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.

Direct discriminant locality preserving projection with Hammerstein polynomial expansion.

PubMed

Chen, Xi; Zhang, Jiashu; Li, Defang

2012-12-01

Discriminant locality preserving projection (DLPP) is a linear approach that encodes discriminant information into the objective of locality preserving projection and improves its classification ability. To enhance the nonlinear description ability of DLPP, we can optimize the objective function of DLPP in reproducing kernel Hilbert space to form a kernel-based discriminant locality preserving projection (KDLPP). However, KDLPP suffers the following problems: 1) larger computational burden; 2) no explicit mapping functions in KDLPP, which results in more computational burden when projecting a new sample into the low-dimensional subspace; and 3) KDLPP cannot obtain optimal discriminant vectors, which exceedingly optimize the objective of DLPP. To overcome the weaknesses of KDLPP, in this paper, a direct discriminant locality preserving projection with Hammerstein polynomial expansion (HPDDLPP) is proposed. The proposed HPDDLPP directly implements the objective of DLPP in high-dimensional second-order Hammerstein polynomial space without matrix inverse, which extracts the optimal discriminant vectors for DLPP without larger computational burden. Compared with some other related classical methods, experimental results for face and palmprint recognition problems indicate the effectiveness of the proposed HPDDLPP.

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.

A Novel Extreme Learning Machine Classification Model for e-Nose Application Based on the Multiple Kernel Approach

PubMed Central

Jian, Yulin; Huang, Daoyu; Yan, Jia; Lu, Kun; Huang, Ying; Wen, Tailai; Zeng, Tanyue; Zhong, Shijie; Xie, Qilong

2017-01-01

A novel classification model, named the quantum-behaved particle swarm optimization (QPSO)-based weighted multiple kernel extreme learning machine (QWMK-ELM), is proposed in this paper. Experimental validation is carried out with two different electronic nose (e-nose) datasets. Being different from the existing multiple kernel extreme learning machine (MK-ELM) algorithms, the combination coefficients of base kernels are regarded as external parameters of single-hidden layer feedforward neural networks (SLFNs). The combination coefficients of base kernels, the model parameters of each base kernel, and the regularization parameter are optimized by QPSO simultaneously before implementing the kernel extreme learning machine (KELM) with the composite kernel function. Four types of common single kernel functions (Gaussian kernel, polynomial kernel, sigmoid kernel, and wavelet kernel) are utilized to constitute different composite kernel functions. Moreover, the method is also compared with other existing classification methods: extreme learning machine (ELM), kernel extreme learning machine (KELM), k-nearest neighbors (KNN), support vector machine (SVM), multi-layer perceptron (MLP), radical basis function neural network (RBFNN), and probabilistic neural network (PNN). The results have demonstrated that the proposed QWMK-ELM outperforms the aforementioned methods, not only in precision, but also in efficiency for gas classification. PMID:28629202

A Novel Extreme Learning Machine Classification Model for e-Nose Application Based on the Multiple Kernel Approach.

PubMed

Jian, Yulin; Huang, Daoyu; Yan, Jia; Lu, Kun; Huang, Ying; Wen, Tailai; Zeng, Tanyue; Zhong, Shijie; Xie, Qilong

2017-06-19

A novel classification model, named the quantum-behaved particle swarm optimization (QPSO)-based weighted multiple kernel extreme learning machine (QWMK-ELM), is proposed in this paper. Experimental validation is carried out with two different electronic nose (e-nose) datasets. Being different from the existing multiple kernel extreme learning machine (MK-ELM) algorithms, the combination coefficients of base kernels are regarded as external parameters of single-hidden layer feedforward neural networks (SLFNs). The combination coefficients of base kernels, the model parameters of each base kernel, and the regularization parameter are optimized by QPSO simultaneously before implementing the kernel extreme learning machine (KELM) with the composite kernel function. Four types of common single kernel functions (Gaussian kernel, polynomial kernel, sigmoid kernel, and wavelet kernel) are utilized to constitute different composite kernel functions. Moreover, the method is also compared with other existing classification methods: extreme learning machine (ELM), kernel extreme learning machine (KELM), k-nearest neighbors (KNN), support vector machine (SVM), multi-layer perceptron (MLP), radical basis function neural network (RBFNN), and probabilistic neural network (PNN). The results have demonstrated that the proposed QWMK-ELM outperforms the aforementioned methods, not only in precision, but also in efficiency for gas classification.

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.

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.

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.

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,…

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.

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.

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.

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.

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 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.

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.

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.

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

New Families of Skewed Higher-Order Kernel Estimators to Solve the BSS/ICA Problem for Multimodal Sources Mixtures.

PubMed

Jabbar, Ahmed Najah

2018-04-13

This letter suggests two new types of asymmetrical higher-order kernels (HOK) that are generated using the orthogonal polynomials Laguerre (positive or right skew) and Bessel (negative or left skew). These skewed HOK are implemented in the blind source separation/independent component analysis (BSS/ICA) algorithm. The tests for these proposed HOK are accomplished using three scenarios to simulate a real environment using actual sound sources, an environment of mixtures of multimodal fast-changing probability density function (pdf) sources that represent a challenge to the symmetrical HOK, and an environment of an adverse case (near gaussian). The separation is performed by minimizing the mutual information (MI) among the mixed sources. The performance of the skewed kernels is compared to the performance of the standard kernels such as Epanechnikov, bisquare, trisquare, and gaussian and the performance of the symmetrical HOK generated using the polynomials Chebyshev1, Chebyshev2, Gegenbauer, Jacobi, and Legendre to the tenth order. The gaussian HOK are generated using the Hermite polynomial and the Wand and Schucany procedure. The comparison among the 96 kernels is based on the average intersymbol interference ratio (AISIR) and the time needed to complete the separation. In terms of AISIR, the skewed kernels' performance is better than that of the standard kernels and rivals most of the symmetrical kernels' performance. The importance of these new skewed HOK is manifested in the environment of the multimodal pdf mixtures. In such an environment, the skewed HOK come in first place compared with the symmetrical HOK. These new families can substitute for symmetrical HOKs in such applications.

Polynomial Supertree Methods Revisited

PubMed Central

Brinkmeyer, Malte; Griebel, Thasso; Böcker, Sebastian

2011-01-01

Supertree methods allow to reconstruct large phylogenetic trees by combining smaller trees with overlapping leaf sets into one, more comprehensive supertree. The most commonly used supertree method, matrix representation with parsimony (MRP), produces accurate supertrees but is rather slow due to the underlying hard optimization problem. In this paper, we present an extensive simulation study comparing the performance of MRP and the polynomial supertree methods MinCut Supertree, Modified MinCut Supertree, Build-with-distances, PhySIC, PhySIC_IST, and super distance matrix. We consider both quality and resolution of the reconstructed supertrees. Our findings illustrate the tradeoff between accuracy and running time in supertree construction, as well as the pros and cons of voting- and veto-based supertree approaches. Based on our results, we make some general suggestions for supertree methods yet to come. PMID:22229028

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

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…

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).

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.

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

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.

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.

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

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.

Advanced Stochastic Collocation Methods for Polynomial Chaos in RAVEN

NASA Astrophysics Data System (ADS)

Talbot, Paul W.

As experiment complexity in fields such as nuclear engineering continually increases, so does the demand for robust computational methods to simulate them. In many simulations, input design parameters and intrinsic experiment properties are sources of uncertainty. Often small perturbations in uncertain parameters have significant impact on the experiment outcome. For instance, in nuclear fuel performance, small changes in fuel thermal conductivity can greatly affect maximum stress on the surrounding cladding. The difficulty quantifying input uncertainty impact in such systems has grown with the complexity of numerical models. Traditionally, uncertainty quantification has been approached using random sampling methods like Monte Carlo. For some models, the input parametric space and corresponding response output space is sufficiently explored with few low-cost calculations. For other models, it is computationally costly to obtain good understanding of the output space. To combat the expense of random sampling, this research explores the possibilities of using advanced methods in Stochastic Collocation for generalized Polynomial Chaos (SCgPC) as an alternative to traditional uncertainty quantification techniques such as Monte Carlo (MC) and Latin Hypercube Sampling (LHS) methods for applications in nuclear engineering. We consider traditional SCgPC construction strategies as well as truncated polynomial spaces using Total Degree and Hyperbolic Cross constructions. We also consider applying anisotropy (unequal treatment of different dimensions) to the polynomial space, and offer methods whereby optimal levels of anisotropy can be approximated. We contribute development to existing adaptive polynomial construction strategies. Finally, we consider High-Dimensional Model Reduction (HDMR) expansions, using SCgPC representations for the subspace terms, and contribute new adaptive methods to construct them. We apply these methods on a series of models of increasing

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 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.

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.

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

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.

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.

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.

Sparse kernel methods for high-dimensional survival data.

PubMed

Evers, Ludger; Messow, Claudia-Martina

2008-07-15

Sparse kernel methods like support vector machines (SVM) have been applied with great success to classification and (standard) regression settings. Existing support vector classification and regression techniques however are not suitable for partly censored survival data, which are typically analysed using Cox's proportional hazards model. As the partial likelihood of the proportional hazards model only depends on the covariates through inner products, it can be 'kernelized'. The kernelized proportional hazards model however yields a solution that is dense, i.e. the solution depends on all observations. One of the key features of an SVM is that it yields a sparse solution, depending only on a small fraction of the training data. We propose two methods. One is based on a geometric idea, where-akin to support vector classification-the margin between the failed observation and the observations currently at risk is maximised. The other approach is based on obtaining a sparse model by adding observations one after another akin to the Import Vector Machine (IVM). Data examples studied suggest that both methods can outperform competing approaches. Software is available under the GNU Public License as an R package and can be obtained from the first author's website http://www.maths.bris.ac.uk/~maxle/software.html.

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.

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.

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.

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

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.

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).

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.

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.

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

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.

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.

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.

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.

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.

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.

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

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.

Sensitivity kernels for viscoelastic loading based on adjoint methods

NASA Astrophysics Data System (ADS)

Al-Attar, David; Tromp, Jeroen

2014-01-01

Observations of glacial isostatic adjustment (GIA) allow for inferences to be made about mantle viscosity, ice sheet history and other related parameters. Typically, this inverse problem can be formulated as minimizing the misfit between the given observations and a corresponding set of synthetic data. When the number of parameters is large, solution of such optimization problems can be computationally challenging. A practical, albeit non-ideal, solution is to use gradient-based optimization. Although the gradient of the misfit required in such methods could be calculated approximately using finite differences, the necessary computation time grows linearly with the number of model parameters, and so this is often infeasible. A far better approach is to apply the `adjoint method', which allows the exact gradient to be calculated from a single solution of the forward problem, along with one solution of the associated adjoint problem. As a first step towards applying the adjoint method to the GIA inverse problem, we consider its application to a simpler viscoelastic loading problem in which gravitationally self-consistent ocean loading is neglected. The earth model considered is non-rotating, self-gravitating, compressible, hydrostatically pre-stressed, laterally heterogeneous and possesses a Maxwell solid rheology. We determine adjoint equations and Fréchet kernels for this problem based on a Lagrange multiplier method. Given an objective functional J defined in terms of the surface deformation fields, we show that its first-order perturbation can be written δ J = int _{MS}K_{η }δ ln η dV +int _{t0}^{t1}int _{partial M}K_{dot{σ }} δ dot{σ } dS dt, where δ ln η = δη/η denotes relative viscosity variations in solid regions MS, dV is the volume element, δ dot{σ } is the perturbation to the time derivative of the surface load which is defined on the earth model's surface ∂M and for times [t0, t1] and dS is the surface element on ∂M. The `viscosity

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.

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…

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

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.

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.

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.

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

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.

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.

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.

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.

Water Quality Sensing and Spatio-Temporal Monitoring Structure with Autocorrelation Kernel Methods.

PubMed

Vizcaíno, Iván P; Carrera, Enrique V; Muñoz-Romero, Sergio; Cumbal, Luis H; Rojo-Álvarez, José Luis

2017-10-16

Pollution on water resources is usually analyzed with monitoring campaigns, which consist of programmed sampling, measurement, and recording of the most representative water quality parameters. These campaign measurements yields a non-uniform spatio-temporal sampled data structure to characterize complex dynamics phenomena. In this work, we propose an enhanced statistical interpolation method to provide water quality managers with statistically interpolated representations of spatial-temporal dynamics. Specifically, our proposal makes efficient use of the a priori available information of the quality parameter measurements through Support Vector Regression (SVR) based on Mercer's kernels. The methods are benchmarked against previously proposed methods in three segments of the Machángara River and one segment of the San Pedro River in Ecuador, and their different dynamics are shown by statistically interpolated spatial-temporal maps. The best interpolation performance in terms of mean absolute error was the SVR with Mercer's kernel given by either the Mahalanobis spatial-temporal covariance matrix or by the bivariate estimated autocorrelation function. In particular, the autocorrelation kernel provides with significant improvement of the estimation quality, consistently for all the six water quality variables, which points out the relevance of including a priori knowledge of the problem.

Evolution method and ``differential hierarchy'' of colored knot polynomials

NASA Astrophysics Data System (ADS)

Mironov, A.; Morozov, A.; Morozov, And.

2013-10-01

We consider braids with repeating patterns inside arbitrary knots which provides a multi-parametric family of knots, depending on the "evolution" parameter, which controls the number of repetitions. The dependence of knot (super)polynomials on such evolution parameters is very easy to find. We apply this evolution method to study of the families of knots and links which include the cases with just two parallel and anti-parallel strands in the braid, like the ordinary twist and 2-strand torus knots/links and counter-oriented 2-strand links. When the answers were available before, they are immediately reproduced, and an essentially new example is added of the "double braid", which is a combination of parallel and anti-parallel 2-strand braids. This study helps us to reveal with the full clarity and partly investigate a mysterious hierarchical structure of the colored HOMFLY polynomials, at least, in (anti)symmetric representations, which extends the original observation for the figure-eight knot to many (presumably all) knots. We demonstrate that this structure is typically respected by the t-deformation to the superpolynomials.

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 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.

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.

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.

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.

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.

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.

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.

Water Quality Sensing and Spatio-Temporal Monitoring Structure with Autocorrelation Kernel Methods

PubMed Central

Vizcaíno, Iván P.; Muñoz-Romero, Sergio; Cumbal, Luis H.

2017-01-01

Pollution on water resources is usually analyzed with monitoring campaigns, which consist of programmed sampling, measurement, and recording of the most representative water quality parameters. These campaign measurements yields a non-uniform spatio-temporal sampled data structure to characterize complex dynamics phenomena. In this work, we propose an enhanced statistical interpolation method to provide water quality managers with statistically interpolated representations of spatial-temporal dynamics. Specifically, our proposal makes efficient use of the a priori available information of the quality parameter measurements through Support Vector Regression (SVR) based on Mercer’s kernels. The methods are benchmarked against previously proposed methods in three segments of the Machángara River and one segment of the San Pedro River in Ecuador, and their different dynamics are shown by statistically interpolated spatial-temporal maps. The best interpolation performance in terms of mean absolute error was the SVR with Mercer’s kernel given by either the Mahalanobis spatial-temporal covariance matrix or by the bivariate estimated autocorrelation function. In particular, the autocorrelation kernel provides with significant improvement of the estimation quality, consistently for all the six water quality variables, which points out the relevance of including a priori knowledge of the problem. PMID:29035333

Kernel methods for large-scale genomic data analysis

PubMed Central

Xing, Eric P.; Schaid, Daniel J.

2015-01-01

Machine learning, particularly kernel methods, has been demonstrated as a promising new tool to tackle the challenges imposed by today’s explosive data growth in genomics. They provide a practical and principled approach to learning how a large number of genetic variants are associated with complex phenotypes, to help reveal the complexity in the relationship between the genetic markers and the outcome of interest. In this review, we highlight the potential key role it will have in modern genomic data processing, especially with regard to integration with classical methods for gene prioritizing, prediction and data fusion. PMID:25053743

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.

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…

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.

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.

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.

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.

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.

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...

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

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.

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.

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

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.

Coherent orthogonal polynomials

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

Celeghini, E., E-mail: celeghini@fi.infn.it; Olmo, M.A. del, E-mail: olmo@fta.uva.es

2013-08-15

We discuss a fundamental characteristic of orthogonal polynomials, like the existence of a Lie algebra behind them, which can be added to their other relevant aspects. At the basis of the complete framework for orthogonal polynomials we include thus–in addition to differential equations, recurrence relations, Hilbert spaces and square integrable functions–Lie algebra theory. We start here from the square integrable functions on the open connected subset of the real line whose bases are related to orthogonal polynomials. All these one-dimensional continuous spaces allow, besides the standard uncountable basis (|x〉), for an alternative countable basis (|n〉). The matrix elements that relatemore » these two bases are essentially the orthogonal polynomials: Hermite polynomials for the line and Laguerre and Legendre polynomials for the half-line and the line interval, respectively. Differential recurrence relations of orthogonal polynomials allow us to realize that they determine an infinite-dimensional irreducible representation of a non-compact Lie algebra, whose second order Casimir C gives rise to the second order differential equation that defines the corresponding family of orthogonal polynomials. Thus, the Weyl–Heisenberg algebra h(1) with C=0 for Hermite polynomials and su(1,1) with C=−1/4 for Laguerre and Legendre polynomials are obtained. Starting from the orthogonal polynomials the Lie algebra is extended both to the whole space of the L{sup 2} functions and to the corresponding Universal Enveloping Algebra and transformation group. Generalized coherent states from each vector in the space L{sup 2} and, in particular, generalized coherent polynomials are thus obtained. -- Highlights: •Fundamental characteristic of orthogonal polynomials (OP): existence of a Lie algebra. •Differential recurrence relations of OP determine a unitary representation of a non-compact Lie group. •2nd order Casimir originates a 2nd order differential equation that

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.

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

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.

Poly-Frobenius-Euler polynomials

NASA Astrophysics Data System (ADS)

Kurt, Burak

2017-07-01

Hamahata [3] defined poly-Euler polynomials and the generalized poly-Euler polynomials. He proved some relations and closed formulas for the poly-Euler polynomials. By this motivation, we define poly-Frobenius-Euler polynomials. We give some relations for this polynomials. Also, we prove the relationships between poly-Frobenius-Euler polynomials and Stirling numbers of the second kind.

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 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.

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.

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

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.

Independence polynomial and matching polynomial of the Koch network

NASA Astrophysics Data System (ADS)

Liao, Yunhua; Xie, Xiaoliang

2015-11-01

The lattice gas model and the monomer-dimer model are two classical models in statistical mechanics. It is well known that the partition functions of these two models are associated with the independence polynomial and the matching polynomial in graph theory, respectively. Both polynomials have been shown to belong to the “#P-complete” class, which indicate the problems are computationally “intractable”. We consider these two polynomials of the Koch networks which are scale-free with small-world effects. Explicit recurrences are derived, and explicit formulae are presented for the number of independent sets of a certain type.

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)

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

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.

Methods in Symbolic Computation and p-Adic Valuations of Polynomials

NASA Astrophysics Data System (ADS)

Guan, Xiao

Symbolic computation has widely appear in many mathematical fields such as combinatorics, number theory and stochastic processes. The techniques created in the area of experimental mathematics provide us efficient ways of symbolic computing and verification of complicated relations. Part I consists of three problems. The first one focuses on a unimodal sequence derived from a quartic integral. Many of its properties are explored with the help of hypergeometric representations and automatic proofs. The second problem tackles the generating function of the reciprocal of Catalan number. It springs from the closed form given by Mathematica. Furthermore, three methods in special functions are used to justify this result. The third issue addresses the closed form solutions for the moments of products of generalized elliptic integrals , which combines the experimental mathematics and classical analysis. Part II concentrates on the p-adic valuations of polynomials from the perspective of trees. For a given polynomial f( n) indexed in positive integers, the package developed in Mathematica will create certain tree structure following a couple of rules. The evolution of such trees are studied both rigorously and experimentally from the view of field extension, nonparametric statistics and random matrix.

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.

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.

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

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…

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…

Modified homotopy perturbation method for solving hypersingular integral equations of the first kind.

PubMed

Eshkuvatov, Z K; Zulkarnain, F S; Nik Long, N M A; Muminov, Z

2016-01-01

Modified homotopy perturbation method (HPM) was used to solve the hypersingular integral equations (HSIEs) of the first kind on the interval [-1,1] with the assumption that the kernel of the hypersingular integral is constant on the diagonal of the domain. Existence of inverse of hypersingular integral operator leads to the convergence of HPM in certain cases. Modified HPM and its norm convergence are obtained in Hilbert space. Comparisons between modified HPM, standard HPM, Bernstein polynomials approach Mandal and Bhattacharya (Appl Math Comput 190:1707-1716, 2007), Chebyshev expansion method Mahiub et al. (Int J Pure Appl Math 69(3):265-274, 2011) and reproducing kernel Chen and Zhou (Appl Math Lett 24:636-641, 2011) are made by solving five examples. Theoretical and practical examples revealed that the modified HPM dominates the standard HPM and others. Finally, it is found that the modified HPM is exact, if the solution of the problem is a product of weights and polynomial functions. For rational solution the absolute error decreases very fast by increasing the number of collocation points.

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%.

MR Image Reconstruction Using Block Matching and Adaptive Kernel Methods.

PubMed

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

2016-01-01

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

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.

Kernel machine methods for integrative analysis of genome-wide methylation and genotyping studies.

PubMed

Zhao, Ni; Zhan, Xiang; Huang, Yen-Tsung; Almli, Lynn M; Smith, Alicia; Epstein, Michael P; Conneely, Karen; Wu, Michael C

2018-03-01

Many large GWAS consortia are expanding to simultaneously examine the joint role of DNA methylation in addition to genotype in the same subjects. However, integrating information from both data types is challenging. In this paper, we propose a composite kernel machine regression model to test the joint epigenetic and genetic effect. Our approach works at the gene level, which allows for a common unit of analysis across different data types. The model compares the pairwise similarities in the phenotype to the pairwise similarities in the genotype and methylation values; and high correspondence is suggestive of association. A composite kernel is constructed to measure the similarities in the genotype and methylation values between pairs of samples. We demonstrate through simulations and real data applications that the proposed approach can correctly control type I error, and is more robust and powerful than using only the genotype or methylation data in detecting trait-associated genes. We applied our method to investigate the genetic and epigenetic regulation of gene expression in response to stressful life events using data that are collected from the Grady Trauma Project. Within the kernel machine testing framework, our methods allow for heterogeneity in effect sizes, nonlinear, and interactive effects, as well as rapid P-value computation. © 2017 WILEY PERIODICALS, INC.

Explaining Support Vector Machines: A Color Based Nomogram

PubMed Central

Van Belle, Vanya; Van Calster, Ben; Van Huffel, Sabine; Suykens, Johan A. K.; Lisboa, Paulo

2016-01-01

Problem setting Support vector machines (SVMs) are very popular tools for classification, regression and other problems. Due to the large choice of kernels they can be applied with, a large variety of data can be analysed using these tools. Machine learning thanks its popularity to the good performance of the resulting models. However, interpreting the models is far from obvious, especially when non-linear kernels are used. Hence, the methods are used as black boxes. As a consequence, the use of SVMs is less supported in areas where interpretability is important and where people are held responsible for the decisions made by models. Objective In this work, we investigate whether SVMs using linear, polynomial and RBF kernels can be explained such that interpretations for model-based decisions can be provided. We further indicate when SVMs can be explained and in which situations interpretation of SVMs is (hitherto) not possible. Here, explainability is defined as the ability to produce the final decision based on a sum of contributions which depend on one single or at most two input variables. Results Our experiments on simulated and real-life data show that explainability of an SVM depends on the chosen parameter values (degree of polynomial kernel, width of RBF kernel and regularization constant). When several combinations of parameter values yield the same cross-validation performance, combinations with a lower polynomial degree or a larger kernel width have a higher chance of being explainable. Conclusions This work summarizes SVM classifiers obtained with linear, polynomial and RBF kernels in a single plot. Linear and polynomial kernels up to the second degree are represented exactly. For other kernels an indication of the reliability of the approximation is presented. The complete methodology is available as an R package and two apps and a movie are provided to illustrate the possibilities offered by the method. PMID:27723811

Using Chebyshev polynomials and approximate inverse triangular factorizations for preconditioning the conjugate gradient method

NASA Astrophysics Data System (ADS)

Kaporin, I. E.

2012-02-01

In order to precondition a sparse symmetric positive definite matrix, its approximate inverse is examined, which is represented as the product of two sparse mutually adjoint triangular matrices. In this way, the solution of the corresponding system of linear algebraic equations (SLAE) by applying the preconditioned conjugate gradient method (CGM) is reduced to performing only elementary vector operations and calculating sparse matrix-vector products. A method for constructing the above preconditioner is described and analyzed. The triangular factor has a fixed sparsity pattern and is optimal in the sense that the preconditioned matrix has a minimum K-condition number. The use of polynomial preconditioning based on Chebyshev polynomials makes it possible to considerably reduce the amount of scalar product operations (at the cost of an insignificant increase in the total number of arithmetic operations). The possibility of an efficient massively parallel implementation of the resulting method for solving SLAEs is discussed. For a sequential version of this method, the results obtained by solving 56 test problems from the Florida sparse matrix collection (which are large-scale and ill-conditioned) are presented. These results show that the method is highly reliable and has low computational costs.

Discrete-time state estimation for stochastic polynomial systems over polynomial observations

NASA Astrophysics Data System (ADS)

Hernandez-Gonzalez, M.; Basin, M.; Stepanov, O.

2018-07-01

This paper presents a solution to the mean-square state estimation problem for stochastic nonlinear polynomial systems over polynomial observations confused with additive white Gaussian noises. The solution is given in two steps: (a) computing the time-update equations and (b) computing the measurement-update equations for the state estimate and error covariance matrix. A closed form of this filter is obtained by expressing conditional expectations of polynomial terms as functions of the state estimate and error covariance. As a particular case, the mean-square filtering equations are derived for a third-degree polynomial system with second-degree polynomial measurements. Numerical simulations show effectiveness of the proposed filter compared to the extended Kalman filter.

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.

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.

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.

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.

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.

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.

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.

Lattice Boltzmann method for bosons and fermions and the fourth-order Hermite polynomial expansion.

PubMed

Coelho, Rodrigo C V; Ilha, Anderson; Doria, Mauro M; Pereira, R M; Aibe, Valter Yoshihiko

2014-04-01

The Boltzmann equation with the Bhatnagar-Gross-Krook collision operator is considered for the Bose-Einstein and Fermi-Dirac equilibrium distribution functions. We show that the expansion of the microscopic velocity in terms of Hermite polynomials must be carried to the fourth order to correctly describe the energy equation. The viscosity and thermal coefficients, previously obtained by Yang et al. [Shi and Yang, J. Comput. Phys. 227, 9389 (2008); Yang and Hung, Phys. Rev. E 79, 056708 (2009)] through the Uehling-Uhlenbeck approach, are also derived here. Thus the construction of a lattice Boltzmann method for the quantum fluid is possible provided that the Bose-Einstein and Fermi-Dirac equilibrium distribution functions are expanded to fourth order in the Hermite polynomials.

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 Accurate Projector Calibration Method Based on Polynomial Distortion Representation

PubMed Central

Liu, Miao; Sun, Changku; Huang, Shujun; Zhang, Zonghua

2015-01-01

In structure light measurement systems or 3D printing systems, the errors caused by optical distortion of a digital projector always affect the precision performance and cannot be ignored. Existing methods to calibrate the projection distortion rely on calibration plate and photogrammetry, so the calibration performance is largely affected by the quality of the plate and the imaging system. This paper proposes a new projector calibration approach that makes use of photodiodes to directly detect the light emitted from a digital projector. By analyzing the output sequence of the photoelectric module, the pixel coordinates can be accurately obtained by the curve fitting method. A polynomial distortion representation is employed to reduce the residuals of the traditional distortion representation model. Experimental results and performance evaluation show that the proposed calibration method is able to avoid most of the disadvantages in traditional methods and achieves a higher accuracy. This proposed method is also practically applicable to evaluate the geometric optical performance of other optical projection system. PMID:26492247

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

Kernel Machine SNP-set Testing under Multiple Candidate Kernels

PubMed Central

Wu, Michael C.; Maity, Arnab; Lee, Seunggeun; Simmons, Elizabeth M.; Harmon, Quaker E.; Lin, Xinyi; Engel, Stephanie M.; Molldrem, Jeffrey J.; Armistead, Paul M.

2013-01-01

Joint testing for the cumulative effect of multiple single nucleotide polymorphisms grouped on the basis of prior biological knowledge has become a popular and powerful strategy for the analysis of large scale genetic association studies. The kernel machine (KM) testing framework is a useful approach that has been proposed for testing associations between multiple genetic variants and many different types of complex traits by comparing pairwise similarity in phenotype between subjects to pairwise similarity in genotype, with similarity in genotype defined via a kernel function. An advantage of the KM framework is its flexibility: choosing different kernel functions allows for different assumptions concerning the underlying model and can allow for improved power. In practice, it is difficult to know which kernel to use a priori since this depends on the unknown underlying trait architecture and selecting the kernel which gives the lowest p-value can lead to inflated type I error. Therefore, we propose practical strategies for KM testing when multiple candidate kernels are present based on constructing composite kernels and based on efficient perturbation procedures. We demonstrate through simulations and real data applications that the procedures protect the type I error rate and can lead to substantially improved power over poor choices of kernels and only modest differences in power versus using the best candidate kernel. PMID:23471868

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.

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%.

Margin-maximizing feature elimination methods for linear and nonlinear kernel-based discriminant functions.

PubMed

Aksu, Yaman; Miller, David J; Kesidis, George; Yang, Qing X

2010-05-01

Feature selection for classification in high-dimensional spaces can improve generalization, reduce classifier complexity, and identify important, discriminating feature "markers." For support vector machine (SVM) classification, a widely used technique is recursive feature elimination (RFE). We demonstrate that RFE is not consistent with margin maximization, central to the SVM learning approach. We thus propose explicit margin-based feature elimination (MFE) for SVMs and demonstrate both improved margin and improved generalization, compared with RFE. Moreover, for the case of a nonlinear kernel, we show that RFE assumes that the squared weight vector 2-norm is strictly decreasing as features are eliminated. We demonstrate this is not true for the Gaussian kernel and, consequently, RFE may give poor results in this case. MFE for nonlinear kernels gives better margin and generalization. We also present an extension which achieves further margin gains, by optimizing only two degrees of freedom--the hyperplane's intercept and its squared 2-norm--with the weight vector orientation fixed. We finally introduce an extension that allows margin slackness. We compare against several alternatives, including RFE and a linear programming method that embeds feature selection within the classifier design. On high-dimensional gene microarray data sets, University of California at Irvine (UCI) repository data sets, and Alzheimer's disease brain image data, MFE methods give promising results.

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.

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.

Numerical Polynomial Homotopy Continuation Method and String Vacua

DOE PAGES

Mehta, Dhagash

2011-01-01

Finding vmore » acua for the four-dimensional effective theories for supergravity which descend from flux compactifications and analyzing them according to their stability is one of the central problems in string phenomenology. Except for some simple toy models, it is, however, difficult to find all the vacua analytically. Recently developed algorithmic methods based on symbolic computer algebra can be of great help in the more realistic models. However, they suffer from serious algorithmic complexities and are limited to small system sizes. In this paper, we review a numerical method called the numerical polynomial homotopy continuation (NPHC) method, first used in the areas of lattice field theories, which by construction finds all of the vacua of a given potential that is known to have only isolated solutions. The NPHC method is known to suffer from no major algorithmic complexities and is embarrassingly parallelizable , and hence its applicability goes way beyond the existing symbolic methods. We first solve a simple toy model as a warm-up example to demonstrate the NPHC method at work. We then show that all the vacua of a more complicated model of a compactified M theory model, which has an S U ( 3 ) structure, can be obtained by using a desktop machine in just about an hour, a feat which was reported to be prohibitively difficult by the existing symbolic methods. Finally, we compare the various technicalities between the two methods.« less

Exact Doppler broadening of tabulated cross sections. [SIGMA 1 kernel broadening method

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

Cullen, D.E.; Weisbin, C.R.

1976-07-01

The SIGMA1 kernel broadening method is presented to Doppler broaden to any required accuracy a cross section that is described by a table of values and linear-linear interpolation in energy-cross section between tabulated values. The method is demonstrated to have no temperature or energy limitations and to be equally applicable to neutron or charged-particle cross sections. The method is qualitatively and quantitatively compared to contemporary approximate methods of Doppler broadening with particular emphasis on the effect of each approximation introduced.

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

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/.

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.

A Novel Mittag-Leffler Kernel Based Hybrid Fault Diagnosis Method for Wheeled Robot Driving System.

PubMed

Yuan, Xianfeng; Song, Mumin; Zhou, Fengyu; Chen, Zhumin; Li, Yan

2015-01-01

The wheeled robots have been successfully applied in many aspects, such as industrial handling vehicles, and wheeled service robots. To improve the safety and reliability of wheeled robots, this paper presents a novel hybrid fault diagnosis framework based on Mittag-Leffler kernel (ML-kernel) support vector machine (SVM) and Dempster-Shafer (D-S) fusion. Using sensor data sampled under different running conditions, the proposed approach initially establishes multiple principal component analysis (PCA) models for fault feature extraction. The fault feature vectors are then applied to train the probabilistic SVM (PSVM) classifiers that arrive at a preliminary fault diagnosis. To improve the accuracy of preliminary results, a novel ML-kernel based PSVM classifier is proposed in this paper, and the positive definiteness of the ML-kernel is proved as well. The basic probability assignments (BPAs) are defined based on the preliminary fault diagnosis results and their confidence values. Eventually, the final fault diagnosis result is archived by the fusion of the BPAs. Experimental results show that the proposed framework not only is capable of detecting and identifying the faults in the robot driving system, but also has better performance in stability and diagnosis accuracy compared with the traditional methods.

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

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 .

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…

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

Kernel Smoothing Methods for Non-Poissonian Seismic Hazard Analysis

NASA Astrophysics Data System (ADS)

Woo, Gordon

2017-04-01

For almost fifty years, the mainstay of probabilistic seismic hazard analysis has been the methodology developed by Cornell, which assumes that earthquake occurrence is a Poisson process, and that the spatial distribution of epicentres can be represented by a set of polygonal source zones, within which seismicity is uniform. Based on Vere-Jones' use of kernel smoothing methods for earthquake forecasting, these methods were adapted in 1994 by the author for application to probabilistic seismic hazard analysis. There is no need for ambiguous boundaries of polygonal source zones, nor for the hypothesis of time independence of earthquake sequences. In Europe, there are many regions where seismotectonic zones are not well delineated, and where there is a dynamic stress interaction between events, so that they cannot be described as independent. From the Amatrice earthquake of 24 August, 2016, the subsequent damaging earthquakes in Central Italy over months were not independent events. Removing foreshocks and aftershocks is not only an ill-defined task, it has a material effect on seismic hazard computation. Because of the spatial dispersion of epicentres, and the clustering of magnitudes for the largest events in a sequence, which might all be around magnitude 6, the specific event causing the highest ground motion can vary from one site location to another. Where significant active faults have been clearly identified geologically, they should be modelled as individual seismic sources. The remaining background seismicity should be modelled as non-Poissonian using statistical kernel smoothing methods. This approach was first applied for seismic hazard analysis at a UK nuclear power plant two decades ago, and should be included within logic-trees for future probabilistic seismic hazard at critical installations within Europe. In this paper, various salient European applications are given.

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.

Enriched reproducing kernel particle method for fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Ying, Yuping; Lian, Yanping; Tang, Shaoqiang; Liu, Wing Kam

2018-06-01

The reproducing kernel particle method (RKPM) has been efficiently applied to problems with large deformations, high gradients and high modal density. In this paper, it is extended to solve a nonlocal problem modeled by a fractional advection-diffusion equation (FADE), which exhibits a boundary layer with low regularity. We formulate this method on a moving least-square approach. Via the enrichment of fractional-order power functions to the traditional integer-order basis for RKPM, leading terms of the solution to the FADE can be exactly reproduced, which guarantees a good approximation to the boundary layer. Numerical tests are performed to verify the proposed approach.

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.

Classification of Phylogenetic Profiles for Protein Function Prediction: An SVM Approach

NASA Astrophysics Data System (ADS)

Kotaru, Appala Raju; Joshi, Ramesh C.

Predicting the function of an uncharacterized protein is a major challenge in post-genomic era due to problems complexity and scale. Having knowledge of protein function is a crucial link in the development of new drugs, better crops, and even the development of biochemicals such as biofuels. Recently numerous high-throughput experimental procedures have been invented to investigate the mechanisms leading to the accomplishment of a protein’s function and Phylogenetic profile is one of them. Phylogenetic profile is a way of representing a protein which encodes evolutionary history of proteins. In this paper we proposed a method for classification of phylogenetic profiles using supervised machine learning method, support vector machine classification along with radial basis function as kernel for identifying functionally linked proteins. We experimentally evaluated the performance of the classifier with the linear kernel, polynomial kernel and compared the results with the existing tree kernel. In our study we have used proteins of the budding yeast saccharomyces cerevisiae genome. We generated the phylogenetic profiles of 2465 yeast genes and for our study we used the functional annotations that are available in the MIPS database. Our experiments show that the performance of the radial basis kernel is similar to polynomial kernel is some functional classes together are better than linear, tree kernel and over all radial basis kernel outperformed the polynomial kernel, linear kernel and tree kernel. In analyzing these results we show that it will be feasible to make use of SVM classifier with radial basis function as kernel to predict the gene functionality using phylogenetic profiles.

Umbral orthogonal polynomials

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

Lopez-Sendino, J. E.; del Olmo, M. A.

2010-12-23

We present an umbral operator version of the classical orthogonal polynomials. We obtain three families which are the umbral counterpart of the Jacobi, Laguerre and Hermite polynomials in the classical case.

On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices

NASA Technical Reports Server (NTRS)

Freund, Roland

1988-01-01

Conjugate gradient type methods are considered for the solution of large linear systems Ax = b with complex coefficient matrices of the type A = T + i(sigma)I where T is Hermitian and sigma, a real scalar. Three different conjugate gradient type approaches with iterates defined by a minimal residual property, a Galerkin type condition, and an Euclidian error minimization, respectively, are investigated. In particular, numerically stable implementations based on the ideas behind Paige and Saunder's SYMMLQ and MINRES for real symmetric matrices are proposed. Error bounds for all three methods are derived. It is shown how the special shift structure of A can be preserved by using polynomial preconditioning. Results on the optimal choice of the polynomial preconditioner are given. Also, some numerical experiments for matrices arising from finite difference approximations to the complex Helmholtz equation are reported.

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.

Field curvature correction method for ultrashort throw ratio projection optics design using an odd polynomial mirror surface.

PubMed

Zhuang, Zhenfeng; Chen, Yanting; Yu, Feihong; Sun, Xiaowei

2014-08-01

This paper presents a field curvature correction method of designing an ultrashort throw ratio (TR) projection lens for an imaging system. The projection lens is composed of several refractive optical elements and an odd polynomial mirror surface. A curved image is formed in a direction away from the odd polynomial mirror surface by the refractive optical elements from the image formed on the digital micromirror device (DMD) panel, and the curved image formed is its virtual image. Then the odd polynomial mirror surface enlarges the curved image and a plane image is formed on the screen. Based on the relationship between the chief ray from the exit pupil of each field of view (FOV) and the corresponding predescribed position on the screen, the initial profile of the freeform mirror surface is calculated by using segments of the hyperbolic according to the laws of reflection. For further optimization, the value of the high-order odd polynomial surface is used to express the freeform mirror surface through a least-squares fitting method. As an example, an ultrashort TR projection lens that realizes projection onto a large 50 in. screen at a distance of only 510 mm is presented. The optical performance for the designed projection lens is analyzed by ray tracing method. Results show that an ultrashort TR projection lens modulation transfer function of over 60% at 0.5 cycles/mm for all optimization fields is achievable with f-number of 2.0, 126° full FOV, <1% distortion, and 0.46 TR. Moreover, in comparing the proposed projection lens' optical specifications to that of traditional projection lenses, aspheric mirror projection lenses, and conventional short TR projection lenses, results indicate that this projection lens has the advantages of ultrashort TR, low f-number, wide full FOV, and small distortion.

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

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

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.

A Novel Mittag-Leffler Kernel Based Hybrid Fault Diagnosis Method for Wheeled Robot Driving System

PubMed Central

Yuan, Xianfeng; Song, Mumin; Chen, Zhumin; Li, Yan

2015-01-01

The wheeled robots have been successfully applied in many aspects, such as industrial handling vehicles, and wheeled service robots. To improve the safety and reliability of wheeled robots, this paper presents a novel hybrid fault diagnosis framework based on Mittag-Leffler kernel (ML-kernel) support vector machine (SVM) and Dempster-Shafer (D-S) fusion. Using sensor data sampled under different running conditions, the proposed approach initially establishes multiple principal component analysis (PCA) models for fault feature extraction. The fault feature vectors are then applied to train the probabilistic SVM (PSVM) classifiers that arrive at a preliminary fault diagnosis. To improve the accuracy of preliminary results, a novel ML-kernel based PSVM classifier is proposed in this paper, and the positive definiteness of the ML-kernel is proved as well. The basic probability assignments (BPAs) are defined based on the preliminary fault diagnosis results and their confidence values. Eventually, the final fault diagnosis result is archived by the fusion of the BPAs. Experimental results show that the proposed framework not only is capable of detecting and identifying the faults in the robot driving system, but also has better performance in stability and diagnosis accuracy compared with the traditional methods. PMID:26229526

Nonlinear PET parametric image reconstruction with MRI information using kernel method

NASA Astrophysics Data System (ADS)

Gong, Kuang; Wang, Guobao; Chen, Kevin T.; Catana, Ciprian; Qi, Jinyi

2017-03-01

Positron Emission Tomography (PET) is a functional imaging modality widely used in oncology, cardiology, and neurology. It is highly sensitive, but suffers from relatively poor spatial resolution, as compared with anatomical imaging modalities, such as magnetic resonance imaging (MRI). With the recent development of combined PET/MR systems, we can improve the PET image quality by incorporating MR information. Previously we have used kernel learning to embed MR information in static PET reconstruction and direct Patlak reconstruction. Here we extend this method to direct reconstruction of nonlinear parameters in a compartment model by using the alternating direction of multiplier method (ADMM) algorithm. Simulation studies show that the proposed method can produce superior parametric images compared with existing methods.

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.

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.

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…

A fuzzy pattern matching method based on graph kernel for lithography hotspot detection

NASA Astrophysics Data System (ADS)

Nitta, Izumi; Kanazawa, Yuzi; Ishida, Tsutomu; Banno, Koji

2017-03-01

In advanced technology nodes, lithography hotspot detection has become one of the most significant issues in design for manufacturability. Recently, machine learning based lithography hotspot detection has been widely investigated, but it has trade-off between detection accuracy and false alarm. To apply machine learning based technique to the physical verification phase, designers require minimizing undetected hotspots to avoid yield degradation. They also need a ranking of similar known patterns with a detected hotspot to prioritize layout pattern to be corrected. To achieve high detection accuracy and to prioritize detected hotspots, we propose a novel lithography hotspot detection method using Delaunay triangulation and graph kernel based machine learning. Delaunay triangulation extracts features of hotspot patterns where polygons locate irregularly and closely one another, and graph kernel expresses inner structure of graphs. Additionally, our method provides similarity between two patterns and creates a list of similar training patterns with a detected hotspot. Experiments results on ICCAD 2012 benchmarks show that our method achieves high accuracy with allowable range of false alarm. We also show the ranking of the similar known patterns with a detected hotspot.

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

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.

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.

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.

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.

Bioactive compounds in cashew nut (Anacardium occidentale L.) kernels: effect of different shelling methods.

PubMed

Trox, Jennifer; Vadivel, Vellingiri; Vetter, Walter; Stuetz, Wolfgang; Scherbaum, Veronika; Gola, Ute; Nohr, Donatus; Biesalski, Hans Konrad

2010-05-12

In the present study, the effects of various conventional shelling methods (oil-bath roasting, direct steam roasting, drying, and open pan roasting) as well as a novel "Flores" hand-cracking method on the levels of bioactive compounds of cashew nut kernels were investigated. The raw cashew nut kernels were found to possess appreciable levels of certain bioactive compounds such as beta-carotene (9.57 microg/100 g of DM), lutein (30.29 microg/100 g of DM), zeaxanthin (0.56 microg/100 g of DM), alpha-tocopherol (0.29 mg/100 g of DM), gamma-tocopherol (1.10 mg/100 g of DM), thiamin (1.08 mg/100 g of DM), stearic acid (4.96 g/100 g of DM), oleic acid (21.87 g/100 g of DM), and linoleic acid (5.55 g/100 g of DM). All of the conventional shelling methods including oil-bath roasting, steam roasting, drying, and open pan roasting revealed a significant reduction, whereas the Flores hand-cracking method exhibited similar levels of carotenoids, thiamin, and unsaturated fatty acids in cashew nuts when compared to raw unprocessed samples.

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.

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.

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.

Kernel Abortion in Maize 1

PubMed Central

Hanft, Jonathan M.; Jones, Robert J.

1986-01-01

Kernels cultured in vitro were induced to abort by high temperature (35°C) and by culturing six kernels/cob piece. Aborting kernels failed to enter a linear phase of dry mass accumulation and had a final mass that was less than 6% of nonaborting field-grown kernels. Kernels induced to abort by high temperature failed to synthesize starch in the endosperm and had elevated sucrose concentrations and low fructose and glucose concentrations in the pedicel during early growth compared to nonaborting kernels. Kernels induced to abort by high temperature also had much lower pedicel soluble acid invertase activities than did nonaborting kernels. These results suggest that high temperature during the lag phase of kernel growth may impair the process of sucrose unloading in the pedicel by indirectly inhibiting soluble acid invertase activity and prevent starch synthesis in the endosperm. Kernels induced to abort by culturing six kernels/cob piece had reduced pedicel fructose, glucose, and sucrose concentrations compared to kernels from field-grown ears. These aborting kernels also had a lower pedicel soluble acid invertase activity compared to nonaborting kernels from the same cob piece and from field-grown ears. The low invertase activity in pedicel tissue of the aborting kernels was probably caused by a lack of substrate (sucrose) for the invertase to cleave due to the intense competition for available assimilates. In contrast to kernels cultured at 35°C, aborting kernels from cob pieces containing all six kernels accumulated starch in a linear fashion. These results indicate that kernels cultured six/cob piece abort because of an inadequate supply of sugar and are similar to apical kernels from field-grown ears that often abort prior to the onset of linear growth. PMID:16664846

Hadamard Factorization of Stable Polynomials

NASA Astrophysics Data System (ADS)

Loredo-Villalobos, Carlos Arturo; Aguirre-Hernández, Baltazar

2011-11-01

The stable (Hurwitz) polynomials are important in the study of differential equations systems and control theory (see [7] and [19]). A property of these polynomials is related to Hadamard product. Consider two polynomials p,q ∈ R[x]:p(x) = anxn+an-1xn-1+...+a1x+a0q(x) = bmx m+bm-1xm-1+...+b1x+b0the Hadamard product (p × q) is defined as (p×q)(x) = akbkxk+ak-1bk-1xk-1+...+a1b1x+a0b0where k = min(m,n). Some results (see [16]) shows that if p,q ∈R[x] are stable polynomials then (p×q) is stable, also, i.e. the Hadamard product is closed; however, the reciprocal is not always true, that is, not all stable polynomial has a factorization into two stable polynomials the same degree n, if n> 4 (see [15]).In this work we will give some conditions to Hadamard factorization existence for stable polynomials.

Novel applications of the temporal kernel method: Historical and future radiative forcing

NASA Astrophysics Data System (ADS)

Portmann, R. W.; Larson, E.; Solomon, S.; Murphy, D. M.

2017-12-01

We present a new estimate of the historical radiative forcing derived from the observed global mean surface temperature and a model derived kernel function. Current estimates of historical radiative forcing are usually derived from climate models. Despite large variability in these models, the multi-model mean tends to do a reasonable job of representing the Earth system and climate. One method of diagnosing the transient radiative forcing in these models requires model output of top of the atmosphere radiative imbalance and global mean temperature anomaly. It is difficult to apply this method to historical observations due to the lack of TOA radiative measurements before CERES. We apply the temporal kernel method (TKM) of calculating radiative forcing to the historical global mean temperature anomaly. This novel approach is compared against the current regression based methods using model outputs and shown to produce consistent forcing estimates giving confidence in the forcing derived from the historical temperature record. The derived TKM radiative forcing provides an estimate of the forcing time series that the average climate model needs to produce the observed temperature record. This forcing time series is found to be in good overall agreement with previous estimates but includes significant differences that will be discussed. The historical anthropogenic aerosol forcing is estimated as a residual from the TKM and found to be consistent with earlier moderate forcing estimates. In addition, this method is applied to future temperature projections to estimate the radiative forcing required to achieve those temperature goals, such as those set in the Paris agreement.

Extending a Property of Cubic Polynomials to Higher-Degree Polynomials

ERIC Educational Resources Information Center

Miller, David A.; Moseley, James

2012-01-01

In this paper, the authors examine a property that holds for all cubic polynomials given two zeros. This property is discovered after reviewing a variety of ways to determine the equation of a cubic polynomial given specific conditions through algebra and calculus. At the end of the article, they will connect the property to a very famous method…

Quantum kernel applications in medicinal chemistry.

PubMed

Huang, Lulu; Massa, Lou

2012-07-01

Progress in the quantum mechanics of biological molecules is being driven by computational advances. The notion of quantum kernels can be introduced to simplify the formalism of quantum mechanics, making it especially suitable for parallel computation of very large biological molecules. The essential idea is to mathematically break large biological molecules into smaller kernels that are calculationally tractable, and then to represent the full molecule by a summation over the kernels. The accuracy of the kernel energy method (KEM) is shown by systematic application to a great variety of molecular types found in biology. These include peptides, proteins, DNA and RNA. Examples are given that explore the KEM across a variety of chemical models, and to the outer limits of energy accuracy and molecular size. KEM represents an advance in quantum biology applicable to problems in medicine and drug design.

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.

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…

On universal knot polynomials

NASA Astrophysics Data System (ADS)

Mironov, A.; Mkrtchyan, R.; Morozov, A.

2016-02-01

We present a universal knot polynomials for 2- and 3-strand torus knots in adjoint representation, by universalization of appropriate Rosso-Jones formula. According to universality, these polynomials coincide with adjoined colored HOMFLY and Kauffman polynomials at SL and SO/Sp lines on Vogel's plane, respectively and give their exceptional group's counterparts on exceptional line. We demonstrate that [m,n]=[n,m] topological invariance, when applicable, take place on the entire Vogel's plane. We also suggest the universal form of invariant of figure eight knot in adjoint representation, and suggest existence of such universalization for any knot in adjoint and its descendant representations. Properties of universal polynomials and applications of these results are discussed.

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.

A Geometric Method for Model Reduction of Biochemical Networks with Polynomial Rate Functions.

PubMed

Samal, Satya Swarup; Grigoriev, Dima; Fröhlich, Holger; Weber, Andreas; Radulescu, Ovidiu

2015-12-01

Model reduction of biochemical networks relies on the knowledge of slow and fast variables. We provide a geometric method, based on the Newton polytope, to identify slow variables of a biochemical network with polynomial rate functions. The gist of the method is the notion of tropical equilibration that provides approximate descriptions of slow invariant manifolds. Compared to extant numerical algorithms such as the intrinsic low-dimensional manifold method, our approach is symbolic and utilizes orders of magnitude instead of precise values of the model parameters. Application of this method to a large collection of biochemical network models supports the idea that the number of dynamical variables in minimal models of cell physiology can be small, in spite of the large number of molecular regulatory actors.

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.

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).

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.

Trajectory Optimization Using Adjoint Method and Chebyshev Polynomial Approximation for Minimizing Fuel Consumption During Climb

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Hornby, Gregory; Ishihara, Abe

2013-01-01

This paper describes two methods of trajectory optimization to obtain an optimal trajectory of minimum-fuel- to-climb for an aircraft. The first method is based on the adjoint method, and the second method is based on a direct trajectory optimization method using a Chebyshev polynomial approximation and cubic spine approximation. The approximate optimal trajectory will be compared with the adjoint-based optimal trajectory which is considered as the true optimal solution of the trajectory optimization problem. The adjoint-based optimization problem leads to a singular optimal control solution which results in a bang-singular-bang optimal control.

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.

Nonparametric Inference of Doubly Stochastic Poisson Process Data via the Kernel Method

PubMed Central

Zhang, Tingting; Kou, S. C.

2010-01-01

Doubly stochastic Poisson processes, also known as the Cox processes, frequently occur in various scientific fields. In this article, motivated primarily by analyzing Cox process data in biophysics, we propose a nonparametric kernel-based inference method. We conduct a detailed study, including an asymptotic analysis, of the proposed method, and provide guidelines for its practical use, introducing a fast and stable regression method for bandwidth selection. We apply our method to real photon arrival data from recent single-molecule biophysical experiments, investigating proteins' conformational dynamics. Our result shows that conformational fluctuation is widely present in protein systems, and that the fluctuation covers a broad range of time scales, highlighting the dynamic and complex nature of proteins' structure. PMID:21258615

Nonparametric Inference of Doubly Stochastic Poisson Process Data via the Kernel Method.

PubMed

Zhang, Tingting; Kou, S C

2010-01-01

Doubly stochastic Poisson processes, also known as the Cox processes, frequently occur in various scientific fields. In this article, motivated primarily by analyzing Cox process data in biophysics, we propose a nonparametric kernel-based inference method. We conduct a detailed study, including an asymptotic analysis, of the proposed method, and provide guidelines for its practical use, introducing a fast and stable regression method for bandwidth selection. We apply our method to real photon arrival data from recent single-molecule biophysical experiments, investigating proteins' conformational dynamics. Our result shows that conformational fluctuation is widely present in protein systems, and that the fluctuation covers a broad range of time scales, highlighting the dynamic and complex nature of proteins' structure.

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.

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.

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.

[Research on the methods for multi-class kernel CSP-based feature extraction].

PubMed

Wang, Jinjia; Zhang, Lingzhi; Hu, Bei

2012-04-01

To relax the presumption of strictly linear patterns in the common spatial patterns (CSP), we studied the kernel CSP (KCSP). A new multi-class KCSP (MKCSP) approach was proposed in this paper, which combines the kernel approach with multi-class CSP technique. In this approach, we used kernel spatial patterns for each class against all others, and extracted signal components specific to one condition from EEG data sets of multiple conditions. Then we performed classification using the Logistic linear classifier. Brain computer interface (BCI) competition III_3a was used in the experiment. Through the experiment, it can be proved that this approach could decompose the raw EEG singles into spatial patterns extracted from multi-class of single trial EEG, and could obtain good classification results.

Determinants with orthogonal polynomial entries

NASA Astrophysics Data System (ADS)

Ismail, Mourad E. H.

2005-06-01

We use moment representations of orthogonal polynomials to evaluate the corresponding Hankel determinants formed by the orthogonal polynomials. We also study the Hankel determinants which start with pn on the top left-hand corner. As examples we evaluate the Hankel determinants whose entries are q-ultraspherical or Al-Salam-Chihara polynomials.

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.

Fast beampattern evaluation by polynomial rooting

NASA Astrophysics Data System (ADS)

Häcker, P.; Uhlich, S.; Yang, B.

2011-07-01

Current automotive radar systems measure the distance, the relative velocity and the direction of objects in their environment. This information enables the car to support the driver. The direction estimation capabilities of a sensor array depend on its beampattern. To find the array configuration leading to the best angle estimation by a global optimization algorithm, a huge amount of beampatterns have to be calculated to detect their maxima. In this paper, a novel algorithm is proposed to find all maxima of an array's beampattern fast and reliably, leading to accelerated array optimizations. The algorithm works for arrays having the sensors on a uniformly spaced grid. We use a general version of the gcd (greatest common divisor) function in order to write the problem as a polynomial. We differentiate and root the polynomial to get the extrema of the beampattern. In addition, we show a method to reduce the computational burden even more by decreasing the order of the polynomial.

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

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.

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.

Computing Tutte polynomials of contact networks in classrooms

NASA Astrophysics Data System (ADS)

Hincapié, Doracelly; Ospina, Juan

2013-05-01

Objective: The topological complexity of contact networks in classrooms and the potential transmission of an infectious disease were analyzed by sex and age. Methods: The Tutte polynomials, some topological properties and the number of spanning trees were used to algebraically compute the topological complexity. Computations were made with the Maple package GraphTheory. Published data of mutually reported social contacts within a classroom taken from primary school, consisting of children in the age ranges of 4-5, 7-8 and 10-11, were used. Results: The algebraic complexity of the Tutte polynomial and the probability of disease transmission increases with age. The contact networks are not bipartite graphs, gender segregation was observed especially in younger children. Conclusion: Tutte polynomials are tools to understand the topology of the contact networks and to derive numerical indexes of such topologies. It is possible to establish relationships between the Tutte polynomial of a given contact network and the potential transmission of an infectious disease within such network

Bayer Demosaicking with Polynomial Interpolation.

PubMed

Wu, Jiaji; Anisetti, Marco; Wu, Wei; Damiani, Ernesto; Jeon, Gwanggil

2016-08-30

Demosaicking is a digital image process to reconstruct full color digital images from incomplete color samples from an image sensor. It is an unavoidable process for many devices incorporating camera sensor (e.g. mobile phones, tablet, etc.). In this paper, we introduce a new demosaicking algorithm based on polynomial interpolation-based demosaicking (PID). Our method makes three contributions: calculation of error predictors, edge classification based on color differences, and a refinement stage using a weighted sum strategy. Our new predictors are generated on the basis of on the polynomial interpolation, and can be used as a sound alternative to other predictors obtained by bilinear or Laplacian interpolation. In this paper we show how our predictors can be combined according to the proposed edge classifier. After populating three color channels, a refinement stage is applied to enhance the image quality and reduce demosaicking artifacts. Our experimental results show that the proposed method substantially improves over existing demosaicking methods in terms of objective performance (CPSNR, S-CIELAB E, and FSIM), and visual performance.

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

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.

A Kernel-Free Particle-Finite Element Method for Hypervelocity Impact Simulation. Chapter 4

NASA Technical Reports Server (NTRS)

Park, Young-Keun; Fahrenthold, Eric P.

2004-01-01

An improved hybrid particle-finite element method has been developed for the simulation of hypervelocity impact problems. Unlike alternative methods, the revised formulation computes the density without reference to any kernel or interpolation functions, for either the density or the rate of dilatation. This simplifies the state space model and leads to a significant reduction in computational cost. The improved method introduces internal energy variables as generalized coordinates in a new formulation of the thermomechanical Lagrange equations. Example problems show good agreement with exact solutions in one dimension and good agreement with experimental data in a three dimensional simulation.

Interpolation and Polynomial Curve Fitting

ERIC Educational Resources Information Center

Yang, Yajun; Gordon, Sheldon P.

2014-01-01

Two points determine a line. Three noncollinear points determine a quadratic function. Four points that do not lie on a lower-degree polynomial curve determine a cubic function. In general, n + 1 points uniquely determine a polynomial of degree n, presuming that they do not fall onto a polynomial of lower degree. The process of finding such a…

Convolution kernels for multi-wavelength imaging

NASA Astrophysics Data System (ADS)

Boucaud, A.; Bocchio, M.; Abergel, A.; Orieux, F.; Dole, H.; Hadj-Youcef, M. A.

2016-12-01

Astrophysical images issued from different instruments and/or spectral bands often require to be processed together, either for fitting or comparison purposes. However each image is affected by an instrumental response, also known as point-spread function (PSF), that depends on the characteristics of the instrument as well as the wavelength and the observing strategy. Given the knowledge of the PSF in each band, a straightforward way of processing images is to homogenise them all to a target PSF using convolution kernels, so that they appear as if they had been acquired by the same instrument. We propose an algorithm that generates such PSF-matching kernels, based on Wiener filtering with a tunable regularisation parameter. This method ensures all anisotropic features in the PSFs to be taken into account. We compare our method to existing procedures using measured Herschel/PACS and SPIRE PSFs and simulated JWST/MIRI PSFs. Significant gains up to two orders of magnitude are obtained with respect to the use of kernels computed assuming Gaussian or circularised PSFs. A software to compute these kernels is available at https://github.com/aboucaud/pypher

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

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.

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...

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.

Thermodynamic characterization of networks using graph polynomials

NASA Astrophysics Data System (ADS)

Ye, Cheng; Comin, César H.; Peron, Thomas K. DM.; Silva, Filipi N.; Rodrigues, Francisco A.; Costa, Luciano da F.; Torsello, Andrea; Hancock, Edwin R.

2015-09-01

In this paper, we present a method for characterizing the evolution of time-varying complex networks by adopting a thermodynamic representation of network structure computed from a polynomial (or algebraic) characterization of graph structure. Commencing from a representation of graph structure based on a characteristic polynomial computed from the normalized Laplacian matrix, we show how the polynomial is linked to the Boltzmann partition function of a network. This allows us to compute a number of thermodynamic quantities for the network, including the average energy and entropy. Assuming that the system does not change volume, we can also compute the temperature, defined as the rate of change of entropy with energy. All three thermodynamic variables can be approximated using low-order Taylor series that can be computed using the traces of powers of the Laplacian matrix, avoiding explicit computation of the normalized Laplacian spectrum. These polynomial approximations allow a smoothed representation of the evolution of networks to be constructed in the thermodynamic space spanned by entropy, energy, and temperature. We show how these thermodynamic variables can be computed in terms of simple network characteristics, e.g., the total number of nodes and node degree statistics for nodes connected by edges. We apply the resulting thermodynamic characterization to real-world time-varying networks representing complex systems in the financial and biological domains. The study demonstrates that the method provides an efficient tool for detecting abrupt changes and characterizing different stages in network evolution.

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.

A sequential method for spline approximation with variable knots. [recursive piecewise polynomial signal processing

NASA Technical Reports Server (NTRS)

Mier Muth, A. M.; Willsky, A. S.

1978-01-01

In this paper we describe a method for approximating a waveform by a spline. The method is quite efficient, as the data are processed sequentially. The basis of the approach is to view the approximation problem as a question of estimation of a polynomial in noise, with the possibility of abrupt changes in the highest derivative. This allows us to bring several powerful statistical signal processing tools into play. We also present some initial results on the application of our technique to the processing of electrocardiograms, where the knot locations themselves may be some of the most important pieces of diagnostic information.

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.

Chaos, Fractals, and Polynomials.

ERIC Educational Resources Information Center

Tylee, J. Louis; Tylee, Thomas B.

1996-01-01

Discusses chaos theory; linear algebraic equations and the numerical solution of polynomials, including the use of the Newton-Raphson technique to find polynomial roots; fractals; search region and coordinate systems; convergence; and generating color fractals on a computer. (LRW)

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

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.

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”.

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

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.

Multi-indexed (q-)Racah polynomials

NASA Astrophysics Data System (ADS)

Odake, Satoru; Sasaki, Ryu

2012-09-01

As the second stage of the project multi-indexed orthogonal polynomials, we present, in the framework of ‘discrete quantum mechanics’ with real shifts in one dimension, the multi-indexed (q-)Racah polynomials. They are obtained from the (q-)Racah polynomials by the multiple application of the discrete analogue of the Darboux transformations or the Crum-Krein-Adler deletion of ‘virtual state’ vectors, in a similar way to the multi-indexed Laguerre and Jacobi polynomials reported earlier. The virtual state vectors are the ‘solutions’ of the matrix Schrödinger equation with negative ‘eigenvalues’, except for one of the two boundary points.

A Distributed Learning Method for ℓ1-Regularized Kernel Machine over Wireless Sensor Networks

PubMed Central

Ji, Xinrong; Hou, Cuiqin; Hou, Yibin; Gao, Fang; Wang, Shulong

2016-01-01

In wireless sensor networks, centralized learning methods have very high communication costs and energy consumption. These are caused by the need to transmit scattered training examples from various sensor nodes to the central fusion center where a classifier or a regression machine is trained. To reduce the communication cost, a distributed learning method for a kernel machine that incorporates ℓ1 norm regularization (ℓ1-regularized) is investigated, and a novel distributed learning algorithm for the ℓ1-regularized kernel minimum mean squared error (KMSE) machine is proposed. The proposed algorithm relies on in-network processing and a collaboration that transmits the sparse model only between single-hop neighboring nodes. This paper evaluates the proposed algorithm with respect to the prediction accuracy, the sparse rate of model, the communication cost and the number of iterations on synthetic and real datasets. The simulation results show that the proposed algorithm can obtain approximately the same prediction accuracy as that obtained by the batch learning method. Moreover, it is significantly superior in terms of the sparse rate of model and communication cost, and it can converge with fewer iterations. Finally, an experiment conducted on a wireless sensor network (WSN) test platform further shows the advantages of the proposed algorithm with respect to communication cost. PMID:27376298

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.

Polynomial sequences for bond percolation critical thresholds

DOE PAGES

Scullard, Christian R.

2011-09-22

In this paper, I compute the inhomogeneous (multi-probability) bond critical surfaces for the (4, 6, 12) and (3 4, 6) using the linearity approximation described in (Scullard and Ziff, J. Stat. Mech. 03021), implemented as a branching process of lattices. I find the estimates for the bond percolation thresholds, pc(4, 6, 12) = 0.69377849... and p c(3 4, 6) = 0.43437077..., compared with Parviainen’s numerical results of p c = 0.69373383... and p c = 0.43430621... . These deviations are of the order 10 -5, as is standard for this method. Deriving thresholds in this way for a given latticemore » leads to a polynomial with integer coefficients, the root in [0, 1] of which gives the estimate for the bond threshold and I show how the method can be refined, leading to a series of higher order polynomials making predictions that likely converge to the exact answer. Finally, I discuss how this fact hints that for certain graphs, such as the kagome lattice, the exact bond threshold may not be the root of any polynomial with integer coefficients.« less

Deep Restricted Kernel Machines Using Conjugate Feature Duality.

PubMed

Suykens, Johan A K

2017-08-01

The aim of this letter is to propose a theory of deep restricted kernel machines offering new foundations for deep learning with kernel machines. From the viewpoint of deep learning, it is partially related to restricted Boltzmann machines, which are characterized by visible and hidden units in a bipartite graph without hidden-to-hidden connections and deep learning extensions as deep belief networks and deep Boltzmann machines. From the viewpoint of kernel machines, it includes least squares support vector machines for classification and regression, kernel principal component analysis (PCA), matrix singular value decomposition, and Parzen-type models. A key element is to first characterize these kernel machines in terms of so-called conjugate feature duality, yielding a representation with visible and hidden units. It is shown how this is related to the energy form in restricted Boltzmann machines, with continuous variables in a nonprobabilistic setting. In this new framework of so-called restricted kernel machine (RKM) representations, the dual variables correspond to hidden features. Deep RKM are obtained by coupling the RKMs. The method is illustrated for deep RKM, consisting of three levels with a least squares support vector machine regression level and two kernel PCA levels. In its primal form also deep feedforward neural networks can be trained within this framework.

7 CFR 981.408 - Inedible kernel.

Code of Federal Regulations, 2014 CFR

2014-01-01

... kernel is modified to mean a kernel, piece, or particle of almond kernel with any defect scored as... purposes of determining inedible kernels, pieces, or particles of almond kernels. [59 FR 39419, Aug. 3...

7 CFR 981.408 - Inedible kernel.

Code of Federal Regulations, 2011 CFR

2011-01-01

... kernel is modified to mean a kernel, piece, or particle of almond kernel with any defect scored as... purposes of determining inedible kernels, pieces, or particles of almond kernels. [59 FR 39419, Aug. 3...

7 CFR 981.408 - Inedible kernel.

Code of Federal Regulations, 2012 CFR

2012-01-01

... kernel is modified to mean a kernel, piece, or particle of almond kernel with any defect scored as... purposes of determining inedible kernels, pieces, or particles of almond kernels. [59 FR 39419, Aug. 3...

7 CFR 981.408 - Inedible kernel.

Code of Federal Regulations, 2013 CFR

2013-01-01

... kernel is modified to mean a kernel, piece, or particle of almond kernel with any defect scored as... purposes of determining inedible kernels, pieces, or particles of almond kernels. [59 FR 39419, Aug. 3...

UNICOS Kernel Internals Application Development

NASA Technical Reports Server (NTRS)

Caredo, Nicholas; Craw, James M. (Technical Monitor)

1995-01-01

Having an understanding of UNICOS Kernel Internals is valuable information. However, having the knowledge is only half the value. The second half comes with knowing how to use this information and apply it to the development of tools. The kernel contains vast amounts of useful information that can be utilized. This paper discusses the intricacies of developing utilities that utilize kernel information. In addition, algorithms, logic, and code will be discussed for accessing kernel information. Code segments will be provided that demonstrate how to locate and read kernel structures. Types of applications that can utilize kernel information will also be discussed.

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.

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.

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.

Applicability of the polynomial chaos expansion method for personalization of a cardiovascular pulse wave propagation model.

PubMed

Huberts, W; Donders, W P; Delhaas, T; van de Vosse, F N

2014-12-01

Patient-specific modeling requires model personalization, which can be achieved in an efficient manner by parameter fixing and parameter prioritization. An efficient variance-based method is using generalized polynomial chaos expansion (gPCE), but it has not been applied in the context of model personalization, nor has it ever been compared with standard variance-based methods for models with many parameters. In this work, we apply the gPCE method to a previously reported pulse wave propagation model and compare the conclusions for model personalization with that of a reference analysis performed with Saltelli's efficient Monte Carlo method. We furthermore differentiate two approaches for obtaining the expansion coefficients: one based on spectral projection (gPCE-P) and one based on least squares regression (gPCE-R). It was found that in general the gPCE yields similar conclusions as the reference analysis but at much lower cost, as long as the polynomial metamodel does not contain unnecessary high order terms. Furthermore, the gPCE-R approach generally yielded better results than gPCE-P. The weak performance of the gPCE-P can be attributed to the assessment of the expansion coefficients using the Smolyak algorithm, which might be hampered by the high number of model parameters and/or by possible non-smoothness in the output space. Copyright © 2014 John Wiley & Sons, Ltd.

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.

An Efficient Method Coupling Kernel Principal Component Analysis with Adjoint-Based Optimal Control and Its Goal-Oriented Extensions

NASA Astrophysics Data System (ADS)

Thimmisetty, C.; Talbot, C.; Tong, C. H.; Chen, X.

2016-12-01

The representativeness of available data poses a significant fundamental challenge to the quantification of uncertainty in geophysical systems. Furthermore, the successful application of machine learning methods to geophysical problems involving data assimilation is inherently constrained by the extent to which obtainable data represent the problem considered. We show how the adjoint method, coupled with optimization based on methods of machine learning, can facilitate the minimization of an objective function defined on a space of significantly reduced dimension. By considering uncertain parameters as constituting a stochastic process, the Karhunen-Loeve expansion and its nonlinear extensions furnish an optimal basis with respect to which optimization using L-BFGS can be carried out. In particular, we demonstrate that kernel PCA can be coupled with adjoint-based optimal control methods to successfully determine the distribution of material parameter values for problems in the context of channelized deformable media governed by the equations of linear elasticity. Since certain subsets of the original data are characterized by different features, the convergence rate of the method in part depends on, and may be limited by, the observations used to furnish the kernel principal component basis. By determining appropriate weights for realizations of the stochastic random field, then, one may accelerate the convergence of the method. To this end, we present a formulation of Weighted PCA combined with a gradient-based means using automatic differentiation to iteratively re-weight observations concurrent with the determination of an optimal reduced set control variables in the feature space. We demonstrate how improvements in the accuracy and computational efficiency of the weighted linear method can be achieved over existing unweighted kernel methods, and discuss nonlinear extensions of the algorithm.

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.

Polynomial Method for PLL Controller Optimization†

PubMed Central

Wang, Ta-Chung; Lall, Sanjay; Chiou, Tsung-Yu

2011-01-01

The Phase-Locked Loop (PLL) is a key component of modern electronic communication and control systems. PLL is designed to extract signals from transmission channels. It plays an important role in systems where it is required to estimate the phase of a received signal, such as carrier tracking from global positioning system satellites. In order to robustly provide centimeter-level accuracy, it is crucial for the PLL to estimate the instantaneous phase of an incoming signal which is usually buried in random noise or some type of interference. This paper presents an approach that utilizes the recent development in the semi-definite programming and sum-of-squares field. A Lyapunov function will be searched as the certificate of the pull-in range of the PLL system. Moreover, a polynomial design procedure is proposed to further refine the controller parameters for system response away from the equilibrium point. Several simulation results as well as an experiment result are provided to show the effectiveness of this approach. PMID:22163973

Density Estimation with Mercer Kernels

NASA Technical Reports Server (NTRS)

Macready, William G.

2003-01-01

We present a new method for density estimation based on Mercer kernels. The density estimate can be understood as the density induced on a data manifold by a mixture of Gaussians fit in a feature space. As is usual, the feature space and data manifold are defined with any suitable positive-definite kernel function. We modify the standard EM algorithm for mixtures of Gaussians to infer the parameters of the density. One benefit of the approach is it's conceptual simplicity, and uniform applicability over many different types of data. Preliminary results are presented for a number of simple problems.

Extending Romanovski polynomials in quantum mechanics

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

Quesne, C.

2013-12-15

Some extensions of the (third-class) Romanovski polynomials (also called Romanovski/pseudo-Jacobi polynomials), which appear in bound-state wavefunctions of rationally extended Scarf II and Rosen-Morse I potentials, are considered. For the former potentials, the generalized polynomials satisfy a finite orthogonality relation, while for the latter an infinite set of relations among polynomials with degree-dependent parameters is obtained. Both types of relations are counterparts of those known for conventional polynomials. In the absence of any direct information on the zeros of the Romanovski polynomials present in denominators, the regularity of the constructed potentials is checked by taking advantage of the disconjugacy properties ofmore » second-order differential equations of Schrödinger type. It is also shown that on going from Scarf I to Scarf II or from Rosen-Morse II to Rosen-Morse I potentials, the variety of rational extensions is narrowed down from types I, II, and III to type III only.« less

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.

Information entropy of Gegenbauer polynomials and Gaussian quadrature

NASA Astrophysics Data System (ADS)

Sánchez-Ruiz, Jorge

2003-05-01

In a recent paper (Buyarov V S, López-Artés P, Martínez-Finkelshtein A and Van Assche W 2000 J. Phys. A: Math. Gen. 33 6549-60), an efficient method was provided for evaluating in closed form the information entropy of the Gegenbauer polynomials C(lambda)n(x) in the case when lambda = l in Bbb N. For given values of n and l, this method requires the computation by means of recurrence relations of two auxiliary polynomials, P(x) and H(x), of degrees 2l - 2 and 2l - 4, respectively. Here it is shown that P(x) is related to the coefficients of the Gaussian quadrature formula for the Gegenbauer weights wl(x) = (1 - x2)l-1/2, and this fact is used to obtain the explicit expression of P(x). From this result, an explicit formula is also given for the polynomial S(x) = limnrightarrowinfty P(1 - x/(2n2)), which is relevant to the study of the asymptotic (n rightarrow infty with l fixed) behaviour of the entropy.

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.

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.

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.

7 CFR 981.7 - Edible kernel.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Edible kernel. 981.7 Section 981.7 Agriculture... Regulating Handling Definitions § 981.7 Edible kernel. Edible kernel means a kernel, piece, or particle of almond kernel that is not inedible. [41 FR 26852, June 30, 1976] ...

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…

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.

A simple and fast method for computing the relativistic Compton Scattering Kernel for radiative transfer

NASA Technical Reports Server (NTRS)

Kershaw, David S.; Prasad, Manoj K.; Beason, J. Douglas

1986-01-01

The Klein-Nishina differential cross section averaged over a relativistic Maxwellian electron distribution is analytically reduced to a single integral, which can then be rapidly evaluated in a variety of ways. A particularly fast method for numerically computing this single integral is presented. This is, to the authors' knowledge, the first correct computation of the Compton scattering kernel.

Unconventional protein sources: apricot seed kernels.

PubMed

Gabrial, G N; El-Nahry, F I; Awadalla, M Z; Girgis, S M

1981-09-01

Hamawy apricot seed kernels (sweet), Amar apricot seed kernels (bitter) and treated Amar apricot kernels (bitterness removed) were evaluated biochemically. All kernels were found to be high in fat (42.2--50.91%), protein (23.74--25.70%) and fiber (15.08--18.02%). Phosphorus, calcium, and iron were determined in all experimental samples. The three different apricot seed kernels were used for extensive study including the qualitative determination of the amino acid constituents by acid hydrolysis, quantitative determination of some amino acids, and biological evaluation of the kernel proteins in order to use them as new protein sources. Weanling albino rats failed to grow on diets containing the Amar apricot seed kernels due to low food consumption because of its bitterness. There was no loss in weight in that case. The Protein Efficiency Ratio data and blood analysis results showed the Hamawy apricot seed kernels to be higher in biological value than treated apricot seed kernels. The Net Protein Ratio data which accounts for both weight, maintenance and growth showed the treated apricot seed kernels to be higher in biological value than both Hamawy and Amar kernels. The Net Protein Ratio for the last two kernels were nearly equal.

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

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

Nodal Statistics for the Van Vleck Polynomials

NASA Astrophysics Data System (ADS)

Bourget, Alain

The Van Vleck polynomials naturally arise from the generalized Lamé equation as the polynomials of degree for which Eq. (1) has a polynomial solution of some degree k. In this paper, we compute the limiting distribution, as well as the limiting mean level spacings distribution of the zeros of any Van Vleck polynomial as N --> ∞.

7 CFR 981.8 - Inedible kernel.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Inedible kernel. 981.8 Section 981.8 Agriculture... Regulating Handling Definitions § 981.8 Inedible kernel. Inedible kernel means a kernel, piece, or particle of almond kernel with any defect scored as serious damage, or damage due to mold, gum, shrivel, or...

7 CFR 51.1415 - Inedible kernels.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 2 2010-01-01 2010-01-01 false Inedible kernels. 51.1415 Section 51.1415 Agriculture... Standards for Grades of Pecans in the Shell 1 Definitions § 51.1415 Inedible kernels. Inedible kernels means that the kernel or pieces of kernels are rancid, moldy, decayed, injured by insects or otherwise...

Quadratic polynomial interpolation on triangular domain

NASA Astrophysics Data System (ADS)

Li, Ying; Zhang, Congcong; Yu, Qian

2018-04-01

In the simulation of natural terrain, the continuity of sample points are not in consonance with each other always, traditional interpolation methods often can't faithfully reflect the shape information which lie in data points. So, a new method for constructing the polynomial interpolation surface on triangular domain is proposed. Firstly, projected the spatial scattered data points onto a plane and then triangulated them; Secondly, A C1 continuous piecewise quadric polynomial patch was constructed on each vertex, all patches were required to be closed to the line-interpolation one as far as possible. Lastly, the unknown quantities were gotten by minimizing the object functions, and the boundary points were treated specially. The result surfaces preserve as many properties of data points as possible under conditions of satisfying certain accuracy and continuity requirements, not too convex meantime. New method is simple to compute and has a good local property, applicable to shape fitting of mines and exploratory wells and so on. The result of new surface is given in experiments.

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.

7 CFR 981.408 - Inedible kernel.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Inedible kernel. 981.408 Section 981.408 Agriculture... Administrative Rules and Regulations § 981.408 Inedible kernel. Pursuant to § 981.8, the definition of inedible kernel is modified to mean a kernel, piece, or particle of almond kernel with any defect scored as...

On Certain Wronskians of Multiple Orthogonal Polynomials

NASA Astrophysics Data System (ADS)

Zhang, Lun; Filipuk, Galina

2014-11-01

We consider determinants of Wronskian type whose entries are multiple orthogonal polynomials associated with a path connecting two multi-indices. By assuming that the weight functions form an algebraic Chebyshev (AT) system, we show that the polynomials represented by the Wronskians keep a constant sign in some cases, while in some other cases oscillatory behavior appears, which generalizes classical results for orthogonal polynomials due to Karlin and Szegő. There are two applications of our results. The first application arises from the observation that the m-th moment of the average characteristic polynomials for multiple orthogonal polynomial ensembles can be expressed as a Wronskian of the type II multiple orthogonal polynomials. Hence, it is straightforward to obtain the distinct behavior of the moments for odd and even m in a special multiple orthogonal ensemble - the AT ensemble. As the second application, we derive some Turán type inequalities for m! ultiple Hermite and multiple Laguerre polynomials (of two kinds). Finally, we study numerically the geometric configuration of zeros for the Wronskians of these multiple orthogonal polynomials. We observe that the zeros have regular configurations in the complex plane, which might be of independent interest.

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.

Defect Analysis Of Quality Palm Kernel Meal Using Statistical Quality Control In Kernels Factory

NASA Astrophysics Data System (ADS)

Sembiring, M. T.; Marbun, N. J.

2018-04-01

The production quality has an important impact retain the totality of characteristics of a product or service to pay attention to its capabilities to meet the needs that have been established. Quality criteria Palm Kernel Meal (PKM) set Factory kernel is as follows: oil content: max 8.50%, water content: max 12,00% and impurity content: max 4.00% While the average quality of the oil content of 8.94%, the water content of 5.51%, and 8.45% impurity content. To identify the defective product quality PKM produced, then used a method of analysis using Statistical Quality Control (SQC). PKM Plant Quality Kernel shows the oil content was 0.44% excess of a predetermined maximum value, and 4.50% impurity content. With excessive PKM content of oil and dirt cause disability content of production for oil, amounted to 854.6078 kg PKM and 8643.193 kg impurity content of PKM. Analysis of the results of cause and effect diagram and SQC, the factors that lead to poor quality of PKM is Ampere second press oil expeller and hours second press oil expeller.

Polynomial Graphs and Symmetry

ERIC Educational Resources Information Center

Goehle, Geoff; Kobayashi, Mitsuo

2013-01-01

Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…

Mathematics of Zernike polynomials: a review.

PubMed

McAlinden, Colm; McCartney, Mark; Moore, Jonathan

2011-11-01

Monochromatic aberrations of the eye principally originate from the cornea and the crystalline lens. Aberrometers operate via differing principles but function by either analysing the reflected wavefront from the retina or by analysing an image on the retina. Aberrations may be described as lower order or higher order aberrations with Zernike polynomials being the most commonly employed fitting method. The complex mathematical aspects with regards the Zernike polynomial expansion series are detailed in this review. Refractive surgery has been a key clinical application of aberrometers; however, more recently aberrometers have been used in a range of other areas ophthalmology including corneal diseases, cataract and retinal imaging. © 2011 The Authors. Clinical and Experimental Ophthalmology © 2011 Royal Australian and New Zealand College of Ophthalmologists.

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.

MR-guided dynamic PET reconstruction with the kernel method and spectral temporal basis functions

NASA Astrophysics Data System (ADS)

Novosad, Philip; Reader, Andrew J.

2016-06-01

Recent advances in dynamic positron emission tomography (PET) reconstruction have demonstrated that it is possible to achieve markedly improved end-point kinetic parameter maps by incorporating a temporal model of the radiotracer directly into the reconstruction algorithm. In this work we have developed a highly constrained, fully dynamic PET reconstruction algorithm incorporating both spectral analysis temporal basis functions and spatial basis functions derived from the kernel method applied to a co-registered T1-weighted magnetic resonance (MR) image. The dynamic PET image is modelled as a linear combination of spatial and temporal basis functions, and a maximum likelihood estimate for the coefficients can be found using the expectation-maximization (EM) algorithm. Following reconstruction, kinetic fitting using any temporal model of interest can be applied. Based on a BrainWeb T1-weighted MR phantom, we performed a realistic dynamic [18F]FDG simulation study with two noise levels, and investigated the quantitative performance of the proposed reconstruction algorithm, comparing it with reconstructions incorporating either spectral analysis temporal basis functions alone or kernel spatial basis functions alone, as well as with conventional frame-independent reconstruction. Compared to the other reconstruction algorithms, the proposed algorithm achieved superior performance, offering a decrease in spatially averaged pixel-level root-mean-square-error on post-reconstruction kinetic parametric maps in the grey/white matter, as well as in the tumours when they were present on the co-registered MR image. When the tumours were not visible in the MR image, reconstruction with the proposed algorithm performed similarly to reconstruction with spectral temporal basis functions and was superior to both conventional frame-independent reconstruction and frame-independent reconstruction with kernel spatial basis functions. Furthermore, we demonstrate that a joint spectral/kernel

MR-guided dynamic PET reconstruction with the kernel method and spectral temporal basis functions.

PubMed

Novosad, Philip; Reader, Andrew J

2016-06-21

Recent advances in dynamic positron emission tomography (PET) reconstruction have demonstrated that it is possible to achieve markedly improved end-point kinetic parameter maps by incorporating a temporal model of the radiotracer directly into the reconstruction algorithm. In this work we have developed a highly constrained, fully dynamic PET reconstruction algorithm incorporating both spectral analysis temporal basis functions and spatial basis functions derived from the kernel method applied to a co-registered T1-weighted magnetic resonance (MR) image. The dynamic PET image is modelled as a linear combination of spatial and temporal basis functions, and a maximum likelihood estimate for the coefficients can be found using the expectation-maximization (EM) algorithm. Following reconstruction, kinetic fitting using any temporal model of interest can be applied. Based on a BrainWeb T1-weighted MR phantom, we performed a realistic dynamic [(18)F]FDG simulation study with two noise levels, and investigated the quantitative performance of the proposed reconstruction algorithm, comparing it with reconstructions incorporating either spectral analysis temporal basis functions alone or kernel spatial basis functions alone, as well as with conventional frame-independent reconstruction. Compared to the other reconstruction algorithms, the proposed algorithm achieved superior performance, offering a decrease in spatially averaged pixel-level root-mean-square-error on post-reconstruction kinetic parametric maps in the grey/white matter, as well as in the tumours when they were present on the co-registered MR image. When the tumours were not visible in the MR image, reconstruction with the proposed algorithm performed similarly to reconstruction with spectral temporal basis functions and was superior to both conventional frame-independent reconstruction and frame-independent reconstruction with kernel spatial basis functions. Furthermore, we demonstrate that a joint spectral/kernel

Kernel Method Based Human Model for Enhancing Interactive Evolutionary Optimization

PubMed Central

Zhao, Qiangfu; Liu, Yong

2015-01-01

A fitness landscape presents the relationship between individual and its reproductive success in evolutionary computation (EC). However, discrete and approximate landscape in an original search space may not support enough and accurate information for EC search, especially in interactive EC (IEC). The fitness landscape of human subjective evaluation in IEC is very difficult and impossible to model, even with a hypothesis of what its definition might be. In this paper, we propose a method to establish a human model in projected high dimensional search space by kernel classification for enhancing IEC search. Because bivalent logic is a simplest perceptual paradigm, the human model is established by considering this paradigm principle. In feature space, we design a linear classifier as a human model to obtain user preference knowledge, which cannot be supported linearly in original discrete search space. The human model is established by this method for predicting potential perceptual knowledge of human. With the human model, we design an evolution control method to enhance IEC search. From experimental evaluation results with a pseudo-IEC user, our proposed model and method can enhance IEC search significantly. PMID:25879050

Approximating exponential and logarithmic functions using polynomial interpolation

NASA Astrophysics Data System (ADS)

Gordon, Sheldon P.; Yang, Yajun

2017-04-01

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is analysed. The results of interpolating polynomials are compared with those of Taylor polynomials.

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.

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.

Percolation critical polynomial as a graph invariant

DOE PAGES

Scullard, Christian R.

2012-10-18

Every lattice for which the bond percolation critical probability can be found exactly possesses a critical polynomial, with the root in [0; 1] providing the threshold. Recent work has demonstrated that this polynomial may be generalized through a definition that can be applied on any periodic lattice. The polynomial depends on the lattice and on its decomposition into identical finite subgraphs, but once these are specified, the polynomial is essentially unique. On lattices for which the exact percolation threshold is unknown, the polynomials provide approximations for the critical probability with the estimates appearing to converge to the exact answer withmore » increasing subgraph size. In this paper, I show how the critical polynomial can be viewed as a graph invariant like the Tutte polynomial. In particular, the critical polynomial is computed on a finite graph and may be found using the deletion-contraction algorithm. This allows calculation on a computer, and I present such results for the kagome lattice using subgraphs of up to 36 bonds. For one of these, I find the prediction p c = 0:52440572:::, which differs from the numerical value, p c = 0:52440503(5), by only 6:9 X 10 -7.« less

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.

Investigation on imperfection sensitivity of composite cylindrical shells using the nonlinearity reduction technique and the polynomial chaos method

NASA Astrophysics Data System (ADS)

Liang, Ke; Sun, Qin; Liu, Xiaoran

2018-05-01

The theoretical buckling load of a perfect cylinder must be reduced by a knock-down factor to account for structural imperfections. The EU project DESICOS proposed a new robust design for imperfection-sensitive composite cylindrical shells using the combination of deterministic and stochastic simulations, however the high computational complexity seriously affects its wider application in aerospace structures design. In this paper, the nonlinearity reduction technique and the polynomial chaos method are implemented into the robust design process, to significantly lower computational costs. The modified Newton-type Koiter-Newton approach which largely reduces the number of degrees of freedom in the nonlinear finite element model, serves as the nonlinear buckling solver to trace the equilibrium paths of geometrically nonlinear structures efficiently. The non-intrusive polynomial chaos method provides the buckling load with an approximate chaos response surface with respect to imperfections and uses buckling solver codes as black boxes. A fast large-sample study can be applied using the approximate chaos response surface to achieve probability characteristics of buckling loads. The performance of the method in terms of reliability, accuracy and computational effort is demonstrated with an unstiffened CFRP cylinder.

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.

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.

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

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.

On the logarithmic-singularity correction in the kernel function method of subsonic lifting-surface theory

NASA Technical Reports Server (NTRS)

Lan, C. E.; Lamar, J. E.

1977-01-01

A logarithmic-singularity correction factor is derived for use in kernel function methods associated with Multhopp's subsonic lifting-surface theory. Because of the form of the factor, a relation was formulated between the numbers of chordwise and spanwise control points needed for good accuracy. This formulation is developed and discussed. Numerical results are given to show the improvement of the computation with the new correction factor.

7 CFR 981.9 - Kernel weight.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Kernel weight. 981.9 Section 981.9 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing Agreements... Regulating Handling Definitions § 981.9 Kernel weight. Kernel weight means the weight of kernels, including...

7 CFR 51.2295 - Half kernel.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 2 2010-01-01 2010-01-01 false Half kernel. 51.2295 Section 51.2295 Agriculture... Standards for Shelled English Walnuts (Juglans Regia) Definitions § 51.2295 Half kernel. Half kernel means the separated half of a kernel with not more than one-eighth broken off. ...

Polynomial approximation of Poincare maps for Hamiltonian system

NASA Technical Reports Server (NTRS)

Froeschle, Claude; Petit, Jean-Marc

1992-01-01

Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.

Oecophylla longinoda (Hymenoptera: Formicidae) Lead to Increased Cashew Kernel Size and Kernel Quality.

PubMed

Anato, F M; Sinzogan, A A C; Offenberg, J; Adandonon, A; Wargui, R B; Deguenon, J M; Ayelo, P M; Vayssières, J-F; Kossou, D K

2017-06-01

Weaver ants, Oecophylla spp., are known to positively affect cashew, Anacardium occidentale L., raw nut yield, but their effects on the kernels have not been reported. We compared nut size and the proportion of marketable kernels between raw nuts collected from trees with and without ants. Raw nuts collected from trees with weaver ants were 2.9% larger than nuts from control trees (i.e., without weaver ants), leading to 14% higher proportion of marketable kernels. On trees with ants, the kernel: raw nut ratio from nuts damaged by formic acid was 4.8% lower compared with nondamaged nuts from the same trees. Weaver ants provided three benefits to cashew production by increasing yields, yielding larger nuts, and by producing greater proportions of marketable kernel mass. © The Authors 2017. Published by Oxford University Press on behalf of Entomological Society of America. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Stochastic subset selection for learning with kernel machines.

PubMed

Rhinelander, Jason; Liu, Xiaoping P

2012-06-01

Kernel machines have gained much popularity in applications of machine learning. Support vector machines (SVMs) are a subset of kernel machines and generalize well for classification, regression, and anomaly detection tasks. The training procedure for traditional SVMs involves solving a quadratic programming (QP) problem. The QP problem scales super linearly in computational effort with the number of training samples and is often used for the offline batch processing of data. Kernel machines operate by retaining a subset of observed data during training. The data vectors contained within this subset are referred to as support vectors (SVs). The work presented in this paper introduces a subset selection method for the use of kernel machines in online, changing environments. Our algorithm works by using a stochastic indexing technique when selecting a subset of SVs when computing the kernel expansion. The work described here is novel because it separates the selection of kernel basis functions from the training algorithm used. The subset selection algorithm presented here can be used in conjunction with any online training technique. It is important for online kernel machines to be computationally efficient due to the real-time requirements of online environments. Our algorithm is an important contribution because it scales linearly with the number of training samples and is compatible with current training techniques. Our algorithm outperforms standard techniques in terms of computational efficiency and provides increased recognition accuracy in our experiments. We provide results from experiments using both simulated and real-world data sets to verify our algorithm.

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.

A New Navigation Satellite Clock Bias Prediction Method Based on Modified Clock-bias Quadratic Polynomial Model

NASA Astrophysics Data System (ADS)

Wang, Y. P.; Lu, Z. P.; Sun, D. S.; Wang, N.

2016-01-01

In order to better express the characteristics of satellite clock bias (SCB) and improve SCB prediction precision, this paper proposed a new SCB prediction model which can take physical characteristics of space-borne atomic clock, the cyclic variation, and random part of SCB into consideration. First, the new model employs a quadratic polynomial model with periodic items to fit and extract the trend term and cyclic term of SCB; then based on the characteristics of fitting residuals, a time series ARIMA ~(Auto-Regressive Integrated Moving Average) model is used to model the residuals; eventually, the results from the two models are combined to obtain final SCB prediction values. At last, this paper uses precise SCB data from IGS (International GNSS Service) to conduct prediction tests, and the results show that the proposed model is effective and has better prediction performance compared with the quadratic polynomial model, grey model, and ARIMA model. In addition, the new method can also overcome the insufficiency of the ARIMA model in model recognition and order determination.

Kernel abortion in maize : I. Carbohydrate concentration patterns and Acid invertase activity of maize kernels induced to abort in vitro.

PubMed

Hanft, J M; Jones, R J

1986-06-01

Kernels cultured in vitro were induced to abort by high temperature (35 degrees C) and by culturing six kernels/cob piece. Aborting kernels failed to enter a linear phase of dry mass accumulation and had a final mass that was less than 6% of nonaborting field-grown kernels. Kernels induced to abort by high temperature failed to synthesize starch in the endosperm and had elevated sucrose concentrations and low fructose and glucose concentrations in the pedicel during early growth compared to nonaborting kernels. Kernels induced to abort by high temperature also had much lower pedicel soluble acid invertase activities than did nonaborting kernels. These results suggest that high temperature during the lag phase of kernel growth may impair the process of sucrose unloading in the pedicel by indirectly inhibiting soluble acid invertase activity and prevent starch synthesis in the endosperm. Kernels induced to abort by culturing six kernels/cob piece had reduced pedicel fructose, glucose, and sucrose concentrations compared to kernels from field-grown ears. These aborting kernels also had a lower pedicel soluble acid invertase activity compared to nonaborting kernels from the same cob piece and from field-grown ears. The low invertase activity in pedicel tissue of the aborting kernels was probably caused by a lack of substrate (sucrose) for the invertase to cleave due to the intense competition for available assimilates. In contrast to kernels cultured at 35 degrees C, aborting kernels from cob pieces containing all six kernels accumulated starch in a linear fashion. These results indicate that kernels cultured six/cob piece abort because of an inadequate supply of sugar and are similar to apical kernels from field-grown ears that often abort prior to the onset of linear growth.

A fast object-oriented Matlab implementation of the Reproducing Kernel Particle Method

NASA Astrophysics Data System (ADS)

Barbieri, Ettore; Meo, Michele

2012-05-01

Novel numerical methods, known as Meshless Methods or Meshfree Methods and, in a wider perspective, Partition of Unity Methods, promise to overcome most of disadvantages of the traditional finite element techniques. The absence of a mesh makes meshfree methods very attractive for those problems involving large deformations, moving boundaries and crack propagation. However, meshfree methods still have significant limitations that prevent their acceptance among researchers and engineers, namely the computational costs. This paper presents an in-depth analysis of computational techniques to speed-up the computation of the shape functions in the Reproducing Kernel Particle Method and Moving Least Squares, with particular focus on their bottlenecks, like the neighbour search, the inversion of the moment matrix and the assembly of the stiffness matrix. The paper presents numerous computational solutions aimed at a considerable reduction of the computational times: the use of kd-trees for the neighbour search, sparse indexing of the nodes-points connectivity and, most importantly, the explicit and vectorized inversion of the moment matrix without using loops and numerical routines.

An Approximate Approach to Automatic Kernel Selection.

PubMed

Ding, Lizhong; Liao, Shizhong

2016-02-02

Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.

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.

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.

Viscozyme L pretreatment on palm kernels improved the aroma of palm kernel oil after kernel roasting.

PubMed

Zhang, Wencan; Leong, Siew Mun; Zhao, Feifei; Zhao, Fangju; Yang, Tiankui; Liu, Shaoquan

2018-05-01

With an interest to enhance the aroma of palm kernel oil (PKO), Viscozyme L, an enzyme complex containing a wide range of carbohydrases, was applied to alter the carbohydrates in palm kernels (PK) to modulate the formation of volatiles upon kernel roasting. After Viscozyme treatment, the content of simple sugars and free amino acids in PK increased by 4.4-fold and 4.5-fold, respectively. After kernel roasting and oil extraction, significantly more 2,5-dimethylfuran, 2-[(methylthio)methyl]-furan, 1-(2-furanyl)-ethanone, 1-(2-furyl)-2-propanone, 5-methyl-2-furancarboxaldehyde and 2-acetyl-5-methylfuran but less 2-furanmethanol and 2-furanmethanol acetate were found in treated PKO; the correlation between their formation and simple sugar profile was estimated by using partial least square regression (PLS1). Obvious differences in pyrroles and Strecker aldehydes were also found between the control and treated PKOs. Principal component analysis (PCA) clearly discriminated the treated PKOs from that of control PKOs on the basis of all volatile compounds. Such changes in volatiles translated into distinct sensory attributes, whereby treated PKO was more caramelic and burnt after aqueous extraction and more nutty, roasty, caramelic and smoky after solvent extraction. Copyright © 2018 Elsevier Ltd. All rights reserved.

Toward an alternative hardness kernel matrix structure in the Electronegativity Equalization Method (EEM).

PubMed

Chaves, J; Barroso, J M; Bultinck, P; Carbó-Dorca, R

2006-01-01

This study presents an alternative of the Electronegativity Equalization Method (EEM), where the usual Coulomb kernel has been transformed into a smooth function. The new framework, as the classical EEM, permits fast calculations of atomic charges in a given molecule for a small computational cost. The original EEM procedure needs to previously calibrate the different implied atomic hardness and electronegativity, using a chosen set of molecules. In the new EEM algorithm half the number of parameters needs to be calibrated, since a relationship between electronegativities and hardnesses has been found.

Simple Proof of Jury Test for Complex Polynomials

NASA Astrophysics Data System (ADS)

Choo, Younseok; Kim, Dongmin

Recently some attempts have been made in the literature to give simple proofs of Jury test for real polynomials. This letter presents a similar result for complex polynomials. A simple proof of Jury test for complex polynomials is provided based on the Rouché's Theorem and a single-parameter characterization of Schur stability property for complex polynomials.

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

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

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

2016-09-01

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

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

Nondestructive In Situ Measurement Method for Kernel Moisture Content in Corn Ear.

PubMed

Zhang, Han-Lin; Ma, Qin; Fan, Li-Feng; Zhao, Peng-Fei; Wang, Jian-Xu; Zhang, Xiao-Dong; Zhu, De-Hai; Huang, Lan; Zhao, Dong-Jie; Wang, Zhong-Yi

2016-12-20

Moisture content is an important factor in corn breeding and cultivation. A corn breed with low moisture at harvest is beneficial for mechanical operations, reduces drying and storage costs after harvesting and, thus, reduces energy consumption. Nondestructive measurement of kernel moisture in an intact corn ear allows us to select corn varieties with seeds that have high dehydration speeds in the mature period. We designed a sensor using a ring electrode pair for nondestructive measurement of the kernel moisture in a corn ear based on a high-frequency detection circuit. Through experiments using the effective scope of the electrodes' electric field, we confirmed that the moisture in the corn cob has little effect on corn kernel moisture measurement. Before the sensor was applied in practice, we investigated temperature and conductivity effects on the output impedance. Results showed that the temperature was linearly related to the output impedance (both real and imaginary parts) of the measurement electrodes and the detection circuit's output voltage. However, the conductivity has a non-monotonic dependence on the output impedance (both real and imaginary parts) of the measurement electrodes and the output voltage of the high-frequency detection circuit. Therefore, we reduced the effect of conductivity on the measurement results through measurement frequency selection. Corn moisture measurement results showed a quadric regression between corn ear moisture and the imaginary part of the output impedance, and there is also a quadric regression between corn kernel moisture and the high-frequency detection circuit output voltage at 100 MHz. In this study, two corn breeds were measured using our sensor and gave R ² values for the quadric regression equation of 0.7853 and 0.8496.

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…

7 CFR 51.1441 - Half-kernel.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 2 2010-01-01 2010-01-01 false Half-kernel. 51.1441 Section 51.1441 Agriculture... Standards for Grades of Shelled Pecans Definitions § 51.1441 Half-kernel. Half-kernel means one of the separated halves of an entire pecan kernel with not more than one-eighth of its original volume missing...

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 particle swarm optimized kernel-based clustering method for crop mapping from multi-temporal polarimetric L-band SAR observations

NASA Astrophysics Data System (ADS)

Tamiminia, Haifa; Homayouni, Saeid; McNairn, Heather; Safari, Abdoreza

2017-06-01

Polarimetric Synthetic Aperture Radar (PolSAR) data, thanks to their specific characteristics such as high resolution, weather and daylight independence, have become a valuable source of information for environment monitoring and management. The discrimination capability of observations acquired by these sensors can be used for land cover classification and mapping. The aim of this paper is to propose an optimized kernel-based C-means clustering algorithm for agriculture crop mapping from multi-temporal PolSAR data. Firstly, several polarimetric features are extracted from preprocessed data. These features are linear polarization intensities, and several statistical and physical based decompositions such as Cloude-Pottier, Freeman-Durden and Yamaguchi techniques. Then, the kernelized version of hard and fuzzy C-means clustering algorithms are applied to these polarimetric features in order to identify crop types. The kernel function, unlike the conventional partitioning clustering algorithms, simplifies the non-spherical and non-linearly patterns of data structure, to be clustered easily. In addition, in order to enhance the results, Particle Swarm Optimization (PSO) algorithm is used to tune the kernel parameters, cluster centers and to optimize features selection. The efficiency of this method was evaluated by using multi-temporal UAVSAR L-band images acquired over an agricultural area near Winnipeg, Manitoba, Canada, during June and July in 2012. The results demonstrate more accurate crop maps using the proposed method when compared to the classical approaches, (e.g. 12% improvement in general). In addition, when the optimization technique is used, greater improvement is observed in crop classification, e.g. 5% in overall. Furthermore, a strong relationship between Freeman-Durden volume scattering component, which is related to canopy structure, and phenological growth stages is observed.

Multi-class Mode of Action Classification of Toxic Compounds Using Logic Based Kernel Methods.

PubMed

Lodhi, Huma; Muggleton, Stephen; Sternberg, Mike J E

2010-09-17

Toxicity prediction is essential for drug design and development of effective therapeutics. In this paper we present an in silico strategy, to identify the mode of action of toxic compounds, that is based on the use of a novel logic based kernel method. The technique uses support vector machines in conjunction with the kernels constructed from first order rules induced by an Inductive Logic Programming system. It constructs multi-class models by using a divide and conquer reduction strategy that splits multi-classes into binary groups and solves each individual problem recursively hence generating an underlying decision list structure. In order to evaluate the effectiveness of the approach for chemoinformatics problems like predictive toxicology, we apply it to toxicity classification in aquatic systems. The method is used to identify and classify 442 compounds with respect to the mode of action. The experimental results show that the technique successfully classifies toxic compounds and can be useful in assessing environmental risks. Experimental comparison of the performance of the proposed multi-class scheme with the standard multi-class Inductive Logic Programming algorithm and multi-class Support Vector Machine yields statistically significant results and demonstrates the potential power and benefits of the approach in identifying compounds of various toxic mechanisms. Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Discrete Tchebycheff orthonormal polynomials and applications

NASA Technical Reports Server (NTRS)

Lear, W. M.

1980-01-01

Discrete Tchebycheff orthonormal polynomials offer a convenient way to make least squares polynomial fits of uniformly spaced discrete data. Computer programs to do so are simple and fast, and appear to be less affected by computer roundoff error, for the higher order fits, than conventional least squares programs. They are useful for any application of polynomial least squares fits: approximation of mathematical functions, noise analysis of radar data, and real time smoothing of noisy data, to name a few.

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

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.

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.

Kernel Abortion in Maize 1

PubMed Central

Hanft, Jonathan M.; Jones, Robert J.

1986-01-01

This study was designed to compare the uptake and distribution of 14C among fructose, glucose, sucrose, and starch in the cob, pedicel, and endosperm tissues of maize (Zea mays L.) kernels induced to abort by high temperature with those that develop normally. Kernels cultured in vitro at 30 and 35°C were transferred to [14C]sucrose media 10 days after pollination. Kernels cultured at 35°C aborted prior to the onset of linear dry matter accumulation. Significant uptake into the cob, pedicel, and endosperm of radioactivity associated with the soluble and starch fractions of the tissues was detected after 24 hours in culture on labeled media. After 8 days in culture on [14C]sucrose media, 48 and 40% of the radioactivity associated with the cob carbohydrates was found in the reducing sugars at 30 and 35°C, respectively. This indicates that some of the sucrose taken up by the cob tissue was cleaved to fructose and glucose in the cob. Of the total carbohydrates, a higher percentage of label was associated with sucrose and a lower percentage with fructose and glucose in pedicel tissue of kernels cultured at 35°C compared to kernels cultured at 30°C. These results indicate that sucrose was not cleaved to fructose and glucose as rapidly during the unloading process in the pedicel of kernels induced to abort by high temperature. Kernels cultured at 35°C had a much lower proportion of label associated with endosperm starch (29%) than did kernels cultured at 30°C (89%). Kernels cultured at 35°C had a correspondingly higher proportion of 14C in endosperm fructose, glucose, and sucrose. These results indicate that starch synthesis in the endosperm is strongly inhibited in kernels induced to abort by high temperature even though there is an adequate supply of sugar. PMID:16664847

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 extensive analysis of disease-gene associations using network integration and fast kernel-based gene prioritization methods.

PubMed

Valentini, Giorgio; Paccanaro, Alberto; Caniza, Horacio; Romero, Alfonso E; Re, Matteo

2014-06-01

In the context of "network medicine", gene prioritization methods represent one of the main tools to discover candidate disease genes by exploiting the large amount of data covering different types of functional relationships between genes. Several works proposed to integrate multiple sources of data to improve disease gene prioritization, but to our knowledge no systematic studies focused on the quantitative evaluation of the impact of network integration on gene prioritization. In this paper, we aim at providing an extensive analysis of gene-disease associations not limited to genetic disorders, and a systematic comparison of different network integration methods for gene prioritization. We collected nine different functional networks representing different functional relationships between genes, and we combined them through both unweighted and weighted network integration methods. We then prioritized genes with respect to each of the considered 708 medical subject headings (MeSH) diseases by applying classical guilt-by-association, random walk and random walk with restart algorithms, and the recently proposed kernelized score functions. The results obtained with classical random walk algorithms and the best single network achieved an average area under the curve (AUC) across the 708 MeSH diseases of about 0.82, while kernelized score functions and network integration boosted the average AUC to about 0.89. Weighted integration, by exploiting the different "informativeness" embedded in different functional networks, outperforms unweighted integration at 0.01 significance level, according to the Wilcoxon signed rank sum test. For each MeSH disease we provide the top-ranked unannotated candidate genes, available for further bio-medical investigation. Network integration is necessary to boost the performances of gene prioritization methods. Moreover the methods based on kernelized score functions can further enhance disease gene ranking results, by adopting both

On multiple orthogonal polynomials for discrete Meixner measures

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

Sorokin, Vladimir N

2010-12-07

The paper examines two examples of multiple orthogonal polynomials generalizing orthogonal polynomials of a discrete variable, meaning thereby the Meixner polynomials. One example is bound up with a discrete Nikishin system, and the other leads to essentially new effects. The limit distribution of the zeros of polynomials is obtained in terms of logarithmic equilibrium potentials and in terms of algebraic curves. Bibliography: 9 titles.

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.

Stochastic Modeling of Flow-Structure Interactions using Generalized Polynomial Chaos

DTIC Science & Technology

2001-09-11

Some basic hypergeometric polynomials that generalize Jacobi polynomials . Memoirs Amer. Math. Soc...scheme, which is represented as a tree structure in figure 1 (following [24]), classifies the hypergeometric orthogonal polynomials and indicates the...2F0(1) 2F0(0) Figure 1: The Askey scheme of orthogonal polynomials The orthogonal polynomials associated with the generalized polynomial chaos,

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

Gaussian quadrature for multiple orthogonal polynomials

NASA Astrophysics Data System (ADS)

Coussement, Jonathan; van Assche, Walter

2005-06-01

We study multiple orthogonal polynomials of type I and type II, which have orthogonality conditions with respect to r measures. These polynomials are connected by their recurrence relation of order r+1. First we show a relation with the eigenvalue problem of a banded lower Hessenberg matrix Ln, containing the recurrence coefficients. As a consequence, we easily find that the multiple orthogonal polynomials of type I and type II satisfy a generalized Christoffel-Darboux identity. Furthermore, we explain the notion of multiple Gaussian quadrature (for proper multi-indices), which is an extension of the theory of Gaussian quadrature for orthogonal polynomials and was introduced by Borges. In particular, we show that the quadrature points and quadrature weights can be expressed in terms of the eigenvalue problem of Ln.

Dirac(-Pauli), Fokker-Planck equations and exceptional Laguerre polynomials

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

Ho, Choon-Lin, E-mail: hcl@mail.tku.edu.tw

2011-04-15

Research Highlights: > Physical examples involving exceptional orthogonal polynomials. > Exceptional polynomials as deformations of classical orthogonal polynomials. > Exceptional polynomials from Darboux-Crum transformation. - Abstract: An interesting discovery in the last two years in the field of mathematical physics has been the exceptional X{sub l} Laguerre and Jacobi polynomials. Unlike the well-known classical orthogonal polynomials which start with constant terms, these new polynomials have lowest degree l = 1, 2, and ..., and yet they form complete set with respect to some positive-definite measure. While the mathematical properties of these new X{sub l} polynomials deserve further analysis, it ismore » also of interest to see if they play any role in physical systems. In this paper we indicate some physical models in which these new polynomials appear as the main part of the eigenfunctions. The systems we consider include the Dirac equations coupled minimally and non-minimally with some external fields, and the Fokker-Planck equations. The systems presented here have enlarged the number of exactly solvable physical systems known so far.« less

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.

Graphical Solution of Polynomial Equations

ERIC Educational Resources Information Center

Grishin, Anatole

2009-01-01

Graphing utilities, such as the ubiquitous graphing calculator, are often used in finding the approximate real roots of polynomial equations. In this paper the author offers a simple graphing technique that allows one to find all solutions of a polynomial equation (1) of arbitrary degree; (2) with real or complex coefficients; and (3) possessing…

Approximating smooth functions using algebraic-trigonometric polynomials

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

Sharapudinov, Idris I

2011-01-14

The problem under consideration is that of approximating classes of smooth functions by algebraic-trigonometric polynomials of the form p{sub n}(t)+{tau}{sub m}(t), where p{sub n}(t) is an algebraic polynomial of degree n and {tau}{sub m}(t)=a{sub 0}+{Sigma}{sub k=1}{sup m}a{sub k} cos k{pi}t + b{sub k} sin k{pi}t is a trigonometric polynomial of order m. The precise order of approximation by such polynomials in the classes W{sup r}{sub {infinity}(}M) and an upper bound for similar approximations in the class W{sup r}{sub p}(M) with 4/3polynomials which the author has introduced andmore » investigated previously. Bibliography: 13 titles.« less

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.

Semi-supervised learning for ordinal Kernel Discriminant Analysis.

PubMed

Pérez-Ortiz, M; Gutiérrez, P A; Carbonero-Ruz, M; Hervás-Martínez, C

2016-12-01

Ordinal classification considers those classification problems where the labels of the variable to predict follow a given order. Naturally, labelled data is scarce or difficult to obtain in this type of problems because, in many cases, ordinal labels are given by a user or expert (e.g. in recommendation systems). Firstly, this paper develops a new strategy for ordinal classification where both labelled and unlabelled data are used in the model construction step (a scheme which is referred to as semi-supervised learning). More specifically, the ordinal version of kernel discriminant learning is extended for this setting considering the neighbourhood information of unlabelled data, which is proposed to be computed in the feature space induced by the kernel function. Secondly, a new method for semi-supervised kernel learning is devised in the context of ordinal classification, which is combined with our developed classification strategy to optimise the kernel parameters. The experiments conducted compare 6 different approaches for semi-supervised learning in the context of ordinal classification in a battery of 30 datasets, showing (1) the good synergy of the ordinal version of discriminant analysis and the use of unlabelled data and (2) the advantage of computing distances in the feature space induced by the kernel function. Copyright © 2016 Elsevier Ltd. All rights reserved.

Modeling adaptive kernels from probabilistic phylogenetic trees.

PubMed

Nicotra, Luca; Micheli, Alessio

2009-01-01

Modeling phylogenetic interactions is an open issue in many computational biology problems. In the context of gene function prediction we introduce a class of kernels for structured data leveraging on a hierarchical probabilistic modeling of phylogeny among species. We derive three kernels belonging to this setting: a sufficient statistics kernel, a Fisher kernel, and a probability product kernel. The new kernels are used in the context of support vector machine learning. The kernels adaptivity is obtained through the estimation of the parameters of a tree structured model of evolution using as observed data phylogenetic profiles encoding the presence or absence of specific genes in a set of fully sequenced genomes. We report results obtained in the prediction of the functional class of the proteins of the budding yeast Saccharomyces cerevisae which favorably compare to a standard vector based kernel and to a non-adaptive tree kernel function. A further comparative analysis is performed in order to assess the impact of the different components of the proposed approach. We show that the key features of the proposed kernels are the adaptivity to the input domain and the ability to deal with structured data interpreted through a graphical model representation.

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.

Single image super-resolution via an iterative reproducing kernel Hilbert space method.

PubMed

Deng, Liang-Jian; Guo, Weihong; Huang, Ting-Zhu

2016-11-01

Image super-resolution, a process to enhance image resolution, has important applications in satellite imaging, high definition television, medical imaging, etc. Many existing approaches use multiple low-resolution images to recover one high-resolution image. In this paper, we present an iterative scheme to solve single image super-resolution problems. It recovers a high quality high-resolution image from solely one low-resolution image without using a training data set. We solve the problem from image intensity function estimation perspective and assume the image contains smooth and edge components. We model the smooth components of an image using a thin-plate reproducing kernel Hilbert space (RKHS) and the edges using approximated Heaviside functions. The proposed method is applied to image patches, aiming to reduce computation and storage. Visual and quantitative comparisons with some competitive approaches show the effectiveness of the proposed method.

Cosmographic analysis with Chebyshev polynomials

NASA Astrophysics Data System (ADS)

Capozziello, Salvatore; D'Agostino, Rocco; Luongo, Orlando

2018-05-01

The limits of standard cosmography are here revised addressing the problem of error propagation during statistical analyses. To do so, we propose the use of Chebyshev polynomials to parametrize cosmic distances. In particular, we demonstrate that building up rational Chebyshev polynomials significantly reduces error propagations with respect to standard Taylor series. This technique provides unbiased estimations of the cosmographic parameters and performs significatively better than previous numerical approximations. To figure this out, we compare rational Chebyshev polynomials with Padé series. In addition, we theoretically evaluate the convergence radius of (1,1) Chebyshev rational polynomial and we compare it with the convergence radii of Taylor and Padé approximations. We thus focus on regions in which convergence of Chebyshev rational functions is better than standard approaches. With this recipe, as high-redshift data are employed, rational Chebyshev polynomials remain highly stable and enable one to derive highly accurate analytical approximations of Hubble's rate in terms of the cosmographic series. Finally, we check our theoretical predictions by setting bounds on cosmographic parameters through Monte Carlo integration techniques, based on the Metropolis-Hastings algorithm. We apply our technique to high-redshift cosmic data, using the Joint Light-curve Analysis supernovae sample and the most recent versions of Hubble parameter and baryon acoustic oscillation measurements. We find that cosmography with Taylor series fails to be predictive with the aforementioned data sets, while turns out to be much more stable using the Chebyshev approach.

Improved scatter correction using adaptive scatter kernel superposition

NASA Astrophysics Data System (ADS)

Sun, M.; Star-Lack, J. M.

2010-11-01

Accurate scatter correction is required to produce high-quality reconstructions of x-ray cone-beam computed tomography (CBCT) scans. This paper describes new scatter kernel superposition (SKS) algorithms for deconvolving scatter from projection data. The algorithms are designed to improve upon the conventional approach whose accuracy is limited by the use of symmetric kernels that characterize the scatter properties of uniform slabs. To model scatter transport in more realistic objects, nonstationary kernels, whose shapes adapt to local thickness variations in the projection data, are proposed. Two methods are introduced: (1) adaptive scatter kernel superposition (ASKS) requiring spatial domain convolutions and (2) fast adaptive scatter kernel superposition (fASKS) where, through a linearity approximation, convolution is efficiently performed in Fourier space. The conventional SKS algorithm, ASKS, and fASKS, were tested with Monte Carlo simulations and with phantom data acquired on a table-top CBCT system matching the Varian On-Board Imager (OBI). All three models accounted for scatter point-spread broadening due to object thickening, object edge effects, detector scatter properties and an anti-scatter grid. Hounsfield unit (HU) errors in reconstructions of a large pelvis phantom with a measured maximum scatter-to-primary ratio over 200% were reduced from -90 ± 58 HU (mean ± standard deviation) with no scatter correction to 53 ± 82 HU with SKS, to 19 ± 25 HU with fASKS and to 13 ± 21 HU with ASKS. HU accuracies and measured contrast were similarly improved in reconstructions of a body-sized elliptical Catphan phantom. The results show that the adaptive SKS methods offer significant advantages over the conventional scatter deconvolution technique.

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

Omnibus risk assessment via accelerated failure time kernel machine modeling.

PubMed

Sinnott, Jennifer A; Cai, Tianxi

2013-12-01

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, Tonini, and Lin, 2011). In this article, we derive testing and prediction methods for KM regression under the accelerated failure time (AFT) 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. © 2013, The International Biometric Society.

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.

Graph Kernels for Molecular Similarity.

PubMed

Rupp, Matthias; Schneider, Gisbert

2010-04-12

Molecular similarity measures are important for many cheminformatics applications like ligand-based virtual screening and quantitative structure-property relationships. Graph kernels are formal similarity measures defined directly on graphs, such as the (annotated) molecular structure graph. Graph kernels are positive semi-definite functions, i.e., they correspond to inner products. This property makes them suitable for use with kernel-based machine learning algorithms such as support vector machines and Gaussian processes. We review the major types of kernels between graphs (based on random walks, subgraphs, and optimal assignments, respectively), and discuss their advantages, limitations, and successful applications in cheminformatics. Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Kernel analysis in TeV gamma-ray selection

NASA Astrophysics Data System (ADS)

Moriarty, P.; Samuelson, F. W.

2000-06-01

We discuss the use of kernel analysis as a technique for selecting gamma-ray candidates in Atmospheric Cherenkov astronomy. The method is applied to observations of the Crab Nebula and Markarian 501 recorded with the Whipple 10 m Atmospheric Cherenkov imaging system, and the results are compared with the standard Supercuts analysis. Since kernel analysis is computationally intensive, we examine approaches to reducing the computational load. Extension of the technique to estimate the energy of the gamma-ray primary is considered. .

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.

Fast template matching with polynomials.

PubMed

Omachi, Shinichiro; Omachi, Masako

2007-08-01

Template matching is widely used for many applications in image and signal processing. This paper proposes a novel template matching algorithm, called algebraic template matching. Given a template and an input image, algebraic template matching efficiently calculates similarities between the template and the partial images of the input image, for various widths and heights. The partial image most similar to the template image is detected from the input image for any location, width, and height. In the proposed algorithm, a polynomial that approximates the template image is used to match the input image instead of the template image. The proposed algorithm is effective especially when the width and height of the template image differ from the partial image to be matched. An algorithm using the Legendre polynomial is proposed for efficient approximation of the template image. This algorithm not only reduces computational costs, but also improves the quality of the approximated image. It is shown theoretically and experimentally that the computational cost of the proposed algorithm is much smaller than the existing methods.

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.

Sliding Window Generalized Kernel Affine Projection Algorithm Using Projection Mappings

NASA Astrophysics Data System (ADS)

Slavakis, Konstantinos; Theodoridis, Sergios

2008-12-01

Very recently, a solution to the kernel-based online classification problem has been given by the adaptive projected subgradient method (APSM). The developed algorithm can be considered as a generalization of a kernel affine projection algorithm (APA) and the kernel normalized least mean squares (NLMS). Furthermore, sparsification of the resulting kernel series expansion was achieved by imposing a closed ball (convex set) constraint on the norm of the classifiers. This paper presents another sparsification method for the APSM approach to the online classification task by generating a sequence of linear subspaces in a reproducing kernel Hilbert space (RKHS). To cope with the inherent memory limitations of online systems and to embed tracking capabilities to the design, an upper bound on the dimension of the linear subspaces is imposed. The underlying principle of the design is the notion of projection mappings. Classification is performed by metric projection mappings, sparsification is achieved by orthogonal projections, while the online system's memory requirements and tracking are attained by oblique projections. The resulting sparsification scheme shows strong similarities with the classical sliding window adaptive schemes. The proposed design is validated by the adaptive equalization problem of a nonlinear communication channel, and is compared with classical and recent stochastic gradient descent techniques, as well as with the APSM's solution where sparsification is performed by a closed ball constraint on the norm of the classifiers.

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. ...

Resummed memory kernels in generalized system-bath master equations

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

Mavros, Michael G.; Van Voorhis, Troy, E-mail: tvan@mit.edu

2014-08-07

Generalized master equations provide a concise formalism for studying reduced population dynamics. Usually, these master equations require a perturbative expansion of the memory kernels governing the dynamics; in order to prevent divergences, these expansions must be resummed. Resummation techniques of perturbation series are ubiquitous in physics, but they have not been readily studied for the time-dependent memory kernels used in generalized master equations. In this paper, we present a comparison of different resummation techniques for such memory kernels up to fourth order. We study specifically the spin-boson Hamiltonian as a model system bath Hamiltonian, treating the diabatic coupling between themore » two states as a perturbation. A novel derivation of the fourth-order memory kernel for the spin-boson problem is presented; then, the second- and fourth-order kernels are evaluated numerically for a variety of spin-boson parameter regimes. We find that resumming the kernels through fourth order using a Padé approximant results in divergent populations in the strong electronic coupling regime due to a singularity introduced by the nature of the resummation, and thus recommend a non-divergent exponential resummation (the “Landau-Zener resummation” of previous work). The inclusion of fourth-order effects in a Landau-Zener-resummed kernel is shown to improve both the dephasing rate and the obedience of detailed balance over simpler prescriptions like the non-interacting blip approximation, showing a relatively quick convergence on the exact answer. The results suggest that including higher-order contributions to the memory kernel of a generalized master equation and performing an appropriate resummation can provide a numerically-exact solution to system-bath dynamics for a general spectral density, opening the way to a new class of methods for treating system-bath dynamics.« less

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.

Optimizing Support Vector Machine Parameters with Genetic Algorithm for Credit Risk Assessment

NASA Astrophysics Data System (ADS)

Manurung, Jonson; Mawengkang, Herman; Zamzami, Elviawaty

2017-12-01

Support vector machine (SVM) is a popular classification method known to have strong generalization capabilities. SVM can solve the problem of classification and linear regression or nonlinear kernel which can be a learning algorithm for the ability of classification and regression. However, SVM also has a weakness that is difficult to determine the optimal parameter value. SVM calculates the best linear separator on the input feature space according to the training data. To classify data which are non-linearly separable, SVM uses kernel tricks to transform the data into a linearly separable data on a higher dimension feature space. The kernel trick using various kinds of kernel functions, such as : linear kernel, polynomial, radial base function (RBF) and sigmoid. Each function has parameters which affect the accuracy of SVM classification. To solve the problem genetic algorithms are proposed to be applied as the optimal parameter value search algorithm thus increasing the best classification accuracy on SVM. Data taken from UCI repository of machine learning database: Australian Credit Approval. The results show that the combination of SVM and genetic algorithms is effective in improving classification accuracy. Genetic algorithms has been shown to be effective in systematically finding optimal kernel parameters for SVM, instead of randomly selected kernel parameters. The best accuracy for data has been upgraded from kernel Linear: 85.12%, polynomial: 81.76%, RBF: 77.22% Sigmoid: 78.70%. However, for bigger data sizes, this method is not practical because it takes a lot of time.

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.

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

On the derivatives of unimodular polynomials

NASA Astrophysics Data System (ADS)

Nevai, P.; Erdélyi, T.

2016-04-01

Let D be the open unit disk of the complex plane; its boundary, the unit circle of the complex plane, is denoted by \\partial D. Let \\mathscr P_n^c denote the set of all algebraic polynomials of degree at most n with complex coefficients. For λ ≥ 0, let {\\mathscr K}_n^λ \\stackrel{{def}}{=} \\biggl\\{P_n: P_n(z) = \\sumk=0^n{ak k^λ z^k}, ak \\in { C}, |a_k| = 1 \\biggr\\} \\subset {\\mathscr P}_n^c.The class \\mathscr K_n^0 is often called the collection of all (complex) unimodular polynomials of degree n. Given a sequence (\\varepsilon_n) of positive numbers tending to 0, we say that a sequence (P_n) of polynomials P_n\\in\\mathscr K_n^λ is \\{λ, (\\varepsilon_n)\\}-ultraflat if \\displaystyle (1-\\varepsilon_n)\\frac{nλ+1/2}{\\sqrt{2λ+1}}≤\\ve......a +1/2}}{\\sqrt{2λ +1}},\\qquad z \\in \\partial D,\\quad n\\in N_0.Although we do not know, in general, whether or not \\{λ, (\\varepsilon_n)\\}-ultraflat sequences of polynomials P_n\\in\\mathscr K_n^λ exist for each fixed λ>0, we make an effort to prove various interesting properties of them. These allow us to conclude that there are no sequences (P_n) of either conjugate, or plain, or skew reciprocal unimodular polynomials P_n\\in\\mathscr K_n^0 such that (Q_n) with Q_n(z)\\stackrel{{def}}{=} zP_n'(z)+1 is a \\{1,(\\varepsilon_n)\\}-ultraflat sequence of polynomials.Bibliography: 18 titles.

Predicting receptor-ligand pairs through kernel learning

PubMed Central

2011-01-01

Background Regulation of cellular events is, often, initiated via extracellular signaling. Extracellular signaling occurs when a circulating ligand interacts with one or more membrane-bound receptors. Identification of receptor-ligand pairs is thus an important and specific form of PPI prediction. Results Given a set of disparate data sources (expression data, domain content, and phylogenetic profile) we seek to predict new receptor-ligand pairs. We create a combined kernel classifier and assess its performance with respect to the Database of Ligand-Receptor Partners (DLRP) 'golden standard' as well as the method proposed by Gertz et al. Among our findings, we discover that our predictions for the tgfβ family accurately reconstruct over 76% of the supported edges (0.76 recall and 0.67 precision) of the receptor-ligand bipartite graph defined by the DLRP "golden standard". In addition, for the tgfβ family, the combined kernel classifier is able to relatively improve upon the Gertz et al. work by a factor of approximately 1.5 when considering that our method has an F-measure of 0.71 while that of Gertz et al. has a value of 0.48. Conclusions The prediction of receptor-ligand pairings is a difficult and complex task. We have demonstrated that using kernel learning on multiple data sources provides a stronger alternative to the existing method in solving this task. PMID:21834994

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.

On adaptive weighted polynomial preconditioning for Hermitian positive definite matrices

NASA Technical Reports Server (NTRS)

Fischer, Bernd; Freund, Roland W.

1992-01-01

The conjugate gradient algorithm for solving Hermitian positive definite linear systems is usually combined with preconditioning in order to speed up convergence. In recent years, there has been a revival of polynomial preconditioning, motivated by the attractive features of the method on modern architectures. Standard techniques for choosing the preconditioning polynomial are based only on bounds for the extreme eigenvalues. Here a different approach is proposed, which aims at adapting the preconditioner to the eigenvalue distribution of the coefficient matrix. The technique is based on the observation that good estimates for the eigenvalue distribution can be derived after only a few steps of the Lanczos process. This information is then used to construct a weight function for a suitable Chebyshev approximation problem. The solution of this problem yields the polynomial preconditioner. In particular, we investigate the use of Bernstein-Szego weights.

Travel-time sensitivity kernels in long-range propagation.

PubMed

Skarsoulis, E K; Cornuelle, B D; Dzieciuch, M A

2009-11-01

Wave-theoretic travel-time sensitivity kernels (TSKs) are calculated in two-dimensional (2D) and three-dimensional (3D) environments and their behavior with increasing propagation range is studied and compared to that of ray-theoretic TSKs and corresponding Fresnel-volumes. The differences between the 2D and 3D TSKs average out when horizontal or cross-range marginals are considered, which indicates that they are not important in the case of range-independent sound-speed perturbations or perturbations of large scale compared to the lateral TSK extent. With increasing range, the wave-theoretic TSKs expand in the horizontal cross-range direction, their cross-range extent being comparable to that of the corresponding free-space Fresnel zone, whereas they remain bounded in the vertical. Vertical travel-time sensitivity kernels (VTSKs)-one-dimensional kernels describing the effect of horizontally uniform sound-speed changes on travel-times-are calculated analytically using a perturbation approach, and also numerically, as horizontal marginals of the corresponding TSKs. Good agreement between analytical and numerical VTSKs, as well as between 2D and 3D VTSKs, is found. As an alternative method to obtain wave-theoretic sensitivity kernels, the parabolic approximation is used; the resulting TSKs and VTSKs are in good agreement with normal-mode results. With increasing range, the wave-theoretic VTSKs approach the corresponding ray-theoretic sensitivity kernels.

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.

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.

Fast metabolite identification with Input Output Kernel Regression.

PubMed

Brouard, Céline; Shen, Huibin; Dührkop, Kai; d'Alché-Buc, Florence; Böcker, Sebastian; Rousu, Juho

2016-06-15

An important problematic of metabolomics is to identify metabolites using tandem mass spectrometry data. Machine learning methods have been proposed recently to solve this problem by predicting molecular fingerprint vectors and matching these fingerprints against existing molecular structure databases. In this work we propose to address the metabolite identification problem using a structured output prediction approach. This type of approach is not limited to vector output space and can handle structured output space such as the molecule space. We use the Input Output Kernel Regression method to learn the mapping between tandem mass spectra and molecular structures. The principle of this method is to encode the similarities in the input (spectra) space and the similarities in the output (molecule) space using two kernel functions. This method approximates the spectra-molecule mapping in two phases. The first phase corresponds to a regression problem from the input space to the feature space associated to the output kernel. The second phase is a preimage problem, consisting in mapping back the predicted output feature vectors to the molecule space. We show that our approach achieves state-of-the-art accuracy in metabolite identification. Moreover, our method has the advantage of decreasing the running times for the training step and the test step by several orders of magnitude over the preceding methods. celine.brouard@aalto.fi Supplementary data are available at Bioinformatics online. © The Author 2016. Published by Oxford University Press.

Fast metabolite identification with Input Output Kernel Regression

PubMed Central

Brouard, Céline; Shen, Huibin; Dührkop, Kai; d'Alché-Buc, Florence; Böcker, Sebastian; Rousu, Juho

2016-01-01

Motivation: An important problematic of metabolomics is to identify metabolites using tandem mass spectrometry data. Machine learning methods have been proposed recently to solve this problem by predicting molecular fingerprint vectors and matching these fingerprints against existing molecular structure databases. In this work we propose to address the metabolite identification problem using a structured output prediction approach. This type of approach is not limited to vector output space and can handle structured output space such as the molecule space. Results: We use the Input Output Kernel Regression method to learn the mapping between tandem mass spectra and molecular structures. The principle of this method is to encode the similarities in the input (spectra) space and the similarities in the output (molecule) space using two kernel functions. This method approximates the spectra-molecule mapping in two phases. The first phase corresponds to a regression problem from the input space to the feature space associated to the output kernel. The second phase is a preimage problem, consisting in mapping back the predicted output feature vectors to the molecule space. We show that our approach achieves state-of-the-art accuracy in metabolite identification. Moreover, our method has the advantage of decreasing the running times for the training step and the test step by several orders of magnitude over the preceding methods. Availability and implementation: Contact: celine.brouard@aalto.fi Supplementary information: Supplementary data are available at Bioinformatics online. PMID:27307628

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

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.

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 accurate and efficient method for evaluating the kernel of the integral equation relating pressure to normalwash in unsteady potential flow

NASA Technical Reports Server (NTRS)

Desmarais, R. N.

1982-01-01

This paper describes an accurate economical method for generating approximations to the kernel of the integral equation relating unsteady pressure to normalwash in nonplanar flow. The method is capable of generating approximations of arbitrary accuracy. It is based on approximating the algebraic part of the non elementary integrals in the kernel by exponential approximations and then integrating termwise. The exponent spacing in the approximation is a geometric sequence. The coefficients and exponent multiplier of the exponential approximation are computed by least squares so the method is completely automated. Exponential approximates generated in this manner are two orders of magnitude more accurate than the exponential approximation that is currently most often used for this purpose. Coefficients for 8, 12, 24, and 72 term approximations are tabulated in the report. Also, since the method is automated, it can be used to generate approximations to attain any desired trade-off between accuracy and computing cost.

7 CFR 981.401 - Adjusted kernel weight.

Code of Federal Regulations, 2012 CFR

2012-01-01

... based on the analysis of a 1,000 gram sample taken from a lot of almonds weighing 10,000 pounds with less than 95 percent kernels, and a 1,000 gram sample taken from a lot of almonds weighing 10,000... percent kernels containing the following: Edible kernels, 530 grams; inedible kernels, 120 grams; foreign...

7 CFR 981.401 - Adjusted kernel weight.

Code of Federal Regulations, 2011 CFR

2011-01-01

... based on the analysis of a 1,000 gram sample taken from a lot of almonds weighing 10,000 pounds with less than 95 percent kernels, and a 1,000 gram sample taken from a lot of almonds weighing 10,000... percent kernels containing the following: Edible kernels, 530 grams; inedible kernels, 120 grams; foreign...

7 CFR 981.401 - Adjusted kernel weight.

Code of Federal Regulations, 2013 CFR

2013-01-01

... based on the analysis of a 1,000 gram sample taken from a lot of almonds weighing 10,000 pounds with less than 95 percent kernels, and a 1,000 gram sample taken from a lot of almonds weighing 10,000... percent kernels containing the following: Edible kernels, 530 grams; inedible kernels, 120 grams; foreign...

7 CFR 981.401 - Adjusted kernel weight.

Code of Federal Regulations, 2010 CFR

2010-01-01

... based on the analysis of a 1,000 gram sample taken from a lot of almonds weighing 10,000 pounds with less than 95 percent kernels, and a 1,000 gram sample taken from a lot of almonds weighing 10,000... percent kernels containing the following: Edible kernels, 530 grams; inedible kernels, 120 grams; foreign...

7 CFR 981.401 - Adjusted kernel weight.

Code of Federal Regulations, 2014 CFR

2014-01-01

... based on the analysis of a 1,000 gram sample taken from a lot of almonds weighing 10,000 pounds with less than 95 percent kernels, and a 1,000 gram sample taken from a lot of almonds weighing 10,000... percent kernels containing the following: Edible kernels, 530 grams; inedible kernels, 120 grams; foreign...

7 CFR 51.1403 - Kernel color classification.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 2 2010-01-01 2010-01-01 false Kernel color classification. 51.1403 Section 51.1403... STANDARDS) United States Standards for Grades of Pecans in the Shell 1 Kernel Color Classification § 51.1403 Kernel color classification. (a) The skin color of pecan kernels may be described in terms of the color...

The Gibbs Phenomenon for Series of Orthogonal Polynomials

ERIC Educational Resources Information Center

Fay, T. H.; Kloppers, P. Hendrik

2006-01-01

This note considers the four classes of orthogonal polynomials--Chebyshev, Hermite, Laguerre, Legendre--and investigates the Gibbs phenomenon at a jump discontinuity for the corresponding orthogonal polynomial series expansions. The perhaps unexpected thing is that the Gibbs constant that arises for each class of polynomials appears to be the same…

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

Analytical Plug-In Method for Kernel Density Estimator Applied to Genetic Neutrality Study

NASA Astrophysics Data System (ADS)

Troudi, Molka; Alimi, Adel M.; Saoudi, Samir

2008-12-01

The plug-in method enables optimization of the bandwidth of the kernel density estimator in order to estimate probability density functions (pdfs). Here, a faster procedure than that of the common plug-in method is proposed. The mean integrated square error (MISE) depends directly upon [InlineEquation not available: see fulltext.] which is linked to the second-order derivative of the pdf. As we intend to introduce an analytical approximation of [InlineEquation not available: see fulltext.], the pdf is estimated only once, at the end of iterations. These two kinds of algorithm are tested on different random variables having distributions known for their difficult estimation. Finally, they are applied to genetic data in order to provide a better characterisation in the mean of neutrality of Tunisian Berber populations.

Adaptive wiener image restoration kernel

DOEpatents

Yuan, Ding [Henderson, NV

2007-06-05

A method and device for restoration of electro-optical image data using an adaptive Wiener filter begins with constructing imaging system Optical Transfer Function, and the Fourier Transformations of the noise and the image. A spatial representation of the imaged object is restored by spatial convolution of the image using a Wiener restoration kernel.

A recursive algorithm for Zernike polynomials

NASA Technical Reports Server (NTRS)

Davenport, J. W.

1982-01-01

The analysis of a function defined on a rotationally symmetric system, with either a circular or annular pupil is discussed. In order to numerically analyze such systems it is typical to expand the given function in terms of a class of orthogonal polynomials. Because of their particular properties, the Zernike polynomials are especially suited for numerical calculations. Developed is a recursive algorithm that can be used to generate the Zernike polynomials up to a given order. The algorithm is recursively defined over J where R(J,N) is the Zernike polynomial of degree N obtained by orthogonalizing the sequence R(J), R(J+2), ..., R(J+2N) over (epsilon, 1). The terms in the preceding row - the (J-1) row - up to the N+1 term is needed for generating the (J,N)th term. Thus, the algorith generates an upper left-triangular table. This algorithm was placed in the computer with the necessary support program also included.

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.

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.

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.

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.

Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation

ERIC Educational Resources Information Center

Gordon, Sheldon P.; Yang, Yajun

2017-01-01

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…

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 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.

Reconstruction of noisy and blurred images using blur kernel

NASA Astrophysics Data System (ADS)

Ellappan, Vijayan; Chopra, Vishal

2017-11-01

Blur is a common in so many digital images. Blur can be caused by motion of the camera and scene object. In this work we proposed a new method for deblurring images. This work uses sparse representation to identify the blur kernel. By analyzing the image coordinates Using coarse and fine, we fetch the kernel based image coordinates and according to that observation we get the motion angle of the shaken or blurred image. Then we calculate the length of the motion kernel using radon transformation and Fourier for the length calculation of the image and we use Lucy Richardson algorithm which is also called NON-Blind(NBID) Algorithm for more clean and less noisy image output. All these operation will be performed in MATLAB IDE.