gmail.com; Pandey, Akhilesh, E-mail: ap0700@mail.jnu.ac.in

2011-08-15

Highlights: > We study crossover ensembles of Jacobi family of random matrices. > We consider correlations for orthogonal-unitary and symplectic-unitary crossovers. > We use the method of skew-orthogonal polynomials and quaternion determinants. > We prove universality of spectral correlations in crossover ensembles. > We discuss applications to quantum conductance and communication theory problems. - Abstract: In a recent paper (S. Kumar, A. Pandey, Phys. Rev. E, 79, 2009, p. 026211) we considered Jacobi family (including Laguerre and Gaussian cases) of random matrix ensembles and reported exact solutions of crossover problems involving time-reversal symmetry breaking. In the present paper we givemore » details of the work. We start with Dyson's Brownian motion description of random matrix ensembles and obtain universal hierarchic relations among the unfolded correlation functions. For arbitrary dimensions we derive the joint probability density (jpd) of eigenvalues for all transitions leading to unitary ensembles as equilibrium ensembles. We focus on the orthogonal-unitary and symplectic-unitary crossovers and give generic expressions for jpd of eigenvalues, two-point kernels and n-level correlation functions. This involves generalization of the theory of skew-orthogonal polynomials to crossover ensembles. We also consider crossovers in the circular ensembles to show the generality of our method. In the large dimensionality limit, correlations in spectra with arbitrary initial density are shown to be universal when expressed in terms of a rescaled symmetry breaking parameter. Applications of our crossover results to communication theory and quantum conductance problems are also briefly discussed.« less

Integration of multi-array sensors and support vector machines for the detection and classification of organophosphate nerve agents

NASA Astrophysics Data System (ADS)

Land, Walker H., Jr.; Sadik, Omowunmi A.; Embrechts, Mark J.; Leibensperger, Dale; Wong, Lut; Wanekaya, Adam; Uematsu, Michiko

2003-08-01

Due to the increased threats of chemical and biological weapons of mass destruction (WMD) by international terrorist organizations, a significant effort is underway to develop tools that can be used to detect and effectively combat biochemical warfare. Furthermore, recent events have highlighted awareness that chemical and biological agents (CBAs) may become the preferred, cheap alternative WMD, because these agents can effectively attack large populations while leaving infrastructures intact. Despite the availability of numerous sensing devices, intelligent hybrid sensors that can detect and degrade CBAs are virtually nonexistent. This paper reports the integration of multi-array sensors with Support Vector Machines (SVMs) for the detection of organophosphates nerve agents using parathion and dichlorvos as model stimulants compounds. SVMs were used for the design and evaluation of new and more accurate data extraction, preprocessing and classification. Experimental results for the paradigms developed using Structural Risk Minimization, show a significant increase in classification accuracy when compared to the existing AromaScan baseline system. Specifically, the results of this research has demonstrated that, for the Parathion versus Dichlorvos pair, when compared to the AromaScan baseline system: (1) a 23% improvement in the overall ROC Az index using the S2000 kernel, with similar improvements with the Gaussian and polynomial (of degree 2) kernels, (2) a significant 173% improvement in specificity with the S2000 kernel. This means that the number of false negative errors were reduced by 173%, while making no false positive errors, when compared to the AromaScan base line performance. (3) The Gaussian and polynomial kernels demonstrated similar specificity at 100% sensitivity. All SVM classifiers provided essentially perfect classification performance for the Dichlorvos versus Trichlorfon pair. For the most difficult classification task, the Parathion versus Paraoxon pair, the following results were achieved (using the three SVM kernels: (1) ROC Az indices from approximately 93% to greater than 99%, (2) partial Az values from ~79% to 93%, (3) specificities from 76% to ~84% at 100 and 98% sensitivity, and (4) PPVs from 73% to ~84% at 100% and 98% sensitivities. These are excellent results, considering only one atom differentiates these nerve agents.

High-performance implementation of Chebyshev filter diagonalization for interior eigenvalue computations

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

Pieper, Andreas; Kreutzer, Moritz; Alvermann, Andreas, E-mail: alvermann@physik.uni-greifswald.de

2016-11-15

We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is approximated with filter polynomials obtained from Chebyshev expansions of window functions. After the discussion of the conceptual foundations of Chebyshev filter diagonalization we analyze the impact of the choice of the damping kernel, search space size, and filter polynomial degree on the computational accuracy and effort, before we describe the necessary steps towards a parallel high-performance implementation. Because Chebyshev filter diagonalization avoids the need formore » matrix inversion it can deal with matrices and problem sizes that are presently not accessible with rational function methods based on direct or iterative linear solvers. To demonstrate the potential of Chebyshev filter diagonalization for large-scale problems of this kind we include as an example the computation of the 10{sup 2} innermost eigenpairs of a topological insulator matrix with dimension 10{sup 9} derived from quantum physics applications.« less

Study of multiband disordered systems using the typical medium dynamical cluster approximation

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

Zhang, Yi; Terletska, Hanna; Moore, C.

We generalize the typical medium dynamical cluster approximation to multiband disordered systems. Using our extended formalism, we perform a systematic study of the nonlocal correlation effects induced by disorder on the density of states and the mobility edge of the three-dimensional two-band Anderson model. We include interband and intraband hopping and an intraband disorder potential. Our results are consistent with those obtained by the transfer matrix and the kernel polynomial methods. We also apply the method to K xFe 2-ySe 2 with Fe vacancies. Despite the strong vacancy disorder and anisotropy, we find the material is not an Anderson insulator.more » Moreover our results demonstrate the application of the typical medium dynamical cluster approximation method to study Anderson localization in real materials.« less

Study of multiband disordered systems using the typical medium dynamical cluster approximation

DOE PAGES

Zhang, Yi; Terletska, Hanna; Moore, C.; ...

2015-11-06

We generalize the typical medium dynamical cluster approximation to multiband disordered systems. Using our extended formalism, we perform a systematic study of the nonlocal correlation effects induced by disorder on the density of states and the mobility edge of the three-dimensional two-band Anderson model. We include interband and intraband hopping and an intraband disorder potential. Our results are consistent with those obtained by the transfer matrix and the kernel polynomial methods. We also apply the method to K xFe 2-ySe 2 with Fe vacancies. Despite the strong vacancy disorder and anisotropy, we find the material is not an Anderson insulator.more » Moreover our results demonstrate the application of the typical medium dynamical cluster approximation method to study Anderson localization in real materials.« less

Semiclassical dynamics of spin density waves

NASA Astrophysics Data System (ADS)

Chern, Gia-Wei; Barros, Kipton; Wang, Zhentao; Suwa, Hidemaro; Batista, Cristian D.

2018-01-01

We present a theoretical framework for equilibrium and nonequilibrium dynamical simulation of quantum states with spin-density-wave (SDW) order. Within a semiclassical adiabatic approximation that retains electron degrees of freedom, we demonstrate that the SDW order parameter obeys a generalized Landau-Lifshitz equation. With the aid of an enhanced kernel polynomial method, our linear-scaling quantum Landau-Lifshitz dynamics (QLLD) method enables dynamical SDW simulations with N ≃105 lattice sites. Our real-space formulation can be used to compute dynamical responses, such as the dynamical structure factor, of complex and even inhomogeneous SDW configurations at zero or finite temperatures. Applying the QLLD to study the relaxation of a noncoplanar topological SDW under the excitation of a short pulse, we further demonstrate the crucial role of spatial correlations and fluctuations in the SDW dynamics.

Application of Vector Spherical Harmonics and Kernel Regression to the Computations of OMM Parameters

NASA Astrophysics Data System (ADS)

Marco, F. J.; Martínez, M. J.; López, J. A.

2015-04-01

The high quality of Hipparcos data in position, proper motion, and parallax has allowed for studies about stellar kinematics with the aim of achieving a better physical understanding of our galaxy, based on accurate calculus of the Ogorodnikov-Milne model (OMM) parameters. The use of discrete least squares is the most common adjustment method, but it may lead to errors mainly because of the inhomogeneous spatial distribution of the data. We present an example of the instability of this method using the case of a function given by a linear combination of Legendre polynomials. These polynomials are basic in the use of vector spherical harmonics, which have been used to compute the OMM parameters by several authors, such as Makarov & Murphy, Mignard & Klioner, and Vityazev & Tsvetkov. To overcome the former problem, we propose the use of a mixed method (see Marco et al.) that includes the extension of the functions of residuals to any point on the celestial sphere. The goal is to be able to work with continuous variables in the calculation of the coefficients of the vector spherical harmonic developments with stability and efficiency. We apply this mixed procedure to the study of the kinematics of the stars in our Galaxy, employing the Hipparcos velocity field data to obtain the OMM parameters. Previously, we tested the method by perturbing the Vectorial Spherical Harmonics model as well as the velocity vector field.

Effective quadrature formula in solving linear integro-differential equations of order two

NASA Astrophysics Data System (ADS)

Eshkuvatov, Z. K.; Kammuji, M.; Long, N. M. A. Nik; Yunus, Arif A. M.

2017-08-01

In this note, we solve general form of Fredholm-Volterra integro-differential equations (IDEs) of order 2 with boundary condition approximately and show that proposed method is effective and reliable. Initially, IDEs is reduced into integral equation of the third kind by using standard integration techniques and identity between multiple and single integrals then truncated Legendre series are used to estimate the unknown function. For the kernel integrals, we have applied Gauss-Legendre quadrature formula and collocation points are chosen as the roots of the Legendre polynomials. Finally, reduce the integral equations of the third kind into the system of algebraic equations and Gaussian elimination method is applied to get approximate solutions. Numerical examples and comparisons with other methods reveal that the proposed method is very effective and dominated others in many cases. General theory of existence of the solution is also discussed.

A multi-domain spectral method for time-fractional differential equations

NASA Astrophysics Data System (ADS)

Chen, Feng; Xu, Qinwu; Hesthaven, Jan S.

2015-07-01

This paper proposes an approach for high-order time integration within a multi-domain setting for time-fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid approach for the numerical integration based on the combination of three-term-recurrence relations of Jacobi polynomials and high-order Gauss quadrature. The different approximations used in the hybrid approach are justified theoretically and through numerical examples. Based on this, we propose a new multi-domain spectral method for high-order accurate time integrations and study its stability properties by identifying the method as a generalized linear method. Numerical experiments confirm hp-convergence for both time-fractional differential equations and time-fractional partial differential equations.

Automatic plankton image classification combining multiple view features via multiple kernel learning.

PubMed

Zheng, Haiyong; Wang, Ruchen; Yu, Zhibin; Wang, Nan; Gu, Zhaorui; Zheng, Bing

2017-12-28

Plankton, including phytoplankton and zooplankton, are the main source of food for organisms in the ocean and form the base of marine food chain. As the fundamental components of marine ecosystems, plankton is very sensitive to environment changes, and the study of plankton abundance and distribution is crucial, in order to understand environment changes and protect marine ecosystems. This study was carried out to develop an extensive applicable plankton classification system with high accuracy for the increasing number of various imaging devices. Literature shows that most plankton image classification systems were limited to only one specific imaging device and a relatively narrow taxonomic scope. The real practical system for automatic plankton classification is even non-existent and this study is partly to fill this gap. Inspired by the analysis of literature and development of technology, we focused on the requirements of practical application and proposed an automatic system for plankton image classification combining multiple view features via multiple kernel learning (MKL). For one thing, in order to describe the biomorphic characteristics of plankton more completely and comprehensively, we combined general features with robust features, especially by adding features like Inner-Distance Shape Context for morphological representation. For another, we divided all the features into different types from multiple views and feed them to multiple classifiers instead of only one by combining different kernel matrices computed from different types of features optimally via multiple kernel learning. Moreover, we also applied feature selection method to choose the optimal feature subsets from redundant features for satisfying different datasets from different imaging devices. We implemented our proposed classification system on three different datasets across more than 20 categories from phytoplankton to zooplankton. The experimental results validated that our system outperforms state-of-the-art plankton image classification systems in terms of accuracy and robustness. This study demonstrated automatic plankton image classification system combining multiple view features using multiple kernel learning. The results indicated that multiple view features combined by NLMKL using three kernel functions (linear, polynomial and Gaussian kernel functions) can describe and use information of features better so that achieve a higher classification accuracy.

H0 from cosmic chronometers and Type Ia supernovae, with Gaussian Processes and the novel Weighted Polynomial Regression method

NASA Astrophysics Data System (ADS)

Gómez-Valent, Adrià; Amendola, Luca

2018-04-01

In this paper we present new constraints on the Hubble parameter H0 using: (i) the available data on H(z) obtained from cosmic chronometers (CCH); (ii) the Hubble rate data points extracted from the supernovae of Type Ia (SnIa) of the Pantheon compilation and the Hubble Space Telescope (HST) CANDELS and CLASH Multy-Cycle Treasury (MCT) programs; and (iii) the local HST measurement of H0 provided by Riess et al. (2018), H0HST=(73.45±1.66) km/s/Mpc. Various determinations of H0 using the Gaussian processes (GPs) method and the most updated list of CCH data have been recently provided by Yu, Ratra & Wang (2018). Using the Gaussian kernel they find H0=(67.42± 4.75) km/s/Mpc. Here we extend their analysis to also include the most released and complete set of SnIa data, which allows us to reduce the uncertainty by a factor ~ 3 with respect to the result found by only considering the CCH information. We obtain H0=(67.06± 1.68) km/s/Mpc, which favors again the lower range of values for H0 and is in tension with H0HST. The tension reaches the 2.71σ level. We round off the GPs determination too by taking also into account the error propagation of the kernel hyperparameters when the CCH with and without H0HST are used in the analysis. In addition, we present a novel method to reconstruct functions from data, which consists in a weighted sum of polynomial regressions (WPR). We apply it from a cosmographic perspective to reconstruct H(z) and estimate H0 from CCH and SnIa measurements. The result obtained with this method, H0=(68.90± 1.96) km/s/Mpc, is fully compatible with the GPs ones. Finally, a more conservative GPs+WPR value is also provided, H0=(68.45± 2.00) km/s/Mpc, which is still almost 2σ away from H0HST.

Georeferencing CAMS data: Polynomial rectification and beyond

NASA Astrophysics Data System (ADS)

Yang, Xinghe

The Calibrated Airborne Multispectral Scanner (CAMS) is a sensor used in the commercial remote sensing program at NASA Stennis Space Center. In geographic applications of the CAMS data, accurate geometric rectification is essential for the analysis of the remotely sensed data and for the integration of the data into Geographic Information Systems (GIS). The commonly used rectification techniques such as the polynomial transformation and ortho rectification have been very successful in the field of remote sensing and GIS for most remote sensing data such as Landsat imagery, SPOT imagery and aerial photos. However, due to the geometric nature of the airborne line scanner which has high spatial frequency distortions, the polynomial model and the ortho rectification technique in current commercial software packages such as Erdas Imagine are not adequate for obtaining sufficient geometric accuracy. In this research, the geometric nature, especially the major distortions, of the CAMS data has been described. An analytical step-by-step geometric preprocessing has been utilized to deal with the potential high frequency distortions of the CAMS data. A generic sensor-independent photogrammetric model has been developed for the ortho-rectification of the CAMS data. Three generalized kernel classes and directional elliptical basis have been formulated into a rectification model of summation of multisurface functions, which is a significant extension to the traditional radial basis functions. The preprocessing mechanism has been fully incorporated into the polynomial, the triangle-based finite element analysis as well as the summation of multisurface functions. While the multisurface functions and the finite element analysis have the characteristics of localization, piecewise logic has been applied to the polynomial and photogrammetric methods, which can produce significant accuracy improvement over the global approach. A software module has been implemented with full integration of data preprocessing and rectification techniques under Erdas Imagine development environment. The final root mean square (RMS) errors for the test CAMS data are about two pixels which are compatible with the random RMS errors existed in the reference map coordinates.

Comparative Study of SVM Methods Combined with Voxel Selection for Object Category Classification on fMRI Data

PubMed Central

Song, Sutao; Zhan, Zhichao; Long, Zhiying; Zhang, Jiacai; Yao, Li

2011-01-01

Background Support vector machine (SVM) has been widely used as accurate and reliable method to decipher brain patterns from functional MRI (fMRI) data. Previous studies have not found a clear benefit for non-linear (polynomial kernel) SVM versus linear one. Here, a more effective non-linear SVM using radial basis function (RBF) kernel is compared with linear SVM. Different from traditional studies which focused either merely on the evaluation of different types of SVM or the voxel selection methods, we aimed to investigate the overall performance of linear and RBF SVM for fMRI classification together with voxel selection schemes on classification accuracy and time-consuming. Methodology/Principal Findings Six different voxel selection methods were employed to decide which voxels of fMRI data would be included in SVM classifiers with linear and RBF kernels in classifying 4-category objects. Then the overall performances of voxel selection and classification methods were compared. Results showed that: (1) Voxel selection had an important impact on the classification accuracy of the classifiers: in a relative low dimensional feature space, RBF SVM outperformed linear SVM significantly; in a relative high dimensional space, linear SVM performed better than its counterpart; (2) Considering the classification accuracy and time-consuming holistically, linear SVM with relative more voxels as features and RBF SVM with small set of voxels (after PCA) could achieve the better accuracy and cost shorter time. Conclusions/Significance The present work provides the first empirical result of linear and RBF SVM in classification of fMRI data, combined with voxel selection methods. Based on the findings, if only classification accuracy was concerned, RBF SVM with appropriate small voxels and linear SVM with relative more voxels were two suggested solutions; if users concerned more about the computational time, RBF SVM with relative small set of voxels when part of the principal components were kept as features was a better choice. PMID:21359184

Comparative study of SVM methods combined with voxel selection for object category classification on fMRI data.

PubMed

Song, Sutao; Zhan, Zhichao; Long, Zhiying; Zhang, Jiacai; Yao, Li

2011-02-16

Support vector machine (SVM) has been widely used as accurate and reliable method to decipher brain patterns from functional MRI (fMRI) data. Previous studies have not found a clear benefit for non-linear (polynomial kernel) SVM versus linear one. Here, a more effective non-linear SVM using radial basis function (RBF) kernel is compared with linear SVM. Different from traditional studies which focused either merely on the evaluation of different types of SVM or the voxel selection methods, we aimed to investigate the overall performance of linear and RBF SVM for fMRI classification together with voxel selection schemes on classification accuracy and time-consuming. Six different voxel selection methods were employed to decide which voxels of fMRI data would be included in SVM classifiers with linear and RBF kernels in classifying 4-category objects. Then the overall performances of voxel selection and classification methods were compared. Results showed that: (1) Voxel selection had an important impact on the classification accuracy of the classifiers: in a relative low dimensional feature space, RBF SVM outperformed linear SVM significantly; in a relative high dimensional space, linear SVM performed better than its counterpart; (2) Considering the classification accuracy and time-consuming holistically, linear SVM with relative more voxels as features and RBF SVM with small set of voxels (after PCA) could achieve the better accuracy and cost shorter time. The present work provides the first empirical result of linear and RBF SVM in classification of fMRI data, combined with voxel selection methods. Based on the findings, if only classification accuracy was concerned, RBF SVM with appropriate small voxels and linear SVM with relative more voxels were two suggested solutions; if users concerned more about the computational time, RBF SVM with relative small set of voxels when part of the principal components were kept as features was a better choice.

Nonlinear Thermoelastic Effects in Surface Mechanics.

DTIC Science & Technology

1980-01-01

remaining quartic polynomial generated by det(A) .0 is presumed to not yield real roots (real characteristics) associated with elastic waves because...0253 UNCLASSIFIED NL NONINEAR THEMLOEIASTIC EFF’ECTS IN SUFC MECHANICS D T ICX2 ) J.1. PFirin General Electric Company. JUN 1 8 8 Schenectady, New York...f - Generalized analytic functions Ei Lagrangian strain components lk - Generalized Cauchy kernels, Eq. (1I) E - Young’s modulus, Pa ulk

Dielectric properties of almond kernels associated with radio frequency and microwave pasteurization

NASA Astrophysics Data System (ADS)

Li, Rui; Zhang, Shuang; Kou, Xiaoxi; Ling, Bo; Wang, Shaojin

2017-02-01

To develop advanced pasteurization treatments based on radio frequency (RF) or microwave (MW) energy, dielectric properties of almond kernels were measured by using an open-ended coaxial-line probe and impedance analyzer at frequencies between 10 and 3000 MHz, moisture contents between 4.2% to 19.6% w.b. and temperatures between 20 and 90 °C. The results showed that both dielectric constant and loss factor of the almond kernels decreased sharply with increasing frequency over the RF range (10-300 MHz), but gradually over the measured MW range (300-3000 MHz). Both dielectric constant and loss factor of almond kernels increased with increasing temperature and moisture content, and largely enhanced at higher temperature and moisture levels. Quadratic polynomial equations were developed to best fit the relationship between dielectric constant or loss factor at 27, 40, 915 or 2450 MHz and sample temperature/moisture content with R2 greater than 0.967. Penetration depth of electromagnetic wave into samples decreased with increasing frequency (27-2450 MHz), moisture content (4.2-19.6% w.b.) and temperature (20-90 °C). The temperature profiles of RF heated almond kernels under three moisture levels were made using experiment and computer simulation based on measured dielectric properties. Based on the result of this study, RF treatment has potential to be practically used for pasteurization of almond kernels with acceptable heating uniformity.

Dielectric properties of almond kernels associated with radio frequency and microwave pasteurization.

PubMed

Li, Rui; Zhang, Shuang; Kou, Xiaoxi; Ling, Bo; Wang, Shaojin

2017-02-10

To develop advanced pasteurization treatments based on radio frequency (RF) or microwave (MW) energy, dielectric properties of almond kernels were measured by using an open-ended coaxial-line probe and impedance analyzer at frequencies between 10 and 3000 MHz, moisture contents between 4.2% to 19.6% w.b. and temperatures between 20 and 90 °C. The results showed that both dielectric constant and loss factor of the almond kernels decreased sharply with increasing frequency over the RF range (10-300 MHz), but gradually over the measured MW range (300-3000 MHz). Both dielectric constant and loss factor of almond kernels increased with increasing temperature and moisture content, and largely enhanced at higher temperature and moisture levels. Quadratic polynomial equations were developed to best fit the relationship between dielectric constant or loss factor at 27, 40, 915 or 2450 MHz and sample temperature/moisture content with R 2 greater than 0.967. Penetration depth of electromagnetic wave into samples decreased with increasing frequency (27-2450 MHz), moisture content (4.2-19.6% w.b.) and temperature (20-90 °C). The temperature profiles of RF heated almond kernels under three moisture levels were made using experiment and computer simulation based on measured dielectric properties. Based on the result of this study, RF treatment has potential to be practically used for pasteurization of almond kernels with acceptable heating uniformity.

Lossy Wavefield Compression for Full-Waveform Inversion

NASA Astrophysics Data System (ADS)

Boehm, C.; Fichtner, A.; de la Puente, J.; Hanzich, M.

2015-12-01

We present lossy compression techniques, tailored to the inexact computation of sensitivity kernels, that significantly reduce the memory requirements of adjoint-based minimization schemes. Adjoint methods are a powerful tool to solve tomography problems in full-waveform inversion (FWI). Yet they face the challenge of massive memory requirements caused by the opposite directions of forward and adjoint simulations and the necessity to access both wavefields simultaneously during the computation of the sensitivity kernel. Thus, storage, I/O operations, and memory bandwidth become key topics in FWI. In this talk, we present strategies for the temporal and spatial compression of the forward wavefield. This comprises re-interpolation with coarse time steps and an adaptive polynomial degree of the spectral element shape functions. In addition, we predict the projection errors on a hierarchy of grids and re-quantize the residuals with an adaptive floating-point accuracy to improve the approximation. Furthermore, we use the first arrivals of adjoint waves to identify "shadow zones" that do not contribute to the sensitivity kernel at all. Updating and storing the wavefield within these shadow zones is skipped, which reduces memory requirements and computational costs at the same time. Compared to check-pointing, our approach has only a negligible computational overhead, utilizing the fact that a sufficiently accurate sensitivity kernel does not require a fully resolved forward wavefield. Furthermore, we use adaptive compression thresholds during the FWI iterations to ensure convergence. Numerical experiments on the reservoir scale and for the Western Mediterranean prove the high potential of this approach with an effective compression factor of 500-1000. Furthermore, it is computationally cheap and easy to integrate in both, finite-differences and finite-element wave propagation codes.

2D/3D facial feature extraction

NASA Astrophysics Data System (ADS)

Çinar Akakin, Hatice; Ali Salah, Albert; Akarun, Lale; Sankur, Bülent

2006-02-01

We propose and compare three different automatic landmarking methods for near-frontal faces. The face information is provided as 480x640 gray-level images in addition to the corresponding 3D scene depth information. All three methods follow a coarse-to-fine suite and use the 3D information in an assist role. The first method employs a combination of principal component analysis (PCA) and independent component analysis (ICA) features to analyze the Gabor feature set. The second method uses a subset of DCT coefficients for template-based matching. These two methods employ SVM classifiers with polynomial kernel functions. The third method uses a mixture of factor analyzers to learn Gabor filter outputs. We contrast the localization performance separately with 2D texture and 3D depth information. Although the 3D depth information per se does not perform as well as texture images in landmark localization, the 3D information has still a beneficial role in eliminating the background and the false alarms.

Entropy of orthogonal polynomials with Freud weights and information entropies of the harmonic oscillator potential

NASA Astrophysics Data System (ADS)

Van Assche, W.; Yáñez, R. J.; Dehesa, J. S.

1995-08-01

The information entropy of the harmonic oscillator potential V(x)=1/2λx2 in both position and momentum spaces can be expressed in terms of the so-called ``entropy of Hermite polynomials,'' i.e., the quantity Sn(H):= -∫-∞+∞H2n(x)log H2n(x) e-x2dx. These polynomials are instances of the polynomials orthogonal with respect to the Freud weights w(x)=exp(-||x||m), m≳0. Here, a very precise and general result of the entropy of Freud polynomials recently established by Aptekarev et al. [J. Math. Phys. 35, 4423-4428 (1994)], specialized to the Hermite kernel (case m=2), leads to an important refined asymptotic expression for the information entropies of very excited states (i.e., for large n) in both position and momentum spaces, to be denoted by Sρ and Sγ, respectively. Briefly, it is shown that, for large values of n, Sρ+1/2logλ≂log(π√2n/e)+o(1) and Sγ-1/2log λ≂log(π√2n/e)+o(1), so that Sρ+Sγ≂log(2π2n/e2)+o(1) in agreement with the generalized indetermination relation of Byalinicki-Birula and Mycielski [Commun. Math. Phys. 44, 129-132 (1975)]. Finally, the rate of convergence of these two information entropies is numerically analyzed. In addition, using a Rakhmanov result, we describe a totally new proof of the leading term of the entropy of Freud polynomials which, naturally, is just a weak version of the aforementioned general result.

Classifying Lower Extremity Muscle Fatigue during Walking using Machine Learning and Inertial Sensors

PubMed Central

Zhang, Jian; Lockhart, Thurmon E.; Soangra, Rahul

2013-01-01

Fatigue in lower extremity musculature is associated with decline in postural stability, motor performance and alters normal walking patterns in human subjects. Automated recognition of lower extremity muscle fatigue condition may be advantageous in early detection of fall and injury risks. Supervised machine learning methods such as Support Vector Machines (SVM) have been previously used for classifying healthy and pathological gait patterns and also for separating old and young gait patterns. In this study we explore the classification potential of SVM in recognition of gait patterns utilizing an inertial measurement unit associated with lower extremity muscular fatigue. Both kinematic and kinetic gait patterns of 17 participants (29±11 years) were recorded and analyzed in normal and fatigued state of walking. Lower extremities were fatigued by performance of a squatting exercise until the participants reached 60% of their baseline maximal voluntary exertion level. Feature selection methods were used to classify fatigue and no-fatigue conditions based on temporal and frequency information of the signals. Additionally, influences of three different kernel schemes (i.e., linear, polynomial, and radial basis function) were investigated for SVM classification. The results indicated that lower extremity muscle fatigue condition influenced gait and loading responses. In terms of the SVM classification results, an accuracy of 96% was reached in distinguishing the two gait patterns (fatigue and no-fatigue) within the same subject using the kinematic, time and frequency domain features. It is also found that linear kernel and RBF kernel were equally good to identify intra-individual fatigue characteristics. These results suggest that intra-subject fatigue classification using gait patterns from an inertial sensor holds considerable potential in identifying “at-risk” gait due to muscle fatigue. PMID:24081829

Fast and accurate Voronoi density gridding from Lagrangian hydrodynamics data

NASA Astrophysics Data System (ADS)

Petkova, Maya A.; Laibe, Guillaume; Bonnell, Ian A.

2018-01-01

Voronoi grids have been successfully used to represent density structures of gas in astronomical hydrodynamics simulations. While some codes are explicitly built around using a Voronoi grid, others, such as Smoothed Particle Hydrodynamics (SPH), use particle-based representations and can benefit from constructing a Voronoi grid for post-processing their output. So far, calculating the density of each Voronoi cell from SPH data has been done numerically, which is both slow and potentially inaccurate. This paper proposes an alternative analytic method, which is fast and accurate. We derive an expression for the integral of a cubic spline kernel over the volume of a Voronoi cell and link it to the density of the cell. Mass conservation is ensured rigorously by the procedure. The method can be applied more broadly to integrate a spherically symmetric polynomial function over the volume of a random polyhedron.

The effect of traditional Persian music on the cardiac functioning of young Iranian women.

PubMed

Abedi, Behzad; Abbasi, Ataollah; Goshvarpour, Atefeh; Khosroshai, Hamid Tayebi; Javanshir, Elnaz

In the past few decades, several studies have reported the physiological effects of listening to music. The physiological effects of different music types on different people are not similar. Therefore, in the present study, we have sought to examine the effects of traditional Persian music on the cardiac function in young women. Twenty-two healthy females participated in this study. ECG signals were recorded in two conditions: rest and music. For each of the 21 ECG signals (15 morphological and six wavelet based feature) features were extracted. SVM classifier was used for the classification of ECG signals during and before the music. The results showed that the mean of heart rate, the mean amplitude of R-wave, T-wave, and P-wave decreased in response to music. Time-frequency analysis revealed that the mean of the absolute values of the detail coefficients at higher scales increased during rest. The overall accuracy of 91.6% was achieved using polynomial kernel and RBF kernel. Using linear kernel, the best result (with the accuracy rate of 100%) was attained. Copyright © 2016. Published by Elsevier B.V.

Mathematics of Computed Tomography

NASA Astrophysics Data System (ADS)

Hawkins, William Grant

A review of the applications of the Radon transform is presented, with emphasis on emission computed tomography and transmission computed tomography. The theory of the 2D and 3D Radon transforms, and the effects of attenuation for emission computed tomography are presented. The algebraic iterative methods, their importance and limitations are reviewed. Analytic solutions of the 2D problem the convolution and frequency filtering methods based on linear shift invariant theory, and the solution of the circular harmonic decomposition by integral transform theory--are reviewed. The relation between the invisible kernels, the inverse circular harmonic transform, and the consistency conditions are demonstrated. The discussion and review are extended to the 3D problem-convolution, frequency filtering, spherical harmonic transform solutions, and consistency conditions. The Cormack algorithm based on reconstruction with Zernike polynomials is reviewed. An analogous algorithm and set of reconstruction polynomials is developed for the spherical harmonic transform. The relations between the consistency conditions, boundary conditions and orthogonal basis functions for the 2D projection harmonics are delineated and extended to the 3D case. The equivalence of the inverse circular harmonic transform, the inverse Radon transform, and the inverse Cormack transform is presented. The use of the number of nodes of a projection harmonic as a filter is discussed. Numerical methods for the efficient implementation of angular harmonic algorithms based on orthogonal functions and stable recursion are presented. The derivation of a lower bound for the signal-to-noise ratio of the Cormack algorithm is derived.

GIS-based support vector machine modeling of earthquake-triggered landslide susceptibility in the Jianjiang River watershed, China

NASA Astrophysics Data System (ADS)

Xu, Chong; Dai, Fuchu; Xu, Xiwei; Lee, Yuan Hsi

2012-04-01

Support vector machine (SVM) modeling is based on statistical learning theory. It involves a training phase with associated input and target output values. In recent years, the method has become increasingly popular. The main purpose of this study is to evaluate the mapping power of SVM modeling in earthquake triggered landslide-susceptibility mapping for a section of the Jianjiang River watershed using a Geographic Information System (GIS) software. The river was affected by the Wenchuan earthquake of May 12, 2008. Visual interpretation of colored aerial photographs of 1-m resolution and extensive field surveys provided a detailed landslide inventory map containing 3147 landslides related to the 2008 Wenchuan earthquake. Elevation, slope angle, slope aspect, distance from seismogenic faults, distance from drainages, and lithology were used as the controlling parameters. For modeling, three groups of positive and negative training samples were used in concert with four different kernel functions. Positive training samples include the centroids of 500 large landslides, those of all 3147 landslides, and 5000 randomly selected points in landslide polygons. Negative training samples include 500, 3147, and 5000 randomly selected points on slopes that remained stable during the Wenchuan earthquake. The four kernel functions are linear, polynomial, radial basis, and sigmoid. In total, 12 cases of landslide susceptibility were mapped. Comparative analyses of landslide-susceptibility probability and area relation curves show that both the polynomial and radial basis functions suitably classified the input data as either landslide positive or negative though the radial basis function was more successful. The 12 generated landslide-susceptibility maps were compared with known landslide centroid locations and landslide polygons to verify the success rate and predictive accuracy of each model. The 12 results were further validated using area-under-curve analysis. Group 3 with 5000 randomly selected points on the landslide polygons, and 5000 randomly selected points along stable slopes gave the best results with a success rate of 79.20% and predictive accuracy of 79.13% under the radial basis function. Of all the results, the sigmoid kernel function was the least skillful when used in concert with the centroid data of all 3147 landslides as positive training samples, and the negative training samples of 3147 randomly selected points in regions of stable slope (success rate = 54.95%; predictive accuracy = 61.85%). This paper also provides suggestions and reference data for selecting appropriate training samples and kernel function types for earthquake triggered landslide-susceptibility mapping using SVM modeling. Predictive landslide-susceptibility maps could be useful in hazard mitigation by helping planners understand the probability of landslides in different regions.

Stochastic Models of Macroscale Quantities for the Prediction of the REV Scale for Multiphase Flow through Porous Media

NASA Astrophysics Data System (ADS)

Talbot, C.; McClure, J. E.; Armstrong, R. T.; Mostaghimi, P.; Hu, Y.; Miller, C. T.

2017-12-01

Microscale experimental and computational methods can be used to evaluate fundamental microscale mechanisms and deduce macroscale constitutive relationships and parameter values. The link between the microscale and the macroscale is especially demanding, because technical issues arise regarding the necessary scale of the system needed for a meaningful set of macroscale measures to be insensitive to the size of the system, which is known as a representative elementary volume (REV). While the REV scale is routinely determined for single-phase flow in porous media, no systematic study of the scale of a REV for the comprehensive set of macroscale measures considered here has been reported in the literature. A comprehensive set of measures of the macroscale state is developed. We further develop and apply methods to predict the REV scale and quantify the uncertainty of the estimate for this set of macroscale quantities. We model the system state in terms of standard errors of macroscale quantities as a multivariate Gaussian process dependent on the size of the domain simulated. We determine predictive distributions of function values and a posterior distributions of weights using standard kernels, as well as a kernel constructed using relationships between physical quantities. For each kernel, we discuss the decay of the mean and covariance with increasing domain size, and use cross-validation to facilitate model selection. The procedure yields a model of the domain size needed to achieve a REV with quantifiable uncertainty. We present results in the context of multiphase fluid flow through a highly resolved realization of sandstone imaged using micro-CT. A 1440x1440x4320 section of the full 2520x2520x5280 imaged medium is simulated using the lattice-Boltzmann method. We compare the fidelity of the predictive model with results obtained by an analogous approach using polynomial regression.

Out-of-Sample Extensions for Non-Parametric Kernel Methods.

PubMed

Pan, Binbin; Chen, Wen-Sheng; Chen, Bo; Xu, Chen; Lai, Jianhuang

2017-02-01

Choosing suitable kernels plays an important role in the performance of kernel methods. Recently, a number of studies were devoted to developing nonparametric kernels. Without assuming any parametric form of the target kernel, nonparametric kernel learning offers a flexible scheme to utilize the information of the data, which may potentially characterize the data similarity better. The kernel methods using nonparametric kernels are referred to as nonparametric kernel methods. However, many nonparametric kernel methods are restricted to transductive learning, where the prediction function is defined only over the data points given beforehand. They have no straightforward extension for the out-of-sample data points, and thus cannot be applied to inductive learning. In this paper, we show how to make the nonparametric kernel methods applicable to inductive learning. The key problem of out-of-sample extension is how to extend the nonparametric kernel matrix to the corresponding kernel function. A regression approach in the hyper reproducing kernel Hilbert space is proposed to solve this problem. Empirical results indicate that the out-of-sample performance is comparable to the in-sample performance in most cases. Experiments on face recognition demonstrate the superiority of our nonparametric kernel method over the state-of-the-art parametric kernel methods.

Optimal algorithm for automatic detection of microaneurysms based on receiver operating characteristic curve

NASA Astrophysics Data System (ADS)

Xu, Lili; Luo, Shuqian

2010-11-01

Microaneurysms (MAs) are the first manifestations of the diabetic retinopathy (DR) as well as an indicator for its progression. Their automatic detection plays a key role for both mass screening and monitoring and is therefore in the core of any system for computer-assisted diagnosis of DR. The algorithm basically comprises the following stages: candidate detection aiming at extracting the patterns possibly corresponding to MAs based on mathematical morphological black top hat, feature extraction to characterize these candidates, and classification based on support vector machine (SVM), to validate MAs. Feature vector and kernel function of SVM selection is very important to the algorithm. We use the receiver operating characteristic (ROC) curve to evaluate the distinguishing performance of different feature vectors and different kernel functions of SVM. The ROC analysis indicates the quadratic polynomial SVM with a combination of features as the input shows the best discriminating performance.

Optimal algorithm for automatic detection of microaneurysms based on receiver operating characteristic curve.

PubMed

Xu, Lili; Luo, Shuqian

2010-01-01

Microaneurysms (MAs) are the first manifestations of the diabetic retinopathy (DR) as well as an indicator for its progression. Their automatic detection plays a key role for both mass screening and monitoring and is therefore in the core of any system for computer-assisted diagnosis of DR. The algorithm basically comprises the following stages: candidate detection aiming at extracting the patterns possibly corresponding to MAs based on mathematical morphological black top hat, feature extraction to characterize these candidates, and classification based on support vector machine (SVM), to validate MAs. Feature vector and kernel function of SVM selection is very important to the algorithm. We use the receiver operating characteristic (ROC) curve to evaluate the distinguishing performance of different feature vectors and different kernel functions of SVM. The ROC analysis indicates the quadratic polynomial SVM with a combination of features as the input shows the best discriminating performance.

Optimized Quasi-Interpolators for Image Reconstruction.

PubMed

Sacht, Leonardo; Nehab, Diego

2015-12-01

We propose new quasi-interpolators for the continuous reconstruction of sampled images, combining a narrowly supported piecewise-polynomial kernel and an efficient digital filter. In other words, our quasi-interpolators fit within the generalized sampling framework and are straightforward to use. We go against standard practice and optimize for approximation quality over the entire Nyquist range, rather than focusing exclusively on the asymptotic behavior as the sample spacing goes to zero. In contrast to previous work, we jointly optimize with respect to all degrees of freedom available in both the kernel and the digital filter. We consider linear, quadratic, and cubic schemes, offering different tradeoffs between quality and computational cost. Experiments with compounded rotations and translations over a range of input images confirm that, due to the additional degrees of freedom and the more realistic objective function, our new quasi-interpolators perform better than the state of the art, at a similar computational cost.

Solutions of interval type-2 fuzzy polynomials using a new ranking method

NASA Astrophysics Data System (ADS)

Rahman, Nurhakimah Ab.; Abdullah, Lazim; Ghani, Ahmad Termimi Ab.; Ahmad, Noor'Ani

2015-10-01

A few years ago, a ranking method have been introduced in the fuzzy polynomial equations. Concept of the ranking method is proposed to find actual roots of fuzzy polynomials (if exists). Fuzzy polynomials are transformed to system of crisp polynomials, performed by using ranking method based on three parameters namely, Value, Ambiguity and Fuzziness. However, it was found that solutions based on these three parameters are quite inefficient to produce answers. Therefore in this study a new ranking method have been developed with the aim to overcome the inherent weakness. The new ranking method which have four parameters are then applied in the interval type-2 fuzzy polynomials, covering the interval type-2 of fuzzy polynomial equation, dual fuzzy polynomial equations and system of fuzzy polynomials. The efficiency of the new ranking method then numerically considered in the triangular fuzzy numbers and the trapezoidal fuzzy numbers. Finally, the approximate solutions produced from the numerical examples indicate that the new ranking method successfully produced actual roots for the interval type-2 fuzzy polynomials.

Spectral imaging using consumer-level devices and kernel-based regression.

PubMed

Heikkinen, Ville; Cámara, Clara; Hirvonen, Tapani; Penttinen, Niko

2016-06-01

Hyperspectral reflectance factor image estimations were performed in the 400-700 nm wavelength range using a portable consumer-level laptop display as an adjustable light source for a trichromatic camera. Targets of interest were ColorChecker Classic samples, Munsell Matte samples, geometrically challenging tempera icon paintings from the turn of the 20th century, and human hands. Measurements and simulations were performed using Nikon D80 RGB camera and Dell Vostro 2520 laptop screen as a light source. Estimations were performed without spectral characteristics of the devices and by emphasizing simplicity for training sets and estimation model optimization. Spectral and color error images are shown for the estimations using line-scanned hyperspectral images as the ground truth. Estimations were performed using kernel-based regression models via a first-degree inhomogeneous polynomial kernel and a Matérn kernel, where in the latter case the median heuristic approach for model optimization and link function for bounded estimation were evaluated. Results suggest modest requirements for a training set and show that all estimation models have markedly improved accuracy with respect to the DE00 color distance (up to 99% for paintings and hands) and the Pearson distance (up to 98% for paintings and 99% for hands) from a weak training set (Digital ColorChecker SG) case when small representative training data were used in the estimation.

Scoliosis curve type classification using kernel machine from 3D trunk image

NASA Astrophysics Data System (ADS)

Adankon, Mathias M.; Dansereau, Jean; Parent, Stefan; Labelle, Hubert; Cheriet, Farida

2012-03-01

Adolescent idiopathic scoliosis (AIS) is a deformity of the spine manifested by asymmetry and deformities of the external surface of the trunk. Classification of scoliosis deformities according to curve type is used to plan management of scoliosis patients. Currently, scoliosis curve type is determined based on X-ray exam. However, cumulative exposure to X-rays radiation significantly increases the risk for certain cancer. In this paper, we propose a robust system that can classify the scoliosis curve type from non invasive acquisition of 3D trunk surface of the patients. The 3D image of the trunk is divided into patches and local geometric descriptors characterizing the surface of the back are computed from each patch and forming the features. We perform the reduction of the dimensionality by using Principal Component Analysis and 53 components were retained. In this work a multi-class classifier is built with Least-squares support vector machine (LS-SVM) which is a kernel classifier. For this study, a new kernel was designed in order to achieve a robust classifier in comparison with polynomial and Gaussian kernel. The proposed system was validated using data of 103 patients with different scoliosis curve types diagnosed and classified by an orthopedic surgeon from the X-ray images. The average rate of successful classification was 93.3% with a better rate of prediction for the major thoracic and lumbar/thoracolumbar types.

Decision support system for diabetic retinopathy using discrete wavelet transform.

PubMed

Noronha, K; Acharya, U R; Nayak, K P; Kamath, S; Bhandary, S V

2013-03-01

Prolonged duration of the diabetes may affect the tiny blood vessels of the retina causing diabetic retinopathy. Routine eye screening of patients with diabetes helps to detect diabetic retinopathy at the early stage. It is very laborious and time-consuming for the doctors to go through many fundus images continuously. Therefore, decision support system for diabetic retinopathy detection can reduce the burden of the ophthalmologists. In this work, we have used discrete wavelet transform and support vector machine classifier for automated detection of normal and diabetic retinopathy classes. The wavelet-based decomposition was performed up to the second level, and eight energy features were extracted. Two energy features from the approximation coefficients of two levels and six energy values from the details in three orientations (horizontal, vertical and diagonal) were evaluated. These features were fed to the support vector machine classifier with various kernel functions (linear, radial basis function, polynomial of orders 2 and 3) to evaluate the highest classification accuracy. We obtained the highest average classification accuracy, sensitivity and specificity of more than 99% with support vector machine classifier (polynomial kernel of order 3) using three discrete wavelet transform features. We have also proposed an integrated index called Diabetic Retinopathy Risk Index using clinically significant wavelet energy features to identify normal and diabetic retinopathy classes using just one number. We believe that this (Diabetic Retinopathy Risk Index) can be used as an adjunct tool by the doctors during the eye screening to cross-check their diagnosis.

Generalized Polynomial Chaos Based Uncertainty Quantification for Planning MRgLITT Procedures

PubMed Central

Fahrenholtz, S.; Stafford, R. J.; Maier, F.; Hazle, J. D.; Fuentes, D.

2014-01-01

Purpose A generalized polynomial chaos (gPC) method is used to incorporate constitutive parameter uncertainties within the Pennes representation of bioheat transfer phenomena. The stochastic temperature predictions of the mathematical model are critically evaluated against MR thermometry data for planning MR-guided Laser Induced Thermal Therapies (MRgLITT). Methods Pennes bioheat transfer model coupled with a diffusion theory approximation of laser tissue interaction was implemented as the underlying deterministic kernel. A probabilistic sensitivity study was used to identify parameters that provide the most variance in temperature output. Confidence intervals of the temperature predictions are compared to MR temperature imaging (MRTI) obtained during phantom and in vivo canine (n=4) MRgLITT experiments. The gPC predictions were quantitatively compared to MRTI data using probabilistic linear and temporal profiles as well as 2-D 60 °C isotherms. Results Within the range of physically meaningful constitutive values relevant to the ablative temperature regime of MRgLITT, the sensitivity study indicated that the optical parameters, particularly the anisotropy factor, created the most variance in the stochastic model's output temperature prediction. Further, within the statistical sense considered, a nonlinear model of the temperature and damage dependent perfusion, absorption, and scattering is captured within the confidence intervals of the linear gPC method. Multivariate stochastic model predictions using parameters with the dominant sensitivities show good agreement with experimental MRTI data. Conclusions Given parameter uncertainties and mathematical modeling approximations of the Pennes bioheat model, the statistical framework demonstrates conservative estimates of the therapeutic heating and has potential for use as a computational prediction tool for thermal therapy planning. PMID:23692295

Multiple zeros of polynomials

NASA Technical Reports Server (NTRS)

Wood, C. A.

1974-01-01

For polynomials of higher degree, iterative numerical methods must be used. Four iterative methods are presented for approximating the zeros of a polynomial using a digital computer. Newton's method and Muller's method are two well known iterative methods which are presented. They extract the zeros of a polynomial by generating a sequence of approximations converging to each zero. However, both of these methods are very unstable when used on a polynomial which has multiple zeros. That is, either they fail to converge to some or all of the zeros, or they converge to very bad approximations of the polynomial's zeros. This material introduces two new methods, the greatest common divisor (G.C.D.) method and the repeated greatest common divisor (repeated G.C.D.) method, which are superior methods for numerically approximating the zeros of a polynomial having multiple zeros. These methods were programmed in FORTRAN 4 and comparisons in time and accuracy are given.

Quantum Support Vector Machine for Big Data Classification

NASA Astrophysics Data System (ADS)

Rebentrost, Patrick; Mohseni, Masoud; Lloyd, Seth

2014-09-01

Supervised machine learning is the classification of new data based on already classified training examples. In this work, we show that the support vector machine, an optimized binary classifier, can be implemented on a quantum computer, with complexity logarithmic in the size of the vectors and the number of training examples. In cases where classical sampling algorithms require polynomial time, an exponential speedup is obtained. At the core of this quantum big data algorithm is a nonsparse matrix exponentiation technique for efficiently performing a matrix inversion of the training data inner-product (kernel) matrix.

Stochastic, real-space, imaginary-time evaluation of third-order Feynman-Goldstone diagrams

NASA Astrophysics Data System (ADS)

Willow, Soohaeng Yoo; Hirata, So

2014-01-01

A new, alternative set of interpretation rules of Feynman-Goldstone diagrams for many-body perturbation theory is proposed, which translates diagrams into algebraic expressions suitable for direct Monte Carlo integrations. A vertex of a diagram is associated with a Coulomb interaction (rather than a two-electron integral) and an edge with the trace of a Green's function in real space and imaginary time. With these, 12 diagrams of third-order many-body perturbation (MP3) theory are converted into 20-dimensional integrals, which are then evaluated by a Monte Carlo method. It uses redundant walkers for convergence acceleration and a weight function for importance sampling in conjunction with the Metropolis algorithm. The resulting Monte Carlo MP3 method has low-rank polynomial size dependence of the operation cost, a negligible memory cost, and a naturally parallel computational kernel, while reproducing the correct correlation energies of small molecules within a few mEh after 106 Monte Carlo steps.

Multiple kernels learning-based biological entity relationship extraction method.

PubMed

Dongliang, Xu; Jingchang, Pan; Bailing, Wang

2017-09-20

Automatic extracting protein entity interaction information from biomedical literature can help to build protein relation network and design new drugs. There are more than 20 million literature abstracts included in MEDLINE, which is the most authoritative textual database in the field of biomedicine, and follow an exponential growth over time. This frantic expansion of the biomedical literature can often be difficult to absorb or manually analyze. Thus efficient and automated search engines are necessary to efficiently explore the biomedical literature using text mining techniques. The P, R, and F value of tag graph method in Aimed corpus are 50.82, 69.76, and 58.61%, respectively. The P, R, and F value of tag graph kernel method in other four evaluation corpuses are 2-5% higher than that of all-paths graph kernel. And The P, R and F value of feature kernel and tag graph kernel fuse methods is 53.43, 71.62 and 61.30%, respectively. The P, R and F value of feature kernel and tag graph kernel fuse methods is 55.47, 70.29 and 60.37%, respectively. It indicated that the performance of the two kinds of kernel fusion methods is better than that of simple kernel. In comparison with the all-paths graph kernel method, the tag graph kernel method is superior in terms of overall performance. Experiments show that the performance of the multi-kernels method is better than that of the three separate single-kernel method and the dual-mutually fused kernel method used hereof in five corpus sets.

Predictability of machine learning techniques to forecast the trends of market index prices: Hypothesis testing for the Korean stock markets.

PubMed

Pyo, Sujin; Lee, Jaewook; Cha, Mincheol; Jang, Huisu

2017-01-01

The prediction of the trends of stocks and index prices is one of the important issues to market participants. Investors have set trading or fiscal strategies based on the trends, and considerable research in various academic fields has been studied to forecast financial markets. This study predicts the trends of the Korea Composite Stock Price Index 200 (KOSPI 200) prices using nonparametric machine learning models: artificial neural network, support vector machines with polynomial and radial basis function kernels. In addition, this study states controversial issues and tests hypotheses about the issues. Accordingly, our results are inconsistent with those of the precedent research, which are generally considered to have high prediction performance. Moreover, Google Trends proved that they are not effective factors in predicting the KOSPI 200 index prices in our frameworks. Furthermore, the ensemble methods did not improve the accuracy of the prediction.

Predictability of machine learning techniques to forecast the trends of market index prices: Hypothesis testing for the Korean stock markets

PubMed Central

Pyo, Sujin; Lee, Jaewook; Cha, Mincheol

2017-01-01

The prediction of the trends of stocks and index prices is one of the important issues to market participants. Investors have set trading or fiscal strategies based on the trends, and considerable research in various academic fields has been studied to forecast financial markets. This study predicts the trends of the Korea Composite Stock Price Index 200 (KOSPI 200) prices using nonparametric machine learning models: artificial neural network, support vector machines with polynomial and radial basis function kernels. In addition, this study states controversial issues and tests hypotheses about the issues. Accordingly, our results are inconsistent with those of the precedent research, which are generally considered to have high prediction performance. Moreover, Google Trends proved that they are not effective factors in predicting the KOSPI 200 index prices in our frameworks. Furthermore, the ensemble methods did not improve the accuracy of the prediction. PMID:29136004

A fast and well-conditioned spectral method for singular integral equations

NASA Astrophysics Data System (ADS)

Slevinsky, Richard Mikael; Olver, Sheehan

2017-03-01

We develop a spectral method for solving univariate singular integral equations over unions of intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the equations as almost-banded infinite-dimensional systems. This is accomplished by utilizing low rank approximations for sparse representations of the bivariate kernels. The resulting system can be solved in O (m2 n) operations using an adaptive QR factorization, where m is the bandwidth and n is the optimal number of unknowns needed to resolve the true solution. The complexity is reduced to O (mn) operations by pre-caching the QR factorization when the same operator is used for multiple right-hand sides. Stability is proved by showing that the resulting linear operator can be diagonally preconditioned to be a compact perturbation of the identity. Applications considered include the Faraday cage, and acoustic scattering for the Helmholtz and gravity Helmholtz equations, including spectrally accurate numerical evaluation of the far- and near-field solution. The JULIA software package SingularIntegralEquations.jl implements our method with a convenient, user-friendly interface.

Solving the interval type-2 fuzzy polynomial equation using the ranking method

NASA Astrophysics Data System (ADS)

Rahman, Nurhakimah Ab.; Abdullah, Lazim

2014-07-01

Polynomial equations with trapezoidal and triangular fuzzy numbers have attracted some interest among researchers in mathematics, engineering and social sciences. There are some methods that have been developed in order to solve these equations. In this study we are interested in introducing the interval type-2 fuzzy polynomial equation and solving it using the ranking method of fuzzy numbers. The ranking method concept was firstly proposed to find real roots of fuzzy polynomial equation. Therefore, the ranking method is applied to find real roots of the interval type-2 fuzzy polynomial equation. We transform the interval type-2 fuzzy polynomial equation to a system of crisp interval type-2 fuzzy polynomial equation. This transformation is performed using the ranking method of fuzzy numbers based on three parameters, namely value, ambiguity and fuzziness. Finally, we illustrate our approach by numerical example.

Assessing the blood volume and heart rate responses during haemodialysis in fluid overloaded patients using support vector regression.

PubMed

Javed, Faizan; Savkin, Andrey V; Chan, Gregory S H; Middleton, Paul M; Malouf, Philip; Steel, Elizabeth; Mackie, James; Lovell, Nigel H

2009-11-01

This study aims to assess the blood volume and heart rate (HR) responses during haemodialysis in fluid overloaded patients by a nonparametric nonlinear regression approach based on a support vector machine (SVM). Relative blood volume (RBV) and electrocardiogram (ECG) was recorded from 23 haemodynamically stable renal failure patients during regular haemodialysis. Modelling was performed on 18 fluid overloaded patients (fluid removal of >2 L). SVM-based regression was used to obtain the models of RBV change with time as well as the percentage change in HR with respect to RBV. Mean squared error (MSE) and goodness of fit (R(2)) were used for comparison among different kernel functions. The design parameters were estimated using a grid search approach and the selected models were validated by a k-fold cross-validation technique. For the model of HR versus RBV change, a radial basis function (RBF) kernel (MSE = 17.37 and R(2) = 0.932) gave the least MSE compared to linear (MSE = 25.97 and R(2) = 0.898) and polynomial (MSE = 18.18 and R(2)= 0.929). The MSE was significantly lower for training data set when using RBF kernel compared to other kernels (p < 0.01). The RBF kernel also provided a slightly better fit of RBV change with time (MSE = 1.12 and R(2) = 0.91) compared to a linear kernel (MSE = 1.46 and R(2) = 0.88). The modelled HR response was characterized by an initial drop and a subsequent rise during progressive reduction in RBV, which may be interpreted as the reflex response to a transition from central hypervolaemia to hypovolaemia. These modelled curves can be used as references to a controller that can be designed to regulate the haemodynamic variables to ensure the stability of patients undergoing haemodialysis.

Online Pairwise Learning Algorithms.

PubMed

Ying, Yiming; Zhou, Ding-Xuan

2016-04-01

Pairwise learning usually refers to a learning task that involves a loss function depending on pairs of examples, among which the most notable ones are bipartite ranking, metric learning, and AUC maximization. In this letter we study an online algorithm for pairwise learning with a least-square loss function in an unconstrained setting of a reproducing kernel Hilbert space (RKHS) that we refer to as the Online Pairwise lEaRning Algorithm (OPERA). In contrast to existing works (Kar, Sriperumbudur, Jain, & Karnick, 2013 ; Wang, Khardon, Pechyony, & Jones, 2012 ), which require that the iterates are restricted to a bounded domain or the loss function is strongly convex, OPERA is associated with a non-strongly convex objective function and learns the target function in an unconstrained RKHS. Specifically, we establish a general theorem that guarantees the almost sure convergence for the last iterate of OPERA without any assumptions on the underlying distribution. Explicit convergence rates are derived under the condition of polynomially decaying step sizes. We also establish an interesting property for a family of widely used kernels in the setting of pairwise learning and illustrate the convergence results using such kernels. Our methodology mainly depends on the characterization of RKHSs using its associated integral operators and probability inequalities for random variables with values in a Hilbert space.

Data Assimilation on a Quantum Annealing Computer: Feasibility and Scalability

NASA Astrophysics Data System (ADS)

Nearing, G. S.; Halem, M.; Chapman, D. R.; Pelissier, C. S.

2014-12-01

Data assimilation is one of the ubiquitous and computationally hard problems in the Earth Sciences. In particular, ensemble-based methods require a large number of model evaluations to estimate the prior probability density over system states, and variational methods require adjoint calculations and iteration to locate the maximum a posteriori solution in the presence of nonlinear models and observation operators. Quantum annealing computers (QAC) like the new D-Wave housed at the NASA Ames Research Center can be used for optimization and sampling, and therefore offers a new possibility for efficiently solving hard data assimilation problems. Coding on the QAC is not straightforward: a problem must be posed as a Quadratic Unconstrained Binary Optimization (QUBO) and mapped to a spherical Chimera graph. We have developed a method for compiling nonlinear 4D-Var problems on the D-Wave that consists of five steps: Emulating the nonlinear model and/or observation function using radial basis functions (RBF) or Chebyshev polynomials. Truncating a Taylor series around each RBF kernel. Reducing the Taylor polynomial to a quadratic using ancilla gadgets. Mapping the real-valued quadratic to a fixed-precision binary quadratic. Mapping the fully coupled binary quadratic to a partially coupled spherical Chimera graph using ancilla gadgets. At present the D-Wave contains 512 qbits (with 1024 and 2048 qbit machines due in the next two years); this machine size allows us to estimate only 3 state variables at each satellite overpass. However, QAC's solve optimization problems using a physical (quantum) system, and therefore do not require iterations or calculation of model adjoints. This has the potential to revolutionize our ability to efficiently perform variational data assimilation, as the size of these computers grows in the coming years.

Implementing Kernel Methods Incrementally by Incremental Nonlinear Projection Trick.

PubMed

Kwak, Nojun

2016-05-20

Recently, the nonlinear projection trick (NPT) was introduced enabling direct computation of coordinates of samples in a reproducing kernel Hilbert space. With NPT, any machine learning algorithm can be extended to a kernel version without relying on the so called kernel trick. However, NPT is inherently difficult to be implemented incrementally because an ever increasing kernel matrix should be treated as additional training samples are introduced. In this paper, an incremental version of the NPT (INPT) is proposed based on the observation that the centerization step in NPT is unnecessary. Because the proposed INPT does not change the coordinates of the old data, the coordinates obtained by INPT can directly be used in any incremental methods to implement a kernel version of the incremental methods. The effectiveness of the INPT is shown by applying it to implement incremental versions of kernel methods such as, kernel singular value decomposition, kernel principal component analysis, and kernel discriminant analysis which are utilized for problems of kernel matrix reconstruction, letter classification, and face image retrieval, respectively.

Stable Numerical Approach for Fractional Delay Differential Equations

NASA Astrophysics Data System (ADS)

Singh, Harendra; Pandey, Rajesh K.; Baleanu, D.

2017-12-01

In this paper, we present a new stable numerical approach based on the operational matrix of integration of Jacobi polynomials for solving fractional delay differential equations (FDDEs). The operational matrix approach converts the FDDE into a system of linear equations, and hence the numerical solution is obtained by solving the linear system. The error analysis of the proposed method is also established. Further, a comparative study of the approximate solutions is provided for the test examples of the FDDE by varying the values of the parameters in the Jacobi polynomials. As in special case, the Jacobi polynomials reduce to the well-known polynomials such as (1) Legendre polynomial, (2) Chebyshev polynomial of second kind, (3) Chebyshev polynomial of third and (4) Chebyshev polynomial of fourth kind respectively. Maximum absolute error and root mean square error are calculated for the illustrated examples and presented in form of tables for the comparison purpose. Numerical stability of the presented method with respect to all four kind of polynomials are discussed. Further, the obtained numerical results are compared with some known methods from the literature and it is observed that obtained results from the proposed method is better than these methods.

Zika virus disease, microcephaly and Guillain-Barré syndrome in Colombia: epidemiological situation during 21 months of the Zika virus outbreak, 2015-2017.

PubMed

Méndez, Nelson; Oviedo-Pastrana, Misael; Mattar, Salim; Caicedo-Castro, Isaac; Arrieta, German

2017-01-01

The Zika virus disease (ZVD) has had a huge impact on public health in Colombia for the numbers of people affected and the presentation of Guillain-Barre syndrome (GBS) and microcephaly cases associated to ZVD. A retrospective descriptive study was carried out, we analyze the epidemiological situation of ZVD and its association with microcephaly and GBS during a 21-month period, from October 2015 to June 2017. The variables studied were: (i) ZVD cases, (ii) ZVD cases in pregnant women, (iii) laboratory-confirmed ZVD in pregnant women, (iv) ZVD cases associated with microcephaly, (v) laboratory-confirmed ZVD associated with microcephaly, and (vi) ZVD associated to GBS cases. Average number of cases, attack rates (AR) and proportions were also calculated. The studied variables were plotted by epidemiological weeks and months. The distribution of ZVD cases in Colombia was mapped across the time using Kernel density estimator and QGIS software; we adopted Kernel Ridge Regression (KRR) and the Gaussian Kernel to estimate the number of Guillain Barre cases given the number of ZVD cases. One hundred eight thousand eighty-seven ZVD cases had been reported in Colombia, including 19,963 (18.5%) in pregnant women, 710 (0.66%) associated with microcephaly (AR, 4.87 cases per 10,000 live births) and 453 (0.42%) ZVD associated to GBS cases (AR, 41.9 GBS cases per 10,000 ZVD cases). It appears the cases of GBS increased in parallel with the cases of ZVD, cases of microcephaly appeared 5 months after recognition of the outbreak. The kernel density map shows that throughout the study period, the states most affected by the Zika outbreak in Colombia were mainly San Andrés and Providencia islands, Casanare, Norte de Santander, Arauca and Huila. The KRR shows that there is no proportional relationship between the number of GBS and ZVD cases. During the cross validation, the RMSE achieved for the second order polynomial kernel, the linear kernel, the sigmoid kernel, and the Gaussian kernel are 9.15, 9.2, 10.7, and 7.2 respectively. This study updates the epidemiological analysis of the ZVD situation in Colombia describes the geographical distribution of ZVD and shows the functional relationship between ZVD cases and GBS.

Comparing Alternative Kernels for the Kernel Method of Test Equating: Gaussian, Logistic, and Uniform Kernels. Research Report. ETS RR-08-12

ERIC Educational Resources Information Center

Lee, Yi-Hsuan; von Davier, Alina A.

2008-01-01

The kernel equating method (von Davier, Holland, & Thayer, 2004) is based on a flexible family of equipercentile-like equating functions that use a Gaussian kernel to continuize the discrete score distributions. While the classical equipercentile, or percentile-rank, equating method carries out the continuization step by linear interpolation,…

Kernel Partial Least Squares for Nonlinear Regression and Discrimination

NASA Technical Reports Server (NTRS)

Rosipal, Roman; Clancy, Daniel (Technical Monitor)

2002-01-01

This paper summarizes recent results on applying the method of partial least squares (PLS) in a reproducing kernel Hilbert space (RKHS). A previously proposed kernel PLS regression model was proven to be competitive with other regularized regression methods in RKHS. The family of nonlinear kernel-based PLS models is extended by considering the kernel PLS method for discrimination. Theoretical and experimental results on a two-class discrimination problem indicate usefulness of the method.

A nodal discontinuous Galerkin approach to 3-D viscoelastic wave propagation in complex geological media

NASA Astrophysics Data System (ADS)

Lambrecht, L.; Lamert, A.; Friederich, W.; Möller, T.; Boxberg, M. S.

2018-03-01

A nodal discontinuous Galerkin (NDG) approach is developed and implemented for the computation of viscoelastic wavefields in complex geological media. The NDG approach combines unstructured tetrahedral meshes with an element-wise, high-order spatial interpolation of the wavefield based on Lagrange polynomials. Numerical fluxes are computed from an exact solution of the heterogeneous Riemann problem. Our implementation offers capabilities for modelling viscoelastic wave propagation in 1-D, 2-D and 3-D settings of very different spatial scale with little logistical overhead. It allows the import of external tetrahedral meshes provided by independent meshing software and can be run in a parallel computing environment. Computation of adjoint wavefields and an interface for the computation of waveform sensitivity kernels are offered. The method is validated in 2-D and 3-D by comparison to analytical solutions and results from a spectral element method. The capabilities of the NDG method are demonstrated through a 3-D example case taken from tunnel seismics which considers high-frequency elastic wave propagation around a curved underground tunnel cutting through inclined and faulted sedimentary strata. The NDG method was coded into the open-source software package NEXD and is available from GitHub.

Increasing accuracy of dispersal kernels in grid-based population models

USGS Publications Warehouse

Slone, D.H.

2011-01-01

Dispersal kernels in grid-based population models specify the proportion, distance and direction of movements within the model landscape. Spatial errors in dispersal kernels can have large compounding effects on model accuracy. Circular Gaussian and Laplacian dispersal kernels at a range of spatial resolutions were investigated, and methods for minimizing errors caused by the discretizing process were explored. Kernels of progressively smaller sizes relative to the landscape grid size were calculated using cell-integration and cell-center methods. These kernels were convolved repeatedly, and the final distribution was compared with a reference analytical solution. For large Gaussian kernels (σ > 10 cells), the total kernel error was <10 &sup-11; compared to analytical results. Using an invasion model that tracked the time a population took to reach a defined goal, the discrete model results were comparable to the analytical reference. With Gaussian kernels that had σ ≤ 0.12 using the cell integration method, or σ ≤ 0.22 using the cell center method, the kernel error was greater than 10%, which resulted in invasion times that were orders of magnitude different than theoretical results. A goal-seeking routine was developed to adjust the kernels to minimize overall error. With this, corrections for small kernels were found that decreased overall kernel error to <10-11 and invasion time error to <5%.

An iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition

NASA Astrophysics Data System (ADS)

Azarnavid, Babak; Parand, Kourosh; Abbasbandy, Saeid

2018-06-01

This article discusses an iterative reproducing kernel method with respect to its effectiveness and capability of solving a fourth-order boundary value problem with nonlinear boundary conditions modeling beams on elastic foundations. Since there is no method of obtaining reproducing kernel which satisfies nonlinear boundary conditions, the standard reproducing kernel methods cannot be used directly to solve boundary value problems with nonlinear boundary conditions as there is no knowledge about the existence and uniqueness of the solution. The aim of this paper is, therefore, to construct an iterative method by the use of a combination of reproducing kernel Hilbert space method and a shooting-like technique to solve the mentioned problems. Error estimation for reproducing kernel Hilbert space methods for nonlinear boundary value problems have yet to be discussed in the literature. In this paper, we present error estimation for the reproducing kernel method to solve nonlinear boundary value problems probably for the first time. Some numerical results are given out to demonstrate the applicability of the method.

Anatomically-Aided PET Reconstruction Using the Kernel Method

PubMed Central

Hutchcroft, Will; Wang, Guobao; Chen, Kevin T.; Catana, Ciprian; Qi, Jinyi

2016-01-01

This paper extends the kernel method that was proposed previously for dynamic PET reconstruction, to incorporate anatomical side information into the PET reconstruction model. In contrast to existing methods that incorporate anatomical information using a penalized likelihood framework, the proposed method incorporates this information in the simpler maximum likelihood (ML) formulation and is amenable to ordered subsets. The new method also does not require any segmentation of the anatomical image to obtain edge information. We compare the kernel method with the Bowsher method for anatomically-aided PET image reconstruction through a simulated data set. Computer simulations demonstrate that the kernel method offers advantages over the Bowsher method in region of interest (ROI) quantification. Additionally the kernel method is applied to a 3D patient data set. The kernel method results in reduced noise at a matched contrast level compared with the conventional ML expectation maximization (EM) algorithm. PMID:27541810

Anatomically-aided PET reconstruction using the kernel method.

PubMed

Hutchcroft, Will; Wang, Guobao; Chen, Kevin T; Catana, Ciprian; Qi, Jinyi

2016-09-21

This paper extends the kernel method that was proposed previously for dynamic PET reconstruction, to incorporate anatomical side information into the PET reconstruction model. In contrast to existing methods that incorporate anatomical information using a penalized likelihood framework, the proposed method incorporates this information in the simpler maximum likelihood (ML) formulation and is amenable to ordered subsets. The new method also does not require any segmentation of the anatomical image to obtain edge information. We compare the kernel method with the Bowsher method for anatomically-aided PET image reconstruction through a simulated data set. Computer simulations demonstrate that the kernel method offers advantages over the Bowsher method in region of interest quantification. Additionally the kernel method is applied to a 3D patient data set. The kernel method results in reduced noise at a matched contrast level compared with the conventional ML expectation maximization algorithm.

Anatomically-aided PET reconstruction using the kernel method

NASA Astrophysics Data System (ADS)

Hutchcroft, Will; Wang, Guobao; Chen, Kevin T.; Catana, Ciprian; Qi, Jinyi

2016-09-01

This paper extends the kernel method that was proposed previously for dynamic PET reconstruction, to incorporate anatomical side information into the PET reconstruction model. In contrast to existing methods that incorporate anatomical information using a penalized likelihood framework, the proposed method incorporates this information in the simpler maximum likelihood (ML) formulation and is amenable to ordered subsets. The new method also does not require any segmentation of the anatomical image to obtain edge information. We compare the kernel method with the Bowsher method for anatomically-aided PET image reconstruction through a simulated data set. Computer simulations demonstrate that the kernel method offers advantages over the Bowsher method in region of interest quantification. Additionally the kernel method is applied to a 3D patient data set. The kernel method results in reduced noise at a matched contrast level compared with the conventional ML expectation maximization algorithm.

Local Observed-Score Kernel Equating

ERIC Educational Resources Information Center

Wiberg, Marie; van der Linden, Wim J.; von Davier, Alina A.

2014-01-01

Three local observed-score kernel equating methods that integrate methods from the local equating and kernel equating frameworks are proposed. The new methods were compared with their earlier counterparts with respect to such measures as bias--as defined by Lord's criterion of equity--and percent relative error. The local kernel item response…

Ranking Support Vector Machine with Kernel Approximation

PubMed Central

Dou, Yong

2017-01-01

Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms. PMID:28293256

Ranking Support Vector Machine with Kernel Approximation.

PubMed

Chen, Kai; Li, Rongchun; Dou, Yong; Liang, Zhengfa; Lv, Qi

2017-01-01

Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms.

Quadratically Convergent Method for Simultaneously Approaching the Roots of Polynomial Solutions of a Class of Differential Equations

NASA Astrophysics Data System (ADS)

Recchioni, Maria Cristina

2001-12-01

This paper investigates the application of the method introduced by L. Pasquini (1989) for simultaneously approaching the zeros of polynomial solutions to a class of second-order linear homogeneous ordinary differential equations with polynomial coefficients to a particular case in which these polynomial solutions have zeros symmetrically arranged with respect to the origin. The method is based on a family of nonlinear equations which is associated with a given class of differential equations. The roots of the nonlinear equations are related to the roots of the polynomial solutions of differential equations considered. Newton's method is applied to find the roots of these nonlinear equations. In (Pasquini, 1994) the nonsingularity of the roots of these nonlinear equations is studied. In this paper, following the lines in (Pasquini, 1994), the nonsingularity of the roots of these nonlinear equations is studied. More favourable results than the ones in (Pasquini, 1994) are proven in the particular case of polynomial solutions with symmetrical zeros. The method is applied to approximate the roots of Hermite-Sobolev type polynomials and Freud polynomials. A lower bound for the smallest positive root of Hermite-Sobolev type polynomials is given via the nonlinear equation. The quadratic convergence of the method is proven. A comparison with a classical method that uses the Jacobi matrices is carried out. We show that the algorithm derived by the proposed method is sometimes preferable to the classical QR type algorithms for computing the eigenvalues of the Jacobi matrices even if these matrices are real and symmetric.

Chiral zero energy modes in two-dimensional disordered Dirac semimetals

NASA Astrophysics Data System (ADS)

Liu, Lei; Yu, Yan; Wu, Hai-Bin; Zhang, Yan-Yang; Liu, Jian-Jun; Li, Shu-Shen

2018-04-01

The vacancy-induced chiral zero energy modes (CZEMs) of chiral-unitary-class (AIII) and chiral-symplectic-class (CII) two-dimensional (2 D ) disordered Dirac semimetals realized on a square bipartite lattice are investigated numerically by using the Kubo-Greenwood formula with the kernel polynomial method. The results show that, for both systems, the CZEMs exhibit the critical delocalization. The CZEM conductivity remains a robust constant (i.e., σ CZEM≈1.05 e2/h ), which is insensitive to the sample sizes, the vacancy concentrations, and the numbers of moments of Chebyshev polynomials, i.e., the dephasing strength. For both kinds of chiral systems, the CZEM conductivities are almost identical. However, they are not equal to that of graphene (i.e., 4 e2/π h ), which belongs to the chiral orthogonal class (BDI) semimetal on a 2 D hexagonal bipartite lattice. In addition, for the case that the vacancy concentrations are different in the two sublattices, the CZEM conductivity vanishes, and thus both systems exhibit localization at the Dirac point. Moreover, a band gap and a mobility gap open around zero energy. The widths of the energy gaps and mobility gaps are increasing with larger vacancy concentration difference. The width of the mobility gap is greater than that of the band gap, and a δ -function-like peak of density of states emerges at the Dirac point within the band gap, implying the existence of numerous localized states.

Application of kernel method in fluorescence molecular tomography

NASA Astrophysics Data System (ADS)

Zhao, Yue; Baikejiang, Reheman; Li, Changqing

2017-02-01

Reconstruction of fluorescence molecular tomography (FMT) is an ill-posed inverse problem. Anatomical guidance in the FMT reconstruction can improve FMT reconstruction efficiently. We have developed a kernel method to introduce the anatomical guidance into FMT robustly and easily. The kernel method is from machine learning for pattern analysis and is an efficient way to represent anatomical features. For the finite element method based FMT reconstruction, we calculate a kernel function for each finite element node from an anatomical image, such as a micro-CT image. Then the fluorophore concentration at each node is represented by a kernel coefficient vector and the corresponding kernel function. In the FMT forward model, we have a new system matrix by multiplying the sensitivity matrix with the kernel matrix. Thus, the kernel coefficient vector is the unknown to be reconstructed following a standard iterative reconstruction process. We convert the FMT reconstruction problem into the kernel coefficient reconstruction problem. The desired fluorophore concentration at each node can be calculated accordingly. Numerical simulation studies have demonstrated that the proposed kernel-based algorithm can improve the spatial resolution of the reconstructed FMT images. In the proposed kernel method, the anatomical guidance can be obtained directly from the anatomical image and is included in the forward modeling. One of the advantages is that we do not need to segment the anatomical image for the targets and background.

Meixner Class of Non-commutative Generalized Stochastic Processes with Freely Independent Values II. The Generating Function

NASA Astrophysics Data System (ADS)

Bożejko, Marek; Lytvynov, Eugene

2011-03-01

Let T be an underlying space with a non-atomic measure σ on it. In [ Comm. Math. Phys. 292, 99-129 (2009)] the Meixner class of non-commutative generalized stochastic processes with freely independent values, {ω=(ω(t))_{tin T}} , was characterized through the continuity of the corresponding orthogonal polynomials. In this paper, we derive a generating function for these orthogonal polynomials. The first question we have to answer is: What should serve as a generating function for a system of polynomials of infinitely many non-commuting variables? We construct a class of operator-valued functions {Z=(Z(t))_{tin T}} such that Z( t) commutes with ω( s) for any {s,tin T}. Then a generating function can be understood as {G(Z,ω)=sum_{n=0}^infty int_{T^n}P^{(n)}(ω(t_1),dots,ω(t_n))Z(t_1)dots Z(t_n)} {σ(dt_1) dots σ(dt_n)} , where {P^{(n)}(ω(t_1),dots,ω(t_n))} is (the kernel of the) n th orthogonal polynomial. We derive an explicit form of G( Z, ω), which has a resolvent form and resembles the generating function in the classical case, albeit it involves integrals of non-commuting operators. We finally discuss a related problem of the action of the annihilation operators {partial_t,t in T} . In contrast to the classical case, we prove that the operators ∂ t related to the free Gaussian and Poisson processes have a property of globality. This result is genuinely infinite-dimensional, since in one dimension one loses the notion of globality.

A survey of kernel-type estimators for copula and their applications

NASA Astrophysics Data System (ADS)

Sumarjaya, I. W.

2017-10-01

Copulas have been widely used to model nonlinear dependence structure. Main applications of copulas include areas such as finance, insurance, hydrology, rainfall to name but a few. The flexibility of copula allows researchers to model dependence structure beyond Gaussian distribution. Basically, a copula is a function that couples multivariate distribution functions to their one-dimensional marginal distribution functions. In general, there are three methods to estimate copula. These are parametric, nonparametric, and semiparametric method. In this article we survey kernel-type estimators for copula such as mirror reflection kernel, beta kernel, transformation method and local likelihood transformation method. Then, we apply these kernel methods to three stock indexes in Asia. The results of our analysis suggest that, albeit variation in information criterion values, the local likelihood transformation method performs better than the other kernel methods.

Prostate cancer detection using machine learning techniques by employing combination of features extracting strategies.

PubMed

Hussain, Lal; Ahmed, Adeel; Saeed, Sharjil; Rathore, Saima; Awan, Imtiaz Ahmed; Shah, Saeed Arif; Majid, Abdul; Idris, Adnan; Awan, Anees Ahmed

2018-02-06

Prostate is a second leading causes of cancer deaths among men. Early detection of cancer can effectively reduce the rate of mortality caused by Prostate cancer. Due to high and multiresolution of MRIs from prostate cancer require a proper diagnostic systems and tools. In the past researchers developed Computer aided diagnosis (CAD) systems that help the radiologist to detect the abnormalities. In this research paper, we have employed novel Machine learning techniques such as Bayesian approach, Support vector machine (SVM) kernels: polynomial, radial base function (RBF) and Gaussian and Decision Tree for detecting prostate cancer. Moreover, different features extracting strategies are proposed to improve the detection performance. The features extracting strategies are based on texture, morphological, scale invariant feature transform (SIFT), and elliptic Fourier descriptors (EFDs) features. The performance was evaluated based on single as well as combination of features using Machine Learning Classification techniques. The Cross validation (Jack-knife k-fold) was performed and performance was evaluated in term of receiver operating curve (ROC) and specificity, sensitivity, Positive predictive value (PPV), negative predictive value (NPV), false positive rate (FPR). Based on single features extracting strategies, SVM Gaussian Kernel gives the highest accuracy of 98.34% with AUC of 0.999. While, using combination of features extracting strategies, SVM Gaussian kernel with texture + morphological, and EFDs + morphological features give the highest accuracy of 99.71% and AUC of 1.00.

Applicability of spectral indices on thickness identification of oil slick

NASA Astrophysics Data System (ADS)

Niu, Yanfei; Shen, Yonglin; Chen, Qihao; Liu, Xiuguo

2016-10-01

Hyperspectral remote sensing technology has played a vital role in the identification and monitoring of oil spill events, and amount of spectral indices have been developed. In this paper, the applicability of six frequently-used indices is analyzed, and a combination of spectral indices in aids of support vector machine (SVM) algorithm is used to identify the oil slicks and corresponding thickness. The six spectral indices are spectral rotation (SR), spectral absorption depth (HI), band ratio of blue and green (BG), band ratio of BG and shortwave infrared index (BGN), 555nm and 645nm normalized by the blue band index (NB) and spectral slope (ND). The experimental study is conducted in the Gulf of Mexico oil spill zone, with Airborne Visible Infrared Imaging Spectrometer (AVIRIS) hyperspectral imagery captured in May 17, 2010. The results show that SR index is the best in all six indices, which can effectively distinguish the thickness of the oil slick and identify it from seawater; HI index and ND index can obviously distinguish oil slick thickness; BG, BGN and NB are more suitable to identify oil slick from seawater. With the comparison among different kernel functions of SVM, the classify accuracy show that the polynomial and RBF kernel functions have the best effect on the separation of oil slick thickness and the relatively pure seawater. The applicability of spectral indices of oil slick and the method of oil film thickness identification will in aids of oil/gas exploration and oil spill monitoring.

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.

Improving prediction of heterodimeric protein complexes using combination with pairwise kernel.

PubMed

Ruan, Peiying; Hayashida, Morihiro; Akutsu, Tatsuya; Vert, Jean-Philippe

2018-02-19

Since many proteins become functional only after they interact with their partner proteins and form protein complexes, it is essential to identify the sets of proteins that form complexes. Therefore, several computational methods have been proposed to predict complexes from the topology and structure of experimental protein-protein interaction (PPI) network. These methods work well to predict complexes involving at least three proteins, but generally fail at identifying complexes involving only two different proteins, called heterodimeric complexes or heterodimers. There is however an urgent need for efficient methods to predict heterodimers, since the majority of known protein complexes are precisely heterodimers. In this paper, we use three promising kernel functions, Min kernel and two pairwise kernels, which are Metric Learning Pairwise Kernel (MLPK) and Tensor Product Pairwise Kernel (TPPK). We also consider the normalization forms of Min kernel. Then, we combine Min kernel or its normalization form and one of the pairwise kernels by plugging. We applied kernels based on PPI, domain, phylogenetic profile, and subcellular localization properties to predicting heterodimers. Then, we evaluate our method by employing C-Support Vector Classification (C-SVC), carrying out 10-fold cross-validation, and calculating the average F-measures. The results suggest that the combination of normalized-Min-kernel and MLPK leads to the best F-measure and improved the performance of our previous work, which had been the best existing method so far. We propose new methods to predict heterodimers, using a machine learning-based approach. We train a support vector machine (SVM) to discriminate interacting vs non-interacting protein pairs, based on informations extracted from PPI, domain, phylogenetic profiles and subcellular localization. We evaluate in detail new kernel functions to encode these data, and report prediction performance that outperforms the state-of-the-art.

Superfast algorithms of multidimensional discrete k-wave transforms and Volterra filtering based on superfast radon transform

NASA Astrophysics Data System (ADS)

Labunets, Valeri G.; Labunets-Rundblad, Ekaterina V.; Astola, Jaakko T.

2001-12-01

Fast algorithms for a wide class of non-separable n-dimensional (nD) discrete unitary K-transforms (DKT) are introduced. They need less 1D DKTs than in the case of the classical radix-2 FFT-type approach. The method utilizes a decomposition of the nD K-transform into the product of a new nD discrete Radon transform and of a set of parallel/independ 1D K-transforms. If the nD K-transform has a separable kernel (e.g., the case of the discrete Fourier transform) our approach leads to decrease of multiplicative complexity by the factor of n comparing to the classical row/column separable approach. It is well known that an n-th order Volterra filter of one dimensional signal can be evaluated by an appropriate nD linear convolution. This work describes new superfast algorithm for Volterra filtering. New approach is based on the superfast discrete Radon and Nussbaumer polynomial transforms.

The formation method of the feature space for the identification of fatigued bills

NASA Astrophysics Data System (ADS)

Kang, Dongshik; Oshiro, Ayumu; Ozawa, Kenji; Mitsui, Ikugo

2014-10-01

Fatigued bills make a trouble such as the paper jam in a bill handling machine. In the discrimination of fatigued bills using an acoustic signal, the variation of an observed bill sound is considered to be one of causes in misclassification. Therefore a technique has demanded in order to make the classification of fatigued bills more efficient. In this paper, we proposed the algorithm that extracted feature quantity of bill sound from acoustic signal using the frequency difference, and carried out discrimination experiment of fatigued bill money by Support Vector Machine(SVM). The feature quantity of frequency difference can represent the frequency components of an acoustic signal is varied by the fatigued degree of bill money. The generalization performance of SVM does not depend on the size of dimensions of the feature space, even in a high dimensional feature space such as bill-acoustic signals. Furthermore, SVM can induce an optimal classifier which considers the combination of features by the virtue of polynomial kernel functions.

Investigation of various energy deposition kernel refinements for the convolution/superposition method

PubMed Central

Huang, Jessie Y.; Eklund, David; Childress, Nathan L.; Howell, Rebecca M.; Mirkovic, Dragan; Followill, David S.; Kry, Stephen F.

2013-01-01

Purpose: Several simplifications used in clinical implementations of the convolution/superposition (C/S) method, specifically, density scaling of water kernels for heterogeneous media and use of a single polyenergetic kernel, lead to dose calculation inaccuracies. Although these weaknesses of the C/S method are known, it is not well known which of these simplifications has the largest effect on dose calculation accuracy in clinical situations. The purpose of this study was to generate and characterize high-resolution, polyenergetic, and material-specific energy deposition kernels (EDKs), as well as to investigate the dosimetric impact of implementing spatially variant polyenergetic and material-specific kernels in a collapsed cone C/S algorithm. Methods: High-resolution, monoenergetic water EDKs and various material-specific EDKs were simulated using the EGSnrc Monte Carlo code. Polyenergetic kernels, reflecting the primary spectrum of a clinical 6 MV photon beam at different locations in a water phantom, were calculated for different depths, field sizes, and off-axis distances. To investigate the dosimetric impact of implementing spatially variant polyenergetic kernels, depth dose curves in water were calculated using two different implementations of the collapsed cone C/S method. The first method uses a single polyenergetic kernel, while the second method fully takes into account spectral changes in the convolution calculation. To investigate the dosimetric impact of implementing material-specific kernels, depth dose curves were calculated for a simplified titanium implant geometry using both a traditional C/S implementation that performs density scaling of water kernels and a novel implementation using material-specific kernels. Results: For our high-resolution kernels, we found good agreement with the Mackie et al. kernels, with some differences near the interaction site for low photon energies (<500 keV). For our spatially variant polyenergetic kernels, we found that depth was the most dominant factor affecting the pattern of energy deposition; however, the effects of field size and off-axis distance were not negligible. For the material-specific kernels, we found that as the density of the material increased, more energy was deposited laterally by charged particles, as opposed to in the forward direction. Thus, density scaling of water kernels becomes a worse approximation as the density and the effective atomic number of the material differ more from water. Implementation of spatially variant, polyenergetic kernels increased the percent depth dose value at 25 cm depth by 2.1%–5.8% depending on the field size, while implementation of titanium kernels gave 4.9% higher dose upstream of the metal cavity (i.e., higher backscatter dose) and 8.2% lower dose downstream of the cavity. Conclusions: Of the various kernel refinements investigated, inclusion of depth-dependent and metal-specific kernels into the C/S method has the greatest potential to improve dose calculation accuracy. Implementation of spatially variant polyenergetic kernels resulted in a harder depth dose curve and thus has the potential to affect beam modeling parameters obtained in the commissioning process. For metal implants, the C/S algorithms generally underestimate the dose upstream and overestimate the dose downstream of the implant. Implementation of a metal-specific kernel mitigated both of these errors. PMID:24320507

Optimal projection method determination by Logdet Divergence and perturbed von-Neumann Divergence.

PubMed

Jiang, Hao; Ching, Wai-Ki; Qiu, Yushan; Cheng, Xiao-Qing

2017-12-14

Positive semi-definiteness is a critical property in kernel methods for Support Vector Machine (SVM) by which efficient solutions can be guaranteed through convex quadratic programming. However, a lot of similarity functions in applications do not produce positive semi-definite kernels. We propose projection method by constructing projection matrix on indefinite kernels. As a generalization of the spectrum method (denoising method and flipping method), the projection method shows better or comparable performance comparing to the corresponding indefinite kernel methods on a number of real world data sets. Under the Bregman matrix divergence theory, we can find suggested optimal λ in projection method using unconstrained optimization in kernel learning. In this paper we focus on optimal λ determination, in the pursuit of precise optimal λ determination method in unconstrained optimization framework. We developed a perturbed von-Neumann divergence to measure kernel relationships. We compared optimal λ determination with Logdet Divergence and perturbed von-Neumann Divergence, aiming at finding better λ in projection method. Results on a number of real world data sets show that projection method with optimal λ by Logdet divergence demonstrate near optimal performance. And the perturbed von-Neumann Divergence can help determine a relatively better optimal projection method. Projection method ia easy to use for dealing with indefinite kernels. And the parameter embedded in the method can be determined through unconstrained optimization under Bregman matrix divergence theory. This may provide a new way in kernel SVMs for varied objectives.

Exploiting graph kernels for high performance biomedical relation extraction.

PubMed

Panyam, Nagesh C; Verspoor, Karin; Cohn, Trevor; Ramamohanarao, Kotagiri

2018-01-30

Relation extraction from biomedical publications is an important task in the area of semantic mining of text. Kernel methods for supervised relation extraction are often preferred over manual feature engineering methods, when classifying highly ordered structures such as trees and graphs obtained from syntactic parsing of a sentence. Tree kernels such as the Subset Tree Kernel and Partial Tree Kernel have been shown to be effective for classifying constituency parse trees and basic dependency parse graphs of a sentence. Graph kernels such as the All Path Graph kernel (APG) and Approximate Subgraph Matching (ASM) kernel have been shown to be suitable for classifying general graphs with cycles, such as the enhanced dependency parse graph of a sentence. In this work, we present a high performance Chemical-Induced Disease (CID) relation extraction system. We present a comparative study of kernel methods for the CID task and also extend our study to the Protein-Protein Interaction (PPI) extraction task, an important biomedical relation extraction task. We discuss novel modifications to the ASM kernel to boost its performance and a method to apply graph kernels for extracting relations expressed in multiple sentences. Our system for CID relation extraction attains an F-score of 60%, without using external knowledge sources or task specific heuristic or rules. In comparison, the state of the art Chemical-Disease Relation Extraction system achieves an F-score of 56% using an ensemble of multiple machine learning methods, which is then boosted to 61% with a rule based system employing task specific post processing rules. For the CID task, graph kernels outperform tree kernels substantially, and the best performance is obtained with APG kernel that attains an F-score of 60%, followed by the ASM kernel at 57%. The performance difference between the ASM and APG kernels for CID sentence level relation extraction is not significant. In our evaluation of ASM for the PPI task, ASM performed better than APG kernel for the BioInfer dataset, in the Area Under Curve (AUC) measure (74% vs 69%). However, for all the other PPI datasets, namely AIMed, HPRD50, IEPA and LLL, ASM is substantially outperformed by the APG kernel in F-score and AUC measures. We demonstrate a high performance Chemical Induced Disease relation extraction, without employing external knowledge sources or task specific heuristics. Our work shows that graph kernels are effective in extracting relations that are expressed in multiple sentences. We also show that the graph kernels, namely the ASM and APG kernels, substantially outperform the tree kernels. Among the graph kernels, we showed the ASM kernel as effective for biomedical relation extraction, with comparable performance to the APG kernel for datasets such as the CID-sentence level relation extraction and BioInfer in PPI. Overall, the APG kernel is shown to be significantly more accurate than the ASM kernel, achieving better performance on most datasets.

The pre-image problem in kernel methods.

PubMed

Kwok, James Tin-yau; Tsang, Ivor Wai-hung

2004-11-01

In this paper, we address the problem of finding the pre-image of a feature vector in the feature space induced by a kernel. This is of central importance in some kernel applications, such as on using kernel principal component analysis (PCA) for image denoising. Unlike the traditional method which relies on nonlinear optimization, our proposed method directly finds the location of the pre-image based on distance constraints in the feature space. It is noniterative, involves only linear algebra and does not suffer from numerical instability or local minimum problems. Evaluations on performing kernel PCA and kernel clustering on the USPS data set show much improved performance.

Multiple kernel SVR based on the MRE for remote sensing water depth fusion detection

NASA Astrophysics Data System (ADS)

Wang, Jinjin; Ma, Yi; Zhang, Jingyu

2018-03-01

Remote sensing has an important means of water depth detection in coastal shallow waters and reefs. Support vector regression (SVR) is a machine learning method which is widely used in data regression. In this paper, SVR is used to remote sensing multispectral bathymetry. Aiming at the problem that the single-kernel SVR method has a large error in shallow water depth inversion, the mean relative error (MRE) of different water depth is retrieved as a decision fusion factor with single kernel SVR method, a multi kernel SVR fusion method based on the MRE is put forward. And taking the North Island of the Xisha Islands in China as an experimentation area, the comparison experiments with the single kernel SVR method and the traditional multi-bands bathymetric method are carried out. The results show that: 1) In range of 0 to 25 meters, the mean absolute error(MAE)of the multi kernel SVR fusion method is 1.5m,the MRE is 13.2%; 2) Compared to the 4 single kernel SVR method, the MRE of the fusion method reduced 1.2% (1.9%) 3.4% (1.8%), and compared to traditional multi-bands method, the MRE reduced 1.9%; 3) In 0-5m depth section, compared to the single kernel method and the multi-bands method, the MRE of fusion method reduced 13.5% to 44.4%, and the distribution of points is more concentrated relative to y=x.

High-throughput method for ear phenotyping and kernel weight estimation in maize using ear digital imaging.

PubMed

Makanza, R; Zaman-Allah, M; Cairns, J E; Eyre, J; Burgueño, J; Pacheco, Ángela; Diepenbrock, C; Magorokosho, C; Tarekegne, A; Olsen, M; Prasanna, B M

2018-01-01

Grain yield, ear and kernel attributes can assist to understand the performance of maize plant under different environmental conditions and can be used in the variety development process to address farmer's preferences. These parameters are however still laborious and expensive to measure. A low-cost ear digital imaging method was developed that provides estimates of ear and kernel attributes i.e., ear number and size, kernel number and size as well as kernel weight from photos of ears harvested from field trial plots. The image processing method uses a script that runs in a batch mode on ImageJ; an open source software. Kernel weight was estimated using the total kernel number derived from the number of kernels visible on the image and the average kernel size. Data showed a good agreement in terms of accuracy and precision between ground truth measurements and data generated through image processing. Broad-sense heritability of the estimated parameters was in the range or higher than that for measured grain weight. Limitation of the method for kernel weight estimation is discussed. The method developed in this work provides an opportunity to significantly reduce the cost of selection in the breeding process, especially for resource constrained crop improvement programs and can be used to learn more about the genetic bases of grain yield determinants.

Kernel-aligned multi-view canonical correlation analysis for image recognition

NASA Astrophysics Data System (ADS)

Su, Shuzhi; Ge, Hongwei; Yuan, Yun-Hao

2016-09-01

Existing kernel-based correlation analysis methods mainly adopt a single kernel in each view. However, only a single kernel is usually insufficient to characterize nonlinear distribution information of a view. To solve the problem, we transform each original feature vector into a 2-dimensional feature matrix by means of kernel alignment, and then propose a novel kernel-aligned multi-view canonical correlation analysis (KAMCCA) method on the basis of the feature matrices. Our proposed method can simultaneously employ multiple kernels to better capture the nonlinear distribution information of each view, so that correlation features learned by KAMCCA can have well discriminating power in real-world image recognition. Extensive experiments are designed on five real-world image datasets, including NIR face images, thermal face images, visible face images, handwritten digit images, and object images. Promising experimental results on the datasets have manifested the effectiveness of our proposed method.

Computing Galois Groups of Eisenstein Polynomials Over P-adic Fields

NASA Astrophysics Data System (ADS)

Milstead, Jonathan

The most efficient algorithms for computing Galois groups of polynomials over global fields are based on Stauduhar's relative resolvent method. These methods are not directly generalizable to the local field case, since they require a field that contains the global field in which all roots of the polynomial can be approximated. We present splitting field-independent methods for computing the Galois group of an Eisenstein polynomial over a p-adic field. Our approach is to combine information from different disciplines. We primarily, make use of the ramification polygon of the polynomial, which is the Newton polygon of a related polynomial. This allows us to quickly calculate several invariants that serve to reduce the number of possible Galois groups. Algorithms by Greve and Pauli very efficiently return the Galois group of polynomials where the ramification polygon consists of one segment as well as information about the subfields of the stem field. Second, we look at the factorization of linear absolute resolvents to further narrow the pool of possible groups.

Modeling State-Space Aeroelastic Systems Using a Simple Matrix Polynomial Approach for the Unsteady Aerodynamics

NASA Technical Reports Server (NTRS)

Pototzky, Anthony S.

2008-01-01

A simple matrix polynomial approach is introduced for approximating unsteady aerodynamics in the s-plane and ultimately, after combining matrix polynomial coefficients with matrices defining the structure, a matrix polynomial of the flutter equations of motion (EOM) is formed. A technique of recasting the matrix-polynomial form of the flutter EOM into a first order form is also presented that can be used to determine the eigenvalues near the origin and everywhere on the complex plane. An aeroservoelastic (ASE) EOM have been generalized to include the gust terms on the right-hand side. The reasons for developing the new matrix polynomial approach are also presented, which are the following: first, the "workhorse" methods such as the NASTRAN flutter analysis lack the capability to consistently find roots near the origin, along the real axis or accurately find roots farther away from the imaginary axis of the complex plane; and, second, the existing s-plane methods, such as the Roger s s-plane approximation method as implemented in ISAC, do not always give suitable fits of some tabular data of the unsteady aerodynamics. A method available in MATLAB is introduced that will accurately fit generalized aerodynamic force (GAF) coefficients in a tabular data form into the coefficients of a matrix polynomial form. The root-locus results from the NASTRAN pknl flutter analysis, the ISAC-Roger's s-plane method and the present matrix polynomial method are presented and compared for accuracy and for the number and locations of roots.

Deploy Nalu/Kokkos algorithmic infrastructure with performance benchmarking.

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

Domino, Stefan P.; Ananthan, Shreyas; Knaus, Robert C.

The former Nalu interior heterogeneous algorithm design, which was originally designed to manage matrix assembly operations over all elemental topology types, has been modified to operate over homogeneous collections of mesh entities. This newly templated kernel design allows for removal of workset variable resize operations that were formerly required at each loop over a Sierra ToolKit (STK) bucket (nominally, 512 entities in size). Extensive usage of the Standard Template Library (STL) std::vector has been removed in favor of intrinsic Kokkos memory views. In this milestone effort, the transition to Kokkos as the underlying infrastructure to support performance and portability onmore » many-core architectures has been deployed for key matrix algorithmic kernels. A unit-test driven design effort has developed a homogeneous entity algorithm that employs a team-based thread parallelism construct. The STK Single Instruction Multiple Data (SIMD) infrastructure is used to interleave data for improved vectorization. The collective algorithm design, which allows for concurrent threading and SIMD management, has been deployed for the core low-Mach element- based algorithm. Several tests to ascertain SIMD performance on Intel KNL and Haswell architectures have been carried out. The performance test matrix includes evaluation of both low- and higher-order methods. The higher-order low-Mach methodology builds on polynomial promotion of the core low-order control volume nite element method (CVFEM). Performance testing of the Kokkos-view/SIMD design indicates low-order matrix assembly kernel speed-up ranging between two and four times depending on mesh loading and node count. Better speedups are observed for higher-order meshes (currently only P=2 has been tested) especially on KNL. The increased workload per element on higher-order meshes bene ts from the wide SIMD width on KNL machines. Combining multiple threads with SIMD on KNL achieves a 4.6x speedup over the baseline, with assembly timings faster than that observed on Haswell architecture. The computational workload of higher-order meshes, therefore, seems ideally suited for the many-core architecture and justi es further exploration of higher-order on NGP platforms. A Trilinos/Tpetra-based multi-threaded GMRES preconditioned by symmetric Gauss Seidel (SGS) represents the core solver infrastructure for the low-Mach advection/diffusion implicit solves. The threaded solver stack has been tested on small problems on NREL's Peregrine system using the newly developed and deployed Kokkos-view/SIMD kernels. fforts are underway to deploy the Tpetra-based solver stack on NERSC Cori system to benchmark its performance at scale on KNL machines.« less

Metabolic network prediction through pairwise rational kernels.

PubMed

Roche-Lima, Abiel; Domaratzki, Michael; Fristensky, Brian

2014-09-26

Metabolic networks are represented by the set of metabolic pathways. Metabolic pathways are a series of biochemical reactions, in which the product (output) from one reaction serves as the substrate (input) to another reaction. Many pathways remain incompletely characterized. One of the major challenges of computational biology is to obtain better models of metabolic pathways. Existing models are dependent on the annotation of the genes. This propagates error accumulation when the pathways are predicted by incorrectly annotated genes. Pairwise classification methods are supervised learning methods used to classify new pair of entities. Some of these classification methods, e.g., Pairwise Support Vector Machines (SVMs), use pairwise kernels. Pairwise kernels describe similarity measures between two pairs of entities. Using pairwise kernels to handle sequence data requires long processing times and large storage. Rational kernels are kernels based on weighted finite-state transducers that represent similarity measures between sequences or automata. They have been effectively used in problems that handle large amount of sequence information such as protein essentiality, natural language processing and machine translations. We create a new family of pairwise kernels using weighted finite-state transducers (called Pairwise Rational Kernel (PRK)) to predict metabolic pathways from a variety of biological data. PRKs take advantage of the simpler representations and faster algorithms of transducers. Because raw sequence data can be used, the predictor model avoids the errors introduced by incorrect gene annotations. We then developed several experiments with PRKs and Pairwise SVM to validate our methods using the metabolic network of Saccharomyces cerevisiae. As a result, when PRKs are used, our method executes faster in comparison with other pairwise kernels. Also, when we use PRKs combined with other simple kernels that include evolutionary information, the accuracy values have been improved, while maintaining lower construction and execution times. The power of using kernels is that almost any sort of data can be represented using kernels. Therefore, completely disparate types of data can be combined to add power to kernel-based machine learning methods. When we compared our proposal using PRKs with other similar kernel, the execution times were decreased, with no compromise of accuracy. We also proved that by combining PRKs with other kernels that include evolutionary information, the accuracy can also also be improved. As our proposal can use any type of sequence data, genes do not need to be properly annotated, avoiding accumulation errors because of incorrect previous annotations.

Cylinder surface test with Chebyshev polynomial fitting method

NASA Astrophysics Data System (ADS)

Yu, Kui-bang; Guo, Pei-ji; Chen, Xi

2017-10-01

Zernike polynomials fitting method is often applied in the test of optical components and systems, used to represent the wavefront and surface error in circular domain. Zernike polynomials are not orthogonal in rectangular region which results in its unsuitable for the test of optical element with rectangular aperture such as cylinder surface. Applying the Chebyshev polynomials which are orthogonal among the rectangular area as an substitution to the fitting method, can solve the problem. Corresponding to a cylinder surface with diameter of 50 mm and F number of 1/7, a measuring system has been designed in Zemax based on Fizeau Interferometry. The expressions of the two-dimensional Chebyshev polynomials has been given and its relationship with the aberration has been presented. Furthermore, Chebyshev polynomials are used as base items to analyze the rectangular aperture test data. The coefficient of different items are obtained from the test data through the method of least squares. Comparing the Chebyshev spectrum in different misalignment, it show that each misalignment is independence and has a certain relationship with the certain Chebyshev terms. The simulation results show that, through the Legendre polynomials fitting method, it will be a great improvement in the efficient of the detection and adjustment of the cylinder surface test.

State-vector formalism and the Legendre polynomial solution for modelling guided waves in anisotropic plates

NASA Astrophysics Data System (ADS)

Zheng, Mingfang; He, Cunfu; Lu, Yan; Wu, Bin

2018-01-01

We presented a numerical method to solve phase dispersion curve in general anisotropic plates. This approach involves an exact solution to the problem in the form of the Legendre polynomial of multiple integrals, which we substituted into the state-vector formalism. In order to improve the efficiency of the proposed method, we made a special effort to demonstrate the analytical methodology. Furthermore, we analyzed the algebraic symmetries of the matrices in the state-vector formalism for anisotropic plates. The basic feature of the proposed method was the expansion of field quantities by Legendre polynomials. The Legendre polynomial method avoid to solve the transcendental dispersion equation, which can only be solved numerically. This state-vector formalism combined with Legendre polynomial expansion distinguished the adjacent dispersion mode clearly, even when the modes were very close. We then illustrated the theoretical solutions of the dispersion curves by this method for isotropic and anisotropic plates. Finally, we compared the proposed method with the global matrix method (GMM), which shows excellent agreement.

Numerical solutions for Helmholtz equations using Bernoulli polynomials

NASA Astrophysics Data System (ADS)

Bicer, Kubra Erdem; Yalcinbas, Salih

2017-07-01

This paper reports a new numerical method based on Bernoulli polynomials for the solution of Helmholtz equations. The method uses matrix forms of Bernoulli polynomials and their derivatives by means of collocation points. Aim of this paper is to solve Helmholtz equations using this matrix relations.

Optimized Kernel Entropy Components.

PubMed

Izquierdo-Verdiguier, Emma; Laparra, Valero; Jenssen, Robert; Gomez-Chova, Luis; Camps-Valls, Gustau

2017-06-01

This brief addresses two main issues of the standard kernel entropy component analysis (KECA) algorithm: the optimization of the kernel decomposition and the optimization of the Gaussian kernel parameter. KECA roughly reduces to a sorting of the importance of kernel eigenvectors by entropy instead of variance, as in the kernel principal components analysis. In this brief, we propose an extension of the KECA method, named optimized KECA (OKECA), that directly extracts the optimal features retaining most of the data entropy by means of compacting the information in very few features (often in just one or two). The proposed method produces features which have higher expressive power. In particular, it is based on the independent component analysis framework, and introduces an extra rotation to the eigen decomposition, which is optimized via gradient-ascent search. This maximum entropy preservation suggests that OKECA features are more efficient than KECA features for density estimation. In addition, a critical issue in both the methods is the selection of the kernel parameter, since it critically affects the resulting performance. Here, we analyze the most common kernel length-scale selection criteria. The results of both the methods are illustrated in different synthetic and real problems. Results show that OKECA returns projections with more expressive power than KECA, the most successful rule for estimating the kernel parameter is based on maximum likelihood, and OKECA is more robust to the selection of the length-scale parameter in kernel density estimation.

Direct calculation of modal parameters from matrix orthogonal polynomials

NASA Astrophysics Data System (ADS)

El-Kafafy, Mahmoud; Guillaume, Patrick

2011-10-01

The object of this paper is to introduce a new technique to derive the global modal parameter (i.e. system poles) directly from estimated matrix orthogonal polynomials. This contribution generalized the results given in Rolain et al. (1994) [5] and Rolain et al. (1995) [6] for scalar orthogonal polynomials to multivariable (matrix) orthogonal polynomials for multiple input multiple output (MIMO) system. Using orthogonal polynomials improves the numerical properties of the estimation process. However, the derivation of the modal parameters from the orthogonal polynomials is in general ill-conditioned if not handled properly. The transformation of the coefficients from orthogonal polynomials basis to power polynomials basis is known to be an ill-conditioned transformation. In this paper a new approach is proposed to compute the system poles directly from the multivariable orthogonal polynomials. High order models can be used without any numerical problems. The proposed method will be compared with existing methods (Van Der Auweraer and Leuridan (1987) [4] Chen and Xu (2003) [7]). For this comparative study, simulated as well as experimental data will be used.

Dynamic PET Image reconstruction for parametric imaging using the HYPR kernel method

NASA Astrophysics Data System (ADS)

Spencer, Benjamin; Qi, Jinyi; Badawi, Ramsey D.; Wang, Guobao

2017-03-01

Dynamic PET image reconstruction is a challenging problem because of the ill-conditioned nature of PET and the lowcounting statistics resulted from short time-frames in dynamic imaging. The kernel method for image reconstruction has been developed to improve image reconstruction of low-count PET data by incorporating prior information derived from high-count composite data. In contrast to most of the existing regularization-based methods, the kernel method embeds image prior information in the forward projection model and does not require an explicit regularization term in the reconstruction formula. Inspired by the existing highly constrained back-projection (HYPR) algorithm for dynamic PET image denoising, we propose in this work a new type of kernel that is simpler to implement and further improves the kernel-based dynamic PET image reconstruction. Our evaluation study using a physical phantom scan with synthetic FDG tracer kinetics has demonstrated that the new HYPR kernel-based reconstruction can achieve a better region-of-interest (ROI) bias versus standard deviation trade-off for dynamic PET parametric imaging than the post-reconstruction HYPR denoising method and the previously used nonlocal-means kernel.

A new sampling scheme for developing metamodels with the zeros of Chebyshev polynomials

NASA Astrophysics Data System (ADS)

Wu, Jinglai; Luo, Zhen; Zhang, Nong; Zhang, Yunqing

2015-09-01

The accuracy of metamodelling is determined by both the sampling and approximation. This article proposes a new sampling method based on the zeros of Chebyshev polynomials to capture the sampling information effectively. First, the zeros of one-dimensional Chebyshev polynomials are applied to construct Chebyshev tensor product (CTP) sampling, and the CTP is then used to construct high-order multi-dimensional metamodels using the 'hypercube' polynomials. Secondly, the CTP sampling is further enhanced to develop Chebyshev collocation method (CCM) sampling, to construct the 'simplex' polynomials. The samples of CCM are randomly and directly chosen from the CTP samples. Two widely studied sampling methods, namely the Smolyak sparse grid and Hammersley, are used to demonstrate the effectiveness of the proposed sampling method. Several numerical examples are utilized to validate the approximation accuracy of the proposed metamodel under different dimensions.

Comparative assessment of orthogonal polynomials for wavefront reconstruction over the square aperture.

PubMed

Ye, Jingfei; Gao, Zhishan; Wang, Shuai; Cheng, Jinlong; Wang, Wei; Sun, Wenqing

2014-10-01

Four orthogonal polynomials for reconstructing a wavefront over a square aperture based on the modal method are currently available, namely, the 2D Chebyshev polynomials, 2D Legendre polynomials, Zernike square polynomials and Numerical polynomials. They are all orthogonal over the full unit square domain. 2D Chebyshev polynomials are defined by the product of Chebyshev polynomials in x and y variables, as are 2D Legendre polynomials. Zernike square polynomials are derived by the Gram-Schmidt orthogonalization process, where the integration region across the full unit square is circumscribed outside the unit circle. Numerical polynomials are obtained by numerical calculation. The presented study is to compare these four orthogonal polynomials by theoretical analysis and numerical experiments from the aspects of reconstruction accuracy, remaining errors, and robustness. Results show that the Numerical orthogonal polynomial is superior to the other three polynomials because of its high accuracy and robustness even in the case of a wavefront with incomplete data.

Comparison of Kernel Equating and Item Response Theory Equating Methods

ERIC Educational Resources Information Center

Meng, Yu

2012-01-01

The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…

Parallel multigrid smoothing: polynomial versus Gauss-Seidel

NASA Astrophysics Data System (ADS)

Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray

2003-07-01

Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines.

Gaussian mass optimization for kernel PCA parameters

NASA Astrophysics Data System (ADS)

Liu, Yong; Wang, Zulin

2011-10-01

This paper proposes a novel kernel parameter optimization method based on Gaussian mass, which aims to overcome the current brute force parameter optimization method in a heuristic way. Generally speaking, the choice of kernel parameter should be tightly related to the target objects while the variance between the samples, the most commonly used kernel parameter, doesn't possess much features of the target, which gives birth to Gaussian mass. Gaussian mass defined in this paper has the property of the invariance of rotation and translation and is capable of depicting the edge, topology and shape information. Simulation results show that Gaussian mass leads a promising heuristic optimization boost up for kernel method. In MNIST handwriting database, the recognition rate improves by 1.6% compared with common kernel method without Gaussian mass optimization. Several promising other directions which Gaussian mass might help are also proposed at the end of the paper.

Unified heat kernel regression for diffusion, kernel smoothing and wavelets on manifolds and its application to mandible growth modeling in CT images.

PubMed

Chung, Moo K; Qiu, Anqi; Seo, Seongho; Vorperian, Houri K

2015-05-01

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel method is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, the method is applied to characterize the localized growth pattern of mandible surfaces obtained in CT images between ages 0 and 20 by regressing the length of displacement vectors with respect to a surface template. Copyright © 2015 Elsevier B.V. All rights reserved.

Cepstrum based feature extraction method for fungus detection

NASA Astrophysics Data System (ADS)

Yorulmaz, Onur; Pearson, Tom C.; Çetin, A. Enis

2011-06-01

In this paper, a method for detection of popcorn kernels infected by a fungus is developed using image processing. The method is based on two dimensional (2D) mel and Mellin-cepstrum computation from popcorn kernel images. Cepstral features that were extracted from popcorn images are classified using Support Vector Machines (SVM). Experimental results show that high recognition rates of up to 93.93% can be achieved for both damaged and healthy popcorn kernels using 2D mel-cepstrum. The success rate for healthy popcorn kernels was found to be 97.41% and the recognition rate for damaged kernels was found to be 89.43%.

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

PubMed

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

2013-05-01

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

Equivalences of the multi-indexed orthogonal polynomials

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

Odake, Satoru

2014-01-15

Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion. Multi-indexed orthogonal polynomials are labeled by a set of degrees of polynomial parts of virtual state wavefunctions. For multi-indexed orthogonal polynomials of Laguerre, Jacobi, Wilson, and Askey-Wilson types, two different index sets may give equivalent multi-indexed orthogonal polynomials. We clarify these equivalences. Multi-indexed orthogonal polynomials with both type I and II indices are proportional to those of type I indices only (or type II indices only) with shifted parameters.

An introduction to kernel-based learning algorithms.

PubMed

Müller, K R; Mika, S; Rätsch, G; Tsuda, K; Schölkopf, B

2001-01-01

This paper provides an introduction to support vector machines, kernel Fisher discriminant analysis, and kernel principal component analysis, as examples for successful kernel-based learning methods. We first give a short background about Vapnik-Chervonenkis theory and kernel feature spaces and then proceed to kernel based learning in supervised and unsupervised scenarios including practical and algorithmic considerations. We illustrate the usefulness of kernel algorithms by discussing applications such as optical character recognition and DNA analysis.

Assessment of Hybrid High-Order methods on curved meshes and comparison with discontinuous Galerkin methods

NASA Astrophysics Data System (ADS)

Botti, Lorenzo; Di Pietro, Daniele A.

2018-10-01

We propose and validate a novel extension of Hybrid High-Order (HHO) methods to meshes featuring curved elements. HHO methods are based on discrete unknowns that are broken polynomials on the mesh and its skeleton. We propose here the use of physical frame polynomials over mesh elements and reference frame polynomials over mesh faces. With this choice, the degree of face unknowns must be suitably selected in order to recover on curved meshes the same convergence rates as on straight meshes. We provide an estimate of the optimal face polynomial degree depending on the element polynomial degree and on the so-called effective mapping order. The estimate is numerically validated through specifically crafted numerical tests. All test cases are conducted considering two- and three-dimensional pure diffusion problems, and include comparisons with discontinuous Galerkin discretizations. The extension to agglomerated meshes with curved boundaries is also considered.

Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT

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

Brabec, Jiri; Lin, Lin; Shao, Meiyue

We present a special symmetric Lanczos algorithm and a kernel polynomial method (KPM) for approximating the absorption spectrum of molecules within the linear response time-dependent density functional theory (TDDFT) framework in the product form. In contrast to existing algorithms, the new algorithms are based on reformulating the original non-Hermitian eigenvalue problem as a product eigenvalue problem and the observation that the product eigenvalue problem is self-adjoint with respect to an appropriately chosen inner product. This allows a simple symmetric Lanczos algorithm to be used to compute the desired absorption spectrum. The use of a symmetric Lanczos algorithm only requires halfmore » of the memory compared with the nonsymmetric variant of the Lanczos algorithm. The symmetric Lanczos algorithm is also numerically more stable than the nonsymmetric version. The KPM algorithm is also presented as a low-memory alternative to the Lanczos approach, but the algorithm may require more matrix-vector multiplications in practice. We discuss the pros and cons of these methods in terms of their accuracy as well as their computational and storage cost. Applications to a set of small and medium-sized molecules are also presented.« less

Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT

DOE PAGES

Brabec, Jiri; Lin, Lin; Shao, Meiyue; ...

2015-10-06

We present a special symmetric Lanczos algorithm and a kernel polynomial method (KPM) for approximating the absorption spectrum of molecules within the linear response time-dependent density functional theory (TDDFT) framework in the product form. In contrast to existing algorithms, the new algorithms are based on reformulating the original non-Hermitian eigenvalue problem as a product eigenvalue problem and the observation that the product eigenvalue problem is self-adjoint with respect to an appropriately chosen inner product. This allows a simple symmetric Lanczos algorithm to be used to compute the desired absorption spectrum. The use of a symmetric Lanczos algorithm only requires halfmore » of the memory compared with the nonsymmetric variant of the Lanczos algorithm. The symmetric Lanczos algorithm is also numerically more stable than the nonsymmetric version. The KPM algorithm is also presented as a low-memory alternative to the Lanczos approach, but the algorithm may require more matrix-vector multiplications in practice. We discuss the pros and cons of these methods in terms of their accuracy as well as their computational and storage cost. Applications to a set of small and medium-sized molecules are also presented.« less

Phase diagram and quantum criticality of disordered Majorana-Weyl fermions

NASA Astrophysics Data System (ADS)

Wilson, Justin; Pixley, Jed; Goswami, Pallab

A three-dimensional px + ipy superconductor hosts gapless Bogoliubov-de Gennes (BdG) quasiparticles which provide an intriguing example of a thermal Hall semimetal (ThSM) phase of Majorana-Weyl fermions. We study the effect of quenched disorder on such a topological phase with both numerical and analytical methods. Using the kernel polynomial method, we compute the average and typical density of states for the BdG quasiparticles; based on this, we construct the disordered phase diagram. We show for infinitesimal disorder, the ThSM is converted into a diffusive thermal Hall metal (ThDM) due to rare statistical fluctuations. Consequently, the phase diagram of the disordered model only consists of ThDM and thermal insulating phases. Nonetheless, there is a cross-over at finite energies from a ThSM regime to a ThDM regime, and we establish the scaling properties of the avoided quantum critical point which marks this cross-over. Additionally, we show the existence of two types of thermal insulators: (i) a trivial thermal band insulator (ThBI), and (ii) a thermal Anderson insulator (AI). We also discuss the experimental relevance of our results for three-dimensional, time reversal symmetry breaking, triplet superconducting states.

Protein Subcellular Localization with Gaussian Kernel Discriminant Analysis and Its Kernel Parameter Selection.

PubMed

Wang, Shunfang; Nie, Bing; Yue, Kun; Fei, Yu; Li, Wenjia; Xu, Dongshu

2017-12-15

Kernel discriminant analysis (KDA) is a dimension reduction and classification algorithm based on nonlinear kernel trick, which can be novelly used to treat high-dimensional and complex biological data before undergoing classification processes such as protein subcellular localization. Kernel parameters make a great impact on the performance of the KDA model. Specifically, for KDA with the popular Gaussian kernel, to select the scale parameter is still a challenging problem. Thus, this paper introduces the KDA method and proposes a new method for Gaussian kernel parameter selection depending on the fact that the differences between reconstruction errors of edge normal samples and those of interior normal samples should be maximized for certain suitable kernel parameters. Experiments with various standard data sets of protein subcellular localization show that the overall accuracy of protein classification prediction with KDA is much higher than that without KDA. Meanwhile, the kernel parameter of KDA has a great impact on the efficiency, and the proposed method can produce an optimum parameter, which makes the new algorithm not only perform as effectively as the traditional ones, but also reduce the computational time and thus improve efficiency.

Phase demodulation method from a single fringe pattern based on correlation with a polynomial form.

PubMed

Robin, Eric; Valle, Valéry; Brémand, Fabrice

2005-12-01

The method presented extracts the demodulated phase from only one fringe pattern. Locally, this method approaches the fringe pattern morphology with the help of a mathematical model. The degree of similarity between the mathematical model and the real fringe is estimated by minimizing a correlation function. To use an optimization process, we have chosen a polynomial form such as a mathematical model. However, the use of a polynomial form induces an identification procedure with the purpose of retrieving the demodulated phase. This method, polynomial modulated phase correlation, is tested on several examples. Its performance, in terms of speed and precision, is presented on very noised fringe patterns.

Orthonormal vector general polynomials derived from the Cartesian gradient of the orthonormal Zernike-based polynomials.

PubMed

Mafusire, Cosmas; Krüger, Tjaart P J

2018-06-01

The concept of orthonormal vector circle polynomials is revisited by deriving a set from the Cartesian gradient of Zernike polynomials in a unit circle using a matrix-based approach. The heart of this model is a closed-form matrix equation of the gradient of Zernike circle polynomials expressed as a linear combination of lower-order Zernike circle polynomials related through a gradient matrix. This is a sparse matrix whose elements are two-dimensional standard basis transverse Euclidean vectors. Using the outer product form of the Cholesky decomposition, the gradient matrix is used to calculate a new matrix, which we used to express the Cartesian gradient of the Zernike circle polynomials as a linear combination of orthonormal vector circle polynomials. Since this new matrix is singular, the orthonormal vector polynomials are recovered by reducing the matrix to its row echelon form using the Gauss-Jordan elimination method. We extend the model to derive orthonormal vector general polynomials, which are orthonormal in a general pupil by performing a similarity transformation on the gradient matrix to give its equivalent in the general pupil. The outer form of the Gram-Schmidt procedure and the Gauss-Jordan elimination method are then applied to the general pupil to generate the orthonormal vector general polynomials from the gradient of the orthonormal Zernike-based polynomials. The performance of the model is demonstrated with a simulated wavefront in a square pupil inscribed in a unit circle.

LoCoH: Non-parameteric kernel methods for constructing home ranges and utilization distributions

USGS Publications Warehouse

Getz, Wayne M.; Fortmann-Roe, Scott; Cross, Paul C.; Lyons, Andrew J.; Ryan, Sadie J.; Wilmers, Christopher C.

2007-01-01

Parametric kernel methods currently dominate the literature regarding the construction of animal home ranges (HRs) and utilization distributions (UDs). These methods frequently fail to capture the kinds of hard boundaries common to many natural systems. Recently a local convex hull (LoCoH) nonparametric kernel method, which generalizes the minimum convex polygon (MCP) method, was shown to be more appropriate than parametric kernel methods for constructing HRs and UDs, because of its ability to identify hard boundaries (e.g., rivers, cliff edges) and convergence to the true distribution as sample size increases. Here we extend the LoCoH in two ways: ‘‘fixed sphere-of-influence,’’ or r -LoCoH (kernels constructed from all points within a fixed radius r of each reference point), and an ‘‘adaptive sphere-of-influence,’’ or a -LoCoH (kernels constructed from all points within a radius a such that the distances of all points within the radius to the reference point sum to a value less than or equal to a ), and compare them to the original ‘‘fixed-number-of-points,’’ or k -LoCoH (all kernels constructed from k -1 nearest neighbors of root points). We also compare these nonparametric LoCoH to parametric kernel methods using manufactured data and data collected from GPS collars on African buffalo in the Kruger National Park, South Africa. Our results demonstrate that LoCoH methods are superior to parametric kernel methods in estimating areas used by animals, excluding unused areas (holes) and, generally, in constructing UDs and HRs arising from the movement of animals influenced by hard boundaries and irregular structures (e.g., rocky outcrops). We also demonstrate that a -LoCoH is generally superior to k - and r -LoCoH (with software for all three methods available at http://locoh.cnr.berkeley.edu).

Development of a single kernel analysis method for detection of 2-acetyl-1-pyrroline in aromatic rice germplasm

USDA-ARS?s Scientific Manuscript database

Solid-phase microextraction (SPME) in conjunction with GC/MS was used to distinguish non-aromatic rice (Oryza sativa, L.) kernels from aromatic rice kernels. In this method, single kernels along with 10 µl of 0.1 ng 2,4,6-Trimethylpyridine (TMP) were placed in sealed vials and heated to 80oC for 18...

Parametric output-only identification of time-varying structures using a kernel recursive extended least squares TARMA approach

NASA Astrophysics Data System (ADS)

Ma, Zhi-Sai; Liu, Li; Zhou, Si-Da; Yu, Lei; Naets, Frank; Heylen, Ward; Desmet, Wim

2018-01-01

The problem of parametric output-only identification of time-varying structures in a recursive manner is considered. A kernelized time-dependent autoregressive moving average (TARMA) model is proposed by expanding the time-varying model parameters onto the basis set of kernel functions in a reproducing kernel Hilbert space. An exponentially weighted kernel recursive extended least squares TARMA identification scheme is proposed, and a sliding-window technique is subsequently applied to fix the computational complexity for each consecutive update, allowing the method to operate online in time-varying environments. The proposed sliding-window exponentially weighted kernel recursive extended least squares TARMA method is employed for the identification of a laboratory time-varying structure consisting of a simply supported beam and a moving mass sliding on it. The proposed method is comparatively assessed against an existing recursive pseudo-linear regression TARMA method via Monte Carlo experiments and shown to be capable of accurately tracking the time-varying dynamics. Furthermore, the comparisons demonstrate the superior achievable accuracy, lower computational complexity and enhanced online identification capability of the proposed kernel recursive extended least squares TARMA approach.

A Comparative Study of Pairwise Learning Methods Based on Kernel Ridge Regression.

PubMed

Stock, Michiel; Pahikkala, Tapio; Airola, Antti; De Baets, Bernard; Waegeman, Willem

2018-06-12

Many machine learning problems can be formulated as predicting labels for a pair of objects. Problems of that kind are often referred to as pairwise learning, dyadic prediction, or network inference problems. During the past decade, kernel methods have played a dominant role in pairwise learning. They still obtain a state-of-the-art predictive performance, but a theoretical analysis of their behavior has been underexplored in the machine learning literature. In this work we review and unify kernel-based algorithms that are commonly used in different pairwise learning settings, ranging from matrix filtering to zero-shot learning. To this end, we focus on closed-form efficient instantiations of Kronecker kernel ridge regression. We show that independent task kernel ridge regression, two-step kernel ridge regression, and a linear matrix filter arise naturally as a special case of Kronecker kernel ridge regression, implying that all these methods implicitly minimize a squared loss. In addition, we analyze universality, consistency, and spectral filtering properties. Our theoretical results provide valuable insights into assessing the advantages and limitations of existing pairwise learning methods.

Novel characterization method of impedance cardiography signals using time-frequency distributions.

PubMed

Escrivá Muñoz, Jesús; Pan, Y; Ge, S; Jensen, E W; Vallverdú, M

2018-03-16

The purpose of this document is to describe a methodology to select the most adequate time-frequency distribution (TFD) kernel for the characterization of impedance cardiography signals (ICG). The predominant ICG beat was extracted from a patient and was synthetized using time-frequency variant Fourier approximations. These synthetized signals were used to optimize several TFD kernels according to a performance maximization. The optimized kernels were tested for noise resistance on a clinical database. The resulting optimized TFD kernels are presented with their performance calculated using newly proposed methods. The procedure explained in this work showcases a new method to select an appropriate kernel for ICG signals and compares the performance of different time-frequency kernels found in the literature for the case of ICG signals. We conclude that, for ICG signals, the performance (P) of the spectrogram with either Hanning or Hamming windows (P = 0.780) and the extended modified beta distribution (P = 0.765) provided similar results, higher than the rest of analyzed kernels. Graphical abstract Flowchart for the optimization of time-frequency distribution kernels for impedance cardiography signals.

Effective Alternating Direction Optimization Methods for Sparsity-Constrained Blind Image Deblurring.

PubMed

Xiong, Naixue; Liu, Ryan Wen; Liang, Maohan; Wu, Di; Liu, Zhao; Wu, Huisi

2017-01-18

Single-image blind deblurring for imaging sensors in the Internet of Things (IoT) is a challenging ill-conditioned inverse problem, which requires regularization techniques to stabilize the image restoration process. The purpose is to recover the underlying blur kernel and latent sharp image from only one blurred image. Under many degraded imaging conditions, the blur kernel could be considered not only spatially sparse, but also piecewise smooth with the support of a continuous curve. By taking advantage of the hybrid sparse properties of the blur kernel, a hybrid regularization method is proposed in this paper to robustly and accurately estimate the blur kernel. The effectiveness of the proposed blur kernel estimation method is enhanced by incorporating both the L 1 -norm of kernel intensity and the squared L 2 -norm of the intensity derivative. Once the accurate estimation of the blur kernel is obtained, the original blind deblurring can be simplified to the direct deconvolution of blurred images. To guarantee robust non-blind deconvolution, a variational image restoration model is presented based on the L 1 -norm data-fidelity term and the total generalized variation (TGV) regularizer of second-order. All non-smooth optimization problems related to blur kernel estimation and non-blind deconvolution are effectively handled by using the alternating direction method of multipliers (ADMM)-based numerical methods. Comprehensive experiments on both synthetic and realistic datasets have been implemented to compare the proposed method with several state-of-the-art methods. The experimental comparisons have illustrated the satisfactory imaging performance of the proposed method in terms of quantitative and qualitative evaluations.

Fast Gaussian kernel learning for classification tasks based on specially structured global optimization.

PubMed

Zhong, Shangping; Chen, Tianshun; He, Fengying; Niu, Yuzhen

2014-09-01

For a practical pattern classification task solved by kernel methods, the computing time is mainly spent on kernel learning (or training). However, the current kernel learning approaches are based on local optimization techniques, and hard to have good time performances, especially for large datasets. Thus the existing algorithms cannot be easily extended to large-scale tasks. In this paper, we present a fast Gaussian kernel learning method by solving a specially structured global optimization (SSGO) problem. We optimize the Gaussian kernel function by using the formulated kernel target alignment criterion, which is a difference of increasing (d.i.) functions. Through using a power-transformation based convexification method, the objective criterion can be represented as a difference of convex (d.c.) functions with a fixed power-transformation parameter. And the objective programming problem can then be converted to a SSGO problem: globally minimizing a concave function over a convex set. The SSGO problem is classical and has good solvability. Thus, to find the global optimal solution efficiently, we can adopt the improved Hoffman's outer approximation method, which need not repeat the searching procedure with different starting points to locate the best local minimum. Also, the proposed method can be proven to converge to the global solution for any classification task. We evaluate the proposed method on twenty benchmark datasets, and compare it with four other Gaussian kernel learning methods. Experimental results show that the proposed method stably achieves both good time-efficiency performance and good classification performance. Copyright © 2014 Elsevier Ltd. All rights reserved.

Finite-frequency sensitivity kernels for global seismic wave propagation based upon adjoint methods

NASA Astrophysics Data System (ADS)

Liu, Qinya; Tromp, Jeroen

2008-07-01

We determine adjoint equations and Fréchet kernels for global seismic wave propagation based upon a Lagrange multiplier method. We start from the equations of motion for a rotating, self-gravitating earth model initially in hydrostatic equilibrium, and derive the corresponding adjoint equations that involve motions on an earth model that rotates in the opposite direction. Variations in the misfit function χ then may be expressed as , where δlnm = δm/m denotes relative model perturbations in the volume V, δlnd denotes relative topographic variations on solid-solid or fluid-solid boundaries Σ, and ∇Σδlnd denotes surface gradients in relative topographic variations on fluid-solid boundaries ΣFS. The 3-D Fréchet kernel Km determines the sensitivity to model perturbations δlnm, and the 2-D kernels Kd and Kd determine the sensitivity to topographic variations δlnd. We demonstrate also how anelasticity may be incorporated within the framework of adjoint methods. Finite-frequency sensitivity kernels are calculated by simultaneously computing the adjoint wavefield forward in time and reconstructing the regular wavefield backward in time. Both the forward and adjoint simulations are based upon a spectral-element method. We apply the adjoint technique to generate finite-frequency traveltime kernels for global seismic phases (P, Pdiff, PKP, S, SKS, depth phases, surface-reflected phases, surface waves, etc.) in both 1-D and 3-D earth models. For 1-D models these adjoint-generated kernels generally agree well with results obtained from ray-based methods. However, adjoint methods do not have the same theoretical limitations as ray-based methods, and can produce sensitivity kernels for any given phase in any 3-D earth model. The Fréchet kernels presented in this paper illustrate the sensitivity of seismic observations to structural parameters and topography on internal discontinuities. These kernels form the basis of future 3-D tomographic inversions.

Algorithms for Solvents and Spectral Factors of Matrix Polynomials

DTIC Science & Technology

1981-01-01

spectral factors of matrix polynomials LEANG S. SHIEHt, YIH T. TSAYt and NORMAN P. COLEMANt A generalized Newton method , based on the contracted gradient...of a matrix poly- nomial, is derived for solving the right (left) solvents and spectral factors of matrix polynomials. Two methods of selecting initial...estimates for rapid convergence of the newly developed numerical method are proposed. Also, new algorithms for solving complete sets of the right

Credit scoring analysis using kernel discriminant

NASA Astrophysics Data System (ADS)

Widiharih, T.; Mukid, M. A.; Mustafid

2018-05-01

Credit scoring model is an important tool for reducing the risk of wrong decisions when granting credit facilities to applicants. This paper investigate the performance of kernel discriminant model in assessing customer credit risk. Kernel discriminant analysis is a non- parametric method which means that it does not require any assumptions about the probability distribution of the input. The main ingredient is a kernel that allows an efficient computation of Fisher discriminant. We use several kernel such as normal, epanechnikov, biweight, and triweight. The models accuracy was compared each other using data from a financial institution in Indonesia. The results show that kernel discriminant can be an alternative method that can be used to determine who is eligible for a credit loan. In the data we use, it shows that a normal kernel is relevant to be selected for credit scoring using kernel discriminant model. Sensitivity and specificity reach to 0.5556 and 0.5488 respectively.

Genomic similarity and kernel methods I: advancements by building on mathematical and statistical foundations.

PubMed

Schaid, Daniel J

2010-01-01

Measures of genomic similarity are the basis of many statistical analytic methods. We review the mathematical and statistical basis of similarity methods, particularly based on kernel methods. A kernel function converts information for a pair of subjects to a quantitative value representing either similarity (larger values meaning more similar) or distance (smaller values meaning more similar), with the requirement that it must create a positive semidefinite matrix when applied to all pairs of subjects. This review emphasizes the wide range of statistical methods and software that can be used when similarity is based on kernel methods, such as nonparametric regression, linear mixed models and generalized linear mixed models, hierarchical models, score statistics, and support vector machines. The mathematical rigor for these methods is summarized, as is the mathematical framework for making kernels. This review provides a framework to move from intuitive and heuristic approaches to define genomic similarities to more rigorous methods that can take advantage of powerful statistical modeling and existing software. A companion paper reviews novel approaches to creating kernels that might be useful for genomic analyses, providing insights with examples [1]. Copyright © 2010 S. Karger AG, Basel.

Differential evolution algorithm-based kernel parameter selection for Fukunaga-Koontz Transform subspaces construction

NASA Astrophysics Data System (ADS)

Binol, Hamidullah; Bal, Abdullah; Cukur, Huseyin

2015-10-01

The performance of the kernel based techniques depends on the selection of kernel parameters. That's why; suitable parameter selection is an important problem for many kernel based techniques. This article presents a novel technique to learn the kernel parameters in kernel Fukunaga-Koontz Transform based (KFKT) classifier. The proposed approach determines the appropriate values of kernel parameters through optimizing an objective function constructed based on discrimination ability of KFKT. For this purpose we have utilized differential evolution algorithm (DEA). The new technique overcomes some disadvantages such as high time consumption existing in the traditional cross-validation method, and it can be utilized in any type of data. The experiments for target detection applications on the hyperspectral images verify the effectiveness of the proposed method.

Novel near-infrared sampling apparatus for single kernel analysis of oil content in maize.

PubMed

Janni, James; Weinstock, B André; Hagen, Lisa; Wright, Steve

2008-04-01

A method of rapid, nondestructive chemical and physical analysis of individual maize (Zea mays L.) kernels is needed for the development of high value food, feed, and fuel traits. Near-infrared (NIR) spectroscopy offers a robust nondestructive method of trait determination. However, traditional NIR bulk sampling techniques cannot be applied successfully to individual kernels. Obtaining optimized single kernel NIR spectra for applied chemometric predictive analysis requires a novel sampling technique that can account for the heterogeneous forms, morphologies, and opacities exhibited in individual maize kernels. In this study such a novel technique is described and compared to less effective means of single kernel NIR analysis. Results of the application of a partial least squares (PLS) derived model for predictive determination of percent oil content per individual kernel are shown.

Hadamard Kernel SVM with applications for breast cancer outcome predictions.

PubMed

Jiang, Hao; Ching, Wai-Ki; Cheung, Wai-Shun; Hou, Wenpin; Yin, Hong

2017-12-21

Breast cancer is one of the leading causes of deaths for women. It is of great necessity to develop effective methods for breast cancer detection and diagnosis. Recent studies have focused on gene-based signatures for outcome predictions. Kernel SVM for its discriminative power in dealing with small sample pattern recognition problems has attracted a lot attention. But how to select or construct an appropriate kernel for a specified problem still needs further investigation. Here we propose a novel kernel (Hadamard Kernel) in conjunction with Support Vector Machines (SVMs) to address the problem of breast cancer outcome prediction using gene expression data. Hadamard Kernel outperform the classical kernels and correlation kernel in terms of Area under the ROC Curve (AUC) values where a number of real-world data sets are adopted to test the performance of different methods. Hadamard Kernel SVM is effective for breast cancer predictions, either in terms of prognosis or diagnosis. It may benefit patients by guiding therapeutic options. Apart from that, it would be a valuable addition to the current SVM kernel families. We hope it will contribute to the wider biology and related communities.

Local coding based matching kernel method for image classification.

PubMed

Song, Yan; McLoughlin, Ian Vince; Dai, Li-Rong

2014-01-01

This paper mainly focuses on how to effectively and efficiently measure visual similarity for local feature based representation. Among existing methods, metrics based on Bag of Visual Word (BoV) techniques are efficient and conceptually simple, at the expense of effectiveness. By contrast, kernel based metrics are more effective, but at the cost of greater computational complexity and increased storage requirements. We show that a unified visual matching framework can be developed to encompass both BoV and kernel based metrics, in which local kernel plays an important role between feature pairs or between features and their reconstruction. Generally, local kernels are defined using Euclidean distance or its derivatives, based either explicitly or implicitly on an assumption of Gaussian noise. However, local features such as SIFT and HoG often follow a heavy-tailed distribution which tends to undermine the motivation behind Euclidean metrics. Motivated by recent advances in feature coding techniques, a novel efficient local coding based matching kernel (LCMK) method is proposed. This exploits the manifold structures in Hilbert space derived from local kernels. The proposed method combines advantages of both BoV and kernel based metrics, and achieves a linear computational complexity. This enables efficient and scalable visual matching to be performed on large scale image sets. To evaluate the effectiveness of the proposed LCMK method, we conduct extensive experiments with widely used benchmark datasets, including 15-Scenes, Caltech101/256, PASCAL VOC 2007 and 2011 datasets. Experimental results confirm the effectiveness of the relatively efficient LCMK method.

Integrating semantic information into multiple kernels for protein-protein interaction extraction from biomedical literatures.

PubMed

Li, Lishuang; Zhang, Panpan; Zheng, Tianfu; Zhang, Hongying; Jiang, Zhenchao; Huang, Degen

2014-01-01

Protein-Protein Interaction (PPI) extraction is an important task in the biomedical information extraction. Presently, many machine learning methods for PPI extraction have achieved promising results. However, the performance is still not satisfactory. One reason is that the semantic resources were basically ignored. In this paper, we propose a multiple-kernel learning-based approach to extract PPIs, combining the feature-based kernel, tree kernel and semantic kernel. Particularly, we extend the shortest path-enclosed tree kernel (SPT) by a dynamic extended strategy to retrieve the richer syntactic information. Our semantic kernel calculates the protein-protein pair similarity and the context similarity based on two semantic resources: WordNet and Medical Subject Heading (MeSH). We evaluate our method with Support Vector Machine (SVM) and achieve an F-score of 69.40% and an AUC of 92.00%, which show that our method outperforms most of the state-of-the-art systems by integrating semantic information.

Improvements to the kernel function method of steady, subsonic lifting surface theory

NASA Technical Reports Server (NTRS)

Medan, R. T.

1974-01-01

The application of a kernel function lifting surface method to three dimensional, thin wing theory is discussed. A technique for determining the influence functions is presented. The technique is shown to require fewer quadrature points, while still calculating the influence functions accurately enough to guarantee convergence with an increasing number of spanwise quadrature points. The method also treats control points on the wing leading and trailing edges. The report introduces and employs an aspect of the kernel function method which apparently has never been used before and which significantly enhances the efficiency of the kernel function approach.

Anderson metal-insulator transitions with classical magnetic impurities

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

Jung, Daniel; Kettemann, Stefan

We study the effects of classical magnetic impurities on the Anderson metal-insulator transition (AMIT) numerically. In particular we find that while a finite concentration of Ising impurities lowers the critical value of the site-diagonal disorder amplitude W{sub c}, in the presence of Heisenberg impurities, W{sub c} is first increased with increasing exchange coupling strength J due to time-reversal symmetry breaking. The resulting scaling with J is compared to analytical predictions by Wegner [1]. The results are obtained numerically, based on a finite-size scaling procedure for the typical density of states [2], which is the geometric average of the local densitymore » of states. The latter can efficiently be calculated using the kernel polynomial method [3]. Although still suffering from methodical shortcomings, our method proves to deliver results close to established results for the orthogonal symmetry class [4]. We extend previous approaches [5] by combining the KPM with a finite-size scaling analysis. We also discuss the relevance of our findings for systems like phosphor-doped silicon (Si:P), which are known to exhibit a quantum phase transition from metal to insulator driven by the interplay of both interaction and disorder, accompanied by the presence of a finite concentration of magnetic moments [6].« less

LZW-Kernel: fast kernel utilizing variable length code blocks from LZW compressors for protein sequence classification.

PubMed

Filatov, Gleb; Bauwens, Bruno; Kertész-Farkas, Attila

2018-05-07

Bioinformatics studies often rely on similarity measures between sequence pairs, which often pose a bottleneck in large-scale sequence analysis. Here, we present a new convolutional kernel function for protein sequences called the LZW-Kernel. It is based on code words identified with the Lempel-Ziv-Welch (LZW) universal text compressor. The LZW-Kernel is an alignment-free method, it is always symmetric, is positive, always provides 1.0 for self-similarity and it can directly be used with Support Vector Machines (SVMs) in classification problems, contrary to normalized compression distance (NCD), which often violates the distance metric properties in practice and requires further techniques to be used with SVMs. The LZW-Kernel is a one-pass algorithm, which makes it particularly plausible for big data applications. Our experimental studies on remote protein homology detection and protein classification tasks reveal that the LZW-Kernel closely approaches the performance of the Local Alignment Kernel (LAK) and the SVM-pairwise method combined with Smith-Waterman (SW) scoring at a fraction of the time. Moreover, the LZW-Kernel outperforms the SVM-pairwise method when combined with BLAST scores, which indicates that the LZW code words might be a better basis for similarity measures than local alignment approximations found with BLAST. In addition, the LZW-Kernel outperforms n-gram based mismatch kernels, hidden Markov model based SAM and Fisher kernel, and protein family based PSI-BLAST, among others. Further advantages include the LZW-Kernel's reliance on a simple idea, its ease of implementation, and its high speed, three times faster than BLAST and several magnitudes faster than SW or LAK in our tests. LZW-Kernel is implemented as a standalone C code and is a free open-source program distributed under GPLv3 license and can be downloaded from https://github.com/kfattila/LZW-Kernel. akerteszfarkas@hse.ru. Supplementary data are available at Bioinformatics Online.

Generalization Performance of Regularized Ranking With Multiscale Kernels.

PubMed

Zhou, Yicong; Chen, Hong; Lan, Rushi; Pan, Zhibin

2016-05-01

The regularized kernel method for the ranking problem has attracted increasing attentions in machine learning. The previous regularized ranking algorithms are usually based on reproducing kernel Hilbert spaces with a single kernel. In this paper, we go beyond this framework by investigating the generalization performance of the regularized ranking with multiscale kernels. A novel ranking algorithm with multiscale kernels is proposed and its representer theorem is proved. We establish the upper bound of the generalization error in terms of the complexity of hypothesis spaces. It shows that the multiscale ranking algorithm can achieve satisfactory learning rates under mild conditions. Experiments demonstrate the effectiveness of the proposed method for drug discovery and recommendation tasks.

Asymptotics for the Fredholm determinant of the sine kernel on a union of intervals

NASA Astrophysics Data System (ADS)

Widom, Harold

1995-07-01

In the bulk scaling limit of the Gaussian Unitary Ensemble of hermitian matrices the probability that an interval of length s contains no eigenvalues is the Fredholm determinant of the sine kernel{sin (x - y)}/{π (x - y)} over this interval. A formal asymptotic expansion for the determinant as s tends to infinity was obtained by Dyson. In this paper we replace a single interval of length s by sJ, where J is a union of m intervals and present a proof of the asymptotics up to second order. The logarithmic derivative with respect to s of the determinant equals a constant (expressible in terms of hyperelliptic integrals) times s, plus a bounded oscillatory function of s (zero if m=1, periodic if m=2, and in general expressible in terms of the solution of a Jacobi inversion problem), plus o(1). Also determined are the asymptotics of the trace of the resolvent operator, which is the ratio in the same model of the probability that the set contains exactly one eigenvalue to the probability that it contains none. The proofs use ideas from orthogonal polynomial theory.

On Making a Distinguished Vertex Minimum Degree by Vertex Deletion

NASA Astrophysics Data System (ADS)

Betzler, Nadja; Bredereck, Robert; Niedermeier, Rolf; Uhlmann, Johannes

For directed and undirected graphs, we study the problem to make a distinguished vertex the unique minimum-(in)degree vertex through deletion of a minimum number of vertices. The corresponding NP-hard optimization problems are motivated by applications concerning control in elections and social network analysis. Continuing previous work for the directed case, we show that the problem is W[2]-hard when parameterized by the graph's feedback arc set number, whereas it becomes fixed-parameter tractable when combining the parameters "feedback vertex set number" and "number of vertices to delete". For the so far unstudied undirected case, we show that the problem is NP-hard and W[1]-hard when parameterized by the "number of vertices to delete". On the positive side, we show fixed-parameter tractability for several parameterizations measuring tree-likeness, including a vertex-linear problem kernel with respect to the parameter "feedback edge set number". On the contrary, we show a non-existence result concerning polynomial-size problem kernels for the combined parameter "vertex cover number and number of vertices to delete", implying corresponding nonexistence results when replacing vertex cover number by treewidth or feedback vertex set number.

Fredholm-Volterra Integral Equation with a Generalized Singular Kernel and its Numerical Solutions

NASA Astrophysics Data System (ADS)

El-Kalla, I. L.; Al-Bugami, A. M.

2010-11-01

In this paper, the existence and uniqueness of solution of the Fredholm-Volterra integral equation (F-VIE), with a generalized singular kernel, are discussed and proved in the spaceL2(Ω)×C(0,T). The Fredholm integral term (FIT) is considered in position while the Volterra integral term (VIT) is considered in time. Using a numerical technique we have a system of Fredholm integral equations (SFIEs). This system of integral equations can be reduced to a linear algebraic system (LAS) of equations by using two different methods. These methods are: Toeplitz matrix method and Product Nyström method. A numerical examples are considered when the generalized kernel takes the following forms: Carleman function, logarithmic form, Cauchy kernel, and Hilbert kernel.

On polynomial preconditioning for indefinite Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland W.

1989-01-01

The minimal residual method is studied combined with polynomial preconditioning for solving large linear systems (Ax = b) with indefinite Hermitian coefficient matrices (A). The standard approach for choosing the polynomial preconditioners leads to preconditioned systems which are positive definite. Here, a different strategy is studied which leaves the preconditioned coefficient matrix indefinite. More precisely, the polynomial preconditioner is designed to cluster the positive, resp. negative eigenvalues of A around 1, resp. around some negative constant. In particular, it is shown that such indefinite polynomial preconditioners can be obtained as the optimal solutions of a certain two parameter family of Chebyshev approximation problems. Some basic results are established for these approximation problems and a Remez type algorithm is sketched for their numerical solution. The problem of selecting the parameters such that the resulting indefinite polynomial preconditioners speeds up the convergence of minimal residual method optimally is also addressed. An approach is proposed based on the concept of asymptotic convergence factors. Finally, some numerical examples of indefinite polynomial preconditioners are given.

The construction of a two-dimensional reproducing kernel function and its application in a biomedical model.

PubMed

Guo, Qi; Shen, Shu-Ting

2016-04-29

There are two major classes of cardiac tissue models: the ionic model and the FitzHugh-Nagumo model. During computer simulation, each model entails solving a system of complex ordinary differential equations and a partial differential equation with non-flux boundary conditions. The reproducing kernel method possesses significant applications in solving partial differential equations. The derivative of the reproducing kernel function is a wavelet function, which has local properties and sensitivities to singularity. Therefore, study on the application of reproducing kernel would be advantageous. Applying new mathematical theory to the numerical solution of the ventricular muscle model so as to improve its precision in comparison with other methods at present. A two-dimensional reproducing kernel function inspace is constructed and applied in computing the solution of two-dimensional cardiac tissue model by means of the difference method through time and the reproducing kernel method through space. Compared with other methods, this method holds several advantages such as high accuracy in computing solutions, insensitivity to different time steps and a slow propagation speed of error. It is suitable for disorderly scattered node systems without meshing, and can arbitrarily change the location and density of the solution on different time layers. The reproducing kernel method has higher solution accuracy and stability in the solutions of the two-dimensional cardiac tissue model.

An Evaluation of Kernel Equating: Parallel Equating with Classical Methods in the SAT Subject Tests[TM] Program. Research Report. ETS RR-09-06

ERIC Educational Resources Information Center

Grant, Mary C.; Zhang, Lilly; Damiano, Michele

2009-01-01

This study investigated kernel equating methods by comparing these methods to operational equatings for two tests in the SAT Subject Tests[TM] program. GENASYS (ETS, 2007) was used for all equating methods and scaled score kernel equating results were compared to Tucker, Levine observed score, chained linear, and chained equipercentile equating…

Non-parametric wall model and methods of identifying boundary conditions for moments in gas flow equations

NASA Astrophysics Data System (ADS)

Liao, Meng; To, Quy-Dong; Léonard, Céline; Monchiet, Vincent

2018-03-01

In this paper, we use the molecular dynamics simulation method to study gas-wall boundary conditions. Discrete scattering information of gas molecules at the wall surface is obtained from collision simulations. The collision data can be used to identify the accommodation coefficients for parametric wall models such as Maxwell and Cercignani-Lampis scattering kernels. Since these scattering kernels are based on a limited number of accommodation coefficients, we adopt non-parametric statistical methods to construct the kernel to overcome these issues. Different from parametric kernels, the non-parametric kernels require no parameter (i.e. accommodation coefficients) and no predefined distribution. We also propose approaches to derive directly the Navier friction and Kapitza thermal resistance coefficients as well as other interface coefficients associated with moment equations from the non-parametric kernels. The methods are applied successfully to systems composed of CH4 or CO2 and graphite, which are of interest to the petroleum industry.

Stochastic Estimation via Polynomial Chaos

DTIC Science & Technology

2015-10-01

AFRL-RW-EG-TR-2015-108 Stochastic Estimation via Polynomial Chaos Douglas V. Nance Air Force Research...COVERED (From - To) 20-04-2015 – 07-08-2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Stochastic Estimation via Polynomial Chaos ...This expository report discusses fundamental aspects of the polynomial chaos method for representing the properties of second order stochastic

Vehicle Sprung Mass Estimation for Rough Terrain

DTIC Science & Technology

2011-03-01

distributions are greater than zero. The multivariate polynomials are functions of the Legendre polynomials (Poularikas (1999...developed methods based on polynomial chaos theory and on the maximum likelihood approach to estimate the most likely value of the vehicle sprung...mass. The polynomial chaos estimator is compared to benchmark algorithms including recursive least squares, recursive total least squares, extended

Volumetric calibration of a plenoptic camera.

PubMed

Hall, Elise Munz; Fahringer, Timothy W; Guildenbecher, Daniel R; Thurow, Brian S

2018-02-01

The volumetric calibration of a plenoptic camera is explored to correct for inaccuracies due to real-world lens distortions and thin-lens assumptions in current processing methods. Two methods of volumetric calibration based on a polynomial mapping function that does not require knowledge of specific lens parameters are presented and compared to a calibration based on thin-lens assumptions. The first method, volumetric dewarping, is executed by creation of a volumetric representation of a scene using the thin-lens assumptions, which is then corrected in post-processing using a polynomial mapping function. The second method, direct light-field calibration, uses the polynomial mapping in creation of the initial volumetric representation to relate locations in object space directly to image sensor locations. The accuracy and feasibility of these methods is examined experimentally by capturing images of a known dot card at a variety of depths. Results suggest that use of a 3D polynomial mapping function provides a significant increase in reconstruction accuracy and that the achievable accuracy is similar using either polynomial-mapping-based method. Additionally, direct light-field calibration provides significant computational benefits by eliminating some intermediate processing steps found in other methods. Finally, the flexibility of this method is shown for a nonplanar calibration.

A new discriminative kernel from probabilistic models.

PubMed

Tsuda, Koji; Kawanabe, Motoaki; Rätsch, Gunnar; Sonnenburg, Sören; Müller, Klaus-Robert

2002-10-01

Recently, Jaakkola and Haussler (1999) proposed a method for constructing kernel functions from probabilistic models. Their so-called Fisher kernel has been combined with discriminative classifiers such as support vector machines and applied successfully in, for example, DNA and protein analysis. Whereas the Fisher kernel is calculated from the marginal log-likelihood, we propose the TOP kernel derived; from tangent vectors of posterior log-odds. Furthermore, we develop a theoretical framework on feature extractors from probabilistic models and use it for analyzing the TOP kernel. In experiments, our new discriminative TOP kernel compares favorably to the Fisher kernel.

Prioritizing individual genetic variants after kernel machine testing using variable selection.

PubMed

He, Qianchuan; Cai, Tianxi; Liu, Yang; Zhao, Ni; Harmon, Quaker E; Almli, Lynn M; Binder, Elisabeth B; Engel, Stephanie M; Ressler, Kerry J; Conneely, Karen N; Lin, Xihong; Wu, Michael C

2016-12-01

Kernel machine learning methods, such as the SNP-set kernel association test (SKAT), have been widely used to test associations between traits and genetic polymorphisms. In contrast to traditional single-SNP analysis methods, these methods are designed to examine the joint effect of a set of related SNPs (such as a group of SNPs within a gene or a pathway) and are able to identify sets of SNPs that are associated with the trait of interest. However, as with many multi-SNP testing approaches, kernel machine testing can draw conclusion only at the SNP-set level, and does not directly inform on which one(s) of the identified SNP set is actually driving the associations. A recently proposed procedure, KerNel Iterative Feature Extraction (KNIFE), provides a general framework for incorporating variable selection into kernel machine methods. In this article, we focus on quantitative traits and relatively common SNPs, and adapt the KNIFE procedure to genetic association studies and propose an approach to identify driver SNPs after the application of SKAT to gene set analysis. Our approach accommodates several kernels that are widely used in SNP analysis, such as the linear kernel and the Identity by State (IBS) kernel. The proposed approach provides practically useful utilities to prioritize SNPs, and fills the gap between SNP set analysis and biological functional studies. Both simulation studies and real data application are used to demonstrate the proposed approach. © 2016 WILEY PERIODICALS, INC.

Long-time uncertainty propagation using generalized polynomial chaos and flow map composition

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

Luchtenburg, Dirk M., E-mail: dluchten@cooper.edu; Brunton, Steven L.; Rowley, Clarence W.

2014-10-01

We present an efficient and accurate method for long-time uncertainty propagation in dynamical systems. Uncertain initial conditions and parameters are both addressed. The method approximates the intermediate short-time flow maps by spectral polynomial bases, as in the generalized polynomial chaos (gPC) method, and uses flow map composition to construct the long-time flow map. In contrast to the gPC method, this approach has spectral error convergence for both short and long integration times. The short-time flow map is characterized by small stretching and folding of the associated trajectories and hence can be well represented by a relatively low-degree basis. The compositionmore » of these low-degree polynomial bases then accurately describes the uncertainty behavior for long integration times. The key to the method is that the degree of the resulting polynomial approximation increases exponentially in the number of time intervals, while the number of polynomial coefficients either remains constant (for an autonomous system) or increases linearly in the number of time intervals (for a non-autonomous system). The findings are illustrated on several numerical examples including a nonlinear ordinary differential equation (ODE) with an uncertain initial condition, a linear ODE with an uncertain model parameter, and a two-dimensional, non-autonomous double gyre flow.« less

An Ensemble Approach to Building Mercer Kernels with Prior Information

NASA Technical Reports Server (NTRS)

Srivastava, Ashok N.; Schumann, Johann; Fischer, Bernd

2005-01-01

This paper presents a new methodology for automatic knowledge driven data mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly dimensional feature space. we describe a new method called Mixture Density Mercer Kernels to learn kernel function directly from data, rather than using pre-defined kernels. These data adaptive kernels can encode prior knowledge in the kernel using a Bayesian formulation, thus allowing for physical information to be encoded in the model. Specifically, we demonstrate the use of the algorithm in situations with extremely small samples of data. We compare the results with existing algorithms on data from the Sloan Digital Sky Survey (SDSS) and demonstrate the method's superior performance against standard methods. The code for these experiments has been generated with the AUTOBAYES tool, which automatically generates efficient and documented C/C++ code from abstract statistical model specifications. The core of the system is a schema library which contains templates for learning and knowledge discovery algorithms like different versions of EM, or numeric optimization methods like conjugate gradient methods. The template instantiation is supported by symbolic-algebraic computations, which allows AUTOBAYES to find closed-form solutions and, where possible, to integrate them into the code.

Statistical classification of drug incidents due to look-alike sound-alike mix-ups.

PubMed

Wong, Zoie Shui Yee

2016-06-01

It has been recognised that medication names that look or sound similar are a cause of medication errors. This study builds statistical classifiers for identifying medication incidents due to look-alike sound-alike mix-ups. A total of 227 patient safety incident advisories related to medication were obtained from the Canadian Patient Safety Institute's Global Patient Safety Alerts system. Eight feature selection strategies based on frequent terms, frequent drug terms and constituent terms were performed. Statistical text classifiers based on logistic regression, support vector machines with linear, polynomial, radial-basis and sigmoid kernels and decision tree were trained and tested. The models developed achieved an average accuracy of above 0.8 across all the model settings. The receiver operating characteristic curves indicated the classifiers performed reasonably well. The results obtained in this study suggest that statistical text classification can be a feasible method for identifying medication incidents due to look-alike sound-alike mix-ups based on a database of advisories from Global Patient Safety Alerts. © The Author(s) 2014.

Boson peak and Ioffe-Regel criterion in amorphous siliconlike materials: The effect of bond directionality.

PubMed

Beltukov, Y M; Fusco, C; Parshin, D A; Tanguy, A

2016-02-01

The vibrational properties of model amorphous materials are studied by combining complete analysis of the vibration modes, dynamical structure factor, and energy diffusivity with exact diagonalization of the dynamical matrix and the kernel polynomial method, which allows a study of very large system sizes. Different materials are studied that differ only by the bending rigidity of the interactions in a Stillinger-Weber modelization used to describe amorphous silicon. The local bending rigidity can thus be used as a control parameter, to tune the sound velocity together with local bonds directionality. It is shown that for all the systems studied, the upper limit of the Boson peak corresponds to the Ioffe-Regel criterion for transverse waves, as well as to a minimum of the diffusivity. The Boson peak is followed by a diffusivity's increase supported by longitudinal phonons. The Ioffe-Regel criterion for transverse waves corresponds to a common characteristic mean-free path of 5-7 Å (which is slightly bigger for longitudinal phonons), while the fine structure of the vibrational density of states is shown to be sensitive to the local bending rigidity.

Prediction of Spirometric Forced Expiratory Volume (FEV1) Data Using Support Vector Regression

NASA Astrophysics Data System (ADS)

Kavitha, A.; Sujatha, C. M.; Ramakrishnan, S.

2010-01-01

In this work, prediction of forced expiratory volume in 1 second (FEV1) in pulmonary function test is carried out using the spirometer and support vector regression analysis. Pulmonary function data are measured with flow volume spirometer from volunteers (N=175) using a standard data acquisition protocol. The acquired data are then used to predict FEV1. Support vector machines with polynomial kernel function with four different orders were employed to predict the values of FEV1. The performance is evaluated by computing the average prediction accuracy for normal and abnormal cases. Results show that support vector machines are capable of predicting FEV1 in both normal and abnormal cases and the average prediction accuracy for normal subjects was higher than that of abnormal subjects. Accuracy in prediction was found to be high for a regularization constant of C=10. Since FEV1 is the most significant parameter in the analysis of spirometric data, it appears that this method of assessment is useful in diagnosing the pulmonary abnormalities with incomplete data and data with poor recording.

Two-dimensional orthonormal trend surfaces for prospecting

NASA Astrophysics Data System (ADS)

Sarma, D. D.; Selvaraj, J. B.

Orthonormal polynomials have distinct advantages over conventional polynomials: the equations for evaluating trend coefficients are not ill-conditioned and the convergence power of this method is greater compared to the least-squares approximation and therefore the approach by orthonormal functions provides a powerful alternative to the least-squares method. In this paper, orthonormal polynomials in two dimensions are obtained using the Gram-Schmidt method for a polynomial series of the type: Z = 1 + x + y + x2 + xy + y2 + … + yn, where x and y are the locational coordinates and Z is the value of the variable under consideration. Trend-surface analysis, which has wide applications in prospecting, has been carried out using the orthonormal polynomial approach for two sample sets of data from India concerned with gold accumulation from the Kolar Gold Field, and gravity data. A comparison of the orthonormal polynomial trend surfaces with those obtained by the classical least-squares method has been made for the two data sets. In both the situations, the orthonormal polynomial surfaces gave an improved fit to the data. A flowchart and a FORTRAN-IV computer program for deriving orthonormal polynomials of any order and for using them to fit trend surfaces is included. The program has provision for logarithmic transformation of the Z variable. If log-transformation is performed the predicted Z values are reconverted to the original units and the trend-surface map generated for use. The illustration of gold assay data related to the Champion lode system of Kolar Gold Fields, for which a 9th-degree orthonormal trend surface was fit, could be used for further prospecting the area.

A Classification of Remote Sensing Image Based on Improved Compound Kernels of Svm

NASA Astrophysics Data System (ADS)

Zhao, Jianing; Gao, Wanlin; Liu, Zili; Mou, Guifen; Lu, Lin; Yu, Lina

The accuracy of RS classification based on SVM which is developed from statistical learning theory is high under small number of train samples, which results in satisfaction of classification on RS using SVM methods. The traditional RS classification method combines visual interpretation with computer classification. The accuracy of the RS classification, however, is improved a lot based on SVM method, because it saves much labor and time which is used to interpret images and collect training samples. Kernel functions play an important part in the SVM algorithm. It uses improved compound kernel function and therefore has a higher accuracy of classification on RS images. Moreover, compound kernel improves the generalization and learning ability of the kernel.

Analytical Solutions for the Resonance Response of Goupillaud-type Elastic Media Using Z-transform Methods

DTIC Science & Technology

2012-02-01

using z-transform methods. The determinant of the resulting global system matrix in the z-space |Am| is a palindromic polynomial with real...resulting global system matrix in the z-space |Am| is a palindromic polynomial with real coefficients. The zeros of the palindromic polynomial are distinct...Goupillaud-type multilayered media. In addition, the present treatment uses a global matrix method that is attributed to Knopoff [16], rather than the

Improving the Bandwidth Selection in Kernel Equating

ERIC Educational Resources Information Center

Andersson, Björn; von Davier, Alina A.

2014-01-01

We investigate the current bandwidth selection methods in kernel equating and propose a method based on Silverman's rule of thumb for selecting the bandwidth parameters. In kernel equating, the bandwidth parameters have previously been obtained by minimizing a penalty function. This minimization process has been criticized by practitioners…

Antioxidant and antimicrobial activities of bitter and sweet apricot (Prunus armeniaca L.) kernels.

PubMed

Yiğit, D; Yiğit, N; Mavi, A

2009-04-01

The present study describes the in vitro antimicrobial and antioxidant activity of methanol and water extracts of sweet and bitter apricot (Prunus armeniaca L.) kernels. The antioxidant properties of apricot kernels were evaluated by determining radical scavenging power, lipid peroxidation inhibition activity and total phenol content measured with a DPPH test, the thiocyanate method and the Folin method, respectively. In contrast to extracts of the bitter kernels, both the water and methanol extracts of sweet kernels have antioxidant potential. The highest percent inhibition of lipid peroxidation (69%) and total phenolic content (7.9 +/- 0.2 microg/mL) were detected in the methanol extract of sweet kernels (Hasanbey) and in the water extract of the same cultivar, respectively. The antimicrobial activities of the above extracts were also tested against human pathogenic microorganisms using a disc-diffusion method, and the minimal inhibitory concentration (MIC) values of each active extract were determined. The most effective antibacterial activity was observed in the methanol and water extracts of bitter kernels and in the methanol extract of sweet kernels against the Gram-positive bacteria Staphylococcus aureus. Additionally, the methanol extracts of the bitter kernels were very potent against the Gram-negative bacteria Escherichia coli (0.312 mg/mL MIC value). Significant anti-candida activity was also observed with the methanol extract of bitter apricot kernels against Candida albicans, consisting of a 14 mm in diameter of inhibition zone and a 0.625 mg/mL MIC value.

Recognition and Quantification of Area Damaged by Oligonychus Perseae in Avocado Leaves

NASA Astrophysics Data System (ADS)

Díaz, Gloria; Romero, Eduardo; Boyero, Juan R.; Malpica, Norberto

The measure of leaf damage is a basic tool in plant epidemiology research. Measuring the area of a great number of leaves is subjective and time consuming. We investigate the use of machine learning approaches for the objective segmentation and quantification of leaf area damaged by mites in avocado leaves. After extraction of the leaf veins, pixels are labeled with a look-up table generated using a Support Vector Machine with a polynomial kernel of degree 3, on the chrominance components of YCrCb color space. Spatial information is included in the segmentation process by rating the degree of membership to a certain class and the homogeneity of the classified region. Results are presented on real images with different degrees of damage.

Elevation data fitting and precision analysis of Google Earth in road survey

NASA Astrophysics Data System (ADS)

Wei, Haibin; Luan, Xiaohan; Li, Hanchao; Jia, Jiangkun; Chen, Zhao; Han, Leilei

2018-05-01

Objective: In order to improve efficiency of road survey and save manpower and material resources, this paper intends to apply Google Earth to the feasibility study stage of road survey and design. Limited by the problem that Google Earth elevation data lacks precision, this paper is focused on finding several different fitting or difference methods to improve the data precision, in order to make every effort to meet the accuracy requirements of road survey and design specifications. Method: On the basis of elevation difference of limited public points, any elevation difference of the other points can be fitted or interpolated. Thus, the precise elevation can be obtained by subtracting elevation difference from the Google Earth data. Quadratic polynomial surface fitting method, cubic polynomial surface fitting method, V4 interpolation method in MATLAB and neural network method are used in this paper to process elevation data of Google Earth. And internal conformity, external conformity and cross correlation coefficient are used as evaluation indexes to evaluate the data processing effect. Results: There is no fitting difference at the fitting point while using V4 interpolation method. Its external conformity is the largest and the effect of accuracy improvement is the worst, so V4 interpolation method is ruled out. The internal and external conformity of the cubic polynomial surface fitting method both are better than those of the quadratic polynomial surface fitting method. The neural network method has a similar fitting effect with the cubic polynomial surface fitting method, but its fitting effect is better in the case of a higher elevation difference. Because the neural network method is an unmanageable fitting model, the cubic polynomial surface fitting method should be mainly used and the neural network method can be used as the auxiliary method in the case of higher elevation difference. Conclusions: Cubic polynomial surface fitting method can obviously improve data precision of Google Earth. The error of data in hilly terrain areas meets the requirement of specifications after precision improvement and it can be used in feasibility study stage of road survey and design.

Representing Lumped Markov Chains by Minimal Polynomials over Field GF(q)

NASA Astrophysics Data System (ADS)

Zakharov, V. M.; Shalagin, S. V.; Eminov, B. F.

2018-05-01

A method has been proposed to represent lumped Markov chains by minimal polynomials over a finite field. The accuracy of representing lumped stochastic matrices, the law of lumped Markov chains depends linearly on the minimum degree of polynomials over field GF(q). The method allows constructing the realizations of lumped Markov chains on linear shift registers with a pre-defined “linear complexity”.

Scatter correction for cone-beam computed tomography using self-adaptive scatter kernel superposition

NASA Astrophysics Data System (ADS)

Xie, Shi-Peng; Luo, Li-Min

2012-06-01

The authors propose a combined scatter reduction and correction method to improve image quality in cone beam computed tomography (CBCT). The scatter kernel superposition (SKS) method has been used occasionally in previous studies. However, this method differs in that a scatter detecting blocker (SDB) was used between the X-ray source and the tested object to model the self-adaptive scatter kernel. This study first evaluates the scatter kernel parameters using the SDB, and then isolates the scatter distribution based on the SKS. The quality of image can be improved by removing the scatter distribution. The results show that the method can effectively reduce the scatter artifacts, and increase the image quality. Our approach increases the image contrast and reduces the magnitude of cupping. The accuracy of the SKS technique can be significantly improved in our method by using a self-adaptive scatter kernel. This method is computationally efficient, easy to implement, and provides scatter correction using a single scan acquisition.

Classification With Truncated Distance Kernel.

PubMed

Huang, Xiaolin; Suykens, Johan A K; Wang, Shuning; Hornegger, Joachim; Maier, Andreas

2018-05-01

This brief proposes a truncated distance (TL1) kernel, which results in a classifier that is nonlinear in the global region but is linear in each subregion. With this kernel, the subregion structure can be trained using all the training data and local linear classifiers can be established simultaneously. The TL1 kernel has good adaptiveness to nonlinearity and is suitable for problems which require different nonlinearities in different areas. Though the TL1 kernel is not positive semidefinite, some classical kernel learning methods are still applicable which means that the TL1 kernel can be directly used in standard toolboxes by replacing the kernel evaluation. In numerical experiments, the TL1 kernel with a pregiven parameter achieves similar or better performance than the radial basis function kernel with the parameter tuned by cross validation, implying the TL1 kernel a promising nonlinear kernel for classification tasks.

FPGA Coprocessor for Accelerated Classification of Images

NASA Technical Reports Server (NTRS)

Pingree, Paula J.; Scharenbroich, Lucas J.; Werne, Thomas A.

2008-01-01

An effort related to that described in the preceding article focuses on developing a spaceborne processing platform for fast and accurate onboard classification of image data, a critical part of modern satellite image processing. The approach again has been to exploit the versatility of recently developed hybrid Virtex-4FX field-programmable gate array (FPGA) to run diverse science applications on embedded processors while taking advantage of the reconfigurable hardware resources of the FPGAs. In this case, the FPGA serves as a coprocessor that implements legacy C-language support-vector-machine (SVM) image-classification algorithms to detect and identify natural phenomena such as flooding, volcanic eruptions, and sea-ice break-up. The FPGA provides hardware acceleration for increased onboard processing capability than previously demonstrated in software. The original C-language program demonstrated on an imaging instrument aboard the Earth Observing-1 (EO-1) satellite implements a linear-kernel SVM algorithm for classifying parts of the images as snow, water, ice, land, or cloud or unclassified. Current onboard processors, such as on EO-1, have limited computing power, extremely limited active storage capability and are no longer considered state-of-the-art. Using commercially available software that translates C-language programs into hardware description language (HDL) files, the legacy C-language program, and two newly formulated programs for a more capable expanded-linear-kernel and a more accurate polynomial-kernel SVM algorithm, have been implemented in the Virtex-4FX FPGA. In tests, the FPGA implementations have exhibited significant speedups over conventional software implementations running on general-purpose hardware.

Deep kernel learning method for SAR image target recognition

NASA Astrophysics Data System (ADS)

Chen, Xiuyuan; Peng, Xiyuan; Duan, Ran; Li, Junbao

2017-10-01

With the development of deep learning, research on image target recognition has made great progress in recent years. Remote sensing detection urgently requires target recognition for military, geographic, and other scientific research. This paper aims to solve the synthetic aperture radar image target recognition problem by combining deep and kernel learning. The model, which has a multilayer multiple kernel structure, is optimized layer by layer with the parameters of Support Vector Machine and a gradient descent algorithm. This new deep kernel learning method improves accuracy and achieves competitive recognition results compared with other learning methods.

Searching Remote Homology with Spectral Clustering with Symmetry in Neighborhood Cluster Kernels

PubMed Central

Maulik, Ujjwal; Sarkar, Anasua

2013-01-01

Remote homology detection among proteins utilizing only the unlabelled sequences is a central problem in comparative genomics. The existing cluster kernel methods based on neighborhoods and profiles and the Markov clustering algorithms are currently the most popular methods for protein family recognition. The deviation from random walks with inflation or dependency on hard threshold in similarity measure in those methods requires an enhancement for homology detection among multi-domain proteins. We propose to combine spectral clustering with neighborhood kernels in Markov similarity for enhancing sensitivity in detecting homology independent of “recent” paralogs. The spectral clustering approach with new combined local alignment kernels more effectively exploits the unsupervised protein sequences globally reducing inter-cluster walks. When combined with the corrections based on modified symmetry based proximity norm deemphasizing outliers, the technique proposed in this article outperforms other state-of-the-art cluster kernels among all twelve implemented kernels. The comparison with the state-of-the-art string and mismatch kernels also show the superior performance scores provided by the proposed kernels. Similar performance improvement also is found over an existing large dataset. Therefore the proposed spectral clustering framework over combined local alignment kernels with modified symmetry based correction achieves superior performance for unsupervised remote homolog detection even in multi-domain and promiscuous domain proteins from Genolevures database families with better biological relevance. Source code available upon request. Contact: sarkar@labri.fr. PMID:23457439

Searching remote homology with spectral clustering with symmetry in neighborhood cluster kernels.

PubMed

Maulik, Ujjwal; Sarkar, Anasua

2013-01-01

Remote homology detection among proteins utilizing only the unlabelled sequences is a central problem in comparative genomics. The existing cluster kernel methods based on neighborhoods and profiles and the Markov clustering algorithms are currently the most popular methods for protein family recognition. The deviation from random walks with inflation or dependency on hard threshold in similarity measure in those methods requires an enhancement for homology detection among multi-domain proteins. We propose to combine spectral clustering with neighborhood kernels in Markov similarity for enhancing sensitivity in detecting homology independent of "recent" paralogs. The spectral clustering approach with new combined local alignment kernels more effectively exploits the unsupervised protein sequences globally reducing inter-cluster walks. When combined with the corrections based on modified symmetry based proximity norm deemphasizing outliers, the technique proposed in this article outperforms other state-of-the-art cluster kernels among all twelve implemented kernels. The comparison with the state-of-the-art string and mismatch kernels also show the superior performance scores provided by the proposed kernels. Similar performance improvement also is found over an existing large dataset. Therefore the proposed spectral clustering framework over combined local alignment kernels with modified symmetry based correction achieves superior performance for unsupervised remote homolog detection even in multi-domain and promiscuous domain proteins from Genolevures database families with better biological relevance. Source code available upon request. sarkar@labri.fr.

The Use of Generalized Laguerre Polynomials in Spectral Methods for Solving Fractional Delay Differential Equations.

PubMed

Khader, M M

2013-10-01

In this paper, an efficient numerical method for solving the fractional delay differential equations (FDDEs) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based on the derived approximate formula of the Laguerre polynomials. The properties of Laguerre polynomials are utilized to reduce FDDEs to a linear or nonlinear system of algebraic equations. Special attention is given to study the error and the convergence analysis of the proposed method. Several numerical examples are provided to confirm that the proposed method is in excellent agreement with the exact solution.

SU-E-T-104: An Examination of Dose in the Buildup and Build-Down Regions

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

Tome, W; Kuo, H; Phillips, J

2015-06-15

Purpose: To examine dose in the buildup and build-down regions and compare measurements made with various models and dosimeters Methods: Dose was examined in a 30×30cm {sup 2} phantom of water-equivalent plastic with 10cm of backscatter for various field sizes. Examination was performed with radiochromic film and optically-stimulated-luminescent-dosimeter (OSLD) chips, and compared against a plane-parallel chamber with a correction factor applied to approximate the response of an extrapolation chamber. For the build-down region, a correction factor to account for table absorption and chamber orientation in the posterior-anterior direction was applied. The measurement depths used for the film were halfway throughmore » their sensitive volumes, and a polynomial best fit curve was used to determine the dose to their surfaces. This chamber was also compared with the dose expected in a clinical kernel-based computer model, and a clinical Boltzmann-transport-equation-based (BTE) computer model. The two models were also compared against each other for cases with air gaps in the buildup region. Results: Within 3mm, all dosimeters and models agreed with the chamber within 10% for all field sizes. At the entrance surface, film differed in comparison with the chamber from +90% to +15%, the BTE-model by +140 to +3%, and the kernel-based model by +20% to −25%, decreasing with increasing field size. At the exit surface, film differed in comparison with the chamber from −10% to −15%, the BTE-model by −53% to −50%, the kernel-based model by −55% to −57%, mostly independent of field size. Conclusion: The largest differences compared with the chamber were found at the surface for all field sizes. Differences decreased with increasing field size and increasing depth in phantom. Air gaps in the buildup region cause dose buildup to occur again post-gap, but the effect decreases with increasing phantom thickness prior to the gap.« less

Volumetric calibration of a plenoptic camera

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

Hall, Elise Munz; Fahringer, Timothy W.; Guildenbecher, Daniel Robert

Here, the volumetric calibration of a plenoptic camera is explored to correct for inaccuracies due to real-world lens distortions and thin-lens assumptions in current processing methods. Two methods of volumetric calibration based on a polynomial mapping function that does not require knowledge of specific lens parameters are presented and compared to a calibration based on thin-lens assumptions. The first method, volumetric dewarping, is executed by creation of a volumetric representation of a scene using the thin-lens assumptions, which is then corrected in post-processing using a polynomial mapping function. The second method, direct light-field calibration, uses the polynomial mapping in creationmore » of the initial volumetric representation to relate locations in object space directly to image sensor locations. The accuracy and feasibility of these methods is examined experimentally by capturing images of a known dot card at a variety of depths. Results suggest that use of a 3D polynomial mapping function provides a significant increase in reconstruction accuracy and that the achievable accuracy is similar using either polynomial-mapping-based method. Additionally, direct light-field calibration provides significant computational benefits by eliminating some intermediate processing steps found in other methods. Finally, the flexibility of this method is shown for a nonplanar calibration.« less

Volumetric calibration of a plenoptic camera

DOE PAGES

Hall, Elise Munz; Fahringer, Timothy W.; Guildenbecher, Daniel Robert; ...

2018-02-01

Here, the volumetric calibration of a plenoptic camera is explored to correct for inaccuracies due to real-world lens distortions and thin-lens assumptions in current processing methods. Two methods of volumetric calibration based on a polynomial mapping function that does not require knowledge of specific lens parameters are presented and compared to a calibration based on thin-lens assumptions. The first method, volumetric dewarping, is executed by creation of a volumetric representation of a scene using the thin-lens assumptions, which is then corrected in post-processing using a polynomial mapping function. The second method, direct light-field calibration, uses the polynomial mapping in creationmore » of the initial volumetric representation to relate locations in object space directly to image sensor locations. The accuracy and feasibility of these methods is examined experimentally by capturing images of a known dot card at a variety of depths. Results suggest that use of a 3D polynomial mapping function provides a significant increase in reconstruction accuracy and that the achievable accuracy is similar using either polynomial-mapping-based method. Additionally, direct light-field calibration provides significant computational benefits by eliminating some intermediate processing steps found in other methods. Finally, the flexibility of this method is shown for a nonplanar calibration.« less

CW-SSIM kernel based random forest for image classification

NASA Astrophysics Data System (ADS)

Fan, Guangzhe; Wang, Zhou; Wang, Jiheng

2010-07-01

Complex wavelet structural similarity (CW-SSIM) index has been proposed as a powerful image similarity metric that is robust to translation, scaling and rotation of images, but how to employ it in image classification applications has not been deeply investigated. In this paper, we incorporate CW-SSIM as a kernel function into a random forest learning algorithm. This leads to a novel image classification approach that does not require a feature extraction or dimension reduction stage at the front end. We use hand-written digit recognition as an example to demonstrate our algorithm. We compare the performance of the proposed approach with random forest learning based on other kernels, including the widely adopted Gaussian and the inner product kernels. Empirical evidences show that the proposed method is superior in its classification power. We also compared our proposed approach with the direct random forest method without kernel and the popular kernel-learning method support vector machine. Our test results based on both simulated and realworld data suggest that the proposed approach works superior to traditional methods without the feature selection procedure.

Improving multivariate Horner schemes with Monte Carlo tree search

NASA Astrophysics Data System (ADS)

Kuipers, J.; Plaat, A.; Vermaseren, J. A. M.; van den Herik, H. J.

2013-11-01

Optimizing the cost of evaluating a polynomial is a classic problem in computer science. For polynomials in one variable, Horner's method provides a scheme for producing a computationally efficient form. For multivariate polynomials it is possible to generalize Horner's method, but this leaves freedom in the order of the variables. Traditionally, greedy schemes like most-occurring variable first are used. This simple textbook algorithm has given remarkably efficient results. Finding better algorithms has proved difficult. In trying to improve upon the greedy scheme we have implemented Monte Carlo tree search, a recent search method from the field of artificial intelligence. This results in better Horner schemes and reduces the cost of evaluating polynomials, sometimes by factors up to two.

Assessing the suitability of fractional polynomial methods in health services research: a perspective on the categorization epidemic.

PubMed

Williams, Jennifer Stewart

2011-07-01

To show how fractional polynomial methods can usefully replace the practice of arbitrarily categorizing data in epidemiology and health services research. A health service setting is used to illustrate a structured and transparent way of representing non-linear data without arbitrary grouping. When age is a regressor its effects on an outcome will be interpreted differently depending upon the placing of cutpoints or the use of a polynomial transformation. Although it is common practice, categorization comes at a cost. Information is lost, and accuracy and statistical power reduced, leading to spurious statistical interpretation of the data. The fractional polynomial method is widely supported by statistical software programs, and deserves greater attention and use.

Perceptually informed synthesis of bandlimited classical waveforms using integrated polynomial interpolation.

PubMed

Välimäki, Vesa; Pekonen, Jussi; Nam, Juhan

2012-01-01

Digital subtractive synthesis is a popular music synthesis method, which requires oscillators that are aliasing-free in a perceptual sense. It is a research challenge to find computationally efficient waveform generation algorithms that produce similar-sounding signals to analog music synthesizers but which are free from audible aliasing. A technique for approximately bandlimited waveform generation is considered that is based on a polynomial correction function, which is defined as the difference of a non-bandlimited step function and a polynomial approximation of the ideal bandlimited step function. It is shown that the ideal bandlimited step function is equivalent to the sine integral, and that integrated polynomial interpolation methods can successfully approximate it. Integrated Lagrange interpolation and B-spline basis functions are considered for polynomial approximation. The polynomial correction function can be added onto samples around each discontinuity in a non-bandlimited waveform to suppress aliasing. Comparison against previously known methods shows that the proposed technique yields the best tradeoff between computational cost and sound quality. The superior method amongst those considered in this study is the integrated third-order B-spline correction function, which offers perceptually aliasing-free sawtooth emulation up to the fundamental frequency of 7.8 kHz at the sample rate of 44.1 kHz. © 2012 Acoustical Society of America.

On Polynomial Solutions of Linear Differential Equations with Polynomial Coefficients

ERIC Educational Resources Information Center

Si, Do Tan

1977-01-01

Demonstrates a method for solving linear differential equations with polynomial coefficients based on the fact that the operators z and D + d/dz are known to be Hermitian conjugates with respect to the Bargman and Louck-Galbraith scalar products. (MLH)

On the Numerical Formulation of Parametric Linear Fractional Transformation (LFT) Uncertainty Models for Multivariate Matrix Polynomial Problems

NASA Technical Reports Server (NTRS)

Belcastro, Christine M.

1998-01-01

Robust control system analysis and design is based on an uncertainty description, called a linear fractional transformation (LFT), which separates the uncertain (or varying) part of the system from the nominal system. These models are also useful in the design of gain-scheduled control systems based on Linear Parameter Varying (LPV) methods. Low-order LFT models are difficult to form for problems involving nonlinear parameter variations. This paper presents a numerical computational method for constructing and LFT model for a given LPV model. The method is developed for multivariate polynomial problems, and uses simple matrix computations to obtain an exact low-order LFT representation of the given LPV system without the use of model reduction. Although the method is developed for multivariate polynomial problems, multivariate rational problems can also be solved using this method by reformulating the rational problem into a polynomial form.

SU-E-T-329: Dosimetric Impact of Implementing Metal Artifact Reduction Methods and Metal Energy Deposition Kernels for Photon Dose Calculations

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

Huang, J; Followill, D; Howell, R

2015-06-15

Purpose: To investigate two strategies for reducing dose calculation errors near metal implants: use of CT metal artifact reduction methods and implementation of metal-based energy deposition kernels in the convolution/superposition (C/S) method. Methods: Radiochromic film was used to measure the dose upstream and downstream of titanium and Cerrobend implants. To assess the dosimetric impact of metal artifact reduction methods, dose calculations were performed using baseline, uncorrected images and metal artifact reduction Methods: Philips O-MAR, GE’s monochromatic gemstone spectral imaging (GSI) using dual-energy CT, and GSI imaging with metal artifact reduction software applied (MARs).To assess the impact of metal kernels, titaniummore » and silver kernels were implemented into a commercial collapsed cone C/S algorithm. Results: The CT artifact reduction methods were more successful for titanium than Cerrobend. Interestingly, for beams traversing the metal implant, we found that errors in the dimensions of the metal in the CT images were more important for dose calculation accuracy than reduction of imaging artifacts. The MARs algorithm caused a distortion in the shape of the titanium implant that substantially worsened the calculation accuracy. In comparison to water kernel dose calculations, metal kernels resulted in better modeling of the increased backscatter dose at the upstream interface but decreased accuracy directly downstream of the metal. We also found that the success of metal kernels was dependent on dose grid size, with smaller calculation voxels giving better accuracy. Conclusion: Our study yielded mixed results, with neither the metal artifact reduction methods nor the metal kernels being globally effective at improving dose calculation accuracy. However, some successes were observed. The MARs algorithm decreased errors downstream of Cerrobend by a factor of two, and metal kernels resulted in more accurate backscatter dose upstream of metals. Thus, these two strategies do have the potential to improve accuracy for patients with metal implants in certain scenarios. This work was supported by Public Health Service grants CA 180803 and CA 10953 awarded by the National Cancer Institute, United States of Health and Human Services, and in part by Mobius Medical Systems.« less

Polynomial probability distribution estimation using the method of moments

PubMed Central

Mattsson, Lars; Rydén, Jesper

2017-01-01

We suggest a procedure for estimating Nth degree polynomial approximations to unknown (or known) probability density functions (PDFs) based on N statistical moments from each distribution. The procedure is based on the method of moments and is setup algorithmically to aid applicability and to ensure rigor in use. In order to show applicability, polynomial PDF approximations are obtained for the distribution families Normal, Log-Normal, Weibull as well as for a bimodal Weibull distribution and a data set of anonymized household electricity use. The results are compared with results for traditional PDF series expansion methods of Gram–Charlier type. It is concluded that this procedure is a comparatively simple procedure that could be used when traditional distribution families are not applicable or when polynomial expansions of probability distributions might be considered useful approximations. In particular this approach is practical for calculating convolutions of distributions, since such operations become integrals of polynomial expressions. Finally, in order to show an advanced applicability of the method, it is shown to be useful for approximating solutions to the Smoluchowski equation. PMID:28394949

Polynomial probability distribution estimation using the method of moments.

PubMed

Munkhammar, Joakim; Mattsson, Lars; Rydén, Jesper

2017-01-01

We suggest a procedure for estimating Nth degree polynomial approximations to unknown (or known) probability density functions (PDFs) based on N statistical moments from each distribution. The procedure is based on the method of moments and is setup algorithmically to aid applicability and to ensure rigor in use. In order to show applicability, polynomial PDF approximations are obtained for the distribution families Normal, Log-Normal, Weibull as well as for a bimodal Weibull distribution and a data set of anonymized household electricity use. The results are compared with results for traditional PDF series expansion methods of Gram-Charlier type. It is concluded that this procedure is a comparatively simple procedure that could be used when traditional distribution families are not applicable or when polynomial expansions of probability distributions might be considered useful approximations. In particular this approach is practical for calculating convolutions of distributions, since such operations become integrals of polynomial expressions. Finally, in order to show an advanced applicability of the method, it is shown to be useful for approximating solutions to the Smoluchowski equation.

Non-stationary component extraction in noisy multicomponent signal using polynomial chirping Fourier transform.

PubMed

Lu, Wenlong; Xie, Junwei; Wang, Heming; Sheng, Chuan

2016-01-01

Inspired by track-before-detection technology in radar, a novel time-frequency transform, namely polynomial chirping Fourier transform (PCFT), is exploited to extract components from noisy multicomponent signal. The PCFT combines advantages of Fourier transform and polynomial chirplet transform to accumulate component energy along a polynomial chirping curve in the time-frequency plane. The particle swarm optimization algorithm is employed to search optimal polynomial parameters with which the PCFT will achieve a most concentrated energy ridge in the time-frequency plane for the target component. The component can be well separated in the polynomial chirping Fourier domain with a narrow-band filter and then reconstructed by inverse PCFT. Furthermore, an iterative procedure, involving parameter estimation, PCFT, filtering and recovery, is introduced to extract components from a noisy multicomponent signal successively. The Simulations and experiments show that the proposed method has better performance in component extraction from noisy multicomponent signal as well as provides more time-frequency details about the analyzed signal than conventional methods.

Seeing It All: Evaluating Supervised Machine Learning Methods for the Classification of Diverse Otariid Behaviours

PubMed Central

Slip, David J.; Hocking, David P.; Harcourt, Robert G.

2016-01-01

Constructing activity budgets for marine animals when they are at sea and cannot be directly observed is challenging, but recent advances in bio-logging technology offer solutions to this problem. Accelerometers can potentially identify a wide range of behaviours for animals based on unique patterns of acceleration. However, when analysing data derived from accelerometers, there are many statistical techniques available which when applied to different data sets produce different classification accuracies. We investigated a selection of supervised machine learning methods for interpreting behavioural data from captive otariids (fur seals and sea lions). We conducted controlled experiments with 12 seals, where their behaviours were filmed while they were wearing 3-axis accelerometers. From video we identified 26 behaviours that could be grouped into one of four categories (foraging, resting, travelling and grooming) representing key behaviour states for wild seals. We used data from 10 seals to train four predictive classification models: stochastic gradient boosting (GBM), random forests, support vector machine using four different kernels and a baseline model: penalised logistic regression. We then took the best parameters from each model and cross-validated the results on the two seals unseen so far. We also investigated the influence of feature statistics (describing some characteristic of the seal), testing the models both with and without these. Cross-validation accuracies were lower than training accuracy, but the SVM with a polynomial kernel was still able to classify seal behaviour with high accuracy (>70%). Adding feature statistics improved accuracies across all models tested. Most categories of behaviour -resting, grooming and feeding—were all predicted with reasonable accuracy (52–81%) by the SVM while travelling was poorly categorised (31–41%). These results show that model selection is important when classifying behaviour and that by using animal characteristics we can strengthen the overall accuracy. PMID:28002450

Comparative Analysis of Various Single-tone Frequency Estimation Techniques in High-order Instantaneous Moments Based Phase Estimation Method

NASA Astrophysics Data System (ADS)

Rajshekhar, G.; Gorthi, Sai Siva; Rastogi, Pramod

2010-04-01

For phase estimation in digital holographic interferometry, a high-order instantaneous moments (HIM) based method was recently developed which relies on piecewise polynomial approximation of phase and subsequent evaluation of the polynomial coefficients using the HIM operator. A crucial step in the method is mapping the polynomial coefficient estimation to single-tone frequency determination for which various techniques exist. The paper presents a comparative analysis of the performance of the HIM operator based method in using different single-tone frequency estimation techniques for phase estimation. The analysis is supplemented by simulation results.

Estimation of Phase in Fringe Projection Technique Using High-order Instantaneous Moments Based Method

NASA Astrophysics Data System (ADS)

Gorthi, Sai Siva; Rajshekhar, G.; Rastogi, Pramod

2010-04-01

For three-dimensional (3D) shape measurement using fringe projection techniques, the information about the 3D shape of an object is encoded in the phase of a recorded fringe pattern. The paper proposes a high-order instantaneous moments based method to estimate phase from a single fringe pattern in fringe projection. The proposed method works by approximating the phase as a piece-wise polynomial and subsequently determining the polynomial coefficients using high-order instantaneous moments to construct the polynomial phase. Simulation results are presented to show the method's potential.

Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach

NASA Astrophysics Data System (ADS)

Nasiri, Alireza; Nguang, Sing Kiong; Swain, Akshya; Almakhles, Dhafer

2018-02-01

This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller.

Multidimensional NMR inversion without Kronecker products: Multilinear inversion

NASA Astrophysics Data System (ADS)

Medellín, David; Ravi, Vivek R.; Torres-Verdín, Carlos

2016-08-01

Multidimensional NMR inversion using Kronecker products poses several challenges. First, kernel compression is only possible when the kernel matrices are separable, and in recent years, there has been an increasing interest in NMR sequences with non-separable kernels. Second, in three or more dimensions, the singular value decomposition is not unique; therefore kernel compression is not well-defined for higher dimensions. Without kernel compression, the Kronecker product yields matrices that require large amounts of memory, making the inversion intractable for personal computers. Finally, incorporating arbitrary regularization terms is not possible using the Lawson-Hanson (LH) or the Butler-Reeds-Dawson (BRD) algorithms. We develop a minimization-based inversion method that circumvents the above problems by using multilinear forms to perform multidimensional NMR inversion without using kernel compression or Kronecker products. The new method is memory efficient, requiring less than 0.1% of the memory required by the LH or BRD methods. It can also be extended to arbitrary dimensions and adapted to include non-separable kernels, linear constraints, and arbitrary regularization terms. Additionally, it is easy to implement because only a cost function and its first derivative are required to perform the inversion.

Adaptive kernel function using line transect sampling

NASA Astrophysics Data System (ADS)

Albadareen, Baker; Ismail, Noriszura

2018-04-01

The estimation of f(0) is crucial in the line transect method which is used for estimating population abundance in wildlife survey's. The classical kernel estimator of f(0) has a high negative bias. Our study proposes an adaptation in the kernel function which is shown to be more efficient than the usual kernel estimator. A simulation study is adopted to compare the performance of the proposed estimators with the classical kernel estimators.

Local polynomial estimation of heteroscedasticity in a multivariate linear regression model and its applications in economics.

PubMed

Su, Liyun; Zhao, Yanyong; Yan, Tianshun; Li, Fenglan

2012-01-01

Multivariate local polynomial fitting is applied to the multivariate linear heteroscedastic regression model. Firstly, the local polynomial fitting is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. One noteworthy feature of our approach is that we avoid the testing for heteroscedasticity by improving the traditional two-stage method. Due to non-parametric technique of local polynomial estimation, it is unnecessary to know the form of heteroscedastic function. Therefore, we can improve the estimation precision, when the heteroscedastic function is unknown. Furthermore, we verify that the regression coefficients is asymptotic normal based on numerical simulations and normal Q-Q plots of residuals. Finally, the simulation results and the local polynomial estimation of real data indicate that our approach is surely effective in finite-sample situations.

Recursive approach to the moment-based phase unwrapping method.

PubMed

Langley, Jason A; Brice, Robert G; Zhao, Qun

2010-06-01

The moment-based phase unwrapping algorithm approximates the phase map as a product of Gegenbauer polynomials, but the weight function for the Gegenbauer polynomials generates artificial singularities along the edge of the phase map. A method is presented to remove the singularities inherent to the moment-based phase unwrapping algorithm by approximating the phase map as a product of two one-dimensional Legendre polynomials and applying a recursive property of derivatives of Legendre polynomials. The proposed phase unwrapping algorithm is tested on simulated and experimental data sets. The results are then compared to those of PRELUDE 2D, a widely used phase unwrapping algorithm, and a Chebyshev-polynomial-based phase unwrapping algorithm. It was found that the proposed phase unwrapping algorithm provides results that are comparable to those obtained by using PRELUDE 2D and the Chebyshev phase unwrapping algorithm.

Weierstrass method for quaternionic polynomial root-finding

NASA Astrophysics Data System (ADS)

Falcão, M. Irene; Miranda, Fernando; Severino, Ricardo; Soares, M. Joana

2018-01-01

Quaternions, introduced by Hamilton in 1843 as a generalization of complex numbers, have found, in more recent years, a wealth of applications in a number of different areas which motivated the design of efficient methods for numerically approximating the zeros of quaternionic polynomials. In fact, one can find in the literature recent contributions to this subject based on the use of complex techniques, but numerical methods relying on quaternion arithmetic remain scarce. In this paper we propose a Weierstrass-like method for finding simultaneously {\\sl all} the zeros of unilateral quaternionic polynomials. The convergence analysis and several numerical examples illustrating the performance of the method are also presented.

Performance Assessment of Kernel Density Clustering for Gene Expression Profile Data

PubMed Central

Zeng, Beiyan; Chen, Yiping P.; Smith, Oscar H.

2003-01-01

Kernel density smoothing techniques have been used in classification or supervised learning of gene expression profile (GEP) data, but their applications to clustering or unsupervised learning of those data have not been explored and assessed. Here we report a kernel density clustering method for analysing GEP data and compare its performance with the three most widely-used clustering methods: hierarchical clustering, K-means clustering, and multivariate mixture model-based clustering. Using several methods to measure agreement, between-cluster isolation, and withincluster coherence, such as the Adjusted Rand Index, the Pseudo F test, the r2 test, and the profile plot, we have assessed the effectiveness of kernel density clustering for recovering clusters, and its robustness against noise on clustering both simulated and real GEP data. Our results show that the kernel density clustering method has excellent performance in recovering clusters from simulated data and in grouping large real expression profile data sets into compact and well-isolated clusters, and that it is the most robust clustering method for analysing noisy expression profile data compared to the other three methods assessed. PMID:18629292

Chebyshev polynomials in the spectral Tau method and applications to Eigenvalue problems

NASA Technical Reports Server (NTRS)

Johnson, Duane

1996-01-01

Chebyshev Spectral methods have received much attention recently as a technique for the rapid solution of ordinary differential equations. This technique also works well for solving linear eigenvalue problems. Specific detail is given to the properties and algebra of chebyshev polynomials; the use of chebyshev polynomials in spectral methods; and the recurrence relationships that are developed. These formula and equations are then applied to several examples which are worked out in detail. The appendix contains an example FORTRAN program used in solving an eigenvalue problem.

Anatomical image-guided fluorescence molecular tomography reconstruction using kernel method

NASA Astrophysics Data System (ADS)

Baikejiang, Reheman; Zhao, Yue; Fite, Brett Z.; Ferrara, Katherine W.; Li, Changqing

2017-05-01

Fluorescence molecular tomography (FMT) is an important in vivo imaging modality to visualize physiological and pathological processes in small animals. However, FMT reconstruction is ill-posed and ill-conditioned due to strong optical scattering in deep tissues, which results in poor spatial resolution. It is well known that FMT image quality can be improved substantially by applying the structural guidance in the FMT reconstruction. An approach to introducing anatomical information into the FMT reconstruction is presented using the kernel method. In contrast to conventional methods that incorporate anatomical information with a Laplacian-type regularization matrix, the proposed method introduces the anatomical guidance into the projection model of FMT. The primary advantage of the proposed method is that it does not require segmentation of targets in the anatomical images. Numerical simulations and phantom experiments have been performed to demonstrate the proposed approach's feasibility. Numerical simulation results indicate that the proposed kernel method can separate two FMT targets with an edge-to-edge distance of 1 mm and is robust to false-positive guidance and inhomogeneity in the anatomical image. For the phantom experiments with two FMT targets, the kernel method has reconstructed both targets successfully, which further validates the proposed kernel method.

Anthraquinones isolated from the browned Chinese chestnut kernels (Castanea mollissima blume)

NASA Astrophysics Data System (ADS)

Zhang, Y. L.; Qi, J. H.; Qin, L.; Wang, F.; Pang, M. X.

2016-08-01

Anthraquinones (AQS) represent a group of secondary metallic products in plants. AQS are often naturally occurring in plants and microorganisms. In a previous study, we found that AQS were produced by enzymatic browning reaction in Chinese chestnut kernels. To find out whether non-enzymatic browning reaction in the kernels could produce AQS too, AQS were extracted from three groups of chestnut kernels: fresh kernels, non-enzymatic browned kernels, and browned kernels, and the contents of AQS were determined. High performance liquid chromatography (HPLC) and nuclear magnetic resonance (NMR) methods were used to identify two compounds of AQS, rehein(1) and emodin(2). AQS were barely exists in the fresh kernels, while both browned kernel groups sample contained a high amount of AQS. Thus, we comfirmed that AQS could be produced during both enzymatic and non-enzymatic browning process. Rhein and emodin were the main components of AQS in the browned kernels.

A Stochastic Mixed Finite Element Heterogeneous Multiscale Method for Flow in Porous Media

DTIC Science & Technology

2010-08-01

applicable for flow in porous media has drawn significant interest in the last few years. Several techniques like generalized polynomial chaos expansions (gPC...represents the stochastic solution as a polynomial approxima- tion. This interpolant is constructed via independent function calls to the de- terministic...of orthogonal polynomials [34,38] or sparse grid approximations [39–41]. It is well known that the global polynomial interpolation cannot resolve lo

Dynamic characteristics of oxygen consumption.

PubMed

Ye, Lin; Argha, Ahmadreza; Yu, Hairong; Celler, Branko G; Nguyen, Hung T; Su, Steven

2018-04-23

Previous studies have indicated that oxygen uptake ([Formula: see text]) is one of the most accurate indices for assessing the cardiorespiratory response to exercise. In most existing studies, the response of [Formula: see text] is often roughly modelled as a first-order system due to the inadequate stimulation and low signal to noise ratio. To overcome this difficulty, this paper proposes a novel nonparametric kernel-based method for the dynamic modelling of [Formula: see text] response to provide a more robust estimation. Twenty healthy non-athlete participants conducted treadmill exercises with monotonous stimulation (e.g., single step function as input). During the exercise, [Formula: see text] was measured and recorded by a popular portable gas analyser ([Formula: see text], COSMED). Based on the recorded data, a kernel-based estimation method was proposed to perform the nonparametric modelling of [Formula: see text]. For the proposed method, a properly selected kernel can represent the prior modelling information to reduce the dependence of comprehensive stimulations. Furthermore, due to the special elastic net formed by [Formula: see text] norm and kernelised [Formula: see text] norm, the estimations are smooth and concise. Additionally, the finite impulse response based nonparametric model which estimated by the proposed method can optimally select the order and fit better in terms of goodness-of-fit comparing to classical methods. Several kernels were introduced for the kernel-based [Formula: see text] modelling method. The results clearly indicated that the stable spline (SS) kernel has the best performance for [Formula: see text] modelling. Particularly, based on the experimental data from 20 participants, the estimated response from the proposed method with SS kernel was significantly better than the results from the benchmark method [i.e., prediction error method (PEM)] ([Formula: see text] vs [Formula: see text]). The proposed nonparametric modelling method is an effective method for the estimation of the impulse response of VO 2 -Speed system. Furthermore, the identified average nonparametric model method can dynamically predict [Formula: see text] response with acceptable accuracy during treadmill exercise.

Kernel reconstruction methods for Doppler broadening - Temperature interpolation by linear combination of reference cross sections at optimally chosen temperatures

NASA Astrophysics Data System (ADS)

Ducru, Pablo; Josey, Colin; Dibert, Karia; Sobes, Vladimir; Forget, Benoit; Smith, Kord

2017-04-01

This article establishes a new family of methods to perform temperature interpolation of nuclear interactions cross sections, reaction rates, or cross sections times the energy. One of these quantities at temperature T is approximated as a linear combination of quantities at reference temperatures (Tj). The problem is formalized in a cross section independent fashion by considering the kernels of the different operators that convert cross section related quantities from a temperature T0 to a higher temperature T - namely the Doppler broadening operation. Doppler broadening interpolation of nuclear cross sections is thus here performed by reconstructing the kernel of the operation at a given temperature T by means of linear combination of kernels at reference temperatures (Tj). The choice of the L2 metric yields optimal linear interpolation coefficients in the form of the solutions of a linear algebraic system inversion. The optimization of the choice of reference temperatures (Tj) is then undertaken so as to best reconstruct, in the L∞ sense, the kernels over a given temperature range [Tmin ,Tmax ]. The performance of these kernel reconstruction methods is then assessed in light of previous temperature interpolation methods by testing them upon isotope 238U. Temperature-optimized free Doppler kernel reconstruction significantly outperforms all previous interpolation-based methods, achieving 0.1% relative error on temperature interpolation of 238U total cross section over the temperature range [ 300 K , 3000 K ] with only 9 reference temperatures.

Online selective kernel-based temporal difference learning.

PubMed

Chen, Xingguo; Gao, Yang; Wang, Ruili

2013-12-01

In this paper, an online selective kernel-based temporal difference (OSKTD) learning algorithm is proposed to deal with large scale and/or continuous reinforcement learning problems. OSKTD includes two online procedures: online sparsification and parameter updating for the selective kernel-based value function. A new sparsification method (i.e., a kernel distance-based online sparsification method) is proposed based on selective ensemble learning, which is computationally less complex compared with other sparsification methods. With the proposed sparsification method, the sparsified dictionary of samples is constructed online by checking if a sample needs to be added to the sparsified dictionary. In addition, based on local validity, a selective kernel-based value function is proposed to select the best samples from the sample dictionary for the selective kernel-based value function approximator. The parameters of the selective kernel-based value function are iteratively updated by using the temporal difference (TD) learning algorithm combined with the gradient descent technique. The complexity of the online sparsification procedure in the OSKTD algorithm is O(n). In addition, two typical experiments (Maze and Mountain Car) are used to compare with both traditional and up-to-date O(n) algorithms (GTD, GTD2, and TDC using the kernel-based value function), and the results demonstrate the effectiveness of our proposed algorithm. In the Maze problem, OSKTD converges to an optimal policy and converges faster than both traditional and up-to-date algorithms. In the Mountain Car problem, OSKTD converges, requires less computation time compared with other sparsification methods, gets a better local optima than the traditional algorithms, and converges much faster than the up-to-date algorithms. In addition, OSKTD can reach a competitive ultimate optima compared with the up-to-date algorithms.

Protein fold recognition using geometric kernel data fusion.

PubMed

Zakeri, Pooya; Jeuris, Ben; Vandebril, Raf; Moreau, Yves

2014-07-01

Various approaches based on features extracted from protein sequences and often machine learning methods have been used in the prediction of protein folds. Finding an efficient technique for integrating these different protein features has received increasing attention. In particular, kernel methods are an interesting class of techniques for integrating heterogeneous data. Various methods have been proposed to fuse multiple kernels. Most techniques for multiple kernel learning focus on learning a convex linear combination of base kernels. In addition to the limitation of linear combinations, working with such approaches could cause a loss of potentially useful information. We design several techniques to combine kernel matrices by taking more involved, geometry inspired means of these matrices instead of convex linear combinations. We consider various sequence-based protein features including information extracted directly from position-specific scoring matrices and local sequence alignment. We evaluate our methods for classification on the SCOP PDB-40D benchmark dataset for protein fold recognition. The best overall accuracy on the protein fold recognition test set obtained by our methods is ∼ 86.7%. This is an improvement over the results of the best existing approach. Moreover, our computational model has been developed by incorporating the functional domain composition of proteins through a hybridization model. It is observed that by using our proposed hybridization model, the protein fold recognition accuracy is further improved to 89.30%. Furthermore, we investigate the performance of our approach on the protein remote homology detection problem by fusing multiple string kernels. The MATLAB code used for our proposed geometric kernel fusion frameworks are publicly available at http://people.cs.kuleuven.be/∼raf.vandebril/homepage/software/geomean.php?menu=5/. © The Author 2014. Published by Oxford University Press.

Classification of autism spectrum disorder using supervised learning of brain connectivity measures extracted from synchrostates

NASA Astrophysics Data System (ADS)

Jamal, Wasifa; Das, Saptarshi; Oprescu, Ioana-Anastasia; Maharatna, Koushik; Apicella, Fabio; Sicca, Federico

2014-08-01

Objective. The paper investigates the presence of autism using the functional brain connectivity measures derived from electro-encephalogram (EEG) of children during face perception tasks. Approach. Phase synchronized patterns from 128-channel EEG signals are obtained for typical children and children with autism spectrum disorder (ASD). The phase synchronized states or synchrostates temporally switch amongst themselves as an underlying process for the completion of a particular cognitive task. We used 12 subjects in each group (ASD and typical) for analyzing their EEG while processing fearful, happy and neutral faces. The minimal and maximally occurring synchrostates for each subject are chosen for extraction of brain connectivity features, which are used for classification between these two groups of subjects. Among different supervised learning techniques, we here explored the discriminant analysis and support vector machine both with polynomial kernels for the classification task. Main results. The leave one out cross-validation of the classification algorithm gives 94.7% accuracy as the best performance with corresponding sensitivity and specificity values as 85.7% and 100% respectively. Significance. The proposed method gives high classification accuracies and outperforms other contemporary research results. The effectiveness of the proposed method for classification of autistic and typical children suggests the possibility of using it on a larger population to validate it for clinical practice.

Automated diagnosis of dry eye using infrared thermography images

NASA Astrophysics Data System (ADS)

Acharya, U. Rajendra; Tan, Jen Hong; Koh, Joel E. W.; Sudarshan, Vidya K.; Yeo, Sharon; Too, Cheah Loon; Chua, Chua Kuang; Ng, E. Y. K.; Tong, Louis

2015-07-01

Dry Eye (DE) is a condition of either decreased tear production or increased tear film evaporation. Prolonged DE damages the cornea causing the corneal scarring, thinning and perforation. There is no single uniform diagnosis test available to date; combinations of diagnostic tests are to be performed to diagnose DE. The current diagnostic methods available are subjective, uncomfortable and invasive. Hence in this paper, we have developed an efficient, fast and non-invasive technique for the automated identification of normal and DE classes using infrared thermography images. The features are extracted from nonlinear method called Higher Order Spectra (HOS). Features are ranked using t-test ranking strategy. These ranked features are fed to various classifiers namely, K-Nearest Neighbor (KNN), Nave Bayesian Classifier (NBC), Decision Tree (DT), Probabilistic Neural Network (PNN), and Support Vector Machine (SVM) to select the best classifier using minimum number of features. Our proposed system is able to identify the DE and normal classes automatically with classification accuracy of 99.8%, sensitivity of 99.8%, and specificity if 99.8% for left eye using PNN and KNN classifiers. And we have reported classification accuracy of 99.8%, sensitivity of 99.9%, and specificity if 99.4% for right eye using SVM classifier with polynomial order 2 kernel.

Interpolation for de-Dopplerisation

NASA Astrophysics Data System (ADS)

Graham, W. R.

2018-05-01

'De-Dopplerisation' is one aspect of a problem frequently encountered in experimental acoustics: deducing an emitted source signal from received data. It is necessary when source and receiver are in relative motion, and requires interpolation of the measured signal. This introduces error. In acoustics, typical current practice is to employ linear interpolation and reduce error by over-sampling. In other applications, more advanced approaches with better performance have been developed. Associated with this work is a large body of theoretical analysis, much of which is highly specialised. Nonetheless, a simple and compact performance metric is available: the Fourier transform of the 'kernel' function underlying the interpolation method. Furthermore, in the acoustics context, it is a more appropriate indicator than other, more abstract, candidates. On this basis, interpolators from three families previously identified as promising - - piecewise-polynomial, windowed-sinc, and B-spline-based - - are compared. The results show that significant improvements over linear interpolation can straightforwardly be obtained. The recommended approach is B-spline-based interpolation, which performs best irrespective of accuracy specification. Its only drawback is a pre-filtering requirement, which represents an additional implementation cost compared to other methods. If this cost is unacceptable, and aliasing errors (on re-sampling) up to approximately 1% can be tolerated, a family of piecewise-cubic interpolators provides the best alternative.

a Unified Matrix Polynomial Approach to Modal Identification

NASA Astrophysics Data System (ADS)

Allemang, R. J.; Brown, D. L.

1998-04-01

One important current focus of modal identification is a reformulation of modal parameter estimation algorithms into a single, consistent mathematical formulation with a corresponding set of definitions and unifying concepts. Particularly, a matrix polynomial approach is used to unify the presentation with respect to current algorithms such as the least-squares complex exponential (LSCE), the polyreference time domain (PTD), Ibrahim time domain (ITD), eigensystem realization algorithm (ERA), rational fraction polynomial (RFP), polyreference frequency domain (PFD) and the complex mode indication function (CMIF) methods. Using this unified matrix polynomial approach (UMPA) allows a discussion of the similarities and differences of the commonly used methods. the use of least squares (LS), total least squares (TLS), double least squares (DLS) and singular value decomposition (SVD) methods is discussed in order to take advantage of redundant measurement data. Eigenvalue and SVD transformation methods are utilized to reduce the effective size of the resulting eigenvalue-eigenvector problem as well.

On polynomial selection for the general number field sieve

NASA Astrophysics Data System (ADS)

Kleinjung, Thorsten

2006-12-01

The general number field sieve (GNFS) is the asymptotically fastest algorithm for factoring large integers. Its runtime depends on a good choice of a polynomial pair. In this article we present an improvement of the polynomial selection method of Montgomery and Murphy which has been used in recent GNFS records.

Putting Priors in Mixture Density Mercer Kernels

NASA Technical Reports Server (NTRS)

Srivastava, Ashok N.; Schumann, Johann; Fischer, Bernd

2004-01-01

This paper presents a new methodology for automatic knowledge driven data mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly infinite dimensional feature space. We describe a new method called Mixture Density Mercer Kernels to learn kernel function directly from data, rather than using predefined kernels. These data adaptive kernels can en- code prior knowledge in the kernel using a Bayesian formulation, thus allowing for physical information to be encoded in the model. We compare the results with existing algorithms on data from the Sloan Digital Sky Survey (SDSS). The code for these experiments has been generated with the AUTOBAYES tool, which automatically generates efficient and documented C/C++ code from abstract statistical model specifications. The core of the system is a schema library which contains template for learning and knowledge discovery algorithms like different versions of EM, or numeric optimization methods like conjugate gradient methods. The template instantiation is supported by symbolic- algebraic computations, which allows AUTOBAYES to find closed-form solutions and, where possible, to integrate them into the code. The results show that the Mixture Density Mercer-Kernel described here outperforms tree-based classification in distinguishing high-redshift galaxies from low- redshift galaxies by approximately 16% on test data, bagged trees by approximately 7%, and bagged trees built on a much larger sample of data by approximately 2%.

Approximate l-fold cross-validation with Least Squares SVM and Kernel Ridge Regression

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

Edwards, Richard E; Zhang, Hao; Parker, Lynne Edwards

2013-01-01

Kernel methods have difficulties scaling to large modern data sets. The scalability issues are based on computational and memory requirements for working with a large matrix. These requirements have been addressed over the years by using low-rank kernel approximations or by improving the solvers scalability. However, Least Squares Support VectorMachines (LS-SVM), a popular SVM variant, and Kernel Ridge Regression still have several scalability issues. In particular, the O(n^3) computational complexity for solving a single model, and the overall computational complexity associated with tuning hyperparameters are still major problems. We address these problems by introducing an O(n log n) approximate l-foldmore » cross-validation method that uses a multi-level circulant matrix to approximate the kernel. In addition, we prove our algorithm s computational complexity and present empirical runtimes on data sets with approximately 1 million data points. We also validate our approximate method s effectiveness at selecting hyperparameters on real world and standard benchmark data sets. Lastly, we provide experimental results on using a multi-level circulant kernel approximation to solve LS-SVM problems with hyperparameters selected using our method.« less

A Kernel-based Lagrangian method for imperfectly-mixed chemical reactions

NASA Astrophysics Data System (ADS)

Schmidt, Michael J.; Pankavich, Stephen; Benson, David A.

2017-05-01

Current Lagrangian (particle-tracking) algorithms used to simulate diffusion-reaction equations must employ a certain number of particles to properly emulate the system dynamics-particularly for imperfectly-mixed systems. The number of particles is tied to the statistics of the initial concentration fields of the system at hand. Systems with shorter-range correlation and/or smaller concentration variance require more particles, potentially limiting the computational feasibility of the method. For the well-known problem of bimolecular reaction, we show that using kernel-based, rather than Dirac delta, particles can significantly reduce the required number of particles. We derive the fixed width of a Gaussian kernel for a given reduced number of particles that analytically eliminates the error between kernel and Dirac solutions at any specified time. We also show how to solve for the fixed kernel size by minimizing the squared differences between solutions over any given time interval. Numerical results show that the width of the kernel should be kept below about 12% of the domain size, and that the analytic equations used to derive kernel width suffer significantly from the neglect of higher-order moments. The simulations with a kernel width given by least squares minimization perform better than those made to match at one specific time. A heuristic time-variable kernel size, based on the previous results, performs on par with the least squares fixed kernel size.

Metabolite identification through multiple kernel learning on fragmentation trees.

PubMed

Shen, Huibin; Dührkop, Kai; Böcker, Sebastian; Rousu, Juho

2014-06-15

Metabolite identification from tandem mass spectrometric data is a key task in metabolomics. Various computational methods have been proposed for the identification of metabolites from tandem mass spectra. Fragmentation tree methods explore the space of possible ways in which the metabolite can fragment, and base the metabolite identification on scoring of these fragmentation trees. Machine learning methods have been used to map mass spectra to molecular fingerprints; predicted fingerprints, in turn, can be used to score candidate molecular structures. Here, we combine fragmentation tree computations with kernel-based machine learning to predict molecular fingerprints and identify molecular structures. We introduce a family of kernels capturing the similarity of fragmentation trees, and combine these kernels using recently proposed multiple kernel learning approaches. Experiments on two large reference datasets show that the new methods significantly improve molecular fingerprint prediction accuracy. These improvements result in better metabolite identification, doubling the number of metabolites ranked at the top position of the candidates list. © The Author 2014. Published by Oxford University Press.

Half-blind remote sensing image restoration with partly unknown degradation

NASA Astrophysics Data System (ADS)

Xie, Meihua; Yan, Fengxia

2017-01-01

The problem of image restoration has been extensively studied for its practical importance and theoretical interest. This paper mainly discusses the problem of image restoration with partly unknown kernel. In this model, the degraded kernel function is known but its parameters are unknown. With this model, we should estimate the parameters in Gaussian kernel and the real image simultaneity. For this new problem, a total variation restoration model is put out and an intersect direction iteration algorithm is designed. Peak Signal to Noise Ratio (PSNR) and Structural Similarity Index Measurement (SSIM) are used to measure the performance of the method. Numerical results show that we can estimate the parameters in kernel accurately, and the new method has both much higher PSNR and much higher SSIM than the expectation maximization (EM) method in many cases. In addition, the accuracy of estimation is not sensitive to noise. Furthermore, even though the support of the kernel is unknown, we can also use this method to get accurate estimation.

Coronary Stent Artifact Reduction with an Edge-Enhancing Reconstruction Kernel - A Prospective Cross-Sectional Study with 256-Slice CT.

PubMed

Tan, Stéphanie; Soulez, Gilles; Diez Martinez, Patricia; Larrivée, Sandra; Stevens, Louis-Mathieu; Goussard, Yves; Mansour, Samer; Chartrand-Lefebvre, Carl

2016-01-01

Metallic artifacts can result in an artificial thickening of the coronary stent wall which can significantly impair computed tomography (CT) imaging in patients with coronary stents. The objective of this study is to assess in vivo visualization of coronary stent wall and lumen with an edge-enhancing CT reconstruction kernel, as compared to a standard kernel. This is a prospective cross-sectional study involving the assessment of 71 coronary stents (24 patients), with blinded observers. After 256-slice CT angiography, image reconstruction was done with medium-smooth and edge-enhancing kernels. Stent wall thickness was measured with both orthogonal and circumference methods, averaging thickness from diameter and circumference measurements, respectively. Image quality was assessed quantitatively using objective parameters (noise, signal to noise (SNR) and contrast to noise (CNR) ratios), as well as visually using a 5-point Likert scale. Stent wall thickness was decreased with the edge-enhancing kernel in comparison to the standard kernel, either with the orthogonal (0.97 ± 0.02 versus 1.09 ± 0.03 mm, respectively; p<0.001) or the circumference method (1.13 ± 0.02 versus 1.21 ± 0.02 mm, respectively; p = 0.001). The edge-enhancing kernel generated less overestimation from nominal thickness compared to the standard kernel, both with the orthogonal (0.89 ± 0.19 versus 1.00 ± 0.26 mm, respectively; p<0.001) and the circumference (1.06 ± 0.26 versus 1.13 ± 0.31 mm, respectively; p = 0.005) methods. The edge-enhancing kernel was associated with lower SNR and CNR, as well as higher background noise (all p < 0.001), in comparison to the medium-smooth kernel. Stent visual scores were higher with the edge-enhancing kernel (p<0.001). In vivo 256-slice CT assessment of coronary stents shows that the edge-enhancing CT reconstruction kernel generates thinner stent walls, less overestimation from nominal thickness, and better image quality scores than the standard kernel.

A ℓ2, 1 norm regularized multi-kernel learning for false positive reduction in Lung nodule CAD.

PubMed

Cao, Peng; Liu, Xiaoli; Zhang, Jian; Li, Wei; Zhao, Dazhe; Huang, Min; Zaiane, Osmar

2017-03-01

The aim of this paper is to describe a novel algorithm for False Positive Reduction in lung nodule Computer Aided Detection(CAD). In this paper, we describes a new CT lung CAD method which aims to detect solid nodules. Specially, we proposed a multi-kernel classifier with a ℓ 2, 1 norm regularizer for heterogeneous feature fusion and selection from the feature subset level, and designed two efficient strategies to optimize the parameters of kernel weights in non-smooth ℓ 2, 1 regularized multiple kernel learning algorithm. The first optimization algorithm adapts a proximal gradient method for solving the ℓ 2, 1 norm of kernel weights, and use an accelerated method based on FISTA; the second one employs an iterative scheme based on an approximate gradient descent method. The results demonstrates that the FISTA-style accelerated proximal descent method is efficient for the ℓ 2, 1 norm formulation of multiple kernel learning with the theoretical guarantee of the convergence rate. Moreover, the experimental results demonstrate the effectiveness of the proposed methods in terms of Geometric mean (G-mean) and Area under the ROC curve (AUC), and significantly outperforms the competing methods. The proposed approach exhibits some remarkable advantages both in heterogeneous feature subsets fusion and classification phases. Compared with the fusion strategies of feature-level and decision level, the proposed ℓ 2, 1 norm multi-kernel learning algorithm is able to accurately fuse the complementary and heterogeneous feature sets, and automatically prune the irrelevant and redundant feature subsets to form a more discriminative feature set, leading a promising classification performance. Moreover, the proposed algorithm consistently outperforms the comparable classification approaches in the literature. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Examining Potential Boundary Bias Effects in Kernel Smoothing on Equating: An Introduction for the Adaptive and Epanechnikov Kernels.

PubMed

Cid, Jaime A; von Davier, Alina A

2015-05-01

Test equating is a method of making the test scores from different test forms of the same assessment comparable. In the equating process, an important step involves continuizing the discrete score distributions. In traditional observed-score equating, this step is achieved using linear interpolation (or an unscaled uniform kernel). In the kernel equating (KE) process, this continuization process involves Gaussian kernel smoothing. It has been suggested that the choice of bandwidth in kernel smoothing controls the trade-off between variance and bias. In the literature on estimating density functions using kernels, it has also been suggested that the weight of the kernel depends on the sample size, and therefore, the resulting continuous distribution exhibits bias at the endpoints, where the samples are usually smaller. The purpose of this article is (a) to explore the potential effects of atypical scores (spikes) at the extreme ends (high and low) on the KE method in distributions with different degrees of asymmetry using the randomly equivalent groups equating design (Study I), and (b) to introduce the Epanechnikov and adaptive kernels as potential alternative approaches to reducing boundary bias in smoothing (Study II). The beta-binomial model is used to simulate observed scores reflecting a range of different skewed shapes.

Partial Deconvolution with Inaccurate Blur Kernel.

PubMed

Ren, Dongwei; Zuo, Wangmeng; Zhang, David; Xu, Jun; Zhang, Lei

2017-10-17

Most non-blind deconvolution methods are developed under the error-free kernel assumption, and are not robust to inaccurate blur kernel. Unfortunately, despite the great progress in blind deconvolution, estimation error remains inevitable during blur kernel estimation. Consequently, severe artifacts such as ringing effects and distortions are likely to be introduced in the non-blind deconvolution stage. In this paper, we tackle this issue by suggesting: (i) a partial map in the Fourier domain for modeling kernel estimation error, and (ii) a partial deconvolution model for robust deblurring with inaccurate blur kernel. The partial map is constructed by detecting the reliable Fourier entries of estimated blur kernel. And partial deconvolution is applied to wavelet-based and learning-based models to suppress the adverse effect of kernel estimation error. Furthermore, an E-M algorithm is developed for estimating the partial map and recovering the latent sharp image alternatively. Experimental results show that our partial deconvolution model is effective in relieving artifacts caused by inaccurate blur kernel, and can achieve favorable deblurring quality on synthetic and real blurry images.Most non-blind deconvolution methods are developed under the error-free kernel assumption, and are not robust to inaccurate blur kernel. Unfortunately, despite the great progress in blind deconvolution, estimation error remains inevitable during blur kernel estimation. Consequently, severe artifacts such as ringing effects and distortions are likely to be introduced in the non-blind deconvolution stage. In this paper, we tackle this issue by suggesting: (i) a partial map in the Fourier domain for modeling kernel estimation error, and (ii) a partial deconvolution model for robust deblurring with inaccurate blur kernel. The partial map is constructed by detecting the reliable Fourier entries of estimated blur kernel. And partial deconvolution is applied to wavelet-based and learning-based models to suppress the adverse effect of kernel estimation error. Furthermore, an E-M algorithm is developed for estimating the partial map and recovering the latent sharp image alternatively. Experimental results show that our partial deconvolution model is effective in relieving artifacts caused by inaccurate blur kernel, and can achieve favorable deblurring quality on synthetic and real blurry images.

Optimal Alignment of Structures for Finite and Periodic Systems.

PubMed

Griffiths, Matthew; Niblett, Samuel P; Wales, David J

2017-10-10

Finding the optimal alignment between two structures is important for identifying the minimum root-mean-square distance (RMSD) between them and as a starting point for calculating pathways. Most current algorithms for aligning structures are stochastic, scale exponentially with the size of structure, and the performance can be unreliable. We present two complementary methods for aligning structures corresponding to isolated clusters of atoms and to condensed matter described by a periodic cubic supercell. The first method (Go-PERMDIST), a branch and bound algorithm, locates the global minimum RMSD deterministically in polynomial time. The run time increases for larger RMSDs. The second method (FASTOVERLAP) is a heuristic algorithm that aligns structures by finding the global maximum kernel correlation between them using fast Fourier transforms (FFTs) and fast SO(3) transforms (SOFTs). For periodic systems, FASTOVERLAP scales with the square of the number of identical atoms in the system, reliably finds the best alignment between structures that are not too distant, and shows significantly better performance than existing algorithms. The expected run time for Go-PERMDIST is longer than FASTOVERLAP for periodic systems. For finite clusters, the FASTOVERLAP algorithm is competitive with existing algorithms. The expected run time for Go-PERMDIST to find the global RMSD between two structures deterministically is generally longer than for existing stochastic algorithms. However, with an earlier exit condition, Go-PERMDIST exhibits similar or better performance.

An algorithmic approach to solving polynomial equations associated with quantum circuits

NASA Astrophysics Data System (ADS)

Gerdt, V. P.; Zinin, M. V.

2009-12-01

In this paper we present two algorithms for reducing systems of multivariate polynomial equations over the finite field F 2 to the canonical triangular form called lexicographical Gröbner basis. This triangular form is the most appropriate for finding solutions of the system. On the other hand, the system of polynomials over F 2 whose variables also take values in F 2 (Boolean polynomials) completely describes the unitary matrix generated by a quantum circuit. In particular, the matrix itself can be computed by counting the number of solutions (roots) of the associated polynomial system. Thereby, efficient construction of the lexicographical Gröbner bases over F 2 associated with quantum circuits gives a method for computing their circuit matrices that is alternative to the direct numerical method based on linear algebra. We compare our implementation of both algorithms with some other software packages available for computing Gröbner bases over F 2.

3DRT-MPASS

NASA Technical Reports Server (NTRS)

Lickly, Ben

2005-01-01

Data from all current JPL missions are stored in files called SPICE kernels. At present, animators who want to use data from these kernels have to either read through the kernels looking for the desired data, or write programs themselves to retrieve information about all the needed objects for their animations. In this project, methods of automating the process of importing the data from the SPICE kernels were researched. In particular, tools were developed for creating basic scenes in Maya, a 3D computer graphics software package, from SPICE kernels.

Spectral/ hp element methods: Recent developments, applications, and perspectives

NASA Astrophysics Data System (ADS)

Xu, Hui; Cantwell, Chris D.; Monteserin, Carlos; Eskilsson, Claes; Engsig-Karup, Allan P.; Sherwin, Spencer J.

2018-02-01

The spectral/ hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a C 0 - continuous expansion. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/ hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/ hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/ hp element method in more complex science and engineering applications are discussed.

MultiDK: A Multiple Descriptor Multiple Kernel Approach for Molecular Discovery and Its Application to Organic Flow Battery Electrolytes.

PubMed

Kim, Sungjin; Jinich, Adrián; Aspuru-Guzik, Alán

2017-04-24

We propose a multiple descriptor multiple kernel (MultiDK) method for efficient molecular discovery using machine learning. We show that the MultiDK method improves both the speed and accuracy of molecular property prediction. We apply the method to the discovery of electrolyte molecules for aqueous redox flow batteries. Using multiple-type-as opposed to single-type-descriptors, we obtain more relevant features for machine learning. Following the principle of "wisdom of the crowds", the combination of multiple-type descriptors significantly boosts prediction performance. Moreover, by employing multiple kernels-more than one kernel function for a set of the input descriptors-MultiDK exploits nonlinear relations between molecular structure and properties better than a linear regression approach. The multiple kernels consist of a Tanimoto similarity kernel and a linear kernel for a set of binary descriptors and a set of nonbinary descriptors, respectively. Using MultiDK, we achieve an average performance of r 2 = 0.92 with a test set of molecules for solubility prediction. We also extend MultiDK to predict pH-dependent solubility and apply it to a set of quinone molecules with different ionizable functional groups to assess their performance as flow battery electrolytes.

Compound analysis via graph kernels incorporating chirality.

PubMed

Brown, J B; Urata, Takashi; Tamura, Takeyuki; Arai, Midori A; Kawabata, Takeo; Akutsu, Tatsuya

2010-12-01

High accuracy is paramount when predicting biochemical characteristics using Quantitative Structural-Property Relationships (QSPRs). Although existing graph-theoretic kernel methods combined with machine learning techniques are efficient for QSPR model construction, they cannot distinguish topologically identical chiral compounds which often exhibit different biological characteristics. In this paper, we propose a new method that extends the recently developed tree pattern graph kernel to accommodate stereoisomers. We show that Support Vector Regression (SVR) with a chiral graph kernel is useful for target property prediction by demonstrating its application to a set of human vitamin D receptor ligands currently under consideration for their potential anti-cancer effects.

A locally adaptive kernel regression method for facies delineation

NASA Astrophysics Data System (ADS)

Fernàndez-Garcia, D.; Barahona-Palomo, M.; Henri, C. V.; Sanchez-Vila, X.

2015-12-01

Facies delineation is defined as the separation of geological units with distinct intrinsic characteristics (grain size, hydraulic conductivity, mineralogical composition). A major challenge in this area stems from the fact that only a few scattered pieces of hydrogeological information are available to delineate geological facies. Several methods to delineate facies are available in the literature, ranging from those based only on existing hard data, to those including secondary data or external knowledge about sedimentological patterns. This paper describes a methodology to use kernel regression methods as an effective tool for facies delineation. The method uses both the spatial and the actual sampled values to produce, for each individual hard data point, a locally adaptive steering kernel function, self-adjusting the principal directions of the local anisotropic kernels to the direction of highest local spatial correlation. The method is shown to outperform the nearest neighbor classification method in a number of synthetic aquifers whenever the available number of hard data is small and randomly distributed in space. In the case of exhaustive sampling, the steering kernel regression method converges to the true solution. Simulations ran in a suite of synthetic examples are used to explore the selection of kernel parameters in typical field settings. It is shown that, in practice, a rule of thumb can be used to obtain suboptimal results. The performance of the method is demonstrated to significantly improve when external information regarding facies proportions is incorporated. Remarkably, the method allows for a reasonable reconstruction of the facies connectivity patterns, shown in terms of breakthrough curves performance.

The NonConforming Virtual Element Method for the Stokes Equations

DOE PAGES

Cangiani, Andrea; Gyrya, Vitaliy; Manzini, Gianmarco

2016-01-01

In this paper, we present the nonconforming virtual element method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component of the velocity is approximated using the nonconforming virtual element space. On each mesh element the local virtual space contains the space of polynomials of up to a given degree, plus suitable nonpolynomial functions. The virtual element functions are implicitly defined as the solution of local Poisson problems with polynomial Neumann boundary conditions. As typical in VEM approaches, the explicit evaluation of the non-polynomial functionsmore » is not required. This approach makes it possible to construct nonconforming (virtual) spaces for any polynomial degree regardless of the parity, for two- and three-dimensional problems, and for meshes with very general polygonal and polyhedral elements. We show that the nonconforming VEM is inf-sup stable and establish optimal a priori error estimates for the velocity and pressure approximations. Finally, numerical examples confirm the convergence analysis and the effectiveness of the method in providing high-order accurate approximations.« less

Local Composite Quantile Regression Smoothing for Harris Recurrent Markov Processes

PubMed Central

Li, Degui; Li, Runze

2016-01-01

In this paper, we study the local polynomial composite quantile regression (CQR) smoothing method for the nonlinear and nonparametric models under the Harris recurrent Markov chain framework. The local polynomial CQR regression method is a robust alternative to the widely-used local polynomial method, and has been well studied in stationary time series. In this paper, we relax the stationarity restriction on the model, and allow that the regressors are generated by a general Harris recurrent Markov process which includes both the stationary (positive recurrent) and nonstationary (null recurrent) cases. Under some mild conditions, we establish the asymptotic theory for the proposed local polynomial CQR estimator of the mean regression function, and show that the convergence rate for the estimator in nonstationary case is slower than that in stationary case. Furthermore, a weighted type local polynomial CQR estimator is provided to improve the estimation efficiency, and a data-driven bandwidth selection is introduced to choose the optimal bandwidth involved in the nonparametric estimators. Finally, we give some numerical studies to examine the finite sample performance of the developed methodology and theory. PMID:27667894

Further Insight and Additional Inference Methods for Polynomial Regression Applied to the Analysis of Congruence

ERIC Educational Resources Information Center

Cohen, Ayala; Nahum-Shani, Inbal; Doveh, Etti

2010-01-01

In their seminal paper, Edwards and Parry (1993) presented the polynomial regression as a better alternative to applying difference score in the study of congruence. Although this method is increasingly applied in congruence research, its complexity relative to other methods for assessing congruence (e.g., difference score methods) was one of the…

Polynomial solutions of the Monge-Ampère equation

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

Aminov, Yu A

2014-11-30

The question of the existence of polynomial solutions to the Monge-Ampère equation z{sub xx}z{sub yy}−z{sub xy}{sup 2}=f(x,y) is considered in the case when f(x,y) is a polynomial. It is proved that if f is a polynomial of the second degree, which is positive for all values of its arguments and has a positive squared part, then no polynomial solution exists. On the other hand, a solution which is not polynomial but is analytic in the whole of the x, y-plane is produced. Necessary and sufficient conditions for the existence of polynomial solutions of degree up to 4 are found and methods for the construction ofmore » such solutions are indicated. An approximation theorem is proved. Bibliography: 10 titles.« less

A polynomial based model for cell fate prediction in human diseases.

PubMed

Ma, Lichun; Zheng, Jie

2017-12-21

Cell fate regulation directly affects tissue homeostasis and human health. Research on cell fate decision sheds light on key regulators, facilitates understanding the mechanisms, and suggests novel strategies to treat human diseases that are related to abnormal cell development. In this study, we proposed a polynomial based model to predict cell fate. This model was derived from Taylor series. As a case study, gene expression data of pancreatic cells were adopted to test and verify the model. As numerous features (genes) are available, we employed two kinds of feature selection methods, i.e. correlation based and apoptosis pathway based. Then polynomials of different degrees were used to refine the cell fate prediction function. 10-fold cross-validation was carried out to evaluate the performance of our model. In addition, we analyzed the stability of the resultant cell fate prediction model by evaluating the ranges of the parameters, as well as assessing the variances of the predicted values at randomly selected points. Results show that, within both the two considered gene selection methods, the prediction accuracies of polynomials of different degrees show little differences. Interestingly, the linear polynomial (degree 1 polynomial) is more stable than others. When comparing the linear polynomials based on the two gene selection methods, it shows that although the accuracy of the linear polynomial that uses correlation analysis outcomes is a little higher (achieves 86.62%), the one within genes of the apoptosis pathway is much more stable. Considering both the prediction accuracy and the stability of polynomial models of different degrees, the linear model is a preferred choice for cell fate prediction with gene expression data of pancreatic cells. The presented cell fate prediction model can be extended to other cells, which may be important for basic research as well as clinical study of cell development related diseases.

Algorithms for computing solvents of unilateral second-order matrix polynomials over prime finite fields using lambda-matrices

NASA Astrophysics Data System (ADS)

Burtyka, Filipp

2018-01-01

The paper considers algorithms for finding diagonalizable and non-diagonalizable roots (so called solvents) of monic arbitrary unilateral second-order matrix polynomial over prime finite field. These algorithms are based on polynomial matrices (lambda-matrices). This is an extension of existing general methods for computing solvents of matrix polynomials over field of complex numbers. We analyze how techniques for complex numbers can be adapted for finite field and estimate asymptotic complexity of the obtained algorithms.

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.

Kernel-PCA data integration with enhanced interpretability

PubMed Central

2014-01-01

Background Nowadays, combining the different sources of information to improve the biological knowledge available is a challenge in bioinformatics. One of the most powerful methods for integrating heterogeneous data types are kernel-based methods. Kernel-based data integration approaches consist of two basic steps: firstly the right kernel is chosen for each data set; secondly the kernels from the different data sources are combined to give a complete representation of the available data for a given statistical task. Results We analyze the integration of data from several sources of information using kernel PCA, from the point of view of reducing dimensionality. Moreover, we improve the interpretability of kernel PCA by adding to the plot the representation of the input variables that belong to any dataset. In particular, for each input variable or linear combination of input variables, we can represent the direction of maximum growth locally, which allows us to identify those samples with higher/lower values of the variables analyzed. Conclusions The integration of different datasets and the simultaneous representation of samples and variables together give us a better understanding of biological knowledge. PMID:25032747

Anatomical image-guided fluorescence molecular tomography reconstruction using kernel method

PubMed Central

Baikejiang, Reheman; Zhao, Yue; Fite, Brett Z.; Ferrara, Katherine W.; Li, Changqing

2017-01-01

Abstract. Fluorescence molecular tomography (FMT) is an important in vivo imaging modality to visualize physiological and pathological processes in small animals. However, FMT reconstruction is ill-posed and ill-conditioned due to strong optical scattering in deep tissues, which results in poor spatial resolution. It is well known that FMT image quality can be improved substantially by applying the structural guidance in the FMT reconstruction. An approach to introducing anatomical information into the FMT reconstruction is presented using the kernel method. In contrast to conventional methods that incorporate anatomical information with a Laplacian-type regularization matrix, the proposed method introduces the anatomical guidance into the projection model of FMT. The primary advantage of the proposed method is that it does not require segmentation of targets in the anatomical images. Numerical simulations and phantom experiments have been performed to demonstrate the proposed approach’s feasibility. Numerical simulation results indicate that the proposed kernel method can separate two FMT targets with an edge-to-edge distance of 1 mm and is robust to false-positive guidance and inhomogeneity in the anatomical image. For the phantom experiments with two FMT targets, the kernel method has reconstructed both targets successfully, which further validates the proposed kernel method. PMID:28464120

Effects of sample size on KERNEL home range estimates

USGS Publications Warehouse

Seaman, D.E.; Millspaugh, J.J.; Kernohan, Brian J.; Brundige, Gary C.; Raedeke, Kenneth J.; Gitzen, Robert A.

1999-01-01

Kernel methods for estimating home range are being used increasingly in wildlife research, but the effect of sample size on their accuracy is not known. We used computer simulations of 10-200 points/home range and compared accuracy of home range estimates produced by fixed and adaptive kernels with the reference (REF) and least-squares cross-validation (LSCV) methods for determining the amount of smoothing. Simulated home ranges varied from simple to complex shapes created by mixing bivariate normal distributions. We used the size of the 95% home range area and the relative mean squared error of the surface fit to assess the accuracy of the kernel home range estimates. For both measures, the bias and variance approached an asymptote at about 50 observations/home range. The fixed kernel with smoothing selected by LSCV provided the least-biased estimates of the 95% home range area. All kernel methods produced similar surface fit for most simulations, but the fixed kernel with LSCV had the lowest frequency and magnitude of very poor estimates. We reviewed 101 papers published in The Journal of Wildlife Management (JWM) between 1980 and 1997 that estimated animal home ranges. A minority of these papers used nonparametric utilization distribution (UD) estimators, and most did not adequately report sample sizes. We recommend that home range studies using kernel estimates use LSCV to determine the amount of smoothing, obtain a minimum of 30 observations per animal (but preferably a?Y50), and report sample sizes in published results.

Development of low-frequency kernel-function aerodynamics for comparison with time-dependent finite-difference methods

NASA Technical Reports Server (NTRS)

Bland, S. R.

1982-01-01

Finite difference methods for unsteady transonic flow frequency use simplified equations in which certain of the time dependent terms are omitted from the governing equations. Kernel functions are derived for two dimensional subsonic flow, and provide accurate solutions of the linearized potential equation with the same time dependent terms omitted. These solutions make possible a direct evaluation of the finite difference codes for the linear problem. Calculations with two of these low frequency kernel functions verify the accuracy of the LTRAN2 and HYTRAN2 finite difference codes. Comparisons of the low frequency kernel function results with the Possio kernel function solution of the complete linear equations indicate the adequacy of the HYTRAN approximation for frequencies in the range of interest for flutter calculations.

Kernel Wiener filter and its application to pattern recognition.

PubMed

Yoshino, Hirokazu; Dong, Chen; Washizawa, Yoshikazu; Yamashita, Yukihiko

2010-11-01

The Wiener filter (WF) is widely used for inverse problems. From an observed signal, it provides the best estimated signal with respect to the squared error averaged over the original and the observed signals among linear operators. The kernel WF (KWF), extended directly from WF, has a problem that an additive noise has to be handled by samples. Since the computational complexity of kernel methods depends on the number of samples, a huge computational cost is necessary for the case. By using the first-order approximation of kernel functions, we realize KWF that can handle such a noise not by samples but as a random variable. We also propose the error estimation method for kernel filters by using the approximations. In order to show the advantages of the proposed methods, we conducted the experiments to denoise images and estimate errors. We also apply KWF to classification since KWF can provide an approximated result of the maximum a posteriori classifier that provides the best recognition accuracy. The noise term in the criterion can be used for the classification in the presence of noise or a new regularization to suppress changes in the input space, whereas the ordinary regularization for the kernel method suppresses changes in the feature space. In order to show the advantages of the proposed methods, we conducted experiments of binary and multiclass classifications and classification in the presence of noise.

Nonlinear Deep Kernel Learning for Image Annotation.

PubMed

Jiu, Mingyuan; Sahbi, Hichem

2017-02-08

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

Multineuron spike train analysis with R-convolution linear combination kernel.

PubMed

Tezuka, Taro

2018-06-01

A spike train kernel provides an effective way of decoding information represented by a spike train. Some spike train kernels have been extended to multineuron spike trains, which are simultaneously recorded spike trains obtained from multiple neurons. However, most of these multineuron extensions were carried out in a kernel-specific manner. In this paper, a general framework is proposed for extending any single-neuron spike train kernel to multineuron spike trains, based on the R-convolution kernel. Special subclasses of the proposed R-convolution linear combination kernel are explored. These subclasses have a smaller number of parameters and make optimization tractable when the size of data is limited. The proposed kernel was evaluated using Gaussian process regression for multineuron spike trains recorded from an animal brain. It was compared with the sum kernel and the population Spikernel, which are existing ways of decoding multineuron spike trains using kernels. The results showed that the proposed approach performs better than these kernels and also other commonly used neural decoding methods. Copyright © 2018 Elsevier Ltd. All rights reserved.

On computing closed forms for summations. [polynomials and rational functions

NASA Technical Reports Server (NTRS)

Moenck, R.

1977-01-01

The problem of finding closed forms for a summation involving polynomials and rational functions is considered. A method closely related to Hermite's method for integration of rational functions derived. The method expresses the sum of a rational function as a rational function part and a transcendental part involving derivatives of the gamma function.

Detection and correction of laser induced breakdown spectroscopy spectral background based on spline interpolation method

NASA Astrophysics Data System (ADS)

Tan, Bing; Huang, Min; Zhu, Qibing; Guo, Ya; Qin, Jianwei

2017-12-01

Laser-induced breakdown spectroscopy (LIBS) is an analytical technique that has gained increasing attention because of many applications. The production of continuous background in LIBS is inevitable because of factors associated with laser energy, gate width, time delay, and experimental environment. The continuous background significantly influences the analysis of the spectrum. Researchers have proposed several background correction methods, such as polynomial fitting, Lorenz fitting and model-free methods. However, less of them apply these methods in the field of LIBS Technology, particularly in qualitative and quantitative analyses. This study proposes a method based on spline interpolation for detecting and estimating the continuous background spectrum according to its smooth property characteristic. Experiment on the background correction simulation indicated that, the spline interpolation method acquired the largest signal-to-background ratio (SBR) over polynomial fitting, Lorenz fitting and model-free method after background correction. These background correction methods all acquire larger SBR values than that acquired before background correction (The SBR value before background correction is 10.0992, whereas the SBR values after background correction by spline interpolation, polynomial fitting, Lorentz fitting, and model-free methods are 26.9576, 24.6828, 18.9770, and 25.6273 respectively). After adding random noise with different kinds of signal-to-noise ratio to the spectrum, spline interpolation method acquires large SBR value, whereas polynomial fitting and model-free method obtain low SBR values. All of the background correction methods exhibit improved quantitative results of Cu than those acquired before background correction (The linear correlation coefficient value before background correction is 0.9776. Moreover, the linear correlation coefficient values after background correction using spline interpolation, polynomial fitting, Lorentz fitting, and model-free methods are 0.9998, 0.9915, 0.9895, and 0.9940 respectively). The proposed spline interpolation method exhibits better linear correlation and smaller error in the results of the quantitative analysis of Cu compared with polynomial fitting, Lorentz fitting and model-free methods, The simulation and quantitative experimental results show that the spline interpolation method can effectively detect and correct the continuous background.

Some comparisons of complexity in dictionary-based and linear computational models.

PubMed

Gnecco, Giorgio; Kůrková, Věra; Sanguineti, Marcello

2011-03-01

Neural networks provide a more flexible approximation of functions than traditional linear regression. In the latter, one can only adjust the coefficients in linear combinations of fixed sets of functions, such as orthogonal polynomials or Hermite functions, while for neural networks, one may also adjust the parameters of the functions which are being combined. However, some useful properties of linear approximators (such as uniqueness, homogeneity, and continuity of best approximation operators) are not satisfied by neural networks. Moreover, optimization of parameters in neural networks becomes more difficult than in linear regression. Experimental results suggest that these drawbacks of neural networks are offset by substantially lower model complexity, allowing accuracy of approximation even in high-dimensional cases. We give some theoretical results comparing requirements on model complexity for two types of approximators, the traditional linear ones and so called variable-basis types, which include neural networks, radial, and kernel models. We compare upper bounds on worst-case errors in variable-basis approximation with lower bounds on such errors for any linear approximator. Using methods from nonlinear approximation and integral representations tailored to computational units, we describe some cases where neural networks outperform any linear approximator. Copyright © 2010 Elsevier Ltd. All rights reserved.

Real-space mapping of topological invariants using artificial neural networks

NASA Astrophysics Data System (ADS)

Carvalho, D.; García-Martínez, N. A.; Lado, J. L.; Fernández-Rossier, J.

2018-03-01

Topological invariants allow one to characterize Hamiltonians, predicting the existence of topologically protected in-gap modes. Those invariants can be computed by tracing the evolution of the occupied wave functions under twisted boundary conditions. However, those procedures do not allow one to calculate a topological invariant by evaluating the system locally, and thus require information about the wave functions in the whole system. Here we show that artificial neural networks can be trained to identify the topological order by evaluating a local projection of the density matrix. We demonstrate this for two different models, a one-dimensional topological superconductor and a two-dimensional quantum anomalous Hall state, both with spatially modulated parameters. Our neural network correctly identifies the different topological domains in real space, predicting the location of in-gap states. By combining a neural network with a calculation of the electronic states that uses the kernel polynomial method, we show that the local evaluation of the invariant can be carried out by evaluating a local quantity, in particular for systems without translational symmetry consisting of tens of thousands of atoms. Our results show that supervised learning is an efficient methodology to characterize the local topology of a system.

Nonlinear data-driven identification of polymer electrolyte membrane fuel cells for diagnostic purposes: A Volterra series approach

NASA Astrophysics Data System (ADS)

Ritzberger, D.; Jakubek, S.

2017-09-01

In this work, a data-driven identification method, based on polynomial nonlinear autoregressive models with exogenous inputs (NARX) and the Volterra series, is proposed to describe the dynamic and nonlinear voltage and current characteristics of polymer electrolyte membrane fuel cells (PEMFCs). The structure selection and parameter estimation of the NARX model is performed on broad-band voltage/current data. By transforming the time-domain NARX model into a Volterra series representation using the harmonic probing algorithm, a frequency-domain description of the linear and nonlinear dynamics is obtained. With the Volterra kernels corresponding to different operating conditions, information from existing diagnostic tools in the frequency domain such as electrochemical impedance spectroscopy (EIS) and total harmonic distortion analysis (THDA) are effectively combined. Additionally, the time-domain NARX model can be utilized for fault detection by evaluating the difference between measured and simulated output. To increase the fault detectability, an optimization problem is introduced which maximizes this output residual to obtain proper excitation frequencies. As a possible extension it is shown, that by optimizing the periodic signal shape itself that the fault detectability is further increased.

Kernel Methods for Mining Instance Data in Ontologies

NASA Astrophysics Data System (ADS)

Bloehdorn, Stephan; Sure, York

The amount of ontologies and meta data available on the Web is constantly growing. The successful application of machine learning techniques for learning of ontologies from textual data, i.e. mining for the Semantic Web, contributes to this trend. However, no principal approaches exist so far for mining from the Semantic Web. We investigate how machine learning algorithms can be made amenable for directly taking advantage of the rich knowledge expressed in ontologies and associated instance data. Kernel methods have been successfully employed in various learning tasks and provide a clean framework for interfacing between non-vectorial data and machine learning algorithms. In this spirit, we express the problem of mining instances in ontologies as the problem of defining valid corresponding kernels. We present a principled framework for designing such kernels by means of decomposing the kernel computation into specialized kernels for selected characteristics of an ontology which can be flexibly assembled and tuned. Initial experiments on real world Semantic Web data enjoy promising results and show the usefulness of our approach.

Aveiro method in reproducing kernel Hilbert spaces under complete dictionary

NASA Astrophysics Data System (ADS)

Mai, Weixiong; Qian, Tao

2017-12-01

Aveiro Method is a sparse representation method in reproducing kernel Hilbert spaces (RKHS) that gives orthogonal projections in linear combinations of reproducing kernels over uniqueness sets. It, however, suffers from determination of uniqueness sets in the underlying RKHS. In fact, in general spaces, uniqueness sets are not easy to be identified, let alone the convergence speed aspect with Aveiro Method. To avoid those difficulties we propose an anew Aveiro Method based on a dictionary and the matching pursuit idea. What we do, in fact, are more: The new Aveiro method will be in relation to the recently proposed, the so called Pre-Orthogonal Greedy Algorithm (P-OGA) involving completion of a given dictionary. The new method is called Aveiro Method Under Complete Dictionary (AMUCD). The complete dictionary consists of all directional derivatives of the underlying reproducing kernels. We show that, under the boundary vanishing condition, bring available for the classical Hardy and Paley-Wiener spaces, the complete dictionary enables an efficient expansion of any given element in the Hilbert space. The proposed method reveals new and advanced aspects in both the Aveiro Method and the greedy algorithm.

Learning a peptide-protein binding affinity predictor with kernel ridge regression

PubMed Central

2013-01-01

Background The cellular function of a vast majority of proteins is performed through physical interactions with other biomolecules, which, most of the time, are other proteins. Peptides represent templates of choice for mimicking a secondary structure in order to modulate protein-protein interaction. They are thus an interesting class of therapeutics since they also display strong activity, high selectivity, low toxicity and few drug-drug interactions. Furthermore, predicting peptides that would bind to a specific MHC alleles would be of tremendous benefit to improve vaccine based therapy and possibly generate antibodies with greater affinity. Modern computational methods have the potential to accelerate and lower the cost of drug and vaccine discovery by selecting potential compounds for testing in silico prior to biological validation. Results We propose a specialized string kernel for small bio-molecules, peptides and pseudo-sequences of binding interfaces. The kernel incorporates physico-chemical properties of amino acids and elegantly generalizes eight kernels, comprised of the Oligo, the Weighted Degree, the Blended Spectrum, and the Radial Basis Function. We provide a low complexity dynamic programming algorithm for the exact computation of the kernel and a linear time algorithm for it’s approximation. Combined with kernel ridge regression and SupCK, a novel binding pocket kernel, the proposed kernel yields biologically relevant and good prediction accuracy on the PepX database. For the first time, a machine learning predictor is capable of predicting the binding affinity of any peptide to any protein with reasonable accuracy. The method was also applied to both single-target and pan-specific Major Histocompatibility Complex class II benchmark datasets and three Quantitative Structure Affinity Model benchmark datasets. Conclusion On all benchmarks, our method significantly (p-value ≤ 0.057) outperforms the current state-of-the-art methods at predicting peptide-protein binding affinities. The proposed approach is flexible and can be applied to predict any quantitative biological activity. Moreover, generating reliable peptide-protein binding affinities will also improve system biology modelling of interaction pathways. Lastly, the method should be of value to a large segment of the research community with the potential to accelerate the discovery of peptide-based drugs and facilitate vaccine development. The proposed kernel is freely available at http://graal.ift.ulaval.ca/downloads/gs-kernel/. PMID:23497081

A fast and objective multidimensional kernel density estimation method: fastKDE

DOE PAGES

O'Brien, Travis A.; Kashinath, Karthik; Cavanaugh, Nicholas R.; ...

2016-03-07

Numerous facets of scientific research implicitly or explicitly call for the estimation of probability densities. Histograms and kernel density estimates (KDEs) are two commonly used techniques for estimating such information, with the KDE generally providing a higher fidelity representation of the probability density function (PDF). Both methods require specification of either a bin width or a kernel bandwidth. While techniques exist for choosing the kernel bandwidth optimally and objectively, they are computationally intensive, since they require repeated calculation of the KDE. A solution for objectively and optimally choosing both the kernel shape and width has recently been developed by Bernacchiamore » and Pigolotti (2011). While this solution theoretically applies to multidimensional KDEs, it has not been clear how to practically do so. A method for practically extending the Bernacchia-Pigolotti KDE to multidimensions is introduced. This multidimensional extension is combined with a recently-developed computational improvement to their method that makes it computationally efficient: a 2D KDE on 10 5 samples only takes 1 s on a modern workstation. This fast and objective KDE method, called the fastKDE method, retains the excellent statistical convergence properties that have been demonstrated for univariate samples. The fastKDE method exhibits statistical accuracy that is comparable to state-of-the-science KDE methods publicly available in R, and it produces kernel density estimates several orders of magnitude faster. The fastKDE method does an excellent job of encoding covariance information for bivariate samples. This property allows for direct calculation of conditional PDFs with fastKDE. It is demonstrated how this capability might be leveraged for detecting non-trivial relationships between quantities in physical systems, such as transitional behavior.« less

Using Adjoint Methods to Improve 3-D Velocity Models of Southern California

NASA Astrophysics Data System (ADS)

Liu, Q.; Tape, C.; Maggi, A.; Tromp, J.

2006-12-01

We use adjoint methods popular in climate and ocean dynamics to calculate Fréchet derivatives for tomographic inversions in southern California. The Fréchet derivative of an objective function χ(m), where m denotes the Earth model, may be written in the generic form δχ=int Km(x) δln m(x) d3x, where δln m=δ m/m denotes the relative model perturbation. For illustrative purposes, we construct the 3-D finite-frequency banana-doughnut kernel Km, corresponding to the misfit of a single traveltime measurement, by simultaneously computing the 'adjoint' wave field s† forward in time and reconstructing the regular wave field s backward in time. The adjoint wave field is produced by using the time-reversed velocity at the receiver as a fictitious source, while the regular wave field is reconstructed on the fly by propagating the last frame of the wave field saved by a previous forward simulation backward in time. The approach is based upon the spectral-element method, and only two simulations are needed to produce density, shear-wave, and compressional-wave sensitivity kernels. This method is applied to the SCEC southern California velocity model. Various density, shear-wave, and compressional-wave sensitivity kernels are presented for different phases in the seismograms. We also generate 'event' kernels for Pnl, S and surface waves, which are the Fréchet kernels of misfit functions that measure the P, S or surface wave traveltime residuals at all the receivers simultaneously for one particular event. Effectively, an event kernel is a sum of weighted Fréchet kernels, with weights determined by the associated traveltime anomalies. By the nature of the 3-D simulation, every event kernel is also computed based upon just two simulations, i.e., its construction costs the same amount of computation time as an individual banana-doughnut kernel. One can think of the sum of the event kernels for all available earthquakes, called the 'misfit' kernel, as a graphical representation of the gradient of the misfit function. With the capability of computing both the value of the misfit function and its gradient, which assimilates the traveltime anomalies, we are ready to use a non-linear conjugate gradient algorithm to iteratively improve velocity models of southern California.

Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

PubMed Central

Chung, Moo K.; Qiu, Anqi; Seo, Seongho; Vorperian, Houri K.

2014-01-01

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface. PMID:25791435

Research on offense and defense technology for iOS kernel security mechanism

NASA Astrophysics Data System (ADS)

Chu, Sijun; Wu, Hao

2018-04-01

iOS is a strong and widely used mobile device system. It's annual profits make up about 90% of the total profits of all mobile phone brands. Though it is famous for its security, there have been many attacks on the iOS operating system, such as the Trident apt attack in 2016. So it is important to research the iOS security mechanism and understand its weaknesses and put forward targeted protection and security check framework. By studying these attacks and previous jailbreak tools, we can see that an attacker could only run a ROP code and gain kernel read and write permissions based on the ROP after exploiting kernel and user layer vulnerabilities. However, the iOS operating system is still protected by the code signing mechanism, the sandbox mechanism, and the not-writable mechanism of the system's disk area. This is far from the steady, long-lasting control that attackers expect. Before iOS 9, breaking these security mechanisms was usually done by modifying the kernel's important data structures and security mechanism code logic. However, after iOS 9, the kernel integrity protection mechanism was added to the 64-bit operating system and none of the previous methods were adapted to the new versions of iOS [1]. But this does not mean that attackers can not break through. Therefore, based on the analysis of the vulnerability of KPP security mechanism, this paper implements two possible breakthrough methods for kernel security mechanism for iOS9 and iOS10. Meanwhile, we propose a defense method based on kernel integrity detection and sensitive API call detection to defense breakthrough method mentioned above. And we make experiments to prove that this method can prevent and detect attack attempts or invaders effectively and timely.

Design of a multiple kernel learning algorithm for LS-SVM by convex programming.

PubMed

Jian, Ling; Xia, Zhonghang; Liang, Xijun; Gao, Chuanhou

2011-06-01

As a kernel based method, the performance of least squares support vector machine (LS-SVM) depends on the selection of the kernel as well as the regularization parameter (Duan, Keerthi, & Poo, 2003). Cross-validation is efficient in selecting a single kernel and the regularization parameter; however, it suffers from heavy computational cost and is not flexible to deal with multiple kernels. In this paper, we address the issue of multiple kernel learning for LS-SVM by formulating it as semidefinite programming (SDP). Furthermore, we show that the regularization parameter can be optimized in a unified framework with the kernel, which leads to an automatic process for model selection. Extensive experimental validations are performed and analyzed. Copyright © 2011 Elsevier Ltd. All rights reserved.

An O(log sup 2 N) parallel algorithm for computing the eigenvalues of a symmetric tridiagonal matrix

NASA Technical Reports Server (NTRS)

Swarztrauber, Paul N.

1989-01-01

An O(log sup 2 N) parallel algorithm is presented for computing the eigenvalues of a symmetric tridiagonal matrix using a parallel algorithm for computing the zeros of the characteristic polynomial. The method is based on a quadratic recurrence in which the characteristic polynomial is constructed on a binary tree from polynomials whose degree doubles at each level. Intervals that contain exactly one zero are determined by the zeros of polynomials at the previous level which ensures that different processors compute different zeros. The exact behavior of the polynomials at the interval endpoints is used to eliminate the usual problems induced by finite precision arithmetic.

Design of k-Space Channel Combination Kernels and Integration with Parallel Imaging

PubMed Central

Beatty, Philip J.; Chang, Shaorong; Holmes, James H.; Wang, Kang; Brau, Anja C. S.; Reeder, Scott B.; Brittain, Jean H.

2014-01-01

Purpose In this work, a new method is described for producing local k-space channel combination kernels using a small amount of low-resolution multichannel calibration data. Additionally, this work describes how these channel combination kernels can be combined with local k-space unaliasing kernels produced by the calibration phase of parallel imaging methods such as GRAPPA, PARS and ARC. Methods Experiments were conducted to evaluate both the image quality and computational efficiency of the proposed method compared to a channel-by-channel parallel imaging approach with image-space sum-of-squares channel combination. Results Results indicate comparable image quality overall, with some very minor differences seen in reduced field-of-view imaging. It was demonstrated that this method enables a speed up in computation time on the order of 3–16X for 32-channel data sets. Conclusion The proposed method enables high quality channel combination to occur earlier in the reconstruction pipeline, reducing computational and memory requirements for image reconstruction. PMID:23943602

A Generalized Sampling and Preconditioning Scheme for Sparse Approximation of Polynomial Chaos Expansions

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

Jakeman, John D.; Narayan, Akil; Zhou, Tao

We propose an algorithm for recovering sparse orthogonal polynomial expansions via collocation. A standard sampling approach for recovering sparse polynomials uses Monte Carlo sampling, from the density of orthogonality, which results in poor function recovery when the polynomial degree is high. Our proposed approach aims to mitigate this limitation by sampling with respect to the weighted equilibrium measure of the parametric domain and subsequently solves a preconditionedmore » $$\\ell^1$$-minimization problem, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function. Our algorithm can be applied to a wide class of orthogonal polynomial families on bounded and unbounded domains, including all classical families. We present theoretical analysis to motivate the algorithm and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. In conclusion, numerical examples are also provided to demonstrate that our proposed algorithm leads to comparable or improved accuracy even when compared with Legendre- and Hermite-specific algorithms.« less

A Generalized Sampling and Preconditioning Scheme for Sparse Approximation of Polynomial Chaos Expansions

DOE PAGES

Jakeman, John D.; Narayan, Akil; Zhou, Tao

2017-06-22

We propose an algorithm for recovering sparse orthogonal polynomial expansions via collocation. A standard sampling approach for recovering sparse polynomials uses Monte Carlo sampling, from the density of orthogonality, which results in poor function recovery when the polynomial degree is high. Our proposed approach aims to mitigate this limitation by sampling with respect to the weighted equilibrium measure of the parametric domain and subsequently solves a preconditionedmore » $$\\ell^1$$-minimization problem, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function. Our algorithm can be applied to a wide class of orthogonal polynomial families on bounded and unbounded domains, including all classical families. We present theoretical analysis to motivate the algorithm and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. In conclusion, numerical examples are also provided to demonstrate that our proposed algorithm leads to comparable or improved accuracy even when compared with Legendre- and Hermite-specific algorithms.« less

High speed sorting of Fusarium-damaged wheat kernels

USDA-ARS?s Scientific Manuscript database

Recent studies have found that resistance to Fusarium fungal infection can be inherited in wheat from one generation to another. However, there is not yet available a cost effective method to separate Fusarium-damaged wheat kernels from undamaged kernels so that wheat breeders can take advantage of...

Fine Mapping and Introgressing a Fissure Resistance Locus

USDA-ARS?s Scientific Manuscript database

Rice (Oryza sativa L.) kernel fissuring is a major concern of both rice producers and millers. Fissures are small cracks in rice kernels that increase breakage among kernels when transported or milled, which decrease the value of processed rice. This study employed molecular gene tagging methods to ...

Weighted Feature Gaussian Kernel SVM for Emotion Recognition

PubMed Central

Jia, Qingxuan

2016-01-01

Emotion recognition with weighted feature based on facial expression is a challenging research topic and has attracted great attention in the past few years. This paper presents a novel method, utilizing subregion recognition rate to weight kernel function. First, we divide the facial expression image into some uniform subregions and calculate corresponding recognition rate and weight. Then, we get a weighted feature Gaussian kernel function and construct a classifier based on Support Vector Machine (SVM). At last, the experimental results suggest that the approach based on weighted feature Gaussian kernel function has good performance on the correct rate in emotion recognition. The experiments on the extended Cohn-Kanade (CK+) dataset show that our method has achieved encouraging recognition results compared to the state-of-the-art methods. PMID:27807443

Local polynomial chaos expansion for linear differential equations with high dimensional random inputs

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

Chen, Yi; Jakeman, John; Gittelson, Claude

2015-01-08

In this paper we present a localized polynomial chaos expansion for partial differential equations (PDE) with random inputs. In particular, we focus on time independent linear stochastic problems with high dimensional random inputs, where the traditional polynomial chaos methods, and most of the existing methods, incur prohibitively high simulation cost. Furthermore, the local polynomial chaos method employs a domain decomposition technique to approximate the stochastic solution locally. In each subdomain, a subdomain problem is solved independently and, more importantly, in a much lower dimensional random space. In a postprocesing stage, accurate samples of the original stochastic problems are obtained frommore » the samples of the local solutions by enforcing the correct stochastic structure of the random inputs and the coupling conditions at the interfaces of the subdomains. Overall, the method is able to solve stochastic PDEs in very large dimensions by solving a collection of low dimensional local problems and can be highly efficient. In our paper we present the general mathematical framework of the methodology and use numerical examples to demonstrate the properties of the method.« less

DNA sequence+shape kernel enables alignment-free modeling of transcription factor binding.

PubMed

Ma, Wenxiu; Yang, Lin; Rohs, Remo; Noble, William Stafford

2017-10-01

Transcription factors (TFs) bind to specific DNA sequence motifs. Several lines of evidence suggest that TF-DNA binding is mediated in part by properties of the local DNA shape: the width of the minor groove, the relative orientations of adjacent base pairs, etc. Several methods have been developed to jointly account for DNA sequence and shape properties in predicting TF binding affinity. However, a limitation of these methods is that they typically require a training set of aligned TF binding sites. We describe a sequence + shape kernel that leverages DNA sequence and shape information to better understand protein-DNA binding preference and affinity. This kernel extends an existing class of k-mer based sequence kernels, based on the recently described di-mismatch kernel. Using three in vitro benchmark datasets, derived from universal protein binding microarrays (uPBMs), genomic context PBMs (gcPBMs) and SELEX-seq data, we demonstrate that incorporating DNA shape information improves our ability to predict protein-DNA binding affinity. In particular, we observe that (i) the k-spectrum + shape model performs better than the classical k-spectrum kernel, particularly for small k values; (ii) the di-mismatch kernel performs better than the k-mer kernel, for larger k; and (iii) the di-mismatch + shape kernel performs better than the di-mismatch kernel for intermediate k values. The software is available at https://bitbucket.org/wenxiu/sequence-shape.git. rohs@usc.edu or william-noble@uw.edu. Supplementary data are available at Bioinformatics online. © The Author(s) 2017. Published by Oxford University Press.

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.

Distributed smoothed tree kernel for protein-protein interaction extraction from the biomedical literature

PubMed Central

Murugesan, Gurusamy; Abdulkadhar, Sabenabanu; Natarajan, Jeyakumar

2017-01-01

Automatic extraction of protein-protein interaction (PPI) pairs from biomedical literature is a widely examined task in biological information extraction. Currently, many kernel based approaches such as linear kernel, tree kernel, graph kernel and combination of multiple kernels has achieved promising results in PPI task. However, most of these kernel methods fail to capture the semantic relation information between two entities. In this paper, we present a special type of tree kernel for PPI extraction which exploits both syntactic (structural) and semantic vectors information known as Distributed Smoothed Tree kernel (DSTK). DSTK comprises of distributed trees with syntactic information along with distributional semantic vectors representing semantic information of the sentences or phrases. To generate robust machine learning model composition of feature based kernel and DSTK were combined using ensemble support vector machine (SVM). Five different corpora (AIMed, BioInfer, HPRD50, IEPA, and LLL) were used for evaluating the performance of our system. Experimental results show that our system achieves better f-score with five different corpora compared to other state-of-the-art systems. PMID:29099838

Distributed smoothed tree kernel for protein-protein interaction extraction from the biomedical literature.

PubMed

Murugesan, Gurusamy; Abdulkadhar, Sabenabanu; Natarajan, Jeyakumar

2017-01-01

Automatic extraction of protein-protein interaction (PPI) pairs from biomedical literature is a widely examined task in biological information extraction. Currently, many kernel based approaches such as linear kernel, tree kernel, graph kernel and combination of multiple kernels has achieved promising results in PPI task. However, most of these kernel methods fail to capture the semantic relation information between two entities. In this paper, we present a special type of tree kernel for PPI extraction which exploits both syntactic (structural) and semantic vectors information known as Distributed Smoothed Tree kernel (DSTK). DSTK comprises of distributed trees with syntactic information along with distributional semantic vectors representing semantic information of the sentences or phrases. To generate robust machine learning model composition of feature based kernel and DSTK were combined using ensemble support vector machine (SVM). Five different corpora (AIMed, BioInfer, HPRD50, IEPA, and LLL) were used for evaluating the performance of our system. Experimental results show that our system achieves better f-score with five different corpora compared to other state-of-the-art systems.

Pulse transmission transmitter including a higher order time derivate filter

DOEpatents

Dress, Jr., William B.; Smith, Stephen F.

2003-09-23

Systems and methods for pulse-transmission low-power communication modes are disclosed. A pulse transmission transmitter includes: a clock; a pseudorandom polynomial generator coupled to the clock, the pseudorandom polynomial generator having a polynomial load input; an exclusive-OR gate coupled to the pseudorandom polynomial generator, the exclusive-OR gate having a serial data input; a programmable delay circuit coupled to both the clock and the exclusive-OR gate; a pulse generator coupled to the programmable delay circuit; and a higher order time derivative filter coupled to the pulse generator. The systems and methods significantly reduce lower-frequency emissions from pulse transmission spread-spectrum communication modes, which reduces potentially harmful interference to existing radio frequency services and users and also simultaneously permit transmission of multiple data bits by utilizing specific pulse shapes.

A nonlinear quality-related fault detection approach based on modified kernel partial least squares.

PubMed

Jiao, Jianfang; Zhao, Ning; Wang, Guang; Yin, Shen

2017-01-01

In this paper, a new nonlinear quality-related fault detection method is proposed based on kernel partial least squares (KPLS) model. To deal with the nonlinear characteristics among process variables, the proposed method maps these original variables into feature space in which the linear relationship between kernel matrix and output matrix is realized by means of KPLS. Then the kernel matrix is decomposed into two orthogonal parts by singular value decomposition (SVD) and the statistics for each part are determined appropriately for the purpose of quality-related fault detection. Compared with relevant existing nonlinear approaches, the proposed method has the advantages of simple diagnosis logic and stable performance. A widely used literature example and an industrial process are used for the performance evaluation for the proposed method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Volterra series truncation and kernel estimation of nonlinear systems in the frequency domain

NASA Astrophysics Data System (ADS)

Zhang, B.; Billings, S. A.

2017-02-01

The Volterra series model is a direct generalisation of the linear convolution integral and is capable of displaying the intrinsic features of a nonlinear system in a simple and easy to apply way. Nonlinear system analysis using Volterra series is normally based on the analysis of its frequency-domain kernels and a truncated description. But the estimation of Volterra kernels and the truncation of Volterra series are coupled with each other. In this paper, a novel complex-valued orthogonal least squares algorithm is developed. The new algorithm provides a powerful tool to determine which terms should be included in the Volterra series expansion and to estimate the kernels and thus solves the two problems all together. The estimated results are compared with those determined using the analytical expressions of the kernels to validate the method. To further evaluate the effectiveness of the method, the physical parameters of the system are also extracted from the measured kernels. Simulation studies demonstrates that the new approach not only can truncate the Volterra series expansion and estimate the kernels of a weakly nonlinear system, but also can indicate the applicability of the Volterra series analysis in a severely nonlinear system case.

On supervised graph Laplacian embedding CA model & kernel construction and its application

NASA Astrophysics Data System (ADS)

Zeng, Junwei; Qian, Yongsheng; Wang, Min; Yang, Yongzhong

2017-01-01

There are many methods to construct kernel with given data attribute information. Gaussian radial basis function (RBF) kernel is one of the most popular ways to construct a kernel. The key observation is that in real-world data, besides the data attribute information, data label information also exists, which indicates the data class. In order to make use of both data attribute information and data label information, in this work, we propose a supervised kernel construction method. Supervised information from training data is integrated into standard kernel construction process to improve the discriminative property of resulting kernel. A supervised Laplacian embedding cellular automaton model is another key application developed for two-lane heterogeneous traffic flow with the safe distance and large-scale truck. Based on the properties of traffic flow in China, we re-calibrate the cell length, velocity, random slowing mechanism and lane-change conditions and use simulation tests to study the relationships among the speed, density and flux. The numerical results show that the large-scale trucks will have great effects on the traffic flow, which are relevant to the proportion of the large-scale trucks, random slowing rate and the times of the lane space change.

On method of solving third-order ordinary differential equations directly using Bernstein polynomials

NASA Astrophysics Data System (ADS)

Khataybeh, S. N.; Hashim, I.

2018-04-01

In this paper, we propose for the first time a method based on Bernstein polynomials for solving directly a class of third-order ordinary differential equations (ODEs). This method gives a numerical solution by converting the equation into a system of algebraic equations which is solved directly. Some numerical examples are given to show the applicability of the method.

Strong stabilization servo controller with optimization of performance criteria.

PubMed

Sarjaš, Andrej; Svečko, Rajko; Chowdhury, Amor

2011-07-01

Synthesis of a simple robust controller with a pole placement technique and a H(∞) metrics is the method used for control of a servo mechanism with BLDC and BDC electric motors. The method includes solving a polynomial equation on the basis of the chosen characteristic polynomial using the Manabe standard polynomial form and parametric solutions. Parametric solutions are introduced directly into the structure of the servo controller. On the basis of the chosen parametric solutions the robustness of a closed-loop system is assessed through uncertainty models and assessment of the norm ‖•‖(∞). The design procedure and the optimization are performed with a genetic algorithm differential evolution - DE. The DE optimization method determines a suboptimal solution throughout the optimization on the basis of a spectrally square polynomial and Šiljak's absolute stability test. The stability of the designed controller during the optimization is being checked with Lipatov's stability condition. Both utilized approaches: Šiljak's test and Lipatov's condition, check the robustness and stability characteristics on the basis of the polynomial's coefficients, and are very convenient for automated design of closed-loop control and for application in optimization algorithms such as DE. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

Accurate Estimation of Solvation Free Energy Using Polynomial Fitting Techniques

PubMed Central

Shyu, Conrad; Ytreberg, F. Marty

2010-01-01

This report details an approach to improve the accuracy of free energy difference estimates using thermodynamic integration data (slope of the free energy with respect to the switching variable λ) and its application to calculating solvation free energy. The central idea is to utilize polynomial fitting schemes to approximate the thermodynamic integration data to improve the accuracy of the free energy difference estimates. Previously, we introduced the use of polynomial regression technique to fit thermodynamic integration data (Shyu and Ytreberg, J Comput Chem 30: 2297–2304, 2009). In this report we introduce polynomial and spline interpolation techniques. Two systems with analytically solvable relative free energies are used to test the accuracy of the interpolation approach. We also use both interpolation and regression methods to determine a small molecule solvation free energy. Our simulations show that, using such polynomial techniques and non-equidistant λ values, the solvation free energy can be estimated with high accuracy without using soft-core scaling and separate simulations for Lennard-Jones and partial charges. The results from our study suggest these polynomial techniques, especially with use of non-equidistant λ values, improve the accuracy for ΔF estimates without demanding additional simulations. We also provide general guidelines for use of polynomial fitting to estimate free energy. To allow researchers to immediately utilize these methods, free software and documentation is provided via http://www.phys.uidaho.edu/ytreberg/software. PMID:20623657

Scuba: scalable kernel-based gene prioritization.

PubMed

Zampieri, Guido; Tran, Dinh Van; Donini, Michele; Navarin, Nicolò; Aiolli, Fabio; Sperduti, Alessandro; Valle, Giorgio

2018-01-25

The uncovering of genes linked to human diseases is a pressing challenge in molecular biology and precision medicine. This task is often hindered by the large number of candidate genes and by the heterogeneity of the available information. Computational methods for the prioritization of candidate genes can help to cope with these problems. In particular, kernel-based methods are a powerful resource for the integration of heterogeneous biological knowledge, however, their practical implementation is often precluded by their limited scalability. We propose Scuba, a scalable kernel-based method for gene prioritization. It implements a novel multiple kernel learning approach, based on a semi-supervised perspective and on the optimization of the margin distribution. Scuba is optimized to cope with strongly unbalanced settings where known disease genes are few and large scale predictions are required. Importantly, it is able to efficiently deal both with a large amount of candidate genes and with an arbitrary number of data sources. As a direct consequence of scalability, Scuba integrates also a new efficient strategy to select optimal kernel parameters for each data source. We performed cross-validation experiments and simulated a realistic usage setting, showing that Scuba outperforms a wide range of state-of-the-art methods. Scuba achieves state-of-the-art performance and has enhanced scalability compared to existing kernel-based approaches for genomic data. This method can be useful to prioritize candidate genes, particularly when their number is large or when input data is highly heterogeneous. The code is freely available at https://github.com/gzampieri/Scuba .

On Partial Fraction Decompositions by Repeated Polynomial Divisions

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2017-01-01

We present a method for finding partial fraction decompositions of rational functions with linear or quadratic factors in the denominators by means of repeated polynomial divisions. This method does not involve differentiation or solving linear equations for obtaining the unknown partial fraction coefficients, which is very suitable for either…

Cross-domain question classification in community question answering via kernel mapping

NASA Astrophysics Data System (ADS)

Su, Lei; Hu, Zuoliang; Yang, Bin; Li, Yiyang; Chen, Jun

2015-10-01

An increasingly popular method for retrieving information is via the community question answering (CQA) systems such as Yahoo! Answers and Baidu Knows. In CQA, question classification plays an important role to find the answers. However, the labeled training examples for statistical question classifier are fairly expensive to obtain, as they require the experienced human efforts. Meanwhile, unlabeled data are readily available. This paper employs the method of domain adaptation via kernel mapping to solve this problem. In detail, the kernel approach is utilized to map the target-domain data and the source-domain data into a common space, where the question classifiers are trained under the closer conditional probabilities. The kernel mapping function is constructed by domain knowledge. Therefore, domain knowledge could be transferred from the labeled examples in the source domain to the unlabeled ones in the targeted domain. The statistical training model can be improved by using a large number of unlabeled data. Meanwhile, the Hadoop Platform is used to construct the mapping mechanism to reduce the time complexity. Map/Reduce enable kernel mapping for domain adaptation in parallel in the Hadoop Platform. Experimental results show that the accuracy of question classification could be improved by the method of kernel mapping. Furthermore, the parallel method in the Hadoop Platform could effective schedule the computing resources to reduce the running time.

Approximate kernel competitive learning.

PubMed

Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang

2015-03-01

Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches. Copyright © 2014 Elsevier Ltd. All rights reserved.

Rotational relaxation of AlO+(1Σ+) in collision with He

NASA Astrophysics Data System (ADS)

Denis-Alpizar, O.; Trabelsi, T.; Hochlaf, M.; Stoecklin, T.

2018-03-01

The rate coefficients for the rotational de-excitation of AlO+ by collisions with He are determined. The possible production mechanisms of the AlO+ ion in both diffuse and dense molecular clouds are first discussed. A set of ab initio interaction energies is computed at the CCSD(T)-F12 level of theory, and a three-dimensional analytical model of the potential energy surface is obtained using a linear combination of reproducing kernel Hilbert space polynomials together with an analytical long range potential. The nuclear spin free close-coupling equations are solved and the de-excitation rotational rate coefficients for the lower 15 rotational states of AlO+ are reported. A propensity rule to favour Δj = -1 transitions is obtained while the hyperfine resolved state-to-state rate coefficients are also discussed.

Polynomial dual energy inverse functions for bone Calcium/Phosphorus ratio determination and experimental evaluation.

PubMed

Sotiropoulou, P; Fountos, G; Martini, N; Koukou, V; Michail, C; Kandarakis, I; Nikiforidis, G

2016-12-01

An X-ray dual energy (XRDE) method was examined, using polynomial nonlinear approximation of inverse functions for the determination of the bone Calcium-to-Phosphorus (Ca/P) mass ratio. Inverse fitting functions with the least-squares estimation were used, to determine calcium and phosphate thicknesses. The method was verified by measuring test bone phantoms with a dedicated dual energy system and compared with previously published dual energy data. The accuracy in the determination of the calcium and phosphate thicknesses improved with the polynomial nonlinear inverse function method, introduced in this work, (ranged from 1.4% to 6.2%), compared to the corresponding linear inverse function method (ranged from 1.4% to 19.5%). Copyright © 2016 Elsevier Ltd. All rights reserved.

Minimizing Higgs potentials via numerical polynomial homotopy continuation

NASA Astrophysics Data System (ADS)

Maniatis, M.; Mehta, D.

2012-08-01

The study of models with extended Higgs sectors requires to minimize the corresponding Higgs potentials, which is in general very difficult. Here, we apply a recently developed method, called numerical polynomial homotopy continuation (NPHC), which guarantees to find all the stationary points of the Higgs potentials with polynomial-like non-linearity. The detection of all stationary points reveals the structure of the potential with maxima, metastable minima, saddle points besides the global minimum. We apply the NPHC method to the most general Higgs potential having two complex Higgs-boson doublets and up to five real Higgs-boson singlets. Moreover the method is applicable to even more involved potentials. Hence the NPHC method allows to go far beyond the limits of the Gröbner basis approach.

A Subspace Semi-Definite programming-based Underestimation (SSDU) method for stochastic global optimization in protein docking*

PubMed Central

Nan, Feng; Moghadasi, Mohammad; Vakili, Pirooz; Vajda, Sandor; Kozakov, Dima; Ch. Paschalidis, Ioannis

2015-01-01

We propose a new stochastic global optimization method targeting protein docking problems. The method is based on finding a general convex polynomial underestimator to the binding energy function in a permissive subspace that possesses a funnel-like structure. We use Principal Component Analysis (PCA) to determine such permissive subspaces. The problem of finding the general convex polynomial underestimator is reduced into the problem of ensuring that a certain polynomial is a Sum-of-Squares (SOS), which can be done via semi-definite programming. The underestimator is then used to bias sampling of the energy function in order to recover a deep minimum. We show that the proposed method significantly improves the quality of docked conformations compared to existing methods. PMID:25914440

Error and Complexity Analysis for a Collocation-Grid-Projection Plus Precorrected-FFT Algorithm for Solving Potential Integral Equations with LaPlace or Helmholtz Kernels

NASA Technical Reports Server (NTRS)

Phillips, J. R.

1996-01-01

In this paper we derive error bounds for a collocation-grid-projection scheme tuned for use in multilevel methods for solving boundary-element discretizations of potential integral equations. The grid-projection scheme is then combined with a precorrected FFT style multilevel method for solving potential integral equations with 1/r and e(sup ikr)/r kernels. A complexity analysis of this combined method is given to show that for homogeneous problems, the method is order n natural log n nearly independent of the kernel. In addition, it is shown analytically and experimentally that for an inhomogeneity generated by a very finely discretized surface, the combined method slows to order n(sup 4/3). Finally, examples are given to show that the collocation-based grid-projection plus precorrected-FFT scheme is competitive with fast-multipole algorithms when considering realistic problems and 1/r kernels, but can be used over a range of spatial frequencies with only a small performance penalty.

Why High-Order Polynomials Should Not Be Used in Regression Discontinuity Designs. NBER Working Paper No. 20405

ERIC Educational Resources Information Center

Gelman, Andrew; Imbens, Guido

2014-01-01

It is common in regression discontinuity analysis to control for high order (third, fourth, or higher) polynomials of the forcing variable. We argue that estimators for causal effects based on such methods can be misleading, and we recommend researchers do not use them, and instead use estimators based on local linear or quadratic polynomials or…

Automatic classification of retinal three-dimensional optical coherence tomography images using principal component analysis network with composite kernels

NASA Astrophysics Data System (ADS)

Fang, Leyuan; Wang, Chong; Li, Shutao; Yan, Jun; Chen, Xiangdong; Rabbani, Hossein

2017-11-01

We present an automatic method, termed as the principal component analysis network with composite kernel (PCANet-CK), for the classification of three-dimensional (3-D) retinal optical coherence tomography (OCT) images. Specifically, the proposed PCANet-CK method first utilizes the PCANet to automatically learn features from each B-scan of the 3-D retinal OCT images. Then, multiple kernels are separately applied to a set of very important features of the B-scans and these kernels are fused together, which can jointly exploit the correlations among features of the 3-D OCT images. Finally, the fused (composite) kernel is incorporated into an extreme learning machine for the OCT image classification. We tested our proposed algorithm on two real 3-D spectral domain OCT (SD-OCT) datasets (of normal subjects and subjects with the macular edema and age-related macular degeneration), which demonstrated its effectiveness.

Tocochromanols composition in kernels recovered from different apricot varieties: RP-HPLC/FLD and RP-UPLC-ESI/MS(n) study.

PubMed

Górnaś, Paweł; Mišina, Inga; Grāvīte, Ilze; Soliven, Arianne; Kaufmane, Edīte; Segliņa, Dalija

2015-01-01

Composition of tocochromanols in kernels recovered from 16 different apricot varieties (Prunus armeniaca L.) was studied. Three tocopherol (T) homologues, namely α, γ and δ, were quantified in all tested samples by an RP-HPLC/FLD method. The γ-T was the main tocopherol homologue identified in apricot kernels and constituted approximately 93% of total detected tocopherols. The RP-UPLC-ESI/MS(n) method detected trace amounts of two tocotrienol homologues α and γ in the apricot kernels. The concentration of individual tocopherol homologues in kernels of different apricots varieties, expressed in mg/100 g dwb, was in the following range: 1.38-4.41 (α-T), 42.48-73.27 (γ-T) and 0.77-2.09 (δ-T). Moreover, the ratio between individual tocopherol homologues α:γ:δ was nearly constant in all varieties and amounted to approximately 2:39:1.

Application of kernel functions for accurate similarity search in large chemical databases.

PubMed

Wang, Xiaohong; Huan, Jun; Smalter, Aaron; Lushington, Gerald H

2010-04-29

Similarity search in chemical structure databases is an important problem with many applications in chemical genomics, drug design, and efficient chemical probe screening among others. It is widely believed that structure based methods provide an efficient way to do the query. Recently various graph kernel functions have been designed to capture the intrinsic similarity of graphs. Though successful in constructing accurate predictive and classification models, graph kernel functions can not be applied to large chemical compound database due to the high computational complexity and the difficulties in indexing similarity search for large databases. To bridge graph kernel function and similarity search in chemical databases, we applied a novel kernel-based similarity measurement, developed in our team, to measure similarity of graph represented chemicals. In our method, we utilize a hash table to support new graph kernel function definition, efficient storage and fast search. We have applied our method, named G-hash, to large chemical databases. Our results show that the G-hash method achieves state-of-the-art performance for k-nearest neighbor (k-NN) classification. Moreover, the similarity measurement and the index structure is scalable to large chemical databases with smaller indexing size, and faster query processing time as compared to state-of-the-art indexing methods such as Daylight fingerprints, C-tree and GraphGrep. Efficient similarity query processing method for large chemical databases is challenging since we need to balance running time efficiency and similarity search accuracy. Our previous similarity search method, G-hash, provides a new way to perform similarity search in chemical databases. Experimental study validates the utility of G-hash in chemical databases.

Sensitivities Kernels of Seismic Traveltimes and Amplitudes for Quality Factor and Boundary Topography

NASA Astrophysics Data System (ADS)

Hsieh, M.; Zhao, L.; Ma, K.

2010-12-01

Finite-frequency approach enables seismic tomography to fully utilize the spatial and temporal distributions of the seismic wavefield to improve resolution. In achieving this goal, one of the most important tasks is to compute efficiently and accurately the (Fréchet) sensitivity kernels of finite-frequency seismic observables such as traveltime and amplitude to the perturbations of model parameters. In scattering-integral approach, the Fréchet kernels are expressed in terms of the strain Green tensors (SGTs), and a pre-established SGT database is necessary to achieve practical efficiency for a three-dimensional reference model in which the SGTs must be calculated numerically. Methods for computing Fréchet kernels for seismic velocities have long been established. In this study, we develop algorithms based on the finite-difference method for calculating Fréchet kernels for the quality factor Qμ and seismic boundary topography. Kernels for the quality factor can be obtained in a way similar to those for seismic velocities with the help of the Hilbert transform. The effects of seismic velocities and quality factor on either traveltime or amplitude are coupled. Kernels for boundary topography involve spatial gradient of the SGTs and they also exhibit interesting finite-frequency characteristics. Examples of quality factor and boundary topography kernels will be shown for a realistic model for the Taiwan region with three-dimensional velocity variation as well as surface and Moho discontinuity topography.

Frequency domain system identification methods - Matrix fraction description approach

NASA Technical Reports Server (NTRS)

Horta, Luca G.; Juang, Jer-Nan

1993-01-01

This paper presents the use of matrix fraction descriptions for least-squares curve fitting of the frequency spectra to compute two matrix polynomials. The matrix polynomials are intermediate step to obtain a linearized representation of the experimental transfer function. Two approaches are presented: first, the matrix polynomials are identified using an estimated transfer function; second, the matrix polynomials are identified directly from the cross/auto spectra of the input and output signals. A set of Markov parameters are computed from the polynomials and subsequently realization theory is used to recover a minimum order state space model. Unevenly spaced frequency response functions may be used. Results from a simple numerical example and an experiment are discussed to highlight some of the important aspect of the algorithm.

On Quantile Regression in Reproducing Kernel Hilbert Spaces with Data Sparsity Constraint

PubMed Central

Zhang, Chong; Liu, Yufeng; Wu, Yichao

2015-01-01

For spline regressions, it is well known that the choice of knots is crucial for the performance of the estimator. As a general learning framework covering the smoothing splines, learning in a Reproducing Kernel Hilbert Space (RKHS) has a similar issue. However, the selection of training data points for kernel functions in the RKHS representation has not been carefully studied in the literature. In this paper we study quantile regression as an example of learning in a RKHS. In this case, the regular squared norm penalty does not perform training data selection. We propose a data sparsity constraint that imposes thresholding on the kernel function coefficients to achieve a sparse kernel function representation. We demonstrate that the proposed data sparsity method can have competitive prediction performance for certain situations, and have comparable performance in other cases compared to that of the traditional squared norm penalty. Therefore, the data sparsity method can serve as a competitive alternative to the squared norm penalty method. Some theoretical properties of our proposed method using the data sparsity constraint are obtained. Both simulated and real data sets are used to demonstrate the usefulness of our data sparsity constraint. PMID:27134575

Super-resolution fusion of complementary panoramic images based on cross-selection kernel regression interpolation.

PubMed

Chen, Lidong; Basu, Anup; Zhang, Maojun; Wang, Wei; Liu, Yu

2014-03-20

A complementary catadioptric imaging technique was proposed to solve the problem of low and nonuniform resolution in omnidirectional imaging. To enhance this research, our paper focuses on how to generate a high-resolution panoramic image from the captured omnidirectional image. To avoid the interference between the inner and outer images while fusing the two complementary views, a cross-selection kernel regression method is proposed. First, in view of the complementarity of sampling resolution in the tangential and radial directions between the inner and the outer images, respectively, the horizontal gradients in the expected panoramic image are estimated based on the scattered neighboring pixels mapped from the outer, while the vertical gradients are estimated using the inner image. Then, the size and shape of the regression kernel are adaptively steered based on the local gradients. Furthermore, the neighboring pixels in the next interpolation step of kernel regression are also selected based on the comparison between the horizontal and vertical gradients. In simulation and real-image experiments, the proposed method outperforms existing kernel regression methods and our previous wavelet-based fusion method in terms of both visual quality and objective evaluation.

Tutte polynomial in functional magnetic resonance imaging

NASA Astrophysics Data System (ADS)

García-Castillón, Marlly V.

2015-09-01

Methods of graph theory are applied to the processing of functional magnetic resonance images. Specifically the Tutte polynomial is used to analyze such kind of images. Functional Magnetic Resonance Imaging provide us connectivity networks in the brain which are represented by graphs and the Tutte polynomial will be applied. The problem of computing the Tutte polynomial for a given graph is #P-hard even for planar graphs. For a practical application the maple packages "GraphTheory" and "SpecialGraphs" will be used. We will consider certain diagram which is depicting functional connectivity, specifically between frontal and posterior areas, in autism during an inferential text comprehension task. The Tutte polynomial for the resulting neural networks will be computed and some numerical invariants for such network will be obtained. Our results show that the Tutte polynomial is a powerful tool to analyze and characterize the networks obtained from functional magnetic resonance imaging.

A method of smoothed particle hydrodynamics using spheroidal kernels

NASA Technical Reports Server (NTRS)

Fulbright, Michael S.; Benz, Willy; Davies, Melvyn B.

1995-01-01

We present a new method of three-dimensional smoothed particle hydrodynamics (SPH) designed to model systems dominated by deformation along a preferential axis. These systems cause severe problems for SPH codes using spherical kernels, which are best suited for modeling systems which retain rough spherical symmetry. Our method allows the smoothing length in the direction of the deformation to evolve independently of the smoothing length in the perpendicular plane, resulting in a kernel with a spheroidal shape. As a result the spatial resolution in the direction of deformation is significantly improved. As a test case we present the one-dimensional homologous collapse of a zero-temperature, uniform-density cloud, which serves to demonstrate the advantages of spheroidal kernels. We also present new results on the problem of the tidal disruption of a star by a massive black hole.

THERMOS. 30-Group ENDF/B Scattered Kernels

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

McCrosson, F.J.; Finch, D.R.

1973-12-01

These data are 30-group THERMOS thermal scattering kernels for P0 to P5 Legendre orders for every temperature of every material from s(alpha,beta) data stored in the ENDF/B library. These scattering kernels were generated using the FLANGE2 computer code. To test the kernels, the integral properties of each set of kernels were determined by a precision integration of the diffusion length equation and compared to experimental measurements of these properties. In general, the agreement was very good. Details of the methods used and results obtained are contained in the reference. The scattering kernels are organized into a two volume magnetic tapemore » library from which they may be retrieved easily for use in any 30-group THERMOS library.« less

Depth-time interpolation of feature trends extracted from mobile microelectrode data with kernel functions.

PubMed

Wong, Stephen; Hargreaves, Eric L; Baltuch, Gordon H; Jaggi, Jurg L; Danish, Shabbar F

2012-01-01

Microelectrode recording (MER) is necessary for precision localization of target structures such as the subthalamic nucleus during deep brain stimulation (DBS) surgery. Attempts to automate this process have produced quantitative temporal trends (feature activity vs. time) extracted from mobile MER data. Our goal was to evaluate computational methods of generating spatial profiles (feature activity vs. depth) from temporal trends that would decouple automated MER localization from the clinical procedure and enhance functional localization in DBS surgery. We evaluated two methods of interpolation (standard vs. kernel) that generated spatial profiles from temporal trends. We compared interpolated spatial profiles to true spatial profiles that were calculated with depth windows, using correlation coefficient analysis. Excellent approximation of true spatial profiles is achieved by interpolation. Kernel-interpolated spatial profiles produced superior correlation coefficient values at optimal kernel widths (r = 0.932-0.940) compared to standard interpolation (r = 0.891). The choice of kernel function and kernel width resulted in trade-offs in smoothing and resolution. Interpolation of feature activity to create spatial profiles from temporal trends is accurate and can standardize and facilitate MER functional localization of subcortical structures. The methods are computationally efficient, enhancing localization without imposing additional constraints on the MER clinical procedure during DBS surgery. Copyright © 2012 S. Karger AG, Basel.

A Network-Based Kernel Machine Test for the Identification of Risk Pathways in Genome-Wide Association Studies

PubMed Central

Freytag, Saskia; Manitz, Juliane; Schlather, Martin; Kneib, Thomas; Amos, Christopher I.; Risch, Angela; Chang-Claude, Jenny; Heinrich, Joachim; Bickeböller, Heike

2014-01-01

Biological pathways provide rich information and biological context on the genetic causes of complex diseases. The logistic kernel machine test integrates prior knowledge on pathways in order to analyze data from genome-wide association studies (GWAS). Here, the kernel converts genomic information of two individuals to a quantitative value reflecting their genetic similarity. With the selection of the kernel one implicitly chooses a genetic effect model. Like many other pathway methods, none of the available kernels accounts for topological structure of the pathway or gene-gene interaction types. However, evidence indicates that connectivity and neighborhood of genes are crucial in the context of GWAS, because genes associated with a disease often interact. Thus, we propose a novel kernel that incorporates the topology of pathways and information on interactions. Using simulation studies, we demonstrate that the proposed method maintains the type I error correctly and can be more effective in the identification of pathways associated with a disease than non-network-based methods. We apply our approach to genome-wide association case control data on lung cancer and rheumatoid arthritis. We identify some promising new pathways associated with these diseases, which may improve our current understanding of the genetic mechanisms. PMID:24434848

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

PubMed

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

2016-05-01

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

A FAST POLYNOMIAL TRANSFORM PROGRAM WITH A MODULARIZED STRUCTURE

NASA Technical Reports Server (NTRS)

Truong, T. K.

1994-01-01

This program utilizes a fast polynomial transformation (FPT) algorithm applicable to two-dimensional mathematical convolutions. Two-dimensional convolution has many applications, particularly in image processing. Two-dimensional cyclic convolutions can be converted to a one-dimensional convolution in a polynomial ring. Traditional FPT methods decompose the one-dimensional cyclic polynomial into polynomial convolutions of different lengths. This program will decompose a cyclic polynomial into polynomial convolutions of the same length. Thus, only FPTs and Fast Fourier Transforms of the same length are required. This modular approach can save computational resources. To further enhance its appeal, the program is written in the transportable 'C' language. The steps in the algorithm are: 1) formulate the modulus reduction equations, 2) calculate the polynomial transforms, 3) multiply the transforms using a generalized fast Fourier transformation, 4) compute the inverse polynomial transforms, and 5) reconstruct the final matrices using the Chinese remainder theorem. Input to this program is comprised of the row and column dimensions and the initial two matrices. The matrices are printed out at all steps, ending with the final reconstruction. This program is written in 'C' for batch execution and has been implemented on the IBM PC series of computers under DOS with a central memory requirement of approximately 18K of 8 bit bytes. This program was developed in 1986.

A kernel function method for computing steady and oscillatory supersonic aerodynamics with interference.

NASA Technical Reports Server (NTRS)

Cunningham, A. M., Jr.

1973-01-01

The method presented uses a collocation technique with the nonplanar kernel function to solve supersonic lifting surface problems with and without interference. A set of pressure functions are developed based on conical flow theory solutions which account for discontinuities in the supersonic pressure distributions. These functions permit faster solution convergence than is possible with conventional supersonic pressure functions. An improper integral of a 3/2 power singularity along the Mach hyperbola of the nonplanar supersonic kernel function is described and treated. The method is compared with other theories and experiment for a variety of cases.

Oscillatory supersonic kernel function method for interfering surfaces

NASA Technical Reports Server (NTRS)

Cunningham, A. M., Jr.

1974-01-01

In the method presented in this paper, a collocation technique is used with the nonplanar supersonic kernel function to solve multiple lifting surface problems with interference in steady or oscillatory flow. The pressure functions used are based on conical flow theory solutions and provide faster solution convergence than is possible with conventional functions. In the application of the nonplanar supersonic kernel function, an improper integral of a 3/2 power singularity along the Mach hyperbola is described and treated. The method is compared with other theories and experiment for two wing-tail configurations in steady and oscillatory flow.

The Continuized Log-Linear Method: An Alternative to the Kernel Method of Continuization in Test Equating

ERIC Educational Resources Information Center

Wang, Tianyou

2008-01-01

Von Davier, Holland, and Thayer (2004) laid out a five-step framework of test equating that can be applied to various data collection designs and equating methods. In the continuization step, they presented an adjusted Gaussian kernel method that preserves the first two moments. This article proposes an alternative continuization method that…

Moisture Adsorption Isotherm and Storability of Hazelnut Inshells and Kernels Produced in Oregon, USA.

PubMed

Jung, Jooyeoun; Wang, Wenjie; McGorrin, Robert J; Zhao, Yanyun

2018-02-01

Moisture adsorption isotherms and storability of dried hazelnut inshells and kernels produced in Oregon were evaluated and compared among cultivars, including Barcelona, Yamhill, and Jefferson. Experimental moisture adsorption data fitted to Guggenheim-Anderson-de Boer (GAB) model, showing less hygroscopic properties in Yamhill than other cultivars of inshells and kernels due to lower content of carbohydrate and protein, but higher content of fat. The safe levels of moisture content (MC, dry basis) of dried inshells and kernels for reaching kernel water activity (a w ) ≤0.65 were estimated using the GAB model as 11.3% and 5.0% for Barcelona, 9.4% and 4.2% for Yamhill, and 10.7% and 4.9% for Jefferson, respectively. Storage conditions (2 °C at 85% to 95% relative humidity [RH], 10 °C at 65% to 75% RH, and 27 °C at 35% to 45% RH), times (0, 4, 8, or 12 mo), and packaging methods (atmosphere vs. vacuum) affected MC, a w , bioactive compounds, lipid oxidation, and enzyme activity of dried hazelnut inshells or kernels. For inshells packaged at woven polypropylene bag, MC and a w of inshells and kernels (inside shells) increased at 2 and 10 °C, but decreased at 27 °C during storage. For kernels, lipid oxidation and polyphenol oxidase activity also increased with extended storage time (P < 0.05), and MC and a w of vacuum packaged samples were more stable during storage than those atmospherically packaged ones. Principal component analysis showed correlation of kernel qualities with storage condition, time, and packaging method. This study demonstrated that the ideal storage condition or packaging method varied among cultivars due to their different moisture adsorption and physicochemical and enzymatic stability during storage. Moisture adsorption isotherm of hazelnut inshells and kernels is useful for predicting the storability of nuts. This study found that water adsorption and storability varied among the different cultivars of nuts, in which Yamhill was less hygroscopic than Barcelona and Jefferson, thus more stable during storage. For ensuring food safety and quality of nuts during storage, each cultivar of kernels should be dried to a certain level of MC. Lipid oxidation and enzyme activity of kernel could be increased with extended storage time. Vacuum packaging was recommended to kernels for reducing moisture adsorption during storage. © 2018 Institute of Food Technologists®.

Protein Analysis Meets Visual Word Recognition: A Case for String Kernels in the Brain

ERIC Educational Resources Information Center

Hannagan, Thomas; Grainger, Jonathan

2012-01-01

It has been recently argued that some machine learning techniques known as Kernel methods could be relevant for capturing cognitive and neural mechanisms (Jakel, Scholkopf, & Wichmann, 2009). We point out that "String kernels," initially designed for protein function prediction and spam detection, are virtually identical to one contending proposal…

Bands selection and classification of hyperspectral images based on hybrid kernels SVM by evolutionary algorithm

NASA Astrophysics Data System (ADS)

Hu, Yan-Yan; Li, Dong-Sheng

2016-01-01

The hyperspectral images(HSI) consist of many closely spaced bands carrying the most object information. While due to its high dimensionality and high volume nature, it is hard to get satisfactory classification performance. In order to reduce HSI data dimensionality preparation for high classification accuracy, it is proposed to combine a band selection method of artificial immune systems (AIS) with a hybrid kernels support vector machine (SVM-HK) algorithm. In fact, after comparing different kernels for hyperspectral analysis, the approach mixed radial basis function kernel (RBF-K) with sigmoid kernel (Sig-K) and applied the optimized hybrid kernels in SVM classifiers. Then the SVM-HK algorithm used to induce the bands selection of an improved version of AIS. The AIS was composed of clonal selection and elite antibody mutation, including evaluation process with optional index factor (OIF). Experimental classification performance was on a San Diego Naval Base acquired by AVIRIS, the HRS dataset shows that the method is able to efficiently achieve bands redundancy removal while outperforming the traditional SVM classifier.

Fully-Automated High-Throughput NMR System for Screening of Haploid Kernels of Maize (Corn) by Measurement of Oil Content

PubMed Central

Xu, Xiaoping; Huang, Qingming; Chen, Shanshan; Yang, Peiqiang; Chen, Shaojiang; Song, Yiqiao

2016-01-01

One of the modern crop breeding techniques uses doubled haploid plants that contain an identical pair of chromosomes in order to accelerate the breeding process. Rapid haploid identification method is critical for large-scale selections of double haploids. The conventional methods based on the color of the endosperm and embryo seeds are slow, manual and prone to error. On the other hand, there exists a significant difference between diploid and haploid seeds generated by high oil inducer, which makes it possible to use oil content to identify the haploid. This paper describes a fully-automated high-throughput NMR screening system for maize haploid kernel identification. The system is comprised of a sampler unit to select a single kernel to feed for measurement of NMR and weight, and a kernel sorter to distribute the kernel according to the measurement result. Tests of the system show a consistent accuracy of 94% with an average screening time of 4 seconds per kernel. Field test result is described and the directions for future improvement are discussed. PMID:27454427

Unsupervised multiple kernel learning for heterogeneous data integration.

PubMed

Mariette, Jérôme; Villa-Vialaneix, Nathalie

2018-03-15

Recent high-throughput sequencing advances have expanded the breadth of available omics datasets and the integrated analysis of multiple datasets obtained on the same samples has allowed to gain important insights in a wide range of applications. However, the integration of various sources of information remains a challenge for systems biology since produced datasets are often of heterogeneous types, with the need of developing generic methods to take their different specificities into account. We propose a multiple kernel framework that allows to integrate multiple datasets of various types into a single exploratory analysis. Several solutions are provided to learn either a consensus meta-kernel or a meta-kernel that preserves the original topology of the datasets. We applied our framework to analyse two public multi-omics datasets. First, the multiple metagenomic datasets, collected during the TARA Oceans expedition, was explored to demonstrate that our method is able to retrieve previous findings in a single kernel PCA as well as to provide a new image of the sample structures when a larger number of datasets are included in the analysis. To perform this analysis, a generic procedure is also proposed to improve the interpretability of the kernel PCA in regards with the original data. Second, the multi-omics breast cancer datasets, provided by The Cancer Genome Atlas, is analysed using a kernel Self-Organizing Maps with both single and multi-omics strategies. The comparison of these two approaches demonstrates the benefit of our integration method to improve the representation of the studied biological system. Proposed methods are available in the R package mixKernel, released on CRAN. It is fully compatible with the mixOmics package and a tutorial describing the approach can be found on mixOmics web site http://mixomics.org/mixkernel/. jerome.mariette@inra.fr or nathalie.villa-vialaneix@inra.fr. Supplementary data are available at Bioinformatics online.

Characterization of non-diffusive transport in plasma turbulence by means of flux-gradient integro-differential kernels

NASA Astrophysics Data System (ADS)

Alcuson, J. A.; Reynolds-Barredo, J. M.; Mier, J. A.; Sanchez, Raul; Del-Castillo-Negrete, Diego; Newman, David E.; Tribaldos, V.

2015-11-01

A method to determine fractional transport exponents in systems dominated by fluid or plasma turbulence is proposed. The method is based on the estimation of the integro-differential kernel that relates values of the fluxes and gradients of the transported field, and its comparison with the family of analytical kernels of the linear fractional transport equation. Although use of this type of kernels has been explored before in this context, the methodology proposed here is rather unique since the connection with specific fractional equations is exploited from the start. The procedure has been designed to be particularly well-suited for application in experimental setups, taking advantage of the fact that kernel determination only requires temporal data of the transported field measured on an Eulerian grid. The simplicity and robustness of the method is tested first by using fabricated data from continuous-time random walk models built with prescribed transport characteristics. Its strengths are then illustrated on numerical Eulerian data gathered from simulations of a magnetically confined turbulent plasma in a near-critical regime, that is known to exhibit superdiffusive radial transport

Cylinder stitching interferometry: with and without overlap regions

NASA Astrophysics Data System (ADS)

Peng, Junzheng; Chen, Dingfu; Yu, Yingjie

2017-06-01

Since the cylinder surface is closed and periodic in the azimuthal direction, existing stitching methods cannot be used to yield the 360° form map. To address this problem, this paper presents two methods for stitching interferometry of cylinder: one requires overlap regions, and the other does not need the overlap regions. For the former, we use the first order approximation of cylindrical coordinate transformation to build the stitching model. With it, the relative parameters between the adjacent sub-apertures can be calculated by the stitching model. For the latter, a set of orthogonal polynomials, termed Legendre Fourier (LF) polynomials, was developed. With these polynomials, individual sub-aperture data can be expanded as composition of inherent form of partial cylinder surface and additional misalignment parameters. Then the 360° form map can be acquired by simultaneously fitting all sub-aperture data with LF polynomials. Finally the two proposed methods are compared under various conditions. The merits and drawbacks of each stitching method are consequently revealed to provide suggestion in acquisition of 360° form map for a precision cylinder.

A new numerical treatment based on Lucas polynomials for 1D and 2D sinh-Gordon equation

NASA Astrophysics Data System (ADS)

Oruç, Ömer

2018-04-01

In this paper, a new mixed method based on Lucas and Fibonacci polynomials is developed for numerical solutions of 1D and 2D sinh-Gordon equations. Firstly time variable discretized by central finite difference and then unknown function and its derivatives are expanded to Lucas series. With the help of these series expansion and Fibonacci polynomials, matrices for differentiation are derived. With this approach, finding the solution of sinh-Gordon equation transformed to finding the solution of an algebraic system of equations. Lucas series coefficients are acquired by solving this system of algebraic equations. Then by plugginging these coefficients into Lucas series expansion numerical solutions can be obtained consecutively. The main objective of this paper is to demonstrate that Lucas polynomial based method is convenient for 1D and 2D nonlinear problems. By calculating L2 and L∞ error norms of some 1D and 2D test problems efficiency and performance of the proposed method is monitored. Acquired accurate results confirm the applicability of the method.

Semiparametric methods for estimation of a nonlinear exposure-outcome relationship using instrumental variables with application to Mendelian randomization.

PubMed

Staley, James R; Burgess, Stephen

2017-05-01

Mendelian randomization, the use of genetic variants as instrumental variables (IV), can test for and estimate the causal effect of an exposure on an outcome. Most IV methods assume that the function relating the exposure to the expected value of the outcome (the exposure-outcome relationship) is linear. However, in practice, this assumption may not hold. Indeed, often the primary question of interest is to assess the shape of this relationship. We present two novel IV methods for investigating the shape of the exposure-outcome relationship: a fractional polynomial method and a piecewise linear method. We divide the population into strata using the exposure distribution, and estimate a causal effect, referred to as a localized average causal effect (LACE), in each stratum of population. The fractional polynomial method performs metaregression on these LACE estimates. The piecewise linear method estimates a continuous piecewise linear function, the gradient of which is the LACE estimate in each stratum. Both methods were demonstrated in a simulation study to estimate the true exposure-outcome relationship well, particularly when the relationship was a fractional polynomial (for the fractional polynomial method) or was piecewise linear (for the piecewise linear method). The methods were used to investigate the shape of relationship of body mass index with systolic blood pressure and diastolic blood pressure. © 2017 The Authors Genetic Epidemiology Published by Wiley Periodicals, Inc.

Semiparametric methods for estimation of a nonlinear exposure‐outcome relationship using instrumental variables with application to Mendelian randomization

PubMed Central

Staley, James R.

2017-01-01

ABSTRACT Mendelian randomization, the use of genetic variants as instrumental variables (IV), can test for and estimate the causal effect of an exposure on an outcome. Most IV methods assume that the function relating the exposure to the expected value of the outcome (the exposure‐outcome relationship) is linear. However, in practice, this assumption may not hold. Indeed, often the primary question of interest is to assess the shape of this relationship. We present two novel IV methods for investigating the shape of the exposure‐outcome relationship: a fractional polynomial method and a piecewise linear method. We divide the population into strata using the exposure distribution, and estimate a causal effect, referred to as a localized average causal effect (LACE), in each stratum of population. The fractional polynomial method performs metaregression on these LACE estimates. The piecewise linear method estimates a continuous piecewise linear function, the gradient of which is the LACE estimate in each stratum. Both methods were demonstrated in a simulation study to estimate the true exposure‐outcome relationship well, particularly when the relationship was a fractional polynomial (for the fractional polynomial method) or was piecewise linear (for the piecewise linear method). The methods were used to investigate the shape of relationship of body mass index with systolic blood pressure and diastolic blood pressure. PMID:28317167

Straight-chain halocarbon forming fluids for TRISO fuel kernel production - Tests with yttria-stabilized zirconia microspheres

NASA Astrophysics Data System (ADS)

Baker, M. P.; King, J. C.; Gorman, B. P.; Braley, J. C.

2015-03-01

Current methods of TRISO fuel kernel production in the United States use a sol-gel process with trichloroethylene (TCE) as the forming fluid. After contact with radioactive materials, the spent TCE becomes a mixed hazardous waste, and high costs are associated with its recycling or disposal. Reducing or eliminating this mixed waste stream would not only benefit the environment, but would also enhance the economics of kernel production. Previous research yielded three candidates for testing as alternatives to TCE: 1-bromotetradecane, 1-chlorooctadecane, and 1-iodododecane. This study considers the production of yttria-stabilized zirconia (YSZ) kernels in silicone oil and the three chosen alternative formation fluids, with subsequent characterization of the produced kernels and used forming fluid. Kernels formed in silicone oil and bromotetradecane were comparable to those produced by previous kernel production efforts, while those produced in chlorooctadecane and iodododecane experienced gelation issues leading to poor kernel formation and geometry.

CompareSVM: supervised, Support Vector Machine (SVM) inference of gene regularity networks.

PubMed

Gillani, Zeeshan; Akash, Muhammad Sajid Hamid; Rahaman, M D Matiur; Chen, Ming

2014-11-30

Predication of gene regularity network (GRN) from expression data is a challenging task. There are many methods that have been developed to address this challenge ranging from supervised to unsupervised methods. Most promising methods are based on support vector machine (SVM). There is a need for comprehensive analysis on prediction accuracy of supervised method SVM using different kernels on different biological experimental conditions and network size. We developed a tool (CompareSVM) based on SVM to compare different kernel methods for inference of GRN. Using CompareSVM, we investigated and evaluated different SVM kernel methods on simulated datasets of microarray of different sizes in detail. The results obtained from CompareSVM showed that accuracy of inference method depends upon the nature of experimental condition and size of the network. For network with nodes (<200) and average (over all sizes of networks), SVM Gaussian kernel outperform on knockout, knockdown, and multifactorial datasets compared to all the other inference methods. For network with large number of nodes (~500), choice of inference method depend upon nature of experimental condition. CompareSVM is available at http://bis.zju.edu.cn/CompareSVM/ .

On one solution of Volterra integral equations of second kind

NASA Astrophysics Data System (ADS)

Myrhorod, V.; Hvozdeva, I.

2016-10-01

A solution of Volterra integral equations of the second kind with separable and difference kernels based on solutions of corresponding equations linking the kernel and resolvent is suggested. On the basis of a discrete functions class, the equations linking the kernel and resolvent are obtained and the methods of their analytical solutions are proposed. A mathematical model of the gas-turbine engine state modification processes in the form of Volterra integral equation of the second kind with separable kernel is offered.

Graph wavelet alignment kernels for drug virtual screening.

PubMed

Smalter, Aaron; Huan, Jun; Lushington, Gerald

2009-06-01

In this paper, we introduce a novel statistical modeling technique for target property prediction, with applications to virtual screening and drug design. In our method, we use graphs to model chemical structures and apply a wavelet analysis of graphs to summarize features capturing graph local topology. We design a novel graph kernel function to utilize the topology features to build predictive models for chemicals via Support Vector Machine classifier. We call the new graph kernel a graph wavelet-alignment kernel. We have evaluated the efficacy of the wavelet-alignment kernel using a set of chemical structure-activity prediction benchmarks. Our results indicate that the use of the kernel function yields performance profiles comparable to, and sometimes exceeding that of the existing state-of-the-art chemical classification approaches. In addition, our results also show that the use of wavelet functions significantly decreases the computational costs for graph kernel computation with more than ten fold speedup.

Kernels, Degrees of Freedom, and Power Properties of Quadratic Distance Goodness-of-Fit Tests

PubMed Central

Lindsay, Bruce G.; Markatou, Marianthi; Ray, Surajit

2014-01-01

In this article, we study the power properties of quadratic-distance-based goodness-of-fit tests. First, we introduce the concept of a root kernel and discuss the considerations that enter the selection of this kernel. We derive an easy to use normal approximation to the power of quadratic distance goodness-of-fit tests and base the construction of a noncentrality index, an analogue of the traditional noncentrality parameter, on it. This leads to a method akin to the Neyman-Pearson lemma for constructing optimal kernels for specific alternatives. We then introduce a midpower analysis as a device for choosing optimal degrees of freedom for a family of alternatives of interest. Finally, we introduce a new diffusion kernel, called the Pearson-normal kernel, and study the extent to which the normal approximation to the power of tests based on this kernel is valid. Supplementary materials for this article are available online. PMID:24764609

Trajectory Optimization for Helicopter Unmanned Aerial Vehicles (UAVs)

DTIC Science & Technology

2010-06-01

the Nth-order derivative of the Legendre Polynomial ( )NL t . Using this method, the range of integration is transformed universally to [-1,+1...which is the interval for Legendre Polynomials . Although the LGL interpolation points are not evenly spaced, they are symmetric about the midpoint 0...the vehicle’s kinematic constraints are parameterized in terms of polynomials of sufficient order, (2) A collision-free criterion is developed and

Quantum models with energy-dependent potentials solvable in terms of exceptional orthogonal polynomials

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

Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu; Department of Physics, Indiana University Northwest, 3400 Broadway, Gary IN 46408; Roy, Pinaki, E-mail: pinaki@isical.ac.in

We construct energy-dependent potentials for which the Schrödinger equations admit solutions in terms of exceptional orthogonal polynomials. Our method of construction is based on certain point transformations, applied to the equations of exceptional Hermite, Jacobi and Laguerre polynomials. We present several examples of boundary-value problems with energy-dependent potentials that admit a discrete spectrum and the corresponding normalizable solutions in closed form.

Kernel reconstruction methods for Doppler broadening — Temperature interpolation by linear combination of reference cross sections at optimally chosen temperatures

DOE PAGES

Ducru, Pablo; Josey, Colin; Dibert, Karia; ...

2017-01-25

This paper establishes a new family of methods to perform temperature interpolation of nuclear interactions cross sections, reaction rates, or cross sections times the energy. One of these quantities at temperature T is approximated as a linear combination of quantities at reference temperatures (T j). The problem is formalized in a cross section independent fashion by considering the kernels of the different operators that convert cross section related quantities from a temperature T 0 to a higher temperature T — namely the Doppler broadening operation. Doppler broadening interpolation of nuclear cross sections is thus here performed by reconstructing the kernelmore » of the operation at a given temperature T by means of linear combination of kernels at reference temperatures (T j). The choice of the L 2 metric yields optimal linear interpolation coefficients in the form of the solutions of a linear algebraic system inversion. The optimization of the choice of reference temperatures (T j) is then undertaken so as to best reconstruct, in the L∞ sense, the kernels over a given temperature range [T min,T max]. The performance of these kernel reconstruction methods is then assessed in light of previous temperature interpolation methods by testing them upon isotope 238U. Temperature-optimized free Doppler kernel reconstruction significantly outperforms all previous interpolation-based methods, achieving 0.1% relative error on temperature interpolation of 238U total cross section over the temperature range [300 K,3000 K] with only 9 reference temperatures.« less

Minimal Polynomial Method for Estimating Parameters of Signals Received by an Antenna Array

NASA Astrophysics Data System (ADS)

Ermolaev, V. T.; Flaksman, A. G.; Elokhin, A. V.; Kuptsov, V. V.

2018-01-01

The effectiveness of the projection minimal polynomial method for solving the problem of determining the number of sources of signals acting on an antenna array (AA) with an arbitrary configuration and their angular directions has been studied. The method proposes estimating the degree of the minimal polynomial of the correlation matrix (CM) of the input process in the AA on the basis of a statistically validated root-mean-square criterion. Special attention is paid to the case of the ultrashort sample of the input process when the number of samples is considerably smaller than the number of AA elements, which is important for multielement AAs. It is shown that the proposed method is more effective in this case than methods based on the AIC (Akaike's Information Criterion) or minimum description length (MDL) criterion.

Metabolomic prediction of yield in hybrid rice.

PubMed

Xu, Shizhong; Xu, Yang; Gong, Liang; Zhang, Qifa

2016-10-01

Rice (Oryza sativa) provides a staple food source for more than 50% of the world's population. An increase in yield can significantly contribute to global food security. Hybrid breeding can potentially help to meet this goal because hybrid rice often shows a considerable increase in yield when compared with pure-bred cultivars. We recently developed a marker-guided prediction method for hybrid yield and showed a substantial increase in yield through genomic hybrid breeding. We now have transcriptomic and metabolomic data as potential resources for prediction. Using six prediction methods, including least absolute shrinkage and selection operator (LASSO), best linear unbiased prediction (BLUP), stochastic search variable selection, partial least squares, and support vector machines using the radial basis function and polynomial kernel function, we found that the predictability of hybrid yield can be further increased using these omic data. LASSO and BLUP are the most efficient methods for yield prediction. For high heritability traits, genomic data remain the most efficient predictors. When metabolomic data are used, the predictability of hybrid yield is almost doubled compared with genomic prediction. Of the 21 945 potential hybrids derived from 210 recombinant inbred lines, selection of the top 10 hybrids predicted from metabolites would lead to a ~30% increase in yield. We hypothesize that each metabolite represents a biologically built-in genetic network for yield; thus, using metabolites for prediction is equivalent to using information integrated from these hidden genetic networks for yield prediction. © 2016 The Authors The Plant Journal © 2016 John Wiley & Sons Ltd.

Polynomial mixture method of solving ordinary differential equations

NASA Astrophysics Data System (ADS)

Shahrir, Mohammad Shazri; Nallasamy, Kumaresan; Ratnavelu, Kuru; Kamali, M. Z. M.

2017-11-01

In this paper, a numerical solution of fuzzy quadratic Riccati differential equation is estimated using a proposed new approach that provides mixture of polynomials where iteratively the right mixture will be generated. This mixture provide a generalized formalism of traditional Neural Networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). This can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that Polynomial Mixture Method (PMM) shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over Mabood et al, RK-4, Multi-Agent NN and Neuro Method (NM).

Charactering baseline shift with 4th polynomial function for portable biomedical near-infrared spectroscopy device

NASA Astrophysics Data System (ADS)

Zhao, Ke; Ji, Yaoyao; Pan, Boan; Li, Ting

2018-02-01

The continuous-wave Near-infrared spectroscopy (NIRS) devices have been highlighted for its clinical and health care applications in noninvasive hemodynamic measurements. The baseline shift of the deviation measurement attracts lots of attentions for its clinical importance. Nonetheless current published methods have low reliability or high variability. In this study, we found a perfect polynomial fitting function for baseline removal, using NIRS. Unlike previous studies on baseline correction for near-infrared spectroscopy evaluation of non-hemodynamic particles, we focused on baseline fitting and corresponding correction method for NIRS and found that the polynomial fitting function at 4th order is greater than the function at 2nd order reported in previous research. Through experimental tests of hemodynamic parameters of the solid phantom, we compared the fitting effect between the 4th order polynomial and the 2nd order polynomial, by recording and analyzing the R values and the SSE (the sum of squares due to error) values. The R values of the 4th order polynomial function fitting are all higher than 0.99, which are significantly higher than the corresponding ones of 2nd order, while the SSE values of the 4th order are significantly smaller than the corresponding ones of the 2nd order. By using the high-reliable and low-variable 4th order polynomial fitting function, we are able to remove the baseline online to obtain more accurate NIRS measurements.

Aflatoxin and nutrient contents of peanut collected from local market and their processed foods

NASA Astrophysics Data System (ADS)

Ginting, E.; Rahmianna, A. A.; Yusnawan, E.

2018-01-01

Peanut is succeptable to aflatoxin contamination and the sources of peanut as well as processing methods considerably affect aflatoxin content of the products. Therefore, the study on aflatoxin and nutrient contents of peanut collected from local market and their processed foods were performed. Good kernels of peanut were prepared into fried peanut, pressed-fried peanut, peanut sauce, peanut press cake, fermented peanut press cake (tempe) and fried tempe, while blended kernels (good and poor kernels) were processed into peanut sauce and tempe and poor kernels were only processed into tempe. The results showed that good and blended kernels which had high number of sound/intact kernels (82,46% and 62,09%), contained 9.8-9.9 ppb of aflatoxin B1, while slightly higher level was seen in poor kernels (12.1 ppb). However, the moisture, ash, protein, and fat contents of the kernels were similar as well as the products. Peanut tempe and fried tempe showed the highest increase in protein content, while decreased fat contents were seen in all products. The increase in aflatoxin B1 of peanut tempe prepared from poor kernels > blended kernels > good kernels. However, it averagely decreased by 61.2% after deep-fried. Excluding peanut tempe and fried tempe, aflatoxin B1 levels in all products derived from good kernels were below the permitted level (15 ppb). This suggests that sorting peanut kernels as ingredients and followed by heat processing would decrease the aflatoxin content in the products.

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

Cangiani, Andrea; Gyrya, Vitaliy; Manzini, Gianmarco

In this paper, we present the nonconforming virtual element method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component of the velocity is approximated using the nonconforming virtual element space. On each mesh element the local virtual space contains the space of polynomials of up to a given degree, plus suitable nonpolynomial functions. The virtual element functions are implicitly defined as the solution of local Poisson problems with polynomial Neumann boundary conditions. As typical in VEM approaches, the explicit evaluation of the non-polynomial functionsmore » is not required. This approach makes it possible to construct nonconforming (virtual) spaces for any polynomial degree regardless of the parity, for two- and three-dimensional problems, and for meshes with very general polygonal and polyhedral elements. We show that the nonconforming VEM is inf-sup stable and establish optimal a priori error estimates for the velocity and pressure approximations. Finally, numerical examples confirm the convergence analysis and the effectiveness of the method in providing high-order accurate approximations.« less

Influence of surface error on electromagnetic performance of reflectors based on Zernike polynomials

NASA Astrophysics Data System (ADS)

Li, Tuanjie; Shi, Jiachen; Tang, Yaqiong

2018-04-01

This paper investigates the influence of surface error distribution on the electromagnetic performance of antennas. The normalized Zernike polynomials are used to describe a smooth and continuous deformation surface. Based on the geometrical optics and piecewise linear fitting method, the electrical performance of reflector described by the Zernike polynomials is derived to reveal the relationship between surface error distribution and electromagnetic performance. Then the relation database between surface figure and electric performance is built for ideal and deformed surfaces to realize rapidly calculation of far-field electric performances. The simulation analysis of the influence of Zernike polynomials on the electrical properties for the axis-symmetrical reflector with the axial mode helical antenna as feed is further conducted to verify the correctness of the proposed method. Finally, the influence rules of surface error distribution on electromagnetic performance are summarized. The simulation results show that some terms of Zernike polynomials may decrease the amplitude of main lobe of antenna pattern, and some may reduce the pointing accuracy. This work extracts a new concept for reflector's shape adjustment in manufacturing process.

Multiple Kernel Learning with Random Effects for Predicting Longitudinal Outcomes and Data Integration

PubMed Central

Chen, Tianle; Zeng, Donglin

2015-01-01

Summary Predicting disease risk and progression is one of the main goals in many clinical research studies. Cohort studies on the natural history and etiology of chronic diseases span years and data are collected at multiple visits. Although kernel-based statistical learning methods are proven to be powerful for a wide range of disease prediction problems, these methods are only well studied for independent data but not for longitudinal data. It is thus important to develop time-sensitive prediction rules that make use of the longitudinal nature of the data. In this paper, we develop a novel statistical learning method for longitudinal data by introducing subject-specific short-term and long-term latent effects through a designed kernel to account for within-subject correlation of longitudinal measurements. Since the presence of multiple sources of data is increasingly common, we embed our method in a multiple kernel learning framework and propose a regularized multiple kernel statistical learning with random effects to construct effective nonparametric prediction rules. Our method allows easy integration of various heterogeneous data sources and takes advantage of correlation among longitudinal measures to increase prediction power. We use different kernels for each data source taking advantage of the distinctive feature of each data modality, and then optimally combine data across modalities. We apply the developed methods to two large epidemiological studies, one on Huntington's disease and the other on Alzheimer's Disease (Alzheimer's Disease Neuroimaging Initiative, ADNI) where we explore a unique opportunity to combine imaging and genetic data to study prediction of mild cognitive impairment, and show a substantial gain in performance while accounting for the longitudinal aspect of the data. PMID:26177419

Flexibly imposing periodicity in kernel independent FMM: A multipole-to-local operator approach

NASA Astrophysics Data System (ADS)

Yan, Wen; Shelley, Michael

2018-02-01

An important but missing component in the application of the kernel independent fast multipole method (KIFMM) is the capability for flexibly and efficiently imposing singly, doubly, and triply periodic boundary conditions. In most popular packages such periodicities are imposed with the hierarchical repetition of periodic boxes, which may give an incorrect answer due to the conditional convergence of some kernel sums. Here we present an efficient method to properly impose periodic boundary conditions using a near-far splitting scheme. The near-field contribution is directly calculated with the KIFMM method, while the far-field contribution is calculated with a multipole-to-local (M2L) operator which is independent of the source and target point distribution. The M2L operator is constructed with the far-field portion of the kernel function to generate the far-field contribution with the downward equivalent source points in KIFMM. This method guarantees the sum of the near-field & far-field converge pointwise to results satisfying periodicity and compatibility conditions. The computational cost of the far-field calculation observes the same O (N) complexity as FMM and is designed to be small by reusing the data computed by KIFMM for the near-field. The far-field calculations require no additional control parameters, and observes the same theoretical error bound as KIFMM. We present accuracy and timing test results for the Laplace kernel in singly periodic domains and the Stokes velocity kernel in doubly and triply periodic domains.

Solution of Fifth-order Korteweg and de Vries Equation by Homotopy perturbation Transform Method using He's Polynomial

NASA Astrophysics Data System (ADS)

Sharma, Dinkar; Singh, Prince; Chauhan, Shubha

2017-06-01

In this paper, a combined form of the Laplace transform method with the homotopy perturbation method is applied to solve nonlinear fifth order Korteweg de Vries (KdV) equations. The method is known as homotopy perturbation transform method (HPTM). The nonlinear terms can be easily handled by the use of He's polynomials. Two test examples are considered to illustrate the present scheme. Further the results are compared with Homotopy perturbation method (HPM).

Improved modeling of clinical data with kernel methods.

PubMed

Daemen, Anneleen; Timmerman, Dirk; Van den Bosch, Thierry; Bottomley, Cecilia; Kirk, Emma; Van Holsbeke, Caroline; Valentin, Lil; Bourne, Tom; De Moor, Bart

2012-02-01

Despite the rise of high-throughput technologies, clinical data such as age, gender and medical history guide clinical management for most diseases and examinations. To improve clinical management, available patient information should be fully exploited. This requires appropriate modeling of relevant parameters. When kernel methods are used, traditional kernel functions such as the linear kernel are often applied to the set of clinical parameters. These kernel functions, however, have their disadvantages due to the specific characteristics of clinical data, being a mix of variable types with each variable its own range. We propose a new kernel function specifically adapted to the characteristics of clinical data. The clinical kernel function provides a better representation of patients' similarity by equalizing the influence of all variables and taking into account the range r of the variables. Moreover, it is robust with respect to changes in r. Incorporated in a least squares support vector machine, the new kernel function results in significantly improved diagnosis, prognosis and prediction of therapy response. This is illustrated on four clinical data sets within gynecology, with an average increase in test area under the ROC curve (AUC) of 0.023, 0.021, 0.122 and 0.019, respectively. Moreover, when combining clinical parameters and expression data in three case studies on breast cancer, results improved overall with use of the new kernel function and when considering both data types in a weighted fashion, with a larger weight assigned to the clinical parameters. The increase in AUC with respect to a standard kernel function and/or unweighted data combination was maximum 0.127, 0.042 and 0.118 for the three case studies. For clinical data consisting of variables of different types, the proposed kernel function--which takes into account the type and range of each variable--has shown to be a better alternative for linear and non-linear classification problems. Copyright © 2011 Elsevier B.V. All rights reserved.

Analytical approximate solutions for a general class of nonlinear delay differential equations.

PubMed

Căruntu, Bogdan; Bota, Constantin

2014-01-01

We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a nonlinear time-delay model from biology. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using other methods.

A Comparison of Kernel Equating and Traditional Equipercentile Equating Methods and the Parametric Bootstrap Methods for Estimating Standard Errors in Equipercentile Equating

ERIC Educational Resources Information Center

Choi, Sae Il

2009-01-01

This study used simulation (a) to compare the kernel equating method to traditional equipercentile equating methods under the equivalent-groups (EG) design and the nonequivalent-groups with anchor test (NEAT) design and (b) to apply the parametric bootstrap method for estimating standard errors of equating. A two-parameter logistic item response…

A Riemann-Hilbert approach to asymptotic questions for orthogonal polynomials

NASA Astrophysics Data System (ADS)

Deift, P.; Kriecherbauer, T.; McLaughlin, K. T.-R.; Venakides, S.; Zhou, X.

2001-08-01

A few years ago the authors introduced a new approach to study asymptotic questions for orthogonal polynomials. In this paper we give an overview of our method and review the results which have been obtained in Deift et al. (Internat. Math. Res. Notices (1997) 759, Comm. Pure Appl. Math. 52 (1999) 1491, 1335), Deift (Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Courant Lecture Notes, Vol. 3, New York University, 1999), Kriecherbauer and McLaughlin (Internat. Math. Res. Notices (1999) 299) and Baik et al. (J. Amer. Math. Soc. 12 (1999) 1119). We mainly consider orthogonal polynomials with respect to weights on the real line which are either (1) Freud-type weights d[alpha](x)=e-Q(x) dx (Q polynomial or Q(x)=x[beta], [beta]>0), or (2) varying weights d[alpha]n(x)=e-nV(x) dx (V analytic, limx-->[infinity] V(x)/logx=[infinity]). We obtain Plancherel-Rotach-type asymptotics in the entire complex plane as well as asymptotic formulae with error estimates for the leading coefficients, for the recurrence coefficients, and for the zeros of the orthogonal polynomials. Our proof starts from an observation of Fokas et al. (Comm. Math. Phys. 142 (1991) 313) that the orthogonal polynomials can be determined as solutions of certain matrix valued Riemann-Hilbert problems. We analyze the Riemann-Hilbert problems by a steepest descent type method introduced by Deift and Zhou (Ann. Math. 137 (1993) 295) and further developed in Deift and Zhou (Comm. Pure Appl. Math. 48 (1995) 277) and Deift et al. (Proc. Nat. Acad. Sci. USA 95 (1998) 450). A crucial step in our analysis is the use of the well-known equilibrium measure which describes the asymptotic distribution of the zeros of the orthogonal polynomials.

Credit scoring analysis using weighted k nearest neighbor

NASA Astrophysics Data System (ADS)

Mukid, M. A.; Widiharih, T.; Rusgiyono, A.; Prahutama, A.

2018-05-01

Credit scoring is a quatitative method to evaluate the credit risk of loan applications. Both statistical methods and artificial intelligence are often used by credit analysts to help them decide whether the applicants are worthy of credit. These methods aim to predict future behavior in terms of credit risk based on past experience of customers with similar characteristics. This paper reviews the weighted k nearest neighbor (WKNN) method for credit assessment by considering the use of some kernels. We use credit data from a private bank in Indonesia. The result shows that the Gaussian kernel and rectangular kernel have a better performance based on the value of percentage corrected classified whose value is 82.4% respectively.

Vis-NIR spectrometric determination of Brix and sucrose in sugar production samples using kernel partial least squares with interval selection based on the successive projections algorithm.

PubMed

de Almeida, Valber Elias; de Araújo Gomes, Adriano; de Sousa Fernandes, David Douglas; Goicoechea, Héctor Casimiro; Galvão, Roberto Kawakami Harrop; Araújo, Mario Cesar Ugulino

2018-05-01

This paper proposes a new variable selection method for nonlinear multivariate calibration, combining the Successive Projections Algorithm for interval selection (iSPA) with the Kernel Partial Least Squares (Kernel-PLS) modelling technique. The proposed iSPA-Kernel-PLS algorithm is employed in a case study involving a Vis-NIR spectrometric dataset with complex nonlinear features. The analytical problem consists of determining Brix and sucrose content in samples from a sugar production system, on the basis of transflectance spectra. As compared to full-spectrum Kernel-PLS, the iSPA-Kernel-PLS models involve a smaller number of variables and display statistically significant superiority in terms of accuracy and/or bias in the predictions. Published by Elsevier B.V.

Optimal Bandwidth Selection in Observed-Score Kernel Equating

ERIC Educational Resources Information Center

Häggström, Jenny; Wiberg, Marie

2014-01-01

The selection of bandwidth in kernel equating is important because it has a direct impact on the equated test scores. The aim of this article is to examine the use of double smoothing when selecting bandwidths in kernel equating and to compare double smoothing with the commonly used penalty method. This comparison was made using both an equivalent…

Computing the Partial Fraction Decomposition of Rational Functions with Irreducible Quadratic Factors in the Denominators

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2012-01-01

In this note, a new method for computing the partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators is presented. This method involves polynomial divisions and substitutions only, without having to solve for the complex roots of the irreducible quadratic polynomial or to solve a system of linear…

Interpolation Hermite Polynomials For Finite Element Method

NASA Astrophysics Data System (ADS)

Gusev, Alexander; Vinitsky, Sergue; Chuluunbaatar, Ochbadrakh; Chuluunbaatar, Galmandakh; Gerdt, Vladimir; Derbov, Vladimir; Góźdź, Andrzej; Krassovitskiy, Pavel

2018-02-01

We describe a new algorithm for analytic calculation of high-order Hermite interpolation polynomials of the simplex and give their classification. A typical example of triangle element, to be built in high accuracy finite element schemes, is given.

A general method for computing Tutte polynomials of self-similar graphs

NASA Astrophysics Data System (ADS)

Gong, Helin; Jin, Xian'an

2017-10-01

Self-similar graphs were widely studied in both combinatorics and statistical physics. Motivated by the construction of the well-known 3-dimensional Sierpiński gasket graphs, in this paper we introduce a family of recursively constructed self-similar graphs whose inner duals are of the self-similar property. By combining the dual property of the Tutte polynomial and the subgraph-decomposition trick, we show that the Tutte polynomial of this family of graphs can be computed in an iterative way and in particular the exact expression of the formula of the number of their spanning trees is derived. Furthermore, we show our method is a general one that is easily extended to compute Tutte polynomials for other families of self-similar graphs such as Farey graphs, 2-dimensional Sierpiński gasket graphs, Hanoi graphs, modified Koch graphs, Apollonian graphs, pseudofractal scale-free web, fractal scale-free network, etc.

Development and Evaluation of a Hydrostatic Dynamical Core Using the Spectral Element/Discontinuous Galerkin Methods

DTIC Science & Technology

2014-04-01

The CG and DG horizontal discretization employs high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto- Legendre ...and DG horizontal discretization employs high-order nodal basis functions 29 associated with Lagrange polynomials based on Gauss-Lobatto- Legendre ...Inside 235 each element we build ( 1)N + Gauss-Lobatto- Legendre (GLL) quadrature points, where N 236 indicate the polynomial order of the basis

The s-Ordered Fock Space Projectors Gained by the General Ordering Theorem

NASA Astrophysics Data System (ADS)

Farid, Shähandeh; Mohammad, Reza Bazrafkan; Mahmoud, Ashrafi

2012-09-01

Employing the general ordering theorem (GOT), operational methods and incomplete 2-D Hermite polynomials, we derive the t-ordered expansion of Fock space projectors. Using the result, the general ordered form of the coherent state projectors is obtained. This indeed gives a new integration formula regarding incomplete 2-D Hermite polynomials. In addition, the orthogonality relation of the incomplete 2-D Hermite polynomials is derived to resolve Dattoli's failure.

Computation of solar wind parameters from the OGO-5 plasma spectrometer data using Hermite polynomials

NASA Technical Reports Server (NTRS)

Neugebauer, M.

1971-01-01

The method used to calculate the velocity, temperature, and density of the solar wind plasma is presented from spectra obtained by attitude-stabilized plasma detectors on the earth satellite OGO 5. The method, which used expansions in terms of Hermite polynomials, is very inexpensive to implement on an electronic computer compared to the least-squares and other iterative methods often used for similar problems.

Applications of discrete element method in modeling of grain postharvest operations

USDA-ARS?s Scientific Manuscript database

Grain kernels are finite and discrete materials. Although flowing grain can behave like a continuum fluid at times, the discontinuous behavior exhibited by grain kernels cannot be simulated solely with conventional continuum-based computer modeling such as finite-element or finite-difference methods...

Kernel-based whole-genome prediction of complex traits: a review.

PubMed

Morota, Gota; Gianola, Daniel

2014-01-01

Prediction of genetic values has been a focus of applied quantitative genetics since the beginning of the 20th century, with renewed interest following the advent of the era of whole genome-enabled prediction. Opportunities offered by the emergence of high-dimensional genomic data fueled by post-Sanger sequencing technologies, especially molecular markers, have driven researchers to extend Ronald Fisher and Sewall Wright's models to confront new challenges. In particular, kernel methods are gaining consideration as a regression method of choice for genome-enabled prediction. Complex traits are presumably influenced by many genomic regions working in concert with others (clearly so when considering pathways), thus generating interactions. Motivated by this view, a growing number of statistical approaches based on kernels attempt to capture non-additive effects, either parametrically or non-parametrically. This review centers on whole-genome regression using kernel methods applied to a wide range of quantitative traits of agricultural importance in animals and plants. We discuss various kernel-based approaches tailored to capturing total genetic variation, with the aim of arriving at an enhanced predictive performance in the light of available genome annotation information. Connections between prediction machines born in animal breeding, statistics, and machine learning are revisited, and their empirical prediction performance is discussed. Overall, while some encouraging results have been obtained with non-parametric kernels, recovering non-additive genetic variation in a validation dataset remains a challenge in quantitative genetics.

GPU-accelerated Kernel Regression Reconstruction for Freehand 3D Ultrasound Imaging.

PubMed

Wen, Tiexiang; Li, Ling; Zhu, Qingsong; Qin, Wenjian; Gu, Jia; Yang, Feng; Xie, Yaoqin

2017-07-01

Volume reconstruction method plays an important role in improving reconstructed volumetric image quality for freehand three-dimensional (3D) ultrasound imaging. By utilizing the capability of programmable graphics processing unit (GPU), we can achieve a real-time incremental volume reconstruction at a speed of 25-50 frames per second (fps). After incremental reconstruction and visualization, hole-filling is performed on GPU to fill remaining empty voxels. However, traditional pixel nearest neighbor-based hole-filling fails to reconstruct volume with high image quality. On the contrary, the kernel regression provides an accurate volume reconstruction method for 3D ultrasound imaging but with the cost of heavy computational complexity. In this paper, a GPU-based fast kernel regression method is proposed for high-quality volume after the incremental reconstruction of freehand ultrasound. The experimental results show that improved image quality for speckle reduction and details preservation can be obtained with the parameter setting of kernel window size of [Formula: see text] and kernel bandwidth of 1.0. The computational performance of the proposed GPU-based method can be over 200 times faster than that on central processing unit (CPU), and the volume with size of 50 million voxels in our experiment can be reconstructed within 10 seconds.

A harmonic polynomial cell (HPC) method for 3D Laplace equation with application in marine hydrodynamics

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

Shao, Yan-Lin, E-mail: yanlin.shao@dnvgl.com; Faltinsen, Odd M.

2014-10-01

We propose a new efficient and accurate numerical method based on harmonic polynomials to solve boundary value problems governed by 3D Laplace equation. The computational domain is discretized by overlapping cells. Within each cell, the velocity potential is represented by the linear superposition of a complete set of harmonic polynomials, which are the elementary solutions of Laplace equation. By its definition, the method is named as Harmonic Polynomial Cell (HPC) method. The characteristics of the accuracy and efficiency of the HPC method are demonstrated by studying analytical cases. Comparisons will be made with some other existing boundary element based methods,more » e.g. Quadratic Boundary Element Method (QBEM) and the Fast Multipole Accelerated QBEM (FMA-QBEM) and a fourth order Finite Difference Method (FDM). To demonstrate the applications of the method, it is applied to some studies relevant for marine hydrodynamics. Sloshing in 3D rectangular tanks, a fully-nonlinear numerical wave tank, fully-nonlinear wave focusing on a semi-circular shoal, and the nonlinear wave diffraction of a bottom-mounted cylinder in regular waves are studied. The comparisons with the experimental results and other numerical results are all in satisfactory agreement, indicating that the present HPC method is a promising method in solving potential-flow problems. The underlying procedure of the HPC method could also be useful in other fields than marine hydrodynamics involved with solving Laplace equation.« less

A dry-inoculation method for nut kernels.

PubMed

Blessington, Tyann; Theofel, Christopher G; Harris, Linda J

2013-04-01

A dry-inoculation method for almonds and walnuts was developed to eliminate the need for the postinoculation drying required for wet-inoculation methods. The survival of Salmonella enterica Enteritidis PT 30 on wet- and dry-inoculated almond and walnut kernels stored under ambient conditions (average: 23 °C; 41 or 47% RH) was then compared over 14 weeks. For wet inoculation, an aqueous Salmonella preparation was added directly to almond or walnut kernels, which were then dried under ambient conditions (3 or 7 days, respectively) to initial nut moisture levels. For the dry inoculation, liquid inoculum was mixed with sterilized sand and dried for 24 h at 40 °C. The dried inoculated sand was mixed with kernels, and the sand was removed by shaking the mixture in a sterile sieve. Mixing procedures to optimize the bacterial transfer from sand to kernel were evaluated; in general, similar levels were achieved on walnuts (4.8-5.2 log CFU/g) and almonds (4.2-5.1 log CFU/g). The decline of Salmonella Enteritidis populations was similar during ambient storage (98 days) for both wet-and dry-inoculation methods for both almonds and walnuts. The dry-inoculation method mimics some of the suspected routes of contamination for tree nuts and may be appropriate for some postharvest challenge studies. Copyright © 2012 Elsevier Ltd. All rights reserved.

Automatic classification of retinal three-dimensional optical coherence tomography images using principal component analysis network with composite kernels.

PubMed

Fang, Leyuan; Wang, Chong; Li, Shutao; Yan, Jun; Chen, Xiangdong; Rabbani, Hossein

2017-11-01

We present an automatic method, termed as the principal component analysis network with composite kernel (PCANet-CK), for the classification of three-dimensional (3-D) retinal optical coherence tomography (OCT) images. Specifically, the proposed PCANet-CK method first utilizes the PCANet to automatically learn features from each B-scan of the 3-D retinal OCT images. Then, multiple kernels are separately applied to a set of very important features of the B-scans and these kernels are fused together, which can jointly exploit the correlations among features of the 3-D OCT images. Finally, the fused (composite) kernel is incorporated into an extreme learning machine for the OCT image classification. We tested our proposed algorithm on two real 3-D spectral domain OCT (SD-OCT) datasets (of normal subjects and subjects with the macular edema and age-related macular degeneration), which demonstrated its effectiveness. (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).

Phenolic compounds and antioxidant activity of kernels and shells of Mexican pecan (Carya illinoinensis).

PubMed

de la Rosa, Laura A; Alvarez-Parrilla, Emilio; Shahidi, Fereidoon

2011-01-12

The phenolic composition and antioxidant activity of pecan kernels and shells cultivated in three regions of the state of Chihuahua, Mexico, were analyzed. High concentrations of total extractable phenolics, flavonoids, and proanthocyanidins were found in kernels, and 5-20-fold higher concentrations were found in shells. Their concentrations were significantly affected by the growing region. Antioxidant activity was evaluated by ORAC, DPPH•, HO•, and ABTS•-- scavenging (TAC) methods. Antioxidant activity was strongly correlated with the concentrations of phenolic compounds. A strong correlation existed among the results obtained using these four methods. Five individual phenolic compounds were positively identified and quantified in kernels: ellagic, gallic, protocatechuic, and p-hydroxybenzoic acids and catechin. Only ellagic and gallic acids could be identified in shells. Seven phenolic compounds were tentatively identified in kernels by means of MS and UV spectral comparison, namely, protocatechuic aldehyde, (epi)gallocatechin, one gallic acid-glucose conjugate, three ellagic acid derivatives, and valoneic acid dilactone.

Study of the convergence behavior of the complex kernel least mean square algorithm.

PubMed

Paul, Thomas K; Ogunfunmi, Tokunbo

2013-09-01

The complex kernel least mean square (CKLMS) algorithm is recently derived and allows for online kernel adaptive learning for complex data. Kernel adaptive methods can be used in finding solutions for neural network and machine learning applications. The derivation of CKLMS involved the development of a modified Wirtinger calculus for Hilbert spaces to obtain the cost function gradient. We analyze the convergence of the CKLMS with different kernel forms for complex data. The expressions obtained enable us to generate theory-predicted mean-square error curves considering the circularity of the complex input signals and their effect on nonlinear learning. Simulations are used for verifying the analysis results.

A robust, high-throughput method for computing maize ear, cob, and kernel attributes automatically from images.

PubMed

Miller, Nathan D; Haase, Nicholas J; Lee, Jonghyun; Kaeppler, Shawn M; de Leon, Natalia; Spalding, Edgar P

2017-01-01

Grain yield of the maize plant depends on the sizes, shapes, and numbers of ears and the kernels they bear. An automated pipeline that can measure these components of yield from easily-obtained digital images is needed to advance our understanding of this globally important crop. Here we present three custom algorithms designed to compute such yield components automatically from digital images acquired by a low-cost platform. One algorithm determines the average space each kernel occupies along the cob axis using a sliding-window Fourier transform analysis of image intensity features. A second counts individual kernels removed from ears, including those in clusters. A third measures each kernel's major and minor axis after a Bayesian analysis of contour points identifies the kernel tip. Dimensionless ear and kernel shape traits that may interrelate yield components are measured by principal components analysis of contour point sets. Increased objectivity and speed compared to typical manual methods are achieved without loss of accuracy as evidenced by high correlations with ground truth measurements and simulated data. Millimeter-scale differences among ear, cob, and kernel traits that ranged more than 2.5-fold across a diverse group of inbred maize lines were resolved. This system for measuring maize ear, cob, and kernel attributes is being used by multiple research groups as an automated Web service running on community high-throughput computing and distributed data storage infrastructure. Users may create their own workflow using the source code that is staged for download on a public repository. © 2016 The Authors. The Plant Journal published by Society for Experimental Biology and John Wiley & Sons Ltd.

Determination of amino acid contents of manketti seeds (Schinziophyton rautanenii) by pre-column derivatisation with 6-aminoquinolyl-N-hydroxysuccinimidyl carbamate and RP-HPLC.

PubMed

Gwatidzo, Luke; Botha, Ben M; McCrindle, Rob I

2013-12-01

Defatted kernel flour from manketti seed kernels (Schinziophyton rautanenii) is an underutilised natural product. The plant grows in the wild, on sandy soils little used for agriculture in Southern Africa. The kernels are rich in protein and have a great potential for improving nutrition. The protein content and amino acid profile of manketti seed kernel were studied, using a new analytical method, in order to evaluate the nutritional value. The crude protein content of the press cake and defatted kernel flour was 29.0% and 67.5%, respectively. Leucine and arginine were found to be the most abundant essential and non-essential amino acids, respectively. The seed kernel contained 4.77 g leucine and 12.34 g arginine/100 g of defatted seed kernel flour. Methionine and proline were the least abundant essential and non-essential amino acids to with 0.23 g methionine and 0.36 g proline/100 g of defatted seed kernel flour, respectively. Validation of the pre-column derivatisation procedure with 6-aminoquinolyl-N-hydroxysuccinimidyl carbamate (AQC) for the determination of amino acids was carried out. The analytical parameters were determined: linearity (0.0025-0.20 mM), accuracy of the derivatisation procedure: 86.7-109.8%, precision (method: 0.72-5.04%, instrumental: 0.14-1.88% and derivatisation: 0.15-2.94% and 0.41-4.32% for intraday and interday, respectively). Limits of detection and quantification were 6.80-157 mg/100 g and 22.7-523 mg/100 g kernel flour, respectively. Copyright © 2013 Elsevier Ltd. All rights reserved.

Minimum Sobolev norm interpolation of scattered derivative data

NASA Astrophysics Data System (ADS)

Chandrasekaran, S.; Gorman, C. H.; Mhaskar, H. N.

2018-07-01

We study the problem of reconstructing a function on a manifold satisfying some mild conditions, given data of the values and some derivatives of the function at arbitrary points on the manifold. While the problem of finding a polynomial of two variables with total degree ≤n given the values of the polynomial and some of its derivatives at exactly the same number of points as the dimension of the polynomial space is sometimes impossible, we show that such a problem always has a solution in a very general situation if the degree of the polynomials is sufficiently large. We give estimates on how large the degree should be, and give explicit constructions for such a polynomial even in a far more general case. As the number of sampling points at which the data is available increases, our polynomials converge to the target function on the set where the sampling points are dense. Numerical examples in single and double precision show that this method is stable, efficient, and of high-order.

Hyperspectral Image Classification via Kernel Sparse Representation

DTIC Science & Technology

2013-01-01

classification algorithms. Moreover, the spatial coherency across neighboring pixels is also incorporated through a kernelized joint sparsity model , where...joint sparsity model , where all of the pixels within a small neighborhood are jointly represented in the feature space by selecting a few common training...hyperspectral imagery, joint spar- sity model , kernel methods, sparse representation. I. INTRODUCTION HYPERSPECTRAL imaging sensors capture images

Filtered selection coupled with support vector machines generate a functionally relevant prediction model for colorectal cancer

PubMed Central

Gabere, Musa Nur; Hussein, Mohamed Aly; Aziz, Mohammad Azhar

2016-01-01

Purpose There has been considerable interest in using whole-genome expression profiles for the classification of colorectal cancer (CRC). The selection of important features is a crucial step before training a classifier. Methods In this study, we built a model that uses support vector machine (SVM) to classify cancer and normal samples using Affymetrix exon microarray data obtained from 90 samples of 48 patients diagnosed with CRC. From the 22,011 genes, we selected the 20, 30, 50, 100, 200, 300, and 500 genes most relevant to CRC using the minimum-redundancy–maximum-relevance (mRMR) technique. With these gene sets, an SVM model was designed using four different kernel types (linear, polynomial, radial basis function [RBF], and sigmoid). Results The best model, which used 30 genes and RBF kernel, outperformed other combinations; it had an accuracy of 84% for both ten fold and leave-one-out cross validations in discriminating the cancer samples from the normal samples. With this 30 genes set from mRMR, six classifiers were trained using random forest (RF), Bayes net (BN), multilayer perceptron (MLP), naïve Bayes (NB), reduced error pruning tree (REPT), and SVM. Two hybrids, mRMR + SVM and mRMR + BN, were the best models when tested on other datasets, and they achieved a prediction accuracy of 95.27% and 91.99%, respectively, compared to other mRMR hybrid models (mRMR + RF, mRMR + NB, mRMR + REPT, and mRMR + MLP). Ingenuity pathway analysis was used to analyze the functions of the 30 genes selected for this model and their potential association with CRC: CDH3, CEACAM7, CLDN1, IL8, IL6R, MMP1, MMP7, and TGFB1 were predicted to be CRC biomarkers. Conclusion This model could be used to further develop a diagnostic tool for predicting CRC based on gene expression data from patient samples. PMID:27330311

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.

Oil point and mechanical behaviour of oil palm kernels in linear compression

NASA Astrophysics Data System (ADS)

Kabutey, Abraham; Herak, David; Choteborsky, Rostislav; Mizera, Čestmír; Sigalingging, Riswanti; Akangbe, Olaosebikan Layi

2017-07-01

The study described the oil point and mechanical properties of roasted and unroasted bulk oil palm kernels under compression loading. The literature information available is very limited. A universal compression testing machine and vessel diameter of 60 mm with a plunger were used by applying maximum force of 100 kN and speed ranging from 5 to 25 mm min-1. The initial pressing height of the bulk kernels was measured at 40 mm. The oil point was determined by a litmus test for each deformation level of 5, 10, 15, 20, and 25 mm at a minimum speed of 5 mmmin-1. The measured parameters were the deformation, deformation energy, oil yield, oil point strain and oil point pressure. Clearly, the roasted bulk kernels required less deformation energy compared to the unroasted kernels for recovering the kernel oil. However, both kernels were not permanently deformed. The average oil point strain was determined at 0.57. The study is an essential contribution to pursuing innovative methods for processing palm kernel oil in rural areas of developing countries.

Multiscale Support Vector Learning With Projection Operator Wavelet Kernel for Nonlinear Dynamical System Identification.

PubMed

Lu, Zhao; Sun, Jing; Butts, Kenneth

2016-02-03

A giant leap has been made in the past couple of decades with the introduction of kernel-based learning as a mainstay for designing effective nonlinear computational learning algorithms. In view of the geometric interpretation of conditional expectation and the ubiquity of multiscale characteristics in highly complex nonlinear dynamic systems [1]-[3], this paper presents a new orthogonal projection operator wavelet kernel, aiming at developing an efficient computational learning approach for nonlinear dynamical system identification. In the framework of multiresolution analysis, the proposed projection operator wavelet kernel can fulfill the multiscale, multidimensional learning to estimate complex dependencies. The special advantage of the projection operator wavelet kernel developed in this paper lies in the fact that it has a closed-form expression, which greatly facilitates its application in kernel learning. To the best of our knowledge, it is the first closed-form orthogonal projection wavelet kernel reported in the literature. It provides a link between grid-based wavelets and mesh-free kernel-based methods. Simulation studies for identifying the parallel models of two benchmark nonlinear dynamical systems confirm its superiority in model accuracy and sparsity.

Customer demand prediction of service-oriented manufacturing using the least square support vector machine optimized by particle swarm optimization algorithm

NASA Astrophysics Data System (ADS)

Cao, Jin; Jiang, Zhibin; Wang, Kangzhou

2017-07-01

Many nonlinear customer satisfaction-related factors significantly influence the future customer demand for service-oriented manufacturing (SOM). To address this issue and enhance the prediction accuracy, this article develops a novel customer demand prediction approach for SOM. The approach combines the phase space reconstruction (PSR) technique with the optimized least square support vector machine (LSSVM). First, the prediction sample space is reconstructed by the PSR to enrich the time-series dynamics of the limited data sample. Then, the generalization and learning ability of the LSSVM are improved by the hybrid polynomial and radial basis function kernel. Finally, the key parameters of the LSSVM are optimized by the particle swarm optimization algorithm. In a real case study, the customer demand prediction of an air conditioner compressor is implemented. Furthermore, the effectiveness and validity of the proposed approach are demonstrated by comparison with other classical predication approaches.

Vietnamese Document Representation and Classification

NASA Astrophysics Data System (ADS)

Nguyen, Giang-Son; Gao, Xiaoying; Andreae, Peter

Vietnamese is very different from English and little research has been done on Vietnamese document classification, or indeed, on any kind of Vietnamese language processing, and only a few small corpora are available for research. We created a large Vietnamese text corpus with about 18000 documents, and manually classified them based on different criteria such as topics and styles, giving several classification tasks of different difficulty levels. This paper introduces a new syllable-based document representation at the morphological level of the language for efficient classification. We tested the representation on our corpus with different classification tasks using six classification algorithms and two feature selection techniques. Our experiments show that the new representation is effective for Vietnamese categorization, and suggest that best performance can be achieved using syllable-pair document representation, an SVM with a polynomial kernel as the learning algorithm, and using Information gain and an external dictionary for feature selection.

Polynomial modal analysis of lamellar diffraction gratings in conical mounting.

PubMed

Randriamihaja, Manjakavola Honore; Granet, Gérard; Edee, Kofi; Raniriharinosy, Karyl

2016-09-01

An efficient numerical modal method for modeling a lamellar grating in conical mounting is presented. Within each region of the grating, the electromagnetic field is expanded onto Legendre polynomials, which allows us to enforce in an exact manner the boundary conditions that determine the eigensolutions. Our code is successfully validated by comparison with results obtained with the analytical modal method.

A Novel Weighted Kernel PCA-Based Method for Optimization and Uncertainty Quantification

NASA Astrophysics Data System (ADS)

Thimmisetty, C.; Talbot, C.; Chen, X.; Tong, C. H.

2016-12-01

It has been demonstrated that machine learning methods can be successfully applied to uncertainty quantification for geophysical systems through the use of the adjoint method coupled with kernel PCA-based optimization. In addition, it has been shown through weighted linear PCA how optimization with respect to both observation weights and feature space control variables can accelerate convergence of such methods. Linear machine learning methods, however, are inherently limited in their ability to represent features of non-Gaussian stochastic random fields, as they are based on only the first two statistical moments of the original data. Nonlinear spatial relationships and multipoint statistics leading to the tortuosity characteristic of channelized media, for example, are captured only to a limited extent by linear PCA. With the aim of coupling the kernel-based and weighted methods discussed, we present a novel mathematical formulation of kernel PCA, Weighted Kernel Principal Component Analysis (WKPCA), that both captures nonlinear relationships and incorporates the attribution of significance levels to different realizations of the stochastic random field of interest. We also demonstrate how new instantiations retaining defining characteristics of the random field can be generated using Bayesian methods. In particular, we present a novel WKPCA-based optimization method that minimizes a given objective function with respect to both feature space random variables and observation weights through which optimal snapshot significance levels and optimal features are learned. We showcase how WKPCA can be applied to nonlinear optimal control problems involving channelized media, and in particular demonstrate an application of the method to learning the spatial distribution of material parameter values in the context of linear elasticity, and discuss further extensions of the method to stochastic inversion.

A contracting-interval program for the Danilewski method. Ph.D. Thesis - Va. Univ.

NASA Technical Reports Server (NTRS)

Harris, J. D.

1971-01-01

The concept of contracting-interval programs is applied to finding the eigenvalues of a matrix. The development is a three-step process in which (1) a program is developed for the reduction of a matrix to Hessenberg form, (2) a program is developed for the reduction of a Hessenberg matrix to colleague form, and (3) the characteristic polynomial with interval coefficients is readily obtained from the interval of colleague matrices. This interval polynomial is then factored into quadratic factors so that the eigenvalues may be obtained. To develop a contracting-interval program for factoring this polynomial with interval coefficients it is necessary to have an iteration method which converges even in the presence of controlled rounding errors. A theorem is stated giving sufficient conditions for the convergence of Newton's method when both the function and its Jacobian cannot be evaluated exactly but errors can be made proportional to the square of the norm of the difference between the previous two iterates. This theorem is applied to prove the convergence of the generalization of the Newton-Bairstow method that is used to obtain quadratic factors of the characteristic polynomial.

Correcting bias in the rational polynomial coefficients of satellite imagery using thin-plate smoothing splines

NASA Astrophysics Data System (ADS)

Shen, Xiang; Liu, Bin; Li, Qing-Quan

2017-03-01

The Rational Function Model (RFM) has proven to be a viable alternative to the rigorous sensor models used for geo-processing of high-resolution satellite imagery. Because of various errors in the satellite ephemeris and instrument calibration, the Rational Polynomial Coefficients (RPCs) supplied by image vendors are often not sufficiently accurate, and there is therefore a clear need to correct the systematic biases in order to meet the requirements of high-precision topographic mapping. In this paper, we propose a new RPC bias-correction method using the thin-plate spline modeling technique. Benefiting from its excellent performance and high flexibility in data fitting, the thin-plate spline model has the potential to remove complex distortions in vendor-provided RPCs, such as the errors caused by short-period orbital perturbations. The performance of the new method was evaluated by using Ziyuan-3 satellite images and was compared against the recently developed least-squares collocation approach, as well as the classical affine-transformation and quadratic-polynomial based methods. The results show that the accuracies of the thin-plate spline and the least-squares collocation approaches were better than the other two methods, which indicates that strong non-rigid deformations exist in the test data because they cannot be adequately modeled by simple polynomial-based methods. The performance of the thin-plate spline method was close to that of the least-squares collocation approach when only a few Ground Control Points (GCPs) were used, and it improved more rapidly with an increase in the number of redundant observations. In the test scenario using 21 GCPs (some of them located at the four corners of the scene), the correction residuals of the thin-plate spline method were about 36%, 37%, and 19% smaller than those of the affine transformation method, the quadratic polynomial method, and the least-squares collocation algorithm, respectively, which demonstrates that the new method can be more effective at removing systematic biases in vendor-supplied RPCs.

Distortion theorems for polynomials on a circle

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

Dubinin, V N

2000-12-31

Inequalities for the derivatives with respect to {phi}=arg z the functions ReP(z), |P(z)|{sup 2} and arg P(z) are established for an algebraic polynomial P(z) at points on the circle |z|=1. These estimates depend, in particular, on the constant term and the leading coefficient of the polynomial P(z) and improve the classical Bernstein and Turan inequalities. The method of proof is based on the techniques of generalized reduced moduli.

Investigation of advanced UQ for CRUD prediction with VIPRE.

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

Eldred, Michael Scott

2011-09-01

This document summarizes the results from a level 3 milestone study within the CASL VUQ effort. It demonstrates the application of 'advanced UQ,' in particular dimension-adaptive p-refinement for polynomial chaos and stochastic collocation. The study calculates statistics for several quantities of interest that are indicators for the formation of CRUD (Chalk River unidentified deposit), which can lead to CIPS (CRUD induced power shift). Stochastic expansion methods are attractive methods for uncertainty quantification due to their fast convergence properties. For smooth functions (i.e., analytic, infinitely-differentiable) in L{sup 2} (i.e., possessing finite variance), exponential convergence rates can be obtained under order refinementmore » for integrated statistical quantities of interest such as mean, variance, and probability. Two stochastic expansion methods are of interest: nonintrusive polynomial chaos expansion (PCE), which computes coefficients for a known basis of multivariate orthogonal polynomials, and stochastic collocation (SC), which forms multivariate interpolation polynomials for known coefficients. Within the DAKOTA project, recent research in stochastic expansion methods has focused on automated polynomial order refinement ('p-refinement') of expansions to support scalability to higher dimensional random input spaces [4, 3]. By preferentially refining only in the most important dimensions of the input space, the applicability of these methods can be extended from O(10{sup 0})-O(10{sup 1}) random variables to O(10{sup 2}) and beyond, depending on the degree of anisotropy (i.e., the extent to which randominput variables have differing degrees of influence on the statistical quantities of interest (QOIs)). Thus, the purpose of this study is to investigate the application of these adaptive stochastic expansion methods to the analysis of CRUD using the VIPRE simulation tools for two different plant models of differing random dimension, anisotropy, and smoothness.« less

A discrete method for modal analysis of overhead line conductor bundles

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

Migdalovici, M.A.; Sireteanu, T.D.; Albrecht, A.A.

The paper presents a mathematical model and a semi-analytical procedure to calculate the vibration modes and eigenfrequencies of single or bundled conductors with spacers which are needed for evaluation of the wind induced vibration of conductors and for optimization of spacer-dampers placement. The method consists in decomposition of conductors in modules and the expansion by polynomial series of unknown displacements on each module. A complete system of polynomials are deduced for this by Legendre polynomials. Each module is considered either boundary conditions at the extremity of the module or the continuity conditions between the modules and also a number ofmore » projections of module equilibrium equation on the polynomials from the expansion series of unknown displacement. The global system of the eigenmodes and eigenfrequencies is of the matrix form: A X + {omega}{sup 2} M X = 0. The theoretical considerations are exemplified on one conductor and on bundle of two conductors with spacers. From this, a method for forced vibration calculus of a single or bundled conductors is also presented.« less

A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models

NASA Technical Reports Server (NTRS)

Giunta, Anthony A.; Watson, Layne T.

1998-01-01

Two methods of creating approximation models are compared through the calculation of the modeling accuracy on test problems involving one, five, and ten independent variables. Here, the test problems are representative of the modeling challenges typically encountered in realistic engineering optimization problems. The first approximation model is a quadratic polynomial created using the method of least squares. This type of polynomial model has seen considerable use in recent engineering optimization studies due to its computational simplicity and ease of use. However, quadratic polynomial models may be of limited accuracy when the response data to be modeled have multiple local extrema. The second approximation model employs an interpolation scheme known as kriging developed in the fields of spatial statistics and geostatistics. This class of interpolating model has the flexibility to model response data with multiple local extrema. However, this flexibility is obtained at an increase in computational expense and a decrease in ease of use. The intent of this study is to provide an initial exploration of the accuracy and modeling capabilities of these two approximation methods.

Tensor calculus in polar coordinates using Jacobi polynomials

NASA Astrophysics Data System (ADS)

Vasil, Geoffrey M.; Burns, Keaton J.; Lecoanet, Daniel; Olver, Sheehan; Brown, Benjamin P.; Oishi, Jeffrey S.

2016-11-01

Spectral methods are an efficient way to solve partial differential equations on domains possessing certain symmetries. The utility of a method depends strongly on the choice of spectral basis. In this paper we describe a set of bases built out of Jacobi polynomials, and associated operators for solving scalar, vector, and tensor partial differential equations in polar coordinates on a unit disk. By construction, the bases satisfy regularity conditions at r = 0 for any tensorial field. The coordinate singularity in a disk is a prototypical case for many coordinate singularities. The work presented here extends to other geometries. The operators represent covariant derivatives, multiplication by azimuthally symmetric functions, and the tensorial relationship between fields. These arise naturally from relations between classical orthogonal polynomials, and form a Heisenberg algebra. Other past work uses more specific polynomial bases for solving equations in polar coordinates. The main innovation in this paper is to use a larger set of possible bases to achieve maximum bandedness of linear operations. We provide a series of applications of the methods, illustrating their ease-of-use and accuracy.

A method for fitting regression splines with varying polynomial order in the linear mixed model.

PubMed

Edwards, Lloyd J; Stewart, Paul W; MacDougall, James E; Helms, Ronald W

2006-02-15

The linear mixed model has become a widely used tool for longitudinal analysis of continuous variables. The use of regression splines in these models offers the analyst additional flexibility in the formulation of descriptive analyses, exploratory analyses and hypothesis-driven confirmatory analyses. We propose a method for fitting piecewise polynomial regression splines with varying polynomial order in the fixed effects and/or random effects of the linear mixed model. The polynomial segments are explicitly constrained by side conditions for continuity and some smoothness at the points where they join. By using a reparameterization of this explicitly constrained linear mixed model, an implicitly constrained linear mixed model is constructed that simplifies implementation of fixed-knot regression splines. The proposed approach is relatively simple, handles splines in one variable or multiple variables, and can be easily programmed using existing commercial software such as SAS or S-plus. The method is illustrated using two examples: an analysis of longitudinal viral load data from a study of subjects with acute HIV-1 infection and an analysis of 24-hour ambulatory blood pressure profiles.

On Everhart Method

NASA Astrophysics Data System (ADS)

Pârv, Bazil

This paper deals with the Everhart numerical integration method, a well-known method in astronomical research. This method, a single-step one, is widely used for numerical integration of motion equation of celestial bodies. For an integration step, this method uses unequally-spaced substeps, defined by the roots of the so-called generating polynomial of Everhart's method. For this polynomial, this paper proposes and proves new recurrence formulae. The Maple computer algebra system was used to find and prove these formulae. Again, Maple seems to be well suited and easy to use in mathematical research.

Polynomial modal analysis of slanted lamellar gratings.

PubMed

Granet, Gérard; Randriamihaja, Manjakavola Honore; Raniriharinosy, Karyl

2017-06-01

The problem of diffraction by slanted lamellar dielectric and metallic gratings in classical mounting is formulated as an eigenvalue eigenvector problem. The numerical solution is obtained by using the moment method with Legendre polynomials as expansion and test functions, which allows us to enforce in an exact manner the boundary conditions which determine the eigensolutions. Our method is successfully validated by comparison with other methods including in the case of highly slanted gratings.

A Comparison of the Kernel Equating Method with Traditional Equating Methods Using SAT[R] Data

ERIC Educational Resources Information Center

Liu, Jinghua; Low, Albert C.

2008-01-01

This study applied kernel equating (KE) in two scenarios: equating to a very similar population and equating to a very different population, referred to as a distant population, using SAT[R] data. The KE results were compared to the results obtained from analogous traditional equating methods in both scenarios. The results indicate that KE results…

A method for deriving lower bounds for the complexity of monotone arithmetic circuits computing real polynomials

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

Gashkov, Sergey B; Sergeev, Igor' S

2012-10-31

This work suggests a method for deriving lower bounds for the complexity of polynomials with positive real coefficients implemented by circuits of functional elements over the monotone arithmetic basis {l_brace}x+y, x {center_dot} y{r_brace} Union {l_brace}a {center_dot} x | a Element-Of R{sub +}{r_brace}. Using this method, several new results are obtained. In particular, we construct examples of polynomials of degree m-1 in each of the n variables with coefficients 0 and 1 having additive monotone complexity m{sup (1-o(1))n} and multiplicative monotone complexity m{sup (1/2-o(1))n} as m{sup n}{yields}{infinity}. In this form, the lower bounds derived here are sharp. Bibliography: 72 titles.

An ensemble method for extracting adverse drug events from social media.

PubMed

Liu, Jing; Zhao, Songzheng; Zhang, Xiaodi

2016-06-01

Because adverse drug events (ADEs) are a serious health problem and a leading cause of death, it is of vital importance to identify them correctly and in a timely manner. With the development of Web 2.0, social media has become a large data source for information on ADEs. The objective of this study is to develop a relation extraction system that uses natural language processing techniques to effectively distinguish between ADEs and non-ADEs in informal text on social media. We develop a feature-based approach that utilizes various lexical, syntactic, and semantic features. Information-gain-based feature selection is performed to address high-dimensional features. Then, we evaluate the effectiveness of four well-known kernel-based approaches (i.e., subset tree kernel, tree kernel, shortest dependency path kernel, and all-paths graph kernel) and several ensembles that are generated by adopting different combination methods (i.e., majority voting, weighted averaging, and stacked generalization). All of the approaches are tested using three data sets: two health-related discussion forums and one general social networking site (i.e., Twitter). When investigating the contribution of each feature subset, the feature-based approach attains the best area under the receiver operating characteristics curve (AUC) values, which are 78.6%, 72.2%, and 79.2% on the three data sets. When individual methods are used, we attain the best AUC values of 82.1%, 73.2%, and 77.0% using the subset tree kernel, shortest dependency path kernel, and feature-based approach on the three data sets, respectively. When using classifier ensembles, we achieve the best AUC values of 84.5%, 77.3%, and 84.5% on the three data sets, outperforming the baselines. Our experimental results indicate that ADE extraction from social media can benefit from feature selection. With respect to the effectiveness of different feature subsets, lexical features and semantic features can enhance the ADE extraction capability. Kernel-based approaches, which can stay away from the feature sparsity issue, are qualified to address the ADE extraction problem. Combining different individual classifiers using suitable combination methods can further enhance the ADE extraction effectiveness. Copyright © 2016 Elsevier B.V. All rights reserved.

Analysis on the misalignment errors between Hartmann-Shack sensor and 45-element deformable mirror

NASA Astrophysics Data System (ADS)

Liu, Lihui; Zhang, Yi; Tao, Jianjun; Cao, Fen; Long, Yin; Tian, Pingchuan; Chen, Shangwu

2017-02-01

Aiming at 45-element adaptive optics system, the model of 45-element deformable mirror is truly built by COMSOL Multiphysics, and every actuator's influence function is acquired by finite element method. The process of this system correcting optical aberration is simulated by making use of procedure, and aiming for Strehl ratio of corrected diffraction facula, in the condition of existing different translation and rotation error between Hartmann-Shack sensor and deformable mirror, the system's correction ability for 3-20 Zernike polynomial wave aberration is analyzed. The computed result shows: the system's correction ability for 3-9 Zernike polynomial wave aberration is higher than that of 10-20 Zernike polynomial wave aberration. The correction ability for 3-20 Zernike polynomial wave aberration does not change with misalignment error changing. With rotation error between Hartmann-Shack sensor and deformable mirror increasing, the correction ability for 3-20 Zernike polynomial wave aberration gradually goes down, and with translation error increasing, the correction ability for 3-9 Zernike polynomial wave aberration gradually goes down, but the correction ability for 10-20 Zernike polynomial wave aberration behave up-and-down depression.

Stability analysis of fuzzy parametric uncertain systems.

PubMed

Bhiwani, R J; Patre, B M

2011-10-01

In this paper, the determination of stability margin, gain and phase margin aspects of fuzzy parametric uncertain systems are dealt. The stability analysis of uncertain linear systems with coefficients described by fuzzy functions is studied. A complexity reduced technique for determining the stability margin for FPUS is proposed. The method suggested is dependent on the order of the characteristic polynomial. In order to find the stability margin of interval polynomials of order less than 5, it is not always necessary to determine and check all four Kharitonov's polynomials. It has been shown that, for determining stability margin of FPUS of order five, four, and three we require only 3, 2, and 1 Kharitonov's polynomials respectively. Only for sixth and higher order polynomials, a complete set of Kharitonov's polynomials are needed to determine the stability margin. Thus for lower order systems, the calculations are reduced to a large extent. This idea has been extended to determine the stability margin of fuzzy interval polynomials. It is also shown that the gain and phase margin of FPUS can be determined analytically without using graphical techniques. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

Multi-PSF fusion in image restoration of range-gated systems

NASA Astrophysics Data System (ADS)

Wang, Canjin; Sun, Tao; Wang, Tingfeng; Miao, Xikui; Wang, Rui

2018-07-01

For the task of image restoration, an accurate estimation of degrading PSF/kernel is the premise of recovering a visually superior image. The imaging process of range-gated imaging system in atmosphere associates with lots of factors, such as back scattering, background radiation, diffraction limit and the vibration of the platform. On one hand, due to the difficulty of constructing models for all factors, the kernels from physical-model based methods are not strictly accurate and practical. On the other hand, there are few strong edges in images, which brings significant errors to most of image-feature-based methods. Since different methods focus on different formation factors of the kernel, their results often complement each other. Therefore, we propose an approach which combines physical model with image features. With an fusion strategy using GCRF (Gaussian Conditional Random Fields) framework, we get a final kernel which is closer to the actual one. Aiming at the problem that ground-truth image is difficult to obtain, we then propose a semi data-driven fusion method in which different data sets are used to train fusion parameters. Finally, a semi blind restoration strategy based on EM (Expectation Maximization) and RL (Richardson-Lucy) algorithm is proposed. Our methods not only models how the lasers transfer in the atmosphere and imaging in the ICCD (Intensified CCD) plane, but also quantifies other unknown degraded factors using image-based methods, revealing how multiple kernel elements interact with each other. The experimental results demonstrate that our method achieves better performance than state-of-the-art restoration approaches.

The sensitivity of catchment hypsometry and hypsometric properties to DEM resolution and polynomial order

NASA Astrophysics Data System (ADS)

Liffner, Joel W.; Hewa, Guna A.; Peel, Murray C.

2018-05-01

Derivation of the hypsometric curve of a catchment, and properties relating to that curve, requires both use of topographical data (commonly in the form of a Digital Elevation Model - DEM), and the estimation of a functional representation of that curve. An early investigation into catchment hypsometry concluded 3rd order polynomials sufficiently describe the hypsometric curve, without the consideration of higher order polynomials, or the sensitivity of hypsometric properties relating to the curve. Another study concluded the hypsometric integral (HI) is robust against changes in DEM resolution, a conclusion drawn from a very limited sample size. Conclusions from these earlier studies have resulted in the adoption of methods deemed to be "sufficient" in subsequent studies, in addition to assumptions that the robustness of the HI extends to other hypsometric properties. This study investigates and demonstrates the sensitivity of hypsometric properties to DEM resolution, DEM type and polynomial order through assessing differences in hypsometric properties derived from 417 catchments and sub-catchments within South Australia. The sensitivity of hypsometric properties across DEM types and polynomial orders is found to be significant, which suggests careful consideration of the methods chosen to derive catchment hypsometric information is required.

A Novel Polygonal Finite Element Method: Virtual Node Method

NASA Astrophysics Data System (ADS)

Tang, X. H.; Zheng, C.; Zhang, J. H.

2010-05-01

Polygonal finite element method (PFEM), which can construct shape functions on polygonal elements, provides greater flexibility in mesh generation. However, the non-polynomial form of traditional PFEM, such as Wachspress method and Mean Value method, leads to inexact numerical integration. Since the integration technique for non-polynomial functions is immature. To overcome this shortcoming, a great number of integration points have to be used to obtain sufficiently exact results, which increases computational cost. In this paper, a novel polygonal finite element method is proposed and called as virtual node method (VNM). The features of present method can be list as: (1) It is a PFEM with polynomial form. Thereby, Hammer integral and Gauss integral can be naturally used to obtain exact numerical integration; (2) Shape functions of VNM satisfy all the requirements of finite element method. To test the performance of VNM, intensive numerical tests are carried out. It found that, in standard patch test, VNM can achieve significantly better results than Wachspress method and Mean Value method. Moreover, it is observed that VNM can achieve better results than triangular 3-node elements in the accuracy test.

Probe-type of superconductivity by impurity in materials with short coherence length: the s-wave and η-wave phases study

NASA Astrophysics Data System (ADS)

Ptok, Andrzej; Jerzy Kapcia, Konrad

2015-04-01

The effects of a single non-magnetic impurity on superconducting states in the Penson-Kolb-Hubbard model have been analyzed. The investigations have been performed within the Hartree-Fock mean field approximation in two steps: (i) the homogeneous system is analysed using the Bogoliubov transformation, whereas (ii) the inhomogeneous system is investigated by self-consistent Bogoliubov-de Gennes equations (with the exact diagonalization and the kernel polynomial method). We analysed both signs of the pair hopping, which correspond to s-wave and η-wave superconductivity. Our results show that an enhancement of the local superconducting gap at the impurity-site occurs for both cases. We obtained that Cooper pairs are scattered (at the impurity site) into the states which are from the neighborhoods of the states, which are commensurate ones with the crystal lattice. Additionally, in the η-phase there are peaks in the local-energy gap (in momentum space), which are connected with long-range oscillations in the spatial distribution of the energy gap, superconducting order parameter (SOP), as well as effective pairing potential. Our results can be contrasted with the experiment and predicts how to experimentally differentiate these two different symmetries of SOP by the scanning tunneling microscopy technique.

Exact solution of corner-modified banded block-Toeplitz eigensystems

NASA Astrophysics Data System (ADS)

Cobanera, Emilio; Alase, Abhijeet; Ortiz, Gerardo; Viola, Lorenza

2017-05-01

Motivated by the challenge of seeking a rigorous foundation for the bulk-boundary correspondence for free fermions, we introduce an algorithm for determining exactly the spectrum and a generalized-eigenvector basis of a class of banded block quasi-Toeplitz matrices that we call corner-modified. Corner modifications of otherwise arbitrary banded block-Toeplitz matrices capture the effect of boundary conditions and the associated breakdown of translational invariance. Our algorithm leverages the interplay between a non-standard, projector-based method of kernel determination (physically, a bulk-boundary separation) and families of linear representations of the algebra of matrix Laurent polynomials. Thanks to the fact that these representations act on infinite-dimensional carrier spaces in which translation symmetry is restored, it becomes possible to determine the eigensystem of an auxiliary projected block-Laurent matrix. This results in an analytic eigenvector Ansatz, independent of the system size, which we prove is guaranteed to contain the full solution of the original finite-dimensional problem. The actual solution is then obtained by imposing compatibility with a boundary matrix, whose shape is also independent of system size. As an application, we show analytically that eigenvectors of short-ranged fermionic tight-binding models may display power-law corrections to exponential behavior, and demonstrate the phenomenon for the paradigmatic Majorana chain of Kitaev.

Finite-frequency tomography using adjoint methods-Methodology and examples using membrane surface waves

NASA Astrophysics Data System (ADS)

Tape, Carl; Liu, Qinya; Tromp, Jeroen

2007-03-01

We employ adjoint methods in a series of synthetic seismic tomography experiments to recover surface wave phase-speed models of southern California. Our approach involves computing the Fréchet derivative for tomographic inversions via the interaction between a forward wavefield, propagating from the source to the receivers, and an `adjoint' wavefield, propagating from the receivers back to the source. The forward wavefield is computed using a 2-D spectral-element method (SEM) and a phase-speed model for southern California. A `target' phase-speed model is used to generate the `data' at the receivers. We specify an objective or misfit function that defines a measure of misfit between data and synthetics. For a given receiver, the remaining differences between data and synthetics are time-reversed and used as the source of the adjoint wavefield. For each earthquake, the interaction between the regular and adjoint wavefields is used to construct finite-frequency sensitivity kernels, which we call event kernels. An event kernel may be thought of as a weighted sum of phase-specific (e.g. P) banana-doughnut kernels, with weights determined by the measurements. The overall sensitivity is simply the sum of event kernels, which defines the misfit kernel. The misfit kernel is multiplied by convenient orthonormal basis functions that are embedded in the SEM code, resulting in the gradient of the misfit function, that is, the Fréchet derivative. A non-linear conjugate gradient algorithm is used to iteratively improve the model while reducing the misfit function. We illustrate the construction of the gradient and the minimization algorithm, and consider various tomographic experiments, including source inversions, structural inversions and joint source-structure inversions. Finally, we draw connections between classical Hessian-based tomography and gradient-based adjoint tomography.

Classification of corn kernels contaminated with aflatoxins using fluorescence and reflectance hyperspectral images analysis

NASA Astrophysics Data System (ADS)

Zhu, Fengle; Yao, Haibo; Hruska, Zuzana; Kincaid, Russell; Brown, Robert; Bhatnagar, Deepak; Cleveland, Thomas

2015-05-01

Aflatoxins are secondary metabolites produced by certain fungal species of the Aspergillus genus. Aflatoxin contamination remains a problem in agricultural products due to its toxic and carcinogenic properties. Conventional chemical methods for aflatoxin detection are time-consuming and destructive. This study employed fluorescence and reflectance visible near-infrared (VNIR) hyperspectral images to classify aflatoxin contaminated corn kernels rapidly and non-destructively. Corn ears were artificially inoculated in the field with toxigenic A. flavus spores at the early dough stage of kernel development. After harvest, a total of 300 kernels were collected from the inoculated ears. Fluorescence hyperspectral imagery with UV excitation and reflectance hyperspectral imagery with halogen illumination were acquired on both endosperm and germ sides of kernels. All kernels were then subjected to chemical analysis individually to determine aflatoxin concentrations. A region of interest (ROI) was created for each kernel to extract averaged spectra. Compared with healthy kernels, fluorescence spectral peaks for contaminated kernels shifted to longer wavelengths with lower intensity, and reflectance values for contaminated kernels were lower with a different spectral shape in 700-800 nm region. Principal component analysis was applied for data compression before classifying kernels into contaminated and healthy based on a 20 ppb threshold utilizing the K-nearest neighbors algorithm. The best overall accuracy achieved was 92.67% for germ side in the fluorescence data analysis. The germ side generally performed better than endosperm side. Fluorescence and reflectance image data achieved similar accuracy.

Vector-valued Jack polynomials and wavefunctions on the torus

NASA Astrophysics Data System (ADS)

Dunkl, Charles F.

2017-06-01

The Hamiltonian of the quantum Calogero-Sutherland model of N identical particles on the circle with 1/r 2 interactions has eigenfunctions consisting of Jack polynomials times the base state. By use of the generalized Jack polynomials taking values in modules of the symmetric group and the matrix solution of a system of linear differential equations one constructs novel eigenfunctions of the Hamiltonian. Like the usual wavefunctions each eigenfunction determines a symmetric probability density on the N-torus. The construction applies to any irreducible representation of the symmetric group. The methods depend on the theory of generalized Jack polynomials due to Griffeth, and the Yang-Baxter graph approach of Luque and the author.

Kernel and divergence techniques in high energy physics separations

NASA Astrophysics Data System (ADS)

Bouř, Petr; Kůs, Václav; Franc, Jiří

2017-10-01

Binary decision trees under the Bayesian decision technique are used for supervised classification of high-dimensional data. We present a great potential of adaptive kernel density estimation as the nested separation method of the supervised binary divergence decision tree. Also, we provide a proof of alternative computing approach for kernel estimates utilizing Fourier transform. Further, we apply our method to Monte Carlo data set from the particle accelerator Tevatron at DØ experiment in Fermilab and provide final top-antitop signal separation results. We have achieved up to 82 % AUC while using the restricted feature selection entering the signal separation procedure.

Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating

ERIC Educational Resources Information Center

Jiang, Yanlin; von Davier, Alina A.; Chen, Haiwen

2012-01-01

This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…

Learning epistatic interactions from sequence-activity data to predict enantioselectivity

NASA Astrophysics Data System (ADS)

Zaugg, Julian; Gumulya, Yosephine; Malde, Alpeshkumar K.; Bodén, Mikael

2017-12-01

Enzymes with a high selectivity are desirable for improving economics of chemical synthesis of enantiopure compounds. To improve enzyme selectivity mutations are often introduced near the catalytic active site. In this compact environment epistatic interactions between residues, where contributions to selectivity are non-additive, play a significant role in determining the degree of selectivity. Using support vector machine regression models we map mutations to the experimentally characterised enantioselectivities for a set of 136 variants of the epoxide hydrolase from the fungus Aspergillus niger (AnEH). We investigate whether the influence a mutation has on enzyme selectivity can be accurately predicted through linear models, and whether prediction accuracy can be improved using higher-order counterparts. Comparing linear and polynomial degree = 2 models, mean Pearson coefficients (r) from 50 {× } 5 -fold cross-validation increase from 0.84 to 0.91 respectively. Equivalent models tested on interaction-minimised sequences achieve values of r=0.90 and r=0.93 . As expected, testing on a simulated control data set with no interactions results in no significant improvements from higher-order models. Additional experimentally derived AnEH mutants are tested with linear and polynomial degree = 2 models, with values increasing from r=0.51 to r=0.87 respectively. The study demonstrates that linear models perform well, however the representation of epistatic interactions in predictive models improves identification of selectivity-enhancing mutations. The improvement is attributed to higher-order kernel functions that represent epistatic interactions between residues.

Learning epistatic interactions from sequence-activity data to predict enantioselectivity

NASA Astrophysics Data System (ADS)

Zaugg, Julian; Gumulya, Yosephine; Malde, Alpeshkumar K.; Bodén, Mikael

2017-12-01

Enzymes with a high selectivity are desirable for improving economics of chemical synthesis of enantiopure compounds. To improve enzyme selectivity mutations are often introduced near the catalytic active site. In this compact environment epistatic interactions between residues, where contributions to selectivity are non-additive, play a significant role in determining the degree of selectivity. Using support vector machine regression models we map mutations to the experimentally characterised enantioselectivities for a set of 136 variants of the epoxide hydrolase from the fungus Aspergillus niger ( AnEH). We investigate whether the influence a mutation has on enzyme selectivity can be accurately predicted through linear models, and whether prediction accuracy can be improved using higher-order counterparts. Comparing linear and polynomial degree = 2 models, mean Pearson coefficients ( r) from 50 {× } 5-fold cross-validation increase from 0.84 to 0.91 respectively. Equivalent models tested on interaction-minimised sequences achieve values of r=0.90 and r=0.93. As expected, testing on a simulated control data set with no interactions results in no significant improvements from higher-order models. Additional experimentally derived AnEH mutants are tested with linear and polynomial degree = 2 models, with values increasing from r=0.51 to r=0.87 respectively. The study demonstrates that linear models perform well, however the representation of epistatic interactions in predictive models improves identification of selectivity-enhancing mutations. The improvement is attributed to higher-order kernel functions that represent epistatic interactions between residues.

Learning epistatic interactions from sequence-activity data to predict enantioselectivity.

PubMed

Zaugg, Julian; Gumulya, Yosephine; Malde, Alpeshkumar K; Bodén, Mikael

2017-12-01

Enzymes with a high selectivity are desirable for improving economics of chemical synthesis of enantiopure compounds. To improve enzyme selectivity mutations are often introduced near the catalytic active site. In this compact environment epistatic interactions between residues, where contributions to selectivity are non-additive, play a significant role in determining the degree of selectivity. Using support vector machine regression models we map mutations to the experimentally characterised enantioselectivities for a set of 136 variants of the epoxide hydrolase from the fungus Aspergillus niger (AnEH). We investigate whether the influence a mutation has on enzyme selectivity can be accurately predicted through linear models, and whether prediction accuracy can be improved using higher-order counterparts. Comparing linear and polynomial degree = 2 models, mean Pearson coefficients (r) from [Formula: see text]-fold cross-validation increase from 0.84 to 0.91 respectively. Equivalent models tested on interaction-minimised sequences achieve values of [Formula: see text] and [Formula: see text]. As expected, testing on a simulated control data set with no interactions results in no significant improvements from higher-order models. Additional experimentally derived AnEH mutants are tested with linear and polynomial degree = 2 models, with values increasing from [Formula: see text] to [Formula: see text] respectively. The study demonstrates that linear models perform well, however the representation of epistatic interactions in predictive models improves identification of selectivity-enhancing mutations. The improvement is attributed to higher-order kernel functions that represent epistatic interactions between residues.

New KF-PP-SVM classification method for EEG in brain-computer interfaces.

PubMed

Yang, Banghua; Han, Zhijun; Zan, Peng; Wang, Qian

2014-01-01

Classification methods are a crucial direction in the current study of brain-computer interfaces (BCIs). To improve the classification accuracy for electroencephalogram (EEG) signals, a novel KF-PP-SVM (kernel fisher, posterior probability, and support vector machine) classification method is developed. Its detailed process entails the use of common spatial patterns to obtain features, based on which the within-class scatter is calculated. Then the scatter is added into the kernel function of a radial basis function to construct a new kernel function. This new kernel is integrated into the SVM to obtain a new classification model. Finally, the output of SVM is calculated based on posterior probability and the final recognition result is obtained. To evaluate the effectiveness of the proposed KF-PP-SVM method, EEG data collected from laboratory are processed with four different classification schemes (KF-PP-SVM, KF-SVM, PP-SVM, and SVM). The results showed that the overall average improvements arising from the use of the KF-PP-SVM scheme as opposed to KF-SVM, PP-SVM and SVM schemes are 2.49%, 5.83 % and 6.49 % respectively.

Molecule kernels: a descriptor- and alignment-free quantitative structure-activity relationship approach.

PubMed

Mohr, Johannes A; Jain, Brijnesh J; Obermayer, Klaus

2008-09-01

Quantitative structure activity relationship (QSAR) analysis is traditionally based on extracting a set of molecular descriptors and using them to build a predictive model. In this work, we propose a QSAR approach based directly on the similarity between the 3D structures of a set of molecules measured by a so-called molecule kernel, which is independent of the spatial prealignment of the compounds. Predictors can be build using the molecule kernel in conjunction with the potential support vector machine (P-SVM), a recently proposed machine learning method for dyadic data. The resulting models make direct use of the structural similarities between the compounds in the test set and a subset of the training set and do not require an explicit descriptor construction. We evaluated the predictive performance of the proposed method on one classification and four regression QSAR datasets and compared its results to the results reported in the literature for several state-of-the-art descriptor-based and 3D QSAR approaches. In this comparison, the proposed molecule kernel method performed better than the other QSAR methods.

Impacts of Sigma Coordinates on the Euler and Navier-Stokes Equations using Continuous Galerkin Methods

DTIC Science & Technology

2009-03-01

the 1- D local basis functions. The 1-D Lagrange polynomial local basis function, using Legendre -Gauss-Lobatto interpolation points, was defined by...cases were run using 10th order polynomials , with contours from -0.05 to 0.525 K with an interval of 0.025 K...after 700 s for reso- lutions: (a) 20, (b) 10, and (c) 5 m. All cases were run using 10th order polynomials , with contours from -0.05 to 0.525 K

Distortion theorems for polynomials on a circle

NASA Astrophysics Data System (ADS)

Dubinin, V. N.

2000-12-01

Inequalities for the derivatives with respect to \\varphi=\\arg z the functions \\operatorname{Re}P(z), \\vert P(z)\\vert^2 and \\arg P(z) are established for an algebraic polynomial P(z) at points on the circle \\vert z\\vert=1. These estimates depend, in particular, on the constant term and the leading coefficient of the polynomial P(z) and improve the classical Bernstein and Turan inequalities. The method of proof is based on the techniques of generalized reduced moduli.

Utilization of spectral-spatial characteristics in shortwave infrared hyperspectral images to classify and identify fungi-contaminated peanuts.

PubMed

Qiao, Xiaojun; Jiang, Jinbao; Qi, Xiaotong; Guo, Haiqiang; Yuan, Deshuai

2017-04-01

It's well-known fungi-contaminated peanuts contain potent carcinogen. Efficiently identifying and separating the contaminated can help prevent aflatoxin entering in food chain. In this study, shortwave infrared (SWIR) hyperspectral images for identifying the prepared contaminated kernels. Feature selection method of analysis of variance (ANOVA) and feature extraction method of nonparametric weighted feature extraction (NWFE) were used to concentrate spectral information into a subspace where contaminated and healthy peanuts can have favorable separability. Then, peanut pixels were classified using SVM. Moreover, image segmentation method of region growing was applied to segment the image as kernel-scale patches and meanwhile to number the kernels. The result shows that pixel-wise classification accuracies are 99.13% for breed A, 96.72% for B and 99.73% for C in learning images, and are 96.32%, 94.2% and 97.51% in validation images. Contaminated peanuts were correctly marked as aberrant kernels in both learning images and validation images. Copyright © 2016 Elsevier Ltd. All rights reserved.

Sub-Network Kernels for Measuring Similarity of Brain Connectivity Networks in Disease Diagnosis.

PubMed

Jie, Biao; Liu, Mingxia; Zhang, Daoqiang; Shen, Dinggang

2018-05-01

As a simple representation of interactions among distributed brain regions, brain networks have been widely applied to automated diagnosis of brain diseases, such as Alzheimer's disease (AD) and its early stage, i.e., mild cognitive impairment (MCI). In brain network analysis, a challenging task is how to measure the similarity between a pair of networks. Although many graph kernels (i.e., kernels defined on graphs) have been proposed for measuring the topological similarity of a pair of brain networks, most of them are defined using general graphs, thus ignoring the uniqueness of each node in brain networks. That is, each node in a brain network denotes a particular brain region, which is a specific characteristics of brain networks. Accordingly, in this paper, we construct a novel sub-network kernel for measuring the similarity between a pair of brain networks and then apply it to brain disease classification. Different from current graph kernels, our proposed sub-network kernel not only takes into account the inherent characteristic of brain networks, but also captures multi-level (from local to global) topological properties of nodes in brain networks, which are essential for defining the similarity measure of brain networks. To validate the efficacy of our method, we perform extensive experiments on subjects with baseline functional magnetic resonance imaging data obtained from the Alzheimer's disease neuroimaging initiative database. Experimental results demonstrate that the proposed method outperforms several state-of-the-art graph-based methods in MCI classification.

A comparison of companion matrix methods to find roots of a trigonometric polynomial

NASA Astrophysics Data System (ADS)

Boyd, John P.

2013-08-01

A trigonometric polynomial is a truncated Fourier series of the form fN(t)≡∑j=0Naj cos(jt)+∑j=1N bj sin(jt). It has been previously shown by the author that zeros of such a polynomial can be computed as the eigenvalues of a companion matrix with elements which are complex valued combinations of the Fourier coefficients, the "CCM" method. However, previous work provided no examples, so one goal of this new work is to experimentally test the CCM method. A second goal is introduce a new alternative, the elimination/Chebyshev algorithm, and experimentally compare it with the CCM scheme. The elimination/Chebyshev matrix (ECM) algorithm yields a companion matrix with real-valued elements, albeit at the price of usefulness only for real roots. The new elimination scheme first converts the trigonometric rootfinding problem to a pair of polynomial equations in the variables (c,s) where c≡cos(t) and s≡sin(t). The elimination method next reduces the system to a single univariate polynomial P(c). We show that this same polynomial is the resultant of the system and is also a generator of the Groebner basis with lexicographic ordering for the system. Both methods give very high numerical accuracy for real-valued roots, typically at least 11 decimal places in Matlab/IEEE 754 16 digit floating point arithmetic. The CCM algorithm is typically one or two decimal places more accurate, though these differences disappear if the roots are "Newton-polished" by a single Newton's iteration. The complex-valued matrix is accurate for complex-valued roots, too, though accuracy decreases with the magnitude of the imaginary part of the root. The cost of both methods scales as O(N3) floating point operations. In spite of intimate connections of the elimination/Chebyshev scheme to two well-established technologies for solving systems of equations, resultants and Groebner bases, and the advantages of using only real-valued arithmetic to obtain a companion matrix with real-valued elements, the ECM algorithm is noticeably inferior to the complex-valued companion matrix in simplicity, ease of programming, and accuracy.

Rare variant testing across methods and thresholds using the multi-kernel sequence kernel association test (MK-SKAT).

PubMed

Urrutia, Eugene; Lee, Seunggeun; Maity, Arnab; Zhao, Ni; Shen, Judong; Li, Yun; Wu, Michael C

Analysis of rare genetic variants has focused on region-based analysis wherein a subset of the variants within a genomic region is tested for association with a complex trait. Two important practical challenges have emerged. First, it is difficult to choose which test to use. Second, it is unclear which group of variants within a region should be tested. Both depend on the unknown true state of nature. Therefore, we develop the Multi-Kernel SKAT (MK-SKAT) which tests across a range of rare variant tests and groupings. Specifically, we demonstrate that several popular rare variant tests are special cases of the sequence kernel association test which compares pair-wise similarity in trait value to similarity in the rare variant genotypes between subjects as measured through a kernel function. Choosing a particular test is equivalent to choosing a kernel. Similarly, choosing which group of variants to test also reduces to choosing a kernel. Thus, MK-SKAT uses perturbation to test across a range of kernels. Simulations and real data analyses show that our framework controls type I error while maintaining high power across settings: MK-SKAT loses power when compared to the kernel for a particular scenario but has much greater power than poor choices.

Pathway-Based Kernel Boosting for the Analysis of Genome-Wide Association Studies

PubMed Central

Manitz, Juliane; Burger, Patricia; Amos, Christopher I.; Chang-Claude, Jenny; Wichmann, Heinz-Erich; Kneib, Thomas; Bickeböller, Heike

2017-01-01

The analysis of genome-wide association studies (GWAS) benefits from the investigation of biologically meaningful gene sets, such as gene-interaction networks (pathways). We propose an extension to a successful kernel-based pathway analysis approach by integrating kernel functions into a powerful algorithmic framework for variable selection, to enable investigation of multiple pathways simultaneously. We employ genetic similarity kernels from the logistic kernel machine test (LKMT) as base-learners in a boosting algorithm. A model to explain case-control status is created iteratively by selecting pathways that improve its prediction ability. We evaluated our method in simulation studies adopting 50 pathways for different sample sizes and genetic effect strengths. Additionally, we included an exemplary application of kernel boosting to a rheumatoid arthritis and a lung cancer dataset. Simulations indicate that kernel boosting outperforms the LKMT in certain genetic scenarios. Applications to GWAS data on rheumatoid arthritis and lung cancer resulted in sparse models which were based on pathways interpretable in a clinical sense. Kernel boosting is highly flexible in terms of considered variables and overcomes the problem of multiple testing. Additionally, it enables the prediction of clinical outcomes. Thus, kernel boosting constitutes a new, powerful tool in the analysis of GWAS data and towards the understanding of biological processes involved in disease susceptibility. PMID:28785300

Pathway-Based Kernel Boosting for the Analysis of Genome-Wide Association Studies.

PubMed

Friedrichs, Stefanie; Manitz, Juliane; Burger, Patricia; Amos, Christopher I; Risch, Angela; Chang-Claude, Jenny; Wichmann, Heinz-Erich; Kneib, Thomas; Bickeböller, Heike; Hofner, Benjamin

2017-01-01

The analysis of genome-wide association studies (GWAS) benefits from the investigation of biologically meaningful gene sets, such as gene-interaction networks (pathways). We propose an extension to a successful kernel-based pathway analysis approach by integrating kernel functions into a powerful algorithmic framework for variable selection, to enable investigation of multiple pathways simultaneously. We employ genetic similarity kernels from the logistic kernel machine test (LKMT) as base-learners in a boosting algorithm. A model to explain case-control status is created iteratively by selecting pathways that improve its prediction ability. We evaluated our method in simulation studies adopting 50 pathways for different sample sizes and genetic effect strengths. Additionally, we included an exemplary application of kernel boosting to a rheumatoid arthritis and a lung cancer dataset. Simulations indicate that kernel boosting outperforms the LKMT in certain genetic scenarios. Applications to GWAS data on rheumatoid arthritis and lung cancer resulted in sparse models which were based on pathways interpretable in a clinical sense. Kernel boosting is highly flexible in terms of considered variables and overcomes the problem of multiple testing. Additionally, it enables the prediction of clinical outcomes. Thus, kernel boosting constitutes a new, powerful tool in the analysis of GWAS data and towards the understanding of biological processes involved in disease susceptibility.

Piecewise polynomial representations of genomic tracks.

PubMed

Tarabichi, Maxime; Detours, Vincent; Konopka, Tomasz

2012-01-01

Genomic data from micro-array and sequencing projects consist of associations of measured values to chromosomal coordinates. These associations can be thought of as functions in one dimension and can thus be stored, analyzed, and interpreted as piecewise-polynomial curves. We present a general framework for building piecewise polynomial representations of genome-scale signals and illustrate some of its applications via examples. We show that piecewise constant segmentation, a typical step in copy-number analyses, can be carried out within this framework for both array and (DNA) sequencing data offering advantages over existing methods in each case. Higher-order polynomial curves can be used, for example, to detect trends and/or discontinuities in transcription levels from RNA-seq data. We give a concrete application of piecewise linear functions to diagnose and quantify alignment quality at exon borders (splice sites). Our software (source and object code) for building piecewise polynomial models is available at http://sourceforge.net/projects/locsmoc/.

New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems

PubMed Central

Abd-Elhameed, W. M.

2014-01-01

This paper is concerned with deriving some new formulae expressing explicitly the high-order derivatives of Jacobi polynomials whose parameters difference is one or two of any degree and of any order in terms of their corresponding Jacobi polynomials. The derivatives formulae for Chebyshev polynomials of third and fourth kinds of any degree and of any order in terms of their corresponding Chebyshev polynomials are deduced as special cases. Some new reduction formulae for summing some terminating hypergeometric functions of unit argument are also deduced. As an application, and with the aid of the new introduced derivatives formulae, an algorithm for solving special sixth-order boundary value problems are implemented with the aid of applying Galerkin method. A numerical example is presented hoping to ascertain the validity and the applicability of the proposed algorithms. PMID:25386599

Polynomial elimination theory and non-linear stability analysis for the Euler equations

NASA Technical Reports Server (NTRS)

Kennon, S. R.; Dulikravich, G. S.; Jespersen, D. C.

1986-01-01

Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

Generation and optimization of superpixels as image processing kernels for Jones matrix optical coherence tomography

PubMed Central

Miyazawa, Arata; Hong, Young-Joo; Makita, Shuichi; Kasaragod, Deepa; Yasuno, Yoshiaki

2017-01-01

Jones matrix-based polarization sensitive optical coherence tomography (JM-OCT) simultaneously measures optical intensity, birefringence, degree of polarization uniformity, and OCT angiography. The statistics of the optical features in a local region, such as the local mean of the OCT intensity, are frequently used for image processing and the quantitative analysis of JM-OCT. Conventionally, local statistics have been computed with fixed-size rectangular kernels. However, this results in a trade-off between image sharpness and statistical accuracy. We introduce a superpixel method to JM-OCT for generating the flexible kernels of local statistics. A superpixel is a cluster of image pixels that is formed by the pixels’ spatial and signal value proximities. An algorithm for superpixel generation specialized for JM-OCT and its optimization methods are presented in this paper. The spatial proximity is in two-dimensional cross-sectional space and the signal values are the four optical features. Hence, the superpixel method is a six-dimensional clustering technique for JM-OCT pixels. The performance of the JM-OCT superpixels and its optimization methods are evaluated in detail using JM-OCT datasets of posterior eyes. The superpixels were found to well preserve tissue structures, such as layer structures, sclera, vessels, and retinal pigment epithelium. And hence, they are more suitable for local statistics kernels than conventional uniform rectangular kernels. PMID:29082073

A shock-capturing SPH scheme based on adaptive kernel estimation

NASA Astrophysics Data System (ADS)

Sigalotti, Leonardo Di G.; López, Hender; Donoso, Arnaldo; Sira, Eloy; Klapp, Jaime

2006-02-01

Here we report a method that converts standard smoothed particle hydrodynamics (SPH) into a working shock-capturing scheme without relying on solutions to the Riemann problem. Unlike existing adaptive SPH simulations, the present scheme is based on an adaptive kernel estimation of the density, which combines intrinsic features of both the kernel and nearest neighbor approaches in a way that the amount of smoothing required in low-density regions is effectively controlled. Symmetrized SPH representations of the gas dynamic equations along with the usual kernel summation for the density are used to guarantee variational consistency. Implementation of the adaptive kernel estimation involves a very simple procedure and allows for a unique scheme that handles strong shocks and rarefactions the same way. Since it represents a general improvement of the integral interpolation on scattered data, it is also applicable to other fluid-dynamic models. When the method is applied to supersonic compressible flows with sharp discontinuities, as in the classical one-dimensional shock-tube problem and its variants, the accuracy of the results is comparable, and in most cases superior, to that obtained from high quality Godunov-type methods and SPH formulations based on Riemann solutions. The extension of the method to two- and three-space dimensions is straightforward. In particular, for the two-dimensional cylindrical Noh's shock implosion and Sedov point explosion problems the present scheme produces much better results than those obtained with conventional SPH codes.

An Evaluation of the Kernel Equating Method: A Special Study with Pseudotests Constructed from Real Test Data. Research Report. ETS RR-06-02

ERIC Educational Resources Information Center

von Davier, Alina A.; Holland, Paul W.; Livingston, Samuel A.; Casabianca, Jodi; Grant, Mary C.; Martin, Kathleen

2006-01-01

This study examines how closely the kernel equating (KE) method (von Davier, Holland, & Thayer, 2004a) approximates the results of other observed-score equating methods--equipercentile and linear equatings. The study used pseudotests constructed of item responses from a real test to simulate three equating designs: an equivalent groups (EG)…

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

O'Brien, Travis A.; Kashinath, Karthik; Cavanaugh, Nicholas R.

Numerous facets of scientific research implicitly or explicitly call for the estimation of probability densities. Histograms and kernel density estimates (KDEs) are two commonly used techniques for estimating such information, with the KDE generally providing a higher fidelity representation of the probability density function (PDF). Both methods require specification of either a bin width or a kernel bandwidth. While techniques exist for choosing the kernel bandwidth optimally and objectively, they are computationally intensive, since they require repeated calculation of the KDE. A solution for objectively and optimally choosing both the kernel shape and width has recently been developed by Bernacchiamore » and Pigolotti (2011). While this solution theoretically applies to multidimensional KDEs, it has not been clear how to practically do so. A method for practically extending the Bernacchia-Pigolotti KDE to multidimensions is introduced. This multidimensional extension is combined with a recently-developed computational improvement to their method that makes it computationally efficient: a 2D KDE on 10 5 samples only takes 1 s on a modern workstation. This fast and objective KDE method, called the fastKDE method, retains the excellent statistical convergence properties that have been demonstrated for univariate samples. The fastKDE method exhibits statistical accuracy that is comparable to state-of-the-science KDE methods publicly available in R, and it produces kernel density estimates several orders of magnitude faster. The fastKDE method does an excellent job of encoding covariance information for bivariate samples. This property allows for direct calculation of conditional PDFs with fastKDE. It is demonstrated how this capability might be leveraged for detecting non-trivial relationships between quantities in physical systems, such as transitional behavior.« less

A Decision-Making Method with Grey Multi-Source Heterogeneous Data and Its Application in Green Supplier Selection

PubMed Central

Dang, Yaoguo; Mao, Wenxin

2018-01-01

In view of the multi-attribute decision-making problem that the attribute values are grey multi-source heterogeneous data, a decision-making method based on kernel and greyness degree is proposed. The definitions of kernel and greyness degree of an extended grey number in a grey multi-source heterogeneous data sequence are given. On this basis, we construct the kernel vector and greyness degree vector of the sequence to whiten the multi-source heterogeneous information, then a grey relational bi-directional projection ranking method is presented. Considering the multi-attribute multi-level decision structure and the causalities between attributes in decision-making problem, the HG-DEMATEL method is proposed to determine the hierarchical attribute weights. A green supplier selection example is provided to demonstrate the rationality and validity of the proposed method. PMID:29510521

A Decision-Making Method with Grey Multi-Source Heterogeneous Data and Its Application in Green Supplier Selection.

PubMed

Sun, Huifang; Dang, Yaoguo; Mao, Wenxin

2018-03-03

In view of the multi-attribute decision-making problem that the attribute values are grey multi-source heterogeneous data, a decision-making method based on kernel and greyness degree is proposed. The definitions of kernel and greyness degree of an extended grey number in a grey multi-source heterogeneous data sequence are given. On this basis, we construct the kernel vector and greyness degree vector of the sequence to whiten the multi-source heterogeneous information, then a grey relational bi-directional projection ranking method is presented. Considering the multi-attribute multi-level decision structure and the causalities between attributes in decision-making problem, the HG-DEMATEL method is proposed to determine the hierarchical attribute weights. A green supplier selection example is provided to demonstrate the rationality and validity of the proposed method.

Improved dynamical scaling analysis using the kernel method for nonequilibrium relaxation.

PubMed

Echinaka, Yuki; Ozeki, Yukiyasu

2016-10-01

The dynamical scaling analysis for the Kosterlitz-Thouless transition in the nonequilibrium relaxation method is improved by the use of Bayesian statistics and the kernel method. This allows data to be fitted to a scaling function without using any parametric model function, which makes the results more reliable and reproducible and enables automatic and faster parameter estimation. Applying this method, the bootstrap method is introduced and a numerical discrimination for the transition type is proposed.

Prediction of Heterodimeric Protein Complexes from Weighted Protein-Protein Interaction Networks Using Novel Features and Kernel Functions

PubMed Central

Ruan, Peiying; Hayashida, Morihiro; Maruyama, Osamu; Akutsu, Tatsuya

2013-01-01

Since many proteins express their functional activity by interacting with other proteins and forming protein complexes, it is very useful to identify sets of proteins that form complexes. For that purpose, many prediction methods for protein complexes from protein-protein interactions have been developed such as MCL, MCODE, RNSC, PCP, RRW, and NWE. These methods have dealt with only complexes with size of more than three because the methods often are based on some density of subgraphs. However, heterodimeric protein complexes that consist of two distinct proteins occupy a large part according to several comprehensive databases of known complexes. In this paper, we propose several feature space mappings from protein-protein interaction data, in which each interaction is weighted based on reliability. Furthermore, we make use of prior knowledge on protein domains to develop feature space mappings, domain composition kernel and its combination kernel with our proposed features. We perform ten-fold cross-validation computational experiments. These results suggest that our proposed kernel considerably outperforms the naive Bayes-based method, which is the best existing method for predicting heterodimeric protein complexes. PMID:23776458

Richardson-Lucy deblurring for the star scene under a thinning motion path

NASA Astrophysics Data System (ADS)

Su, Laili; Shao, Xiaopeng; Wang, Lin; Wang, Haixin; Huang, Yining

2015-05-01

This paper puts emphasis on how to model and correct image blur that arises from a camera's ego motion while observing a distant star scene. Concerning the significance of accurate estimation of point spread function (PSF), a new method is employed to obtain blur kernel by thinning star motion path. In particular, how the blurred star image can be corrected to reconstruct the clear scene with a thinning motion blur model which describes the camera's path is presented. This thinning motion path to build blur kernel model is more effective at modeling the spatially motion blur introduced by camera's ego motion than conventional blind estimation of kernel-based PSF parameterization. To gain the reconstructed image, firstly, an improved thinning algorithm is used to obtain the star point trajectory, so as to extract the blur kernel of the motion-blurred star image. Then how motion blur model can be incorporated into the Richardson-Lucy (RL) deblurring algorithm, which reveals its overall effectiveness, is detailed. In addition, compared with the conventional estimated blur kernel, experimental results show that the proposed method of using thinning algorithm to get the motion blur kernel is of less complexity, higher efficiency and better accuracy, which contributes to better restoration of the motion-blurred star images.

Grey Language Hesitant Fuzzy Group Decision Making Method Based on Kernel and Grey Scale

PubMed Central

Diao, Yuzhu; Hu, Aqin

2018-01-01

Based on grey language multi-attribute group decision making, a kernel and grey scale scoring function is put forward according to the definition of grey language and the meaning of the kernel and grey scale. The function introduces grey scale into the decision-making method to avoid information distortion. This method is applied to the grey language hesitant fuzzy group decision making, and the grey correlation degree is used to sort the schemes. The effectiveness and practicability of the decision-making method are further verified by the industry chain sustainable development ability evaluation example of a circular economy. Moreover, its simplicity and feasibility are verified by comparing it with the traditional grey language decision-making method and the grey language hesitant fuzzy weighted arithmetic averaging (GLHWAA) operator integration method after determining the index weight based on the grey correlation. PMID:29498699

Grey Language Hesitant Fuzzy Group Decision Making Method Based on Kernel and Grey Scale.

PubMed

Li, Qingsheng; Diao, Yuzhu; Gong, Zaiwu; Hu, Aqin

2018-03-02

Based on grey language multi-attribute group decision making, a kernel and grey scale scoring function is put forward according to the definition of grey language and the meaning of the kernel and grey scale. The function introduces grey scale into the decision-making method to avoid information distortion. This method is applied to the grey language hesitant fuzzy group decision making, and the grey correlation degree is used to sort the schemes. The effectiveness and practicability of the decision-making method are further verified by the industry chain sustainable development ability evaluation example of a circular economy. Moreover, its simplicity and feasibility are verified by comparing it with the traditional grey language decision-making method and the grey language hesitant fuzzy weighted arithmetic averaging (GLHWAA) operator integration method after determining the index weight based on the grey correlation.

On the integral inversion of satellite-to-satellite velocity differences for local gravity field recovery: a theoretical study

NASA Astrophysics Data System (ADS)

Eshagh, Mehdi; Šprlák, Michal

2016-02-01

The gravity field can be recovered locally from the satellite-to-satellite velocity differences (VDs) between twin-satellites moving in the same orbit. To do so, three different integral formulae are derived in this paper to recover geoid height, radial component of gravity anomaly and gravity disturbance at sea level. Their kernel functions contain the product of two Legendre polynomials with different arguments. Such kernels are relatively complicated and it may be impossible to find their closed-forms. However, we could find the one related to recovering the geoid height from the VD data. The use of spectral forms of the kernels is possible and one does not have to generate them to very high degrees. The kernel functions are well-behaving meaning that they reduce the contribution of far-zone data and for example a cap margin of 7° is enough for recovering gravity anomalies. This means that the inversion area should be larger by 7° from all directions than the desired area to reduce the effect of spatial truncation error of the integral formula. Numerical studies using simulated data over Fennoscandia showed that when the distance between the twin-satellites is small, higher frequencies of the anomalies can be recovered from the VD data. In the ideal case of having short distance between the satellites flying at 250 km level, recovering radial component of gravity anomaly with an accuracy of 7 mGal is possible over Fennoscandia, if the VD data is contaminated only with the spatial truncation error, which is an ideal assumption. However, the problem is that the power of VD signal is very low when the satellites are close and it is very difficult to recognise the signal amongst the noise of the VD data. We also show that for a successful determination of gravity anomalies at sea level from an altitude of 250 km mean VDs with better accuracy than 0.01 mm/s are required. When coloured noise at this level is used for the VDs at 250 km with separation of 300 km, the accuracy of recovery will be about 11 mGal over Fennoscandia. In the case of using the real velocities of the satellites, the main problems are downward/upward continuation of the VDs on the mean orbital sphere and taking the azimuthal integration of them.

Classification of cardiovascular tissues using LBP based descriptors and a cascade SVM.

PubMed

Mazo, Claudia; Alegre, Enrique; Trujillo, Maria

2017-08-01

Histological images have characteristics, such as texture, shape, colour and spatial structure, that permit the differentiation of each fundamental tissue and organ. Texture is one of the most discriminative features. The automatic classification of tissues and organs based on histology images is an open problem, due to the lack of automatic solutions when treating tissues without pathologies. In this paper, we demonstrate that it is possible to automatically classify cardiovascular tissues using texture information and Support Vector Machines (SVM). Additionally, we realised that it is feasible to recognise several cardiovascular organs following the same process. The texture of histological images was described using Local Binary Patterns (LBP), LBP Rotation Invariant (LBPri), Haralick features and different concatenations between them, representing in this way its content. Using a SVM with linear kernel, we selected the more appropriate descriptor that, for this problem, was a concatenation of LBP and LBPri. Due to the small number of the images available, we could not follow an approach based on deep learning, but we selected the classifier who yielded the higher performance by comparing SVM with Random Forest and Linear Discriminant Analysis. Once SVM was selected as the classifier with a higher area under the curve that represents both higher recall and precision, we tuned it evaluating different kernels, finding that a linear SVM allowed us to accurately separate four classes of tissues: (i) cardiac muscle of the heart, (ii) smooth muscle of the muscular artery, (iii) loose connective tissue, and (iv) smooth muscle of the large vein and the elastic artery. The experimental validation was conducted using 3000 blocks of 100 × 100 sized pixels, with 600 blocks per class and the classification was assessed using a 10-fold cross-validation. using LBP as the descriptor, concatenated with LBPri and a SVM with linear kernel, the main four classes of tissues were recognised with an AUC higher than 0.98. A polynomial kernel was then used to separate the elastic artery and vein, yielding an AUC in both cases superior to 0.98. Following the proposed approach, it is possible to separate with very high precision (AUC greater than 0.98) the fundamental tissues of the cardiovascular system along with some organs, such as the heart, arteries and veins. Copyright © 2017 Elsevier B.V. All rights reserved.

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

Jakeman, John D.; Narayan, Akil; Zhou, Tao

We propose an algorithm for recovering sparse orthogonal polynomial expansions via collocation. A standard sampling approach for recovering sparse polynomials uses Monte Carlo sampling, from the density of orthogonality, which results in poor function recovery when the polynomial degree is high. Our proposed approach aims to mitigate this limitation by sampling with respect to the weighted equilibrium measure of the parametric domain and subsequently solves a preconditionedmore » $$\\ell^1$$-minimization problem, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function. Our algorithm can be applied to a wide class of orthogonal polynomial families on bounded and unbounded domains, including all classical families. We present theoretical analysis to motivate the algorithm and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. In conclusion, numerical examples are also provided to demonstrate that our proposed algorithm leads to comparable or improved accuracy even when compared with Legendre- and Hermite-specific algorithms.« less

An Online Gravity Modeling Method Applied for High Precision Free-INS

PubMed Central

Wang, Jing; Yang, Gongliu; Li, Jing; Zhou, Xiao

2016-01-01

For real-time solution of inertial navigation system (INS), the high-degree spherical harmonic gravity model (SHM) is not applicable because of its time and space complexity, in which traditional normal gravity model (NGM) has been the dominant technique for gravity compensation. In this paper, a two-dimensional second-order polynomial model is derived from SHM according to the approximate linear characteristic of regional disturbing potential. Firstly, deflections of vertical (DOVs) on dense grids are calculated with SHM in an external computer. And then, the polynomial coefficients are obtained using these DOVs. To achieve global navigation, the coefficients and applicable region of polynomial model are both updated synchronously in above computer. Compared with high-degree SHM, the polynomial model takes less storage and computational time at the expense of minor precision. Meanwhile, the model is more accurate than NGM. Finally, numerical test and INS experiment show that the proposed method outperforms traditional gravity models applied for high precision free-INS. PMID:27669261

An Online Gravity Modeling Method Applied for High Precision Free-INS.

PubMed

Wang, Jing; Yang, Gongliu; Li, Jing; Zhou, Xiao

2016-09-23

For real-time solution of inertial navigation system (INS), the high-degree spherical harmonic gravity model (SHM) is not applicable because of its time and space complexity, in which traditional normal gravity model (NGM) has been the dominant technique for gravity compensation. In this paper, a two-dimensional second-order polynomial model is derived from SHM according to the approximate linear characteristic of regional disturbing potential. Firstly, deflections of vertical (DOVs) on dense grids are calculated with SHM in an external computer. And then, the polynomial coefficients are obtained using these DOVs. To achieve global navigation, the coefficients and applicable region of polynomial model are both updated synchronously in above computer. Compared with high-degree SHM, the polynomial model takes less storage and computational time at the expense of minor precision. Meanwhile, the model is more accurate than NGM. Finally, numerical test and INS experiment show that the proposed method outperforms traditional gravity models applied for high precision free-INS.

Feature extraction via KPCA for classification of gait patterns.

PubMed

Wu, Jianning; Wang, Jue; Liu, Li

2007-06-01

Automated recognition of gait pattern change is important in medical diagnostics as well as in the early identification of at-risk gait in the elderly. We evaluated the use of Kernel-based Principal Component Analysis (KPCA) to extract more gait features (i.e., to obtain more significant amounts of information about human movement) and thus to improve the classification of gait patterns. 3D gait data of 24 young and 24 elderly participants were acquired using an OPTOTRAK 3020 motion analysis system during normal walking, and a total of 36 gait spatio-temporal and kinematic variables were extracted from the recorded data. KPCA was used first for nonlinear feature extraction to then evaluate its effect on a subsequent classification in combination with learning algorithms such as support vector machines (SVMs). Cross-validation test results indicated that the proposed technique could allow spreading the information about the gait's kinematic structure into more nonlinear principal components, thus providing additional discriminatory information for the improvement of gait classification performance. The feature extraction ability of KPCA was affected slightly with different kernel functions as polynomial and radial basis function. The combination of KPCA and SVM could identify young-elderly gait patterns with 91% accuracy, resulting in a markedly improved performance compared to the combination of PCA and SVM. These results suggest that nonlinear feature extraction by KPCA improves the classification of young-elderly gait patterns, and holds considerable potential for future applications in direct dimensionality reduction and interpretation of multiple gait signals.

Determination of active ingredients in corn silk, leaf, and kernel by capillary electrophoresis with electrochemicaI detection.

PubMed

Lin, Miao; Chu, Qing-Cui; Tian, Xiu-Hui; Ye, Jian-Nong

2007-01-01

Corn has been known for its accumulation of flavones and phenolic acids. However, many parts of corn, except kernel, have not drawn much attention. In this work, a method based on capillary zone electrophoresis with electrochemical detection has been used for the separation and determination of epicatechin, rutin, ascorbic acid (Vc), kaempferol, chlorogenic acid, and quercetin in corn silk, leaf, and kernel. The distribution comparison of the ingredients among silk, leaf, and kernel is discussed. Several important factors--including running buffer acidity, separation voltage, and working electrode potential--were evaluated to acquire the optimum analysis conditions. Under the optimum conditions, the analytes could be well separated within 19 min in a 40-mmol/L borate buffer (pH 9.2). The response was linear over three orders of magnitude with detection limits (S/N = 3) ranging from 4.97 x 10(-8) to 9.75 x 10(-8) g/mL. The method has been successfully applied for the analysis of corn silk, leaf, and kernel with satisfactory results.

Bicubic uniform B-spline wavefront fitting technology applied in computer-generated holograms

NASA Astrophysics Data System (ADS)

Cao, Hui; Sun, Jun-qiang; Chen, Guo-jie

2006-02-01

This paper presented a bicubic uniform B-spline wavefront fitting technology to figure out the analytical expression for object wavefront used in Computer-Generated Holograms (CGHs). In many cases, to decrease the difficulty of optical processing, off-axis CGHs rather than complex aspherical surface elements are used in modern advanced military optical systems. In order to design and fabricate off-axis CGH, we have to fit out the analytical expression for object wavefront. Zernike Polynomial is competent for fitting wavefront of centrosymmetric optical systems, but not for axisymmetrical optical systems. Although adopting high-degree polynomials fitting method would achieve higher fitting precision in all fitting nodes, the greatest shortcoming of this method is that any departure from the fitting nodes would result in great fitting error, which is so-called pulsation phenomenon. Furthermore, high-degree polynomials fitting method would increase the calculation time in coding computer-generated hologram and solving basic equation. Basing on the basis function of cubic uniform B-spline and the character mesh of bicubic uniform B-spline wavefront, bicubic uniform B-spline wavefront are described as the product of a series of matrices. Employing standard MATLAB routines, four kinds of different analytical expressions for object wavefront are fitted out by bicubic uniform B-spline as well as high-degree polynomials. Calculation results indicate that, compared with high-degree polynomials, bicubic uniform B-spline is a more competitive method to fit out the analytical expression for object wavefront used in off-axis CGH, for its higher fitting precision and C2 continuity.

Kernel-based least squares policy iteration for reinforcement learning.

PubMed

Xu, Xin; Hu, Dewen; Lu, Xicheng

2007-07-01

In this paper, we present a kernel-based least squares policy iteration (KLSPI) algorithm for reinforcement learning (RL) in large or continuous state spaces, which can be used to realize adaptive feedback control of uncertain dynamic systems. By using KLSPI, near-optimal control policies can be obtained without much a priori knowledge on dynamic models of control plants. In KLSPI, Mercer kernels are used in the policy evaluation of a policy iteration process, where a new kernel-based least squares temporal-difference algorithm called KLSTD-Q is proposed for efficient policy evaluation. To keep the sparsity and improve the generalization ability of KLSTD-Q solutions, a kernel sparsification procedure based on approximate linear dependency (ALD) is performed. Compared to the previous works on approximate RL methods, KLSPI makes two progresses to eliminate the main difficulties of existing results. One is the better convergence and (near) optimality guarantee by using the KLSTD-Q algorithm for policy evaluation with high precision. The other is the automatic feature selection using the ALD-based kernel sparsification. Therefore, the KLSPI algorithm provides a general RL method with generalization performance and convergence guarantee for large-scale Markov decision problems (MDPs). Experimental results on a typical RL task for a stochastic chain problem demonstrate that KLSPI can consistently achieve better learning efficiency and policy quality than the previous least squares policy iteration (LSPI) algorithm. Furthermore, the KLSPI method was also evaluated on two nonlinear feedback control problems, including a ship heading control problem and the swing up control of a double-link underactuated pendulum called acrobot. Simulation results illustrate that the proposed method can optimize controller performance using little a priori information of uncertain dynamic systems. It is also demonstrated that KLSPI can be applied to online learning control by incorporating an initial controller to ensure online performance.

A Fast Multiple-Kernel Method With Applications to Detect Gene-Environment Interaction.

PubMed

Marceau, Rachel; Lu, Wenbin; Holloway, Shannon; Sale, Michèle M; Worrall, Bradford B; Williams, Stephen R; Hsu, Fang-Chi; Tzeng, Jung-Ying

2015-09-01

Kernel machine (KM) models are a powerful tool for exploring associations between sets of genetic variants and complex traits. Although most KM methods use a single kernel function to assess the marginal effect of a variable set, KM analyses involving multiple kernels have become increasingly popular. Multikernel analysis allows researchers to study more complex problems, such as assessing gene-gene or gene-environment interactions, incorporating variance-component based methods for population substructure into rare-variant association testing, and assessing the conditional effects of a variable set adjusting for other variable sets. The KM framework is robust, powerful, and provides efficient dimension reduction for multifactor analyses, but requires the estimation of high dimensional nuisance parameters. Traditional estimation techniques, including regularization and the "expectation-maximization (EM)" algorithm, have a large computational cost and are not scalable to large sample sizes needed for rare variant analysis. Therefore, under the context of gene-environment interaction, we propose a computationally efficient and statistically rigorous "fastKM" algorithm for multikernel analysis that is based on a low-rank approximation to the nuisance effect kernel matrices. Our algorithm is applicable to various trait types (e.g., continuous, binary, and survival traits) and can be implemented using any existing single-kernel analysis software. Through extensive simulation studies, we show that our algorithm has similar performance to an EM-based KM approach for quantitative traits while running much faster. We also apply our method to the Vitamin Intervention for Stroke Prevention (VISP) clinical trial, examining gene-by-vitamin effects on recurrent stroke risk and gene-by-age effects on change in homocysteine level. © 2015 WILEY PERIODICALS, INC.

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.

Seismic Imaging of VTI, HTI and TTI based on Adjoint Methods

NASA Astrophysics Data System (ADS)

Rusmanugroho, H.; Tromp, J.

2014-12-01

Recent studies show that isotropic seismic imaging based on adjoint method reduces low-frequency artifact caused by diving waves, which commonly occur in two-wave wave-equation migration, such as Reverse Time Migration (RTM). Here, we derive new expressions of sensitivity kernels for Vertical Transverse Isotropy (VTI) using the Thomsen parameters (ɛ, δ, γ) plus the P-, and S-wave speeds (α, β) as well as via the Chen & Tromp (GJI 2005) parameters (A, C, N, L, F). For Horizontal Transverse Isotropy (HTI), these parameters depend on an azimuthal angle φ, where the tilt angle θ is equivalent to 90°, and for Tilted Transverse Isotropy (TTI), these parameters depend on both the azimuth and tilt angles. We calculate sensitivity kernels for each of these two approaches. Individual kernels ("images") are numerically constructed based on the interaction between the regular and adjoint wavefields in smoothed models which are in practice estimated through Full-Waveform Inversion (FWI). The final image is obtained as a result of summing all shots, which are well distributed to sample the target model properly. The impedance kernel, which is a sum of sensitivity kernels of density and the Thomsen or Chen & Tromp parameters, looks crisp and promising for seismic imaging. The other kernels suffer from low-frequency artifacts, similar to traditional seismic imaging conditions. However, all sensitivity kernels are important for estimating the gradient of the misfit function, which, in combination with a standard gradient-based inversion algorithm, is used to minimize the objective function in FWI.

Omnibus Risk Assessment via Accelerated Failure Time Kernel Machine Modeling

PubMed Central

Sinnott, Jennifer A.; Cai, Tianxi

2013-01-01

Summary Integrating genomic information with traditional clinical risk factors to improve the prediction of disease outcomes could profoundly change the practice of medicine. However, the large number of potential markers and possible complexity of the relationship between markers and disease make it difficult to construct accurate risk prediction models. Standard approaches for identifying important markers often rely on marginal associations or linearity assumptions and may not capture non-linear or interactive effects. In recent years, much work has been done to group genes into pathways and networks. Integrating such biological knowledge into statistical learning could potentially improve model interpretability and reliability. One effective approach is to employ a kernel machine (KM) framework, which can capture nonlinear effects if nonlinear kernels are used (Scholkopf and Smola, 2002; Liu et al., 2007, 2008). For survival outcomes, KM regression modeling and testing procedures have been derived under a proportional hazards (PH) assumption (Li and Luan, 2003; Cai et al., 2011). In this paper, we derive testing and prediction methods for KM regression under the accelerated failure time model, a useful alternative to the PH model. We approximate the null distribution of our test statistic using resampling procedures. When multiple kernels are of potential interest, it may be unclear in advance which kernel to use for testing and estimation. We propose a robust Omnibus Test that combines information across kernels, and an approach for selecting the best kernel for estimation. The methods are illustrated with an application in breast cancer. PMID:24328713

An improved robust blind motion de-blurring algorithm for remote sensing images

NASA Astrophysics Data System (ADS)

He, Yulong; Liu, Jin; Liang, Yonghui

2016-10-01

Shift-invariant motion blur can be modeled as a convolution of the true latent image and the blur kernel with additive noise. Blind motion de-blurring estimates a sharp image from a motion blurred image without the knowledge of the blur kernel. This paper proposes an improved edge-specific motion de-blurring algorithm which proved to be fit for processing remote sensing images. We find that an inaccurate blur kernel is the main factor to the low-quality restored images. To improve image quality, we do the following contributions. For the robust kernel estimation, first, we adapt the multi-scale scheme to make sure that the edge map could be constructed accurately; second, an effective salient edge selection method based on RTV (Relative Total Variation) is used to extract salient structure from texture; third, an alternative iterative method is introduced to perform kernel optimization, in this step, we adopt l1 and l0 norm as the priors to remove noise and ensure the continuity of blur kernel. For the final latent image reconstruction, an improved adaptive deconvolution algorithm based on TV-l2 model is used to recover the latent image; we control the regularization weight adaptively in different region according to the image local characteristics in order to preserve tiny details and eliminate noise and ringing artifacts. Some synthetic remote sensing images are used to test the proposed algorithm, and results demonstrate that the proposed algorithm obtains accurate blur kernel and achieves better de-blurring results.

Permutation invariant polynomial neural network approach to fitting potential energy surfaces. II. Four-atom systems

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

Li, Jun; Jiang, Bin; Guo, Hua, E-mail: hguo@unm.edu

2013-11-28

A rigorous, general, and simple method to fit global and permutation invariant potential energy surfaces (PESs) using neural networks (NNs) is discussed. This so-called permutation invariant polynomial neural network (PIP-NN) method imposes permutation symmetry by using in its input a set of symmetry functions based on PIPs. For systems with more than three atoms, it is shown that the number of symmetry functions in the input vector needs to be larger than the number of internal coordinates in order to include both the primary and secondary invariant polynomials. This PIP-NN method is successfully demonstrated in three atom-triatomic reactive systems, resultingmore » in full-dimensional global PESs with average errors on the order of meV. These PESs are used in full-dimensional quantum dynamical calculations.« less

Structured Kernel Subspace Learning for Autonomous Robot Navigation.

PubMed

Kim, Eunwoo; Choi, Sungjoon; Oh, Songhwai

2018-02-14

This paper considers two important problems for autonomous robot navigation in a dynamic environment, where the goal is to predict pedestrian motion and control a robot with the prediction for safe navigation. While there are several methods for predicting the motion of a pedestrian and controlling a robot to avoid incoming pedestrians, it is still difficult to safely navigate in a dynamic environment due to challenges, such as the varying quality and complexity of training data with unwanted noises. This paper addresses these challenges simultaneously by proposing a robust kernel subspace learning algorithm based on the recent advances in nuclear-norm and l 1 -norm minimization. We model the motion of a pedestrian and the robot controller using Gaussian processes. The proposed method efficiently approximates a kernel matrix used in Gaussian process regression by learning low-rank structured matrix (with symmetric positive semi-definiteness) to find an orthogonal basis, which eliminates the effects of erroneous and inconsistent data. Based on structured kernel subspace learning, we propose a robust motion model and motion controller for safe navigation in dynamic environments. We evaluate the proposed robust kernel learning in various tasks, including regression, motion prediction, and motion control problems, and demonstrate that the proposed learning-based systems are robust against outliers and outperform existing regression and navigation methods.

Reachability Analysis in Probabilistic Biological Networks.

PubMed

Gabr, Haitham; Todor, Andrei; Dobra, Alin; Kahveci, Tamer

2015-01-01

Extra-cellular molecules trigger a response inside the cell by initiating a signal at special membrane receptors (i.e., sources), which is then transmitted to reporters (i.e., targets) through various chains of interactions among proteins. Understanding whether such a signal can reach from membrane receptors to reporters is essential in studying the cell response to extra-cellular events. This problem is drastically complicated due to the unreliability of the interaction data. In this paper, we develop a novel method, called PReach (Probabilistic Reachability), that precisely computes the probability that a signal can reach from a given collection of receptors to a given collection of reporters when the underlying signaling network is uncertain. This is a very difficult computational problem with no known polynomial-time solution. PReach represents each uncertain interaction as a bi-variate polynomial. It transforms the reachability problem to a polynomial multiplication problem. We introduce novel polynomial collapsing operators that associate polynomial terms with possible paths between sources and targets as well as the cuts that separate sources from targets. These operators significantly shrink the number of polynomial terms and thus the running time. PReach has much better time complexity than the recent solutions for this problem. Our experimental results on real data sets demonstrate that this improvement leads to orders of magnitude of reduction in the running time over the most recent methods. Availability: All the data sets used, the software implemented and the alignments found in this paper are available at http://bioinformatics.cise.ufl.edu/PReach/.

Efficient computer algebra algorithms for polynomial matrices in control design

NASA Technical Reports Server (NTRS)

Baras, J. S.; Macenany, D. C.; Munach, R.

1989-01-01

The theory of polynomial matrices plays a key role in the design and analysis of multi-input multi-output control and communications systems using frequency domain methods. Examples include coprime factorizations of transfer functions, cannonical realizations from matrix fraction descriptions, and the transfer function design of feedback compensators. Typically, such problems abstract in a natural way to the need to solve systems of Diophantine equations or systems of linear equations over polynomials. These and other problems involving polynomial matrices can in turn be reduced to polynomial matrix triangularization procedures, a result which is not surprising given the importance of matrix triangularization techniques in numerical linear algebra. Matrices with entries from a field and Gaussian elimination play a fundamental role in understanding the triangularization process. In the case of polynomial matrices, matrices with entries from a ring for which Gaussian elimination is not defined and triangularization is accomplished by what is quite properly called Euclidean elimination. Unfortunately, the numerical stability and sensitivity issues which accompany floating point approaches to Euclidean elimination are not very well understood. New algorithms are presented which circumvent entirely such numerical issues through the use of exact, symbolic methods in computer algebra. The use of such error-free algorithms guarantees that the results are accurate to within the precision of the model data--the best that can be hoped for. Care must be taken in the design of such algorithms due to the phenomenon of intermediate expressions swell.

Kernel learning at the first level of inference.

PubMed

Cawley, Gavin C; Talbot, Nicola L C

2014-05-01

Kernel learning methods, whether Bayesian or frequentist, typically involve multiple levels of inference, with the coefficients of the kernel expansion being determined at the first level and the kernel and regularisation parameters carefully tuned at the second level, a process known as model selection. Model selection for kernel machines is commonly performed via optimisation of a suitable model selection criterion, often based on cross-validation or theoretical performance bounds. However, if there are a large number of kernel parameters, as for instance in the case of automatic relevance determination (ARD), there is a substantial risk of over-fitting the model selection criterion, resulting in poor generalisation performance. In this paper we investigate the possibility of learning the kernel, for the Least-Squares Support Vector Machine (LS-SVM) classifier, at the first level of inference, i.e. parameter optimisation. The kernel parameters and the coefficients of the kernel expansion are jointly optimised at the first level of inference, minimising a training criterion with an additional regularisation term acting on the kernel parameters. The key advantage of this approach is that the values of only two regularisation parameters need be determined in model selection, substantially alleviating the problem of over-fitting the model selection criterion. The benefits of this approach are demonstrated using a suite of synthetic and real-world binary classification benchmark problems, where kernel learning at the first level of inference is shown to be statistically superior to the conventional approach, improves on our previous work (Cawley and Talbot, 2007) and is competitive with Multiple Kernel Learning approaches, but with reduced computational expense. Copyright © 2014 Elsevier Ltd. All rights reserved.

Kernel and Traditional Equipercentile Equating with Degrees of Presmoothing. Research Report. ETS RR-07-15

ERIC Educational Resources Information Center

Moses, Tim; Holland, Paul

2007-01-01

The purpose of this study was to empirically evaluate the impact of loglinear presmoothing accuracy on equating bias and variability across chained and post-stratification equating methods, kernel and percentile-rank continuization methods, and sample sizes. The results of evaluating presmoothing on equating accuracy generally agreed with those of…

A scalable kernel-based semisupervised metric learning algorithm with out-of-sample generalization ability.

PubMed

Yeung, Dit-Yan; Chang, Hong; Dai, Guang

2008-11-01

In recent years, metric learning in the semisupervised setting has aroused a lot of research interest. One type of semisupervised metric learning utilizes supervisory information in the form of pairwise similarity or dissimilarity constraints. However, most methods proposed so far are either limited to linear metric learning or unable to scale well with the data set size. In this letter, we propose a nonlinear metric learning method based on the kernel approach. By applying low-rank approximation to the kernel matrix, our method can handle significantly larger data sets. Moreover, our low-rank approximation scheme can naturally lead to out-of-sample generalization. Experiments performed on both artificial and real-world data show very promising results.

A kernel adaptive algorithm for quaternion-valued inputs.

PubMed

Paul, Thomas K; Ogunfunmi, Tokunbo

2015-10-01

The use of quaternion data can provide benefit in applications like robotics and image recognition, and particularly for performing transforms in 3-D space. Here, we describe a kernel adaptive algorithm for quaternions. A least mean square (LMS)-based method was used, resulting in the derivation of the quaternion kernel LMS (Quat-KLMS) algorithm. Deriving this algorithm required describing the idea of a quaternion reproducing kernel Hilbert space (RKHS), as well as kernel functions suitable with quaternions. A modified HR calculus for Hilbert spaces was used to find the gradient of cost functions defined on a quaternion RKHS. In addition, the use of widely linear (or augmented) filtering is proposed to improve performance. The benefit of the Quat-KLMS and widely linear forms in learning nonlinear transformations of quaternion data are illustrated with simulations.

Genomic Prediction of Genotype × Environment Interaction Kernel Regression Models.

PubMed

Cuevas, Jaime; Crossa, José; Soberanis, Víctor; Pérez-Elizalde, Sergio; Pérez-Rodríguez, Paulino; Campos, Gustavo de Los; Montesinos-López, O A; Burgueño, Juan

2016-11-01

In genomic selection (GS), genotype × environment interaction (G × E) can be modeled by a marker × environment interaction (M × E). The G × E may be modeled through a linear kernel or a nonlinear (Gaussian) kernel. In this study, we propose using two nonlinear Gaussian kernels: the reproducing kernel Hilbert space with kernel averaging (RKHS KA) and the Gaussian kernel with the bandwidth estimated through an empirical Bayesian method (RKHS EB). We performed single-environment analyses and extended to account for G × E interaction (GBLUP-G × E, RKHS KA-G × E and RKHS EB-G × E) in wheat ( L.) and maize ( L.) data sets. For single-environment analyses of wheat and maize data sets, RKHS EB and RKHS KA had higher prediction accuracy than GBLUP for all environments. For the wheat data, the RKHS KA-G × E and RKHS EB-G × E models did show up to 60 to 68% superiority over the corresponding single environment for pairs of environments with positive correlations. For the wheat data set, the models with Gaussian kernels had accuracies up to 17% higher than that of GBLUP-G × E. For the maize data set, the prediction accuracy of RKHS EB-G × E and RKHS KA-G × E was, on average, 5 to 6% higher than that of GBLUP-G × E. The superiority of the Gaussian kernel models over the linear kernel is due to more flexible kernels that accounts for small, more complex marker main effects and marker-specific interaction effects. Copyright © 2016 Crop Science Society of America.

Inference of Spatio-Temporal Functions Over Graphs via Multikernel Kriged Kalman Filtering

NASA Astrophysics Data System (ADS)

Ioannidis, Vassilis N.; Romero, Daniel; Giannakis, Georgios B.

2018-06-01

Inference of space-time varying signals on graphs emerges naturally in a plethora of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes, given their values over a subset of vertices and time instants. The present paper develops a graph-aware kernel-based kriged Kalman filter that accounts for the spatio-temporal variations, and offers efficient online reconstruction, even for dynamically evolving network topologies. The kernel-based learning framework bypasses the need for statistical information by capitalizing on the smoothness that graph signals exhibit with respect to the underlying graph. To address the challenge of selecting the appropriate kernel, the proposed filter is combined with a multi-kernel selection module. Such a data-driven method selects a kernel attuned to the signal dynamics on-the-fly within the linear span of a pre-selected dictionary. The novel multi-kernel learning algorithm exploits the eigenstructure of Laplacian kernel matrices to reduce computational complexity. Numerical tests with synthetic and real data demonstrate the superior reconstruction performance of the novel approach relative to state-of-the-art alternatives.

CLAss-Specific Subspace Kernel Representations and Adaptive Margin Slack Minimization for Large Scale Classification.

PubMed

Yu, Yinan; Diamantaras, Konstantinos I; McKelvey, Tomas; Kung, Sun-Yuan

2018-02-01

In kernel-based classification models, given limited computational power and storage capacity, operations over the full kernel matrix becomes prohibitive. In this paper, we propose a new supervised learning framework using kernel models for sequential data processing. The framework is based on two components that both aim at enhancing the classification capability with a subset selection scheme. The first part is a subspace projection technique in the reproducing kernel Hilbert space using a CLAss-specific Subspace Kernel representation for kernel approximation. In the second part, we propose a novel structural risk minimization algorithm called the adaptive margin slack minimization to iteratively improve the classification accuracy by an adaptive data selection. We motivate each part separately, and then integrate them into learning frameworks for large scale data. We propose two such frameworks: the memory efficient sequential processing for sequential data processing and the parallelized sequential processing for distributed computing with sequential data acquisition. We test our methods on several benchmark data sets and compared with the state-of-the-art techniques to verify the validity of the proposed techniques.

A two-step, fourth-order method with energy preserving properties

NASA Astrophysics Data System (ADS)

Brugnano, Luigi; Iavernaro, Felice; Trigiante, Donato

2012-09-01

We introduce a family of fourth-order two-step methods that preserve the energy function of canonical polynomial Hamiltonian systems. As is the case with linear mutistep and one-leg methods, a prerogative of the new formulae is that the associated nonlinear systems to be solved at each step of the integration procedure have the very same dimension of the underlying continuous problem. The key tools in the new methods are the line integral associated with a conservative vector field (such as the one defined by a Hamiltonian dynamical system) and its discretization obtained by the aid of a quadrature formula. Energy conservation is equivalent to the requirement that the quadrature is exact, which turns out to be always the case in the event that the Hamiltonian function is a polynomial and the degree of precision of the quadrature formula is high enough. The non-polynomial case is also discussed and a number of test problems are finally presented in order to compare the behavior of the new methods to the theoretical results.

Design of reinforced areas of concrete column using quadratic polynomials

NASA Astrophysics Data System (ADS)

Arif Gunadi, Tjiang; Parung, Herman; Rachman Djamaluddin, Abd; Arwin Amiruddin, A.

2017-11-01

Designing of reinforced concrete columns mostly carried out by a simple planning method which uses column interaction diagram. However, the application of this method is limited because it valids only for certain compressive strenght of the concrete and yield strength of the reinforcement. Thus, a more applicable method is still in need. Another method is the use of quadratic polynomials as a basis for the approach in designing reinforced concrete columns, where the ratio of neutral lines to the effective height of a cross section (ξ) if associated with ξ in the same cross-section with different reinforcement ratios is assumed to form a quadratic polynomial. This is identical to the basic principle used in the Simpson rule for numerical integral using quadratic polynomials and had a sufficiently accurate level of accuracy. The basis of this approach to be used both the normal force equilibrium and the moment equilibrium. The abscissa of the intersection of the two curves is the ratio that had been mentioned, since it fulfill both of the equilibrium. The application of this method is relatively more complicated than the existing method but provided with tables and graphs (N vs ξN ) and (M vs ξM ) so that its used could be simplified. The uniqueness of these tables are only distinguished based on the compresssive strength of the concrete, so in application it could be combined with various yield strenght of the reinforcement available in the market. This method could be solved by using programming languages such as Fortran.

Graph characterization via Ihara coefficients.

PubMed

Ren, Peng; Wilson, Richard C; Hancock, Edwin R

2011-02-01

The novel contributions of this paper are twofold. First, we demonstrate how to characterize unweighted graphs in a permutation-invariant manner using the polynomial coefficients from the Ihara zeta function, i.e., the Ihara coefficients. Second, we generalize the definition of the Ihara coefficients to edge-weighted graphs. For an unweighted graph, the Ihara zeta function is the reciprocal of a quasi characteristic polynomial of the adjacency matrix of the associated oriented line graph. Since the Ihara zeta function has poles that give rise to infinities, the most convenient numerically stable representation is to work with the coefficients of the quasi characteristic polynomial. Moreover, the polynomial coefficients are invariant to vertex order permutations and also convey information concerning the cycle structure of the graph. To generalize the representation to edge-weighted graphs, we make use of the reduced Bartholdi zeta function. We prove that the computation of the Ihara coefficients for unweighted graphs is a special case of our proposed method for unit edge weights. We also present a spectral analysis of the Ihara coefficients and indicate their advantages over other graph spectral methods. We apply the proposed graph characterization method to capturing graph-class structure and clustering graphs. Experimental results reveal that the Ihara coefficients are more effective than methods based on Laplacian spectra.

Parametric analysis of ATM solar array.

NASA Technical Reports Server (NTRS)

Singh, B. K.; Adkisson, W. B.

1973-01-01

The paper discusses the methods used for the calculation of ATM solar array performance characteristics and provides the parametric analysis of solar panels used in SKYLAB. To predict the solar array performance under conditions other than test conditions, a mathematical model has been developed. Four computer programs have been used to convert the solar simulator test data to the parametric curves. The first performs module summations, the second determines average solar cell characteristics which will cause a mathematical model to generate a curve matching the test data, the third is a polynomial fit program which determines the polynomial equations for the solar cell characteristics versus temperature, and the fourth program uses the polynomial coefficients generated by the polynomial curve fit program to generate the parametric data.

A spatial scan statistic for nonisotropic two-level risk cluster.

PubMed

Li, Xiao-Zhou; Wang, Jin-Feng; Yang, Wei-Zhong; Li, Zhong-Jie; Lai, Sheng-Jie

2012-01-30

Spatial scan statistic methods are commonly used for geographical disease surveillance and cluster detection. The standard spatial scan statistic does not model any variability in the underlying risks of subregions belonging to a detected cluster. For a multilevel risk cluster, the isotonic spatial scan statistic could model a centralized high-risk kernel in the cluster. Because variations in disease risks are anisotropic owing to different social, economical, or transport factors, the real high-risk kernel will not necessarily take the central place in a whole cluster area. We propose a spatial scan statistic for a nonisotropic two-level risk cluster, which could be used to detect a whole cluster and a noncentralized high-risk kernel within the cluster simultaneously. The performance of the three methods was evaluated through an intensive simulation study. Our proposed nonisotropic two-level method showed better power and geographical precision with two-level risk cluster scenarios, especially for a noncentralized high-risk kernel. Our proposed method is illustrated using the hand-foot-mouth disease data in Pingdu City, Shandong, China in May 2009, compared with two other methods. In this practical study, the nonisotropic two-level method is the only way to precisely detect a high-risk area in a detected whole cluster. Copyright © 2011 John Wiley & Sons, Ltd.

Optimization of fixture layouts of glass laser optics using multiple kernel regression.

PubMed

Su, Jianhua; Cao, Enhua; Qiao, Hong

2014-05-10

We aim to build an integrated fixturing model to describe the structural properties and thermal properties of the support frame of glass laser optics. Therefore, (a) a near global optimal set of clamps can be computed to minimize the surface shape error of the glass laser optic based on the proposed model, and (b) a desired surface shape error can be obtained by adjusting the clamping forces under various environmental temperatures based on the model. To construct the model, we develop a new multiple kernel learning method and call it multiple kernel support vector functional regression. The proposed method uses two layer regressions to group and order the data sources by the weights of the kernels and the factors of the layers. Because of that, the influences of the clamps and the temperature can be evaluated by grouping them into different layers.

Nonparametric entropy estimation using kernel densities.

PubMed

Lake, Douglas E

2009-01-01

The entropy of experimental data from the biological and medical sciences provides additional information over summary statistics. Calculating entropy involves estimates of probability density functions, which can be effectively accomplished using kernel density methods. Kernel density estimation has been widely studied and a univariate implementation is readily available in MATLAB. The traditional definition of Shannon entropy is part of a larger family of statistics, called Renyi entropy, which are useful in applications that require a measure of the Gaussianity of data. Of particular note is the quadratic entropy which is related to the Friedman-Tukey (FT) index, a widely used measure in the statistical community. One application where quadratic entropy is very useful is the detection of abnormal cardiac rhythms, such as atrial fibrillation (AF). Asymptotic and exact small-sample results for optimal bandwidth and kernel selection to estimate the FT index are presented and lead to improved methods for entropy estimation.

Sensitivity Kernels for the Cross-Convolution Measure: Eliminate the Source in Waveform Tomography

NASA Astrophysics Data System (ADS)

Menke, W. H.

2017-12-01

We use the adjoint method to derive sensitivity kernels for the cross-convolution measure, a goodness-of-fit criterion that is applicable to seismic data containing closely-spaced multiple arrivals, such as reverberating compressional waves and split shear waves. In addition to a general formulation, specific expressions for sensitivity with respect to density, Lamé parameter and shear modulus are derived for a isotropic elastic solid. As is typical of adjoint methods, the kernels depend upon an adjoint field, the source of which, in this case, is the reference displacement field, pre-multiplied by a matrix of cross-correlations of components of the observed field. We use a numerical simulation to evaluate the resolving power of a topographic inversion that employs the cross-convolution measure. The estimated resolving kernel shows is point-like, indicating that the cross-convolution measure will perform well in waveform tomography settings.

Primary decomposition of zero-dimensional ideals over finite fields

NASA Astrophysics Data System (ADS)

Gao, Shuhong; Wan, Daqing; Wang, Mingsheng

2009-03-01

A new algorithm is presented for computing primary decomposition of zero-dimensional ideals over finite fields. Like Berlekamp's algorithm for univariate polynomials, the new method is based on the invariant subspace of the Frobenius map acting on the quotient algebra. The dimension of the invariant subspace equals the number of primary components, and a basis of the invariant subspace yields a complete decomposition. Unlike previous approaches for decomposing multivariate polynomial systems, the new method does not need primality testing nor any generic projection, instead it reduces the general decomposition problem directly to root finding of univariate polynomials over the ground field. Also, it is shown how Groebner basis structure can be used to get partial primary decomposition without any root finding.

Sparse Event Modeling with Hierarchical Bayesian Kernel Methods

DTIC Science & Technology

2016-01-05

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

Characterization of high order spatial discretizations and lumping techniques for discontinuous finite element SN transport

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

Maginot, P. G.; Ragusa, J. C.; Morel, J. E.

2013-07-01

We examine several possible methods of mass matrix lumping for discontinuous finite element discrete ordinates transport using a Lagrange interpolatory polynomial trial space. Though positive outflow angular flux is guaranteed with traditional mass matrix lumping in a purely absorbing 1-D slab cell for the linear discontinuous approximation, we show that when used with higher degree interpolatory polynomial trial spaces, traditional lumping does yield strictly positive outflows and does not increase in accuracy with an increase in trial space polynomial degree. As an alternative, we examine methods which are 'self-lumping'. Self-lumping methods yield diagonal mass matrices by using numerical quadrature restrictedmore » to the Lagrange interpolatory points. Using equally-spaced interpolatory points, self-lumping is achieved through the use of closed Newton-Cotes formulas, resulting in strictly positive outflows in pure absorbers for odd power polynomials in 1-D slab geometry. By changing interpolatory points from the traditional equally-spaced points to the quadrature points of the Gauss-Legendre or Lobatto-Gauss-Legendre quadratures, it is possible to generate solution representations with a diagonal mass matrix and a strictly positive outflow for any degree polynomial solution representation in a pure absorber medium in 1-D slab geometry. Further, there is no inherent limit to local truncation error order of accuracy when using interpolatory points that correspond to the quadrature points of high order accuracy numerical quadrature schemes. (authors)« less

Comparisons of geoid models over Alaska computed with different Stokes' kernel modifications

NASA Astrophysics Data System (ADS)

Li, X.; Wang, Y.

2011-01-01

Various Stokes kernel modification methods have been developed over the years. The goal of this paper is to test the most commonly used Stokes kernel modifications numerically by using Alaska as a test area and EGM08 as a reference model. The tests show that some methods are more sensitive than others to the integration cap sizes. For instance, using the methods of Vaníček and Kleusberg or Featherstone et al. with kernel modification at degree 60, the geoid decreases by 30 cm (on average) when the cap size increases from 1° to 25°. The corresponding changes in the methods of Wong and Gore and Heck and Grüninger are only at the 1 cm level. At high modification degrees, above 360, the methods of Vaníček and Kleusberg and Featherstone et al become unstable because of numerical problems in the modification coefficients; similar conclusions have been reported by Featherstone (2003). In contrast, the methods of Wong and Gore, Heck and Grüninger and the least-squares spectral combination are stable at any modification degree, though they do not provide as good fit as the best case of the Molodenskii-type methods at the GPS/Leveling benchmarks. However, certain tests for choosing the cap size and modification degree have to be performed in advance to avoid abrupt mean geoid changes if the latter methods are applied.

Antidiarrhoeal efficacy of Mangifera indica seed kernel on Swiss albino mice.

PubMed

Rajan, S; Suganya, H; Thirunalasundari, T; Jeeva, S

2012-08-01

To examine the antidiarrhoeal activity of alcoholic and aqueous seed kernel extract of Mangifera indica (M. indica) on castor oil-induced diarrhoeal activity in Swiss albino mice. Mango seed kernels were processed and extracted using alcohol and water. Antidiarrhoeal activity of the extracts were assessed using intestinal motility and faecal score methods. Aqueous and alcoholic extracts of M. indica significantly reduced intestinal motility and faecal score in Swiss albino mice. The present study shows the traditional claim on the use of M. indica seed kernel for treating diarrhoea in Southern parts of India. Copyright © 2012 Hainan Medical College. Published by Elsevier B.V. All rights reserved.

Linked-cluster formulation of electron-hole interaction kernel in real-space representation without using unoccupied states.

PubMed

Bayne, Michael G; Scher, Jeremy A; Ellis, Benjamin H; Chakraborty, Arindam

2018-05-21

Electron-hole or quasiparticle representation plays a central role in describing electronic excitations in many-electron systems. For charge-neutral excitation, the electron-hole interaction kernel is the quantity of interest for calculating important excitation properties such as optical gap, optical spectra, electron-hole recombination and electron-hole binding energies. The electron-hole interaction kernel can be formally derived from the density-density correlation function using both Green's function and TDDFT formalism. The accurate determination of the electron-hole interaction kernel remains a significant challenge for precise calculations of optical properties in the GW+BSE formalism. From the TDDFT perspective, the electron-hole interaction kernel has been viewed as a path to systematic development of frequency-dependent exchange-correlation functionals. Traditional approaches, such as MBPT formalism, use unoccupied states (which are defined with respect to Fermi vacuum) to construct the electron-hole interaction kernel. However, the inclusion of unoccupied states has long been recognized as the leading computational bottleneck that limits the application of this approach for larger finite systems. In this work, an alternative derivation that avoids using unoccupied states to construct the electron-hole interaction kernel is presented. The central idea of this approach is to use explicitly correlated geminal functions for treating electron-electron correlation for both ground and excited state wave functions. Using this ansatz, it is derived using both diagrammatic and algebraic techniques that the electron-hole interaction kernel can be expressed only in terms of linked closed-loop diagrams. It is proved that the cancellation of unlinked diagrams is a consequence of linked-cluster theorem in real-space representation. The electron-hole interaction kernel derived in this work was used to calculate excitation energies in many-electron systems and results were found to be in good agreement with the EOM-CCSD and GW+BSE methods. The numerical results highlight the effectiveness of the developed method for overcoming the computational barrier of accurately determining the electron-hole interaction kernel to applications of large finite systems such as quantum dots and nanorods.

Spectrofluorimetric determination of melatonin in kernels of four different Pistacia varieties after ultrasound-assisted solid-liquid extraction.

PubMed

Oladi, Elham; Mohamadi, Maryam; Shamspur, Tayebeh; Mostafavi, Ali

2014-11-11

Melatonin is normally consumed to regulate the body's biological cycle. However it also has therapeutic properties, such as anti-tumor, anti-aging and protects the immune system. There are some reports on the presence of melatonin in edible kernels such as walnuts, but the extraction of melatonin from pistachio kernels is reported here for the first time. For this, the methanolic extract of pistachio kernels was exposed to gas chromatography/mass spectrometry analysis which confirmed the presence of melatonin. A fluorescence-based method was applied for the determination of melatonin in different extracts. When excited at λ=275 nm, the fluorescence emission intensity of melatonin was measured at λ=366 nm. Ultrasound-assisted solid-liquid extraction was used for the extraction of melatonin from pistachio kernels prior to fluorimetric determination. To achieve the highest extraction recovery, the main parameters affecting the extraction efficiency such as extracting solvent type and volume, temperature, sonication time and pH were evaluated. Under the optimized conditions, a linear dependence of fluorescence intensity on melatonin concentration was observed in the range of 0.0040-0.160 μg mL(-1), with a detection limit of 0.0036 μg mL(-1). This method was applied successfully for measuring and comparing the melatonin content in the kernels of four different varieties of Pistacia including Ahmad Aghaei, Akbari, Kalle Qouchi and Fandoghi. In addition, the results obtained were compared with those obtained using GC/MS. A good agreement was observed indicating the reliability of the proposed method. Copyright © 2014 Elsevier B.V. All rights reserved.

Spectrofluorimetric determination of melatonin in kernels of four different Pistacia varieties after ultrasound-assisted solid-liquid extraction

NASA Astrophysics Data System (ADS)

Oladi, Elham; Mohamadi, Maryam; Shamspur, Tayebeh; Mostafavi, Ali

2014-11-01

Melatonin is normally consumed to regulate the body's biological cycle. However it also has therapeutic properties, such as anti-tumor, anti-aging and protects the immune system. There are some reports on the presence of melatonin in edible kernels such as walnuts, but the extraction of melatonin from pistachio kernels is reported here for the first time. For this, the methanolic extract of pistachio kernels was exposed to gas chromatography/mass spectrometry analysis which confirmed the presence of melatonin. A fluorescence-based method was applied for the determination of melatonin in different extracts. When excited at λ = 275 nm, the fluorescence emission intensity of melatonin was measured at λ = 366 nm. Ultrasound-assisted solid-liquid extraction was used for the extraction of melatonin from pistachio kernels prior to fluorimetric determination. To achieve the highest extraction recovery, the main parameters affecting the extraction efficiency such as extracting solvent type and volume, temperature, sonication time and pH were evaluated. Under the optimized conditions, a linear dependence of fluorescence intensity on melatonin concentration was observed in the range of 0.0040-0.160 μg mL-1, with a detection limit of 0.0036 μg mL-1. This method was applied successfully for measuring and comparing the melatonin content in the kernels of four different varieties of Pistacia including Ahmad Aghaei, Akbari, Kalle Qouchi and Fandoghi. In addition, the results obtained were compared with those obtained using GC/MS. A good agreement was observed indicating the reliability of the proposed method.

Classification and quantification analysis of peach kernel from different origins with near-infrared diffuse reflection spectroscopy

PubMed Central

Liu, Wei; Wang, Zhen-Zhong; Qing, Jian-Ping; Li, Hong-Juan; Xiao, Wei

2014-01-01

Background: Peach kernels which contain kinds of fatty acids play an important role in the regulation of a variety of physiological and biological functions. Objective: To establish an innovative and rapid diffuse reflectance near-infrared spectroscopy (DR-NIR) analysis method along with chemometric techniques for the qualitative and quantitative determination of a peach kernel. Materials and Methods: Peach kernel samples from nine different origins were analyzed with high-performance liquid chromatography (HPLC) as a reference method. DR-NIR is in the spectral range 1100-2300 nm. Principal component analysis (PCA) and partial least squares regression (PLSR) algorithm were applied to obtain prediction models, The Savitzky-Golay derivative and first derivative were adopted for the spectral pre-processing, PCA was applied to classify the varieties of those samples. For the quantitative calibration, the models of linoleic and oleinic acids were established with the PLSR algorithm and the optimal principal component (PC) numbers were selected with leave-one-out (LOO) cross-validation. The established models were evaluated with the root mean square error of deviation (RMSED) and corresponding correlation coefficients (R2). Results: The PCA results of DR-NIR spectra yield clear classification of the two varieties of peach kernel. PLSR had a better predictive ability. The correlation coefficients of the two calibration models were above 0.99, and the RMSED of linoleic and oleinic acids were 1.266% and 1.412%, respectively. Conclusion: The DR-NIR combined with PCA and PLSR algorithm could be used efficiently to identify and quantify peach kernels and also help to solve variety problem. PMID:25422544

The discrete Toda equation revisited: dual β-Grothendieck polynomials, ultradiscretization, and static solitons

NASA Astrophysics Data System (ADS)

Iwao, Shinsuke; Nagai, Hidetomo

2018-04-01

This paper presents a study of the discrete Toda equation that was introduced in 1977. In this paper, it is proved that the determinantal solution of the discrete Toda equation, obtained via the Lax formalism, is naturally related to the dual Grothendieck polynomials, a K-theoretic generalization of the Schur polynomials. A tropical permanent solution to the ultradiscrete Toda equation is also derived. The proposed method gives a tropical algebraic representation of the static solitons. Lastly, a new cellular automaton realization of the ultradiscrete Toda equation is proposed.

P- and S-wave Receiver Function Imaging with Scattering Kernels

NASA Astrophysics Data System (ADS)

Hansen, S. M.; Schmandt, B.

2017-12-01

Full waveform inversion provides a flexible approach to the seismic parameter estimation problem and can account for the full physics of wave propagation using numeric simulations. However, this approach requires significant computational resources due to the demanding nature of solving the forward and adjoint problems. This issue is particularly acute for temporary passive-source seismic experiments (e.g. PASSCAL) that have traditionally relied on teleseismic earthquakes as sources resulting in a global scale forward problem. Various approximation strategies have been proposed to reduce the computational burden such as hybrid methods that embed a heterogeneous regional scale model in a 1D global model. In this study, we focus specifically on the problem of scattered wave imaging (migration) using both P- and S-wave receiver function data. The proposed method relies on body-wave scattering kernels that are derived from the adjoint data sensitivity kernels which are typically used for full waveform inversion. The forward problem is approximated using ray theory yielding a computationally efficient imaging algorithm that can resolve dipping and discontinuous velocity interfaces in 3D. From the imaging perspective, this approach is closely related to elastic reverse time migration. An energy stable finite-difference method is used to simulate elastic wave propagation in a 2D hypothetical subduction zone model. The resulting synthetic P- and S-wave receiver function datasets are used to validate the imaging method. The kernel images are compared with those generated by the Generalized Radon Transform (GRT) and Common Conversion Point stacking (CCP) methods. These results demonstrate the potential of the kernel imaging approach to constrain lithospheric structure in complex geologic environments with sufficiently dense recordings of teleseismic data. This is demonstrated using a receiver function dataset from the Central California Seismic Experiment which shows several dipping interfaces related to the tectonic assembly of this region. Figure 1. Scattering kernel examples for three receiver function phases. A) direct P-to-s (Ps), B) direct S-to-p and C) free-surface PP-to-s (PPs).

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

NASA Astrophysics Data System (ADS)

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

2015-05-01

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

Anelastic sensitivity kernels with parsimonious storage for adjoint tomography and full waveform inversion

NASA Astrophysics Data System (ADS)

Komatitsch, Dimitri; Xie, Zhinan; Bozdaǧ, Ebru; Sales de Andrade, Elliott; Peter, Daniel; Liu, Qinya; Tromp, Jeroen

2016-09-01

We introduce a technique to compute exact anelastic sensitivity kernels in the time domain using parsimonious disk storage. The method is based on a reordering of the time loop of time-domain forward/adjoint wave propagation solvers combined with the use of a memory buffer. It avoids instabilities that occur when time-reversing dissipative wave propagation simulations. The total number of required time steps is unchanged compared to usual acoustic or elastic approaches. The cost is reduced by a factor of 4/3 compared to the case in which anelasticity is partially accounted for by accommodating the effects of physical dispersion. We validate our technique by performing a test in which we compare the Kα sensitivity kernel to the exact kernel obtained by saving the entire forward calculation. This benchmark confirms that our approach is also exact. We illustrate the importance of including full attenuation in the calculation of sensitivity kernels by showing significant differences with physical-dispersion-only kernels.

Single kernel method for detection of 2-acetyl-1-pyrroline in aromatic rice germplasm using SPME-GC/MS

USDA-ARS?s Scientific Manuscript database

INTRODUCTION Aromatic rice or fragrant rice, (Oryza sativa L.), has a strong popcorn-like aroma due to the presence of a five-membered N-heterocyclic ring compound known as 2-acetyl-1-pyrroline (2-AP). To date, existing methods for detecting this compound in rice require the use of several kernels. ...