Science.gov

Sample records for covariate-adjusted nonlinear regression

  1. Mapping Lifetime Brain Volumetry with Covariate-Adjusted Restricted Cubic Spline Regression from Cross-sectional Multi-site MRI.

    PubMed

    Huo, Yuankai; Aboud, Katherine; Kang, Hakmook; Cutting, Laurie E; Landman, Bennett A

    2016-10-01

    Understanding brain volumetry is essential to understand neurodevelopment and disease. Historically, age-related changes have been studied in detail for specific age ranges (e.g., early childhood, teen, young adults, elderly, etc.) or more sparsely sampled for wider considerations of lifetime aging. Recent advancements in data sharing and robust processing have made available considerable quantities of brain images from normal, healthy volunteers. However, existing analysis approaches have had difficulty addressing (1) complex volumetric developments on the large cohort across the life time (e.g., beyond cubic age trends), (2) accounting for confound effects, and (3) maintaining an analysis framework consistent with the general linear model (GLM) approach pervasive in neuroscience. To address these challenges, we propose to use covariate-adjusted restricted cubic spline (C-RCS) regression within a multi-site cross-sectional framework. This model allows for flexible consideration of non-linear age-associated patterns while accounting for traditional covariates and interaction effects. As a demonstration of this approach on lifetime brain aging, we derive normative volumetric trajectories and 95% confidence intervals from 5111 healthy patients from 64 sites while accounting for confounding sex, intracranial volume and field strength effects. The volumetric results are shown to be consistent with traditional studies that have explored more limited age ranges using single-site analyses. This work represents the first integration of C-RCS with neuroimaging and the derivation of structural covariance networks (SCNs) from a large study of multi-site, cross-sectional data.

  2. A Proportional Hazards Regression Model for the Sub-distribution with Covariates Adjusted Censoring Weight for Competing Risks Data

    PubMed Central

    HE, PENG; ERIKSSON, FRANK; SCHEIKE, THOMAS H.; ZHANG, MEI-JIE

    2015-01-01

    With competing risks data, one often needs to assess the treatment and covariate effects on the cumulative incidence function. Fine and Gray proposed a proportional hazards regression model for the subdistribution of a competing risk with the assumption that the censoring distribution and the covariates are independent. Covariate-dependent censoring sometimes occurs in medical studies. In this paper, we study the proportional hazards regression model for the subdistribution of a competing risk with proper adjustments for covariate-dependent censoring. We consider a covariate-adjusted weight function by fitting the Cox model for the censoring distribution and using the predictive probability for each individual. Our simulation study shows that the covariate-adjusted weight estimator is basically unbiased when the censoring time depends on the covariates, and the covariate-adjusted weight approach works well for the variance estimator as well. We illustrate our methods with bone marrow transplant data from the Center for International Blood and Marrow Transplant Research (CIBMTR). Here cancer relapse and death in complete remission are two competing risks. PMID:27034534

  3. Combining biomarkers for classification with covariate adjustment.

    PubMed

    Kim, Soyoung; Huang, Ying

    2017-03-09

    Combining multiple markers can improve classification accuracy compared with using a single marker. In practice, covariates associated with markers or disease outcome can affect the performance of a biomarker or biomarker combination in the population. The covariate-adjusted receiver operating characteristic (ROC) curve has been proposed as a tool to tease out the covariate effect in the evaluation of a single marker; this curve characterizes the classification accuracy solely because of the marker of interest. However, research on the effect of covariates on the performance of marker combinations and on how to adjust for the covariate effect when combining markers is still lacking. In this article, we examine the effect of covariates on classification performance of linear marker combinations and propose to adjust for covariates in combining markers by maximizing the nonparametric estimate of the area under the covariate-adjusted ROC curve. The proposed method provides a way to estimate the best linear biomarker combination that is robust to risk model assumptions underlying alternative regression-model-based methods. The proposed estimator is shown to be consistent and asymptotically normally distributed. We conduct simulations to evaluate the performance of our estimator in cohort and case/control designs and compare several different weighting strategies during estimation with respect to efficiency. Our estimator is also compared with alternative regression-model-based estimators or estimators that maximize the empirical area under the ROC curve, with respect to bias and efficiency. We apply the proposed method to a biomarker study from an human immunodeficiency virus vaccine trial. Copyright © 2017 John Wiley & Sons, Ltd.

  4. An evaluation of bias in propensity score-adjusted non-linear regression models.

    PubMed

    Wan, Fei; Mitra, Nandita

    2016-04-19

    Propensity score methods are commonly used to adjust for observed confounding when estimating the conditional treatment effect in observational studies. One popular method, covariate adjustment of the propensity score in a regression model, has been empirically shown to be biased in non-linear models. However, no compelling underlying theoretical reason has been presented. We propose a new framework to investigate bias and consistency of propensity score-adjusted treatment effects in non-linear models that uses a simple geometric approach to forge a link between the consistency of the propensity score estimator and the collapsibility of non-linear models. Under this framework, we demonstrate that adjustment of the propensity score in an outcome model results in the decomposition of observed covariates into the propensity score and a remainder term. Omission of this remainder term from a non-collapsible regression model leads to biased estimates of the conditional odds ratio and conditional hazard ratio, but not for the conditional rate ratio. We further show, via simulation studies, that the bias in these propensity score-adjusted estimators increases with larger treatment effect size, larger covariate effects, and increasing dissimilarity between the coefficients of the covariates in the treatment model versus the outcome model.

  5. Covariate-Adjusted Precision Matrix Estimation with an Application in Genetical Genomics

    PubMed Central

    Cai, T. Tony; Li, Hongzhe; Liu, Weidong; Xie, Jichun

    2017-01-01

    Summary Motivated by analysis of genetical genomics data, we introduce a sparse high dimensional multivariate regression model for studying conditional independence relationships among a set of genes adjusting for possible genetic effects. The precision matrix in the model specifies a covariate-adjusted Gaussian graph, which presents the conditional dependence structure of gene expression after the confounding genetic effects on gene expression are taken into account. We present a covariate-adjusted precision matrix estimation method using a constrained ℓ1 minimization, which can be easily implemented by linear programming. Asymptotic convergence rates in various matrix norms and sign consistency are established for the estimators of the regression coefficients and the precision matrix, allowing both the number of genes and the number of the genetic variants to diverge. Simulation shows that the proposed method results in significant improvements in both precision matrix estimation and graphical structure selection when compared to the standard Gaussian graphical model assuming constant means. The proposed method is also applied to analyze a yeast genetical genomics data for the identification of the gene network among a set of genes in the mitogen-activated protein kinase pathway.

  6. Inverse probability weighting for covariate adjustment in randomized studies.

    PubMed

    Shen, Changyu; Li, Xiaochun; Li, Lingling

    2014-02-20

    Covariate adjustment in randomized clinical trials has the potential benefit of precision gain. It also has the potential pitfall of reduced objectivity as it opens the possibility of selecting a 'favorable' model that yields strong treatment benefit estimate. Although there is a large volume of statistical literature targeting on the first aspect, realistic solutions to enforce objective inference and improve precision are rare. As a typical randomized trial needs to accommodate many implementation issues beyond statistical considerations, maintaining the objectivity is at least as important as precision gain if not more, particularly from the perspective of the regulatory agencies. In this article, we propose a two-stage estimation procedure based on inverse probability weighting to achieve better precision without compromising objectivity. The procedure is designed in a way such that the covariate adjustment is performed before seeing the outcome, effectively reducing the possibility of selecting a 'favorable' model that yields a strong intervention effect. Both theoretical and numerical properties of the estimation procedure are presented. Application of the proposed method to a real data example is presented.

  7. A method for nonlinear exponential regression analysis

    NASA Technical Reports Server (NTRS)

    Junkin, B. G.

    1971-01-01

    A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.

  8. Learning Inverse Rig Mappings by Nonlinear Regression.

    PubMed

    Holden, Daniel; Saito, Jun; Komura, Taku

    2016-11-11

    We present a framework to design inverse rig-functions - functions that map low level representations of a character's pose such as joint positions or surface geometry to the representation used by animators called the animation rig. Animators design scenes using an animation rig, a framework widely adopted in animation production which allows animators to design character poses and geometry via intuitive parameters and interfaces. Yet most state-of-the-art computer animation techniques control characters through raw, low level representations such as joint angles, joint positions, or vertex coordinates. This difference often stops the adoption of state-of-the-art techniques in animation production. Our framework solves this issue by learning a mapping between the low level representations of the pose and the animation rig. We use nonlinear regression techniques, learning from example animation sequences designed by the animators. When new motions are provided in the skeleton space, the learned mapping is used to estimate the rig controls that reproduce such a motion. We introduce two nonlinear functions for producing such a mapping: Gaussian process regression and feedforward neural networks. The appropriate solution depends on the nature of the rig and the amount of data available for training. We show our framework applied to various examples including articulated biped characters, quadruped characters, facial animation rigs, and deformable characters. With our system, animators have the freedom to apply any motion synthesis algorithm to arbitrary rigging and animation pipelines for immediate editing. This greatly improves the productivity of 3D animation, while retaining the flexibility and creativity of artistic input.

  9. The Effect of Aggregation in Nonlinear Regression.

    DTIC Science & Technology

    1984-04-01

    This truncation is the source of the nonlinearity in the model (1.1). Physically, the intercept a represents baseload con- sumption, such as for...BIAS b FOR 75 AGGREGATE DATA SETS FIT TO THE ENERGY MODEL Bias Smoothing Error Standard Error A A Parameter e b = E(8 - 63) e - e s.e.(e BASELOAD a...s.e. ) e BASELOAD a -0.037 -0.30 1.35 (Th/cu-d) HEAT RATE 6 0.0033 0.44 0.224 (Th/cu-OFd) REFERENCE TEMPERATURE T -0.28 -0.25 64.1 (OF) NORMALIZED

  10. Nonparametric randomization-based covariate adjustment for stratified analysis of time-to-event or dichotomous outcomes.

    PubMed

    Hussey, Michael A; Koch, Gary G; Preisser, John S; Saville, Benjamin R

    2016-01-01

    Time-to-event or dichotomous outcomes in randomized clinical trials often have analyses using the Cox proportional hazards model or conditional logistic regression, respectively, to obtain covariate-adjusted log hazard (or odds) ratios. Nonparametric Randomization-Based Analysis of Covariance (NPANCOVA) can be applied to unadjusted log hazard (or odds) ratios estimated from a model containing treatment as the only explanatory variable. These adjusted estimates are stratified population-averaged treatment effects and only require a valid randomization to the two treatment groups and avoid key modeling assumptions (e.g., proportional hazards in the case of a Cox model) for the adjustment variables. The methodology has application in the regulatory environment where such assumptions cannot be verified a priori. Application of the methodology is illustrated through three examples on real data from two randomized trials.

  11. Sample Size for Confidence Interval of Covariate-Adjusted Mean Difference

    ERIC Educational Resources Information Center

    Liu, Xiaofeng Steven

    2010-01-01

    This article provides a way to determine adequate sample size for the confidence interval of covariate-adjusted mean difference in randomized experiments. The standard error of adjusted mean difference depends on covariate variance and balance, which are two unknown quantities at the stage of planning sample size. If covariate observations are…

  12. Validity of a Residualized Dependent Variable after Pretest Covariance Adjustments: Still the Same Variable?

    ERIC Educational Resources Information Center

    Nimon, Kim; Henson, Robin K.

    2015-01-01

    The authors empirically examined whether the validity of a residualized dependent variable after covariance adjustment is comparable to that of the original variable of interest. When variance of a dependent variable is removed as a result of one or more covariates, the residual variance may not reflect the same meaning. Using the pretest-posttest…

  13. Covariate Adjustment Strategy Increases Power in the Randomized Controlled Trial With Discrete-Time Survival Endpoints

    ERIC Educational Resources Information Center

    Safarkhani, Maryam; Moerbeek, Mirjam

    2013-01-01

    In a randomized controlled trial, a decision needs to be made about the total number of subjects for adequate statistical power. One way to increase the power of a trial is by including a predictive covariate in the model. In this article, the effects of various covariate adjustment strategies on increasing the power is studied for discrete-time…

  14. Comparison of Propensity Score Methods and Covariate Adjustment: Evaluation in 4 Cardiovascular Studies.

    PubMed

    Elze, Markus C; Gregson, John; Baber, Usman; Williamson, Elizabeth; Sartori, Samantha; Mehran, Roxana; Nichols, Melissa; Stone, Gregg W; Pocock, Stuart J

    2017-01-24

    Propensity scores (PS) are an increasingly popular method to adjust for confounding in observational studies. Propensity score methods have theoretical advantages over conventional covariate adjustment, but their relative performance in real-word scenarios is poorly characterized. We used datasets from 4 large-scale cardiovascular observational studies (PROMETHEUS, ADAPT-DES [the Assessment of Dual AntiPlatelet Therapy with Drug-Eluting Stents], THIN [The Health Improvement Network], and CHARM [Candesartan in Heart Failure-Assessment of Reduction in Mortality and Morbidity]) to compare the performance of conventional covariate adjustment with 4 common PS methods: matching, stratification, inverse probability weighting, and use of PS as a covariate. We found that stratification performed poorly with few outcome events, and inverse probability weighting gave imprecise estimates of treatment effect and undue influence to a small number of observations when substantial confounding was present. Covariate adjustment and matching performed well in all of our examples, although matching tended to give less precise estimates in some cases. PS methods are not necessarily superior to conventional covariate adjustment, and care should be taken to select the most suitable method.

  15. Cardiovascular Response Identification Based on Nonlinear Support Vector Regression

    NASA Astrophysics Data System (ADS)

    Wang, Lu; Su, Steven W.; Chan, Gregory S. H.; Celler, Branko G.; Cheng, Teddy M.; Savkin, Andrey V.

    This study experimentally investigates the relationships between central cardiovascular variables and oxygen uptake based on nonlinear analysis and modeling. Ten healthy subjects were studied using cycle-ergometry exercise tests with constant workloads ranging from 25 Watt to 125 Watt. Breath by breath gas exchange, heart rate, cardiac output, stroke volume and blood pressure were measured at each stage. The modeling results proved that the nonlinear modeling method (Support Vector Regression) outperforms traditional regression method (reducing Estimation Error between 59% and 80%, reducing Testing Error between 53% and 72%) and is the ideal approach in the modeling of physiological data, especially with small training data set.

  16. 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.

  17. Symmetric Nonlinear Regression. Research Report. ETS RR-07-13

    ERIC Educational Resources Information Center

    Antal, Tamás

    2007-01-01

    An estimation tool for symmetric univariate nonlinear regression is presented. The method is based on introducing a nontrivial set of affine coordinates for diffeomorphisms of the real line. The main ingredient making the computations possible is the Connes-Moscovici Hopf algebra of these affine coordinates.

  18. An Excel Solver Exercise to Introduce Nonlinear Regression

    ERIC Educational Resources Information Center

    Pinder, Jonathan P.

    2013-01-01

    Business students taking business analytics courses that have significant predictive modeling components, such as marketing research, data mining, forecasting, and advanced financial modeling, are introduced to nonlinear regression using application software that is a "black box" to the students. Thus, although correct models are…

  19. Covariate-Adjusted Linear Mixed Effects Model with an Application to Longitudinal Data

    PubMed Central

    Nguyen, Danh V.; Şentürk, Damla; Carroll, Raymond J.

    2009-01-01

    Linear mixed effects (LME) models are useful for longitudinal data/repeated measurements. We propose a new class of covariate-adjusted LME models for longitudinal data that nonparametrically adjusts for a normalizing covariate. The proposed approach involves fitting a parametric LME model to the data after adjusting for the nonparametric effects of a baseline confounding covariate. In particular, the effect of the observable covariate on the response and predictors of the LME model is modeled nonparametrically via smooth unknown functions. In addition to covariate-adjusted estimation of fixed/population parameters and random effects, an estimation procedure for the variance components is also developed. Numerical properties of the proposed estimators are investigated with simulation studies. The consistency and convergence rates of the proposed estimators are also established. An application to a longitudinal data set on calcium absorption, accounting for baseline distortion from body mass index, illustrates the proposed methodology. PMID:19266053

  20. Adjusting for covariate effects on classification accuracy using the covariate-adjusted receiver operating characteristic curve.

    PubMed

    Janes, Holly; Pepe, Margaret S

    2009-06-01

    Recent scientific and technological innovations have produced an abundance of potential markers that are being investigated for their use in disease screening and diagnosis. In evaluating these markers, it is often necessary to account for covariates associated with the marker of interest. Covariates may include subject characteristics, expertise of the test operator, test procedures or aspects of specimen handling. In this paper, we propose the covariate-adjusted receiver operating characteristic curve, a measure of covariate-adjusted classification accuracy. Nonparametric and semiparametric estimators are proposed, asymptotic distribution theory is provided and finite sample performance is investigated. For illustration we characterize the age-adjusted discriminatory accuracy of prostate-specific antigen as a biomarker for prostate cancer.

  1. Semiparametric maximum likelihood for nonlinear regression with measurement errors.

    PubMed

    Suh, Eun-Young; Schafer, Daniel W

    2002-06-01

    This article demonstrates semiparametric maximum likelihood estimation of a nonlinear growth model for fish lengths using imprecisely measured ages. Data on the species corvina reina, found in the Gulf of Nicoya, Costa Rica, consist of lengths and imprecise ages for 168 fish and precise ages for a subset of 16 fish. The statistical problem may therefore be classified as nonlinear errors-in-variables regression with internal validation data. Inferential techniques are based on ideas extracted from several previous works on semiparametric maximum likelihood for errors-in-variables problems. The illustration of the example clarifies practical aspects of the associated computational, inferential, and data analytic techniques.

  2. Adaptive Modeling: An Approach for Incorporating Nonlinearity in Regression Analyses.

    PubMed

    Knafl, George J; Barakat, Lamia P; Hanlon, Alexandra L; Hardie, Thomas; Knafl, Kathleen A; Li, Yimei; Deatrick, Janet A

    2017-02-01

    Although regression relationships commonly are treated as linear, this often is not the case. An adaptive approach is described for identifying nonlinear relationships based on power transforms of predictor (or independent) variables and for assessing whether or not relationships are distinctly nonlinear. It is also possible to model adaptively both means and variances of continuous outcome (or dependent) variables and to adaptively power transform positive-valued continuous outcomes, along with their predictors. Example analyses are provided of data from parents in a nursing study on emotional-health-related quality of life for childhood brain tumor survivors as a function of the effort to manage the survivors' condition. These analyses demonstrate that relationships, including moderation relationships, can be distinctly nonlinear, that conclusions about means can be affected by accounting for non-constant variances, and that outcome transformation along with predictor transformation can provide distinct improvements and can resolve skewness problems.© 2017 Wiley Periodicals, Inc.

  3. Detecting influential observations in nonlinear regression modeling of groundwater flow

    USGS Publications Warehouse

    Yager, R.M.

    1998-01-01

    Nonlinear regression is used to estimate optimal parameter values in models of groundwater flow to ensure that differences between predicted and observed heads and flows do not result from nonoptimal parameter values. Parameter estimates can be affected, however, by observations that disproportionately influence the regression, such as outliers that exert undue leverage on the objective function. Certain statistics developed for linear regression can be used to detect influential observations in nonlinear regression if the models are approximately linear. This paper discusses the application of Cook's D, which measures the effect of omitting a single observation on a set of estimated parameter values, and the statistical parameter DFBETAS, which quantifies the influence of an observation on each parameter. The influence statistics were used to (1) identify the influential observations in the calibration of a three-dimensional, groundwater flow model of a fractured-rock aquifer through nonlinear regression, and (2) quantify the effect of omitting influential observations on the set of estimated parameter values. Comparison of the spatial distribution of Cook's D with plots of model sensitivity shows that influential observations correspond to areas where the model heads are most sensitive to certain parameters, and where predicted groundwater flow rates are largest. Five of the six discharge observations were identified as influential, indicating that reliable measurements of groundwater flow rates are valuable data in model calibration. DFBETAS are computed and examined for an alternative model of the aquifer system to identify a parameterization error in the model design that resulted in overestimation of the effect of anisotropy on horizontal hydraulic conductivity.

  4. Effects of model sensitivity and nonlinearity on nonlinear regression of ground water flow

    USGS Publications Warehouse

    Yager, R.M.

    2004-01-01

    Nonlinear regression is increasingly applied to the calibration of hydrologic models through the use of perturbation methods to compute the Jacobian or sensitivity matrix required by the Gauss-Newton optimization method. Sensitivities obtained by perturbation methods can be less accurate than those obtained by direct differentiation, however, and concern has arisen that the optimal parameter values and the associated parameter covariance matrix computed by perturbation could also be less accurate. Sensitivities computed by both perturbation and direct differentiation were applied in nonlinear regression calibration of seven ground water flow models. The two methods gave virtually identical optimum parameter values and covariances for the three models that were relatively linear and two of the models that were relatively nonlinear, but gave widely differing results for two other nonlinear models. The perturbation method performed better than direct differentiation in some regressions with the nonlinear models, apparently because approximate sensitivities computed for an interval yielded better search directions than did more accurately computed sensitivities for a point. The method selected to avoid overshooting minima on the error surface when updating parameter values with the Gauss-Newton procedure appears for nonlinear models to be more important than the method of sensitivity calculation in controlling regression convergence.

  5. A nonlinear regression model-based predictive control algorithm.

    PubMed

    Dubay, R; Abu-Ayyad, M; Hernandez, J M

    2009-04-01

    This paper presents a unique approach for designing a nonlinear regression model-based predictive controller (NRPC) for single-input-single-output (SISO) and multi-input-multi-output (MIMO) processes that are common in industrial applications. The innovation of this strategy is that the controller structure allows nonlinear open-loop modeling to be conducted while closed-loop control is executed every sampling instant. Consequently, the system matrix is regenerated every sampling instant using a continuous function providing a more accurate prediction of the plant. Computer simulations are carried out on nonlinear plants, demonstrating that the new approach is easily implemented and provides tight control. Also, the proposed algorithm is implemented on two real time SISO applications; a DC motor, a plastic injection molding machine and a nonlinear MIMO thermal system comprising three temperature zones to be controlled with interacting effects. The experimental closed-loop responses of the proposed algorithm were compared to a multi-model dynamic matrix controller (MPC) with improved results for various set point trajectories. Good disturbance rejection was attained, resulting in improved tracking of multi-set point profiles in comparison to multi-model MPC.

  6. A note on the empirical likelihood confidence band for hazards ratio with covariate adjustment.

    PubMed

    Zhu, Shihong; Yang, Yifan; Zhou, Mai

    2015-09-01

    In medical studies comparing two treatments in the presence of censored data, the stratified Cox model is an important tool that has the ability to flexibly handle non-proportional hazards while allowing parsimonious covariate adjustment. In order to capture the cumulative treatment effect, the ratio of the treatment specific cumulative baseline hazards is often used as a measure of the treatment effect. Pointwise and simultaneous confidence bands associated with the estimated ratio provide a global picture of how the treatment effect evolves over time. Recently, Dong and Matthews (2012, Biometrics 68, 408-418) proposed to construct a pointwise confidence interval for the ratio using a plug-in type empirical likelihood approach. However, their result on the limiting distribution of the empirical likelihood ratio is generally incorrect and the resulting confidence interval is asymptotically undercovering. In this article, we derive the correct limiting distribution for the likelihood ratio statistic. We also present simulation studies to demonstrate the effectiveness of our approach.

  7. Asymptotically Normal and Efficient Estimation of Covariate-Adjusted Gaussian Graphical Model

    PubMed Central

    Chen, Mengjie; Ren, Zhao; Zhao, Hongyu; Zhou, Harrison

    2015-01-01

    A tuning-free procedure is proposed to estimate the covariate-adjusted Gaussian graphical model. For each finite subgraph, this estimator is asymptotically normal and efficient. As a consequence, a confidence interval can be obtained for each edge. The procedure enjoys easy implementation and efficient computation through parallel estimation on subgraphs or edges. We further apply the asymptotic normality result to perform support recovery through edge-wise adaptive thresholding. This support recovery procedure is called ANTAC, standing for Asymptotically Normal estimation with Thresholding after Adjusting Covariates. ANTAC outperforms other methodologies in the literature in a range of simulation studies. We apply ANTAC to identify gene-gene interactions using an eQTL dataset. Our result achieves better interpretability and accuracy in comparison with CAMPE. PMID:27499564

  8. Development and Application of Nonlinear Land-Use Regression Models

    NASA Astrophysics Data System (ADS)

    Champendal, Alexandre; Kanevski, Mikhail; Huguenot, Pierre-Emmanuel

    2014-05-01

    The problem of air pollution modelling in urban zones is of great importance both from scientific and applied points of view. At present there are several fundamental approaches either based on science-based modelling (air pollution dispersion) or on the application of space-time geostatistical methods (e.g. family of kriging models or conditional stochastic simulations). Recently, there were important developments in so-called Land Use Regression (LUR) models. These models take into account geospatial information (e.g. traffic network, sources of pollution, average traffic, population census, land use, etc.) at different scales, for example, using buffering operations. Usually the dimension of the input space (number of independent variables) is within the range of (10-100). It was shown that LUR models have some potential to model complex and highly variable patterns of air pollution in urban zones. Most of LUR models currently used are linear models. In the present research the nonlinear LUR models are developed and applied for Geneva city. Mainly two nonlinear data-driven models were elaborated: multilayer perceptron and random forest. An important part of the research deals also with a comprehensive exploratory data analysis using statistical, geostatistical and time series tools. Unsupervised self-organizing maps were applied to better understand space-time patterns of the pollution. The real data case study deals with spatial-temporal air pollution data of Geneva (2002-2011). Nitrogen dioxide (NO2) has caught our attention. It has effects on human health and on plants; NO2 contributes to the phenomenon of acid rain. The negative effects of nitrogen dioxides on plants are the reduction of the growth, production and pesticide resistance. And finally, the effects on materials: nitrogen dioxide increases the corrosion. The data used for this study consist of a set of 106 NO2 passive sensors. 80 were used to build the models and the remaining 36 have constituted

  9. Fault prediction for nonlinear stochastic system with incipient faults based on particle filter and nonlinear regression.

    PubMed

    Ding, Bo; Fang, Huajing

    2017-03-31

    This paper is concerned with the fault prediction for the nonlinear stochastic system with incipient faults. Based on the particle filter and the reasonable assumption about the incipient faults, the modified fault estimation algorithm is proposed, and the system state is estimated simultaneously. According to the modified fault estimation, an intuitive fault detection strategy is introduced. Once each of the incipient fault is detected, the parameters of which are identified by a nonlinear regression method. Then, based on the estimated parameters, the future fault signal can be predicted. Finally, the effectiveness of the proposed method is verified by the simulations of the Three-tank system.

  10. Piecewise nonlinear regression: a statistical look at lamp performance

    NASA Astrophysics Data System (ADS)

    Halverson, Galen D.; Hamilton, M. Guyene

    1996-09-01

    Ultraviolet (UV) thickness measurement equipment has little room for variation when determining ultra thin films which are 70 angstroms or less. High lamp performance is critical for measurement validity. A quality conscious semiconductor must have data to verify a vendor claim of 'The lamp performance will perform with no degradation for up to (xxx) hours of normal operation.' In this article we review a real case where data was collected and examined to answer important questions about lamp performance in UV measurement equipment. How long could a lamp be used before performance degraded enough to necessitate a lamp replacement? This article will illustrate how we used standards and actual measurements to collect data for this study. Plots are included showing actual collected data followed by a discussion of alternative methods for statistical examination of the data. This discussion will include an illustration of an original and useful statistical approach for determining the point in time when degradation is noticeable. The method for examining data begins with a well known but not too frequency used concept known as piecewise linear regression with a fixed point of join. Then we enhance the method by turning the join point into a variable that is 'floated' using an iterative non-linear regression approach.

  11. The Allometry of Coarse Root Biomass: Log-Transformed Linear Regression or Nonlinear Regression?

    PubMed Central

    Lai, Jiangshan; Yang, Bo; Lin, Dunmei; Kerkhoff, Andrew J.; Ma, Keping

    2013-01-01

    Precise estimation of root biomass is important for understanding carbon stocks and dynamics in forests. Traditionally, biomass estimates are based on allometric scaling relationships between stem diameter and coarse root biomass calculated using linear regression (LR) on log-transformed data. Recently, it has been suggested that nonlinear regression (NLR) is a preferable fitting method for scaling relationships. But while this claim has been contested on both theoretical and empirical grounds, and statistical methods have been developed to aid in choosing between the two methods in particular cases, few studies have examined the ramifications of erroneously applying NLR. Here, we use direct measurements of 159 trees belonging to three locally dominant species in east China to compare the LR and NLR models of diameter-root biomass allometry. We then contrast model predictions by estimating stand coarse root biomass based on census data from the nearby 24-ha Gutianshan forest plot and by testing the ability of the models to predict known root biomass values measured on multiple tropical species at the Pasoh Forest Reserve in Malaysia. Based on likelihood estimates for model error distributions, as well as the accuracy of extrapolative predictions, we find that LR on log-transformed data is superior to NLR for fitting diameter-root biomass scaling models. More importantly, inappropriately using NLR leads to grossly inaccurate stand biomass estimates, especially for stands dominated by smaller trees. PMID:24116197

  12. A Simulation Study on the Performance of the Simple Difference and Covariance-Adjusted Scores in Randomized Experimental Designs

    ERIC Educational Resources Information Center

    Petscher, Yaacov; Schatschneider, Christopher

    2011-01-01

    Research by Huck and McLean (1975) demonstrated that the covariance-adjusted score is more powerful than the simple difference score, yet recent reviews indicate researchers are equally likely to use either score type in two-wave randomized experimental designs. A Monte Carlo simulation was conducted to examine the conditions under which the…

  13. INVESTIGATING DIFFERENCES IN BRAIN FUNCTIONAL NETWORKS USING HIERARCHICAL COVARIATE-ADJUSTED INDEPENDENT COMPONENT ANALYSIS

    PubMed Central

    Shi, Ran

    2016-01-01

    Human brains perform tasks via complex functional networks consisting of separated brain regions. A popular approach to characterize brain functional networks in fMRI studies is independent component analysis (ICA), which is a powerful method to reconstruct latent source signals from their linear mixtures. In many fMRI studies, an important goal is to investigate how brain functional networks change according to specific clinical and demographic variabilities. Existing ICA methods, however, cannot directly incorporate covariate effects in ICA decomposition. Heuristic post-ICA analysis to address this need can be inaccurate and inefficient. In this paper, we propose a hierarchical covariate-adjusted ICA (hc-ICA) model that provides a formal statistical framework for estimating covariate effects and testing differences between brain functional networks. Our method provides a more reliable and powerful statistical tool for evaluating group differences in brain functional networks while appropriately controlling for potential confounding factors. We present an analytically tractable EM algorithm to obtain maximum likelihood estimates of our model. We also develop a subspace-based approximate EM that runs significantly faster while retaining high accuracy. To test the differences in functional networks, we introduce a voxel-wise approximate inference procedure which eliminates the need of computationally expensive covariance matrix estimation and inversion. We demonstrate the advantages of our methods over the existing method via simulation studies. We apply our method to an fMRI study to investigate differences in brain functional networks associated with post-traumatic stress disorder (PTSD).

  14. A Stable and Efficient Algorithm for Nonlinear Orthogonal Distance Regression.

    DTIC Science & Technology

    1985-12-01

    problem as total least squares. Britt .- and Luecke [BriL73] consider the nonlinear case as well as the nonlinear implicit case and present an...REFERENCES (Bar74] Bard, Y. (1974), Nonlinear Parameter Estimation, Academic Press, New York. [BriL73] Britt , H. I., and R. H. Luecke (1973),"The

  15. Comparison between Linear and Nonlinear Regression in a Laboratory Heat Transfer Experiment

    ERIC Educational Resources Information Center

    Gonçalves, Carine Messias; Schwaab, Marcio; Pinto, José Carlos

    2013-01-01

    In order to interpret laboratory experimental data, undergraduate students are used to perform linear regression through linearized versions of nonlinear models. However, the use of linearized models can lead to statistically biased parameter estimates. Even so, it is not an easy task to introduce nonlinear regression and show for the students…

  16. Predicting dissolved oxygen concentration using kernel regression modeling approaches with nonlinear hydro-chemical data.

    PubMed

    Singh, Kunwar P; Gupta, Shikha; Rai, Premanjali

    2014-05-01

    Kernel function-based regression models were constructed and applied to a nonlinear hydro-chemical dataset pertaining to surface water for predicting the dissolved oxygen levels. Initial features were selected using nonlinear approach. Nonlinearity in the data was tested using BDS statistics, which revealed the data with nonlinear structure. Kernel ridge regression, kernel principal component regression, kernel partial least squares regression, and support vector regression models were developed using the Gaussian kernel function and their generalization and predictive abilities were compared in terms of several statistical parameters. Model parameters were optimized using the cross-validation procedure. The proposed kernel regression methods successfully captured the nonlinear features of the original data by transforming it to a high dimensional feature space using the kernel function. Performance of all the kernel-based modeling methods used here were comparable both in terms of predictive and generalization abilities. Values of the performance criteria parameters suggested for the adequacy of the constructed models to fit the nonlinear data and their good predictive capabilities.

  17. Testing nonlinear regression parameters under heteroscedastic, normally distributed errors.

    PubMed

    Kimura, D K

    1990-09-01

    Likelihood ratio tests for parameters estimated assuming normally distributed errors are examined under a variety of homoscedastic and heteroscedastic variance assumptions. It is assumed that gamma ij, the jth observation from the ith population, is distributed as N[mu(chi ij, beta i), (sigma i mu(chi ij, beta i)theta i)2]. By varying sigma 2i and theta i, this model contains the most obvious examples of homoscedastic and heteroscedastic variability. Under this model, the null hypothesis of equal beta i's can easily be tested using the likelihood ratio criterion. Also considered is the two-sample chi-square statistic, chi 2t = U'S-1 U, where U is the difference vector of nonlinear least squares parameter estimates and S is an estimate of the covariance matrix of U. Monte Carlo simulation using the von Bertalanffy growth curve as an example is used to evaluate several test statistics for Type I error rates under different sampling assumptions.

  18. A comparative study between nonlinear regression and nonparametric approaches for modelling Phalaris paradoxa seedling emergence

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Parametric non-linear regression (PNR) techniques commonly are used to develop weed seedling emergence models. Such techniques, however, require statistical assumptions that are difficult to meet. To examine and overcome these limitations, we compared PNR with a nonparametric estimation technique. F...

  19. Improving sub-pixel imperviousness change prediction by ensembling heterogeneous non-linear regression models

    NASA Astrophysics Data System (ADS)

    Drzewiecki, Wojciech

    2016-12-01

    In this work nine non-linear regression models were compared for sub-pixel impervious surface area mapping from Landsat images. The comparison was done in three study areas both for accuracy of imperviousness coverage evaluation in individual points in time and accuracy of imperviousness change assessment. The performance of individual machine learning algorithms (Cubist, Random Forest, stochastic gradient boosting of regression trees, k-nearest neighbors regression, random k-nearest neighbors regression, Multivariate Adaptive Regression Splines, averaged neural networks, and support vector machines with polynomial and radial kernels) was also compared with the performance of heterogeneous model ensembles constructed from the best models trained using particular techniques. The results proved that in case of sub-pixel evaluation the most accurate prediction of change may not necessarily be based on the most accurate individual assessments. When single methods are considered, based on obtained results Cubist algorithm may be advised for Landsat based mapping of imperviousness for single dates. However, Random Forest may be endorsed when the most reliable evaluation of imperviousness change is the primary goal. It gave lower accuracies for individual assessments, but better prediction of change due to more correlated errors of individual predictions. Heterogeneous model ensembles performed for individual time points assessments at least as well as the best individual models. In case of imperviousness change assessment the ensembles always outperformed single model approaches. It means that it is possible to improve the accuracy of sub-pixel imperviousness change assessment using ensembles of heterogeneous non-linear regression models.

  20. A regularization corrected score method for nonlinear regression models with covariate error.

    PubMed

    Zucker, David M; Gorfine, Malka; Li, Yi; Tadesse, Mahlet G; Spiegelman, Donna

    2013-03-01

    Many regression analyses involve explanatory variables that are measured with error, and failing to account for this error is well known to lead to biased point and interval estimates of the regression coefficients. We present here a new general method for adjusting for covariate error. Our method consists of an approximate version of the Stefanski-Nakamura corrected score approach, using the method of regularization to obtain an approximate solution of the relevant integral equation. We develop the theory in the setting of classical likelihood models; this setting covers, for example, linear regression, nonlinear regression, logistic regression, and Poisson regression. The method is extremely general in terms of the types of measurement error models covered, and is a functional method in the sense of not involving assumptions on the distribution of the true covariate. We discuss the theoretical properties of the method and present simulation results in the logistic regression setting (univariate and multivariate). For illustration, we apply the method to data from the Harvard Nurses' Health Study concerning the relationship between physical activity and breast cancer mortality in the period following a diagnosis of breast cancer.

  1. Non-linear modeling using fuzzy principal component regression for Vidyaranyapuram sewage treatment plant, Mysore - India.

    PubMed

    Sulthana, Ayesha; Latha, K C; Imran, Mohammad; Rathan, Ramya; Sridhar, R; Balasubramanian, S

    2014-01-01

    Fuzzy principal component regression (FPCR) is proposed to model the non-linear process of sewage treatment plant (STP) data matrix. The dimension reduction of voluminous data was done by principal component analysis (PCA). The PCA score values were partitioned by fuzzy-c-means (FCM) clustering, and a Takagi-Sugeno-Kang (TSK) fuzzy model was built based on the FCM functions. The FPCR approach was used to predict the reduction in chemical oxygen demand (COD) and biological oxygen demand (BOD) of treated wastewater of Vidyaranyapuram STP with respect to the relations modeled between fuzzy partitioned PCA scores and target output. The designed FPCR model showed the ability to capture the behavior of non-linear processes of STP. The predicted values of reduction in COD and BOD were analyzed by performing the linear regression analysis. The predicted values for COD and BOD reduction showed positive correlation with the observed data.

  2. A comparison of several methods of solving nonlinear regression groundwater flow problems.

    USGS Publications Warehouse

    Cooley, R.L.

    1985-01-01

    Computational efficiency and computer memory requirements for four methods of minimizing functions were compared for four test nonlinear-regression steady state groundwater flow problems. The fastest methods were the Marquardt and quasi-linearization methods, which required almost identical computer times and numbers of iterations; the next fastest was the quasi-Newton method, and last was the Fletcher-Reeves method, which did not converge in 100 iterations for two of the problems.-from Author

  3. An Investigation of Nonlinear Controls and Regression-Adjusted Estimators for Variance Reduction in Computer Simulation

    DTIC Science & Technology

    1991-03-01

    Adjusted Estimators for Variance 1Redutilol in Computer Simutlation by Riichiardl L. R’ r March, 1991 D~issertation Advisor: Peter A.W. Lewis Approved for...OF NONLINEAR CONTROLS AND REGRESSION-ADJUSTED ESTIMATORS FOR VARIANCE REDUCTION IN COMPUTER SIMULATION 12. Personal Author(s) Richard L. Ressler 13a...necessary and identify by block number) This dissertation develops new techniques for variance reduction in computer simulation. It demonstrates that

  4. Multilayer perceptron for robust nonlinear interval regression analysis using genetic algorithms.

    PubMed

    Hu, Yi-Chung

    2014-01-01

    On the basis of fuzzy regression, computational models in intelligence such as neural networks have the capability to be applied to nonlinear interval regression analysis for dealing with uncertain and imprecise data. When training data are not contaminated by outliers, computational models perform well by including almost all given training data in the data interval. Nevertheless, since training data are often corrupted by outliers, robust learning algorithms employed to resist outliers for interval regression analysis have been an interesting area of research. Several approaches involving computational intelligence are effective for resisting outliers, but the required parameters for these approaches are related to whether the collected data contain outliers or not. Since it seems difficult to prespecify the degree of contamination beforehand, this paper uses multilayer perceptron to construct the robust nonlinear interval regression model using the genetic algorithm. Outliers beyond or beneath the data interval will impose slight effect on the determination of data interval. Simulation results demonstrate that the proposed method performs well for contaminated datasets.

  5. A Nonlinear Causality Estimator Based on Non-Parametric Multiplicative Regression

    PubMed Central

    Nicolaou, Nicoletta; Constandinou, Timothy G.

    2016-01-01

    Causal prediction has become a popular tool for neuroscience applications, as it allows the study of relationships between different brain areas during rest, cognitive tasks or brain disorders. We propose a nonparametric approach for the estimation of nonlinear causal prediction for multivariate time series. In the proposed estimator, CNPMR, Autoregressive modeling is replaced by Nonparametric Multiplicative Regression (NPMR). NPMR quantifies interactions between a response variable (effect) and a set of predictor variables (cause); here, we modified NPMR for model prediction. We also demonstrate how a particular measure, the sensitivity Q, could be used to reveal the structure of the underlying causal relationships. We apply CNPMR on artificial data with known ground truth (5 datasets), as well as physiological data (2 datasets). CNPMR correctly identifies both linear and nonlinear causal connections that are present in the artificial data, as well as physiologically relevant connectivity in the real data, and does not seem to be affected by filtering. The Sensitivity measure also provides useful information about the latent connectivity.The proposed estimator addresses many of the limitations of linear Granger causality and other nonlinear causality estimators. CNPMR is compared with pairwise and conditional Granger causality (linear) and Kernel-Granger causality (nonlinear). The proposed estimator can be applied to pairwise or multivariate estimations without any modifications to the main method. Its nonpametric nature, its ability to capture nonlinear relationships and its robustness to filtering make it appealing for a number of applications. PMID:27378901

  6. A Nonlinear Causality Estimator Based on Non-Parametric Multiplicative Regression.

    PubMed

    Nicolaou, Nicoletta; Constandinou, Timothy G

    2016-01-01

    Causal prediction has become a popular tool for neuroscience applications, as it allows the study of relationships between different brain areas during rest, cognitive tasks or brain disorders. We propose a nonparametric approach for the estimation of nonlinear causal prediction for multivariate time series. In the proposed estimator, C NPMR , Autoregressive modeling is replaced by Nonparametric Multiplicative Regression (NPMR). NPMR quantifies interactions between a response variable (effect) and a set of predictor variables (cause); here, we modified NPMR for model prediction. We also demonstrate how a particular measure, the sensitivity Q, could be used to reveal the structure of the underlying causal relationships. We apply C NPMR on artificial data with known ground truth (5 datasets), as well as physiological data (2 datasets). C NPMR correctly identifies both linear and nonlinear causal connections that are present in the artificial data, as well as physiologically relevant connectivity in the real data, and does not seem to be affected by filtering. The Sensitivity measure also provides useful information about the latent connectivity.The proposed estimator addresses many of the limitations of linear Granger causality and other nonlinear causality estimators. C NPMR is compared with pairwise and conditional Granger causality (linear) and Kernel-Granger causality (nonlinear). The proposed estimator can be applied to pairwise or multivariate estimations without any modifications to the main method. Its nonpametric nature, its ability to capture nonlinear relationships and its robustness to filtering make it appealing for a number of applications.

  7. Comparison of Linear and Non-linear Regression Analysis to Determine Pulmonary Pressure in Hyperthyroidism

    PubMed Central

    Scarneciu, Camelia C.; Sangeorzan, Livia; Rus, Horatiu; Scarneciu, Vlad D.; Varciu, Mihai S.; Andreescu, Oana; Scarneciu, Ioan

    2017-01-01

    Objectives: This study aimed at assessing the incidence of pulmonary hypertension (PH) at newly diagnosed hyperthyroid patients and at finding a simple model showing the complex functional relation between pulmonary hypertension in hyperthyroidism and the factors causing it. Methods: The 53 hyperthyroid patients (H-group) were evaluated mainly by using an echocardiographical method and compared with 35 euthyroid (E-group) and 25 healthy people (C-group). In order to identify the factors causing pulmonary hypertension the statistical method of comparing the values of arithmetical means is used. The functional relation between the two random variables (PAPs and each of the factors determining it within our research study) can be expressed by linear or non-linear function. By applying the linear regression method described by a first-degree equation the line of regression (linear model) has been determined; by applying the non-linear regression method described by a second degree equation, a parabola-type curve of regression (non-linear or polynomial model) has been determined. We made the comparison and the validation of these two models by calculating the determination coefficient (criterion 1), the comparison of residuals (criterion 2), application of AIC criterion (criterion 3) and use of F-test (criterion 4). Results: From the H-group, 47% have pulmonary hypertension completely reversible when obtaining euthyroidism. The factors causing pulmonary hypertension were identified: previously known- level of free thyroxin, pulmonary vascular resistance, cardiac output; new factors identified in this study- pretreatment period, age, systolic blood pressure. According to the four criteria and to the clinical judgment, we consider that the polynomial model (graphically parabola- type) is better than the linear one. Conclusions: The better model showing the functional relation between the pulmonary hypertension in hyperthyroidism and the factors identified in this study is

  8. An ensemble Kalman filter for statistical estimation of physics constrained nonlinear regression models

    SciTech Connect

    Harlim, John; Mahdi, Adam; Majda, Andrew J.

    2014-01-15

    A central issue in contemporary science is the development of nonlinear data driven statistical–dynamical models for time series of noisy partial observations from nature or a complex model. It has been established recently that ad-hoc quadratic multi-level regression models can have finite-time blow-up of statistical solutions and/or pathological behavior of their invariant measure. Recently, a new class of physics constrained nonlinear regression models were developed to ameliorate this pathological behavior. Here a new finite ensemble Kalman filtering algorithm is developed for estimating the state, the linear and nonlinear model coefficients, the model and the observation noise covariances from available partial noisy observations of the state. Several stringent tests and applications of the method are developed here. In the most complex application, the perfect model has 57 degrees of freedom involving a zonal (east–west) jet, two topographic Rossby waves, and 54 nonlinearly interacting Rossby waves; the perfect model has significant non-Gaussian statistics in the zonal jet with blocked and unblocked regimes and a non-Gaussian skewed distribution due to interaction with the other 56 modes. We only observe the zonal jet contaminated by noise and apply the ensemble filter algorithm for estimation. Numerically, we find that a three dimensional nonlinear stochastic model with one level of memory mimics the statistical effect of the other 56 modes on the zonal jet in an accurate fashion, including the skew non-Gaussian distribution and autocorrelation decay. On the other hand, a similar stochastic model with zero memory levels fails to capture the crucial non-Gaussian behavior of the zonal jet from the perfect 57-mode model.

  9. Aboveground biomass and carbon stocks modelling using non-linear regression model

    NASA Astrophysics Data System (ADS)

    Ain Mohd Zaki, Nurul; Abd Latif, Zulkiflee; Nazip Suratman, Mohd; Zainee Zainal, Mohd

    2016-06-01

    Aboveground biomass (AGB) is an important source of uncertainty in the carbon estimation for the tropical forest due to the variation biodiversity of species and the complex structure of tropical rain forest. Nevertheless, the tropical rainforest holds the most extensive forest in the world with the vast diversity of tree with layered canopies. With the usage of optical sensor integrate with empirical models is a common way to assess the AGB. Using the regression, the linkage between remote sensing and a biophysical parameter of the forest may be made. Therefore, this paper exemplifies the accuracy of non-linear regression equation of quadratic function to estimate the AGB and carbon stocks for the tropical lowland Dipterocarp forest of Ayer Hitam forest reserve, Selangor. The main aim of this investigation is to obtain the relationship between biophysical parameter field plots with the remotely-sensed data using nonlinear regression model. The result showed that there is a good relationship between crown projection area (CPA) and carbon stocks (CS) with Pearson Correlation (p < 0.01), the coefficient of correlation (r) is 0.671. The study concluded that the integration of Worldview-3 imagery with the canopy height model (CHM) raster based LiDAR were useful in order to quantify the AGB and carbon stocks for a larger sample area of the lowland Dipterocarp forest.

  10. Confidence intervals for a crop yield-loss function in nonlinear regression

    SciTech Connect

    Lee, E.H.; Tingey, D.T.; Hogsett, W.E.

    1990-01-01

    Quantifying the relationship between chronic pollutant exposure and the ensuring biological response requires consideration of nonlinear functions that are flexible enough to generate a wide range of response curves. The linear approximation interval estimates for ozone-induced relative crop yield loss are sensitive to parameter curvature effects in nonlinear regression. The adequacy of Wald's confidence interval for proportional response is studied using the nonlinearity measures proposed by Bates and Watts (1980), Cook and Goldberg (1986), and Clarke (1987a b) and the profile t plots of Bates and Watts (1988). Numerical examples comparing Wald's, likelihood ratio, the bootstrap, and Clarke's adjusted 95% confidence intervals for relative crop yield loss are presented for a number of ozone exposure studies conducted by the National Crop Loss Assessment Network (NCLAN) program. At ambient levels of ozone concentration, the effects of nonlinearity were significant and invalidated the adequacy of Wald's confidence interval. Depending upon the severity of the curvature effects, an alternative interval (i.e., Clarke's adjustment to Wald's interval or the likelihood ratio interval) for proportional yield loss should be considered.

  11. Describing Adequacy of cure with maximum hardness ratios and non-linear regression.

    PubMed

    Bouschlicher, Murray; Berning, Kristen; Qian, Fang

    2008-01-01

    Knoop Hardness (KH) ratios (HR) > or = 80% are commonly used as criteria for the adequate cure of a composite. These per-specimen HRs can be misleading, as both numerator and denominator may increase concurrently, prior to reaching an asymptotic, top-surface maximum hardness value (H(MAX)). Extended cure times were used to establish H(MAX) and descriptive statistics, and non-linear regression analysis were used to describe the relationship between exposure duration and HR and predict the time required for HR-H(MAX) = 80%. Composite samples 2.00 x 5.00 mm diameter (n = 5/grp) were cured for 10 seconds, 20 seconds, 40 seconds, 60 seconds, 90 seconds, 120 seconds, 180 seconds and 240 seconds in a 2-composite x 2-light curing unit design. A microhybrid (Point 4, P4) or microfill resin (Heliomolar, HM) composite was cured with a QTH or LED light curing unit and then stored in the dark for 24 hours prior to KH testing. Non-linear regression was calculated with: H = (H(MAX)-c)(1-e(-kt)) +c, H(MAX) = maximum hardness (a theoretical asymptotic value), c = constant (t = 0), k = rate constant and t = exposure duration describes the relationship between radiant exposure (irradiance x time) and HRs. Exposure durations for HR-H(MAX) = 80% were calculated. Two-sample t-tests for pairwise comparisons evaluated relative performance of the light curing units for similar surface x composite x exposure (10-90s). A good measure of goodness-of-fit of the non-linear regression, r2, ranged from 0.68-0.95. (mean = 0.82). Microhybrid (P4) exposure to achieve HR-H(MAX = 80% was 21 seconds for QTH and 34 seconds for the LED light curing unit. Corresponding values for microfill (HM) were 71 and 74 seconds, respectively. P4 HR-H(MAX) of LED vs QTH was statistically similar for 10 to 40 seconds, while HM HR-H(MAX) of LED was significantly lower than QTH for 10 to 40 seconds. It was concluded that redefined hardness ratios based on maximum hardness used in conjunction with non-linear regression

  12. Inference of dense spectral reflectance images from sparse reflectance measurement using non-linear regression modeling

    NASA Astrophysics Data System (ADS)

    Deglint, Jason; Kazemzadeh, Farnoud; Wong, Alexander; Clausi, David A.

    2015-09-01

    One method to acquire multispectral images is to sequentially capture a series of images where each image contains information from a different bandwidth of light. Another method is to use a series of beamsplitters and dichroic filters to guide different bandwidths of light onto different cameras. However, these methods are very time consuming and expensive and perform poorly in dynamic scenes or when observing transient phenomena. An alternative strategy to capturing multispectral data is to infer this data using sparse spectral reflectance measurements captured using an imaging device with overlapping bandpass filters, such as a consumer digital camera using a Bayer filter pattern. Currently the only method of inferring dense reflectance spectra is the Wiener adaptive filter, which makes Gaussian assumptions about the data. However, these assumptions may not always hold true for all data. We propose a new technique to infer dense reflectance spectra from sparse spectral measurements through the use of a non-linear regression model. The non-linear regression model used in this technique is the random forest model, which is an ensemble of decision trees and trained via the spectral characterization of the optical imaging system and spectral data pair generation. This model is then evaluated by spectrally characterizing different patches on the Macbeth color chart, as well as by reconstructing inferred multispectral images. Results show that the proposed technique can produce inferred dense reflectance spectra that correlate well with the true dense reflectance spectra, which illustrates the merits of the technique.

  13. Nonlinear regression modeling of nutrient loads in streams: A Bayesian approach

    USGS Publications Warehouse

    Qian, S.S.; Reckhow, K.H.; Zhai, J.; McMahon, G.

    2005-01-01

    A Bayesian nonlinear regression modeling method is introduced and compared with the least squares method for modeling nutrient loads in stream networks. The objective of the study is to better model spatial correlation in river basin hydrology and land use for improving the model as a forecasting tool. The Bayesian modeling approach is introduced in three steps, each with a more complicated model and data error structure. The approach is illustrated using a data set from three large river basins in eastern North Carolina. Results indicate that the Bayesian model better accounts for model and data uncertainties than does the conventional least squares approach. Applications of the Bayesian models for ambient water quality standards compliance and TMDL assessment are discussed. Copyright 2005 by the American Geophysical Union.

  14. Modeling nonlinear relationships in ERP data using mixed-effects regression with R examples.

    PubMed

    Tremblay, Antoine; Newman, Aaron J

    2015-01-01

    In the analysis of psychological and psychophysiological data, the relationship between two variables is often assumed to be a straight line. This may be due to the prevalence of the general linear model in data analysis in these fields, which makes this assumption implicitly. However, there are many problems for which this assumption does not hold. In this paper, we show that, in the analysis of event-related potential (ERP) data, the assumption of linearity comes at a cost and may significantly affect the inferences drawn from the data. We demonstrate why the assumption of linearity should be relaxed and how to model nonlinear relationships between ERP amplitudes and predictor variables within the familiar framework of generalized linear models, using regression splines and mixed-effects modeling.

  15. Simultaneous confidence bands for nonlinear regression models with application to population pharmacokinetic analyses.

    PubMed

    Gsteiger, S; Bretz, F; Liu, W

    2011-07-01

    Many applications in biostatistics rely on nonlinear regression models, such as, for example, population pharmacokinetic and pharmacodynamic modeling, or modeling approaches for dose-response characterization and dose selection. Such models are often expressed as nonlinear mixed-effects models, which are implemented in all major statistical software packages. Inference on the model curve can be based on the estimated parameters, from which pointwise confidence intervals for the mean profile at any single point in the covariate region (time, dose, etc.) can be derived. These pointwise confidence intervals, however, should not be used for simultaneous inferences beyond that single covariate value. If assessment over the entire covariate region is required, the joint coverage probability by using the combined pointwise confidence intervals is likely to be less than the nominal coverage probability. In this paper we consider simultaneous confidence bands for the mean profile over the covariate region of interest and propose two large-sample methods for their construction. The first method is based on the Schwarz inequality and an asymptotic χ(2) distribution. The second method relies on simulating from a multivariate normal distribution. We illustrate the methods with the pharmacokinetics of theophylline. In addition, we report the results of an extensive simulation study to investigate the operating characteristics of the two construction methods. Finally, we present extensions to construct simultaneous confidence bands for the difference of two models and to assess equivalence between two models in biosimilarity applications.

  16. On the use of log-transformation vs. nonlinear regression for analyzing biological power laws

    USGS Publications Warehouse

    Xiao, X.; White, E.P.; Hooten, M.B.; Durham, S.L.

    2011-01-01

    Power-law relationships are among the most well-studied functional relationships in biology. Recently the common practice of fitting power laws using linear regression (LR) on log-transformed data has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations, we demonstrate that the error distribution determines which method performs better, with NLR better characterizing data with additive, homoscedastic, normal error and LR better characterizing data with multiplicative, heteroscedastic, lognormal error. Analysis of 471 biological power laws shows that both forms of error occur in nature. While previous analyses based on log-transformation appear to be generally valid, future analyses should choose methods based on a combination of biological plausibility and analysis of the error distribution. We provide detailed guidelines and associated computer code for doing so, including a model averaging approach for cases where the error structure is uncertain. ?? 2011 by the Ecological Society of America.

  17. Nonlinear Trimodal Regression Analysis of Radiodensitometric Distributions to Quantify Sarcopenic and Sequelae Muscle Degeneration

    PubMed Central

    Árnadóttir, Í.; Gíslason, M. K.; Carraro, U.

    2016-01-01

    Muscle degeneration has been consistently identified as an independent risk factor for high mortality in both aging populations and individuals suffering from neuromuscular pathology or injury. While there is much extant literature on its quantification and correlation to comorbidities, a quantitative gold standard for analyses in this regard remains undefined. Herein, we hypothesize that rigorously quantifying entire radiodensitometric distributions elicits more muscle quality information than average values reported in extant methods. This study reports the development and utility of a nonlinear trimodal regression analysis method utilized on radiodensitometric distributions of upper leg muscles from CT scans of a healthy young adult, a healthy elderly subject, and a spinal cord injury patient. The method was then employed with a THA cohort to assess pre- and postsurgical differences in their healthy and operative legs. Results from the initial representative models elicited high degrees of correlation to HU distributions, and regression parameters highlighted physiologically evident differences between subjects. Furthermore, results from the THA cohort echoed physiological justification and indicated significant improvements in muscle quality in both legs following surgery. Altogether, these results highlight the utility of novel parameters from entire HU distributions that could provide insight into the optimal quantification of muscle degeneration. PMID:28115982

  18. On the use of log-transformation vs. nonlinear regression for analyzing biological power laws.

    PubMed

    Xiao, Xiao; White, Ethan P; Hooten, Mevin B; Durham, Susan L

    2011-10-01

    Power-law relationships are among the most well-studied functional relationships in biology. Recently the common practice of fitting power laws using linear regression (LR) on log-transformed data has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations, we demonstrate that the error distribution determines which method performs better, with NLR better characterizing data with additive, homoscedastic, normal error and LR better characterizing data with multiplicative, heteroscedastic, lognormal error. Analysis of 471 biological power laws shows that both forms of error occur in nature. While previous analyses based on log-transformation appear to be generally valid, future analyses should choose methods based on a combination of biological plausibility and analysis of the error distribution. We provide detailed guidelines and associated computer code for doing so, including a model averaging approach for cases where the error structure is uncertain.

  19. Estimate error of frequency-dependent Q introduced by linear regression and its nonlinear implementation

    NASA Astrophysics Data System (ADS)

    Li, Guofa; Huang, Wei; Zheng, Hao; Zhang, Baoqing

    2016-02-01

    The spectral ratio method (SRM) is widely used to estimate quality factor Q via the linear regression of seismic attenuation under the assumption of a constant Q. However, the estimate error will be introduced when this assumption is violated. For the frequency-dependent Q described by a power-law function, we derived the analytical expression of estimate error as a function of the power-law exponent γ and the ratio of the bandwidth to the central frequency σ . Based on the theoretical analysis, we found that the estimate errors are mainly dominated by the exponent γ , and less affected by the ratio σ . This phenomenon implies that the accuracy of the Q estimate can hardly be improved by adjusting the width and range of the frequency band. Hence, we proposed a two-parameter regression method to estimate the frequency-dependent Q from the nonlinear seismic attenuation. The proposed method was tested using the direct waves acquired by a near-surface cross-hole survey, and its reliability was evaluated in comparison with the result of SRM.

  20. A Nonlinear Adaptive Beamforming Algorithm Based on Least Squares Support Vector Regression

    PubMed Central

    Wang, Lutao; Jin, Gang; Li, Zhengzhou; Xu, Hongbin

    2012-01-01

    To overcome the performance degradation in the presence of steering vector mismatches, strict restrictions on the number of available snapshots, and numerous interferences, a novel beamforming approach based on nonlinear least-square support vector regression machine (LS-SVR) is derived in this paper. In this approach, the conventional linearly constrained minimum variance cost function used by minimum variance distortionless response (MVDR) beamformer is replaced by a squared-loss function to increase robustness in complex scenarios and provide additional control over the sidelobe level. Gaussian kernels are also used to obtain better generalization capacity. This novel approach has two highlights, one is a recursive regression procedure to estimate the weight vectors on real-time, the other is a sparse model with novelty criterion to reduce the final size of the beamformer. The analysis and simulation tests show that the proposed approach offers better noise suppression capability and achieve near optimal signal-to-interference-and-noise ratio (SINR) with a low computational burden, as compared to other recently proposed robust beamforming techniques.

  1. Using Recursive Regression to Explore Nonlinear Relationships and Interactions: A Tutorial Applied to a Multicultural Education Study

    ERIC Educational Resources Information Center

    Strang, Kenneth David

    2009-01-01

    This paper discusses how a seldom-used statistical procedure, recursive regression (RR), can numerically and graphically illustrate data-driven nonlinear relationships and interaction of variables. This routine falls into the family of exploratory techniques, yet a few interesting features make it a valuable compliment to factor analysis and…

  2. A comparative study between nonlinear regression and artificial neural network approaches for modelling wild oat (Avena fatua) field emergence

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Non-linear regression techniques are used widely to fit weed field emergence patterns to soil microclimatic indices using S-type functions. Artificial neural networks present interesting and alternative features for such modeling purposes. In this work, a univariate hydrothermal-time based Weibull m...

  3. A Bayesian Nonlinear Mixed-Effects Regression Model for the Characterization of Early Bactericidal Activity of Tuberculosis Drugs

    PubMed Central

    Burger, Divan Aristo; Schall, Robert

    2015-01-01

    Trials of the early bactericidal activity (EBA) of tuberculosis (TB) treatments assess the decline, during the first few days to weeks of treatment, in colony forming unit (CFU) count of Mycobacterium tuberculosis in the sputum of patients with smear-microscopy-positive pulmonary TB. Profiles over time of CFU data have conventionally been modeled using linear, bilinear, or bi-exponential regression. We propose a new biphasic nonlinear regression model for CFU data that comprises linear and bilinear regression models as special cases and is more flexible than bi-exponential regression models. A Bayesian nonlinear mixed-effects (NLME) regression model is fitted jointly to the data of all patients from a trial, and statistical inference about the mean EBA of TB treatments is based on the Bayesian NLME regression model. The posterior predictive distribution of relevant slope parameters of the Bayesian NLME regression model provides insight into the nature of the EBA of TB treatments; specifically, the posterior predictive distribution allows one to judge whether treatments are associated with monolinear or bilinear decline of log(CFU) count, and whether CFU count initially decreases fast, followed by a slower rate of decrease, or vice versa. PMID:25322214

  4. Growth curve by Gompertz nonlinear regression model in female and males in tambaqui (Colossoma macropomum).

    PubMed

    De Mello, Fernanda; Oliveira, Carlos A L; Ribeiro, Ricardo P; Resende, Emiko K; Povh, Jayme A; Fornari, Darci C; Barreto, Rogério V; McManus, Concepta; Streit, Danilo

    2015-01-01

    Was evaluated the pattern of growth among females and males of tambaqui by Gompertz nonlinear regression model. Five traits of economic importance were measured on 145 animals during the three years, totaling 981 morphometric data analyzed. Different curves were adjusted between males and females for body weight, height and head length and only one curve was adjusted to the width and body length. The asymptotic weight (a) and relative growth rate to maturity (k) were different between sexes in animals with ± 5 kg; slaughter weight practiced by a specific niche market, very profitable. However, there was no difference between males and females up to ± 2 kg; slaughter weight established to supply the bigger consumer market. Females showed weight greater than males (± 280 g), which are more suitable for fish farming purposes defined for the niche market to larger animals. In general, males had lower maximum growth rate (8.66 g / day) than females (9.34 g / day), however, reached faster than females, 476 and 486 days growth rate, respectively. The height and length body are the traits that contributed most to the weight at 516 days (P <0.001).

  5. Trace analysis of acids and bases by conductometric titration with multiparametric non-linear regression.

    PubMed

    Coelho, Lúcia H G; Gutz, Ivano G R

    2006-03-15

    A chemometric method for analysis of conductometric titration data was introduced to extend its applicability to lower concentrations and more complex acid-base systems. Auxiliary pH measurements were made during the titration to assist the calculation of the distribution of protonable species on base of known or guessed equilibrium constants. Conductivity values of each ionized or ionizable species possibly present in the sample were introduced in a general equation where the only unknown parameters were the total concentrations of (conjugated) bases and of strong electrolytes not involved in acid-base equilibria. All these concentrations were adjusted by a multiparametric nonlinear regression (NLR) method, based on the Levenberg-Marquardt algorithm. This first conductometric titration method with NLR analysis (CT-NLR) was successfully applied to simulated conductometric titration data and to synthetic samples with multiple components at concentrations as low as those found in rainwater (approximately 10 micromol L(-1)). It was possible to resolve and quantify mixtures containing a strong acid, formic acid, acetic acid, ammonium ion, bicarbonate and inert electrolyte with accuracy of 5% or better.

  6. Technical Note: Predicting ruminal methane inhibition by condensed tannins using nonlinear exponential decay regression analysis.

    PubMed

    Naumann, H D; Tedeschi, L O; Fonseca, M A

    2015-11-01

    Methane (CH) is a potent greenhouse gas that is normally produced by microbial fermentation in the rumen and released to the environment mainly during eructation. Prediction of ruminal CH production is important for ruminant nutrition, especially for the determination of ME intake to assess the amount of total GE available for metabolism by an animal. Equations have been developed to predict ruminal CH production based on dietary constituents, but none have considered condensed tannins (CT), which are known to impact CH production by ruminants. The objective was to develop an equation to predict ruminal CH, accounting for CT effects. Methane production data were acquired from 48-h in vitro fermentation of a diverse group of warm-season perennial forage legumes containing different concentrations of CT over the course of 3 yr ( = 113). The following nonlinear exponential decay regression equation was developed: CH₄ = 113.6 × exp (-0.1751 x CT) - 2.18), [corrected] in which CH is expressed in grams per kilogram of fermentable organic matter and CT is in percentage of the DM. This equation predicted that CH production could be reduced by approximately 50% when CT is 3.9% DM. This equation is likely more accurate when screening CT-containing forages for their potential ability to mitigate in vitro CH production by ruminants when the CT concentration is greater than 3% DM. Therefore, despite the degree of variability in ruminal CH production, this equation could be used as a tool for screening CT-containing forages for their potential to inhibit ruminal CH. Future research should focus on the development of predictive equations when other potential reducers of ruminal CH are used in conjunction with CT.

  7. What's the Risk? A Simple Approach for Estimating Adjusted Risk Measures from Nonlinear Models Including Logistic Regression

    PubMed Central

    Kleinman, Lawrence C; Norton, Edward C

    2009-01-01

    Objective To develop and validate a general method (called regression risk analysis) to estimate adjusted risk measures from logistic and other nonlinear multiple regression models. We show how to estimate standard errors for these estimates. These measures could supplant various approximations (e.g., adjusted odds ratio [AOR]) that may diverge, especially when outcomes are common. Study Design Regression risk analysis estimates were compared with internal standards as well as with Mantel–Haenszel estimates, Poisson and log-binomial regressions, and a widely used (but flawed) equation to calculate adjusted risk ratios (ARR) from AOR. Data Collection Data sets produced using Monte Carlo simulations. Principal Findings Regression risk analysis accurately estimates ARR and differences directly from multiple regression models, even when confounders are continuous, distributions are skewed, outcomes are common, and effect size is large. It is statistically sound and intuitive, and has properties favoring it over other methods in many cases. Conclusions Regression risk analysis should be the new standard for presenting findings from multiple regression analysis of dichotomous outcomes for cross-sectional, cohort, and population-based case–control studies, particularly when outcomes are common or effect size is large. PMID:18793213

  8. A comparative study of linear and non-linear regression analysis for ammonium exchange by clinoptilolite zeolite.

    PubMed

    Karadag, Dogan; Koc, Yunus; Turan, Mustafa; Ozturk, Mustafa

    2007-06-01

    Ammonium ion exchange from aqueous solution using clinoptilolite zeolite was investigated at laboratory scale. Batch experimental studies were conducted to evaluate the effect of various parameters such as pH, zeolite dosage, contact time, initial ammonium concentration and temperature. Freundlich and Langmuir isotherm models and pseudo-second-order model were fitted to experimental data. Linear and non-linear regression methods were compared to determine the best fitting of isotherm and kinetic model to experimental data. The rate limiting mechanism of ammonium uptake by zeolite was determined as chemical exchange. Non-linear regression has better performance for analyzing experimental data and Freundlich model was better than Langmuir to represent equilibrium data.

  9. Comparison of Linear and Non-Linear Regression Models to Estimate Leaf Area Index of Dryland Shrubs.

    NASA Astrophysics Data System (ADS)

    Dashti, H.; Glenn, N. F.; Ilangakoon, N. T.; Mitchell, J.; Dhakal, S.; Spaete, L.

    2015-12-01

    Leaf area index (LAI) is a key parameter in global ecosystem studies. LAI is considered a forcing variable in land surface processing models since ecosystem dynamics are highly correlated to LAI. In response to environmental limitations, plants in semiarid ecosystems have smaller leaf area, making accurate estimation of LAI by remote sensing a challenging issue. Optical remote sensing (400-2500 nm) techniques to estimate LAI are based either on radiative transfer models (RTMs) or statistical approaches. Considering the complex radiation field of dry ecosystems, simple 1-D RTMs lead to poor results, and on the other hand, inversion of more complex 3-D RTMs is a demanding task which requires the specification of many variables. A good alternative to physical approaches is using methods based on statistics. Similar to many natural phenomena, there is a non-linear relationship between LAI and top of canopy electromagnetic waves reflected to optical sensors. Non-linear regression models can better capture this relationship. However, considering the problem of a few numbers of observations in comparison to the feature space (nnon-linear regression techniques were investigated to estimate LAI. Our study area is located in southwestern Idaho, Great Basin. Sagebrush (Artemisia tridentata spp) serves a critical role in maintaining the structure of this ecosystem. Using a leaf area meter (Accupar LP-80), LAI values were measured in the field. Linear Partial Least Square regression and non-linear, tree based Random Forest regression have been implemented to estimate the LAI of sagebrush from hyperspectral data (AVIRIS-ng) collected in late summer 2014. Cross validation of results indicate that PLS can provide comparable results to Random Forest.

  10. Bayesian quantile regression for nonlinear mixed-effects joint models for longitudinal data in the presence of mismeasured covariate errors.

    PubMed

    Huang, Yangxin; Chen, Jiaqing; Qiu, Huahai

    2016-12-09

    Quantile regression (QR) models have recently received increasing attention in longitudinal studies where measurements of the same individuals are taken repeatedly over time. When continuous (longitudinal) responses follow a distribution that is quite different from a normal distribution, usual mean regression (MR)-based linear models may fail to produce efficient estimators, whereas QR-based linear models may perform satisfactorily. To the best of our knowledge, there have been very few studies on QR-based nonlinear models for longitudinal data in comparison to MR-based nonlinear models. In this article, we study QR-based nonlinear mixed-effects (NLME) joint models for longitudinal data with non-central location and outliers and/or heavy tails in response, and non-normality and measurement errors in covariate under Bayesian framework. The proposed QR-based modeling method is compared with an MR-based one by an AIDS clinical dataset and through simulation studies. The proposed QR joint modeling approach can be not only applied to AIDS clinical studies, but also may have general applications in other fields as long as relevant technical specifications are met.

  11. Multivariate nonlinear regression analysis of trajectory tracking performance using force reflecting joystick in chronic stroke-induced hemiparesis.

    PubMed

    Feng, Xin; Winters, Jack M

    2011-01-01

    Individualizing a neurorehabilitation training protocol requires understanding the performance of subjects with various capabilities under different task settings. We use multivariate regression to evaluate the performance of subjects with stroke-induced hemiparesis in trajectory tracking tasks using a force-reflecting joystick. A nonlinear effect was consistently shown in both dimensions of force field strength and impairment level for selected kinematic performance measures, with greatest sensitivity at lower force fields. This suggests that the form of a force field may play a different "role" for subjects with various impairment levels, and confirms that to achieve optimized therapeutic benefit, it is necessary to personalize interfaces.

  12. A Bayesian Hierarchical Non-Linear Regression Model in Receiver Operating Characteristic Analysis of Clustered Continuous Diagnostic Data

    PubMed Central

    Zou, Kelly H.; O’Malley, A. James

    2005-01-01

    Receiver operating characteristic (ROC) analysis is a useful evaluative method of diagnostic accuracy. A Bayesian hierarchical nonlinear regression model for ROC analysis was developed. A validation analysis of diagnostic accuracy was conducted using prospective multi-center clinical trial prostate cancer biopsy data collected from three participating centers. The gold standard was based on radical prostatectomy to determine local and advanced disease. To evaluate the diagnostic performance of PSA level at fixed levels of Gleason score, a normality transformation was applied to the outcome data. A hierarchical regression analysis incorporating the effects of cluster (clinical center) and cancer risk (low, intermediate, and high) was performed, and the area under the ROC curve (AUC) was estimated. PMID:16161801

  13. Bias associated with using the estimated propensity score as a regression covariate.

    PubMed

    Hade, Erinn M; Lu, Bo

    2014-01-15

    The use of propensity score methods to adjust for selection bias in observational studies has become increasingly popular in public health and medical research. A substantial portion of studies using propensity score adjustment treat the propensity score as a conventional regression predictor. Through a Monte Carlo simulation study, Austin and colleagues. investigated the bias associated with treatment effect estimation when the propensity score is used as a covariate in nonlinear regression models, such as logistic regression and Cox proportional hazards models. We show that the bias exists even in a linear regression model when the estimated propensity score is used and derive the explicit form of the bias. We also conduct an extensive simulation study to compare the performance of such covariate adjustment with propensity score stratification, propensity score matching, inverse probability of treatment weighted method, and nonparametric functional estimation using splines. The simulation scenarios are designed to reflect real data analysis practice. Instead of specifying a known parametric propensity score model, we generate the data by considering various degrees of overlap of the covariate distributions between treated and control groups. Propensity score matching excels when the treated group is contained within a larger control pool, while the model-based adjustment may have an edge when treated and control groups do not have too much overlap. Overall, adjusting for the propensity score through stratification or matching followed by regression or using splines, appears to be a good practical strategy.

  14. Application of nonlinear-regression methods to a ground-water flow model of the Albuquerque Basin, New Mexico

    USGS Publications Warehouse

    Tiedeman, C.R.; Kernodle, J.M.; McAda, D.P.

    1998-01-01

    This report documents the application of nonlinear-regression methods to a numerical model of ground-water flow in the Albuquerque Basin, New Mexico. In the Albuquerque Basin, ground water is the primary source for most water uses. Ground-water withdrawal has steadily increased since the 1940's, resulting in large declines in water levels in the Albuquerque area. A ground-water flow model was developed in 1994 and revised and updated in 1995 for the purpose of managing basin ground- water resources. In the work presented here, nonlinear-regression methods were applied to a modified version of the previous flow model. Goals of this work were to use regression methods to calibrate the model with each of six different configurations of the basin subsurface and to assess and compare optimal parameter estimates, model fit, and model error among the resulting calibrations. The Albuquerque Basin is one in a series of north trending structural basins within the Rio Grande Rift, a region of Cenozoic crustal extension. Mountains, uplifts, and fault zones bound the basin, and rock units within the basin include pre-Santa Fe Group deposits, Tertiary Santa Fe Group basin fill, and post-Santa Fe Group volcanics and sediments. The Santa Fe Group is greater than 14,000 feet (ft) thick in the central part of the basin. During deposition of the Santa Fe Group, crustal extension resulted in development of north trending normal faults with vertical displacements of as much as 30,000 ft. Ground-water flow in the Albuquerque Basin occurs primarily in the Santa Fe Group and post-Santa Fe Group deposits. Water flows between the ground-water system and surface-water bodies in the inner valley of the basin, where the Rio Grande, a network of interconnected canals and drains, and Cochiti Reservoir are located. Recharge to the ground-water flow system occurs as infiltration of precipitation along mountain fronts and infiltration of stream water along tributaries to the Rio Grande; subsurface

  15. Bayesian regression analysis of data with random effects covariates from nonlinear longitudinal measurements

    PubMed Central

    De la Cruz, Rolando; Meza, Cristian; Arribas-Gil, Ana; Carroll, Raymond J.

    2016-01-01

    Joint models for a wide class of response variables and longitudinal measurements consist on a mixed-effects model to fit longitudinal trajectories whose random effects enter as covariates in a generalized linear model for the primary response. They provide a useful way to assess association between these two kinds of data, which in clinical studies are often collected jointly on a series of individuals and may help understanding, for instance, the mechanisms of recovery of a certain disease or the efficacy of a given therapy. When a nonlinear mixed-effects model is used to fit the longitudinal trajectories, the existing estimation strategies based on likelihood approximations have been shown to exhibit some computational efficiency problems (De la Cruz et al., 2011). In this article we consider a Bayesian estimation procedure for the joint model with a nonlinear mixed-effects model for the longitudinal data and a generalized linear model for the primary response. The proposed prior structure allows for the implementation of an MCMC sampler. Moreover, we consider that the errors in the longitudinal model may be correlated. We apply our method to the analysis of hormone levels measured at the early stages of pregnancy that can be used to predict normal versus abnormal pregnancy outcomes. We also conduct a simulation study to assess the importance of modelling correlated errors and quantify the consequences of model misspecification. PMID:27274601

  16. Non-linear Regression and Machine Learning for Streamflow Prediction and Climate Change Impact Analysis

    NASA Astrophysics Data System (ADS)

    Shortridge, J.; Guikema, S.; Zaitchik, B. F.

    2015-12-01

    In the past decade, machine-learning methods for empirical rainfall-runoff modeling have seen extensive development. However, the majority of research has focused on a small number of methods, such as artificial neural networks, while not considering other approaches for non-parametric regression that have been developed in recent years. These methods may be able to achieve comparable predictive accuracy to ANN's and more easily provide physical insights into the system of interest through evaluation of covariate influence. Additionally, these methods could provide a straightforward, computationally efficient way of evaluating climate change impacts in basins where data to support physical hydrologic models is limited. In this paper, we use multiple regression and machine-learning approaches to predict monthly streamflow in five highly-seasonal rivers in the highlands of Ethiopia. We find that generalized additive models, random forests, and cubist models achieve better predictive accuracy than ANNs in many basins assessed and are also able to outperform physical models developed for the same region. We discuss some challenges that could hinder the use of such models for climate impact assessment, such as biases resulting from model formulation and prediction under extreme climate conditions, and suggest methods for preventing and addressing these challenges. Finally, we demonstrate how predictor variable influence can be assessed to provide insights into the physical functioning of data-sparse watersheds.

  17. Determination of the pKa of ionizable enzyme groups by nonlinear regression using a second degree equation.

    PubMed

    O'Reilly, S; Riveros, M C

    1994-01-01

    A second degree equation fitted by nonlinear regression for the analysis of the pH effect on enzyme activity is proposed for diprotic enzyme systems. This method allows the calculation of two molecular dissociation constants (KE1 and KE2 for the free enzyme, KES1 and KES2 for the ES complex) and the pH independent parameters (Vmax and Vmax/Km). The method is validated by bibliographic (alpha-chymotrypsin) and experimental data (almond beta-D-glucosidase). No significant differences were found between present data and those previously reported in the literature using similar experimental conditions. This method works using comparatively few [H+] concentration values within a narrow pH range, preferentially around the optimum, being adequate for diprotic systems with close pKa values.

  18. Determination of Constitutive Equation for Thermo-mechanical Processing of INCONEL 718 Through Double Multivariate Nonlinear Regression Analysis

    NASA Astrophysics Data System (ADS)

    Hussain, Mirza Zahid; Li, Fuguo; Wang, Jing; Yuan, Zhanwei; Li, Pan; Wu, Tao

    2015-07-01

    The present study comprises the determination of constitutive relationship for thermo-mechanical processing of INCONEL 718 through double multivariate nonlinear regression, a newly developed approach which not only considers the effect of strain, strain rate, and temperature on flow stress but also explains the interaction effect of these thermo-mechanical parameters on flow behavior of the alloy. Hot isothermal compression experiments were performed on Gleeble-3500 thermo-mechanical testing machine in the temperature range of 1153 to 1333 K within the strain rate range of 0.001 to 10 s-1. The deformation behavior of INCONEL 718 is analyzed and summarized by establishing the high temperature deformation constitutive equation. The calculated correlation coefficient ( R) and average absolute relative error ( AARE) underline the precision of proposed constitutive model.

  19. Estimation of the maximum safe level of feed ingredients by spline or broken-line nonlinear regression models.

    PubMed

    Alhotan, R A; Vedenov, D V; Pesti, G M

    2016-10-04

    The use of non-linear regression models in the analysis of biological data has led to advances in poultry nutrition. Spline or broken-line nonlinear regression models are commonly used to estimate nutritional requirements. One particular application of broken-line models is estimating the maximum safe level (MSL) of feed ingredients beyond which the ingredients become toxic, resulting in reduced performance. The objectives of this study were to evaluate the effectiveness of broken-line models (broken-line linear or BLL; and broken-line quadratic or BLQ) in estimating the MSL; to identify the most efficient design of feeding trials by finding the optimal number of ingredient levels and replications; and to re-estimate the MSL of various test ingredients reported in the nutrition literature for comparison purposes. The Maximum Ingredient level Optimization Workbook (MIOW) was developed to simulate a series of experiments and estimate the MSL and the corresponding descriptive statistics (SD, SE, CI, and R(2)). The results showed that the broken-line models provided good estimates of the MSL (small SE and high R(2)) with the BLL model producing higher MSL values as compared to the BLQ model. Increasing the number of experimental replications or ingredient levels (independently of each other) reduced the SE of the MSL with diminishing returns. The SE of the MSL was reduced with increasing the size (total pens) of the simulated experiments by increasing either the number of replications or levels or both. The evaluation of MSLs reported in the existing literature revealed that the multiple range procedure used to determine the MSL in several reports can both overestimate and underestimate the MSL compared to the results obtained by the broken-line models. The results suggest that the broken-line linear models can be used in lieu of the multiple range test to estimate the MSL of feed ingredients along with the corresponding descriptive statistics, such as the SE of the

  20. Deconvolution of antibody affinities and concentrations by non-linear regression analysis of competitive ELISA data.

    SciTech Connect

    Stevens, F. J.; Bobrovnik, S. A.; Biosciences Division; Palladin Inst. Biochemistry

    2007-12-01

    Physiological responses of the adaptive immune system are polyclonal in nature whether induced by a naturally occurring infection, by vaccination to prevent infection or, in the case of animals, by challenge with antigen to generate reagents of research or commercial significance. The composition of the polyclonal responses is distinct to each individual or animal and changes over time. Differences exist in the affinities of the constituents and their relative proportion of the responsive population. In addition, some of the antibodies bind to different sites on the antigen, whereas other pairs of antibodies are sterically restricted from concurrent interaction with the antigen. Even if generation of a monoclonal antibody is the ultimate goal of a project, the quality of the resulting reagent is ultimately related to the characteristics of the initial immune response. It is probably impossible to quantitatively parse the composition of a polyclonal response to antigen. However, molecular regression allows further parameterization of a polyclonal antiserum in the context of certain simplifying assumptions. The antiserum is described as consisting of two competing populations of high- and low-affinity and unknown relative proportions. This simple model allows the quantitative determination of representative affinities and proportions. These parameters may be of use in evaluating responses to vaccines, to evaluating continuity of antibody production whether in vaccine recipients or animals used for the production of antisera, or in optimizing selection of donors for the production of monoclonal antibodies.

  1. An Optimization-Based Method for Feature Ranking in Nonlinear Regression Problems.

    PubMed

    Bravi, Luca; Piccialli, Veronica; Sciandrone, Marco

    2016-02-03

    In this paper, we consider the feature ranking problem, where, given a set of training instances, the task is to associate a score with the features in order to assess their relevance. Feature ranking is a very important tool for decision support systems, and may be used as an auxiliary step of feature selection to reduce the high dimensionality of real-world data. We focus on regression problems by assuming that the process underlying the generated data can be approximated by a continuous function (for instance, a feedforward neural network). We formally state the notion of relevance of a feature by introducing a minimum zero-norm inversion problem of a neural network, which is a nonsmooth, constrained optimization problem. We employ a concave approximation of the zero-norm function, and we define a smooth, global optimization problem to be solved in order to assess the relevance of the features. We present the new feature ranking method based on the solution of instances of the global optimization problem depending on the available training data. Computational experiments on both artificial and real data sets are performed, and point out that the proposed feature ranking method is a valid alternative to existing methods in terms of effectiveness. The obtained results also show that the method is costly in terms of CPU time, and this may be a limitation in the solution of large-dimensional problems.

  2. A step-by-step guide to non-linear regression analysis of experimental data using a Microsoft Excel spreadsheet.

    PubMed

    Brown, A M

    2001-06-01

    The objective of this present study was to introduce a simple, easily understood method for carrying out non-linear regression analysis based on user input functions. While it is relatively straightforward to fit data with simple functions such as linear or logarithmic functions, fitting data with more complicated non-linear functions is more difficult. Commercial specialist programmes are available that will carry out this analysis, but these programmes are expensive and are not intuitive to learn. An alternative method described here is to use the SOLVER function of the ubiquitous spreadsheet programme Microsoft Excel, which employs an iterative least squares fitting routine to produce the optimal goodness of fit between data and function. The intent of this paper is to lead the reader through an easily understood step-by-step guide to implementing this method, which can be applied to any function in the form y=f(x), and is well suited to fast, reliable analysis of data in all fields of biology.

  3. Weighted PARAFAC and Non-linear Regression for Handling Intensity Changes in Fluorescence Spectroscopy caused by pH Fluctuations.

    PubMed

    Svendsen, Carina; Skov, Thomas; van den Berg, Frans W J

    2016-07-22

    Fluorescence spectroscopy is a sensitive and selective technique, which can be of great value in bioprocesses to provide online, real-time measures of chemical compounds. Although fluorescence spectroscopy is a widely studied method, not much attention has been given to issues concerning intensity variations in the fluorescence landscapes due to pH fluctuations. This study elucidates how pH fluctuations cause intensity changes in fluorescence measurements and thereby decreases the quality of the subsequent quantification. A photo-degradation process of riboflavin was investigated by fluorescence spectroscopy and used as a model system. A two-step modeling approach, combining weighted PARAllel FACtor analysis (PARAFAC) with weighted non-linear regression of the known reaction kinetics, is suggested as a way of handling the fluorescence intensity shifts caused by the pH changes. The suggested strategy makes it possible to compensate for uncertainties in the shifted data and thereby obtain more reliable concentration profiles for the chemical compounds and kinetic parameters of the reaction.

  4. Characterization of acid functional groups of carbon dots by nonlinear regression data fitting of potentiometric titration curves

    NASA Astrophysics Data System (ADS)

    Alves, Larissa A.; de Castro, Arthur H.; de Mendonça, Fernanda G.; de Mesquita, João P.

    2016-05-01

    The oxygenated functional groups present on the surface of carbon dots with an average size of 2.7 ± 0.5 nm were characterized by a variety of techniques. In particular, we discussed the fit data of potentiometric titration curves using a nonlinear regression method based on the Levenberg-Marquardt algorithm. The results obtained by statistical treatment of the titration curve data showed that the best fit was obtained considering the presence of five Brønsted-Lowry acids on the surface of the carbon dots with constant ionization characteristics of carboxylic acids, cyclic ester, phenolic and pyrone-like groups. The total number of oxygenated acid groups obtained was 5 mmol g-1, with approximately 65% (∼2.9 mmol g-1) originating from groups with pKa < 6. The methodology showed good reproducibility and stability with standard deviations below 5%. The nature of the groups was independent of small variations in experimental conditions, i.e. the mass of carbon dots titrated and initial concentration of HCl solution. Finally, we believe that the methodology used here, together with other characterization techniques, is a simple, fast and powerful tool to characterize the complex acid-base properties of these so interesting and intriguing nanoparticles.

  5. Rapid measurement of total acid content (TAC) in vinegar using near infrared spectroscopy based on efficient variables selection algorithm and nonlinear regression tools.

    PubMed

    Chen, Quansheng; Ding, Jiao; Cai, Jianrong; Zhao, Jiewen

    2012-11-15

    Total acid content (TAC) is an important index in assessing vinegar quality. This work attempted to determine TAC in vinegar using near infrared spectroscopy. We systematically studied variable selection and nonlinear regression in calibrating regression models. First, the efficient spectra intervals were selected by synergy interval PLS (Si-PLS); then, two nonlinear regression tools, which were extreme learning machine (ELM) and back propagation artificial neural network (BP-ANN), were attempted. Experiments showed that the model based on ELM and Si-PLS (Si-ELM) was superior to others, and the optimum results were achieved as follows: the root mean square error of prediction (RMSEP) was 0.2486 g/100mL, and the correlation coefficient (R(p)) was 0.9712 in the prediction set. This work demonstrated that the TAC in vinegar could be rapidly measured by NIR spectroscopy and Si-ELM algorithm showed its superiority in model calibration.

  6. Extension of the modified Poisson regression model to prospective studies with correlated binary data.

    PubMed

    Zou, G Y; Donner, Allan

    2013-12-01

    The Poisson regression model using a sandwich variance estimator has become a viable alternative to the logistic regression model for the analysis of prospective studies with independent binary outcomes. The primary advantage of this approach is that it readily provides covariate-adjusted risk ratios and associated standard errors. In this article, the model is extended to studies with correlated binary outcomes as arise in longitudinal or cluster randomization studies. The key step involves a cluster-level grouping strategy for the computation of the middle term in the sandwich estimator. For a single binary exposure variable without covariate adjustment, this approach results in risk ratio estimates and standard errors that are identical to those found in the survey sampling literature. Simulation results suggest that it is reliable for studies with correlated binary data, provided the total number of clusters is at least 50. Data from observational and cluster randomized studies are used to illustrate the methods.

  7. Comparison of various error functions in predicting the optimum isotherm by linear and non-linear regression analysis for the sorption of basic red 9 by activated carbon.

    PubMed

    Kumar, K Vasanth; Porkodi, K; Rocha, F

    2008-01-15

    A comparison of linear and non-linear regression method in selecting the optimum isotherm was made to the experimental equilibrium data of basic red 9 sorption by activated carbon. The r(2) was used to select the best fit linear theoretical isotherm. In the case of non-linear regression method, six error functions namely coefficient of determination (r(2)), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), the average relative error (ARE), sum of the errors squared (ERRSQ) and sum of the absolute errors (EABS) were used to predict the parameters involved in the two and three parameter isotherms and also to predict the optimum isotherm. Non-linear regression was found to be a better way to obtain the parameters involved in the isotherms and also the optimum isotherm. For two parameter isotherm, MPSD was found to be the best error function in minimizing the error distribution between the experimental equilibrium data and predicted isotherms. In the case of three parameter isotherm, r(2) was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. The present study showed that the size of the error function alone is not a deciding factor to choose the optimum isotherm. In addition to the size of error function, the theory behind the predicted isotherm should be verified with the help of experimental data while selecting the optimum isotherm. A coefficient of non-determination, K(2) was explained and was found to be very useful in identifying the best error function while selecting the optimum isotherm.

  8. Bayesian quantile regression-based nonlinear mixed-effects joint models for time-to-event and longitudinal data with multiple features.

    PubMed

    Huang, Yangxin; Chen, Jiaqing

    2016-12-30

    This article explores Bayesian joint models for a quantile of longitudinal response, mismeasured covariate and event time outcome with an attempt to (i) characterize the entire conditional distribution of the response variable based on quantile regression that may be more robust to outliers and misspecification of error distribution; (ii) tailor accuracy from measurement error, evaluate non-ignorable missing observations, and adjust departures from normality in covariate; and (iii) overcome shortages of confidence in specifying a time-to-event model. When statistical inference is carried out for a longitudinal data set with non-central location, non-linearity, non-normality, measurement error, and missing values as well as event time with being interval censored, it is important to account for the simultaneous treatment of these data features in order to obtain more reliable and robust inferential results. Toward this end, we develop Bayesian joint modeling approach to simultaneously estimating all parameters in the three models: quantile regression-based nonlinear mixed-effects model for response using asymmetric Laplace distribution, linear mixed-effects model with skew-t distribution for mismeasured covariate in the presence of informative missingness and accelerated failure time model with unspecified nonparametric distribution for event time. We apply the proposed modeling approach to analyzing an AIDS clinical data set and conduct simulation studies to assess the performance of the proposed joint models and method. Copyright © 2016 John Wiley & Sons, Ltd.

  9. Isotherms and thermodynamics by linear and non-linear regression analysis for the sorption of methylene blue onto activated carbon: comparison of various error functions.

    PubMed

    Kumar, K Vasanth; Porkodi, K; Rocha, F

    2008-03-01

    A comparison of linear and non-linear regression method in selecting the optimum isotherm was made to the experimental equilibrium data of methylene blue sorption by activated carbon. The r2 was used to select the best fit linear theoretical isotherm. In the case of non-linear regression method, six error functions, namely coefficient of determination (r2), hybrid fractional error function (HYBRID), Marquardt's percent standard deviation (MPSD), average relative error (ARE), sum of the errors squared (ERRSQ) and sum of the absolute errors (EABS) were used to predict the parameters involved in the two and three parameter isotherms and also to predict the optimum isotherm. For two parameter isotherm, MPSD was found to be the best error function in minimizing the error distribution between the experimental equilibrium data and predicted isotherms. In the case of three parameter isotherm, r2 was found to be the best error function to minimize the error distribution structure between experimental equilibrium data and theoretical isotherms. The present study showed that the size of the error function alone is not a deciding factor to choose the optimum isotherm. In addition to the size of error function, the theory behind the predicted isotherm should be verified with the help of experimental data while selecting the optimum isotherm. A coefficient of non-determination, K2 was explained and was found to be very useful in identifying the best error function while selecting the optimum isotherm.

  10. Monte Carlo simulation of parameter confidence intervals for non-linear regression analysis of biological data using Microsoft Excel.

    PubMed

    Lambert, Ronald J W; Mytilinaios, Ioannis; Maitland, Luke; Brown, Angus M

    2012-08-01

    This study describes a method to obtain parameter confidence intervals from the fitting of non-linear functions to experimental data, using the SOLVER and Analysis ToolPaK Add-In of the Microsoft Excel spreadsheet. Previously we have shown that Excel can fit complex multiple functions to biological data, obtaining values equivalent to those returned by more specialized statistical or mathematical software. However, a disadvantage of using the Excel method was the inability to return confidence intervals for the computed parameters or the correlations between them. Using a simple Monte-Carlo procedure within the Excel spreadsheet (without recourse to programming), SOLVER can provide parameter estimates (up to 200 at a time) for multiple 'virtual' data sets, from which the required confidence intervals and correlation coefficients can be obtained. The general utility of the method is exemplified by applying it to the analysis of the growth of Listeria monocytogenes, the growth inhibition of Pseudomonas aeruginosa by chlorhexidine and the further analysis of the electrophysiological data from the compound action potential of the rodent optic nerve.

  11. Retrieval of aerosol optical depth from surface solar radiation measurements using machine learning algorithms, non-linear regression and a radiative transfer-based look-up table

    NASA Astrophysics Data System (ADS)

    Huttunen, Jani; Kokkola, Harri; Mielonen, Tero; Esa Juhani Mononen, Mika; Lipponen, Antti; Reunanen, Juha; Vilhelm Lindfors, Anders; Mikkonen, Santtu; Erkki Juhani Lehtinen, Kari; Kouremeti, Natalia; Bais, Alkiviadis; Niska, Harri; Arola, Antti

    2016-07-01

    In order to have a good estimate of the current forcing by anthropogenic aerosols, knowledge on past aerosol levels is needed. Aerosol optical depth (AOD) is a good measure for aerosol loading. However, dedicated measurements of AOD are only available from the 1990s onward. One option to lengthen the AOD time series beyond the 1990s is to retrieve AOD from surface solar radiation (SSR) measurements taken with pyranometers. In this work, we have evaluated several inversion methods designed for this task. We compared a look-up table method based on radiative transfer modelling, a non-linear regression method and four machine learning methods (Gaussian process, neural network, random forest and support vector machine) with AOD observations carried out with a sun photometer at an Aerosol Robotic Network (AERONET) site in Thessaloniki, Greece. Our results show that most of the machine learning methods produce AOD estimates comparable to the look-up table and non-linear regression methods. All of the applied methods produced AOD values that corresponded well to the AERONET observations with the lowest correlation coefficient value being 0.87 for the random forest method. While many of the methods tended to slightly overestimate low AODs and underestimate high AODs, neural network and support vector machine showed overall better correspondence for the whole AOD range. The differences in producing both ends of the AOD range seem to be caused by differences in the aerosol composition. High AODs were in most cases those with high water vapour content which might affect the aerosol single scattering albedo (SSA) through uptake of water into aerosols. Our study indicates that machine learning methods benefit from the fact that they do not constrain the aerosol SSA in the retrieval, whereas the LUT method assumes a constant value for it. This would also mean that machine learning methods could have potential in reproducing AOD from SSR even though SSA would have changed during

  12. Fouling resistance prediction using artificial neural network nonlinear auto-regressive with exogenous input model based on operating conditions and fluid properties correlations

    NASA Astrophysics Data System (ADS)

    Biyanto, Totok R.

    2016-06-01

    Fouling in a heat exchanger in Crude Preheat Train (CPT) refinery is an unsolved problem that reduces the plant efficiency, increases fuel consumption and CO2 emission. The fouling resistance behavior is very complex. It is difficult to develop a model using first principle equation to predict the fouling resistance due to different operating conditions and different crude blends. In this paper, Artificial Neural Networks (ANN) MultiLayer Perceptron (MLP) with input structure using Nonlinear Auto-Regressive with eXogenous (NARX) is utilized to build the fouling resistance model in shell and tube heat exchanger (STHX). The input data of the model are flow rates and temperatures of the streams of the heat exchanger, physical properties of product and crude blend data. This model serves as a predicting tool to optimize operating conditions and preventive maintenance of STHX. The results show that the model can capture the complexity of fouling characteristics in heat exchanger due to thermodynamic conditions and variations in crude oil properties (blends). It was found that the Root Mean Square Error (RMSE) are suitable to capture the nonlinearity and complexity of the STHX fouling resistance during phases of training and validation.

  13. Non-linear partial least square regression increases the estimation accuracy of grass nitrogen and phosphorus using in situ hyperspectral and environmental data

    NASA Astrophysics Data System (ADS)

    Ramoelo, A.; Skidmore, A. K.; Cho, M. A.; Mathieu, R.; Heitkönig, I. M. A.; Dudeni-Tlhone, N.; Schlerf, M.; Prins, H. H. T.

    2013-08-01

    Grass nitrogen (N) and phosphorus (P) concentrations are direct indicators of rangeland quality and provide imperative information for sound management of wildlife and livestock. It is challenging to estimate grass N and P concentrations using remote sensing in the savanna ecosystems. These areas are diverse and heterogeneous in soil and plant moisture, soil nutrients, grazing pressures, and human activities. The objective of the study is to test the performance of non-linear partial least squares regression (PLSR) for predicting grass N and P concentrations through integrating in situ hyperspectral remote sensing and environmental variables (climatic, edaphic and topographic). Data were collected along a land use gradient in the greater Kruger National Park region. The data consisted of: (i) in situ-measured hyperspectral spectra, (ii) environmental variables and measured grass N and P concentrations. The hyperspectral variables included published starch, N and protein spectral absorption features, red edge position, narrow-band indices such as simple ratio (SR) and normalized difference vegetation index (NDVI). The results of the non-linear PLSR were compared to those of conventional linear PLSR. Using non-linear PLSR, integrating in situ hyperspectral and environmental variables yielded the highest grass N and P estimation accuracy (R2 = 0.81, root mean square error (RMSE) = 0.08, and R2 = 0.80, RMSE = 0.03, respectively) as compared to using remote sensing variables only, and conventional PLSR. The study demonstrates the importance of an integrated modeling approach for estimating grass quality which is a crucial effort towards effective management and planning of protected and communal savanna ecosystems.

  14. A comparison of Bayesian and non-linear regression methods for robust estimation of pharmacokinetics in DCE-MRI and how it affects cancer diagnosis.

    PubMed

    Dikaios, Nikolaos; Atkinson, David; Tudisca, Chiara; Purpura, Pierpaolo; Forster, Martin; Ahmed, Hashim; Beale, Timothy; Emberton, Mark; Punwani, Shonit

    2017-03-01

    The aim of this work is to compare Bayesian Inference for nonlinear models with commonly used traditional non-linear regression (NR) algorithms for estimating tracer kinetics in Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCE-MRI). The algorithms are compared in terms of accuracy, and reproducibility under different initialization settings. Further it is investigated how a more robust estimation of tracer kinetics affects cancer diagnosis. The derived tracer kinetics from the Bayesian algorithm were validated against traditional NR algorithms (i.e. Levenberg-Marquardt, simplex) in terms of accuracy on a digital DCE phantom and in terms of goodness-of-fit (Kolmogorov-Smirnov test) on ROI-based concentration time courses from two different patient cohorts. The first cohort consisted of 76 men, 20 of whom had significant peripheral zone prostate cancer (any cancer-core-length (CCL) with Gleason>3+3 or any-grade with CCL>=4mm) following transperineal template prostate mapping biopsy. The second cohort consisted of 9 healthy volunteers and 24 patients with head and neck squamous cell carcinoma. The diagnostic ability of the derived tracer kinetics was assessed with receiver operating characteristic area under curve (ROC AUC) analysis. The Bayesian algorithm accurately recovered the ground-truth tracer kinetics for the digital DCE phantom consistently improving the Structural Similarity Index (SSIM) across the 50 different initializations compared to NR. For optimized initialization, Bayesian did not improve significantly the fitting accuracy on both patient cohorts, and it only significantly improved the ve ROC AUC on the HN population from ROC AUC=0.56 for the simplex to ROC AUC=0.76. For both cohorts, the values and the diagnostic ability of tracer kinetic parameters estimated with the Bayesian algorithm weren't affected by their initialization. To conclude, the Bayesian algorithm led to a more accurate and reproducible quantification of tracer kinetic

  15. Nonlinear Regression Methods for Estimation

    DTIC Science & Technology

    2005-09-01

    accuracy when the geometric dilution of precision ( GDOP ) causes collinearity, which in turn brings about poor position estimates. The main goal is...measurements are needed to wash-out the 168 measurement noise. Furthermore, the measurement arrangement’s geometry ( GDOP ) strongly impacts the achievable...Newton algorithm, 61 geometric dilution of precision, see GDOP initial parameter estimate, 91 iterative least squares, see ILS Kalman filtering, 10

  16. Sleep duration and risk of all-cause mortality: A flexible, non-linear, meta-regression of 40 prospective cohort studies.

    PubMed

    Liu, Tong-Zu; Xu, Chang; Rota, Matteo; Cai, Hui; Zhang, Chao; Shi, Ming-Jun; Yuan, Rui-Xia; Weng, Hong; Meng, Xiang-Yu; Kwong, Joey S W; Sun, Xin

    2017-04-01

    Approximately 27-37% of the general population experience prolonged sleep duration and 12-16% report shortened sleep duration. However, prolonged or shortened sleep duration may be associated with serious health problems. A comprehensive, flexible, non-linear meta-regression with restricted cubic spline (RCS) was used to investigate the dose-response relationship between sleep duration and all-cause mortality in adults. Medline (Ovid), Embase, EBSCOhost-PsycINFO, and EBSCOhost-CINAHL Plus databases, reference lists of relevant review articles, and included studies were searched up to Nov. 29, 2015. Prospective cohort studies investigating the association between sleep duration and all-cause mortality in adults with at least three categories of sleep duration were eligible for inclusion. We eventually included in our study 40 cohort studies enrolling 2,200,425 participants with 271,507 deaths. A J-shaped association between sleep duration and all-cause mortality was present: compared with 7 h of sleep (reference for 24-h sleep duration), both shortened and prolonged sleep durations were associated with increased risk of all-cause mortality (4 h: relative risk [RR] = 1.05; 95% confidence interval [CI] = 1.02-1.07; 5 h: RR = 1.06; 95% CI = 1.03-1.09; 6 h: RR = 1.04; 95% CI = 1.03-1.06; 8 h: RR = 1.03; 95% CI = 1.02-1.05; 9 h: RR = 1.13; 95% CI = 1.10-1.16; 10 h: RR = 1.25; 95% CI = 1.22-1.28; 11 h: RR = 1.38; 95% CI = 1.33-1.44; n = 29; P < 0.01 for non-linear test). With regard to the night-sleep duration, prolonged night-sleep duration was associated with increased all-cause mortality (8 h: RR = 1.01; 95% CI = 0.99-1.02; 9 h: RR = 1.08; 95% CI = 1.05-1.11; 10 h: RR = 1.24; 95% CI = 1.21-1.28; n = 13; P < 0.01 for non-linear test). Subgroup analysis showed females with short sleep duration a day (<7 h) were at high risk of all-cause mortality (4 h: RR = 1.07; 95% CI = 1.02-1.13; 5 h: RR = 1.08; 95

  17. Boosted Beta Regression

    PubMed Central

    Schmid, Matthias; Wickler, Florian; Maloney, Kelly O.; Mitchell, Richard; Fenske, Nora; Mayr, Andreas

    2013-01-01

    Regression analysis with a bounded outcome is a common problem in applied statistics. Typical examples include regression models for percentage outcomes and the analysis of ratings that are measured on a bounded scale. In this paper, we consider beta regression, which is a generalization of logit models to situations where the response is continuous on the interval (0,1). Consequently, beta regression is a convenient tool for analyzing percentage responses. The classical approach to fit a beta regression model is to use maximum likelihood estimation with subsequent AIC-based variable selection. As an alternative to this established - yet unstable - approach, we propose a new estimation technique called boosted beta regression. With boosted beta regression estimation and variable selection can be carried out simultaneously in a highly efficient way. Additionally, both the mean and the variance of a percentage response can be modeled using flexible nonlinear covariate effects. As a consequence, the new method accounts for common problems such as overdispersion and non-binomial variance structures. PMID:23626706

  18. Logistic Regression

    NASA Astrophysics Data System (ADS)

    Grégoire, G.

    2014-12-01

    The logistic regression originally is intended to explain the relationship between the probability of an event and a set of covariables. The model's coefficients can be interpreted via the odds and odds ratio, which are presented in introduction of the chapter. The observations are possibly got individually, then we speak of binary logistic regression. When they are grouped, the logistic regression is said binomial. In our presentation we mainly focus on the binary case. For statistical inference the main tool is the maximum likelihood methodology: we present the Wald, Rao and likelihoods ratio results and their use to compare nested models. The problems we intend to deal with are essentially the same as in multiple linear regression: testing global effect, individual effect, selection of variables to build a model, measure of the fitness of the model, prediction of new values… . The methods are demonstrated on data sets using R. Finally we briefly consider the binomial case and the situation where we are interested in several events, that is the polytomous (multinomial) logistic regression and the particular case of ordinal logistic regression.

  19. Combining the regression discontinuity design and propensity score-based weighting to improve causal inference in program evaluation.

    PubMed

    Linden, Ariel; Adams, John L

    2012-04-01

    The regression discontinuity (RD) design is considered to be the closest to a randomized trial that can be applied in non-experimental settings. The design relies on a cut-off point on a continuous baseline variable to assign individuals to treatment. The individuals just to the right and left of the cut-off are assumed to be exchangeable - as in a randomized trial. Any observed discontinuity in the relationship between the assignment variable and outcome is therefore considered evidence of a treatment effect. In this paper, we describe key advances in the RD design over the past decade and illustrate their implementation using data from a health management intervention. We then introduce the propensity score-based weighting technique as a complement to the RD design to correct for imbalances in baseline characteristics between treated and non-treated groups that may bias RD results. We find that the weighting strategy outperforms standard regression covariate adjustment in the present data. One clear advantage of the weighting technique over regression covariate adjustment is that we can directly inspect the degree to which balance was achieved. Because of its relative simplicity and tremendous utility, the RD design (either alone or combined with propensity score weighting adjustment) should be considered as an alternative approach to evaluate health management program effectiveness when using observational data.

  20. Novel approaches to the calculation and comparison of thermoregulatory parameters: Non-linear regression of metabolic rate and evaporative water loss in Australian rodents.

    PubMed

    Tomlinson, Sean

    2016-04-01

    The calculation and comparison of physiological characteristics of thermoregulation has provided insight into patterns of ecology and evolution for over half a century. Thermoregulation has typically been explored using linear techniques; I explore the application of non-linear scaling to more accurately calculate and compare characteristics and thresholds of thermoregulation, including the basal metabolic rate (BMR), peak metabolic rate (PMR) and the lower (Tlc) and upper (Tuc) critical limits to the thermo-neutral zone (TNZ) for Australian rodents. An exponentially-modified logistic function accurately characterised the response of metabolic rate to ambient temperature, while evaporative water loss was accurately characterised by a Michaelis-Menten function. When these functions were used to resolve unique parameters for the nine species studied here, the estimates of BMR and TNZ were consistent with the previously published estimates. The approach resolved differences in rates of metabolism and water loss between subfamilies of Australian rodents that haven't been quantified before. I suggest that non-linear scaling is not only more effective than the established segmented linear techniques, but also is more objective. This approach may allow broader and more flexible comparison of characteristics of thermoregulation, but it needs testing with a broader array of taxa than those used here.

  1. Examining Non-Linear Associations between Accelerometer-Measured Physical Activity, Sedentary Behavior, and All-Cause Mortality Using Segmented Cox Regression

    PubMed Central

    Lee, Paul H.

    2016-01-01

    Healthy adults are advised to perform at least 150 min of moderate-intensity physical activity weekly, but this advice is based on studies using self-reports of questionable validity. This study examined the dose-response relationship of accelerometer-measured physical activity and sedentary behaviors on all-cause mortality using segmented Cox regression to empirically determine the break-points of the dose-response relationship. Data from 7006 adult participants aged 18 or above in the National Health and Nutrition Examination Survey waves 2003–2004 and 2005–2006 were included in the analysis and linked with death certificate data using a probabilistic matching approach in the National Death Index through December 31, 2011. Physical activity and sedentary behavior were measured using ActiGraph model 7164 accelerometer over the right hip for 7 consecutive days. Each minute with accelerometer count <100; 1952–5724; and ≥5725 were classified as sedentary, moderate-intensity physical activity, and vigorous-intensity physical activity, respectively. Segmented Cox regression was used to estimate the hazard ratio (HR) of time spent in sedentary behaviors, moderate-intensity physical activity, and vigorous-intensity physical activity and all-cause mortality, adjusted for demographic characteristics, health behaviors, and health conditions. Data were analyzed in 2016. During 47,119 person-year of follow-up, 608 deaths occurred. Each additional hour per day of sedentary behaviors was associated with a HR of 1.15 (95% CI 1.01, 1.31) among participants who spend at least 10.9 h per day on sedentary behaviors, and each additional minute per day spent on moderate-intensity physical activity was associated with a HR of 0.94 (95% CI 0.91, 0.96) among participants with daily moderate-intensity physical activity ≤14.1 min. Associations of moderate physical activity and sedentary behaviors on all-cause mortality were independent of each other. To conclude, evidence from

  2. Resolving model parameter values from carbon and nitrogen stock measurements in a wide range of tropical mature forests using nonlinear inversion and regression trees

    USGS Publications Warehouse

    Liu, S.; Anderson, P.; Zhou, G.; Kauffman, B.; Hughes, F.; Schimel, D.; Watson, Vicente; Tosi, Joseph

    2008-01-01

    Objectively assessing the performance of a model and deriving model parameter values from observations are critical and challenging in landscape to regional modeling. In this paper, we applied a nonlinear inversion technique to calibrate the ecosystem model CENTURY against carbon (C) and nitrogen (N) stock measurements collected from 39 mature tropical forest sites in seven life zones in Costa Rica. Net primary productivity from the Moderate-Resolution Imaging Spectroradiometer (MODIS), C and N stocks in aboveground live biomass, litter, coarse woody debris (CWD), and in soils were used to calibrate the model. To investigate the resolution of available observations on the number of adjustable parameters, inversion was performed using nine setups of adjustable parameters. Statistics including observation sensitivity, parameter correlation coefficient, parameter sensitivity, and parameter confidence limits were used to evaluate the information content of observations, resolution of model parameters, and overall model performance. Results indicated that soil organic carbon content, soil nitrogen content, and total aboveground biomass carbon had the highest information contents, while measurements of carbon in litter and nitrogen in CWD contributed little to the parameter estimation processes. The available information could resolve the values of 2-4 parameters. Adjusting just one parameter resulted in under-fitting and unacceptable model performance, while adjusting five parameters simultaneously led to over-fitting. Results further indicated that the MODIS NPP values were compressed as compared with the spatial variability of net primary production (NPP) values inferred from inverse modeling. Using inverse modeling to infer NPP and other sensitive model parameters from C and N stock observations provides an opportunity to utilize data collected by national to regional forest inventory systems to reduce the uncertainties in the carbon cycle and generate valuable

  3. Steganalysis using logistic regression

    NASA Astrophysics Data System (ADS)

    Lubenko, Ivans; Ker, Andrew D.

    2011-02-01

    We advocate Logistic Regression (LR) as an alternative to the Support Vector Machine (SVM) classifiers commonly used in steganalysis. LR offers more information than traditional SVM methods - it estimates class probabilities as well as providing a simple classification - and can be adapted more easily and efficiently for multiclass problems. Like SVM, LR can be kernelised for nonlinear classification, and it shows comparable classification accuracy to SVM methods. This work is a case study, comparing accuracy and speed of SVM and LR classifiers in detection of LSB Matching and other related spatial-domain image steganography, through the state-of-art 686-dimensional SPAM feature set, in three image sets.

  4. Covariate-adjusted confidence interval for the intraclass correlation coefficient.

    PubMed

    Shoukri, Mohamed M; Donner, Allan; El-Dali, Abdelmoneim

    2013-09-01

    A crucial step in designing a new study is to estimate the required sample size. For a design involving cluster sampling, the appropriate sample size depends on the so-called design effect, which is a function of the average cluster size and the intracluster correlation coefficient (ICC). It is well-known that under the framework of hierarchical and generalized linear models, a reduction in residual error may be achieved by including risk factors as covariates. In this paper we show that the covariate design, indicating whether the covariates are measured at the cluster level or at the within-cluster subject level affects the estimation of the ICC, and hence the design effect. Therefore, the distinction between these two types of covariates should be made at the design stage. In this paper we use the nested-bootstrap method to assess the accuracy of the estimated ICC for continuous and binary response variables under different covariate structures. The codes of two SAS macros are made available by the authors for interested readers to facilitate the construction of confidence intervals for the ICC. Moreover, using Monte Carlo simulations we evaluate the relative efficiency of the estimators and evaluate the accuracy of the coverage probabilities of a 95% confidence interval on the population ICC. The methodology is illustrated using a published data set of blood pressure measurements taken on family members.

  5. Inference for a Nonlinear Semimartingale Regression Model.

    DTIC Science & Technology

    1987-11-01

    increases. If K is left continuous and of bounded variation , then by integration by parts (see Dellacherie and Meyer (1982), Chapter VIII, (19.4)) for n...dt uniformly in z as n oo, where x- = .K 2(u) du. (c) Suppose A1-A3, B1, B2 hold, K is left continuous, of bounded variation and nwn - 00, nw 3 -3 0

  6. Measures of Nonlinearity for Segmented Regression Models,

    DTIC Science & Technology

    1983-08-01

    daily consumption is constant at the baseload level a as long as the average outdoor temperature T is above a reference temperature T, and increases In...discussed below in Section 5. For the energy model, we will consider estimation of the reference temperature T, baseload a, and heating rate by the method of

  7. Regression: A Bibliography.

    ERIC Educational Resources Information Center

    Pedrini, D. T.; Pedrini, Bonnie C.

    Regression, another mechanism studied by Sigmund Freud, has had much research, e.g., hypnotic regression, frustration regression, schizophrenic regression, and infra-human-animal regression (often directly related to fixation). Many investigators worked with hypnotic age regression, which has a long history, going back to Russian reflexologists.…

  8. Ridge Regression: A Panacea?

    ERIC Educational Resources Information Center

    Walton, Joseph M.; And Others

    1978-01-01

    Ridge regression is an approach to the problem of large standard errors of regression estimates of intercorrelated regressors. The effect of ridge regression on the estimated squared multiple correlation coefficient is discussed and illustrated. (JKS)

  9. Regression modeling of ground-water flow

    USGS Publications Warehouse

    Cooley, R.L.; Naff, R.L.

    1985-01-01

    Nonlinear multiple regression methods are developed to model and analyze groundwater flow systems. Complete descriptions of regression methodology as applied to groundwater flow models allow scientists and engineers engaged in flow modeling to apply the methods to a wide range of problems. Organization of the text proceeds from an introduction that discusses the general topic of groundwater flow modeling, to a review of basic statistics necessary to properly apply regression techniques, and then to the main topic: exposition and use of linear and nonlinear regression to model groundwater flow. Statistical procedures are given to analyze and use the regression models. A number of exercises and answers are included to exercise the student on nearly all the methods that are presented for modeling and statistical analysis. Three computer programs implement the more complex methods. These three are a general two-dimensional, steady-state regression model for flow in an anisotropic, heterogeneous porous medium, a program to calculate a measure of model nonlinearity with respect to the regression parameters, and a program to analyze model errors in computed dependent variables such as hydraulic head. (USGS)

  10. Regressive systemic sclerosis.

    PubMed Central

    Black, C; Dieppe, P; Huskisson, T; Hart, F D

    1986-01-01

    Systemic sclerosis is a disease which usually progresses or reaches a plateau with persistence of symptoms and signs. Regression is extremely unusual. Four cases of established scleroderma are described in which regression is well documented. The significance of this observation and possible mechanisms of disease regression are discussed. Images PMID:3718012

  11. NCCS Regression Test Harness

    SciTech Connect

    Tharrington, Arnold N.

    2015-09-09

    The NCCS Regression Test Harness is a software package that provides a framework to perform regression and acceptance testing on NCCS High Performance Computers. The package is written in Python and has only the dependency of a Subversion repository to store the regression tests.

  12. Unitary Response Regression Models

    ERIC Educational Resources Information Center

    Lipovetsky, S.

    2007-01-01

    The dependent variable in a regular linear regression is a numerical variable, and in a logistic regression it is a binary or categorical variable. In these models the dependent variable has varying values. However, there are problems yielding an identity output of a constant value which can also be modelled in a linear or logistic regression with…

  13. Fully Regressive Melanoma

    PubMed Central

    Ehrsam, Eric; Kallini, Joseph R.; Lebas, Damien; Modiano, Philippe; Cotten, Hervé

    2016-01-01

    Fully regressive melanoma is a phenomenon in which the primary cutaneous melanoma becomes completely replaced by fibrotic components as a result of host immune response. Although 10 to 35 percent of cases of cutaneous melanomas may partially regress, fully regressive melanoma is very rare; only 47 cases have been reported in the literature to date. AH of the cases of fully regressive melanoma reported in the literature were diagnosed in conjunction with metastasis on a patient. The authors describe a case of fully regressive melanoma without any metastases at the time of its diagnosis. Characteristic findings on dermoscopy, as well as the absence of melanoma on final biopsy, confirmed the diagnosis. PMID:27672418

  14. Morse–Smale Regression

    SciTech Connect

    Gerber, Samuel; Rubel, Oliver; Bremer, Peer -Timo; Pascucci, Valerio; Whitaker, Ross T.

    2012-01-19

    This paper introduces a novel partition-based regression approach that incorporates topological information. Partition-based regression typically introduces a quality-of-fit-driven decomposition of the domain. The emphasis in this work is on a topologically meaningful segmentation. Thus, the proposed regression approach is based on a segmentation induced by a discrete approximation of the Morse–Smale complex. This yields a segmentation with partitions corresponding to regions of the function with a single minimum and maximum that are often well approximated by a linear model. This approach yields regression models that are amenable to interpretation and have good predictive capacity. Typically, regression estimates are quantified by their geometrical accuracy. For the proposed regression, an important aspect is the quality of the segmentation itself. Thus, this article introduces a new criterion that measures the topological accuracy of the estimate. The topological accuracy provides a complementary measure to the classical geometrical error measures and is very sensitive to overfitting. The Morse–Smale regression is compared to state-of-the-art approaches in terms of geometry and topology and yields comparable or improved fits in many cases. Finally, a detailed study on climate-simulation data demonstrates the application of the Morse–Smale regression. Supplementary Materials are available online and contain an implementation of the proposed approach in the R package msr, an analysis and simulations on the stability of the Morse–Smale complex approximation, and additional tables for the climate-simulation study.

  15. Improved Regression Calibration

    ERIC Educational Resources Information Center

    Skrondal, Anders; Kuha, Jouni

    2012-01-01

    The likelihood for generalized linear models with covariate measurement error cannot in general be expressed in closed form, which makes maximum likelihood estimation taxing. A popular alternative is regression calibration which is computationally efficient at the cost of inconsistent estimation. We propose an improved regression calibration…

  16. Morse-Smale Regression

    PubMed Central

    Gerber, Samuel; Rübel, Oliver; Bremer, Peer-Timo; Pascucci, Valerio; Whitaker, Ross T.

    2012-01-01

    This paper introduces a novel partition-based regression approach that incorporates topological information. Partition-based regression typically introduce a quality-of-fit-driven decomposition of the domain. The emphasis in this work is on a topologically meaningful segmentation. Thus, the proposed regression approach is based on a segmentation induced by a discrete approximation of the Morse-Smale complex. This yields a segmentation with partitions corresponding to regions of the function with a single minimum and maximum that are often well approximated by a linear model. This approach yields regression models that are amenable to interpretation and have good predictive capacity. Typically, regression estimates are quantified by their geometrical accuracy. For the proposed regression, an important aspect is the quality of the segmentation itself. Thus, this paper introduces a new criterion that measures the topological accuracy of the estimate. The topological accuracy provides a complementary measure to the classical geometrical error measures and is very sensitive to over-fitting. The Morse-Smale regression is compared to state-of-the-art approaches in terms of geometry and topology and yields comparable or improved fits in many cases. Finally, a detailed study on climate-simulation data demonstrates the application of the Morse-Smale regression. Supplementary materials are available online and contain an implementation of the proposed approach in the R package msr, an analysis and simulations on the stability of the Morse-Smale complex approximation and additional tables for the climate-simulation study. PMID:23687424

  17. George: Gaussian Process regression

    NASA Astrophysics Data System (ADS)

    Foreman-Mackey, Daniel

    2015-11-01

    George is a fast and flexible library, implemented in C++ with Python bindings, for Gaussian Process regression useful for accounting for correlated noise in astronomical datasets, including those for transiting exoplanet discovery and characterization and stellar population modeling.

  18. Understanding poisson regression.

    PubMed

    Hayat, Matthew J; Higgins, Melinda

    2014-04-01

    Nurse investigators often collect study data in the form of counts. Traditional methods of data analysis have historically approached analysis of count data either as if the count data were continuous and normally distributed or with dichotomization of the counts into the categories of occurred or did not occur. These outdated methods for analyzing count data have been replaced with more appropriate statistical methods that make use of the Poisson probability distribution, which is useful for analyzing count data. The purpose of this article is to provide an overview of the Poisson distribution and its use in Poisson regression. Assumption violations for the standard Poisson regression model are addressed with alternative approaches, including addition of an overdispersion parameter or negative binomial regression. An illustrative example is presented with an application from the ENSPIRE study, and regression modeling of comorbidity data is included for illustrative purposes.

  19. [Understanding logistic regression].

    PubMed

    El Sanharawi, M; Naudet, F

    2013-10-01

    Logistic regression is one of the most common multivariate analysis models utilized in epidemiology. It allows the measurement of the association between the occurrence of an event (qualitative dependent variable) and factors susceptible to influence it (explicative variables). The choice of explicative variables that should be included in the logistic regression model is based on prior knowledge of the disease physiopathology and the statistical association between the variable and the event, as measured by the odds ratio. The main steps for the procedure, the conditions of application, and the essential tools for its interpretation are discussed concisely. We also discuss the importance of the choice of variables that must be included and retained in the regression model in order to avoid the omission of important confounding factors. Finally, by way of illustration, we provide an example from the literature, which should help the reader test his or her knowledge.

  20. Practical Session: Logistic Regression

    NASA Astrophysics Data System (ADS)

    Clausel, M.; Grégoire, G.

    2014-12-01

    An exercise is proposed to illustrate the logistic regression. One investigates the different risk factors in the apparition of coronary heart disease. It has been proposed in Chapter 5 of the book of D.G. Kleinbaum and M. Klein, "Logistic Regression", Statistics for Biology and Health, Springer Science Business Media, LLC (2010) and also by D. Chessel and A.B. Dufour in Lyon 1 (see Sect. 6 of http://pbil.univ-lyon1.fr/R/pdf/tdr341.pdf). This example is based on data given in the file evans.txt coming from http://www.sph.emory.edu/dkleinb/logreg3.htm#data.

  1. Ridge Regression: A Regression Procedure for Analyzing correlated Independent Variables

    ERIC Educational Resources Information Center

    Rakow, Ernest A.

    1978-01-01

    Ridge regression is a technique used to ameliorate the problem of highly correlated independent variables in multiple regression analysis. This paper explains the fundamentals of ridge regression and illustrates its use. (JKS)

  2. Modern Regression Discontinuity Analysis

    ERIC Educational Resources Information Center

    Bloom, Howard S.

    2012-01-01

    This article provides a detailed discussion of the theory and practice of modern regression discontinuity (RD) analysis for estimating the effects of interventions or treatments. Part 1 briefly chronicles the history of RD analysis and summarizes its past applications. Part 2 explains how in theory an RD analysis can identify an average effect of…

  3. Multiple linear regression analysis

    NASA Technical Reports Server (NTRS)

    Edwards, T. R.

    1980-01-01

    Program rapidly selects best-suited set of coefficients. User supplies only vectors of independent and dependent data and specifies confidence level required. Program uses stepwise statistical procedure for relating minimal set of variables to set of observations; final regression contains only most statistically significant coefficients. Program is written in FORTRAN IV for batch execution and has been implemented on NOVA 1200.

  4. Explorations in Statistics: Regression

    ERIC Educational Resources Information Center

    Curran-Everett, Douglas

    2011-01-01

    Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This seventh installment of "Explorations in Statistics" explores regression, a technique that estimates the nature of the relationship between two things for which we may only surmise a mechanistic or predictive…

  5. Nonlinear Waves

    DTIC Science & Technology

    1989-06-15

    following surprising situation. Namely associated with the integrable nonlinear Schrodinger equations are standard numerical schemes which exhibit at...36. An Initial Boundary Value Problem for the Nonlinear Schrodinger Equations , A.S. Fokas, Physica D March 1989. 37. Evolution Theory, Periodic... gravity waves and wave excitation phenomena related to moving pressure distributions; numerical approximation and computation; nonlinear optics; and

  6. Calculating a Stepwise Ridge Regression.

    ERIC Educational Resources Information Center

    Morris, John D.

    1986-01-01

    Although methods for using ordinary least squares regression computer programs to calculate a ridge regression are available, the calculation of a stepwise ridge regression requires a special purpose algorithm and computer program. The correct stepwise ridge regression procedure is given, and a parallel FORTRAN computer program is described.…

  7. Orthogonal Regression: A Teaching Perspective

    ERIC Educational Resources Information Center

    Carr, James R.

    2012-01-01

    A well-known approach to linear least squares regression is that which involves minimizing the sum of squared orthogonal projections of data points onto the best fit line. This form of regression is known as orthogonal regression, and the linear model that it yields is known as the major axis. A similar method, reduced major axis regression, is…

  8. Structural regression trees

    SciTech Connect

    Kramer, S.

    1996-12-31

    In many real-world domains the task of machine learning algorithms is to learn a theory for predicting numerical values. In particular several standard test domains used in Inductive Logic Programming (ILP) are concerned with predicting numerical values from examples and relational and mostly non-determinate background knowledge. However, so far no ILP algorithm except one can predict numbers and cope with nondeterminate background knowledge. (The only exception is a covering algorithm called FORS.) In this paper we present Structural Regression Trees (SRT), a new algorithm which can be applied to the above class of problems. SRT integrates the statistical method of regression trees into ILP. It constructs a tree containing a literal (an atomic formula or its negation) or a conjunction of literals in each node, and assigns a numerical value to each leaf. SRT provides more comprehensible results than purely statistical methods, and can be applied to a class of problems most other ILP systems cannot handle. Experiments in several real-world domains demonstrate that the approach is competitive with existing methods, indicating that the advantages are not at the expense of predictive accuracy.

  9. Semiparametric regression in capture-recapture modeling.

    PubMed

    Gimenez, O; Crainiceanu, C; Barbraud, C; Jenouvrier, S; Morgan, B J T

    2006-09-01

    Capture-recapture models were developed to estimate survival using data arising from marking and monitoring wild animals over time. Variation in survival may be explained by incorporating relevant covariates. We propose nonparametric and semiparametric regression methods for estimating survival in capture-recapture models. A fully Bayesian approach using Markov chain Monte Carlo simulations was employed to estimate the model parameters. The work is illustrated by a study of Snow petrels, in which survival probabilities are expressed as nonlinear functions of a climate covariate, using data from a 40-year study on marked individuals, nesting at Petrels Island, Terre Adélie.

  10. Nonlinear supratransmission

    NASA Astrophysics Data System (ADS)

    Geniet, F.; Leon, J.

    2003-05-01

    A nonlinear system possessing a natural forbidden band gap can transmit energy of a signal with a frequency in the gap, as recently shown for a nonlinear chain of coupled pendulums (Geniet and Leon 2002 Phys. Rev. Lett. 89 134102). This process of nonlinear supratransmission, occurring at a threshold that is exactly predictable in many cases, is shown to have a simple experimental realization with a mechanical chain of pendulums coupled by a coil spring. It is then analysed in more detail. First we go to different (nonintegrable) systems which do sustain nonlinear supratransmission. Then a Josephson transmission line (a one-dimensional array of short Josephson junctions coupled through superconducting wires) is shown to also sustain nonlinear supratransmission, though being related to a different class of boundary conditions, and despite the presence of damping, finiteness, and discreteness. Finally, the mechanism at the origin of nonlinear supratransmission is found to be a nonlinear instability, and this is briefly discussed here.

  11. A Nonlinear Regression Procedure for Evoked Potential Data Analysis.

    DTIC Science & Technology

    1985-06-01

    XBAR+X (I) YBAR - YBAR +V (I) CONTINUE XBAR=XBAR/N VBAR= YBAR /N A-0. B-O. DO 10 I=19N C-X(I)-XBAR A=A+ Y (I)*C -36- B=B+C**2 *10 CONTINUE BSLP=A/B BI NT=YDAR...and duration of the latency effect following impact, the following exponential model was proposed: y = B + St + h(t)D + h(t)Aexp(t/T) + £(t) (1) where... y is the value of the shift in latency with respect to the preimpact baseline average evoked potential (AEP

  12. Regression Segmentation for M³ Spinal Images.

    PubMed

    Wang, Zhijie; Zhen, Xiantong; Tay, KengYeow; Osman, Said; Romano, Walter; Li, Shuo

    2015-08-01

    Clinical routine often requires to analyze spinal images of multiple anatomic structures in multiple anatomic planes from multiple imaging modalities (M(3)). Unfortunately, existing methods for segmenting spinal images are still limited to one specific structure, in one specific plane or from one specific modality (S(3)). In this paper, we propose a novel approach, Regression Segmentation, that is for the first time able to segment M(3) spinal images in one single unified framework. This approach formulates the segmentation task innovatively as a boundary regression problem: modeling a highly nonlinear mapping function from substantially diverse M(3) images directly to desired object boundaries. Leveraging the advancement of sparse kernel machines, regression segmentation is fulfilled by a multi-dimensional support vector regressor (MSVR) which operates in an implicit, high dimensional feature space where M(3) diversity and specificity can be systematically categorized, extracted, and handled. The proposed regression segmentation approach was thoroughly tested on images from 113 clinical subjects including both disc and vertebral structures, in both sagittal and axial planes, and from both MRI and CT modalities. The overall result reaches a high dice similarity index (DSI) 0.912 and a low boundary distance (BD) 0.928 mm. With our unified and expendable framework, an efficient clinical tool for M(3) spinal image segmentation can be easily achieved, and will substantially benefit the diagnosis and treatment of spinal diseases.

  13. Ridge regression processing

    NASA Technical Reports Server (NTRS)

    Kuhl, Mark R.

    1990-01-01

    Current navigation requirements depend on a geometric dilution of precision (GDOP) criterion. As long as the GDOP stays below a specific value, navigation requirements are met. The GDOP will exceed the specified value when the measurement geometry becomes too collinear. A new signal processing technique, called Ridge Regression Processing, can reduce the effects of nearly collinear measurement geometry; thereby reducing the inflation of the measurement errors. It is shown that the Ridge signal processor gives a consistently better mean squared error (MSE) in position than the Ordinary Least Mean Squares (OLS) estimator. The applicability of this technique is currently being investigated to improve the following areas: receiver autonomous integrity monitoring (RAIM), coverage requirements, availability requirements, and precision approaches.

  14. Testing in Microbiome-Profiling Studies with MiRKAT, the Microbiome Regression-Based Kernel Association Test

    PubMed Central

    Zhao, Ni; Chen, Jun; Carroll, Ian M.; Ringel-Kulka, Tamar; Epstein, Michael P.; Zhou, Hua; Zhou, Jin J.; Ringel, Yehuda; Li, Hongzhe; Wu, Michael C.

    2015-01-01

    High-throughput sequencing technology has enabled population-based studies of the role of the human microbiome in disease etiology and exposure response. Distance-based analysis is a popular strategy for evaluating the overall association between microbiome diversity and outcome, wherein the phylogenetic distance between individuals’ microbiome profiles is computed and tested for association via permutation. Despite their practical popularity, distance-based approaches suffer from important challenges, especially in selecting the best distance and extending the methods to alternative outcomes, such as survival outcomes. We propose the microbiome regression-based kernel association test (MiRKAT), which directly regresses the outcome on the microbiome profiles via the semi-parametric kernel machine regression framework. MiRKAT allows for easy covariate adjustment and extension to alternative outcomes while non-parametrically modeling the microbiome through a kernel that incorporates phylogenetic distance. It uses a variance-component score statistic to test for the association with analytical p value calculation. The model also allows simultaneous examination of multiple distances, alleviating the problem of choosing the best distance. Our simulations demonstrated that MiRKAT provides correctly controlled type I error and adequate power in detecting overall association. “Optimal” MiRKAT, which considers multiple candidate distances, is robust in that it suffers from little power loss in comparison to when the best distance is used and can achieve tremendous power gain in comparison to when a poor distance is chosen. Finally, we applied MiRKAT to real microbiome datasets to show that microbial communities are associated with smoking and with fecal protease levels after confounders are controlled for. PMID:25957468

  15. Perioperative factors predicting poor outcome in elderly patients following emergency general surgery: a multivariate regression analysis

    PubMed Central

    Lees, Mackenzie C.; Merani, Shaheed; Tauh, Keerit; Khadaroo, Rachel G.

    2015-01-01

    Background Older adults (≥ 65 yr) are the fastest growing population and are presenting in increasing numbers for acute surgical care. Emergency surgery is frequently life threatening for older patients. Our objective was to identify predictors of mortality and poor outcome among elderly patients undergoing emergency general surgery. Methods We conducted a retrospective cohort study of patients aged 65–80 years undergoing emergency general surgery between 2009 and 2010 at a tertiary care centre. Demographics, comorbidities, in-hospital complications, mortality and disposition characteristics of patients were collected. Logistic regression analysis was used to identify covariate-adjusted predictors of in-hospital mortality and discharge of patients home. Results Our analysis included 257 patients with a mean age of 72 years; 52% were men. In-hospital mortality was 12%. Mortality was associated with patients who had higher American Society of Anesthesiologists (ASA) class (odds ratio [OR] 3.85, 95% confidence interval [CI] 1.43–10.33, p = 0.008) and in-hospital complications (OR 1.93, 95% CI 1.32–2.83, p = 0.001). Nearly two-thirds of patients discharged home were younger (OR 0.92, 95% CI 0.85–0.99, p = 0.036), had lower ASA class (OR 0.45, 95% CI 0.27–0.74, p = 0.002) and fewer in-hospital complications (OR 0.69, 95% CI 0.53–0.90, p = 0.007). Conclusion American Society of Anesthesiologists class and in-hospital complications are perioperative predictors of mortality and disposition in the older surgical population. Understanding the predictors of poor outcome and the importance of preventing in-hospital complications in older patients will have important clinical utility in terms of preoperative counselling, improving health care and discharging patients home. PMID:26204143

  16. Logarithmic Transformations in Regression: Do You Transform Back Correctly?

    ERIC Educational Resources Information Center

    Dambolena, Ismael G.; Eriksen, Steven E.; Kopcso, David P.

    2009-01-01

    The logarithmic transformation is often used in regression analysis for a variety of purposes such as the linearization of a nonlinear relationship between two or more variables. We have noticed that when this transformation is applied to the response variable, the computation of the point estimate of the conditional mean of the original response…

  17. Effects of Participation in a Post-Secondary Honors Program with Covariate Adjustment Using Propensity Score

    ERIC Educational Resources Information Center

    Furtwengler, Scott R.

    2015-01-01

    The present study sought to determine the extent to which participation in a post-secondary honors program affected academic achievement. Archival data were collected on three cohorts of high-achieving students at a large public university. Propensity scores were calculated on factors predicting participation in honors and used as the covariate.…

  18. The Generalized Johnson-Neyman Procedures: An Approach to Covariate Adjustment and Interaction Analysis.

    ERIC Educational Resources Information Center

    Forster, Fred

    Statistical methods are described for diagnosing and treating three important problems in covariate tests of significance: curvilinearity, covariable effectiveness, and treatment-covariable interaction. Six major assumptions, prerequisites for covariate procedure, are discussed in detail: (1) normal distribution, (2) homogeneity of variances, (3)…

  19. Evaluating differential effects using regression interactions and regression mixture models

    PubMed Central

    Van Horn, M. Lee; Jaki, Thomas; Masyn, Katherine; Howe, George; Feaster, Daniel J.; Lamont, Andrea E.; George, Melissa R. W.; Kim, Minjung

    2015-01-01

    Research increasingly emphasizes understanding differential effects. This paper focuses on understanding regression mixture models, a relatively new statistical methods for assessing differential effects by comparing results to using an interactive term in linear regression. The research questions which each model answers, their formulation, and their assumptions are compared using Monte Carlo simulations and real data analysis. The capabilities of regression mixture models are described and specific issues to be addressed when conducting regression mixtures are proposed. The paper aims to clarify the role that regression mixtures can take in the estimation of differential effects and increase awareness of the benefits and potential pitfalls of this approach. Regression mixture models are shown to be a potentially effective exploratory method for finding differential effects when these effects can be defined by a small number of classes of respondents who share a typical relationship between a predictor and an outcome. It is also shown that the comparison between regression mixture models and interactions becomes substantially more complex as the number of classes increases. It is argued that regression interactions are well suited for direct tests of specific hypotheses about differential effects and regression mixtures provide a useful approach for exploring effect heterogeneity given adequate samples and study design. PMID:26556903

  20. Boosted Regression Tree Models to Explain Watershed Nutrient Concentrations and Biological Condition

    EPA Science Inventory

    Boosted regression tree (BRT) models were developed to quantify the nonlinear relationships between landscape variables and nutrient concentrations in a mesoscale mixed land cover watershed during base-flow conditions. Factors that affect instream biological components, based on ...

  1. Multivariate adaptive regression splines models for the prediction of energy expenditure in children and adolescents

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Advanced mathematical models have the potential to capture the complex metabolic and physiological processes that result in heat production, or energy expenditure (EE). Multivariate adaptive regression splines (MARS), is a nonparametric method that estimates complex nonlinear relationships by a seri...

  2. Evaluating Differential Effects Using Regression Interactions and Regression Mixture Models

    ERIC Educational Resources Information Center

    Van Horn, M. Lee; Jaki, Thomas; Masyn, Katherine; Howe, George; Feaster, Daniel J.; Lamont, Andrea E.; George, Melissa R. W.; Kim, Minjung

    2015-01-01

    Research increasingly emphasizes understanding differential effects. This article focuses on understanding regression mixture models, which are relatively new statistical methods for assessing differential effects by comparing results to using an interactive term in linear regression. The research questions which each model answers, their…

  3. Error bounds in cascading regressions

    USGS Publications Warehouse

    Karlinger, M.R.; Troutman, B.M.

    1985-01-01

    Cascading regressions is a technique for predicting a value of a dependent variable when no paired measurements exist to perform a standard regression analysis. Biases in coefficients of a cascaded-regression line as well as error variance of points about the line are functions of the correlation coefficient between dependent and independent variables. Although this correlation cannot be computed because of the lack of paired data, bounds can be placed on errors through the required properties of the correlation coefficient. The potential meansquared error of a cascaded-regression prediction can be large, as illustrated through an example using geomorphologic data. ?? 1985 Plenum Publishing Corporation.

  4. Logistic Regression: Concept and Application

    ERIC Educational Resources Information Center

    Cokluk, Omay

    2010-01-01

    The main focus of logistic regression analysis is classification of individuals in different groups. The aim of the present study is to explain basic concepts and processes of binary logistic regression analysis intended to determine the combination of independent variables which best explain the membership in certain groups called dichotomous…

  5. Precision Efficacy Analysis for Regression.

    ERIC Educational Resources Information Center

    Brooks, Gordon P.

    When multiple linear regression is used to develop a prediction model, sample size must be large enough to ensure stable coefficients. If the derivation sample size is inadequate, the model may not predict well for future subjects. The precision efficacy analysis for regression (PEAR) method uses a cross- validity approach to select sample sizes…

  6. Nonlinear channelizer.

    PubMed

    In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D; Leung, Daniel; Liu, Norman; Meadows, Brian K; Gordon, Frank; Bulsara, Adi R; Palacios, Antonio

    2012-12-01

    The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.

  7. Rank regression: an alternative regression approach for data with outliers.

    PubMed

    Chen, Tian; Tang, Wan; Lu, Ying; Tu, Xin

    2014-10-01

    Linear regression models are widely used in mental health and related health services research. However, the classic linear regression analysis assumes that the data are normally distributed, an assumption that is not met by the data obtained in many studies. One method of dealing with this problem is to use semi-parametric models, which do not require that the data be normally distributed. But semi-parametric models are quite sensitive to outlying observations, so the generated estimates are unreliable when study data includes outliers. In this situation, some researchers trim the extreme values prior to conducting the analysis, but the ad-hoc rules used for data trimming are based on subjective criteria so different methods of adjustment can yield different results. Rank regression provides a more objective approach to dealing with non-normal data that includes outliers. This paper uses simulated and real data to illustrate this useful regression approach for dealing with outliers and compares it to the results generated using classical regression models and semi-parametric regression models.

  8. Practical Session: Simple Linear Regression

    NASA Astrophysics Data System (ADS)

    Clausel, M.; Grégoire, G.

    2014-12-01

    Two exercises are proposed to illustrate the simple linear regression. The first one is based on the famous Galton's data set on heredity. We use the lm R command and get coefficients estimates, standard error of the error, R2, residuals …In the second example, devoted to data related to the vapor tension of mercury, we fit a simple linear regression, predict values, and anticipate on multiple linear regression. This pratical session is an excerpt from practical exercises proposed by A. Dalalyan at EPNC (see Exercises 1 and 2 of http://certis.enpc.fr/~dalalyan/Download/TP_ENPC_4.pdf).

  9. Multiple Regression and Its Discontents

    ERIC Educational Resources Information Center

    Snell, Joel C.; Marsh, Mitchell

    2012-01-01

    Multiple regression is part of a larger statistical strategy originated by Gauss. The authors raise questions about the theory and suggest some changes that would make room for Mandelbrot and Serendipity.

  10. Wrong Signs in Regression Coefficients

    NASA Technical Reports Server (NTRS)

    McGee, Holly

    1999-01-01

    When using parametric cost estimation, it is important to note the possibility of the regression coefficients having the wrong sign. A wrong sign is defined as a sign on the regression coefficient opposite to the researcher's intuition and experience. Some possible causes for the wrong sign discussed in this paper are a small range of x's, leverage points, missing variables, multicollinearity, and computational error. Additionally, techniques for determining the cause of the wrong sign are given.

  11. Nonlinear Systems.

    ERIC Educational Resources Information Center

    Seider, Warren D.; Ungar, Lyle H.

    1987-01-01

    Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…

  12. Nonlinear Acoustics

    DTIC Science & Technology

    1974-02-14

    Wester- velt. [60] Streaming. In 1831, Michael Faraday [61] noted that currents of air were set up in the neighborhood of vibrating plates-the first... ducei in the case of a paramettc amy (from Berktay an Leahy 141). C’ "". k•, SEC 10.1 NONLINEAR ACOUSTICS 345 The principal results of their analysis

  13. Nonlinear resonance

    NASA Astrophysics Data System (ADS)

    Kevorkian, J.

    This report discusses research in the area of slowly varying nonlinear oscillatory systems. Some of the topics discussed are as follows: adiabatic invariants and transient resonance in very slowly varying Hamiltonian systems; sustained resonance in very slowly varying Hamiltonian systems; free-electron lasers with very slow wiggler taper; and bursting oscillators.

  14. XRA image segmentation using regression

    NASA Astrophysics Data System (ADS)

    Jin, Jesse S.

    1996-04-01

    Segmentation is an important step in image analysis. Thresholding is one of the most important approaches. There are several difficulties in segmentation, such as automatic selecting threshold, dealing with intensity distortion and noise removal. We have developed an adaptive segmentation scheme by applying the Central Limit Theorem in regression. A Gaussian regression is used to separate the distribution of background from foreground in a single peak histogram. The separation will help to automatically determine the threshold. A small 3 by 3 widow is applied and the modal of the local histogram is used to overcome noise. Thresholding is based on local weighting, where regression is used again for parameter estimation. A connectivity test is applied to the final results to remove impulse noise. We have applied the algorithm to x-ray angiogram images to extract brain arteries. The algorithm works well for single peak distribution where there is no valley in the histogram. The regression provides a method to apply knowledge in clustering. Extending regression for multiple-level segmentation needs further investigation.

  15. Regression with Differential Equation Models

    DTIC Science & Technology

    1976-04-01

    Perturbation methods are used in the control program and QUASH for I ease of programming. For information regarding this theory, see Refer- ence 5, Doiron ...Nonlinear Multipoint Boundary Value Problem. For the series Applied Mathematics and Computation. Addison Wesly Publishing Company. 5) Childs, Bart, Doiron

  16. Kernel regression for fMRI pattern prediction

    PubMed Central

    Chu, Carlton; Ni, Yizhao; Tan, Geoffrey; Saunders, Craig J.; Ashburner, John

    2011-01-01

    This paper introduces two kernel-based regression schemes to decode or predict brain states from functional brain scans as part of the Pittsburgh Brain Activity Interpretation Competition (PBAIC) 2007, in which our team was awarded first place. Our procedure involved image realignment, spatial smoothing, detrending of low-frequency drifts, and application of multivariate linear and non-linear kernel regression methods: namely kernel ridge regression (KRR) and relevance vector regression (RVR). RVR is based on a Bayesian framework, which automatically determines a sparse solution through maximization of marginal likelihood. KRR is the dual-form formulation of ridge regression, which solves regression problems with high dimensional data in a computationally efficient way. Feature selection based on prior knowledge about human brain function was also used. Post-processing by constrained deconvolution and re-convolution was used to furnish the prediction. This paper also contains a detailed description of how prior knowledge was used to fine tune predictions of specific “feature ratings,” which we believe is one of the key factors in our prediction accuracy. The impact of pre-processing was also evaluated, demonstrating that different pre-processing may lead to significantly different accuracies. Although the original work was aimed at the PBAIC, many techniques described in this paper can be generally applied to any fMRI decoding works to increase the prediction accuracy. PMID:20348000

  17. Survival Data and Regression Models

    NASA Astrophysics Data System (ADS)

    Grégoire, G.

    2014-12-01

    We start this chapter by introducing some basic elements for the analysis of censored survival data. Then we focus on right censored data and develop two types of regression models. The first one concerns the so-called accelerated failure time models (AFT), which are parametric models where a function of a parameter depends linearly on the covariables. The second one is a semiparametric model, where the covariables enter in a multiplicative form in the expression of the hazard rate function. The main statistical tool for analysing these regression models is the maximum likelihood methodology and, in spite we recall some essential results about the ML theory, we refer to the chapter "Logistic Regression" for a more detailed presentation.

  18. Regressive evolution in Astyanax cavefish.

    PubMed

    Jeffery, William R

    2009-01-01

    A diverse group of animals, including members of most major phyla, have adapted to life in the perpetual darkness of caves. These animals are united by the convergence of two regressive phenotypes, loss of eyes and pigmentation. The mechanisms of regressive evolution are poorly understood. The teleost Astyanax mexicanus is of special significance in studies of regressive evolution in cave animals. This species includes an ancestral surface dwelling form and many con-specific cave-dwelling forms, some of which have evolved their recessive phenotypes independently. Recent advances in Astyanax development and genetics have provided new information about how eyes and pigment are lost during cavefish evolution; namely, they have revealed some of the molecular and cellular mechanisms involved in trait modification, the number and identity of the underlying genes and mutations, the molecular basis of parallel evolution, and the evolutionary forces driving adaptation to the cave environment.

  19. Cactus: An Introduction to Regression

    ERIC Educational Resources Information Center

    Hyde, Hartley

    2008-01-01

    When the author first used "VisiCalc," the author thought it a very useful tool when he had the formulas. But how could he design a spreadsheet if there was no known formula for the quantities he was trying to predict? A few months later, the author relates he learned to use multiple linear regression software and suddenly it all clicked into…

  20. Multiple Regression: A Leisurely Primer.

    ERIC Educational Resources Information Center

    Daniel, Larry G.; Onwuegbuzie, Anthony J.

    Multiple regression is a useful statistical technique when the researcher is considering situations in which variables of interest are theorized to be multiply caused. It may also be useful in those situations in which the researchers is interested in studies of predictability of phenomena of interest. This paper provides an introduction to…

  1. Weighting Regressions by Propensity Scores

    ERIC Educational Resources Information Center

    Freedman, David A.; Berk, Richard A.

    2008-01-01

    Regressions can be weighted by propensity scores in order to reduce bias. However, weighting is likely to increase random error in the estimates, and to bias the estimated standard errors downward, even when selection mechanisms are well understood. Moreover, in some cases, weighting will increase the bias in estimated causal parameters. If…

  2. Quantile Regression with Censored Data

    ERIC Educational Resources Information Center

    Lin, Guixian

    2009-01-01

    The Cox proportional hazards model and the accelerated failure time model are frequently used in survival data analysis. They are powerful, yet have limitation due to their model assumptions. Quantile regression offers a semiparametric approach to model data with possible heterogeneity. It is particularly powerful for censored responses, where the…

  3. Hierarchical Adaptive Regression Kernels for Regression with Functional Predictors

    PubMed Central

    Woodard, Dawn B.; Crainiceanu, Ciprian; Ruppert, David

    2013-01-01

    We propose a new method for regression using a parsimonious and scientifically interpretable representation of functional predictors. Our approach is designed for data that exhibit features such as spikes, dips, and plateaus whose frequency, location, size, and shape varies stochastically across subjects. We propose Bayesian inference of the joint functional and exposure models, and give a method for efficient computation. We contrast our approach with existing state-of-the-art methods for regression with functional predictors, and show that our method is more effective and efficient for data that include features occurring at varying locations. We apply our methodology to a large and complex dataset from the Sleep Heart Health Study, to quantify the association between sleep characteristics and health outcomes. Software and technical appendices are provided in online supplemental materials. PMID:24293988

  4. Regression Verification Using Impact Summaries

    NASA Technical Reports Server (NTRS)

    Backes, John; Person, Suzette J.; Rungta, Neha; Thachuk, Oksana

    2013-01-01

    Regression verification techniques are used to prove equivalence of syntactically similar programs. Checking equivalence of large programs, however, can be computationally expensive. Existing regression verification techniques rely on abstraction and decomposition techniques to reduce the computational effort of checking equivalence of the entire program. These techniques are sound but not complete. In this work, we propose a novel approach to improve scalability of regression verification by classifying the program behaviors generated during symbolic execution as either impacted or unimpacted. Our technique uses a combination of static analysis and symbolic execution to generate summaries of impacted program behaviors. The impact summaries are then checked for equivalence using an o-the-shelf decision procedure. We prove that our approach is both sound and complete for sequential programs, with respect to the depth bound of symbolic execution. Our evaluation on a set of sequential C artifacts shows that reducing the size of the summaries can help reduce the cost of software equivalence checking. Various reduction, abstraction, and compositional techniques have been developed to help scale software verification techniques to industrial-sized systems. Although such techniques have greatly increased the size and complexity of systems that can be checked, analysis of large software systems remains costly. Regression analysis techniques, e.g., regression testing [16], regression model checking [22], and regression verification [19], restrict the scope of the analysis by leveraging the differences between program versions. These techniques are based on the idea that if code is checked early in development, then subsequent versions can be checked against a prior (checked) version, leveraging the results of the previous analysis to reduce analysis cost of the current version. Regression verification addresses the problem of proving equivalence of closely related program

  5. Interaction Models for Functional Regression

    PubMed Central

    USSET, JOSEPH; STAICU, ANA-MARIA; MAITY, ARNAB

    2015-01-01

    A functional regression model with a scalar response and multiple functional predictors is proposed that accommodates two-way interactions in addition to their main effects. The proposed estimation procedure models the main effects using penalized regression splines, and the interaction effect by a tensor product basis. Extensions to generalized linear models and data observed on sparse grids or with measurement error are presented. A hypothesis testing procedure for the functional interaction effect is described. The proposed method can be easily implemented through existing software. Numerical studies show that fitting an additive model in the presence of interaction leads to both poor estimation performance and lost prediction power, while fitting an interaction model where there is in fact no interaction leads to negligible losses. The methodology is illustrated on the AneuRisk65 study data. PMID:26744549

  6. Interactive natural image segmentation via spline regression.

    PubMed

    Xiang, Shiming; Nie, Feiping; Zhang, Chunxia; Zhang, Changshui

    2009-07-01

    This paper presents an interactive algorithm for segmentation of natural images. The task is formulated as a problem of spline regression, in which the spline is derived in Sobolev space and has a form of a combination of linear and Green's functions. Besides its nonlinear representation capability, one advantage of this spline in usage is that, once it has been constructed, no parameters need to be tuned to data. We define this spline on the user specified foreground and background pixels, and solve its parameters (the combination coefficients of functions) from a group of linear equations. To speed up spline construction, K-means clustering algorithm is employed to cluster the user specified pixels. By taking the cluster centers as representatives, this spline can be easily constructed. The foreground object is finally cut out from its background via spline interpolation. The computational complexity of the proposed algorithm is linear in the number of the pixels to be segmented. Experiments on diverse natural images, with comparison to existing algorithms, illustrate the validity of our method.

  7. Boosted Regression Tree Models to Explain Watershed ...

    EPA Pesticide Factsheets

    Boosted regression tree (BRT) models were developed to quantify the nonlinear relationships between landscape variables and nutrient concentrations in a mesoscale mixed land cover watershed during base-flow conditions. Factors that affect instream biological components, based on the Index of Biotic Integrity (IBI), were also analyzed. Seasonal BRT models at two spatial scales (watershed and riparian buffered area [RBA]) for nitrite-nitrate (NO2-NO3), total Kjeldahl nitrogen, and total phosphorus (TP) and annual models for the IBI score were developed. Two primary factors — location within the watershed (i.e., geographic position, stream order, and distance to a downstream confluence) and percentage of urban land cover (both scales) — emerged as important predictor variables. Latitude and longitude interacted with other factors to explain the variability in summer NO2-NO3 concentrations and IBI scores. BRT results also suggested that location might be associated with indicators of sources (e.g., land cover), runoff potential (e.g., soil and topographic factors), and processes not easily represented by spatial data indicators. Runoff indicators (e.g., Hydrological Soil Group D and Topographic Wetness Indices) explained a substantial portion of the variability in nutrient concentrations as did point sources for TP in the summer months. The results from our BRT approach can help prioritize areas for nutrient management in mixed-use and heavily impacted watershed

  8. Non-crossing weighted kernel quantile regression with right censored data.

    PubMed

    Bang, Sungwan; Eo, Soo-Heang; Cho, Yong Mee; Jhun, Myoungshic; Cho, HyungJun

    2016-01-01

    Regarding survival data analysis in regression modeling, multiple conditional quantiles are useful summary statistics to assess covariate effects on survival times. In this study, we consider an estimation problem of multiple nonlinear quantile functions with right censored survival data. To account for censoring in estimating a nonlinear quantile function, weighted kernel quantile regression (WKQR) has been developed by using the kernel trick and inverse-censoring-probability weights. However, the individually estimated quantile functions based on the WKQR often cross each other and consequently violate the basic properties of quantiles. To avoid this problem of quantile crossing, we propose the non-crossing weighted kernel quantile regression (NWKQR), which estimates multiple nonlinear conditional quantile functions simultaneously by enforcing the non-crossing constraints on kernel coefficients. The numerical results are presented to demonstrate the competitive performance of the proposed NWKQR over the WKQR.

  9. Astronomical Methods for Nonparametric Regression

    NASA Astrophysics Data System (ADS)

    Steinhardt, Charles L.; Jermyn, Adam

    2017-01-01

    I will discuss commonly used techniques for nonparametric regression in astronomy. We find that several of them, particularly running averages and running medians, are generically biased, asymmetric between dependent and independent variables, and perform poorly in recovering the underlying function, even when errors are present only in one variable. We then examine less-commonly used techniques such as Multivariate Adaptive Regressive Splines and Boosted Trees and find them superior in bias, asymmetry, and variance both theoretically and in practice under a wide range of numerical benchmarks. In this context the chief advantage of the common techniques is runtime, which even for large datasets is now measured in microseconds compared with milliseconds for the more statistically robust techniques. This points to a tradeoff between bias, variance, and computational resources which in recent years has shifted heavily in favor of the more advanced methods, primarily driven by Moore's Law. Along these lines, we also propose a new algorithm which has better overall statistical properties than all techniques examined thus far, at the cost of significantly worse runtime, in addition to providing guidance on choosing the nonparametric regression technique most suitable to any specific problem. We then examine the more general problem of errors in both variables and provide a new algorithm which performs well in most cases and lacks the clear asymmetry of existing non-parametric methods, which fail to account for errors in both variables.

  10. Deep Wavelet Scattering for Quantum Energy Regression

    NASA Astrophysics Data System (ADS)

    Hirn, Matthew

    Physical functionals are usually computed as solutions of variational problems or from solutions of partial differential equations, which may require huge computations for complex systems. Quantum chemistry calculations of ground state molecular energies is such an example. Indeed, if x is a quantum molecular state, then the ground state energy E0 (x) is the minimum eigenvalue solution of the time independent Schrödinger Equation, which is computationally intensive for large systems. Machine learning algorithms do not simulate the physical system but estimate solutions by interpolating values provided by a training set of known examples {(xi ,E0 (xi) } i <= n . However, precise interpolations may require a number of examples that is exponential in the system dimension, and are thus intractable. This curse of dimensionality may be circumvented by computing interpolations in smaller approximation spaces, which take advantage of physical invariants. Linear regressions of E0 over a dictionary Φ ={ϕk } k compute an approximation E 0 as: E 0 (x) =∑kwkϕk (x) , where the weights {wk } k are selected to minimize the error between E0 and E 0 on the training set. The key to such a regression approach then lies in the design of the dictionary Φ. It must be intricate enough to capture the essential variability of E0 (x) over the molecular states x of interest, while simple enough so that evaluation of Φ (x) is significantly less intensive than a direct quantum mechanical computation (or approximation) of E0 (x) . In this talk we present a novel dictionary Φ for the regression of quantum mechanical energies based on the scattering transform of an intermediate, approximate electron density representation ρx of the state x. The scattering transform has the architecture of a deep convolutional network, composed of an alternating sequence of linear filters and nonlinear maps. Whereas in many deep learning tasks the linear filters are learned from the training data, here

  11. Regression analysis of non-contact acousto-thermal signature data

    NASA Astrophysics Data System (ADS)

    Criner, Amanda; Schehl, Norman

    2016-05-01

    The non-contact acousto-thermal signature (NCATS) is a nondestructive evaluation technique with potential to detect fatigue in materials such as noisy titanium and polymer matrix composites. The underlying physical mechanisms and properties may be determined by parameter estimation via nonlinear regression. The nonlinear regression analysis formulation, including the underlying models, is discussed. Several models and associated data analyses are given along with the assumptions implicit in the underlying model. The results are anomalous. These anomalous results are evaluated with respect to the accuracy of the implicit assumptions.

  12. Comparison Between Linear and Non-parametric Regression Models for Genome-Enabled Prediction in Wheat

    PubMed Central

    Pérez-Rodríguez, Paulino; Gianola, Daniel; González-Camacho, Juan Manuel; Crossa, José; Manès, Yann; Dreisigacker, Susanne

    2012-01-01

    In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-linearity on markers) were reproducing kernel Hilbert space (RKHS) regression, Bayesian regularized neural networks (BRNN), and radial basis function neural networks (RBFNN). These statistical models were compared using 306 elite wheat lines from CIMMYT genotyped with 1717 diversity array technology (DArT) markers and two traits, days to heading (DTH) and grain yield (GY), measured in each of 12 environments. It was found that the three non-linear models had better overall prediction accuracy than the linear regression specification. Results showed a consistent superiority of RKHS and RBFNN over the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B models. PMID:23275882

  13. Regression analysis of cytopathological data

    SciTech Connect

    Whittemore, A.S.; McLarty, J.W.; Fortson, N.; Anderson, K.

    1982-12-01

    Epithelial cells from the human body are frequently labelled according to one of several ordered levels of abnormality, ranging from normal to malignant. The label of the most abnormal cell in a specimen determines the score for the specimen. This paper presents a model for the regression of specimen scores against continuous and discrete variables, as in host exposure to carcinogens. Application to data and tests for adequacy of model fit are illustrated using sputum specimens obtained from a cohort of former asbestos workers.

  14. New Nonlinear Multigrid Analysis

    NASA Technical Reports Server (NTRS)

    Xie, Dexuan

    1996-01-01

    The nonlinear multigrid is an efficient algorithm for solving the system of nonlinear equations arising from the numerical discretization of nonlinear elliptic boundary problems. In this paper, we present a new nonlinear multigrid analysis as an extension of the linear multigrid theory presented by Bramble. In particular, we prove the convergence of the nonlinear V-cycle method for a class of mildly nonlinear second order elliptic boundary value problems which do not have full elliptic regularity.

  15. Multiatlas segmentation as nonparametric regression.

    PubMed

    Awate, Suyash P; Whitaker, Ross T

    2014-09-01

    This paper proposes a novel theoretical framework to model and analyze the statistical characteristics of a wide range of segmentation methods that incorporate a database of label maps or atlases; such methods are termed as label fusion or multiatlas segmentation. We model these multiatlas segmentation problems as nonparametric regression problems in the high-dimensional space of image patches. We analyze the nonparametric estimator's convergence behavior that characterizes expected segmentation error as a function of the size of the multiatlas database. We show that this error has an analytic form involving several parameters that are fundamental to the specific segmentation problem (determined by the chosen anatomical structure, imaging modality, registration algorithm, and label-fusion algorithm). We describe how to estimate these parameters and show that several human anatomical structures exhibit the trends modeled analytically. We use these parameter estimates to optimize the regression estimator. We show that the expected error for large database sizes is well predicted by models learned on small databases. Thus, a few expert segmentations can help predict the database sizes required to keep the expected error below a specified tolerance level. Such cost-benefit analysis is crucial for deploying clinical multiatlas segmentation systems.

  16. Multiatlas Segmentation as Nonparametric Regression

    PubMed Central

    Awate, Suyash P.; Whitaker, Ross T.

    2015-01-01

    This paper proposes a novel theoretical framework to model and analyze the statistical characteristics of a wide range of segmentation methods that incorporate a database of label maps or atlases; such methods are termed as label fusion or multiatlas segmentation. We model these multiatlas segmentation problems as nonparametric regression problems in the high-dimensional space of image patches. We analyze the nonparametric estimator’s convergence behavior that characterizes expected segmentation error as a function of the size of the multiatlas database. We show that this error has an analytic form involving several parameters that are fundamental to the specific segmentation problem (determined by the chosen anatomical structure, imaging modality, registration algorithm, and label-fusion algorithm). We describe how to estimate these parameters and show that several human anatomical structures exhibit the trends modeled analytically. We use these parameter estimates to optimize the regression estimator. We show that the expected error for large database sizes is well predicted by models learned on small databases. Thus, a few expert segmentations can help predict the database sizes required to keep the expected error below a specified tolerance level. Such cost-benefit analysis is crucial for deploying clinical multiatlas segmentation systems. PMID:24802528

  17. Demonstration of leapfrogging for implementing nonlinear model predictive control on a heat exchanger.

    PubMed

    Sridhar, Upasana Manimegalai; Govindarajan, Anand; Rhinehart, R Russell

    2016-01-01

    This work reveals the applicability of a relatively new optimization technique, Leapfrogging, for both nonlinear regression modeling and a methodology for nonlinear model-predictive control. Both are relatively simple, yet effective. The application on a nonlinear, pilot-scale, shell-and-tube heat exchanger reveals practicability of the techniques.

  18. Robust and efficient estimation with weighted composite quantile regression

    NASA Astrophysics Data System (ADS)

    Jiang, Xuejun; Li, Jingzhi; Xia, Tian; Yan, Wanfeng

    2016-09-01

    In this paper we introduce a weighted composite quantile regression (CQR) estimation approach and study its application in nonlinear models such as exponential models and ARCH-type models. The weighted CQR is augmented by using a data-driven weighting scheme. With the error distribution unspecified, the proposed estimators share robustness from quantile regression and achieve nearly the same efficiency as the oracle maximum likelihood estimator (MLE) for a variety of error distributions including the normal, mixed-normal, Student's t, Cauchy distributions, etc. We also suggest an algorithm for the fast implementation of the proposed methodology. Simulations are carried out to compare the performance of different estimators, and the proposed approach is used to analyze the daily S&P 500 Composite index, which verifies the effectiveness and efficiency of our theoretical results.

  19. Adaptive support vector regression for UAV flight control.

    PubMed

    Shin, Jongho; Jin Kim, H; Kim, Youdan

    2011-01-01

    This paper explores an application of support vector regression for adaptive control of an unmanned aerial vehicle (UAV). Unlike neural networks, support vector regression (SVR) generates global solutions, because SVR basically solves quadratic programming (QP) problems. With this advantage, the input-output feedback-linearized inverse dynamic model and the compensation term for the inversion error are identified off-line, which we call I-SVR (inversion SVR) and C-SVR (compensation SVR), respectively. In order to compensate for the inversion error and the unexpected uncertainty, an online adaptation algorithm for the C-SVR is proposed. Then, the stability of the overall error dynamics is analyzed by the uniformly ultimately bounded property in the nonlinear system theory. In order to validate the effectiveness of the proposed adaptive controller, numerical simulations are performed on the UAV model.

  20. Recognition of caudal regression syndrome.

    PubMed

    Boulas, Mari M

    2009-04-01

    Caudal regression syndrome, also referred to as caudal dysplasia and sacral agenesis syndrome, is a rare congenital malformation characterized by varying degrees of developmental failure early in gestation. It involves the lower extremities, the lumbar and coccygeal vertebrae, and corresponding segments of the spinal cord. This is a rare disorder, and true pathogenesis is unclear. The etiology is thought to be related to maternal diabetes, genetic predisposition, and vascular hypoperfusion, but no true causative factor has been determined. Fetal diagnostic tools allow for early recognition of the syndrome, and careful examination of the newborn is essential to determine the extent of the disorder. Associated organ system dysfunction depends on the severity of the disease. Related defects are structural, and systematic problems including respiratory, cardiac, gastrointestinal, urinary, orthopedic, and neurologic can be present in varying degrees of severity and in different combinations. A multidisciplinary approach to management is crucial. Because the primary pathology is irreversible, treatment is only supportive.

  1. Practical Session: Multiple Linear Regression

    NASA Astrophysics Data System (ADS)

    Clausel, M.; Grégoire, G.

    2014-12-01

    Three exercises are proposed to illustrate the simple linear regression. In the first one investigates the influence of several factors on atmospheric pollution. It has been proposed by D. Chessel and A.B. Dufour in Lyon 1 (see Sect. 6 of http://pbil.univ-lyon1.fr/R/pdf/tdr33.pdf) and is based on data coming from 20 cities of U.S. Exercise 2 is an introduction to model selection whereas Exercise 3 provides a first example of analysis of variance. Exercises 2 and 3 have been proposed by A. Dalalyan at ENPC (see Exercises 2 and 3 of http://certis.enpc.fr/~dalalyan/Download/TP_ENPC_5.pdf).

  2. Lumbar herniated disc: spontaneous regression

    PubMed Central

    Yüksel, Kasım Zafer

    2017-01-01

    Background Low back pain is a frequent condition that results in substantial disability and causes admission of patients to neurosurgery clinics. To evaluate and present the therapeutic outcomes in lumbar disc hernia (LDH) patients treated by means of a conservative approach, consisting of bed rest and medical therapy. Methods This retrospective cohort was carried out in the neurosurgery departments of hospitals in Kahramanmaraş city and 23 patients diagnosed with LDH at the levels of L3−L4, L4−L5 or L5−S1 were enrolled. Results The average age was 38.4 ± 8.0 and the chief complaint was low back pain and sciatica radiating to one or both lower extremities. Conservative treatment was administered. Neurological examination findings, durations of treatment and intervals until symptomatic recovery were recorded. Laségue tests and neurosensory examination revealed that mild neurological deficits existed in 16 of our patients. Previously, 5 patients had received physiotherapy and 7 patients had been on medical treatment. The number of patients with LDH at the level of L3−L4, L4−L5, and L5−S1 were 1, 13, and 9, respectively. All patients reported that they had benefit from medical treatment and bed rest, and radiologic improvement was observed simultaneously on MRI scans. The average duration until symptomatic recovery and/or regression of LDH symptoms was 13.6 ± 5.4 months (range: 5−22). Conclusions It should be kept in mind that lumbar disc hernias could regress with medical treatment and rest without surgery, and there should be an awareness that these patients could recover radiologically. This condition must be taken into account during decision making for surgical intervention in LDH patients devoid of indications for emergent surgery. PMID:28119770

  3. Filtering by nonlinear systems.

    PubMed

    Campos Cantón, E; González Salas, J S; Urías, J

    2008-12-01

    Synchronization of nonlinear systems forced by external signals is formalized as the response of a nonlinear filter. Sufficient conditions for a nonlinear system to behave as a filter are given. Some examples of generalized chaos synchronization are shown to actually be special cases of nonlinear filtering.

  4. Genetics Home Reference: caudal regression syndrome

    MedlinePlus

    ... of a genetic condition? Genetic and Rare Diseases Information Center Frequency Caudal regression syndrome is estimated to occur in 1 to ... parts of the skeleton, gastrointestinal system, and genitourinary ... caudal regression syndrome results from the presence of an abnormal ...

  5. Getting Straight: Everything You Always Wanted to Know about the Title I Regression Model and Curvilinearity.

    ERIC Educational Resources Information Center

    Echternacht, Gary; Swinton, Spencer

    Title I evaluations using the RMC Model C design depend for their interpretation on the assumption that the regression of posttest on pretest is linear across the cut score level when there is no treatment; but there are many instances where nonlinearities may occur. If one applies the analysis of covariance, or model C analysis, large errors may…

  6. Semiparametric regression during 2003–2007*

    PubMed Central

    Ruppert, David; Wand, M.P.; Carroll, Raymond J.

    2010-01-01

    Semiparametric regression is a fusion between parametric regression and nonparametric regression that integrates low-rank penalized splines, mixed model and hierarchical Bayesian methodology – thus allowing more streamlined handling of longitudinal and spatial correlation. We review progress in the field over the five-year period between 2003 and 2007. We find semiparametric regression to be a vibrant field with substantial involvement and activity, continual enhancement and widespread application. PMID:20305800

  7. Bayesian Unimodal Density Regression for Causal Inference

    ERIC Educational Resources Information Center

    Karabatsos, George; Walker, Stephen G.

    2011-01-01

    Karabatsos and Walker (2011) introduced a new Bayesian nonparametric (BNP) regression model. Through analyses of real and simulated data, they showed that the BNP regression model outperforms other parametric and nonparametric regression models of common use, in terms of predictive accuracy of the outcome (dependent) variable. The other,…

  8. Developmental Regression in Autism Spectrum Disorders

    ERIC Educational Resources Information Center

    Rogers, Sally J.

    2004-01-01

    The occurrence of developmental regression in autism is one of the more puzzling features of this disorder. Although several studies have documented the validity of parental reports of regression using home videos, accumulating data suggest that most children who demonstrate regression also demonstrated previous, subtle, developmental differences.…

  9. Standards for Standardized Logistic Regression Coefficients

    ERIC Educational Resources Information Center

    Menard, Scott

    2011-01-01

    Standardized coefficients in logistic regression analysis have the same utility as standardized coefficients in linear regression analysis. Although there has been no consensus on the best way to construct standardized logistic regression coefficients, there is now sufficient evidence to suggest a single best approach to the construction of a…

  10. Regression Analysis by Example. 5th Edition

    ERIC Educational Resources Information Center

    Chatterjee, Samprit; Hadi, Ali S.

    2012-01-01

    Regression analysis is a conceptually simple method for investigating relationships among variables. Carrying out a successful application of regression analysis, however, requires a balance of theoretical results, empirical rules, and subjective judgment. "Regression Analysis by Example, Fifth Edition" has been expanded and thoroughly…

  11. Synthesizing Regression Results: A Factored Likelihood Method

    ERIC Educational Resources Information Center

    Wu, Meng-Jia; Becker, Betsy Jane

    2013-01-01

    Regression methods are widely used by researchers in many fields, yet methods for synthesizing regression results are scarce. This study proposes using a factored likelihood method, originally developed to handle missing data, to appropriately synthesize regression models involving different predictors. This method uses the correlations reported…

  12. Streamflow forecasting using functional regression

    NASA Astrophysics Data System (ADS)

    Masselot, Pierre; Dabo-Niang, Sophie; Chebana, Fateh; Ouarda, Taha B. M. J.

    2016-07-01

    Streamflow, as a natural phenomenon, is continuous in time and so are the meteorological variables which influence its variability. In practice, it can be of interest to forecast the whole flow curve instead of points (daily or hourly). To this end, this paper introduces the functional linear models and adapts it to hydrological forecasting. More precisely, functional linear models are regression models based on curves instead of single values. They allow to consider the whole process instead of a limited number of time points or features. We apply these models to analyse the flow volume and the whole streamflow curve during a given period by using precipitations curves. The functional model is shown to lead to encouraging results. The potential of functional linear models to detect special features that would have been hard to see otherwise is pointed out. The functional model is also compared to the artificial neural network approach and the advantages and disadvantages of both models are discussed. Finally, future research directions involving the functional model in hydrology are presented.

  13. Survival analysis and Cox regression.

    PubMed

    Benítez-Parejo, N; Rodríguez del Águila, M M; Pérez-Vicente, S

    2011-01-01

    The data provided by clinical trials are often expressed in terms of survival. The analysis of survival comprises a series of statistical analytical techniques in which the measurements analysed represent the time elapsed between a given exposure and the outcome of a certain event. Despite the name of these techniques, the outcome in question does not necessarily have to be either survival or death, and may be healing versus no healing, relief versus pain, complication versus no complication, relapse versus no relapse, etc. The present article describes the analysis of survival from both a descriptive perspective, based on the Kaplan-Meier estimation method, and in terms of bivariate comparisons using the log-rank statistic. Likewise, a description is provided of the Cox regression models for the study of risk factors or covariables associated to the probability of survival. These models are defined in both simple and multiple forms, and a description is provided of how they are calculated and how the postulates for application are checked - accompanied by illustrating examples with the shareware application R.

  14. Estimating equivalence with quantile regression

    USGS Publications Warehouse

    Cade, B.S.

    2011-01-01

    Equivalence testing and corresponding confidence interval estimates are used to provide more enlightened statistical statements about parameter estimates by relating them to intervals of effect sizes deemed to be of scientific or practical importance rather than just to an effect size of zero. Equivalence tests and confidence interval estimates are based on a null hypothesis that a parameter estimate is either outside (inequivalence hypothesis) or inside (equivalence hypothesis) an equivalence region, depending on the question of interest and assignment of risk. The former approach, often referred to as bioequivalence testing, is often used in regulatory settings because it reverses the burden of proof compared to a standard test of significance, following a precautionary principle for environmental protection. Unfortunately, many applications of equivalence testing focus on establishing average equivalence by estimating differences in means of distributions that do not have homogeneous variances. I discuss how to compare equivalence across quantiles of distributions using confidence intervals on quantile regression estimates that detect differences in heterogeneous distributions missed by focusing on means. I used one-tailed confidence intervals based on inequivalence hypotheses in a two-group treatment-control design for estimating bioequivalence of arsenic concentrations in soils at an old ammunition testing site and bioequivalence of vegetation biomass at a reclaimed mining site. Two-tailed confidence intervals based both on inequivalence and equivalence hypotheses were used to examine quantile equivalence for negligible trends over time for a continuous exponential model of amphibian abundance. ?? 2011 by the Ecological Society of America.

  15. Comparative analysis of regression and artificial neural network models for wind speed prediction

    NASA Astrophysics Data System (ADS)

    Bilgili, Mehmet; Sahin, Besir

    2010-11-01

    In this study, wind speed was modeled by linear regression (LR), nonlinear regression (NLR) and artificial neural network (ANN) methods. A three-layer feedforward artificial neural network structure was constructed and a backpropagation algorithm was used for the training of ANNs. To get a successful simulation, firstly, the correlation coefficients between all of the meteorological variables (wind speed, ambient temperature, atmospheric pressure, relative humidity and rainfall) were calculated taking two variables in turn for each calculation. All independent variables were added to the simple regression model. Then, the method of stepwise multiple regression was applied for the selection of the “best” regression equation (model). Thus, the best independent variables were selected for the LR and NLR models and also used in the input layer of the ANN. The results obtained by all methods were compared to each other. Finally, the ANN method was found to provide better performance than the LR and NLR methods.

  16. [Application of spline-based Cox regression on analyzing data from follow-up studies].

    PubMed

    Dong, Ying; Yu, Jin-ming; Hu, Da-yi

    2012-09-01

    With R, this study involved the application of the spline-based Cox regression to analyze data related to follow-up studies when the two basic assumptions of Cox proportional hazards regression were not satisfactory. Results showed that most of the continuous covariates contributed nonlinearly to mortality risk while the effects of three covariates were time-dependent. After considering multiple covariates in spline-based Cox regression, when the ankle brachial index (ABI) decreased by 0.1, the hazard ratio (HR) for all-cause death was 1.071. The spline-based Cox regression method could be applied to analyze the data related to follow-up studies when the assumptions of Cox proportional hazards regression were violated.

  17. Time series regression model for infectious disease and weather.

    PubMed

    Imai, Chisato; Armstrong, Ben; Chalabi, Zaid; Mangtani, Punam; Hashizume, Masahiro

    2015-10-01

    Time series regression has been developed and long used to evaluate the short-term associations of air pollution and weather with mortality or morbidity of non-infectious diseases. The application of the regression approaches from this tradition to infectious diseases, however, is less well explored and raises some new issues. We discuss and present potential solutions for five issues often arising in such analyses: changes in immune population, strong autocorrelations, a wide range of plausible lag structures and association patterns, seasonality adjustments, and large overdispersion. The potential approaches are illustrated with datasets of cholera cases and rainfall from Bangladesh and influenza and temperature in Tokyo. Though this article focuses on the application of the traditional time series regression to infectious diseases and weather factors, we also briefly introduce alternative approaches, including mathematical modeling, wavelet analysis, and autoregressive integrated moving average (ARIMA) models. Modifications proposed to standard time series regression practice include using sums of past cases as proxies for the immune population, and using the logarithm of lagged disease counts to control autocorrelation due to true contagion, both of which are motivated from "susceptible-infectious-recovered" (SIR) models. The complexity of lag structures and association patterns can often be informed by biological mechanisms and explored by using distributed lag non-linear models. For overdispersed models, alternative distribution models such as quasi-Poisson and negative binomial should be considered. Time series regression can be used to investigate dependence of infectious diseases on weather, but may need modifying to allow for features specific to this context.

  18. Developmental regression in autism spectrum disorder.

    PubMed

    Al Backer, Nouf Backer

    2015-01-01

    The occurrence of developmental regression in autism spectrum disorder (ASD) is one of the most puzzling phenomena of this disorder. A little is known about the nature and mechanism of developmental regression in ASD. About one-third of young children with ASD lose some skills during the preschool period, usually speech, but sometimes also nonverbal communication, social or play skills are also affected. There is a lot of evidence suggesting that most children who demonstrate regression also had previous, subtle, developmental differences. It is difficult to predict the prognosis of autistic children with developmental regression. It seems that the earlier development of social, language, and attachment behaviors followed by regression does not predict the later recovery of skills or better developmental outcomes. The underlying mechanisms that lead to regression in autism are unknown. The role of subclinical epilepsy in the developmental regression of children with autism remains unclear.

  19. Semi-supervised classification via local spline regression.

    PubMed

    Xiang, Shiming; Nie, Feiping; Zhang, Changshui

    2010-11-01

    This paper presents local spline regression for semi-supervised classification. The core idea in our approach is to introduce splines developed in Sobolev space to map the data points directly to be class labels. The spline is composed of polynomials and Green's functions. It is smooth, nonlinear, and able to interpolate the scattered data points with high accuracy. Specifically, in each neighborhood, an optimal spline is estimated via regularized least squares regression. With this spline, each of the neighboring data points is mapped to be a class label. Then, the regularized loss is evaluated and further formulated in terms of class label vector. Finally, all of the losses evaluated in local neighborhoods are accumulated together to measure the global consistency on the labeled and unlabeled data. To achieve the goal of semi-supervised classification, an objective function is constructed by combining together the global loss of the local spline regressions and the squared errors of the class labels of the labeled data. In this way, a transductive classification algorithm is developed in which a globally optimal classification can be finally obtained. In the semi-supervised learning setting, the proposed algorithm is analyzed and addressed into the Laplacian regularization framework. Comparative classification experiments on many public data sets and applications to interactive image segmentation and image matting illustrate the validity of our method.

  20. Batch Mode Active Learning for Regression With Expected Model Change.

    PubMed

    Cai, Wenbin; Zhang, Muhan; Zhang, Ya

    2016-04-20

    While active learning (AL) has been widely studied for classification problems, limited efforts have been done on AL for regression. In this paper, we introduce a new AL framework for regression, expected model change maximization (EMCM), which aims at choosing the unlabeled data instances that result in the maximum change of the current model once labeled. The model change is quantified as the difference between the current model parameters and the updated parameters after the inclusion of the newly selected examples. In light of the stochastic gradient descent learning rule, we approximate the change as the gradient of the loss function with respect to each single candidate instance. Under the EMCM framework, we propose novel AL algorithms for the linear and nonlinear regression models. In addition, by simulating the behavior of the sequential AL policy when applied for k iterations, we further extend the algorithms to batch mode AL to simultaneously choose a set of k most informative instances at each query time. Extensive experimental results on both UCI and StatLib benchmark data sets have demonstrated that the proposed algorithms are highly effective and efficient.

  1. Reporting on covariate adjustment in randomised controlled trials before and after revision of the 2001 CONSORT statement: a literature review

    PubMed Central

    2010-01-01

    Objectives To evaluate the use and reporting of adjusted analysis in randomised controlled trials (RCTs) and compare the quality of reporting before and after the revision of the CONSORT Statement in 2001. Design Comparison of two cross sectional samples of published articles. Data Sources Journal articles indexed on PubMed in December 2000 and December 2006. Study Selection Parallel group RCTs with a full publication carried out in humans and published in English Main outcome measures Proportion of articles reported adjusted analysis; use of adjusted analysis; the reason for adjustment; the method of adjustment and the reporting of adjusted analysis results in the main text and abstract. Results In both cohorts, 25% of studies reported adjusted analysis (84/355 in 2000 vs 113/422 in 2006). Compared with articles reporting only unadjusted analyses, articles that reported adjusted analyses were more likely to specify primary outcomes, involve multiple centers, perform stratified randomization, be published in general medical journals, and recruit larger sample sizes. In both years a minority of articles explained why and how covariates were selected for adjustment (20% to 30%). Almost all articles specified the statistical methods used for adjustment (99% in 2000 vs 100% in 2006) but only 5% and 10%, respectively, reported both adjusted and unadjusted results as recommended in the CONSORT guidelines. Conclusion There was no evidence of change in the reporting of adjusted analysis results five years after the revision of the CONSORT Statement and only a few articles adhered fully to the CONSORT recommendations. PMID:20482769

  2. Nonlinear Hysteretic Torsional Waves

    NASA Astrophysics Data System (ADS)

    Cabaret, J.; Béquin, P.; Theocharis, G.; Andreev, V.; Gusev, V. E.; Tournat, V.

    2015-07-01

    We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.

  3. Nonlinear Hysteretic Torsional Waves.

    PubMed

    Cabaret, J; Béquin, P; Theocharis, G; Andreev, V; Gusev, V E; Tournat, V

    2015-07-31

    We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.

  4. Process modeling with the regression network.

    PubMed

    van der Walt, T; Barnard, E; van Deventer, J

    1995-01-01

    A new connectionist network topology called the regression network is proposed. The structural and underlying mathematical features of the regression network are investigated. Emphasis is placed on the intricacies of the optimization process for the regression network and some measures to alleviate these difficulties of optimization are proposed and investigated. The ability of the regression network algorithm to perform either nonparametric or parametric optimization, as well as a combination of both, is also highlighted. It is further shown how the regression network can be used to model systems which are poorly understood on the basis of sparse data. A semi-empirical regression network model is developed for a metallurgical processing operation (a hydrocyclone classifier) by building mechanistic knowledge into the connectionist structure of the regression network model. Poorly understood aspects of the process are provided for by use of nonparametric regions within the structure of the semi-empirical connectionist model. The performance of the regression network model is compared to the corresponding generalization performance results obtained by some other nonparametric regression techniques.

  5. Quantile regression applied to spectral distance decay

    USGS Publications Warehouse

    Rocchini, D.; Cade, B.S.

    2008-01-01

    Remotely sensed imagery has long been recognized as a powerful support for characterizing and estimating biodiversity. Spectral distance among sites has proven to be a powerful approach for detecting species composition variability. Regression analysis of species similarity versus spectral distance allows us to quantitatively estimate the amount of turnover in species composition with respect to spectral and ecological variability. In classical regression analysis, the residual sum of squares is minimized for the mean of the dependent variable distribution. However, many ecological data sets are characterized by a high number of zeroes that add noise to the regression model. Quantile regressions can be used to evaluate trend in the upper quantiles rather than a mean trend across the whole distribution of the dependent variable. In this letter, we used ordinary least squares (OLS) and quantile regressions to estimate the decay of species similarity versus spectral distance. The achieved decay rates were statistically nonzero (p < 0.01), considering both OLS and quantile regressions. Nonetheless, the OLS regression estimate of the mean decay rate was only half the decay rate indicated by the upper quantiles. Moreover, the intercept value, representing the similarity reached when the spectral distance approaches zero, was very low compared with the intercepts of the upper quantiles, which detected high species similarity when habitats are more similar. In this letter, we demonstrated the power of using quantile regressions applied to spectral distance decay to reveal species diversity patterns otherwise lost or underestimated by OLS regression. ?? 2008 IEEE.

  6. [From clinical judgment to linear regression model.

    PubMed

    Palacios-Cruz, Lino; Pérez, Marcela; Rivas-Ruiz, Rodolfo; Talavera, Juan O

    2013-01-01

    When we think about mathematical models, such as linear regression model, we think that these terms are only used by those engaged in research, a notion that is far from the truth. Legendre described the first mathematical model in 1805, and Galton introduced the formal term in 1886. Linear regression is one of the most commonly used regression models in clinical practice. It is useful to predict or show the relationship between two or more variables as long as the dependent variable is quantitative and has normal distribution. Stated in another way, the regression is used to predict a measure based on the knowledge of at least one other variable. Linear regression has as it's first objective to determine the slope or inclination of the regression line: Y = a + bx, where "a" is the intercept or regression constant and it is equivalent to "Y" value when "X" equals 0 and "b" (also called slope) indicates the increase or decrease that occurs when the variable "x" increases or decreases in one unit. In the regression line, "b" is called regression coefficient. The coefficient of determination (R(2)) indicates the importance of independent variables in the outcome.

  7. Geodesic least squares regression on information manifolds

    SciTech Connect

    Verdoolaege, Geert

    2014-12-05

    We present a novel regression method targeted at situations with significant uncertainty on both the dependent and independent variables or with non-Gaussian distribution models. Unlike the classic regression model, the conditional distribution of the response variable suggested by the data need not be the same as the modeled distribution. Instead they are matched by minimizing the Rao geodesic distance between them. This yields a more flexible regression method that is less constrained by the assumptions imposed through the regression model. As an example, we demonstrate the improved resistance of our method against some flawed model assumptions and we apply this to scaling laws in magnetic confinement fusion.

  8. Predicting Antitumor Activity of Peptides by Consensus of Regression Models Trained on a Small Data Sample

    PubMed Central

    Radman, Andreja; Gredičak, Matija; Kopriva, Ivica; Jerić, Ivanka

    2011-01-01

    Predicting antitumor activity of compounds using regression models trained on a small number of compounds with measured biological activity is an ill-posed inverse problem. Yet, it occurs very often within the academic community. To counteract, up to some extent, overfitting problems caused by a small training data, we propose to use consensus of six regression models for prediction of biological activity of virtual library of compounds. The QSAR descriptors of 22 compounds related to the opioid growth factor (OGF, Tyr-Gly-Gly-Phe-Met) with known antitumor activity were used to train regression models: the feed-forward artificial neural network, the k-nearest neighbor, sparseness constrained linear regression, the linear and nonlinear (with polynomial and Gaussian kernel) support vector machine. Regression models were applied on a virtual library of 429 compounds that resulted in six lists with candidate compounds ranked by predicted antitumor activity. The highly ranked candidate compounds were synthesized, characterized and tested for an antiproliferative activity. Some of prepared peptides showed more pronounced activity compared with the native OGF; however, they were less active than highly ranked compounds selected previously by the radial basis function support vector machine (RBF SVM) regression model. The ill-posedness of the related inverse problem causes unstable behavior of trained regression models on test data. These results point to high complexity of prediction based on the regression models trained on a small data sample. PMID:22272081

  9. Nonlinear regime-switching state-space (RSSS) models.

    PubMed

    Chow, Sy-Miin; Zhang, Guangjian

    2013-10-01

    Nonlinear dynamic factor analysis models extend standard linear dynamic factor analysis models by allowing time series processes to be nonlinear at the latent level (e.g., involving interaction between two latent processes). In practice, it is often of interest to identify the phases--namely, latent "regimes" or classes--during which a system is characterized by distinctly different dynamics. We propose a new class of models, termed nonlinear regime-switching state-space (RSSS) models, which subsumes regime-switching nonlinear dynamic factor analysis models as a special case. In nonlinear RSSS models, the change processes within regimes, represented using a state-space model, are allowed to be nonlinear. An estimation procedure obtained by combining the extended Kalman filter and the Kim filter is proposed as a way to estimate nonlinear RSSS models. We illustrate the utility of nonlinear RSSS models by fitting a nonlinear dynamic factor analysis model with regime-specific cross-regression parameters to a set of experience sampling affect data. The parallels between nonlinear RSSS models and other well-known discrete change models in the literature are discussed briefly.

  10. Quantile regression neural networks: Implementation in R and application to precipitation downscaling

    NASA Astrophysics Data System (ADS)

    Cannon, Alex J.

    2011-09-01

    The qrnn package for R implements the quantile regression neural network, which is an artificial neural network extension of linear quantile regression. The model formulation follows from previous work on the estimation of censored regression quantiles. The result is a nonparametric, nonlinear model suitable for making probabilistic predictions of mixed discrete-continuous variables like precipitation amounts, wind speeds, or pollutant concentrations, as well as continuous variables. A differentiable approximation to the quantile regression error function is adopted so that gradient-based optimization algorithms can be used to estimate model parameters. Weight penalty and bootstrap aggregation methods are used to avoid overfitting. For convenience, functions for quantile-based probability density, cumulative distribution, and inverse cumulative distribution functions are also provided. Package functions are demonstrated on a simple precipitation downscaling task.

  11. Using GA-Ridge regression to select hydro-geological parameters influencing groundwater pollution vulnerability.

    PubMed

    Ahn, Jae Joon; Kim, Young Min; Yoo, Keunje; Park, Joonhong; Oh, Kyong Joo

    2012-11-01

    For groundwater conservation and management, it is important to accurately assess groundwater pollution vulnerability. This study proposed an integrated model using ridge regression and a genetic algorithm (GA) to effectively select the major hydro-geological parameters influencing groundwater pollution vulnerability in an aquifer. The GA-Ridge regression method determined that depth to water, net recharge, topography, and the impact of vadose zone media were the hydro-geological parameters that influenced trichloroethene pollution vulnerability in a Korean aquifer. When using these selected hydro-geological parameters, the accuracy was improved for various statistical nonlinear and artificial intelligence (AI) techniques, such as multinomial logistic regression, decision trees, artificial neural networks, and case-based reasoning. These results provide a proof of concept that the GA-Ridge regression is effective at determining influential hydro-geological parameters for the pollution vulnerability of an aquifer, and in turn, improves the AI performance in assessing groundwater pollution vulnerability.

  12. Suppression Situations in Multiple Linear Regression

    ERIC Educational Resources Information Center

    Shieh, Gwowen

    2006-01-01

    This article proposes alternative expressions for the two most prevailing definitions of suppression without resorting to the standardized regression modeling. The formulation provides a simple basis for the examination of their relationship. For the two-predictor regression, the author demonstrates that the previous results in the literature are…

  13. Regression Analysis: Legal Applications in Institutional Research

    ERIC Educational Resources Information Center

    Frizell, Julie A.; Shippen, Benjamin S., Jr.; Luna, Andrew L.

    2008-01-01

    This article reviews multiple regression analysis, describes how its results should be interpreted, and instructs institutional researchers on how to conduct such analyses using an example focused on faculty pay equity between men and women. The use of multiple regression analysis will be presented as a method with which to compare salaries of…

  14. Principles of Quantile Regression and an Application

    ERIC Educational Resources Information Center

    Chen, Fang; Chalhoub-Deville, Micheline

    2014-01-01

    Newer statistical procedures are typically introduced to help address the limitations of those already in practice or to deal with emerging research needs. Quantile regression (QR) is introduced in this paper as a relatively new methodology, which is intended to overcome some of the limitations of least squares mean regression (LMR). QR is more…

  15. Three-Dimensional Modeling in Linear Regression.

    ERIC Educational Resources Information Center

    Herman, James D.

    Linear regression examines the relationship between one or more independent (predictor) variables and a dependent variable. By using a particular formula, regression determines the weights needed to minimize the error term for a given set of predictors. With one predictor variable, the relationship between the predictor and the dependent variable…

  16. A Practical Guide to Regression Discontinuity

    ERIC Educational Resources Information Center

    Jacob, Robin; Zhu, Pei; Somers, Marie-Andrée; Bloom, Howard

    2012-01-01

    Regression discontinuity (RD) analysis is a rigorous nonexperimental approach that can be used to estimate program impacts in situations in which candidates are selected for treatment based on whether their value for a numeric rating exceeds a designated threshold or cut-point. Over the last two decades, the regression discontinuity approach has…

  17. Regression Analysis and the Sociological Imagination

    ERIC Educational Resources Information Center

    De Maio, Fernando

    2014-01-01

    Regression analysis is an important aspect of most introductory statistics courses in sociology but is often presented in contexts divorced from the central concerns that bring students into the discipline. Consequently, we present five lesson ideas that emerge from a regression analysis of income inequality and mortality in the USA and Canada.

  18. Symplectic geometry spectrum regression for prediction of noisy time series

    NASA Astrophysics Data System (ADS)

    Xie, Hong-Bo; Dokos, Socrates; Sivakumar, Bellie; Mengersen, Kerrie

    2016-05-01

    We present the symplectic geometry spectrum regression (SGSR) technique as well as a regularized method based on SGSR for prediction of nonlinear time series. The main tool of analysis is the symplectic geometry spectrum analysis, which decomposes a time series into the sum of a small number of independent and interpretable components. The key to successful regularization is to damp higher order symplectic geometry spectrum components. The effectiveness of SGSR and its superiority over local approximation using ordinary least squares are demonstrated through prediction of two noisy synthetic chaotic time series (Lorenz and Rössler series), and then tested for prediction of three real-world data sets (Mississippi River flow data and electromyographic and mechanomyographic signal recorded from human body).

  19. Atherosclerotic plaque regression: fact or fiction?

    PubMed

    Shanmugam, Nesan; Román-Rego, Ana; Ong, Peter; Kaski, Juan Carlos

    2010-08-01

    Coronary artery disease is the major cause of death in the western world. The formation and rapid progression of atheromatous plaques can lead to serious cardiovascular events in patients with atherosclerosis. The better understanding, in recent years, of the mechanisms leading to atheromatous plaque growth and disruption and the availability of powerful HMG CoA-reductase inhibitors (statins) has permitted the consideration of plaque regression as a realistic therapeutic goal. This article reviews the existing evidence underpinning current therapeutic strategies aimed at achieving atherosclerotic plaque regression. In this review we also discuss imaging modalities for the assessment of plaque regression, predictors of regression and whether plaque regression is associated with a survival benefit.

  20. Should metacognition be measured by logistic regression?

    PubMed

    Rausch, Manuel; Zehetleitner, Michael

    2017-03-01

    Are logistic regression slopes suitable to quantify metacognitive sensitivity, i.e. the efficiency with which subjective reports differentiate between correct and incorrect task responses? We analytically show that logistic regression slopes are independent from rating criteria in one specific model of metacognition, which assumes (i) that rating decisions are based on sensory evidence generated independently of the sensory evidence used for primary task responses and (ii) that the distributions of evidence are logistic. Given a hierarchical model of metacognition, logistic regression slopes depend on rating criteria. According to all considered models, regression slopes depend on the primary task criterion. A reanalysis of previous data revealed that massive numbers of trials are required to distinguish between hierarchical and independent models with tolerable accuracy. It is argued that researchers who wish to use logistic regression as measure of metacognitive sensitivity need to control the primary task criterion and rating criteria.

  1. Almost efficient estimation of relative risk regression

    PubMed Central

    Fitzmaurice, Garrett M.; Lipsitz, Stuart R.; Arriaga, Alex; Sinha, Debajyoti; Greenberg, Caprice; Gawande, Atul A.

    2014-01-01

    Relative risks (RRs) are often considered the preferred measures of association in prospective studies, especially when the binary outcome of interest is common. In particular, many researchers regard RRs to be more intuitively interpretable than odds ratios. Although RR regression is a special case of generalized linear models, specifically with a log link function for the binomial (or Bernoulli) outcome, the resulting log-binomial regression does not respect the natural parameter constraints. Because log-binomial regression does not ensure that predicted probabilities are mapped to the [0,1] range, maximum likelihood (ML) estimation is often subject to numerical instability that leads to convergence problems. To circumvent these problems, a number of alternative approaches for estimating RR regression parameters have been proposed. One approach that has been widely studied is the use of Poisson regression estimating equations. The estimating equations for Poisson regression yield consistent, albeit inefficient, estimators of the RR regression parameters. We consider the relative efficiency of the Poisson regression estimator and develop an alternative, almost efficient estimator for the RR regression parameters. The proposed method uses near-optimal weights based on a Maclaurin series (Taylor series expanded around zero) approximation to the true Bernoulli or binomial weight function. This yields an almost efficient estimator while avoiding convergence problems. We examine the asymptotic relative efficiency of the proposed estimator for an increase in the number of terms in the series. Using simulations, we demonstrate the potential for convergence problems with standard ML estimation of the log-binomial regression model and illustrate how this is overcome using the proposed estimator. We apply the proposed estimator to a study of predictors of pre-operative use of beta blockers among patients undergoing colorectal surgery after diagnosis of colon cancer. PMID

  2. Modeling the toxicity of aromatic compounds to tetrahymena pyriformis: the response surface methodology with nonlinear methods.

    PubMed

    Ren, Shijin

    2003-01-01

    Response surface models based on multiple linear regression had previously been developed for the toxicity of aromatic chemicals to Tetrahymena pyriformis. However, a nonlinear relationship between toxicity and one of the molecular descriptors in the response surface model was observed. In this study, response surface models were established using six nonlinear modeling methods to handle the nonlinearity exhibited in the aromatic chemicals data set. All models were validated using the method of cross-validation, and prediction accuracy was tested on an external data set. Results showed that response surface models based on locally weighted regression scatter plot smoothing (LOESS), multivariate adaptive regression splines (MARS), neural networks (NN), and projection pursuit regression (PPR) provided satisfactory power of model fitting and prediction and had similar applicabilities. The response surface models based on nonlinear methods were difficult to interpret and conservative in discriminating toxicity mechanisms.

  3. Investigating bias in squared regression structure coefficients

    PubMed Central

    Nimon, Kim F.; Zientek, Linda R.; Thompson, Bruce

    2015-01-01

    The importance of structure coefficients and analogs of regression weights for analysis within the general linear model (GLM) has been well-documented. The purpose of this study was to investigate bias in squared structure coefficients in the context of multiple regression and to determine if a formula that had been shown to correct for bias in squared Pearson correlation coefficients and coefficients of determination could be used to correct for bias in squared regression structure coefficients. Using data from a Monte Carlo simulation, this study found that squared regression structure coefficients corrected with Pratt's formula produced less biased estimates and might be more accurate and stable estimates of population squared regression structure coefficients than estimates with no such corrections. While our findings are in line with prior literature that identified multicollinearity as a predictor of bias in squared regression structure coefficients but not coefficients of determination, the findings from this study are unique in that the level of predictive power, number of predictors, and sample size were also observed to contribute bias in squared regression structure coefficients. PMID:26217273

  4. Investigating bias in squared regression structure coefficients.

    PubMed

    Nimon, Kim F; Zientek, Linda R; Thompson, Bruce

    2015-01-01

    The importance of structure coefficients and analogs of regression weights for analysis within the general linear model (GLM) has been well-documented. The purpose of this study was to investigate bias in squared structure coefficients in the context of multiple regression and to determine if a formula that had been shown to correct for bias in squared Pearson correlation coefficients and coefficients of determination could be used to correct for bias in squared regression structure coefficients. Using data from a Monte Carlo simulation, this study found that squared regression structure coefficients corrected with Pratt's formula produced less biased estimates and might be more accurate and stable estimates of population squared regression structure coefficients than estimates with no such corrections. While our findings are in line with prior literature that identified multicollinearity as a predictor of bias in squared regression structure coefficients but not coefficients of determination, the findings from this study are unique in that the level of predictive power, number of predictors, and sample size were also observed to contribute bias in squared regression structure coefficients.

  5. REGRESSION APPROXIMATIONS FOR TRANSPORT MODEL CONSTRAINT SETS IN COMBINED AQUIFER SIMULATION-OPTIMIZATION STUDIES.

    USGS Publications Warehouse

    Alley, William M.

    1986-01-01

    Problems involving the combined use of contaminant transport models and nonlinear optimization schemes can be very expensive to solve. This paper explores the use of transport models with ordinary regression and regression on ranks to develop approximate response functions of concentrations at critical locations as a function of pumping and recharge at decision wells. These response functions combined with other constraints can often be solved very easily and may suggest reasonable starting points for combined simulation-management modeling or even relatively efficient operating schemes in themselves.

  6. A regression technique for evaluation and quantification for water quality parameters from remote sensing data

    NASA Technical Reports Server (NTRS)

    Whitlock, C. H.; Kuo, C. Y.

    1979-01-01

    The objective of this paper is to define optical physics and/or environmental conditions under which the linear multiple-regression should be applicable. An investigation of the signal-response equations is conducted and the concept is tested by application to actual remote sensing data from a laboratory experiment performed under controlled conditions. Investigation of the signal-response equations shows that the exact solution for a number of optical physics conditions is of the same form as a linearized multiple-regression equation, even if nonlinear contributions from surface reflections, atmospheric constituents, or other water pollutants are included. Limitations on achieving this type of solution are defined.

  7. Relative risk regression analysis of epidemiologic data.

    PubMed

    Prentice, R L

    1985-11-01

    Relative risk regression methods are described. These methods provide a unified approach to a range of data analysis problems in environmental risk assessment and in the study of disease risk factors more generally. Relative risk regression methods are most readily viewed as an outgrowth of Cox's regression and life model. They can also be viewed as a regression generalization of more classical epidemiologic procedures, such as that due to Mantel and Haenszel. In the context of an epidemiologic cohort study, relative risk regression methods extend conventional survival data methods and binary response (e.g., logistic) regression models by taking explicit account of the time to disease occurrence while allowing arbitrary baseline disease rates, general censorship, and time-varying risk factors. This latter feature is particularly relevant to many environmental risk assessment problems wherein one wishes to relate disease rates at a particular point in time to aspects of a preceding risk factor history. Relative risk regression methods also adapt readily to time-matched case-control studies and to certain less standard designs. The uses of relative risk regression methods are illustrated and the state of development of these procedures is discussed. It is argued that asymptotic partial likelihood estimation techniques are now well developed in the important special case in which the disease rates of interest have interpretations as counting process intensity functions. Estimation of relative risks processes corresponding to disease rates falling outside this class has, however, received limited attention. The general area of relative risk regression model criticism has, as yet, not been thoroughly studied, though a number of statistical groups are studying such features as tests of fit, residuals, diagnostics and graphical procedures. Most such studies have been restricted to exponential form relative risks as have simulation studies of relative risk estimation

  8. A comparison of regression and regression-kriging for soil characterization using remote sensing imagery

    Technology Transfer Automated Retrieval System (TEKTRAN)

    In precision agriculture regression has been used widely to quality the relationship between soil attributes and other environmental variables. However, spatial correlation existing in soil samples usually makes the regression model suboptimal. In this study, a regression-kriging method was attemp...

  9. Modelling of filariasis in East Java with Poisson regression and generalized Poisson regression models

    NASA Astrophysics Data System (ADS)

    Darnah

    2016-04-01

    Poisson regression has been used if the response variable is count data that based on the Poisson distribution. The Poisson distribution assumed equal dispersion. In fact, a situation where count data are over dispersion or under dispersion so that Poisson regression inappropriate because it may underestimate the standard errors and overstate the significance of the regression parameters, and consequently, giving misleading inference about the regression parameters. This paper suggests the generalized Poisson regression model to handling over dispersion and under dispersion on the Poisson regression model. The Poisson regression model and generalized Poisson regression model will be applied the number of filariasis cases in East Java. Based regression Poisson model the factors influence of filariasis are the percentage of families who don't behave clean and healthy living and the percentage of families who don't have a healthy house. The Poisson regression model occurs over dispersion so that we using generalized Poisson regression. The best generalized Poisson regression model showing the factor influence of filariasis is percentage of families who don't have healthy house. Interpretation of result the model is each additional 1 percentage of families who don't have healthy house will add 1 people filariasis patient.

  10. Regressive language in severe head injury.

    PubMed

    Thomsen, I V; Skinhoj, E

    1976-09-01

    In a follow-up study of 50 patients with severe head injuries three patients had echolalia. One patient with initially global aphasia had echolalia for some weeks when he started talking. Another patient with severe diffuse brain damage, dementia, and emotional regression had echolalia. The dysfunction was considered a detour performance. In the third patient echolalia and palilalia were details in a total pattern of regression lasting for months. The patient, who had extensive frontal atrophy secondary to a very severe head trauma, presented an extreme state of regression returning to a foetal-body pattern and behaving like a baby.

  11. Regression of altitude-produced cardiac hypertrophy.

    NASA Technical Reports Server (NTRS)

    Sizemore, D. A.; Mcintyre, T. W.; Van Liere, E. J.; Wilson , M. F.

    1973-01-01

    The rate of regression of cardiac hypertrophy with time has been determined in adult male albino rats. The hypertrophy was induced by intermittent exposure to simulated high altitude. The percentage hypertrophy was much greater (46%) in the right ventricle than in the left (16%). The regression could be adequately fitted to a single exponential function with a half-time of 6.73 plus or minus 0.71 days (90% CI). There was no significant difference in the rates of regression for the two ventricles.

  12. The Current and Future Use of Ridge Regression for Prediction in Quantitative Genetics

    PubMed Central

    de Vlaming, Ronald; Groenen, Patrick J. F.

    2015-01-01

    In recent years, there has been a considerable amount of research on the use of regularization methods for inference and prediction in quantitative genetics. Such research mostly focuses on selection of markers and shrinkage of their effects. In this review paper, the use of ridge regression for prediction in quantitative genetics using single-nucleotide polymorphism data is discussed. In particular, we consider (i) the theoretical foundations of ridge regression, (ii) its link to commonly used methods in animal breeding, (iii) the computational feasibility, and (iv) the scope for constructing prediction models with nonlinear effects (e.g., dominance and epistasis). Based on a simulation study we gauge the current and future potential of ridge regression for prediction of human traits using genome-wide SNP data. We conclude that, for outcomes with a relatively simple genetic architecture, given current sample sizes in most cohorts (i.e., N < 10,000) the predictive accuracy of ridge regression is slightly higher than the classical genome-wide association study approach of repeated simple regression (i.e., one regression per SNP). However, both capture only a small proportion of the heritability. Nevertheless, we find evidence that for large-scale initiatives, such as biobanks, sample sizes can be achieved where ridge regression compared to the classical approach improves predictive accuracy substantially. PMID:26273586

  13. The Current and Future Use of Ridge Regression for Prediction in Quantitative Genetics.

    PubMed

    de Vlaming, Ronald; Groenen, Patrick J F

    2015-01-01

    In recent years, there has been a considerable amount of research on the use of regularization methods for inference and prediction in quantitative genetics. Such research mostly focuses on selection of markers and shrinkage of their effects. In this review paper, the use of ridge regression for prediction in quantitative genetics using single-nucleotide polymorphism data is discussed. In particular, we consider (i) the theoretical foundations of ridge regression, (ii) its link to commonly used methods in animal breeding, (iii) the computational feasibility, and (iv) the scope for constructing prediction models with nonlinear effects (e.g., dominance and epistasis). Based on a simulation study we gauge the current and future potential of ridge regression for prediction of human traits using genome-wide SNP data. We conclude that, for outcomes with a relatively simple genetic architecture, given current sample sizes in most cohorts (i.e., N < 10,000) the predictive accuracy of ridge regression is slightly higher than the classical genome-wide association study approach of repeated simple regression (i.e., one regression per SNP). However, both capture only a small proportion of the heritability. Nevertheless, we find evidence that for large-scale initiatives, such as biobanks, sample sizes can be achieved where ridge regression compared to the classical approach improves predictive accuracy substantially.

  14. Nonlinear rotordynamics analysis

    NASA Technical Reports Server (NTRS)

    Day, W. B.

    1985-01-01

    The special nonlinearities of the Jeffcott equations in rotordynamics are examined. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot firing ground testing. Deadband, side force and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency is defined and used to develop the solutions of the nonlinear Jeffcott equations as asympotic expansions. This nonlinear natural frequency which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies. Numerical solutions are included for comparison with the analysis. Also, nonlinear frequency-response tables are made for a typical range of values.

  15. Principles of Nonlinear Optics

    DTIC Science & Technology

    1989-11-01

    Holography 74 6.2 Semiclassical Analysis 77 7. The Nonlinear Schrodinger Equation and Soliton Propagation 81 8. Conclusion Ancession For 86 ETis -GRA...is analyzed through the nonlinear Schrodinger equation , which is first heuristically derived. The distortionless pulses arising out of a balance...Eq. (71) has the same form as the nonlinear Schrodinger equation (2], (4], [17], (20], which is used to explain soliton propagation through fibers (21

  16. Nonlinear Ship Dynamics

    DTIC Science & Technology

    1992-07-07

    mrtegrating the original governing differential equation. 2. A. H. Nayfeh, " Parametric Identification of Nonlinear Dynamic Systems," Computers...Structures, Vol. 20. No. 1-3. 1985, pp. 487-493. A parametric identification technique that exploits nonlinear resonances and comparisons of the behavior of...617-631. Presentations 1. A. H. Vn’.yfeh, " Parametric Identification of Nonlinear Dynamic Systems," Symposium on Advances and Trends in Structures

  17. A new bivariate negative binomial regression model

    NASA Astrophysics Data System (ADS)

    Faroughi, Pouya; Ismail, Noriszura

    2014-12-01

    This paper introduces a new form of bivariate negative binomial (BNB-1) regression which can be fitted to bivariate and correlated count data with covariates. The BNB regression discussed in this study can be fitted to bivariate and overdispersed count data with positive, zero or negative correlations. The joint p.m.f. of the BNB1 distribution is derived from the product of two negative binomial marginals with a multiplicative factor parameter. Several testing methods were used to check overdispersion and goodness-of-fit of the model. Application of BNB-1 regression is illustrated on Malaysian motor insurance dataset. The results indicated that BNB-1 regression has better fit than bivariate Poisson and BNB-2 models with regards to Akaike information criterion.

  18. Some Simple Computational Formulas for Multiple Regression

    ERIC Educational Resources Information Center

    Aiken, Lewis R., Jr.

    1974-01-01

    Short-cut formulas are presented for direct computation of the beta weights, the standard errors of the beta weights, and the multiple correlation coefficient for multiple regression problems involving three independent variables and one dependent variable. (Author)

  19. An introduction to multilevel regression models.

    PubMed

    Austin, P C; Goel, V; van Walraven, C

    2001-01-01

    Data in health research are frequently structured hierarchically. For example, data may consist of patients nested within physicians, who in turn may be nested in hospitals or geographic regions. Fitting regression models that ignore the hierarchical structure of the data can lead to false inferences being drawn from the data. Implementing a statistical analysis that takes into account the hierarchical structure of the data requires special methodologies. In this paper, we introduce the concept of hierarchically structured data, and present an introduction to hierarchical regression models. We then compare the performance of a traditional regression model with that of a hierarchical regression model on a dataset relating test utilization at the annual health exam with patient and physician characteristics. In comparing the resultant models, we see that false inferences can be drawn by ignoring the structure of the data.

  20. Multiple Instance Regression with Structured Data

    NASA Technical Reports Server (NTRS)

    Wagstaff, Kiri L.; Lane, Terran; Roper, Alex

    2008-01-01

    This slide presentation reviews the use of multiple instance regression with structured data from multiple and related data sets. It applies the concept to a practical problem, that of estimating crop yield using remote sensed country wide weekly observations.

  1. Bayesian Comparison of Two Regression Lines.

    ERIC Educational Resources Information Center

    Tsutakawa, Robert K.

    1978-01-01

    A Bayesian solution is presented for the Johnson-Neyman problem (whether or not the distance between two regression lines is statistically significant over a finite interval of the independent variable). (Author/CTM)

  2. TWSVR: Regression via Twin Support Vector Machine.

    PubMed

    Khemchandani, Reshma; Goyal, Keshav; Chandra, Suresh

    2016-02-01

    Taking motivation from Twin Support Vector Machine (TWSVM) formulation, Peng (2010) attempted to propose Twin Support Vector Regression (TSVR) where the regressor is obtained via solving a pair of quadratic programming problems (QPPs). In this paper we argue that TSVR formulation is not in the true spirit of TWSVM. Further, taking motivation from Bi and Bennett (2003), we propose an alternative approach to find a formulation for Twin Support Vector Regression (TWSVR) which is in the true spirit of TWSVM. We show that our proposed TWSVR can be derived from TWSVM for an appropriately constructed classification problem. To check the efficacy of our proposed TWSVR we compare its performance with TSVR and classical Support Vector Regression(SVR) on various regression datasets.

  3. Nonlinear magnetic metamaterials.

    PubMed

    Shadrivov, Ilya V; Kozyrev, Alexander B; van der Weide, Daniel W; Kivshar, Yuri S

    2008-12-08

    We study experimentally nonlinear tunable magnetic metamaterials operating at microwave frequencies. We fabricate the nonlinear metamaterial composed of double split-ring resonators where a varactor diode is introduced into each resonator so that the magnetic resonance can be tuned dynamically by varying the input power. We demonstrate that at higher powers the transmission of the metamaterial becomes power-dependent and, as a result, such metamaterial can demonstrate various nonlinear properties. In particular, we study experimentally the power-dependent shift of the transmission band and demonstrate nonlinearity-induced enhancement (or suppression) of wave transmission.

  4. Nonlinearity-reduced interferometer

    NASA Astrophysics Data System (ADS)

    Wu, Chien-ming

    2007-12-01

    Periodic nonlinearity is a systematic error limiting the accuracy of displacement measurements at the nanometer level. It results from many causes such as the frequency mixing, polarization mixing, polarization-frequency mixing, and the ghost reflections. An interferometer having accuracy in displacement measurement of less than one-nanometer is necessary in nanometrology. To meet the requirement, the periodic nonlinearity should be less than deep sub-nanometer. In this paper, a nonlinearity-reduced interferometry has been proposed. Both the linear- and straightness-interferometer were tested. The developed interferometer demonstrated of a residual nonlinearity less than 25 pm.

  5. Marginal longitudinal semiparametric regression via penalized splines

    PubMed Central

    Kadiri, M. Al; Carroll, R.J.; Wand, M.P.

    2010-01-01

    We study the marginal longitudinal nonparametric regression problem and some of its semiparametric extensions. We point out that, while several elaborate proposals for efficient estimation have been proposed, a relative simple and straightforward one, based on penalized splines, has not. After describing our approach, we then explain how Gibbs sampling and the BUGS software can be used to achieve quick and effective implementation. Illustrations are provided for nonparametric regression and additive models. PMID:21037941

  6. Discriminative Elastic-Net Regularized Linear Regression.

    PubMed

    Zhang, Zheng; Lai, Zhihui; Xu, Yong; Shao, Ling; Wu, Jian; Xie, Guo-Sen

    2017-03-01

    In this paper, we aim at learning compact and discriminative linear regression models. Linear regression has been widely used in different problems. However, most of the existing linear regression methods exploit the conventional zero-one matrix as the regression targets, which greatly narrows the flexibility of the regression model. Another major limitation of these methods is that the learned projection matrix fails to precisely project the image features to the target space due to their weak discriminative capability. To this end, we present an elastic-net regularized linear regression (ENLR) framework, and develop two robust linear regression models which possess the following special characteristics. First, our methods exploit two particular strategies to enlarge the margins of different classes by relaxing the strict binary targets into a more feasible variable matrix. Second, a robust elastic-net regularization of singular values is introduced to enhance the compactness and effectiveness of the learned projection matrix. Third, the resulting optimization problem of ENLR has a closed-form solution in each iteration, which can be solved efficiently. Finally, rather than directly exploiting the projection matrix for recognition, our methods employ the transformed features as the new discriminate representations to make final image classification. Compared with the traditional linear regression model and some of its variants, our method is much more accurate in image classification. Extensive experiments conducted on publicly available data sets well demonstrate that the proposed framework can outperform the state-of-the-art methods. The MATLAB codes of our methods can be available at http://www.yongxu.org/lunwen.html.

  7. The Geometry of Enhancement in Multiple Regression

    ERIC Educational Resources Information Center

    Waller, Niels G.

    2011-01-01

    In linear multiple regression, "enhancement" is said to occur when R[superscript 2] = b[prime]r greater than r[prime]r, where b is a p x 1 vector of standardized regression coefficients and r is a p x 1 vector of correlations between a criterion y and a set of standardized regressors, x. When p = 1 then b [is congruent to] r and…

  8. A step-by-step regressed pediatric kidney depth formula validated by a reasonable index

    PubMed Central

    Hongwei, Si; Yingmao, Chen; Li, Li; Guangyu, Ma; Liuhai, Shen; Zhifang, Wu; Mingzhe, Shao; Sijin, Li

    2017-01-01

    Abstract In predicting pediatric kidney depth, we are especially interested in that the errors of most estimates are within a narrow range. Therefore, this study was intended to use the proportion of estimates within a range of −5 to 5 mm (P5 mm) to evaluate the formulas and tried to regress a kidney depth formula for children. The enrolled children aged from 1 to 19 years were randomly sampled into group A and group B (75% and 25% of all recruits, respectively). Using data of the group A, the test formula was regressed by nonlinear regression and subsequently Passing & Bablok regression, and validated in group B. The Raynaud, Gordon, Tonnesen, Taylor, and the test formulas were evaluated in the 2 groups. Accuracy was evaluated by bias, absolute bias, and P5 mm; and precision was evaluated by correlation coefficient. In addition, root-mean square error was used as a mixed index for both accuracy and precision. Body weight, height, and age did not have significant differences between the 2 groups. In the nonlinear regression, coefficients of the formula (kidney depth = a × weight/height + b × age) from group A were in narrower 95% confidence intervals. After the Passing & Bablok regression, biases of left and right kidney estimates were significantly decreased. In the evaluation of formulas, the test formula was obviously better than other formulas mentioned above, and P5 mm for left and right kidneys was about 60%. Among children younger than 10 years, P5 mm was even more than 70% for left and right kidney depths. To predict pediatric kidney depth, accuracy and precision of a step-by-step regressed formula were better than the 4 “standard” formulas. PMID:28353617

  9. [Iris movement mediates pupillary membrane regression].

    PubMed

    Morizane, Yuki

    2007-11-01

    In the course of mammalian lens development, a transient capillary meshwork called as the pupillary membrane (PM) forms. It is located in the pupil area to nourish the anterior surface of the lens, and then regresses to clear the optical path. Although the involvement of the apoptotic process has been reported in PM regression, the initiating factor remains unknown. We initially found that regression of the PM coincided with the development of iris motility, and that iris movement caused cessation and resumption of blood flow within the PM. Therefore, we investigated whether the development of the capacity of the iris to constrict and dilate can function as an essential signal that induces apoptosis in the PM. Continuous inhibition of iris movement with mydriatic agents suppressed apoptosis of the PM and resulted in the persistence of PM in rats. The distribution of apoptotic cells in the regressing PM was diffuse and showed no apparent localization. These results indicated that iris movement induced regression of the PM by changing the blood flow within it. This study suggests the importance of the physiological interactions between tissues-in this case, the iris and the PM-as a signal to advance vascular regression during organ development.

  10. Multiple-Instance Regression with Structured Data

    NASA Technical Reports Server (NTRS)

    Wagstaff, Kiri L.; Lane, Terran; Roper, Alex

    2008-01-01

    We present a multiple-instance regression algorithm that models internal bag structure to identify the items most relevant to the bag labels. Multiple-instance regression (MIR) operates on a set of bags with real-valued labels, each containing a set of unlabeled items, in which the relevance of each item to its bag label is unknown. The goal is to predict the labels of new bags from their contents. Unlike previous MIR methods, MI-ClusterRegress can operate on bags that are structured in that they contain items drawn from a number of distinct (but unknown) distributions. MI-ClusterRegress simultaneously learns a model of the bag's internal structure, the relevance of each item, and a regression model that accurately predicts labels for new bags. We evaluated this approach on the challenging MIR problem of crop yield prediction from remote sensing data. MI-ClusterRegress provided predictions that were more accurate than those obtained with non-multiple-instance approaches or MIR methods that do not model the bag structure.

  11. Nonlinear Simulation of the Tooth Enamel Spectrum for EPR Dosimetry

    NASA Astrophysics Data System (ADS)

    Kirillov, V. A.; Dubovsky, S. V.

    2016-07-01

    Software was developed where initial EPR spectra of tooth enamel were deconvoluted based on nonlinear simulation, line shapes and signal amplitudes in the model initial spectrum were calculated, the regression coefficient was evaluated, and individual spectra were summed. Software validation demonstrated that doses calculated using it agreed excellently with the applied radiation doses and the doses reconstructed by the method of additive doses.

  12. Efficient Inference of Parsimonious Phenomenological Models of Cellular Dynamics Using S-Systems and Alternating Regression

    PubMed Central

    Daniels, Bryan C.; Nemenman, Ilya

    2015-01-01

    The nonlinearity of dynamics in systems biology makes it hard to infer them from experimental data. Simple linear models are computationally efficient, but cannot incorporate these important nonlinearities. An adaptive method based on the S-system formalism, which is a sensible representation of nonlinear mass-action kinetics typically found in cellular dynamics, maintains the efficiency of linear regression. We combine this approach with adaptive model selection to obtain efficient and parsimonious representations of cellular dynamics. The approach is tested by inferring the dynamics of yeast glycolysis from simulated data. With little computing time, it produces dynamical models with high predictive power and with structural complexity adapted to the difficulty of the inference problem. PMID:25806510

  13. Analysis of regression confidence intervals and Bayesian credible intervals for uncertainty quantification

    NASA Astrophysics Data System (ADS)

    Lu, Dan; Ye, Ming; Hill, Mary C.

    2012-09-01

    Confidence intervals based on classical regression theories augmented to include prior information and credible intervals based on Bayesian theories are conceptually different ways to quantify parametric and predictive uncertainties. Because both confidence and credible intervals are used in environmental modeling, we seek to understand their differences and similarities. This is of interest in part because calculating confidence intervals typically requires tens to thousands of model runs, while Bayesian credible intervals typically require tens of thousands to millions of model runs. Given multi-Gaussian distributed observation errors, our theoretical analysis shows that, for linear or linearized-nonlinear models, confidence and credible intervals are always numerically identical when consistent prior information is used. For nonlinear models, nonlinear confidence and credible intervals can be numerically identical if parameter confidence regions defined using the approximate likelihood method and parameter credible regions estimated using Markov chain Monte Carlo realizations are numerically identical and predictions are a smooth, monotonic function of the parameters. Both occur if intrinsic model nonlinearity is small. While the conditions of Gaussian errors and small intrinsic model nonlinearity are violated by many environmental models, heuristic tests using analytical and numerical models suggest that linear and nonlinear confidence intervals can be useful approximations of uncertainty even under significantly nonideal conditions. In the context of epistemic model error for a complex synthetic nonlinear groundwater problem, the linear and nonlinear confidence and credible intervals for individual models performed similarly enough to indicate that the computationally frugal confidence intervals can be useful in many circumstances. Experiences with these groundwater models are expected to be broadly applicable to many environmental models. We suggest that for

  14. Spacecraft nonlinear control

    NASA Technical Reports Server (NTRS)

    Sheen, Jyh-Jong; Bishop, Robert H.

    1992-01-01

    The feedback linearization technique is applied to the problem of spacecraft attitude control and momentum management with control moment gyros (CMGs). The feedback linearization consists of a coordinate transformation, which transforms the system to a companion form, and a nonlinear feedback control law to cancel the nonlinear dynamics resulting in a linear equivalent model. Pole placement techniques are then used to place the closed-loop poles. The coordinate transformation proposed here evolves from three output functions of relative degree four, three, and two, respectively. The nonlinear feedback control law is presented. Stability in a neighborhood of a controllable torque equilibrium attitude (TEA) is guaranteed and this fact is demonstrated by the simulation results. An investigation of the nonlinear control law shows that singularities exist in the state space outside the neighborhood of the controllable TEA. The nonlinear control law is simplified by a standard linearization technique and it is shown that the linearized nonlinear controller provides a natural way to select control gains for the multiple-input, multiple-output system. Simulation results using the linearized nonlinear controller show good performance relative to the nonlinear controller in the neighborhood of the TEA.

  15. Optically Nonlinear Polymeric Materials.

    DTIC Science & Technology

    1983-01-01

    optical chromophores into the hydrophobic portions of the polymer, second order . ,nonlinear optical effects may be obtained. Experimental 01 0...8217V cinnamaldehyde , giving the polymer shown in Figure 3. This chromophore should have greater optical nonlinearity because of its better electron

  16. Nonlinear Optics and Applications

    NASA Technical Reports Server (NTRS)

    Abdeldayem, Hossin A. (Editor); Frazier, Donald O. (Editor)

    2007-01-01

    Nonlinear optics is the result of laser beam interaction with materials and started with the advent of lasers in the early 1960s. The field is growing daily and plays a major role in emerging photonic technology. Nonlinear optics play a major role in many of the optical applications such as optical signal processing, optical computers, ultrafast switches, ultra-short pulsed lasers, sensors, laser amplifiers, and many others. This special review volume on Nonlinear Optics and Applications is intended for those who want to be aware of the most recent technology. This book presents a survey of the recent advances of nonlinear optical applications. Emphasis will be on novel devices and materials, switching technology, optical computing, and important experimental results. Recent developments in topics which are of historical interest to researchers, and in the same time of potential use in the fields of all-optical communication and computing technologies, are also included. Additionally, a few new related topics which might provoke discussion are presented. The book includes chapters on nonlinear optics and applications; the nonlinear Schrodinger and associated equations that model spatio-temporal propagation; the supercontinuum light source; wideband ultrashort pulse fiber laser sources; lattice fabrication as well as their linear and nonlinear light guiding properties; the second-order EO effect (Pockels), the third-order (Kerr) and thermo-optical effects in optical waveguides and their applications in optical communication; and, the effect of magnetic field and its role in nonlinear optics, among other chapters.

  17. Nonlinear Maneuver Autopilot

    NASA Technical Reports Server (NTRS)

    Menon, P. K. A.; Badgett, M. E.; Walker, R. A.

    1992-01-01

    Trajectory-control laws based on singular-perturbation theory and nonlinear dynamical modeling. Nonlinear maneuver autopilot commands flight-test trajectories of F-15 airplane. Underlying theory of controller enables separation of variables processed in fast and slow control loops, reducing amount of computation required.

  18. Lasers for nonlinear microscopy.

    PubMed

    Wise, Frank

    2013-03-01

    Various versions of nonlinear microscopy are revolutionizing the life sciences, almost all of which are made possible because of the development of ultrafast lasers. In this article, the main properties and technical features of short-pulse lasers used in nonlinear microscopy are summarized. Recent research results on fiber lasers that will impact future instruments are also discussed.

  19. Review of the Software Package "Scientist": Mathematical Modeling/Differential and Nonlinear Equations.

    ERIC Educational Resources Information Center

    Scheidt, Douglas M.

    1995-01-01

    Reviews three functions of the "Scientist" software package useful for the social sciences: nonlinear curve fitting, parameter estimation, and data/regression plotting. Social scientists are likely to find limitations and unfamiliar procedures in "Scientist". Its value lies in its visual presentation of data and regression curves and the…

  20. Anticipating Mathematics Performance: A Cross-Validation Comparison of AID3 and Regression. AIR 1988 Annual Forum Paper.

    ERIC Educational Resources Information Center

    Bloom, Allan M.; And Others

    In response to the increasing importance of student performance in required classes, research was conducted to compare two prediction procedures, linear modeling using multiple regression and nonlinear modeling using AID3. Performance in the first college math course (College Mathematics, Calculus, or Business Calculus Matrices) was the dependent…

  1. MULTILINEAR TENSOR REGRESSION FOR LONGITUDINAL RELATIONAL DATA.

    PubMed

    Hoff, Peter D

    2015-09-01

    A fundamental aspect of relational data, such as from a social network, is the possibility of dependence among the relations. In particular, the relations between members of one pair of nodes may have an effect on the relations between members of another pair. This article develops a type of regression model to estimate such effects in the context of longitudinal and multivariate relational data, or other data that can be represented in the form of a tensor. The model is based on a general multilinear tensor regression model, a special case of which is a tensor autoregression model in which the tensor of relations at one time point are parsimoniously regressed on relations from previous time points. This is done via a separable, or Kronecker-structured, regression parameter along with a separable covariance model. In the context of an analysis of longitudinal multivariate relational data, it is shown how the multilinear tensor regression model can represent patterns that often appear in relational and network data, such as reciprocity and transitivity.

  2. On regression adjustment for the propensity score.

    PubMed

    Vansteelandt, S; Daniel, R M

    2014-10-15

    Propensity scores are widely adopted in observational research because they enable adjustment for high-dimensional confounders without requiring models for their association with the outcome of interest. The results of statistical analyses based on stratification, matching or inverse weighting by the propensity score are therefore less susceptible to model extrapolation than those based solely on outcome regression models. This is attractive because extrapolation in outcome regression models may be alarming, yet difficult to diagnose, when the exposed and unexposed individuals have very different covariate distributions. Standard regression adjustment for the propensity score forms an alternative to the aforementioned propensity score methods, but the benefits of this are less clear because it still involves modelling the outcome in addition to the propensity score. In this article, we develop novel insights into the properties of this adjustment method. We demonstrate that standard tests of the null hypothesis of no exposure effect (based on robust variance estimators), as well as particular standardised effects obtained from such adjusted regression models, are robust against misspecification of the outcome model when a propensity score model is correctly specified; they are thus not vulnerable to the aforementioned problem of extrapolation. We moreover propose efficient estimators for these standardised effects, which retain a useful causal interpretation even when the propensity score model is misspecified, provided the outcome regression model is correctly specified.

  3. Hyperglycemia impairs atherosclerosis regression in mice.

    PubMed

    Gaudreault, Nathalie; Kumar, Nikit; Olivas, Victor R; Eberlé, Delphine; Stephens, Kyle; Raffai, Robert L

    2013-12-01

    Diabetic patients are known to be more susceptible to atherosclerosis and its associated cardiovascular complications. However, the effects of hyperglycemia on atherosclerosis regression remain unclear. We hypothesized that hyperglycemia impairs atherosclerosis regression by modulating the biological function of lesional macrophages. HypoE (Apoe(h/h)Mx1-Cre) mice express low levels of apolipoprotein E (apoE) and develop atherosclerosis when fed a high-fat diet. Atherosclerosis regression occurs in these mice upon plasma lipid lowering induced by a change in diet and the restoration of apoE expression. We examined the morphological characteristics of regressed lesions and assessed the biological function of lesional macrophages isolated with laser-capture microdissection in euglycemic and hyperglycemic HypoE mice. Hyperglycemia induced by streptozotocin treatment impaired lesion size reduction (36% versus 14%) and lipid loss (38% versus 26%) after the reversal of hyperlipidemia. However, decreases in lesional macrophage content and remodeling in both groups of mice were similar. Gene expression analysis revealed that hyperglycemia impaired cholesterol transport by modulating ATP-binding cassette A1, ATP-binding cassette G1, scavenger receptor class B family member (CD36), scavenger receptor class B1, and wound healing pathways in lesional macrophages during atherosclerosis regression. Hyperglycemia impairs both reduction in size and loss of lipids from atherosclerotic lesions upon plasma lipid lowering without significantly affecting the remodeling of the vascular wall.

  4. Regression models for estimating coseismic landslide displacement

    USGS Publications Warehouse

    Jibson, R.W.

    2007-01-01

    Newmark's sliding-block model is widely used to estimate coseismic slope performance. Early efforts to develop simple regression models to estimate Newmark displacement were based on analysis of the small number of strong-motion records then available. The current availability of a much larger set of strong-motion records dictates that these regression equations be updated. Regression equations were generated using data derived from a collection of 2270 strong-motion records from 30 worldwide earthquakes. The regression equations predict Newmark displacement in terms of (1) critical acceleration ratio, (2) critical acceleration ratio and earthquake magnitude, (3) Arias intensity and critical acceleration, and (4) Arias intensity and critical acceleration ratio. These equations are well constrained and fit the data well (71% < R2 < 88%), but they have standard deviations of about 0.5 log units, such that the range defined by the mean ?? one standard deviation spans about an order of magnitude. These regression models, therefore, are not recommended for use in site-specific design, but rather for regional-scale seismic landslide hazard mapping or for rapid preliminary screening of sites. ?? 2007 Elsevier B.V. All rights reserved.

  5. Reconstruction of transcriptional network from microarray data using combined mutual information and network-assisted regression.

    PubMed

    Wang, X-D; Qi, Y-X; Jiang, Z-L

    2011-03-01

    Many methods had been developed on inferring transcriptional network from gene expression. However, it is still necessary to design new method that discloses more detailed and exact network information. Using network-assisted regression, the authors combined the averaged three-way mutual information (AMI3) and non-linear ordinary differential equation (ODE) model to infer the transcriptional network, and to obtain both the topological structure and the regulatory dynamics. Synthetic and experimental data were used to evaluate the performance of the above approach. In comparison with the previous methods based on mutual information, AMI3 obtained higher precision with the same sensitivity. To describe the regulatory dynamics between transcription factors and target genes, network-assisted regression and regression without network, respectively, were applied in the steady-state and time series microarray data. The results revealed that comparing with regression without network, network-assisted regression increased the precision, but decreased the fitting goodness. Then, the authors reconstructed the transcriptional network of Escherichia coli and simulated the regulatory dynamics of genes. Furthermore, the authors' approach identified potential transcription factors regulating yeast cell cycle. In conclusion, network-assisted regression, combined AMI3 and ODE model, was a more precisely to infer the topological structure and the regulatory dynamics of transcriptional network from microarray data. [Includes supplementary material].

  6. Spontaneous skin regression and predictors of skin regression in Thai scleroderma patients.

    PubMed

    Foocharoen, Chingching; Mahakkanukrauh, Ajanee; Suwannaroj, Siraphop; Nanagara, Ratanavadee

    2011-09-01

    Skin tightness is a major clinical manifestation of systemic sclerosis (SSc). Importantly for both clinicians and patients, spontaneous regression of the fibrosis process has been documented. The purpose of this study is to identify the incidence and related clinical characteristics of spontaneous regression among Thai SSc patients. A historical cohort with 4 years of follow-up was performed among SSc patients over 15 years of age diagnosed with SSc between January 1, 2005 and December 31, 2006 in Khon Kaen, Thailand. The start date was the date of the first symptom and the end date was the date of the skin score ≤2. To estimate the respective probability of regression and to assess the associated factors, the Kaplan-Meier method and Cox regression analysis was used. One hundred seventeen cases of SSc were included with a female to male ratio of 1.5:1. Thirteen patients (11.1%) experienced regression. The incidence rate of spontaneous skin regression was 0.31 per 100 person-months and the average duration of SSc at the time of regression was 35.9±15.6 months (range, 15.7-60 months). The factors that negatively correlated with regression were (a) diffuse cutaneous type, (b) Raynaud's phenomenon, (c) esophageal dysmotility, and (d) colchicine treatment at onset with a respective hazard ratio (HR) of 0.19, 0.19, 0.26, and 0.20. By contrast, the factor that positively correlated with regression was active alveolitis with cyclophosphamide therapy at onset with an HR of 4.23 (95% CI, 1.23-14.10). After regression analysis, only Raynaud's phenomenon at onset and diffuse cutaneous type had a significantly negative correlation to regression. A spontaneous regression of the skin fibrosis process was not uncommon among Thai SSc patients. The factors suggesting a poor predictor for cutaneous manifestation were Raynaud's phenomenon, diffuse cutaneous type while early cyclophosphamide therapy might be related to a better skin outcome.

  7. Fatigue design of a cellular phone folder using regression model-based multi-objective optimization

    NASA Astrophysics Data System (ADS)

    Kim, Young Gyun; Lee, Jongsoo

    2016-08-01

    In a folding cellular phone, the folding device is repeatedly opened and closed by the user, which eventually results in fatigue damage, particularly to the front of the folder. Hence, it is important to improve the safety and endurance of the folder while also reducing its weight. This article presents an optimal design for the folder front that maximizes its fatigue endurance while minimizing its thickness. Design data for analysis and optimization were obtained experimentally using a test jig. Multi-objective optimization was carried out using a nonlinear regression model. Three regression methods were employed: back-propagation neural networks, logistic regression and support vector machines. The AdaBoost ensemble technique was also used to improve the approximation. Two-objective Pareto-optimal solutions were identified using the non-dominated sorting genetic algorithm (NSGA-II). Finally, a numerically optimized solution was validated against experimental product data, in terms of both fatigue endurance and thickness index.

  8. Mixed-effects Gaussian process functional regression models with application to dose-response curve prediction.

    PubMed

    Shi, J Q; Wang, B; Will, E J; West, R M

    2012-11-20

    We propose a new semiparametric model for functional regression analysis, combining a parametric mixed-effects model with a nonparametric Gaussian process regression model, namely a mixed-effects Gaussian process functional regression model. The parametric component can provide explanatory information between the response and the covariates, whereas the nonparametric component can add nonlinearity. We can model the mean and covariance structures simultaneously, combining the information borrowed from other subjects with the information collected from each individual subject. We apply the model to dose-response curves that describe changes in the responses of subjects for differing levels of the dose of a drug or agent and have a wide application in many areas. We illustrate the method for the management of renal anaemia. An individual dose-response curve is improved when more information is included by this mechanism from the subject/patient over time, enabling a patient-specific treatment regime.

  9. Parametric modeling of quantile regression coefficient functions.

    PubMed

    Frumento, Paolo; Bottai, Matteo

    2016-03-01

    Estimating the conditional quantiles of outcome variables of interest is frequent in many research areas, and quantile regression is foremost among the utilized methods. The coefficients of a quantile regression model depend on the order of the quantile being estimated. For example, the coefficients for the median are generally different from those of the 10th centile. In this article, we describe an approach to modeling the regression coefficients as parametric functions of the order of the quantile. This approach may have advantages in terms of parsimony, efficiency, and may expand the potential of statistical modeling. Goodness-of-fit measures and testing procedures are discussed, and the results of a simulation study are presented. We apply the method to analyze the data that motivated this work. The described method is implemented in the qrcm R package.

  10. Computing aspects of power for multiple regression.

    PubMed

    Dunlap, William P; Xin, Xue; Myers, Leann

    2004-11-01

    Rules of thumb for power in multiple regression research abound. Most such rules dictate the necessary sample size, but they are based only upon the number of predictor variables, usually ignoring other critical factors necessary to compute power accurately. Other guides to power in multiple regression typically use approximate rather than precise equations for the underlying distribution; entail complex preparatory computations; require interpolation with tabular presentation formats; run only under software such as Mathmatica or SAS that may not be immediately available to the user; or are sold to the user as parts of power computation packages. In contrast, the program we offer herein is immediately downloadable at no charge, runs under Windows, is interactive, self-explanatory, flexible to fit the user's own regression problems, and is as accurate as single precision computation ordinarily permits.

  11. Uncertainty quantification in DIC with Kriging regression

    NASA Astrophysics Data System (ADS)

    Wang, Dezhi; DiazDelaO, F. A.; Wang, Weizhuo; Lin, Xiaoshan; Patterson, Eann A.; Mottershead, John E.

    2016-03-01

    A Kriging regression model is developed as a post-processing technique for the treatment of measurement uncertainty in classical subset-based Digital Image Correlation (DIC). Regression is achieved by regularising the sample-point correlation matrix using a local, subset-based, assessment of the measurement error with assumed statistical normality and based on the Sum of Squared Differences (SSD) criterion. This leads to a Kriging-regression model in the form of a Gaussian process representing uncertainty on the Kriging estimate of the measured displacement field. The method is demonstrated using numerical and experimental examples. Kriging estimates of displacement fields are shown to be in excellent agreement with 'true' values for the numerical cases and in the experimental example uncertainty quantification is carried out using the Gaussian random process that forms part of the Kriging model. The root mean square error (RMSE) on the estimated displacements is produced and standard deviations on local strain estimates are determined.

  12. A tutorial on Bayesian Normal linear regression

    NASA Astrophysics Data System (ADS)

    Klauenberg, Katy; Wübbeler, Gerd; Mickan, Bodo; Harris, Peter; Elster, Clemens

    2015-12-01

    Regression is a common task in metrology and often applied to calibrate instruments, evaluate inter-laboratory comparisons or determine fundamental constants, for example. Yet, a regression model cannot be uniquely formulated as a measurement function, and consequently the Guide to the Expression of Uncertainty in Measurement (GUM) and its supplements are not applicable directly. Bayesian inference, however, is well suited to regression tasks, and has the advantage of accounting for additional a priori information, which typically robustifies analyses. Furthermore, it is anticipated that future revisions of the GUM shall also embrace the Bayesian view. Guidance on Bayesian inference for regression tasks is largely lacking in metrology. For linear regression models with Gaussian measurement errors this tutorial gives explicit guidance. Divided into three steps, the tutorial first illustrates how a priori knowledge, which is available from previous experiments, can be translated into prior distributions from a specific class. These prior distributions have the advantage of yielding analytical, closed form results, thus avoiding the need to apply numerical methods such as Markov Chain Monte Carlo. Secondly, formulas for the posterior results are given, explained and illustrated, and software implementations are provided. In the third step, Bayesian tools are used to assess the assumptions behind the suggested approach. These three steps (prior elicitation, posterior calculation, and robustness to prior uncertainty and model adequacy) are critical to Bayesian inference. The general guidance given here for Normal linear regression tasks is accompanied by a simple, but real-world, metrological example. The calibration of a flow device serves as a running example and illustrates the three steps. It is shown that prior knowledge from previous calibrations of the same sonic nozzle enables robust predictions even for extrapolations.

  13. Salience Assignment for Multiple-Instance Regression

    NASA Technical Reports Server (NTRS)

    Wagstaff, Kiri L.; Lane, Terran

    2007-01-01

    We present a Multiple-Instance Learning (MIL) algorithm for determining the salience of each item in each bag with respect to the bag's real-valued label. We use an alternating-projections constrained optimization approach to simultaneously learn a regression model and estimate all salience values. We evaluate this algorithm on a significant real-world problem, crop yield modeling, and demonstrate that it provides more extensive, intuitive, and stable salience models than Primary-Instance Regression, which selects a single relevant item from each bag.

  14. The Lax-Onsager regression `theorem' revisited

    NASA Astrophysics Data System (ADS)

    Lax, Melvin

    2000-05-01

    It is stated by Ford and O'Connell in this festschrift issue and elsewhere that "there is no quantum regression theorem" although Lax "obtained a formula for correlation in a driven quantum system that has come to be called the quantum regression theorem". This produces a puzzle: "How can it be that a non-existent theorem gives correct results?" Clarification will be provided in this paper by a description of the Lax procedure, with a quantitative estimate of the error for a damped harmonic oscillator based on expressions published in the 1960's.

  15. Nonlinear GARCH model and 1 / f noise

    NASA Astrophysics Data System (ADS)

    Kononovicius, A.; Ruseckas, J.

    2015-06-01

    Auto-regressive conditionally heteroskedastic (ARCH) family models are still used, by practitioners in business and economic policy making, as a conditional volatility forecasting models. Furthermore ARCH models still are attracting an interest of the researchers. In this contribution we consider the well known GARCH(1,1) process and its nonlinear modifications, reminiscent of NGARCH model. We investigate the possibility to reproduce power law statistics, probability density function and power spectral density, using ARCH family models. For this purpose we derive stochastic differential equations from the GARCH processes in consideration. We find the obtained equations to be similar to a general class of stochastic differential equations known to reproduce power law statistics. We show that linear GARCH(1,1) process has power law distribution, but its power spectral density is Brownian noise-like. However, the nonlinear modifications exhibit both power law distribution and power spectral density of the 1 /fβ form, including 1 / f noise.

  16. Nonlinear cochlear mechanics.

    PubMed

    Zweig, George

    2016-05-01

    An earlier paper characterizing the linear mechanical response of the organ of Corti [J. Acoust. Soc. Am. 138, 1102-1121 (2015)] is extended to the nonlinear domain. Assuming the existence of nonlinear oscillators nonlocally coupled through the pressure they help create, the oscillator equations are derived and examined when the stimuli are modulated tones and clicks. The nonlinearities are constrained by the requirements of oscillator stability and the invariance of zero crossings in the click response to changes in click amplitude. The nonlinear oscillator equations for tones are solved in terms of the fluid pressure that drives them, and its time derivative, presumably a proxy for forces created by outer hair cells. The pressure equation is reduced to quadrature, the integrand depending on the oscillators' responses. The resulting nonlocally coupled nonlinear equations for the pressure, and oscillator amplitudes and phases, are solved numerically in terms of the fluid pressure at the stapes. Methods for determining the nonlinear damping directly from measurements are described. Once the oscillators have been characterized from their tone and click responses, the mechanical response of the cochlea to natural sounds may be computed numerically. Signal processing inspired by cochlear mechanics opens up a new area of nonlocal nonlinear time-frequency analysis.

  17. Demonstration of a Fiber Optic Regression Probe

    NASA Technical Reports Server (NTRS)

    Korman, Valentin; Polzin, Kurt A.

    2010-01-01

    The capability to provide localized, real-time monitoring of material regression rates in various applications has the potential to provide a new stream of data for development testing of various components and systems, as well as serving as a monitoring tool in flight applications. These applications include, but are not limited to, the regression of a combusting solid fuel surface, the ablation of the throat in a chemical rocket or the heat shield of an aeroshell, and the monitoring of erosion in long-life plasma thrusters. The rate of regression in the first application is very fast, while the second and third are increasingly slower. A recent fundamental sensor development effort has led to a novel regression, erosion, and ablation sensor technology (REAST). The REAST sensor allows for measurement of real-time surface erosion rates at a discrete surface location. The sensor is optical, using two different, co-located fiber-optics to perform the regression measurement. The disparate optical transmission properties of the two fiber-optics makes it possible to measure the regression rate by monitoring the relative light attenuation through the fibers. As the fibers regress along with the parent material in which they are embedded, the relative light intensities through the two fibers changes, providing a measure of the regression rate. The optical nature of the system makes it relatively easy to use in a variety of harsh, high temperature environments, and it is also unaffected by the presence of electric and magnetic fields. In addition, the sensor could be used to perform optical spectroscopy on the light emitted by a process and collected by fibers, giving localized measurements of various properties. The capability to perform an in-situ measurement of material regression rates is useful in addressing a variety of physical issues in various applications. An in-situ measurement allows for real-time data regarding the erosion rates, providing a quick method for

  18. Gaussian Process Regression for Uncertainty Estimation on Ecosystem Data

    NASA Astrophysics Data System (ADS)

    Menzer, O.; Moffat, A.; Lasslop, G.; Reichstein, M.

    2011-12-01

    The flow of carbon between terrestrial ecosystems and the atmosphere is mainly driven by nonlinear, complex and time-lagged processes. Understanding the associated ecosystem responses and climatic feedbacks is a key challenge regarding climate change questions such as increasing atmospheric CO2 levels. Usually, the underlying relationships are implemented in models as prescribed functions which interlink numerous meteorological, radiative and gas exchange variables. In contrast, supervised Machine Learning algorithms, such as Artificial Neural Networks or Gaussian Processes, allow for an insight into the relationships directly from a data perspective. Micrometeorological, high resolution measurements at flux towers of the FLUXNET observational network are an essential tool for obtaining quantifications of the ecosystem variables, as they continuously record e.g. CO2 exchange, solar radiation and air temperature. In order to facilitate the investigation of the interactions and feedbacks between these variables, several challenging data properties need to be taken into account: noisy, multidimensional and incomplete (Moffat, Accepted). The task of estimating uncertainties in such micrometeorological measurements can be addressed by Gaussian Processes (GPs), a modern nonparametric method for nonlinear regression. The GP approach has recently been shown to be a powerful modeling tool, regardless of the input dimensionality, the degree of nonlinearity and the noise level (Rasmussen and Williams, 2006). Heteroscedastic Gaussian Processes (HGPs) are a specialized GP method for data with a varying, inhomogeneous noise variance (Goldberg et al., 1998; Kersting et al., 2007), as usually observed in CO2 flux measurements (Richardson et al., 2006). Here, we showed by an evaluation of the HGP performance in several artificial experiments and a comparison to existing nonlinear regression methods, that their outstanding ability is to capture measurement noise levels, concurrently

  19. Studying Individual Differences in Predictability with Gamma Regression and Nonlinear Multilevel Models

    ERIC Educational Resources Information Center

    Culpepper, Steven Andrew

    2010-01-01

    Statistical prediction remains an important tool for decisions in a variety of disciplines. An equally important issue is identifying factors that contribute to more or less accurate predictions. The time series literature includes well developed methods for studying predictability and volatility over time. This article develops…

  20. A Nonlinear Regression Model Estimating Single Source Concentrations of Primary and Secondarily Formed 2.5

    EPA Science Inventory

    Various approaches and tools exist to estimate local and regional PM2.5 impacts from a single emissions source, ranging from simple screening techniques to Gaussian based dispersion models and complex grid-based Eulerian photochemical transport models. These approache...

  1. Metamaterials with conformational nonlinearity

    PubMed Central

    Lapine, Mikhail; Shadrivov, Ilya V.; Powell, David A.; Kivshar, Yuri S.

    2011-01-01

    Within a decade of fruitful development, metamaterials became a prominent area of research, bridging theoretical and applied electrodynamics, electrical engineering and material science. Being man-made structures, metamaterials offer a particularly useful playground to develop interdisciplinary concepts. Here we demonstrate a novel principle in metamaterial assembly which integrates electromagnetic, mechanical, and thermal responses within their elements. Through these mechanisms, the conformation of the meta-molecules changes, providing a dual mechanism for nonlinearity and offering nonlinear chirality. Our proposal opens a wide road towards further developments of nonlinear metamaterials and photonic structures, adding extra flexibility to their design and control. PMID:22355655

  2. Nonlinear ordinary difference equations

    NASA Technical Reports Server (NTRS)

    Caughey, T. K.

    1979-01-01

    Future space vehicles will be relatively large and flexible, and active control will be necessary to maintain geometrical configuration. While the stresses and strains in these space vehicles are not expected to be excessively large, their cumulative effects will cause significant geometrical nonlinearities to appear in the equations of motion, in addition to the nonlinearities caused by material properties. Since the only effective tool for the analysis of such large complex structures is the digital computer, it will be necessary to gain a better understanding of the nonlinear ordinary difference equations which result from the time discretization of the semidiscrete equations of motion for such structures.

  3. Gaussian conditional random fields for regression in remote sensing

    NASA Astrophysics Data System (ADS)

    Radosavljevic, Vladan

    In recent years many remote sensing instruments of various properties have been employed in an attempt to better characterize important geophysical phenomena. Satellite instruments provide an exceptional opportunity for global long-term observations of the land, the biosphere, the atmosphere, and the oceans. The collected data are used for estimation and better understanding of geophysical parameters such as land cover type, atmospheric properties, or ocean temperature. Achieving accurate estimations of such parameters is an important requirement for development of models able to predict global climate changes. One of the most challenging climate research problems is estimation of global composition, load, and variability of aerosols, small airborne particles that reflect and absorb incoming solar radiation. The existing algorithm for aerosol prediction from satellite observations is deterministic and manually tuned by domain scientist. In contrast to domain-driven method, we show that aerosol prediction is achievable by completely data-driven approaches. These statistical methods consist of learning of nonlinear regression models to predict aerosol load using the satellite observations as inputs. Measurements from unevenly distributed ground-based sites over the world are used as proxy to ground-truth outputs. Although statistical methods achieve better accuracy than deterministic method this setup is appropriate when data are independently and identically distributed (IID). The IID assumption is often violated in remote sensing where data exhibit temporal, spatial, or spatio-temporal dependencies. In such cases, the traditional supervised learning approaches could result in a model with degraded accuracy. Conditional random fields (CRF) are widely used for predicting output variables that have some internal structure. Most of the CRF research has been done on structured classification where the outputs are discrete. We propose a CRF model for continuous outputs

  4. Creativity and Regression on the Rorschach.

    ERIC Educational Resources Information Center

    Lazar, Billie S.

    This paper describes the results of a study to further test and replicate previous studies partially supporting Kris's view that creativity is a regression in the service of the ego. For this sample of 42 female art and business college students, it was predicted that (1) highly creative Ss (measured by the Torrance Tests) produce more, and more…

  5. Locating the Extrema of Fungible Regression Weights

    ERIC Educational Resources Information Center

    Waller, Niels G.; Jones, Jeff A.

    2009-01-01

    In a multiple regression analysis with three or more predictors, every set of alternate weights belongs to an infinite class of "fungible weights" (Waller, Psychometrica, "in press") that yields identical "SSE" (sum of squared errors) and R[superscript 2] values. When the R[superscript 2] using the alternate weights is a fixed value, fungible…

  6. Assessing risk factors for periodontitis using regression

    NASA Astrophysics Data System (ADS)

    Lobo Pereira, J. A.; Ferreira, Maria Cristina; Oliveira, Teresa

    2013-10-01

    Multivariate statistical analysis is indispensable to assess the associations and interactions between different factors and the risk of periodontitis. Among others, regression analysis is a statistical technique widely used in healthcare to investigate and model the relationship between variables. In our work we study the impact of socio-demographic, medical and behavioral factors on periodontal health. Using regression, linear and logistic models, we can assess the relevance, as risk factors for periodontitis disease, of the following independent variables (IVs): Age, Gender, Diabetic Status, Education, Smoking status and Plaque Index. The multiple linear regression analysis model was built to evaluate the influence of IVs on mean Attachment Loss (AL). Thus, the regression coefficients along with respective p-values will be obtained as well as the respective p-values from the significance tests. The classification of a case (individual) adopted in the logistic model was the extent of the destruction of periodontal tissues defined by an Attachment Loss greater than or equal to 4 mm in 25% (AL≥4mm/≥25%) of sites surveyed. The association measures include the Odds Ratios together with the correspondent 95% confidence intervals.

  7. Predicting Social Trust with Binary Logistic Regression

    ERIC Educational Resources Information Center

    Adwere-Boamah, Joseph; Hufstedler, Shirley

    2015-01-01

    This study used binary logistic regression to predict social trust with five demographic variables from a national sample of adult individuals who participated in The General Social Survey (GSS) in 2012. The five predictor variables were respondents' highest degree earned, race, sex, general happiness and the importance of personally assisting…

  8. Invariant Ordering of Item-Total Regressions

    ERIC Educational Resources Information Center

    Tijmstra, Jesper; Hessen, David J.; van der Heijden, Peter G. M.; Sijtsma, Klaas

    2011-01-01

    A new observable consequence of the property of invariant item ordering is presented, which holds under Mokken's double monotonicity model for dichotomous data. The observable consequence is an invariant ordering of the item-total regressions. Kendall's measure of concordance "W" and a weighted version of this measure are proposed as measures for…

  9. Superquantile Regression: Theory, Algorithms, and Applications

    DTIC Science & Technology

    2014-12-01

    buffered reliability, uncertainty quantification, surrogate estimation, superquantile tracking, dualization of risk 147 Unclassified Unclassified...series of numerical examples that show some of the ap- plication of superquantile regression, such as superquantile tracking and surrogate estimation...dissertation by surrogate estimation. It usually occurs when the explanatory random variable is beyond our direct control, but the dependence between the

  10. A Skew-Normal Mixture Regression Model

    ERIC Educational Resources Information Center

    Liu, Min; Lin, Tsung-I

    2014-01-01

    A challenge associated with traditional mixture regression models (MRMs), which rest on the assumption of normally distributed errors, is determining the number of unobserved groups. Specifically, even slight deviations from normality can lead to the detection of spurious classes. The current work aims to (a) examine how sensitive the commonly…

  11. Categorical Variables in Multiple Regression: Some Cautions.

    ERIC Educational Resources Information Center

    O'Grady, Kevin E.; Medoff, Deborah R.

    1988-01-01

    Limitations of dummy coding and nonsense coding as methods of coding categorical variables for use as predictors in multiple regression analysis are discussed. The combination of these approaches often yields estimates and tests of significance that are not intended by researchers for inclusion in their models. (SLD)

  12. Revisiting Regression in Autism: Heller's "Dementia Infantilis"

    ERIC Educational Resources Information Center

    Westphal, Alexander; Schelinski, Stefanie; Volkmar, Fred; Pelphrey, Kevin

    2013-01-01

    Theodor Heller first described a severe regression of adaptive function in normally developing children, something he termed dementia infantilis, over one 100 years ago. Dementia infantilis is most closely related to the modern diagnosis, childhood disintegrative disorder. We translate Heller's paper, Uber Dementia Infantilis, and discuss…

  13. A Spline Regression Model for Latent Variables

    ERIC Educational Resources Information Center

    Harring, Jeffrey R.

    2014-01-01

    Spline (or piecewise) regression models have been used in the past to account for patterns in observed data that exhibit distinct phases. The changepoint or knot marking the shift from one phase to the other, in many applications, is an unknown parameter to be estimated. As an extension of this framework, this research considers modeling the…

  14. Model building in nonproportional hazard regression.

    PubMed

    Rodríguez-Girondo, Mar; Kneib, Thomas; Cadarso-Suárez, Carmen; Abu-Assi, Emad

    2013-12-30

    Recent developments of statistical methods allow for a very flexible modeling of covariates affecting survival times via the hazard rate, including also the inspection of possible time-dependent associations. Despite their immediate appeal in terms of flexibility, these models typically introduce additional difficulties when a subset of covariates and the corresponding modeling alternatives have to be chosen, that is, for building the most suitable model for given data. This is particularly true when potentially time-varying associations are given. We propose to conduct a piecewise exponential representation of the original survival data to link hazard regression with estimation schemes based on of the Poisson likelihood to make recent advances for model building in exponential family regression accessible also in the nonproportional hazard regression context. A two-stage stepwise selection approach, an approach based on doubly penalized likelihood, and a componentwise functional gradient descent approach are adapted to the piecewise exponential regression problem. These three techniques were compared via an intensive simulation study. An application to prognosis after discharge for patients who suffered a myocardial infarction supplements the simulation to demonstrate the pros and cons of the approaches in real data analyses.

  15. Commonality Analysis for the Regression Case.

    ERIC Educational Resources Information Center

    Murthy, Kavita

    Commonality analysis is a procedure for decomposing the coefficient of determination (R superscript 2) in multiple regression analyses into the percent of variance in the dependent variable associated with each independent variable uniquely, and the proportion of explained variance associated with the common effects of predictors in various…

  16. Prediction of dynamical systems by symbolic regression

    NASA Astrophysics Data System (ADS)

    Quade, Markus; Abel, Markus; Shafi, Kamran; Niven, Robert K.; Noack, Bernd R.

    2016-07-01

    We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or simplified models need to be found. We focus on symbolic regression methods as a part of machine learning. These algorithms are capable of learning an analytically tractable model from data, a highly valuable property. Symbolic regression methods can be considered as generalized regression methods. We investigate two particular algorithms, the so-called fast function extraction which is a generalized linear regression algorithm, and genetic programming which is a very general method. Both are able to combine functions in a certain way such that a good model for the prediction of the temporal evolution of a dynamical system can be identified. We illustrate the algorithms by finding a prediction for the evolution of a harmonic oscillator based on measurements, by detecting an arriving front in an excitable system, and as a real-world application, the prediction of solar power production based on energy production observations at a given site together with the weather forecast.

  17. Prediction of dynamical systems by symbolic regression.

    PubMed

    Quade, Markus; Abel, Markus; Shafi, Kamran; Niven, Robert K; Noack, Bernd R

    2016-07-01

    We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or simplified models need to be found. We focus on symbolic regression methods as a part of machine learning. These algorithms are capable of learning an analytically tractable model from data, a highly valuable property. Symbolic regression methods can be considered as generalized regression methods. We investigate two particular algorithms, the so-called fast function extraction which is a generalized linear regression algorithm, and genetic programming which is a very general method. Both are able to combine functions in a certain way such that a good model for the prediction of the temporal evolution of a dynamical system can be identified. We illustrate the algorithms by finding a prediction for the evolution of a harmonic oscillator based on measurements, by detecting an arriving front in an excitable system, and as a real-world application, the prediction of solar power production based on energy production observations at a given site together with the weather forecast.

  18. A Constrained Linear Estimator for Multiple Regression

    ERIC Educational Resources Information Center

    Davis-Stober, Clintin P.; Dana, Jason; Budescu, David V.

    2010-01-01

    "Improper linear models" (see Dawes, Am. Psychol. 34:571-582, "1979"), such as equal weighting, have garnered interest as alternatives to standard regression models. We analyze the general circumstances under which these models perform well by recasting a class of "improper" linear models as "proper" statistical models with a single predictor. We…

  19. Assumptions of Multiple Regression: Correcting Two Misconceptions

    ERIC Educational Resources Information Center

    Williams, Matt N.; Gomez Grajales, Carlos Alberto; Kurkiewicz, Dason

    2013-01-01

    In 2002, an article entitled "Four assumptions of multiple regression that researchers should always test" by Osborne and Waters was published in "PARE." This article has gone on to be viewed more than 275,000 times (as of August 2013), and it is one of the first results displayed in a Google search for "regression…

  20. The Shadow Side of Regressive Groups.

    ERIC Educational Resources Information Center

    McClure, Bud A.

    1994-01-01

    Contends that inability of groups to address conflict, encourage dissenting views, and face their negative characteristics can result in destructive behavior toward others that remains largely outside awareness of individual members. Examines regressive group characteristics; behavior of United States during Persian Gulf War is used to highlight…

  1. Moving the Bar: Transformations in Linear Regression.

    ERIC Educational Resources Information Center

    Miranda, Janet

    The assumption that is most important to the hypothesis testing procedure of multiple linear regression is the assumption that the residuals are normally distributed, but this assumption is not always tenable given the realities of some data sets. When normal distribution of the residuals is not met, an alternative method can be initiated. As an…

  2. Nonlinear optomechanical pressure

    NASA Astrophysics Data System (ADS)

    Conti, Claudio; Boyd, Robert

    2014-03-01

    A transparent material exhibits ultrafast optical nonlinearity and is subject to optical pressure if irradiated by a laser beam. However, the effect of nonlinearity on optical pressure is often overlooked, even if a nonlinear optical pressure may be potentially employed in many applications, such as optical manipulation, biophysics, cavity optomechanics, quantum optics, and optical tractors, and is relevant in fundamental problems such as the Abraham-Minkoswky dilemma or the Casimir effect. Here, we show that an ultrafast nonlinear polarization gives indeed a contribution to the optical pressure that also is negative in certain spectral ranges; the theoretical analysis is confirmed by first-principles simulations. An order-of-magnitude estimate shows that the effect can be observable by measuring the deflection of a membrane made by graphene.

  3. Nonlinear Structural Analysis

    NASA Technical Reports Server (NTRS)

    1984-01-01

    Nonlinear structural analysis techniques for engine structures and components are addressed. The finite element method and boundary element method are discussed in terms of stress and structural analyses of shells, plates, and laminates.

  4. Nonlinear Dynamics in Cardiology

    PubMed Central

    Krogh-Madsen, Trine; Christini, David J.

    2013-01-01

    The dynamics of many cardiac arrhythmias, as well as the nature of transitions between different heart rhythms, have long been considered evidence of nonlinear phenomena playing a direct role in cardiac arrhythmogenesis. In most types of cardiac disease, the pathology develops slowly and gradually, often over many years. In contrast, arrhythmias often occur suddenly. In nonlinear systems, sudden changes in qualitative dynamics can, counter-intuitively, result from a gradual change in a system parameter –this is known as a bifurcation. Here, we review how nonlinearities in cardiac electrophysiology influence normal and abnormal rhythms and how bifurcations change the dynamics. In particular, we focus on the many recent developments in computational modeling at the cellular level focused on intracellular calcium dynamics. We discuss two areas where recent experimental and modeling work have suggested the importance of nonlinearities in calcium dynamics: repolarization alternans and pacemaker cell automaticity. PMID:22524390

  5. Adaptive and Nonlinear Control

    DTIC Science & Technology

    1992-02-29

    in [22], we also applied the concept of zero dynamics to the problem of exact linearization of a nonlinear control system by dynamic feedback. Exact ...nonlinear systems, although it was well-known that the conditions for exact linearization are very stringent and consequently do not apply to a broad...29th IEEE Conference n Decision and Control, Invited Paper delivered by Dr. Gilliam. Exact Linearization of Zero Dynamics, 29th IEEE Conference on

  6. Perturbed nonlinear differential equations

    NASA Technical Reports Server (NTRS)

    Proctor, T. G.

    1974-01-01

    For perturbed nonlinear systems, a norm, other than the supremum norm, is introduced on some spaces of continuous functions. This makes possible the study of new types of behavior. A study is presented on a perturbed nonlinear differential equation defined on a half line, and the existence of a family of solutions with special boundedness properties is established. The ideas developed are applied to the study of integral manifolds, and examples are given.

  7. Embedded Sensors for Measuring Surface Regression

    NASA Technical Reports Server (NTRS)

    Gramer, Daniel J.; Taagen, Thomas J.; Vermaak, Anton G.

    2006-01-01

    The development and evaluation of new hybrid and solid rocket motors requires accurate characterization of the propellant surface regression as a function of key operational parameters. These characteristics establish the propellant flow rate and are prime design drivers affecting the propulsion system geometry, size, and overall performance. There is a similar need for the development of advanced ablative materials, and the use of conventional ablatives exposed to new operational environments. The Miniature Surface Regression Sensor (MSRS) was developed to serve these applications. It is designed to be cast or embedded in the material of interest and regresses along with it. During this process, the resistance of the sensor is related to its instantaneous length, allowing the real-time thickness of the host material to be established. The time derivative of this data reveals the instantaneous surface regression rate. The MSRS could also be adapted to perform similar measurements for a variety of other host materials when it is desired to monitor thicknesses and/or regression rate for purposes of safety, operational control, or research. For example, the sensor could be used to monitor the thicknesses of brake linings or racecar tires and indicate when they need to be replaced. At the time of this reporting, over 200 of these sensors have been installed into a variety of host materials. An MSRS can be made in either of two configurations, denoted ladder and continuous (see Figure 1). A ladder MSRS includes two highly electrically conductive legs, across which narrow strips of electrically resistive material are placed at small increments of length. These strips resemble the rungs of a ladder and are electrically equivalent to many tiny resistors connected in parallel. A substrate material provides structural support for the legs and rungs. The instantaneous sensor resistance is read by an external signal conditioner via wires attached to the conductive legs on the

  8. Robust Nonlinear Neural Codes

    NASA Astrophysics Data System (ADS)

    Yang, Qianli; Pitkow, Xaq

    2015-03-01

    Most interesting natural sensory stimuli are encoded in the brain in a form that can only be decoded nonlinearly. But despite being a core function of the brain, nonlinear population codes are rarely studied and poorly understood. Interestingly, the few existing models of nonlinear codes are inconsistent with known architectural features of the brain. In particular, these codes have information content that scales with the size of the cortical population, even if that violates the data processing inequality by exceeding the amount of information entering the sensory system. Here we provide a valid theory of nonlinear population codes by generalizing recent work on information-limiting correlations in linear population codes. Although these generalized, nonlinear information-limiting correlations bound the performance of any decoder, they also make decoding more robust to suboptimal computation, allowing many suboptimal decoders to achieve nearly the same efficiency as an optimal decoder. Although these correlations are extremely difficult to measure directly, particularly for nonlinear codes, we provide a simple, practical test by which one can use choice-related activity in small populations of neurons to determine whether decoding is suboptimal or optimal and limited by correlated noise. We conclude by describing an example computation in the vestibular system where this theory applies. QY and XP was supported by a grant from the McNair foundation.

  9. Nonlinear systems in medicine.

    PubMed Central

    Higgins, John P.

    2002-01-01

    Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states. PMID:14580107

  10. Pescara benchmarks: nonlinear identification

    NASA Astrophysics Data System (ADS)

    Gandino, E.; Garibaldi, L.; Marchesiello, S.

    2011-07-01

    Recent nonlinear methods are suitable for identifying large systems with lumped nonlinearities, but in practice most structural nonlinearities are distributed and an ideal nonlinear identification method should cater for them as well. In order to extend the current NSI method to be applied also on realistic large engineering structures, a modal counterpart of the method is proposed in this paper. The modal NSI technique is applied on one of the reinforced concrete beams that have been tested in Pescara, under the project titled "Monitoring and diagnostics of railway bridges by means of the analysis of the dynamic response due to train crossing", financed by Italian Ministry of Research. The beam showed a softening nonlinear behaviour, so that the nonlinearity concerning the first mode is characterized and its force contribution is quantified. Moreover, estimates for the modal parameters are obtained and the model is validated by comparing the measured and the reconstructed output. The identified estimates are also used to accurately predict the behaviour of the same beam, when subject to different initial conditions.

  11. Logistic models--an odd(s) kind of regression.

    PubMed

    Jupiter, Daniel C

    2013-01-01

    The logistic regression model bears some similarity to the multivariable linear regression with which we are familiar. However, the differences are great enough to warrant a discussion of the need for and interpretation of logistic regression.

  12. Detection method of nonlinearity errors by statistical signal analysis in heterodyne Michelson interferometer.

    PubMed

    Hu, Juju; Hu, Haijiang; Ji, Yinghua

    2010-03-15

    Periodic nonlinearity that ranges from tens of nanometers to a few nanometers in heterodyne interferometer limits its use in high accuracy measurement. A novel method is studied to detect the nonlinearity errors based on the electrical subdivision and the analysis method of statistical signal in heterodyne Michelson interferometer. Under the movement of micropositioning platform with the uniform velocity, the method can detect the nonlinearity errors by using the regression analysis and Jackknife estimation. Based on the analysis of the simulations, the method can estimate the influence of nonlinearity errors and other noises for the dimensions measurement in heterodyne Michelson interferometer.

  13. Parametric regression model for survival data: Weibull regression model as an example

    PubMed Central

    2016-01-01

    Weibull regression model is one of the most popular forms of parametric regression model that it provides estimate of baseline hazard function, as well as coefficients for covariates. Because of technical difficulties, Weibull regression model is seldom used in medical literature as compared to the semi-parametric proportional hazard model. To make clinical investigators familiar with Weibull regression model, this article introduces some basic knowledge on Weibull regression model and then illustrates how to fit the model with R software. The SurvRegCensCov package is useful in converting estimated coefficients to clinical relevant statistics such as hazard ratio (HR) and event time ratio (ETR). Model adequacy can be assessed by inspecting Kaplan-Meier curves stratified by categorical variable. The eha package provides an alternative method to model Weibull regression model. The check.dist() function helps to assess goodness-of-fit of the model. Variable selection is based on the importance of a covariate, which can be tested using anova() function. Alternatively, backward elimination starting from a full model is an efficient way for model development. Visualization of Weibull regression model after model development is interesting that it provides another way to report your findings. PMID:28149846

  14. The comparison of robust partial least squares regression with robust principal component regression on a real

    NASA Astrophysics Data System (ADS)

    Polat, Esra; Gunay, Suleyman

    2013-10-01

    One of the problems encountered in Multiple Linear Regression (MLR) is multicollinearity, which causes the overestimation of the regression parameters and increase of the variance of these parameters. Hence, in case of multicollinearity presents, biased estimation procedures such as classical Principal Component Regression (CPCR) and Partial Least Squares Regression (PLSR) are then performed. SIMPLS algorithm is the leading PLSR algorithm because of its speed, efficiency and results are easier to interpret. However, both of the CPCR and SIMPLS yield very unreliable results when the data set contains outlying observations. Therefore, Hubert and Vanden Branden (2003) have been presented a robust PCR (RPCR) method and a robust PLSR (RPLSR) method called RSIMPLS. In RPCR, firstly, a robust Principal Component Analysis (PCA) method for high-dimensional data on the independent variables is applied, then, the dependent variables are regressed on the scores using a robust regression method. RSIMPLS has been constructed from a robust covariance matrix for high-dimensional data and robust linear regression. The purpose of this study is to show the usage of RPCR and RSIMPLS methods on an econometric data set, hence, making a comparison of two methods on an inflation model of Turkey. The considered methods have been compared in terms of predictive ability and goodness of fit by using a robust Root Mean Squared Error of Cross-validation (R-RMSECV), a robust R2 value and Robust Component Selection (RCS) statistic.

  15. Use of Multiple Correlation Analysis and Multiple Regression Analysis.

    ERIC Educational Resources Information Center

    Huberty, Carl J.; Petoskey, Martha D.

    1999-01-01

    Distinguishes between multiple correlation and multiple regression analysis. Illustrates suggested information reporting methods and reviews the use of regression methods when dealing with problems of missing data. (SK)

  16. Using Edge Voxel Information to Improve Motion Regression for rs-fMRI Connectivity Studies.

    PubMed

    Patriat, Rémi; Molloy, Erin K; Birn, Rasmus M

    2015-11-01

    Recent fMRI studies have outlined the critical impact of in-scanner head motion, particularly on estimates of functional connectivity. Common strategies to reduce the influence of motion include realignment as well as the inclusion of nuisance regressors, such as the 6 realignment parameters, their first derivatives, time-shifted versions of the realignment parameters, and the squared parameters. However, these regressors have limited success at noise reduction. We hypothesized that using nuisance regressors consisting of the principal components (PCs) of edge voxel time series would be better able to capture slice-specific and nonlinear signal changes, thus explaining more variance, improving data quality (i.e., lower DVARS and temporal SNR), and reducing the effect of motion on default-mode network connectivity. Functional MRI data from 22 healthy adult subjects were preprocessed using typical motion regression approaches as well as nuisance regression derived from edge voxel time courses. Results were evaluated in the presence and absence of both global signal regression and motion censoring. Nuisance regressors derived from signal intensity time courses at the edge of the brain significantly improved motion correction compared to using only the realignment parameters and their derivatives. Of the models tested, only the edge voxel regression models were able to eliminate significant differences in default-mode network connectivity between high- and low-motion subjects regardless of the use of global signal regression or censoring.

  17. Prediction of soil temperature using regression and artificial neural network models

    NASA Astrophysics Data System (ADS)

    Bilgili, Mehmet

    2010-12-01

    In this study, monthly soil temperature was modeled by linear regression (LR), nonlinear regression (NLR) and artificial neural network (ANN) methods. The soil temperature and other meteorological parameters, which have been taken from Adana meteorological station, were observed between the years of 2000 and 2007 by the Turkish State Meteorological Service (TSMS). The soil temperatures were measured at depths of 5, 10, 20, 50 and 100 cm below the ground level. A three-layer feed-forward ANN structure was constructed and a back-propagation algorithm was used for the training of ANNs. In order to get a successful simulation, the correlation coefficients between all of the meteorological variables (soil temperature, atmospheric temperature, atmospheric pressure, relative humidity, wind speed, rainfall, global solar radiation and sunshine duration) were calculated taking them two by two. First, all independent variables were split into two time periods such as cold and warm seasons. They were added to the enter regression model. Then, the method of stepwise multiple regression was applied for the selection of the "best" regression equation (model). Thus, the best independent variables were selected for the LR and NLR models and they were also used in the input layer of the ANN method. Results of these methods were compared to each other. Finally, the ANN method was found to provide better performance than the LR and NLR methods.

  18. Face Recognition with Pose Variations and Misalignment via Orthogonal Procrustes Regression.

    PubMed

    Tai, Ying; Yang, Jian; Zhang, Yigong; Luo, Lei; Qian, Jianjun; Chen, Yu

    2016-04-06

    Linear regression based method is a hot topic in face recognition community. Recently, sparse representation and collaborative representation based classifiers for face recognition have been proposed and attracted great attention. However, most of the existing regression analysis based methods are sensitive to pose variations. In this paper, we introduce the orthogonal Procrustes problem (OPP) as a model to handle pose variations existed in two-dimensional face images. OPP seeks an optimal linear transformation between two images with different poses so as to make the transformed image best fits the other one. We integrate OPP into the regression model and propose the orthogonal Procrustes regression (OPR) model. To address the problem that the linear transformation is not suitable for handling highly non-linear pose variation, we further adopt a progressive strategy and propose the stacked orthogonal Procrustes regression (stacked OPR). As a practical framework, OPR can handle face alignment, pose correction and face representation simultaneously. We optimize the proposed model via an efficient alternating iterative algorithm and experimental results on three popular face databases, CMU PIE database, CMU Multi-PIE database and LFW database, demonstrate the effectiveness of our proposed method.

  19. Risk prediction for myocardial infarction via generalized functional regression models.

    PubMed

    Ieva, Francesca; Paganoni, Anna M

    2016-08-01

    In this paper, we propose a generalized functional linear regression model for a binary outcome indicating the presence/absence of a cardiac disease with multivariate functional data among the relevant predictors. In particular, the motivating aim is the analysis of electrocardiographic traces of patients whose pre-hospital electrocardiogram (ECG) has been sent to 118 Dispatch Center of Milan (the Italian free-toll number for emergencies) by life support personnel of the basic rescue units. The statistical analysis starts with a preprocessing of ECGs treated as multivariate functional data. The signals are reconstructed from noisy observations. The biological variability is then removed by a nonlinear registration procedure based on landmarks. Thus, in order to perform a data-driven dimensional reduction, a multivariate functional principal component analysis is carried out on the variance-covariance matrix of the reconstructed and registered ECGs and their first derivatives. We use the scores of the Principal Components decomposition as covariates in a generalized linear model to predict the presence of the disease in a new patient. Hence, a new semi-automatic diagnostic procedure is proposed to estimate the risk of infarction (in the case of interest, the probability of being affected by Left Bundle Brunch Block). The performance of this classification method is evaluated and compared with other methods proposed in literature. Finally, the robustness of the procedure is checked via leave-j-out techniques.

  20. A generalized multivariate regression model for modelling ocean wave heights

    NASA Astrophysics Data System (ADS)

    Wang, X. L.; Feng, Y.; Swail, V. R.

    2012-04-01

    In this study, a generalized multivariate linear regression model is developed to represent the relationship between 6-hourly ocean significant wave heights (Hs) and the corresponding 6-hourly mean sea level pressure (MSLP) fields. The model is calibrated using the ERA-Interim reanalysis of Hs and MSLP fields for 1981-2000, and is validated using the ERA-Interim reanalysis for 2001-2010 and ERA40 reanalysis of Hs and MSLP for 1958-2001. The performance of the fitted model is evaluated in terms of Pierce skill score, frequency bias index, and correlation skill score. Being not normally distributed, wave heights are subjected to a data adaptive Box-Cox transformation before being used in the model fitting. Also, since 6-hourly data are being modelled, lag-1 autocorrelation must be and is accounted for. The models with and without Box-Cox transformation, and with and without accounting for autocorrelation, are inter-compared in terms of their prediction skills. The fitted MSLP-Hs relationship is then used to reconstruct historical wave height climate from the 6-hourly MSLP fields taken from the Twentieth Century Reanalysis (20CR, Compo et al. 2011), and to project possible future wave height climates using CMIP5 model simulations of MSLP fields. The reconstructed and projected wave heights, both seasonal means and maxima, are subject to a trend analysis that allows for non-linear (polynomial) trends.

  1. Random forest regression for magnetic resonance image synthesis.

    PubMed

    Jog, Amod; Carass, Aaron; Roy, Snehashis; Pham, Dzung L; Prince, Jerry L

    2017-01-01

    By choosing different pulse sequences and their parameters, magnetic resonance imaging (MRI) can generate a large variety of tissue contrasts. This very flexibility, however, can yield inconsistencies with MRI acquisitions across datasets or scanning sessions that can in turn cause inconsistent automated image analysis. Although image synthesis of MR images has been shown to be helpful in addressing this problem, an inability to synthesize both T2-weighted brain images that include the skull and FLuid Attenuated Inversion Recovery (FLAIR) images has been reported. The method described herein, called REPLICA, addresses these limitations. REPLICA is a supervised random forest image synthesis approach that learns a nonlinear regression to predict intensities of alternate tissue contrasts given specific input tissue contrasts. Experimental results include direct image comparisons between synthetic and real images, results from image analysis tasks on both synthetic and real images, and comparison against other state-of-the-art image synthesis methods. REPLICA is computationally fast, and is shown to be comparable to other methods on tasks they are able to perform. Additionally REPLICA has the capability to synthesize both T2-weighted images of the full head and FLAIR images, and perform intensity standardization between different imaging datasets.

  2. Comparison of asymptotic confidence sets for regression in small samples.

    PubMed

    Kolobkov, Dmitry; Demin, Oleg; Metelkin, Evgeny

    2016-01-01

    In case of small samples, asymptotic confidence sets may be inaccurate, with their actual coverage probability far from a nominal confidence level. In a single framework, we consider four popular asymptotic methods of confidence estimation. These methods are based on model linearization, F-test, likelihood ratio test, and nonparametric bootstrapping procedure. Next, we apply each of these methods to derive three types of confidence sets: confidence intervals, confidence regions, and pointwise confidence bands. Finally, to estimate the actual coverage of these confidence sets, we conduct a simulation study on three regression problems. A linear model and nonlinear Hill and Gompertz models are tested in conditions of different sample size and experimental noise. The simulation study comprises calculation of the actual coverage of confidence sets over pseudo-experimental datasets for each model. For confidence intervals, such metrics as width and simultaneous coverage are also considered. Our comparison shows that the F-test and linearization methods are the most suitable for the construction of confidence intervals, the F-test - for confidence regions and the linearization - for pointwise confidence bands.

  3. Multiple regression analyses in the prediction of aerospace instrument costs

    NASA Astrophysics Data System (ADS)

    Tran, Linh

    The aerospace industry has been investing for decades in ways to improve its efficiency in estimating the project life cycle cost (LCC). One of the major focuses in the LCC is the cost/prediction of aerospace instruments done during the early conceptual design phase of the project. The accuracy of early cost predictions affects the project scheduling and funding, and it is often the major cause for project cost overruns. The prediction of instruments' cost is based on the statistical analysis of these independent variables: Mass (kg), Power (watts), Instrument Type, Technology Readiness Level (TRL), Destination: earth orbiting or planetary, Data rates (kbps), Number of bands, Number of channels, Design life (months), and Development duration (months). This author is proposing a cost prediction approach of aerospace instruments based on these statistical analyses: Clustering Analysis, Principle Components Analysis (PCA), Bootstrap, and multiple regressions (both linear and non-linear). In the proposed approach, the Cost Estimating Relationship (CER) will be developed for the dependent variable Instrument Cost by using a combination of multiple independent variables. "The Full Model" will be developed and executed to estimate the full set of nine variables. The SAS program, Excel, Automatic Cost Estimating Integrate Tool (ACEIT) and Minitab are the tools to aid the analysis. Through the analysis, the cost drivers will be identified which will help develop an ultimate cost estimating software tool for the Instrument Cost prediction and optimization of future missions.

  4. Model selection for logistic regression models

    NASA Astrophysics Data System (ADS)

    Duller, Christine

    2012-09-01

    Model selection for logistic regression models decides which of some given potential regressors have an effect and hence should be included in the final model. The second interesting question is whether a certain factor is heterogeneous among some subsets, i.e. whether the model should include a random intercept or not. In this paper these questions will be answered with classical as well as with Bayesian methods. The application show some results of recent research projects in medicine and business administration.

  5. Modeling confounding by half-sibling regression

    PubMed Central

    Schölkopf, Bernhard; Hogg, David W.; Wang, Dun; Foreman-Mackey, Daniel; Janzing, Dominik; Simon-Gabriel, Carl-Johann; Peters, Jonas

    2016-01-01

    We describe a method for removing the effect of confounders to reconstruct a latent quantity of interest. The method, referred to as “half-sibling regression,” is inspired by recent work in causal inference using additive noise models. We provide a theoretical justification, discussing both independent and identically distributed as well as time series data, respectively, and illustrate the potential of the method in a challenging astronomy application. PMID:27382154

  6. Modeling confounding by half-sibling regression.

    PubMed

    Schölkopf, Bernhard; Hogg, David W; Wang, Dun; Foreman-Mackey, Daniel; Janzing, Dominik; Simon-Gabriel, Carl-Johann; Peters, Jonas

    2016-07-05

    We describe a method for removing the effect of confounders to reconstruct a latent quantity of interest. The method, referred to as "half-sibling regression," is inspired by recent work in causal inference using additive noise models. We provide a theoretical justification, discussing both independent and identically distributed as well as time series data, respectively, and illustrate the potential of the method in a challenging astronomy application.

  7. Satellite rainfall retrieval by logistic regression

    NASA Technical Reports Server (NTRS)

    Chiu, Long S.

    1986-01-01

    The potential use of logistic regression in rainfall estimation from satellite measurements is investigated. Satellite measurements provide covariate information in terms of radiances from different remote sensors.The logistic regression technique can effectively accommodate many covariates and test their significance in the estimation. The outcome from the logistical model is the probability that the rainrate of a satellite pixel is above a certain threshold. By varying the thresholds, a rainrate histogram can be obtained, from which the mean and the variant can be estimated. A logistical model is developed and applied to rainfall data collected during GATE, using as covariates the fractional rain area and a radiance measurement which is deduced from a microwave temperature-rainrate relation. It is demonstrated that the fractional rain area is an important covariate in the model, consistent with the use of the so-called Area Time Integral in estimating total rain volume in other studies. To calibrate the logistical model, simulated rain fields generated by rainfield models with prescribed parameters are needed. A stringent test of the logistical model is its ability to recover the prescribed parameters of simulated rain fields. A rain field simulation model which preserves the fractional rain area and lognormality of rainrates as found in GATE is developed. A stochastic regression model of branching and immigration whose solutions are lognormally distributed in some asymptotic limits has also been developed.

  8. Transfer Learning Based on Logistic Regression

    NASA Astrophysics Data System (ADS)

    Paul, A.; Rottensteiner, F.; Heipke, C.

    2015-08-01

    In this paper we address the problem of classification of remote sensing images in the framework of transfer learning with a focus on domain adaptation. The main novel contribution is a method for transductive transfer learning in remote sensing on the basis of logistic regression. Logistic regression is a discriminative probabilistic classifier of low computational complexity, which can deal with multiclass problems. This research area deals with methods that solve problems in which labelled training data sets are assumed to be available only for a source domain, while classification is needed in the target domain with different, yet related characteristics. Classification takes place with a model of weight coefficients for hyperplanes which separate features in the transformed feature space. In term of logistic regression, our domain adaptation method adjusts the model parameters by iterative labelling of the target test data set. These labelled data features are iteratively added to the current training set which, at the beginning, only contains source features and, simultaneously, a number of source features are deleted from the current training set. Experimental results based on a test series with synthetic and real data constitutes a first proof-of-concept of the proposed method.

  9. Variable Selection in Semiparametric Regression Modeling.

    PubMed

    Li, Runze; Liang, Hua

    2008-01-01

    In this paper, we are concerned with how to select significant variables in semiparametric modeling. Variable selection for semiparametric regression models consists of two components: model selection for nonparametric components and select significant variables for parametric portion. Thus, it is much more challenging than that for parametric models such as linear models and generalized linear models because traditional variable selection procedures including stepwise regression and the best subset selection require model selection to nonparametric components for each submodel. This leads to very heavy computational burden. In this paper, we propose a class of variable selection procedures for semiparametric regression models using nonconcave penalized likelihood. The newly proposed procedures are distinguished from the traditional ones in that they delete insignificant variables and estimate the coefficients of significant variables simultaneously. This allows us to establish the sampling properties of the resulting estimate. We first establish the rate of convergence of the resulting estimate. With proper choices of penalty functions and regularization parameters, we then establish the asymptotic normality of the resulting estimate, and further demonstrate that the proposed procedures perform as well as an oracle procedure. Semiparametric generalized likelihood ratio test is proposed to select significant variables in the nonparametric component. We investigate the asymptotic behavior of the proposed test and demonstrate its limiting null distribution follows a chi-squared distribution, which is independent of the nuisance parameters. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedures.

  10. Quantile regression modeling for Malaysian automobile insurance premium data

    NASA Astrophysics Data System (ADS)

    Fuzi, Mohd Fadzli Mohd; Ismail, Noriszura; Jemain, Abd Aziz

    2015-09-01

    Quantile regression is a robust regression to outliers compared to mean regression models. Traditional mean regression models like Generalized Linear Model (GLM) are not able to capture the entire distribution of premium data. In this paper we demonstrate how a quantile regression approach can be used to model net premium data to study the effects of change in the estimates of regression parameters (rating classes) on the magnitude of response variable (pure premium). We then compare the results of quantile regression model with Gamma regression model. The results from quantile regression show that some rating classes increase as quantile increases and some decrease with decreasing quantile. Further, we found that the confidence interval of median regression (τ = O.5) is always smaller than Gamma regression in all risk factors.

  11. Higher-order Multivariable Polynomial Regression to Estimate Human Affective States.

    PubMed

    Wei, Jie; Chen, Tong; Liu, Guangyuan; Yang, Jiemin

    2016-03-21

    From direct observations, facial, vocal, gestural, physiological, and central nervous signals, estimating human affective states through computational models such as multivariate linear-regression analysis, support vector regression, and artificial neural network, have been proposed in the past decade. In these models, linear models are generally lack of precision because of ignoring intrinsic nonlinearities of complex psychophysiological processes; and nonlinear models commonly adopt complicated algorithms. To improve accuracy and simplify model, we introduce a new computational modeling method named as higher-order multivariable polynomial regression to estimate human affective states. The study employs standardized pictures in the International Affective Picture System to induce thirty subjects' affective states, and obtains pure affective patterns of skin conductance as input variables to the higher-order multivariable polynomial model for predicting affective valence and arousal. Experimental results show that our method is able to obtain efficient correlation coefficients of 0.98 and 0.96 for estimation of affective valence and arousal, respectively. Moreover, the method may provide certain indirect evidences that valence and arousal have their brain's motivational circuit origins. Thus, the proposed method can serve as a novel one for efficiently estimating human affective states.

  12. Higher-order Multivariable Polynomial Regression to Estimate Human Affective States

    NASA Astrophysics Data System (ADS)

    Wei, Jie; Chen, Tong; Liu, Guangyuan; Yang, Jiemin

    2016-03-01

    From direct observations, facial, vocal, gestural, physiological, and central nervous signals, estimating human affective states through computational models such as multivariate linear-regression analysis, support vector regression, and artificial neural network, have been proposed in the past decade. In these models, linear models are generally lack of precision because of ignoring intrinsic nonlinearities of complex psychophysiological processes; and nonlinear models commonly adopt complicated algorithms. To improve accuracy and simplify model, we introduce a new computational modeling method named as higher-order multivariable polynomial regression to estimate human affective states. The study employs standardized pictures in the International Affective Picture System to induce thirty subjects’ affective states, and obtains pure affective patterns of skin conductance as input variables to the higher-order multivariable polynomial model for predicting affective valence and arousal. Experimental results show that our method is able to obtain efficient correlation coefficients of 0.98 and 0.96 for estimation of affective valence and arousal, respectively. Moreover, the method may provide certain indirect evidences that valence and arousal have their brain’s motivational circuit origins. Thus, the proposed method can serve as a novel one for efficiently estimating human affective states.

  13. Higher-order Multivariable Polynomial Regression to Estimate Human Affective States

    PubMed Central

    Wei, Jie; Chen, Tong; Liu, Guangyuan; Yang, Jiemin

    2016-01-01

    From direct observations, facial, vocal, gestural, physiological, and central nervous signals, estimating human affective states through computational models such as multivariate linear-regression analysis, support vector regression, and artificial neural network, have been proposed in the past decade. In these models, linear models are generally lack of precision because of ignoring intrinsic nonlinearities of complex psychophysiological processes; and nonlinear models commonly adopt complicated algorithms. To improve accuracy and simplify model, we introduce a new computational modeling method named as higher-order multivariable polynomial regression to estimate human affective states. The study employs standardized pictures in the International Affective Picture System to induce thirty subjects’ affective states, and obtains pure affective patterns of skin conductance as input variables to the higher-order multivariable polynomial model for predicting affective valence and arousal. Experimental results show that our method is able to obtain efficient correlation coefficients of 0.98 and 0.96 for estimation of affective valence and arousal, respectively. Moreover, the method may provide certain indirect evidences that valence and arousal have their brain’s motivational circuit origins. Thus, the proposed method can serve as a novel one for efficiently estimating human affective states. PMID:26996254

  14. Algebraic Nonlinear Collective Motion

    NASA Astrophysics Data System (ADS)

    Troupe, J.; Rosensteel, G.

    1998-11-01

    Finite-dimensional Lie algebras of vector fields determine geometrical collective models in quantum and classical physics. Every set of vector fields on Euclidean space that generates the Lie algebra sl(3, R) and contains the angular momentum algebra so(3) is determined. The subset of divergence-free sl(3, R) vector fields is proven to be indexed by a real numberΛ. TheΛ=0 solution is the linear representation that corresponds to the Riemann ellipsoidal model. The nonlinear group action on Euclidean space transforms a certain family of deformed droplets among themselves. For positiveΛ, the droplets have a neck that becomes more pronounced asΛincreases; for negativeΛ, the droplets contain a spherical bubble of radius |Λ|1/3. The nonlinear vector field algebra is extended to the nonlinear general collective motion algebra gcm(3) which includes the inertia tensor. The quantum algebraic models of nonlinear nuclear collective motion are given by irreducible unitary representations of the nonlinear gcm(3) Lie algebra. These representations model fissioning isotopes (Λ>0) and bubble and two-fluid nuclei (Λ<0).

  15. Does Nonlinear Modeling Play a Role in Plasmid Bioprocess Monitoring using Fourier Transform Infrared Spectra?

    PubMed

    Lopes, Marta B; Calado, Cecília R C; Figueiredo, Mário A T; Bioucas-Dias, José M

    2016-11-16

    The monitoring of biopharmaceutical products using Fourier transform infrared (FT-IR) spectroscopy relies on calibration techniques involving the acquisition of spectra of bioprocess samples along the process. The most commonly used method for that purpose is partial least squares (PLS) regression, under the assumption that a linear model is valid. Despite being successful in the presence of small nonlinearities, linear methods may fail in the presence of strong nonlinearities. This paper studies the potential usefulness of nonlinear regression methods for predicting, from in situ near-infrared (NIR) and mid-infrared (MIR) spectra acquired in high-throughput mode, biomass and plasmid concentrations in Escherichia coli DH5-α cultures producing the plasmid model pVAX-LacZ. The linear methods PLS and ridge regression (RR) are compared with their kernel (nonlinear) versions, kPLS and kRR, as well as with the (also nonlinear) relevance vector machine (RVM) and Gaussian process regression (GPR). For the systems studied, RR provided better predictive performances compared to the remaining methods. Moreover, the results point to further investigation based on larger data sets whenever differences in predictive accuracy between a linear method and its kernelized version could not be found. The use of nonlinear methods, however, shall be judged regarding the additional computational cost required to tune their additional parameters, especially when the less computationally demanding linear methods herein studied are able to successfully monitor the variables under study.

  16. Transform-both-sides nonlinear models for in vitro pharmacokinetic experiments.

    PubMed

    Latif, A H M Mahbub; Gilmour, Steven G

    2015-06-01

    Transform-both-sides nonlinear models have proved useful in many experimental applications including those in pharmaceutical sciences and biochemistry. The maximum likelihood method is commonly used to fit transform-both-sides nonlinear models, where the regression and transformation parameters are estimated simultaneously. In this paper, an analysis of variance-based method is described in detail for estimating transform-both-sides nonlinear models from randomized experiments. It estimates the transformation parameter from the full treatment model and then the regression parameters are estimated conditionally on this estimate of the transformation parameter. The analysis of variance method is computationally simpler compared with the maximum likelihood method of estimation and allows a more natural separation of different sources of lack of fit. Simulation studies show that the analysis of variance method can provide unbiased estimators of complex transform-both-sides nonlinear models, such as transform-both-sides random coefficient nonlinear regression models and transform-both-sides fixed coefficient nonlinear regression models with random block effects.

  17. Noise model based ν-support vector regression with its application to short-term wind speed forecasting.

    PubMed

    Hu, Qinghua; Zhang, Shiguang; Xie, Zongxia; Mi, Jusheng; Wan, Jie

    2014-09-01

    Support vector regression (SVR) techniques are aimed at discovering a linear or nonlinear structure hidden in sample data. Most existing regression techniques take the assumption that the error distribution is Gaussian. However, it was observed that the noise in some real-world applications, such as wind power forecasting and direction of the arrival estimation problem, does not satisfy Gaussian distribution, but a beta distribution, Laplacian distribution, or other models. In these cases the current regression techniques are not optimal. According to the Bayesian approach, we derive a general loss function and develop a technique of the uniform model of ν-support vector regression for the general noise model (N-SVR). The Augmented Lagrange Multiplier method is introduced to solve N-SVR. Numerical experiments on artificial data sets, UCI data and short-term wind speed prediction are conducted. The results show the effectiveness of the proposed technique.

  18. Nonlinear Waves in Waveguides

    NASA Astrophysics Data System (ADS)

    Leble, Sergei B.

    S.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory.

  19. Nonlinear optomechanics with graphene

    NASA Astrophysics Data System (ADS)

    Shaffer, Airlia; Patil, Yogesh Sharad; Cheung, Hil F. H.; Wang, Ke; Vengalattore, Mukund

    2016-05-01

    To date, studies of cavity optomechanics have been limited to exploiting the linear interactions between the light and mechanics. However, investigations of quantum signal transduction, quantum enhanced metrology and manybody physics with optomechanics each require strong, nonlinear interactions. Graphene nanomembranes are an exciting prospect for realizing such studies due to their inherently nonlinear nature and low mass. We fabricate large graphene nanomembranes and study their mechanical and optical properties. By using dark ground imaging techniques, we correlate their eigenmode shapes with the measured dissipation. We study their hysteretic response present even at low driving amplitudes, and their nonlinear dissipation. Finally, we discuss ongoing efforts to use these resonators for studies of quantum optomechanics and force sensing. This work is supported by the DARPA QuASAR program through a Grant from the ARO.

  20. Nonlinear optical Galton board

    SciTech Connect

    Navarrete-Benlloch, C.; Perez, A.; Roldan, Eugenio

    2007-06-15

    We generalize the concept of optical Galton board (OGB), first proposed by Bouwmeester et al. [Phys. Rev. A 61, 013410 (2000)], by introducing the possibility of nonlinear self-phase modulation on the wave function during the walker evolution. If the original Galton board illustrates classical diffusion, the OGB, which can be understood as a grid of Landau-Zener crossings, illustrates the influence of interference on diffusion, and is closely connected with the quantum walk. Our nonlinear generalization of the OGB shows new phenomena, the most striking of which is the formation of nondispersive pulses in the field distribution (solitonlike structures). These exhibit a variety of dynamical behaviors, including ballistic motion, dynamical localization, nonelastic collisions, and chaotic behavior, in the sense that the dynamics is very sensitive to the nonlinearity strength.

  1. Mission assurance increased with regression testing

    NASA Astrophysics Data System (ADS)

    Lang, R.; Spezio, M.

    Knowing what to test is an important attribute in any testing campaign, especially when it has to be right or the mission could be in jeopardy. The New Horizons mission, developed and operated by the John Hopkins University Applied Physics Laboratory, received a planned major upgrade to their Mission Operations and Control (MOC) ground system architecture. Early in the mission planning it was recognized that the ground system platform would require an upgrade to assure continued support of technology used for spacecraft operations. With the planned update to the six year operational ground architecture from Solaris 8 to Solaris 10, it was critical that the new architecture maintain critical operations and control functions. The New Horizons spacecraft is heading to its historic rendezvous with Pluto in July 2015 and then proceeding into the Kuiper Belt. This paper discusses the Independent Software Acceptance Testing (ISAT) Regression test campaign that played a critical role to assure the continued success of the New Horizons mission. The New Horizons ISAT process was designed to assure all the requirements were being met for the ground software functions developed to support the mission objectives. The ISAT team developed a test plan with a series of test case designs. The test objectives were to verify that the software developed from the requirements functioned as expected in the operational environment. As the test cases were developed and executed, a regression test suite was identified at the functional level. This regression test suite would serve as a crucial resource in assuring the operational system continued to function as required with such a large scale change being introduced. Some of the New Horizons ground software changes required modifications to the most critical functions of the operational software. Of particular concern was the new MOC architecture (Solaris 10) is Intel based and little endian, and the legacy architecture (Solaris 8) was SPA

  2. Mapping geogenic radon potential by regression kriging.

    PubMed

    Pásztor, László; Szabó, Katalin Zsuzsanna; Szatmári, Gábor; Laborczi, Annamária; Horváth, Ákos

    2016-02-15

    Radon ((222)Rn) gas is produced in the radioactive decay chain of uranium ((238)U) which is an element that is naturally present in soils. Radon is transported mainly by diffusion and convection mechanisms through the soil depending mainly on the physical and meteorological parameters of the soil and can enter and accumulate in buildings. Health risks originating from indoor radon concentration can be attributed to natural factors and is characterized by geogenic radon potential (GRP). Identification of areas with high health risks require spatial modeling, that is, mapping of radon risk. In addition to geology and meteorology, physical soil properties play a significant role in the determination of GRP. In order to compile a reliable GRP map for a model area in Central-Hungary, spatial auxiliary information representing GRP forming environmental factors were taken into account to support the spatial inference of the locally measured GRP values. Since the number of measured sites was limited, efficient spatial prediction methodologies were searched for to construct a reliable map for a larger area. Regression kriging (RK) was applied for the interpolation using spatially exhaustive auxiliary data on soil, geology, topography, land use and climate. RK divides the spatial inference into two parts. Firstly, the deterministic component of the target variable is determined by a regression model. The residuals of the multiple linear regression analysis represent the spatially varying but dependent stochastic component, which are interpolated by kriging. The final map is the sum of the two component predictions. Overall accuracy of the map was tested by Leave-One-Out Cross-Validation. Furthermore the spatial reliability of the resultant map is also estimated by the calculation of the 90% prediction interval of the local prediction values. The applicability of the applied method as well as that of the map is discussed briefly.

  3. Monthly streamflow forecasting using Gaussian Process Regression

    NASA Astrophysics Data System (ADS)

    Sun, Alexander Y.; Wang, Dingbao; Xu, Xianli

    2014-04-01

    Streamflow forecasting plays a critical role in nearly all aspects of water resources planning and management. In this work, Gaussian Process Regression (GPR), an effective kernel-based machine learning algorithm, is applied to probabilistic streamflow forecasting. GPR is built on Gaussian process, which is a stochastic process that generalizes multivariate Gaussian distribution to infinite-dimensional space such that distributions over function values can be defined. The GPR algorithm provides a tractable and flexible hierarchical Bayesian framework for inferring the posterior distribution of streamflows. The prediction skill of the algorithm is tested for one-month-ahead prediction using the MOPEX database, which includes long-term hydrometeorological time series collected from 438 basins across the U.S. from 1948 to 2003. Comparisons with linear regression and artificial neural network models indicate that GPR outperforms both regression methods in most cases. The GPR prediction of MOPEX basins is further examined using the Budyko framework, which helps to reveal the close relationships among water-energy partitions, hydrologic similarity, and predictability. Flow regime modification and the resulting loss of predictability have been a major concern in recent years because of climate change and anthropogenic activities. The persistence of streamflow predictability is thus examined by extending the original MOPEX data records to 2012. Results indicate relatively strong persistence of streamflow predictability in the extended period, although the low-predictability basins tend to show more variations. Because many low-predictability basins are located in regions experiencing fast growth of human activities, the significance of sustainable development and water resources management can be even greater for those regions.

  4. Multiple linear regression for isotopic measurements

    NASA Astrophysics Data System (ADS)

    Garcia Alonso, J. I.

    2012-04-01

    There are two typical applications of isotopic measurements: the detection of natural variations in isotopic systems and the detection man-made variations using enriched isotopes as indicators. For both type of measurements accurate and precise isotope ratio measurements are required. For the so-called non-traditional stable isotopes, multicollector ICP-MS instruments are usually applied. In many cases, chemical separation procedures are required before accurate isotope measurements can be performed. The off-line separation of Rb and Sr or Nd and Sm is the classical procedure employed to eliminate isobaric interferences before multicollector ICP-MS measurement of Sr and Nd isotope ratios. Also, this procedure allows matrix separation for precise and accurate Sr and Nd isotope ratios to be obtained. In our laboratory we have evaluated the separation of Rb-Sr and Nd-Sm isobars by liquid chromatography and on-line multicollector ICP-MS detection. The combination of this chromatographic procedure with multiple linear regression of the raw chromatographic data resulted in Sr and Nd isotope ratios with precisions and accuracies typical of off-line sample preparation procedures. On the other hand, methods for the labelling of individual organisms (such as a given plant, fish or animal) are required for population studies. We have developed a dual isotope labelling procedure which can be unique for a given individual, can be inherited in living organisms and it is stable. The detection of the isotopic signature is based also on multiple linear regression. The labelling of fish and its detection in otoliths by Laser Ablation ICP-MS will be discussed using trout and salmon as examples. As a conclusion, isotope measurement procedures based on multiple linear regression can be a viable alternative in multicollector ICP-MS measurements.

  5. Nonlinear magnetohydrodynamic stability

    NASA Technical Reports Server (NTRS)

    Bauer, F.; Betancourt, O.; Garabedian, P.

    1981-01-01

    The computer code developed by Bauer et al. (1978) for the study of the magnetohydrodynamic equilibrium and stability of a plasma in toroidal geometry is extended so that the growth rates of instabilities may be estimated more accurately. The original code, which is based on the variational principle of ideal magnetohydrodynamics, is upgraded by the introduction of a nonlinear formula for the growth rate of an unstable mode which acts as a quantitative measure of instability that is important in estimating numerical errors. The revised code has been applied to the determination of the nonlinear saturation, ballooning modes and beta limits for tokamaks, stellarators and torsatrons.

  6. Nonlinear Fault Diagnosis,

    DTIC Science & Technology

    1981-05-01

    Systems, New York, Marcel Dekker, (to appear). 3. Desoer , C.A. and S.E. Kuh, Basic Circuit Theory, McGraw-Hill, New York, 1969, pp. 423-425. 130 NONLINEAR...DIAGNOSIS A 7*ssior For 1 MU3 CRA&T IY’IC TAB Ju-st i.cat IC- P.U A: CONTENTS Fault Diagnosis in Electronic Circuits , R. Saeks and R.-w. Liu...Vincentelli and R. Saeks .............. 61 Multitest Diagnosibility of Nonlinear Circuits and Systems, A. Sangiovanni-Vincentelli and R. Saeks

  7. Nonlinear Wave Propagation

    DTIC Science & Technology

    2015-05-07

    honeycomb lattices, M.J. Ablowitz and Y. Zhu, SIAM J. Appl. Math. 87 (2013) 19591979 11. Nonlinear Temporal-Spatial Surface Plasmon Polaritons , M. J. Ablowitz...temporal-spatial surface plasmon polaritons . Op- tics Communications, 330:49–55, 2014. 37 [39] M.C. Rechtsman, Y. Plotnik, J.M. Zeuner, , D. Song, Z...honeycomb lattices, M.J. Ablowitz and Y. Zhu, SIAM J. Appl. Math., Vol. 87 (2013) 1959-1979 11. Nonlinear Temporal-Spatial Surface Plasmon Polaritons

  8. Problems of nonlinear deformation

    NASA Astrophysics Data System (ADS)

    Grigoliuk, E. I.; Shalashilin, V. I.

    A method of continuing the solution is discussed with respect to a parameter for a certain class of nonlinear problems in solid mechanics. Modifications of the method are developed in order to implement a unified continuation process at regular and limit points in the set of solutions, with extensions to nonlinear boundary value problems. Algorithms are developed for solving large deflection problems of elastic arches and large axisymmetric deflection problems for shells of revolution. In particular, the algorithms are used for the analysis of large deflections of circular arches and toroidal shells. Examples of natural vibration and stability problems for parallelograms and trapezoidal membranes and panels are given.

  9. Solitons in nonlinear optics

    SciTech Connect

    Maimistov, Andrei I

    2010-11-13

    The classic examples of optical phenomena resulting in the appearance of solitons are self-focusing, self-induced transparency, and parametric three-wave interaction. To date, the list of the fields of nonlinear optics and models where solitons play an important role has significantly expanded. Now long-lived or stable solitary waves are called solitons, including, for example, dissipative, gap, parametric, and topological solitons. This review considers nonlinear optics models giving rise to the appearance of solitons in a narrow sense: solitary waves corresponding to the solutions of completely integrable systems of equations basic for the models being discussed. (review)

  10. Nonlinear aerodynamic wing design

    NASA Technical Reports Server (NTRS)

    Bonner, Ellwood

    1985-01-01

    The applicability of new nonlinear theoretical techniques is demonstrated for supersonic wing design. The new technology was utilized to define outboard panels for an existing advanced tactical fighter model. Mach 1.6 maneuver point design and multi-operating point compromise surfaces were developed and tested. High aerodynamic efficiency was achieved at the design conditions. A corollary result was that only modest supersonic penalties were incurred to meet multiple aerodynamic requirements. The nonlinear potential analysis of a practical configuration arrangement correlated well with experimental data.

  11. Nonlinear interferometric vibrational imaging.

    PubMed

    Marks, Daniel L; Boppart, Stephen A

    2004-03-26

    Coherent anti-Stokes Raman scattering (CARS) processes are "coherent," but the phase of the anti-Stokes radiation is lost by most incoherent spectroscopic CARS measurements. We propose a Raman microscopy imaging method called nonlinear interferometric vibrational imaging, which measures Raman spectra by obtaining the temporal anti-Stokes signal through nonlinear interferometry. With a more complete knowledge of the anti-Stokes signal, we show through simulations that a high-resolution Raman spectrum can be obtained of a molecule in a single pulse using broad band radiation. This could be useful for identifying the three-dimensional spatial distribution of molecular species in tissue.

  12. Perturbed nonlinear differential equations

    NASA Technical Reports Server (NTRS)

    Proctor, T. G.

    1972-01-01

    The existence of a solution defined for all t and possessing a type of boundedness property is established for the perturbed nonlinear system y = f(t,y) + F(t,y). The unperturbed system x = f(t,x) has a dichotomy in which some solutions exist and are well behaved as t increases to infinity, and some solution exists and are well behaved as t decreases to minus infinity. A similar study is made for a perturbed nonlinear differential equation defined on a half line, R+, and the existence of a family of solutions with special boundedness properties is established. The ideas are applied to integral manifolds.

  13. Min-Max Bias Robust Regression.

    DTIC Science & Technology

    1987-08-01

    2 UL uIImImmIIIEllmlllllllll llEllllhllllEI El 1 .1 25 11111 -.4 ___ . .. . . N ~ . MIN- MAX BIAS ROBUST REGRESSION by R. D. Martin V. J. Yohai R. H...shown than an S-estimate based on a jump-function type p solves the n- max bias problem for the class of NI-estimates with very general scale. This...5, (X() -- .5 and the rin- max estimator approaches the least median of squared residuals estimator introduced by Rousseeuw [J. Am. Statist. Assoc

  14. Learning regulatory programs by threshold SVD regression.

    PubMed

    Ma, Xin; Xiao, Luo; Wong, Wing Hung

    2014-11-04

    We formulate a statistical model for the regulation of global gene expression by multiple regulatory programs and propose a thresholding singular value decomposition (T-SVD) regression method for learning such a model from data. Extensive simulations demonstrate that this method offers improved computational speed and higher sensitivity and specificity over competing approaches. The method is used to analyze microRNA (miRNA) and long noncoding RNA (lncRNA) data from The Cancer Genome Atlas (TCGA) consortium. The analysis yields previously unidentified insights into the combinatorial regulation of gene expression by noncoding RNAs, as well as findings that are supported by evidence from the literature.

  15. Postpartum Regression of a Presumed Cavernous Meningioma

    PubMed Central

    Phang, See Yung; Whitfield, Peter

    2016-01-01

    Meningiomas are known to be more common in females than males. They are also known in rare cases to grow in size during pregnancy, which can complicate its management. We describe a 31-year-old Caucasian woman who presented with blurring of her vision and diplopia during the third trimester of her pregnancy. Magnetic resonance imaging (MRI) showed a small left cavernous sinus meningioma. The patient was treated conservatively until her uncomplicated delivery. A postpartum MRI scan showed complete regression of the suspected meningioma. Currently the patient is contemplating a further pregnancy. PMID:27066285

  16. An operational GLS model for hydrologic regression

    USGS Publications Warehouse

    Tasker, Gary D.; Stedinger, J.R.

    1989-01-01

    Recent Monte Carlo studies have documented the value of generalized least squares (GLS) procedures to estimate empirical relationships between streamflow statistics and physiographic basin characteristics. This paper presents a number of extensions of the GLS method that deal with realities and complexities of regional hydrologic data sets that were not addressed in the simulation studies. These extensions include: (1) a more realistic model of the underlying model errors; (2) smoothed estimates of cross correlation of flows; (3) procedures for including historical flow data; (4) diagnostic statistics describing leverage and influence for GLS regression; and (5) the formulation of a mathematical program for evaluating future gaging activities. ?? 1989.

  17. Inferring gene regression networks with model trees

    PubMed Central

    2010-01-01

    Background Novel strategies are required in order to handle the huge amount of data produced by microarray technologies. To infer gene regulatory networks, the first step is to find direct regulatory relationships between genes building the so-called gene co-expression networks. They are typically generated using correlation statistics as pairwise similarity measures. Correlation-based methods are very useful in order to determine whether two genes have a strong global similarity but do not detect local similarities. Results We propose model trees as a method to identify gene interaction networks. While correlation-based methods analyze each pair of genes, in our approach we generate a single regression tree for each gene from the remaining genes. Finally, a graph from all the relationships among output and input genes is built taking into account whether the pair of genes is statistically significant. For this reason we apply a statistical procedure to control the false discovery rate. The performance of our approach, named REGNET, is experimentally tested on two well-known data sets: Saccharomyces Cerevisiae and E.coli data set. First, the biological coherence of the results are tested. Second the E.coli transcriptional network (in the Regulon database) is used as control to compare the results to that of a correlation-based method. This experiment shows that REGNET performs more accurately at detecting true gene associations than the Pearson and Spearman zeroth and first-order correlation-based methods. Conclusions REGNET generates gene association networks from gene expression data, and differs from correlation-based methods in that the relationship between one gene and others is calculated simultaneously. Model trees are very useful techniques to estimate the numerical values for the target genes by linear regression functions. They are very often more precise than linear regression models because they can add just different linear regressions to separate

  18. Introduction to the use of regression models in epidemiology.

    PubMed

    Bender, Ralf

    2009-01-01

    Regression modeling is one of the most important statistical techniques used in analytical epidemiology. By means of regression models the effect of one or several explanatory variables (e.g., exposures, subject characteristics, risk factors) on a response variable such as mortality or cancer can be investigated. From multiple regression models, adjusted effect estimates can be obtained that take the effect of potential confounders into account. Regression methods can be applied in all epidemiologic study designs so that they represent a universal tool for data analysis in epidemiology. Different kinds of regression models have been developed in dependence on the measurement scale of the response variable and the study design. The most important methods are linear regression for continuous outcomes, logistic regression for binary outcomes, Cox regression for time-to-event data, and Poisson regression for frequencies and rates. This chapter provides a nontechnical introduction to these regression models with illustrating examples from cancer research.

  19. Regression-based estimation of ERP waveforms: I. The rERP framework

    PubMed Central

    Smith, Nathaniel J.; Kutas, Marta

    2014-01-01

    ERP averaging is an extraordinarily successful method, but can only be applied to a limited range of experimental designs. We introduce the regression-based rERP framework, which extends ERP averaging to handle arbitrary combinations of categorical and continuous covariates, partial confounding, non-linear effects, and overlapping responses to distinct events, all within a single unified system. rERPs enable a richer variety of paradigms (including high-N naturalistic designs) while preserving the advantages of traditional ERPs. This article provides an accessible introduction to what rERPs are, why they are useful, how they are computed, and when we should expect them to be effective, particularly in cases of partial confounding. A companion article discusses how non-linear effects and overlap correction can be handled within this framework, as well as practical considerations around baselining, filtering, statistical testing, and artifact rejection. Free software implementing these techniques is available. PMID:25141770

  20. Bias and uncertainty in regression-calibrated models of groundwater flow in heterogeneous media

    USGS Publications Warehouse

    Cooley, R.L.; Christensen, S.

    2006-01-01

    Groundwater models need to account for detailed but generally unknown spatial variability (heterogeneity) of the hydrogeologic model inputs. To address this problem we replace the large, m-dimensional stochastic vector ?? that reflects both small and large scales of heterogeneity in the inputs by a lumped or smoothed m-dimensional approximation ????*, where ?? is an interpolation matrix and ??* is a stochastic vector of parameters. Vector ??* has small enough dimension to allow its estimation with the available data. The consequence of the replacement is that model function f(????*) written in terms of the approximate inputs is in error with respect to the same model function written in terms of ??, ??,f(??), which is assumed to be nearly exact. The difference f(??) - f(????*), termed model error, is spatially correlated, generates prediction biases, and causes standard confidence and prediction intervals to be too small. Model error is accounted for in the weighted nonlinear regression methodology developed to estimate ??* and assess model uncertainties by incorporating the second-moment matrix of the model errors into the weight matrix. Techniques developed by statisticians to analyze classical nonlinear regression methods are extended to analyze the revised method. The analysis develops analytical expressions for bias terms reflecting the interaction of model nonlinearity and model error, for correction factors needed to adjust the sizes of confidence and prediction intervals for this interaction, and for correction factors needed to adjust the sizes of confidence and prediction intervals for possible use of a diagonal weight matrix in place of the correct one. If terms expressing the degree of intrinsic nonlinearity for f(??) and f(????*) are small, then most of the biases are small and the correction factors are reduced in magnitude. Biases, correction factors, and confidence and prediction intervals were obtained for a test problem for which model error is

  1. An Investigation of Sleep Characteristics, EEG Abnormalities and Epilepsy in Developmentally Regressed and Non-Regressed Children with Autism

    ERIC Educational Resources Information Center

    Giannotti, Flavia; Cortesi, Flavia; Cerquiglini, Antonella; Miraglia, Daniela; Vagnoni, Cristina; Sebastiani, Teresa; Bernabei, Paola

    2008-01-01

    This study investigated sleep of children with autism and developmental regression and the possible relationship with epilepsy and epileptiform abnormalities. Participants were 104 children with autism (70 non-regressed, 34 regressed) and 162 typically developing children (TD). Results suggested that the regressed group had higher incidence of…

  2. Regression Models For Saffron Yields in Iran

    NASA Astrophysics Data System (ADS)

    S. H, Sanaeinejad; S. N, Hosseini

    Saffron is an important crop in social and economical aspects in Khorassan Province (Northeast of Iran). In this research wetried to evaluate trends of saffron yield in recent years and to study the relationship between saffron yield and the climate change. A regression analysis was used to predict saffron yield based on 20 years of yield data in Birjand, Ghaen and Ferdows cities.Climatologically data for the same periods was provided by database of Khorassan Climatology Center. Climatologically data includedtemperature, rainfall, relative humidity and sunshine hours for ModelI, and temperature and rainfall for Model II. The results showed the coefficients of determination for Birjand, Ferdows and Ghaen for Model I were 0.69, 0.50 and 0.81 respectively. Also coefficients of determination for the same cities for model II were 0.53, 0.50 and 0.72 respectively. Multiple regression analysisindicated that among weather variables, temperature was the key parameter for variation ofsaffron yield. It was concluded that increasing temperature at spring was the main cause of declined saffron yield during recent years across the province. Finally, yield trend was predicted for the last 5 years using time series analysis.

  3. Supporting Regularized Logistic Regression Privately and Efficiently.

    PubMed

    Li, Wenfa; Liu, Hongzhe; Yang, Peng; Xie, Wei

    2016-01-01

    As one of the most popular statistical and machine learning models, logistic regression with regularization has found wide adoption in biomedicine, social sciences, information technology, and so on. These domains often involve data of human subjects that are contingent upon strict privacy regulations. Concerns over data privacy make it increasingly difficult to coordinate and conduct large-scale collaborative studies, which typically rely on cross-institution data sharing and joint analysis. Our work here focuses on safeguarding regularized logistic regression, a widely-used statistical model while at the same time has not been investigated from a data security and privacy perspective. We consider a common use scenario of multi-institution collaborative studies, such as in the form of research consortia or networks as widely seen in genetics, epidemiology, social sciences, etc. To make our privacy-enhancing solution practical, we demonstrate a non-conventional and computationally efficient method leveraging distributing computing and strong cryptography to provide comprehensive protection over individual-level and summary data. Extensive empirical evaluations on several studies validate the privacy guarantee, efficiency and scalability of our proposal. We also discuss the practical implications of our solution for large-scale studies and applications from various disciplines, including genetic and biomedical studies, smart grid, network analysis, etc.

  4. Quantile Regression Models for Current Status Data.

    PubMed

    Ou, Fang-Shu; Zeng, Donglin; Cai, Jianwen

    2016-11-01

    Current status data arise frequently in demography, epidemiology, and econometrics where the exact failure time cannot be determined but is only known to have occurred before or after a known observation time. We propose a quantile regression model to analyze current status data, because it does not require distributional assumptions and the coefficients can be interpreted as direct regression effects on the distribution of failure time in the original time scale. Our model assumes that the conditional quantile of failure time is a linear function of covariates. We assume conditional independence between the failure time and observation time. An M-estimator is developed for parameter estimation which is computed using the concave-convex procedure and its confidence intervals are constructed using a subsampling method. Asymptotic properties for the estimator are derived and proven using modern empirical process theory. The small sample performance of the proposed method is demonstrated via simulation studies. Finally, we apply the proposed method to analyze data from the Mayo Clinic Study of Aging.

  5. Double linear regression classification for face recognition

    NASA Astrophysics Data System (ADS)

    Feng, Qingxiang; Zhu, Qi; Tang, Lin-Lin; Pan, Jeng-Shyang

    2015-02-01

    A new classifier designed based on linear regression classification (LRC) classifier and simple-fast representation-based classifier (SFR), named double linear regression classification (DLRC) classifier, is proposed for image recognition in this paper. As we all know, the traditional LRC classifier only uses the distance between test image vectors and predicted image vectors of the class subspace for classification. And the SFR classifier uses the test image vectors and the nearest image vectors of the class subspace to classify the test sample. However, the DLRC classifier computes out the predicted image vectors of each class subspace and uses all the predicted vectors to construct a novel robust global space. Then, the DLRC utilizes the novel global space to get the novel predicted vectors of each class for classification. A mass number of experiments on AR face database, JAFFE face database, Yale face database, Extended YaleB face database, and PIE face database are used to evaluate the performance of the proposed classifier. The experimental results show that the proposed classifier achieves better recognition rate than the LRC classifier, SFR classifier, and several other classifiers.

  6. A Gibbs sampler for multivariate linear regression

    NASA Astrophysics Data System (ADS)

    Mantz, Adam B.

    2016-04-01

    Kelly described an efficient algorithm, using Gibbs sampling, for performing linear regression in the fairly general case where non-zero measurement errors exist for both the covariates and response variables, where these measurements may be correlated (for the same data point), where the response variable is affected by intrinsic scatter in addition to measurement error, and where the prior distribution of covariates is modelled by a flexible mixture of Gaussians rather than assumed to be uniform. Here, I extend the Kelly algorithm in two ways. First, the procedure is generalized to the case of multiple response variables. Secondly, I describe how to model the prior distribution of covariates using a Dirichlet process, which can be thought of as a Gaussian mixture where the number of mixture components is learned from the data. I present an example of multivariate regression using the extended algorithm, namely fitting scaling relations of the gas mass, temperature, and luminosity of dynamically relaxed galaxy clusters as a function of their mass and redshift. An implementation of the Gibbs sampler in the R language, called LRGS, is provided.

  7. Scientific Progress or Regress in Sports Physiology?

    PubMed

    Böning, Dieter

    2016-11-01

    In modern societies there is strong belief in scientific progress, but, unfortunately, a parallel partial regress occurs because of often avoidable mistakes. Mistakes are mainly forgetting, erroneous theories, errors in experiments and manuscripts, prejudice, selected publication of "positive" results, and fraud. An example of forgetting is that methods introduced decades ago are used without knowing the underlying theories: Basic articles are no longer read or cited. This omission may cause incorrect interpretation of results. For instance, false use of actual base excess instead of standard base excess for calculation of the number of hydrogen ions leaving the muscles raised the idea that an unknown fixed acid is produced in addition to lactic acid during exercise. An erroneous theory led to the conclusion that lactate is not the anion of a strong acid but a buffer. Mistakes occur after incorrect application of a method, after exclusion of unwelcome values, during evaluation of measurements by false calculations, or during preparation of manuscripts. Co-authors, as well as reviewers, do not always carefully read papers before publication. Peer reviewers might be biased against a hypothesis or an author. A general problem is selected publication of positive results. An example of fraud in sports medicine is the presence of doped subjects in groups of investigated athletes. To reduce regress, it is important that investigators search both original and recent articles on a topic and conscientiously examine the data. All co-authors and reviewers should read the text thoroughly and inspect all tables and figures in a manuscript.

  8. Supporting Regularized Logistic Regression Privately and Efficiently

    PubMed Central

    Li, Wenfa; Liu, Hongzhe; Yang, Peng; Xie, Wei

    2016-01-01

    As one of the most popular statistical and machine learning models, logistic regression with regularization has found wide adoption in biomedicine, social sciences, information technology, and so on. These domains often involve data of human subjects that are contingent upon strict privacy regulations. Concerns over data privacy make it increasingly difficult to coordinate and conduct large-scale collaborative studies, which typically rely on cross-institution data sharing and joint analysis. Our work here focuses on safeguarding regularized logistic regression, a widely-used statistical model while at the same time has not been investigated from a data security and privacy perspective. We consider a common use scenario of multi-institution collaborative studies, such as in the form of research consortia or networks as widely seen in genetics, epidemiology, social sciences, etc. To make our privacy-enhancing solution practical, we demonstrate a non-conventional and computationally efficient method leveraging distributing computing and strong cryptography to provide comprehensive protection over individual-level and summary data. Extensive empirical evaluations on several studies validate the privacy guarantee, efficiency and scalability of our proposal. We also discuss the practical implications of our solution for large-scale studies and applications from various disciplines, including genetic and biomedical studies, smart grid, network analysis, etc. PMID:27271738

  9. A reconsideration of the concept of regression.

    PubMed

    Dowling, A Scott

    2004-01-01

    Regression has been a useful psychoanalytic concept, linking present mental functioning with past experiences and levels of functioning. The concept originated as an extension of the evolutionary zeitgeist of the day as enunciated by H. Spencer and H. Jackson and applied by Freud to psychological phenomena. The value system implicit in the contrast of evolution/progression vs dissolution/regression has given rise to unfortunate and powerful assumptions of social, cultural, developmental and individual value as embodied in notions of "higher," "lower;" "primitive," "mature," "archaic," and "advanced." The unhelpful results of these assumptions are evident, for example, in attitudes concerning cultural, sexual, and social "correctness, " same-sex object choice, and goals of treatment. An alternative, a continuously constructed, continuously emerging mental life, in analogy to the ever changing, continuous physical body, is suggested. This view retains the fundamentals of psychoanalysis, for example, unconscious mental life, drive, defense, and psychic structure, but stresses a functional, ever changing, present oriented understanding of mental life as contrasted with a static, onion-layered view.

  10. Shape regression for vertebra fracture quantification

    NASA Astrophysics Data System (ADS)

    Lund, Michael Tillge; de Bruijne, Marleen; Tanko, Laszlo B.; Nielsen, Mads

    2005-04-01

    Accurate and reliable identification and quantification of vertebral fractures constitute a challenge both in clinical trials and in diagnosis of osteoporosis. Various efforts have been made to develop reliable, objective, and reproducible methods for assessing vertebral fractures, but at present there is no consensus concerning a universally accepted diagnostic definition of vertebral fractures. In this project we want to investigate whether or not it is possible to accurately reconstruct the shape of a normal vertebra, using a neighbouring vertebra as prior information. The reconstructed shape can then be used to develop a novel vertebra fracture measure, by comparing the segmented vertebra shape with its reconstructed normal shape. The vertebrae in lateral x-rays of the lumbar spine were manually annotated by a medical expert. With this dataset we built a shape model, with equidistant point distribution between the four corner points. Based on the shape model, a multiple linear regression model of a normal vertebra shape was developed for each dataset using leave-one-out cross-validation. The reconstructed shape was calculated for each dataset using these regression models. The average prediction error for the annotated shape was on average 3%.

  11. Regression-based model of skin diffuse reflectance for skin color analysis

    NASA Astrophysics Data System (ADS)

    Tsumura, Norimichi; Kawazoe, Daisuke; Nakaguchi, Toshiya; Ojima, Nobutoshi; Miyake, Yoichi

    2008-11-01

    A simple regression-based model of skin diffuse reflectance is developed based on reflectance samples calculated by Monte Carlo simulation of light transport in a two-layered skin model. This reflectance model includes the values of spectral reflectance in the visible spectra for Japanese women. The modified Lambert Beer law holds in the proposed model with a modified mean free path length in non-linear density space. The averaged RMS and maximum errors of the proposed model were 1.1 and 3.1%, respectively, in the above range.

  12. Heterogeneity in drug abuse among juvenile offenders: is mixture regression more informative than standard regression?

    PubMed

    Montgomery, Katherine L; Vaughn, Michael G; Thompson, Sanna J; Howard, Matthew O

    2013-11-01

    Research on juvenile offenders has largely treated this population as a homogeneous group. However, recent findings suggest that this at-risk population may be considerably more heterogeneous than previously believed. This study compared mixture regression analyses with standard regression techniques in an effort to explain how known factors such as distress, trauma, and personality are associated with drug abuse among juvenile offenders. Researchers recruited 728 juvenile offenders from Missouri juvenile correctional facilities for participation in this study. Researchers investigated past-year substance use in relation to the following variables: demographic characteristics (gender, ethnicity, age, familial use of public assistance), antisocial behavior, and mental illness symptoms (psychopathic traits, psychiatric distress, and prior trauma). Results indicated that standard and mixed regression approaches identified significant variables related to past-year substance use among this population; however, the mixture regression methods provided greater specificity in results. Mixture regression analytic methods may help policy makers and practitioners better understand and intervene with the substance-related subgroups of juvenile offenders.

  13. HOS network-based classification of power quality events via regression algorithms

    NASA Astrophysics Data System (ADS)

    Palomares Salas, José Carlos; González de la Rosa, Juan José; Sierra Fernández, José María; Pérez, Agustín Agüera

    2015-12-01

    This work compares seven regression algorithms implemented in artificial neural networks (ANNs) supported by 14 power-quality features, which are based in higher-order statistics. Combining time and frequency domain estimators to deal with non-stationary measurement sequences, the final goal of the system is the implementation in the future smart grid to guarantee compatibility between all equipment connected. The principal results are based in spectral kurtosis measurements, which easily adapt to the impulsive nature of the power quality events. These results verify that the proposed technique is capable of offering interesting results for power quality (PQ) disturbance classification. The best results are obtained using radial basis networks, generalized regression, and multilayer perceptron, mainly due to the non-linear nature of data.

  14. Nonlinear Pricing in Energy and Environmental Markets

    NASA Astrophysics Data System (ADS)

    Ito, Koichiro

    This dissertation consists of three empirical studies on nonlinear pricing in energy and environmental markets. The first investigates how consumers respond to multi-tier nonlinear price schedules for residential electricity. Chapter 2 asks a similar research question for residential water pricing. Finally, I examine the effect of nonlinear financial rewards for energy conservation by applying a regression discontinuity design to a large-scale electricity rebate program that was implemented in California. Economic theory generally assumes that consumers respond to marginal prices when making economic decisions, but this assumption may not hold for complex price schedules. The chapter "Do Consumers Respond to Marginal or Average Price? Evidence from Nonlinear Electricity Pricing" provides empirical evidence that consumers respond to average price rather than marginal price when faced with nonlinear electricity price schedules. Nonlinear price schedules, such as progressive income tax rates and multi-tier electricity prices, complicate economic decisions by creating multiple marginal prices for the same good. Evidence from laboratory experiments suggests that consumers facing such price schedules may respond to average price as a heuristic. I empirically test this prediction using field data by exploiting price variation across a spatial discontinuity in electric utility service areas. The territory border of two electric utilities lies within several city boundaries in southern California. As a result, nearly identical households experience substantially different nonlinear electricity price schedules. Using monthly household-level panel data from 1999 to 2008, I find strong evidence that consumers respond to average price rather than marginal or expected marginal price. I show that even though this sub-optimizing behavior has a minimal impact on individual welfare, it can critically alter the policy implications of nonlinear pricing. The second chapter " How Do

  15. Nonlinear phased array imaging

    NASA Astrophysics Data System (ADS)

    Croxford, Anthony J.; Cheng, Jingwei; Potter, Jack N.

    2016-04-01

    A technique is presented for imaging acoustic nonlinearity within a specimen using ultrasonic phased arrays. Acoustic nonlinearity is measured by evaluating the difference in energy of the transmission bandwidth within the diffuse field produced through different focusing modes. The two different modes being classical beam forming, where delays are applied to different element of a phased array to physically focus the energy at a single location (parallel firing) and focusing in post processing, whereby one element at a time is fired and a focused image produced in post processing (sequential firing). Although these two approaches are linearly equivalent the difference in physical displacement within the specimen leads to differences in nonlinear effects. These differences are localized to the areas where the amplitude is different, essentially confining the differences to the focal point. Direct measurement at the focal point are however difficult to make. In order to measure this the diffuse field is used. It is a statistical property of the diffuse field that it represents the total energy in the system. If the energy in the diffuse field for both the sequential and parallel firing case is measured then the difference between these, within the input signal bandwidth, is largely due to differences at the focal spot. This difference therefore gives a localized measurement of where energy is moving out of the transmission bandwidth due to nonlinear effects. This technique is used to image fatigue cracks and other damage types undetectable with conventional linear ultrasonic measurements.

  16. Intramolecular and nonlinear dynamics

    SciTech Connect

    Davis, M.J.

    1993-12-01

    Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.

  17. Nonlinear optical inves

    NASA Astrophysics Data System (ADS)

    Zidan, M. D.; Arfan, A.; Allahham, A.

    2017-03-01

    Z-scan technique was used to investigate the nonlinear optical properties of Quinine and 1-(carboxymethyl)-6-methoxy-4-(3-(3-vinylpiperidin-4-yl) propanoyl) quinolin-1-ium chloride (Quinotoxine) salts. The two salts were characterized using UV-visible, FTIR and NMR measurements. The characterization spectra confirm the expected molecular structure of the prepared "Quinotoxine " salt. The z-scan measurements were performed with a CW Diode laser at 635 nm wavelength and 26 mW power. The nonlinear absorption coefficient (β), nonlinear refractive index (n2), the ground-state absorption cross sections (σg), the excited-state absorption cross sections (σex) and thermo-optic coefficient of the samples were determined. Our results reveal that the σex is higher than the σg indicating that the reverse saturable absorption (RSA) is the dominating mechanism for the observed absorption nonlinearities. The results suggest that this material should be considered as a promising candidate for future optical devices applications.

  18. Nonlinear silicon photonics

    NASA Astrophysics Data System (ADS)

    Tsia, Kevin K.; Jalali, Bahram

    2010-05-01

    An intriguing optical property of silicon is that it exhibits a large third-order optical nonlinearity, with orders-ofmagnitude larger than that of silica glass in the telecommunication band. This allows efficient nonlinear optical interaction at relatively low power levels in a small footprint. Indeed, we have witnessed a stunning progress in harnessing the Raman and Kerr effects in silicon as the mechanisms for enabling chip-scale optical amplification, lasing, and wavelength conversion - functions that until recently were perceived to be beyond the reach of silicon. With all the continuous efforts developing novel techniques, nonlinear silicon photonics is expected to be able to reach even beyond the prior achievements. Instead of providing a comprehensive overview of this field, this manuscript highlights a number of new branches of nonlinear silicon photonics, which have not been fully recognized in the past. In particular, they are two-photon photovoltaic effect, mid-wave infrared (MWIR) silicon photonics, broadband Raman effects, inverse Raman scattering, and periodically-poled silicon (PePSi). These novel effects and techniques could create a new paradigm for silicon photonics and extend its utility beyond the traditionally anticipated applications.

  19. Nonlinear plasmonic nanorulers.

    PubMed

    Butet, Jérémy; Martin, Olivier J F

    2014-05-27

    The evaluation of distances as small as few nanometers using optical waves is a very challenging task that can pave the way for the development of new applications in biotechnology and nanotechnology. In this article, we propose a new measurement method based on the control of the nonlinear optical response of plasmonic nanostructures by means of Fano resonances. It is shown that Fano resonances resulting from the coupling between a bright mode and a dark mode at the fundamental wavelength enable unprecedented and direct manipulation of the nonlinear electromagnetic sources at the nanoscale. In the case of second harmonic generation from gold nanodolmens, the different nonlinear sources distributions induced by the different coupling regimes are clearly revealed in the far-field distribution. Hence, the configuration of the nanostructure can be accurately determined in 3-dimensions by recording the wave scattered at the second harmonic wavelength. Indeed, the conformation of the different elements building the system is encoded in the nonlinear far-field distribution, making second harmonic generation a promising tool for reading 3-dimension plasmonic nanorulers. Furthemore, it is shown that 3-dimension plasmonic nanorulers can be implemented with simpler geometries than in the linear regime while providing complete information on the structure conformation, including the top nanobar position and orientation.

  20. Generalized Nonlinear Yule Models

    NASA Astrophysics Data System (ADS)

    Lansky, Petr; Polito, Federico; Sacerdote, Laura

    2016-11-01

    With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.

  1. Nonlinear Theory and Breakdown

    NASA Technical Reports Server (NTRS)

    Smith, Frank

    2007-01-01

    The main points of recent theoretical and computational studies on boundary-layer transition and turbulence are to be highlighted. The work is based on high Reynolds numbers and attention is drawn to nonlinear interactions, breakdowns and scales. The research focuses in particular on truly nonlinear theories, i.e. those for which the mean-flow profile is completely altered from its original state. There appear to be three such theories dealing with unsteady nonlinear pressure-displacement interactions (I), with vortex/wave interactions (II), and with Euler-scale flows (III). Specific recent findings noted for these three, and in quantitative agreement with experiments, are the following. Nonlinear finite-time break-ups occur in I, leading to sublayer eruption and vortex formation; here the theory agrees with experiments (Nishioka) regarding the first spike. II gives rise to finite-distance blowup of displacement thickness, then interaction and break-up as above; this theory agrees with experiments (Klebanoff, Nishioka) on the formation of three-dimensional streets. III leads to the prediction of turbulent boundary-layer micro-scale, displacement-and stress-sublayer-thicknesses.

  2. Nonlinear Image Denoising Methodologies

    DTIC Science & Technology

    2002-05-01

    53 5.3 A Multiscale Approach to Scale-Space Analysis . . . . . . . . . . . . . . . . 53 5.4...etc. In this thesis, Our approach to denoising is first based on a controlled nonlinear stochastic random walk to achieve a scale space analysis ( as in... stochastic treatment or interpretation of the diffusion. In addition, unless a specific stopping time is known to be adequate, the resulting evolution

  3. Nonlinear dynamics experiments

    SciTech Connect

    Fischer, W.

    2011-01-01

    The goal of nonlinear dynamics experiments is to improve the understanding of single particle effects that increase the particle amplitude and lead to loss. Particle motion in storage rings is nearly conservative and for transverse dynamics the Hamiltonian in action angle variables (I{sub x},I{sub y},{phi}{sub x},{phi}{sub y}) near an isolated resonance k{nu}{sub x} + l{nu}{sub y} {approx} p is H = I{sub x}{nu}{sub x0} + I{sub y}{nu}{sub y0} + g(I{sub x}, I{sub y}) + h(I{sub x}, I{sub y})cos(k{phi}{sub x} + l{phi}{sub y} - p{theta}), (1) where k, l, p are integers, {theta} = 2{pi}s/L is the azimuth, and s and L are the path length and circumference respectively. The amplitude dependent tunes are given by {nu}{sub x,y}(I{sub x},I{sub y}) = {nu}{sub x0,y0} + {partial_derivative}g(I{sub x},I{sub y})/{partial_derivative}I{sub x,y} (2) and h(I{sub x},I{sub y}) is the resonance driving term (RDT). If the motion is governed by multiple resonances, h(I{sub x},I{sub y}) has to be replace by a series of terms. The particle motion is completely determined by the terms g and h, which can be calculated from higher order multipoles (Sec. ??), or obtained from simulations. Deviations from pure Hamiltonian motion occur due to synchrotron radiation damping (Sec. ??) in lepton or very high energy hadron rings, parameter variations, and diffusion processes such as residual gas and intrabeam scattering. The time scale of the non-Hamiltonian process determines the applicability of the Hamiltonian analysis. Transverse nonlinearities are introduced through sextupoles or higher order multipoles and magnetic field errors in dipoles and quadrupoles. Sextupoles can already drive all resonances. The beam-beam interaction and space charge also introduce nonlinear fields. Intentionally introduced nonlinearities are used to extract beam on a resonance or through capture in stable islands. Localization and minimization of nonlinearities in a ring is a general strategy to decrease emittance growth

  4. Selection on plasticity of seasonal life-history traits using random regression mixed model analysis

    PubMed Central

    Brommer, Jon E; Kontiainen, Pekka; Pietiäinen, Hannu

    2012-01-01

    Theory considers the covariation of seasonal life-history traits as an optimal reaction norm, implying that deviating from this reaction norm reduces fitness. However, the estimation of reaction-norm properties (i.e., elevation, linear slope, and higher order slope terms) and the selection on these is statistically challenging. We here advocate the use of random regression mixed models to estimate reaction-norm properties and the use of bivariate random regression to estimate selection on these properties within a single model. We illustrate the approach by random regression mixed models on 1115 observations of clutch sizes and laying dates of 361 female Ural owl Strix uralensis collected over 31 years to show that (1) there is variation across individuals in the slope of their clutch size–laying date relationship, and that (2) there is selection on the slope of the reaction norm between these two traits. Hence, natural selection potentially drives the negative covariance in clutch size and laying date in this species. The random-regression approach is hampered by inability to estimate nonlinear selection, but avoids a number of disadvantages (stats-on-stats, connecting reaction-norm properties to fitness). The approach is of value in describing and studying selection on behavioral reaction norms (behavioral syndromes) or life-history reaction norms. The approach can also be extended to consider the genetic underpinning of reaction-norm properties. PMID:22837818

  5. Face Recognition With Pose Variations and Misalignment via Orthogonal Procrustes Regression.

    PubMed

    Tai, Ying; Yang, Jian; Zhang, Yigong; Luo, Lei; Qian, Jianjun; Chen, Yu

    2016-06-01

    A linear regression-based method is a hot topic in face recognition community. Recently, sparse representation and collaborative representation-based classifiers for face recognition have been proposed and attracted great attention. However, most of the existing regression analysis-based methods are sensitive to pose variations. In this paper, we introduce the orthogonal Procrustes problem (OPP) as a model to handle pose variations existed in 2D face images. OPP seeks an optimal linear transformation between two images with different poses so as to make the transformed image best fits the other one. We integrate OPP into the regression model and propose the orthogonal Procrustes regression (OPR) model. To address the problem that the linear transformation is not suitable for handling highly non-linear pose variation, we further adopt a progressive strategy and propose the stacked OPR. As a practical framework, OPR can handle face alignment, pose correction, and face representation simultaneously. We optimize the proposed model via an efficient alternating iterative algorithm, and experimental results on three popular face databases, such as CMU PIE database, CMU Multi-PIE database, and LFW database, demonstrate the effectiveness of our proposed method.

  6. A novel strategy for forensic age prediction by DNA methylation and support vector regression model

    PubMed Central

    Xu, Cheng; Qu, Hongzhu; Wang, Guangyu; Xie, Bingbing; Shi, Yi; Yang, Yaran; Zhao, Zhao; Hu, Lan; Fang, Xiangdong; Yan, Jiangwei; Feng, Lei

    2015-01-01

    High deviations resulting from prediction model, gender and population difference have limited age estimation application of DNA methylation markers. Here we identified 2,957 novel age-associated DNA methylation sites (P < 0.01 and R2 > 0.5) in blood of eight pairs of Chinese Han female monozygotic twins. Among them, nine novel sites (false discovery rate < 0.01), along with three other reported sites, were further validated in 49 unrelated female volunteers with ages of 20–80 years by Sequenom Massarray. A total of 95 CpGs were covered in the PCR products and 11 of them were built the age prediction models. After comparing four different models including, multivariate linear regression, multivariate nonlinear regression, back propagation neural network and support vector regression, SVR was identified as the most robust model with the least mean absolute deviation from real chronological age (2.8 years) and an average accuracy of 4.7 years predicted by only six loci from the 11 loci, as well as an less cross-validated error compared with linear regression model. Our novel strategy provides an accurate measurement that is highly useful in estimating the individual age in forensic practice as well as in tracking the aging process in other related applications. PMID:26635134

  7. Factor complexity of crash occurrence: An empirical demonstration using boosted regression trees.

    PubMed

    Chung, Yi-Shih

    2013-12-01

    Factor complexity is a characteristic of traffic crashes. This paper proposes a novel method, namely boosted regression trees (BRT), to investigate the complex and nonlinear relationships in high-variance traffic crash data. The Taiwanese 2004-2005 single-vehicle motorcycle crash data are used to demonstrate the utility of BRT. Traditional logistic regression and classification and regression tree (CART) models are also used to compare their estimation results and external validities. Both the in-sample cross-validation and out-of-sample validation results show that an increase in tree complexity provides improved, although declining, classification performance, indicating a limited factor complexity of single-vehicle motorcycle crashes. The effects of crucial variables including geographical, time, and sociodemographic factors explain some fatal crashes. Relatively unique fatal crashes are better approximated by interactive terms, especially combinations of behavioral factors. BRT models generally provide improved transferability than conventional logistic regression and CART models. This study also discusses the implications of the results for devising safety policies.

  8. Dielectric Nonlinear Transmission Line (Postprint)

    DTIC Science & Technology

    2011-12-01

    Technical Paper 3. DATES COVERED (From - To) 2011 4. TITLE AND SUBTITLE Dielectric Nonlinear Transmission Line (POSTPRINT) 5a. CONTRACT NUMBER...14. ABSTRACT A parallel plate nonlinear transmission line (NLTL) was constructed. Periodic loading of nonlinear dielectric slabs provides the...846-9101 Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std. 239.18 Dielectric Nonlinear Transmission Line David M. French, Brad W. Hoff

  9. KNN-based local linear regression for the analysis and simulation of low flow extremes under climatic influence

    NASA Astrophysics Data System (ADS)

    Lee, Taesam; Ouarda, Taha B. M. J.; Yoon, Sunkwon

    2017-02-01

    Climate change frequently causes highly nonlinear and irregular behaviors in hydroclimatic systems. The stochastic simulation of hydroclimatic variables reproduces such irregular behaviors and is beneficial for assessing their impact on other regimes. The objective of the current study is to propose a novel method, a k-nearest neighbor (KNN) based on the local linear regression method (KLR), to reproduce nonlinear and heteroscedastic relations in hydroclimatic variables. The proposed model was validated with a nonlinear, heteroscedastic, lag-1 time dependent test function. The validation results of the test function show that the key statistics, nonlinear dependence, and heteroscedascity of the test data are reproduced well by the KLR model. In contrast, a traditional resampling technique, KNN resampling (KNNR), shows some biases with respect to key statistics, such as the variance and lag-1 correlation. Furthermore, the proposed KLR model was used to simulate the annual minimum of the consecutive 7-day average daily mean flow (Min7D) of the Romaine River, Quebec. The observed and extended North Atlantic Oscillation (NAO) index is incorporated into the model. The case study results of the observed period illustrate that the KLR model sufficiently reproduced key statistics and the nonlinear heteroscedasticity relation. For the future period, a lower mean is observed, which indicates that drier conditions other than normal might be expected in the next decade in the Romaine River. Overall, it is concluded that the KLR model can be a good alternative for simulating irregular and nonlinear behaviors in hydroclimatic variables.

  10. Compactons in Nonlinear Schroedinger Lattices with Strong Nonlinearity Management

    SciTech Connect

    Abdullaev, F. Kh.; Kevrekidis, P. G.; Salerno, M.

    2010-09-10

    The existence of compactons in the discrete nonlinear Schroedinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. In the averaged discrete nonlinear Schroedinger equation, the resulting effective interwell tunneling depends on the modulation parameters and on the field amplitude. This introduces nonlinear dispersion in the system and can lead to a prototypical realization of single- or multisite stable discrete compactons in nonlinear optical waveguide and Bose-Einstein condensate arrays. These structures can dynamically arise out of Gaussian or compactly supported initial data.

  11. Program for Nonlinear Structural Analysis

    DTIC Science & Technology

    1981-09-01

    November 1970. 2. R. E. Jones and W. L. Salus , "Survey and Development of Finite Elements for Nonlineer Structural Analysis", Volume II, "Nonlinear Shell...1970. 2. R. E. Jones and W. L. Salus , "Survey and Development of Finite Elements for Nonlinear Structural Analysis," Volume II, "Nonlinear Shell

  12. Cubication of Conservative Nonlinear Oscillators

    ERIC Educational Resources Information Center

    Belendez, Augusto; Alvarez, Mariela L.; Fernandez, Elena; Pascual, Immaculada

    2009-01-01

    A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…

  13. Estimates on compressed neural networks regression.

    PubMed

    Zhang, Yongquan; Li, Youmei; Sun, Jianyong; Ji, Jiabing

    2015-03-01

    When the neural element number n of neural networks is larger than the sample size m, the overfitting problem arises since there are more parameters than actual data (more variable than constraints). In order to overcome the overfitting problem, we propose to reduce the number of neural elements by using compressed projection A which does not need to satisfy the condition of Restricted Isometric Property (RIP). By applying probability inequalities and approximation properties of the feedforward neural networks (FNNs), we prove that solving the FNNs regression learning algorithm in the compressed domain instead of the original domain reduces the sample error at the price of an increased (but controlled) approximation error, where the covering number theory is used to estimate the excess error, and an upper bound of the excess error is given.

  14. [Logistic regression against a divergent Bayesian network].

    PubMed

    Sánchez Trujillo, Noel Antonio

    2015-02-03

    This article is a discussion about two statistical tools used for prediction and causality assessment: logistic regression and Bayesian networks. Using data of a simulated example from a study assessing factors that might predict pulmonary emphysema (where fingertip pigmentation and smoking are considered); we posed the following questions. Is pigmentation a confounding, causal or predictive factor? Is there perhaps another factor, like smoking, that confounds? Is there a synergy between pigmentation and smoking? The results, in terms of prediction, are similar with the two techniques; regarding causation, differences arise. We conclude that, in decision-making, the sum of both: a statistical tool, used with common sense, and previous evidence, taking years or even centuries to develop; is better than the automatic and exclusive use of statistical resources.

  15. Conjoined legs: Sirenomelia or caudal regression syndrome?

    PubMed Central

    Das, Sakti Prasad; Ojha, Niranjan; Ganesh, G Shankar; Mohanty, Ram Narayan

    2013-01-01

    Presence of single umbilical persistent vitelline artery distinguishes sirenomelia from caudal regression syndrome. We report a case of a12-year-old boy who had bilateral umbilical arteries presented with fusion of both legs in the lower one third of leg. Both feet were rudimentary. The right foot had a valgus rocker-bottom deformity. All toes were present but rudimentary. The left foot showed absence of all toes. Physical examination showed left tibia vara. The chest evaluation in sitting revealed pigeon chest and elevated right shoulder. Posterior examination of the trunk showed thoracic scoliosis with convexity to right. The patient was operated and at 1 year followup the boy had two separate legs with a good aesthetic and functional results. PMID:23960288

  16. Macrophages, dendritic cells, and regression of atherosclerosis

    PubMed Central

    Feig, Jonathan E.; Feig, Jessica L.

    2012-01-01

    Atherosclerosis is the number one cause of death in the Western world. It results from the interaction between modified lipoproteins and cells such as macrophages, dendritic cells (DCs), T cells, and other cellular elements present in the arterial wall. This inflammatory process can ultimately lead to the development of complex lesions, or plaques, that protrude into the arterial lumen. Ultimately, plaque rupture and thrombosis can occur leading to the clinical complications of myocardial infarction or stroke. Although each of the cell types plays roles in the pathogenesis of atherosclerosis, the focus of this review will be primarily on the macrophages and DCs. The role of these two cell types in atherosclerosis is discussed, with a particular emphasis on their involvement in atherosclerosis regression. PMID:22934038

  17. Reliable prediction intervals with regression neural networks.

    PubMed

    Papadopoulos, Harris; Haralambous, Haris

    2011-10-01

    This paper proposes an extension to conventional regression neural networks (NNs) for replacing the point predictions they produce with prediction intervals that satisfy a required level of confidence. Our approach follows a novel machine learning framework, called Conformal Prediction (CP), for assigning reliable confidence measures to predictions without assuming anything more than that the data are independent and identically distributed (i.i.d.). We evaluate the proposed method on four benchmark datasets and on the problem of predicting Total Electron Content (TEC), which is an important parameter in trans-ionospheric links; for the latter we use a dataset of more than 60000 TEC measurements collected over a period of 11 years. Our experimental results show that the prediction intervals produced by our method are both well calibrated and tight enough to be useful in practice.

  18. Subgroup finding via Bayesian additive regression trees.

    PubMed

    Sivaganesan, Siva; Müller, Peter; Huang, Bin

    2017-03-09

    We provide a Bayesian decision theoretic approach to finding subgroups that have elevated treatment effects. Our approach separates the modeling of the response variable from the task of subgroup finding and allows a flexible modeling of the response variable irrespective of potential subgroups of interest. We use Bayesian additive regression trees to model the response variable and use a utility function defined in terms of a candidate subgroup and the predicted response for that subgroup. Subgroups are identified by maximizing the expected utility where the expectation is taken with respect to the posterior predictive distribution of the response, and the maximization is carried out over an a priori specified set of candidate subgroups. Our approach allows subgroups based on both quantitative and categorical covariates. We illustrate the approach using simulated data set study and a real data set. Copyright © 2017 John Wiley & Sons, Ltd.

  19. Sparse brain network using penalized linear regression

    NASA Astrophysics Data System (ADS)

    Lee, Hyekyoung; Lee, Dong Soo; Kang, Hyejin; Kim, Boong-Nyun; Chung, Moo K.

    2011-03-01

    Sparse partial correlation is a useful connectivity measure for brain networks when it is difficult to compute the exact partial correlation in the small-n large-p setting. In this paper, we formulate the problem of estimating partial correlation as a sparse linear regression with a l1-norm penalty. The method is applied to brain network consisting of parcellated regions of interest (ROIs), which are obtained from FDG-PET images of the autism spectrum disorder (ASD) children and the pediatric control (PedCon) subjects. To validate the results, we check their reproducibilities of the obtained brain networks by the leave-one-out cross validation and compare the clustered structures derived from the brain networks of ASD and PedCon.

  20. Censored Median Regression and Profile Empirical Likelihood

    PubMed Central

    Subramanian, Sundarraman

    2007-01-01

    We implement profile empirical likelihood based inference for censored median regression models. Inference for any specified sub-vector is carried out by profiling out the nuisance parameters from the “plug-in” empirical likelihood ratio function proposed by Qin and Tsao. To obtain the critical value of the profile empirical likelihood ratio statistic, we first investigate its asymptotic distribution. The limiting distribution is a sum of weighted chi square distributions. Unlike for the full empirical likelihood, however, the derived asymptotic distribution has intractable covariance structure. Therefore, we employ the bootstrap to obtain the critical value, and compare the resulting confidence intervals with the ones obtained through Basawa and Koul’s minimum dispersion statistic. Furthermore, we obtain confidence intervals for the age and treatment effects in a lung cancer data set. PMID:19112527

  1. Early development and regression in Rett syndrome.

    PubMed

    Lee, J Y L; Leonard, H; Piek, J P; Downs, J

    2013-12-01

    This study utilized developmental profiling to examine symptoms in 14 girls with genetically confirmed Rett syndrome and whose families were participating in the Australian Rett syndrome or InterRett database. Regression was mostly characterized by loss of hand and/or communication skills (13/14) except one girl demonstrated slowing of skill development. Social withdrawal and inconsolable crying often developed simultaneously (9/14), with social withdrawal for shorter duration than inconsolable crying. Previously acquired gross motor skills declined in just over half of the sample (8/14), mostly observed as a loss of balance. Early abnormalities such as vomiting and strabismus were also seen. Our findings provide additional insight into the early clinical profile of Rett syndrome.

  2. Tolerance bounds for log gamma regression models

    NASA Technical Reports Server (NTRS)

    Jones, R. A.; Scholz, F. W.; Ossiander, M.; Shorack, G. R.

    1985-01-01

    The present procedure for finding lower confidence bounds for the quantiles of Weibull populations, on the basis of the solution of a quadratic equation, is more accurate than current Monte Carlo tables and extends to any location-scale family. It is shown that this method is accurate for all members of the log gamma(K) family, where K = 1/2 to infinity, and works well for censored data, while also extending to regression data. An even more accurate procedure involving an approximation to the Lawless (1982) conditional procedure, with numerical integrations whose tables are independent of the data, is also presented. These methods are applied to the case of failure strengths of ceramic specimens from each of three billets of Si3N4, which have undergone flexural strength testing.

  3. Magnetotelluric Data, Stable Distributions and Stable Regression

    NASA Astrophysics Data System (ADS)

    Chave, A. D.

    2013-12-01

    The author has noted for many years that the residuals from robust or bounded influence estimates of the magnetotelluric response function are systematically long tailed compared to a Gaussian or Rayleigh distribution. Consequently, the standard statistical model of a Gaussian core contaminated by a fraction of outlying data is not really valid. However, the typical result is an improvement on ordinary least squares, and has become standard in the electromagnetic induction community. A recent re-evaluation of the statistics of magnetotelluric response function estimation has shown that, in almost all cases, the residuals are alpha stable rather than Gaussian. Alpha stable distributions are characterized by four parameters: a shape parameter lying on (0, 2], a skewness parameter, a scale parameter and a location parameter, and cannot be expressed in closed form except for a few special cases. When the shape parameter is 2, the result is Gaussian, but when it is smaller the resulting distribution has infinite variance. Typical magnetotelluric residuals are alpha stable with a shape parameter lying between 1 and 2. This suggests that robust methods improve response function estimates by eliminating data corresponding to the largest stable residuals while leaving the bulk of the population alone. A better statistical approach is based on stable regression that directly accommodates the actual residual distribution without eliminating the most extreme ones. This paper will introduce such an algorithm, and illustrate its functionality with a variety of magnetotelluric data. Further work remains to produce a robust stable regression algorithm that will eliminate real outliers such as lightning strikes or instrument problems without affecting the bulk stable population. Stable distributions are intimately associated with fractional derivative physical processes. Since the Maxwell equations and the constitutive relations pertaining to the earth do not contain any fractional

  4. Collaborative Regression-based Anatomical Landmark Detection

    PubMed Central

    Gao, Yaozong; Shen, Dinggang

    2015-01-01

    Anatomical landmark detection plays an important role in medical image analysis, e.g., for registration, segmentation and quantitative analysis. Among various existing methods for landmark detection, regression-based methods recently have drawn much attention due to robustness and efficiency. In such methods, landmarks are localized through voting from all image voxels, which is completely different from classification-based methods that use voxel-wise classification to detect landmarks. Despite robustness, the accuracy of regression-based landmark detection methods is often limited due to 1) inclusion of uninformative image voxels in the voting procedure, and 2) lack of effective ways to incorporate inter-landmark spatial dependency into the detection step. In this paper, we propose a collaborative landmark detection framework to address these limitations. The concept of collaboration is reflected in two aspects. 1) Multi-resolution collaboration. A multi-resolution strategy is proposed to hierarchically localize landmarks by gradually excluding uninformative votes from faraway voxels. Moreover, for the informative voxels near the landmark, a spherical sampling strategy is also designed in the training stage to improve their prediction accuracy. 2) Inter-landmark collaboration. A confidence-based landmark detection strategy is proposed to improve the detection accuracy of “difficult-to-detect” landmarks by using spatial guidance from “easy-to-detect” landmarks. To evaluate our method, we conducted experiments extensively on three datasets for detecting prostate landmarks and head & neck landmarks in computed tomography (CT) images, and also dental landmarks in cone beam computed tomography (CBCT) images. The results show the effectiveness of our collaborative landmark detection framework in improving landmark detection accuracy, compared to other state-of-the-art methods. PMID:26579736

  5. Collaborative regression-based anatomical landmark detection

    NASA Astrophysics Data System (ADS)

    Gao, Yaozong; Shen, Dinggang

    2015-12-01

    Anatomical landmark detection plays an important role in medical image analysis, e.g. for registration, segmentation and quantitative analysis. Among the various existing methods for landmark detection, regression-based methods have recently attracted much attention due to their robustness and efficiency. In these methods, landmarks are localised through voting from all image voxels, which is completely different from the classification-based methods that use voxel-wise classification to detect landmarks. Despite their robustness, the accuracy of regression-based landmark detection methods is often limited due to (1) the inclusion of uninformative image voxels in the voting procedure, and (2) the lack of effective ways to incorporate inter-landmark spatial dependency into the detection step. In this paper, we propose a collaborative landmark detection framework to address these limitations. The concept of collaboration is reflected in two aspects. (1) Multi-resolution collaboration. A multi-resolution strategy is proposed to hierarchically localise landmarks by gradually excluding uninformative votes from faraway voxels. Moreover, for informative voxels near the landmark, a spherical sampling strategy is also designed at the training stage to improve their prediction accuracy. (2) Inter-landmark collaboration. A confidence-based landmark detection strategy is proposed to improve the detection accuracy of ‘difficult-to-detect’ landmarks by using spatial guidance from ‘easy-to-detect’ landmarks. To evaluate our method, we conducted experiments extensively on three datasets for detecting prostate landmarks and head & neck landmarks in computed tomography images, and also dental landmarks in cone beam computed tomography images. The results show the effectiveness of our collaborative landmark detection framework in improving landmark detection accuracy, compared to other state-of-the-art methods.

  6. Logistic Regression Applied to Seismic Discrimination

    SciTech Connect

    BG Amindan; DN Hagedorn

    1998-10-08

    The usefulness of logistic discrimination was examined in an effort to learn how it performs in a regional seismic setting. Logistic discrimination provides an easily understood method, works with user-defined models and few assumptions about the population distributions, and handles both continuous and discrete data. Seismic event measurements from a data set compiled by Los Alamos National Laboratory (LANL) of Chinese events recorded at station WMQ were used in this demonstration study. PNNL applied logistic regression techniques to the data. All possible combinations of the Lg and Pg measurements were tried, and a best-fit logistic model was created. The best combination of Lg and Pg frequencies for predicting the source of a seismic event (earthquake or explosion) used Lg{sub 3.0-6.0} and Pg{sub 3.0-6.0} as the predictor variables. A cross-validation test was run, which showed that this model was able to correctly predict 99.7% earthquakes and 98.0% explosions for this given data set. Two other models were identified that used Pg and Lg measurements from the 1.5 to 3.0 Hz frequency range. Although these other models did a good job of correctly predicting the earthquakes, they were not as effective at predicting the explosions. Two possible biases were discovered which affect the predicted probabilities for each outcome. The first bias was due to this being a case-controlled study. The sampling fractions caused a bias in the probabilities that were calculated using the models. The second bias is caused by a change in the proportions for each event. If at a later date the proportions (a priori probabilities) of explosions versus earthquakes change, this would cause a bias in the predicted probability for an event. When using logistic regression, the user needs to be aware of the possible biases and what affect they will have on the predicted probabilities.

  7. Cervical Cancer Regression Measured Using Weekly Magnetic Resonance Imaging During Fractionated Radiotherapy: Radiobiologic Modeling and Correlation With Tumor Hypoxia

    SciTech Connect

    Lim, Karen; Chan, Philip; Haider, Masoom; Cho, Young-Bin; Hill, Richard P.; Milosevic, Michael

    2008-01-01

    Purpose: To measure regression of cancer of the uterine cervix during external beam radiotherapy using magnetic resonance imaging, derive radiobiologic parameters from a mathematical model of tumor regression, and compare these parameters with the pretreatment measurements of tumor hypoxia. Methods and Materials: A total of 27 eligible patients undergoing external beam radiotherapy for cervical cancer underwent weekly magnetic resonance imaging scans. The tumor volume was assessed on each of these scans and the rate of regression plotted. A radiobiologic model was formulated to simulate the effect on tumor regression of the surviving proportion of cells after 2 Gy (SP{sub 2}), the cell clearance constant (clearance of irreparably damaged cells from the tumor [T{sub c}]), and accelerated repopulation. Nonlinear regression analysis was used to fit the radiobiologic model to the magnetic resonance imaging-derived tumor volumes and to derive the estimates of SP{sub 2} and T{sub c} for each patient. These were compared to the pretreatment hypoxia measurements. Results: The initial tumor volume was 8-209 cm{sup 3}. The relative reduction in volume during treatment was 0.02-0.79. The simulations using representative values of the independent biologic variables derived from published data showed SP{sub 2} and T{sub c} to strongly influence the shape of the volume-response curves. Nonlinear regression analysis yielded a median SP{sub 2} of 0.71 and median T{sub c} of 10 days. Tumors with a high SP{sub 2} >0.71 were significantly more hypoxic at diagnosis (p = 0.02). Conclusion: The results of our study have shown that cervical cancer regresses during external beam radiotherapy, although marked variability is present among patients and is influenced by underlying biologic processes, including cellular sensitivity to radiotherapy and proliferation. Better understanding of the biologic mechanisms might facilitate novel adaptive treatment strategies in future studies.

  8. Nonlinear electrostatic drift Kelvin-Helmholtz instability

    NASA Technical Reports Server (NTRS)

    Sharma, Avadhesh C.; Srivastava, Krishna M.

    1993-01-01

    Nonlinear analysis of electrostatic drift Kelvin-Helmholtz instability is performed. It is shown that the analysis leads to the propagation of the weakly nonlinear dispersive waves, and the nonlinear behavior is governed by the nonlinear Burger's equation.

  9. Differences scores: regression-based reliable difference and the regression-based confidence interval.

    PubMed

    Charter, Richard A

    2009-04-01

    Over 50 years ago Payne and Jones (1957) developed what has been labeled the traditional reliable difference formula that continues to be useful as a significance test for the difference between two test scores. The traditional reliable difference is based on the standard error of measurement (SEM) and has been updated to a confidence interval approach. As an alternative to the traditional reliable difference, this article presents the regression-based reliable difference that is based on the standard error of estimate (SEE) and estimated true scores. This new approach should be attractive to clinicians preferring the idea of scores regressing toward the mean. The new approach is also presented in confidence interval form with an interpretation that can be viewed as a statement of all hypotheses that are tenable and consistent with the observed data and has the backing of several authorities. Two well-known conceptualizations for true score confidence intervals are the traditional and regression-based. Now clinicians favoring the regression-based conceptualization are not restricted to the use of traditional model when testing score differences using confidence intervals.

  10. Least-Squares Linear Regression and Schrodinger's Cat: Perspectives on the Analysis of Regression Residuals.

    ERIC Educational Resources Information Center

    Hecht, Jeffrey B.

    The analysis of regression residuals and detection of outliers are discussed, with emphasis on determining how deviant an individual data point must be to be considered an outlier and the impact that multiple suspected outlier data points have on the process of outlier determination and treatment. Only bivariate (one dependent and one independent)…

  11. Optothermal nonlinearity of silica aerogel

    NASA Astrophysics Data System (ADS)

    Braidotti, Maria Chiara; Gentilini, Silvia; Fleming, Adam; Samuels, Michiel C.; Di Falco, Andrea; Conti, Claudio

    2016-07-01

    We report on the characterization of silica aerogel thermal optical nonlinearity, obtained by z-scan technique. The results show that typical silica aerogels have nonlinear optical coefficient similar to that of glass (≃10-12 m2/W), with negligible optical nonlinear absorption. The nonlinear coefficient can be increased to values in the range of 10-10 m2/W by embedding an absorbing dye in the aerogel. This value is one order of magnitude higher than that observed in the pure dye and in typical highly nonlinear materials like liquid crystals.

  12. Nonlinear computer-generated holograms

    NASA Astrophysics Data System (ADS)

    Shapira, Asia; Juwiler, Irit; Arie, Ady

    2011-08-01

    We propose a novel technique for arbitrary wavefront shaping in quadratic nonlinear crystals by introducing the concept of computer-generated holograms (CGHs) into the nonlinear optical regime. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into the first three Hermite--Gaussian beams at the second harmonic in a stoichiometric lithium tantalate nonlinear crystal, and we characterize its efficiency dependence on the fundamental power and the crystal temperature. Nonlinear CGHs open new possibilities in the fields of nonlinear beam shaping, mode conversion, and beam steering.

  13. Genomic selection using regularized linear regression models: ridge regression, lasso, elastic net and their extensions

    PubMed Central

    2012-01-01

    Background Genomic selection (GS) is emerging as an efficient and cost-effective method for estimating breeding values using molecular markers distributed over the entire genome. In essence, it involves estimating the simultaneous effects of all genes or chromosomal segments and combining the estimates to predict the total genomic breeding value (GEBV). Accurate prediction of GEBVs is a central and recurring challenge in plant and animal breeding. The existence of a bewildering array of approaches for predicting breeding values using markers underscores the importance of identifying approaches able to efficiently and accurately predict breeding values. Here, we comparatively evaluate the predictive performance of six regularized linear regression methods-- ridge regression, ridge regression BLUP, lasso, adaptive lasso, elastic net and adaptive elastic net-- for predicting GEBV using dense SNP markers. Methods We predicted GEBVs for a quantitative trait using a dataset on 3000 progenies of 20 sires and 200 dams and an accompanying genome consisting of five chromosomes with 9990 biallelic SNP-marker loci simulated for the QTL-MAS 2011 workshop. We applied all the six methods that use penalty-based (regularization) shrinkage to handle datasets with far more predictors than observations. The lasso, elastic net and their adaptive extensions further possess the desirable property that they simultaneously select relevant predictive markers and optimally estimate their effects. The regression models were trained with a subset of 2000 phenotyped and genotyped individuals and used to predict GEBVs for the remaining 1000 progenies without phenotypes. Predictive accuracy was assessed using the root mean squared error, the Pearson correlation between predicted GEBVs and (1) the true genomic value (TGV), (2) the true breeding value (TBV) and (3) the simulated phenotypic values based on fivefold cross-validation (CV). Results The elastic net, lasso, adaptive lasso and the

  14. Nonlinear metamaterials for holography

    NASA Astrophysics Data System (ADS)

    Almeida, Euclides; Bitton, Ora; Prior, Yehiam

    2016-08-01

    A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three-dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years, it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multilayer metamaterial holograms. A background free image is formed at a new frequency--the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analysed and prospects for future device applications are discussed.

  15. Nonlinear metamaterials for holography

    PubMed Central

    Almeida, Euclides; Bitton, Ora

    2016-01-01

    A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three-dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years, it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multilayer metamaterial holograms. A background free image is formed at a new frequency—the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analysed and prospects for future device applications are discussed. PMID:27545581

  16. Nonlinear Magnetic Beach

    NASA Astrophysics Data System (ADS)

    Arefiev, A.; Breizman, B.

    2000-10-01

    The ion response to the rf-field in the magnetic beach problem can be essentially nonlinear. This paper presents a self-consistent theory of the rf-wave propagation and ion motion through the ion cyclotron resonance. An important ingredient of the problem is the ion flow along the magnetic field. The flow velocity limits the time the ions spend at the resonance, which in turn limits the ion energy gain. A feature that makes the problem nonlinear is that the flow accelerates under the effect of the grad B force and rf-pressure. This acceleration can produce a steep decrease in the plasma density at the resonance, resulting in partial reflection of the incident wave. *Work supported by VASIMR project at NASA and by U.S. DOE Contract DE-FG03-96ER-54346.

  17. Nonlinear Photonics 2014: introduction.

    PubMed

    Akhmediev, N; Kartashov, Yaroslav

    2015-01-12

    International Conference "Nonlinear Photonics-2014" took place in Barcelona, Spain on July 27-31, 2014. It was a part of the "Advanced Photonics Congress" which is becoming a traditional notable event in the world of photonics. The current focus issue of Optics Express contains contributions from the participants of the Conference and the Congress. The articles in this focus issue by no means represent the total number of the congress contributions (around 400). However, it demonstrates wide range of topics covered at the event. The next conference of this series is to be held in 2016 in Australia, which is the home of many researchers working in the field of photonics in general and nonlinear photonics in particular.

  18. Augmented nonlinear differentiator design

    NASA Astrophysics Data System (ADS)

    Shao, Xingling; Liu, Jun; Yang, Wei; Tang, Jun; Li, Jie

    2017-06-01

    This paper presents a sigmoid function based augmented nonlinear differentiator (AND) for calculating the noise-less time derivative from a noisy measurement. The prominent advantages of the present differentiation technique are: (i) compared to the existing tracking differentiators, better noise suppression ability can be achieved without appreciable delay; (ii) the enhanced noise-filtering mechanism not only can be applied to the designed differentiator, but also can be extended for improving noise-tolerance capability of the available differentiators. In addition, the convergence property and robustness performance against noises are investigated via singular perturbation theory and describing function method, respectively. Also, comparison with several classical differentiators is given to illustrate the superiority of AND in noise suppression. Finally, applications on autopilot design and displacement following for nonlinear mass spring mechanical system are given to demonstrate the effectiveness and applicability of the proposed AND technique.

  19. Nonlinear differential equations

    SciTech Connect

    Dresner, L.

    1988-01-01

    This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.

  20. Nonlinear terahertz superconducting plasmonics

    NASA Astrophysics Data System (ADS)

    Wu, Jingbo; Zhang, Caihong; Liang, Lanju; Jin, Biaobing; Kawayama, Iwao; Murakami, Hironaru; Kang, Lin; Xu, Weiwei; Wang, Huabing; Chen, Jian; Tonouchi, Masayoshi; Wu, Peiheng

    2014-10-01

    Nonlinear terahertz (THz) transmission through subwavelength hole array in superconducting niobium nitride (NbN) film is experimentally investigated using intense THz pulses. The good agreement between the measurement and numerical simulations indicates that the field strength dependent transmission mainly arises from the nonlinear properties of the superconducting film. Under weak THz pulses, the transmission peak can be tuned over a frequency range of 145 GHz which is attributed to the high kinetic inductance of 50 nm-thick NbN film. Utilizing the THz pump-THz probe spectroscopy, we study the dynamic process of transmission spectra and demonstrate that the transition time of such superconducting plasmonic device is within 5 ps.

  1. Research in nonlinear structural and solid mechanics

    NASA Technical Reports Server (NTRS)

    Mccomb, H. G., Jr. (Compiler); Noor, A. K. (Compiler)

    1980-01-01

    Nonlinear analysis of building structures and numerical solution of nonlinear algebraic equations and Newton's method are discussed. Other topics include: nonlinear interaction problems; solution procedures for nonlinear problems; crash dynamics and advanced nonlinear applications; material characterization, contact problems, and inelastic response; and formulation aspects and special software for nonlinear analysis.

  2. Nonlinear Guided Waves

    DTIC Science & Technology

    1991-08-19

    experiments," contributed paper, topical meeting on Integrated Photonics , Hilton Head (1990). 20. S. Trillo, S. Wabnitz, B. Diano, and E. M. Wright...34Picosecond pulse switching in semiconductor active nonlinear directional couplers," contributed paper, topical meeting on Integrated Photonics , Hilton...meeting on Integrated Photonics , Hilton Head (1990). 22. E. M. Wright, "Amplifier and laser switches," invited paper, workshop on Semiconductor Laser

  3. Nonlinear Neural Network Oscillator.

    DTIC Science & Technology

    A nonlinear oscillator (10) includes a neural network (12) having at least one output (12a) for outputting a one dimensional vector. The neural ... neural network and the input of the input layer for modifying a magnitude and/or a polarity of the one dimensional output vector prior to the sample of...first or a second direction. Connection weights of the neural network are trained on a deterministic sequence of data from a chaotic source or may be a

  4. Mathematical Nonlinear Optics

    DTIC Science & Technology

    1998-09-11

    34Evolution of Bloch electrons with Applied Electromagnetic Fields: the Semiclassical Equations ", European Jour- nal of Applied Mathematics (1996...establishment (with Jalal Shatah) of the existence of homoclinic orbits with complex spa- tial structure for perturbed NLS equations . This existence...a very small amount of diffraction. (v) McLaughlin (with T. Ueda) have in progress a study of precursors for model nonlinear wave equations . This

  5. Mathematical Nonlinear Optics

    DTIC Science & Technology

    1994-01-03

    August, 1991. Thesis - "Applications of the Inverse Spectral Transform to a Korteweg - DeVries Equation with a Kuramoto-Sivashinsky-Type Perturbation... equations , the mathematical theory of nematic optics involves strong coupling between the electromagnetic and nematic director (molecular orientation... equations for the electric field E coupled to a nonlinear parabolic equation for the director n, a field of unit vectors which describes the local molecular

  6. Surface nonlinear optics

    SciTech Connect

    Shen, Y.R.; Chen, C.K.; de Castro, A.R.B.

    1980-01-01

    Surface electromagnetic waves are waves propagating along the interface of two media. Their existence was predicted by Sommerfield in 1909. In recent years, interesting applications have been found in the study of overlayers and molecular adsorption on surfaces, in probing of phase transitions, and in measurements of refractive indices. In the laboratory, the nonlinear interaction of surface electromagnetic waves were studied. The preliminary results of this recent venture in this area are presented.

  7. Nonlinear Wave Propagation

    DTIC Science & Technology

    2009-02-09

    of parameters. Hence one expects that the solutions of the two equations , PES and NLS, are comparable. In Fig. 3 we plot the two solutions for...power saturated term, in the PES equation ) have stable soliton solutions or mode-locking evolution. In general the solitons are found to be unstable...literature. Generally speaking, the above lattice equations omitting nonlinear terms have solutions propagating along z direction, i.e., ψ(r, z) = e−iµzϕ(r

  8. Nonlinear Wave Propagation

    DTIC Science & Technology

    1983-12-30

    Equation * Discrete IST and numerical simulations * Long time asymptotic solutions of nonlinear evolution equations * Painlevf equations . Focussing...larger class of solutions io KdV than does the Gel’fand-’Levitan equation . Specifically we have shown by direct calculation that if 0(k;x,t) solves oV...Investigation of the full generality of the solutions of KdV via this new formulation. (b) Developnent of similar types - integral equations for

  9. Nonlinear Wave Propagation.

    DTIC Science & Technology

    1987-11-23

    generalized wave equation (GWE) when (z) 0 (1-Z2)/2: - X(z). (1.5) The compatibility condition required for the existence of solutions to these B~icklund...Phys. tion of a class of nonlocal nonlinear evolution equations , A 15 (1982) 781. INS *47, Clarkson University (1985), to be published in J. Math... semilinear form. The above approach will fail if there exist linearizable quasilinear equations which can not be mapped to a semilinear from. It is shown in

  10. Cognitive Nonlinear Radar

    DTIC Science & Technology

    2013-01-01

    Devices and Method for Detecting Emplacement of Improvised Explosive Devices, U. S. Patent 7,680,599, Mar. 16, 2010. 11. Steele, D.; Rotondo, F.; Houck...Patent 7,987,068, Jul. 26, 2011. 9 14. Keller, W. Active Improvised Explosive Device (IED) Electronic Signature Detection , U. S. Patent...operate without interfering with each other. The CNR uses a narrowband, nonlinear radar target detection methodology. This methodology has the advantage

  11. Filamentation with nonlinear Bessel vortices.

    PubMed

    Jukna, V; Milián, C; Xie, C; Itina, T; Dudley, J; Courvoisier, F; Couairon, A

    2014-10-20

    We present a new type of ring-shaped filaments featured by stationary nonlinear high-order Bessel solutions to the laser beam propagation equation. Two different regimes are identified by direct numerical simulations of the nonlinear propagation of axicon focused Gaussian beams carrying helicity in a Kerr medium with multiphoton absorption: the stable nonlinear propagation regime corresponds to a slow beam reshaping into one of the stationary nonlinear high-order Bessel solutions, called nonlinear Bessel vortices. The region of existence of nonlinear Bessel vortices is found semi-analytically. The influence of the Kerr nonlinearity and nonlinear losses on the beam shape is presented. Direct numerical simulations highlight the role of attractors played by nonlinear Bessel vortices in the stable propagation regime. Large input powers or small cone angles lead to the unstable propagation regime where nonlinear Bessel vortices break up into an helical multiple filament pattern or a more irregular structure. Nonlinear Bessel vortices are shown to be sufficiently intense to generate a ring-shaped filamentary ionized channel in the medium which is foreseen as opening the way to novel applications in laser material processing of transparent dielectrics.

  12. Spatial vulnerability assessments by regression kriging

    NASA Astrophysics Data System (ADS)

    Pásztor, László; Laborczi, Annamária; Takács, Katalin; Szatmári, Gábor

    2016-04-01

    information representing IEW or GRP forming environmental factors were taken into account to support the spatial inference of the locally experienced IEW frequency and measured GRP values respectively. An efficient spatial prediction methodology was applied to construct reliable maps, namely regression kriging (RK) using spatially exhaustive auxiliary data on soil, geology, topography, land use and climate. RK divides the spatial inference into two parts. Firstly the deterministic component of the target variable is determined by a regression model. The residuals of the multiple linear regression analysis represent the spatially varying but dependent stochastic component, which are interpolated by kriging. The final map is the sum of the two component predictions. Application of RK also provides the possibility of inherent accuracy assessment. The resulting maps are characterized by global and local measures of its accuracy. Additionally the method enables interval estimation for spatial extension of the areas of predefined risk categories. All of these outputs provide useful contribution to spatial planning, action planning and decision making. Acknowledgement: Our work was partly supported by the Hungarian National Scientific Research Foundation (OTKA, Grant No. K105167).

  13. Nonlinear gyrokinetic equations

    SciTech Connect

    Dubin, D.H.E.; Krommes, J.A.; Oberman, C.; Lee, W.W.

    1983-03-01

    Nonlinear gyrokinetic equations are derived from a systematic Hamiltonian theory. The derivation employs Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asymptotically small gyroradius. For definiteness, we emphasize the limit of electrostatic fluctuations in slab geometry; however, there is a straight-forward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and various of its limits are considered. The weak turbulence theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev is derived from an asystematic truncation of the equations, implying that this equation fails to consider all gyrokinetic effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry-Horton and Hasegawa-Mima equations as limiting cases of our theory, several new nonlinear terms absent from conventional theories appear and are discussed.

  14. Is this scaling nonlinear?

    PubMed Central

    2016-01-01

    One of the most celebrated findings in complex systems in the last decade is that different indexes y (e.g. patents) scale nonlinearly with the population x of the cities in which they appear, i.e. y∼xβ,β≠1. More recently, the generality of this finding has been questioned in studies that used new databases and different definitions of city boundaries. In this paper, we investigate the existence of nonlinear scaling, using a probabilistic framework in which fluctuations are accounted for explicitly. In particular, we show that this allows not only to (i) estimate β and confidence intervals, but also to (ii) quantify the evidence in favour of β≠1 and (iii) test the hypothesis that the observations are compatible with the nonlinear scaling. We employ this framework to compare five different models to 15 different datasets and we find that the answers to points (i)–(iii) crucially depend on the fluctuations contained in the data, on how they are modelled, and on the fact that the city sizes are heavy-tailed distributed. PMID:27493764

  15. Quantum well nonlinear microcavities

    NASA Astrophysics Data System (ADS)

    Oudar, J. L.; Kuszelewicz, R.; Sfez, B.; Pellat, D.; Azoulay, R.

    We report on recent progress in reducing the power threshold of all-optical bistable quantum well vertical microcavities. Significant improvements are achieved through an increase of the cavity finesse, together with a reduction of the device active layer thickness. A critical intensity of 5 μW/μm 2 has been observed on a microcavity of finesse 250, with a nonlinear medium of only 18 GaAs quantum wells of 10 nm thickness. Further improvements of the Bragg mirror quality resulted in a finesse of 700 and a power-lifetime product of 15 fJ/μm 2. Microresonator pixellation allows to obtain 2-dimensional arrays. A thermally-induced alloy-mixing technique is described, which produced a 110 meV carrier confinement energy, together with a refractive index change of -.012, averaged over the 2.6 μm nonlinear medium thickness. The resulting electrical and optical confinement is shown to improve the nonlinear characteristics, by limiting lateral carrier diffusion and light diffraction.

  16. Regression-kriging for characterizing soils with remotesensing data

    NASA Astrophysics Data System (ADS)

    Ge, Yufeng; Thomasson, J. Alex; Sui, Ruixiu; Wooten, James

    2011-09-01

    In precision agriculture regression has been used widely to quantify the relationship between soil attributes and other environmental variables. However, spatial correlation existing in soil samples usually violates a basic assumption of regression: sample independence. In this study, a regression-kriging method was attempted in relating soil properties to the remote sensing image of a cotton field near Vance, Mississippi, USA. The regression-kriging model was developed and tested by using 273 soil samples collected from the field. The result showed that by properly incorporating the spatial correlation information of regression residuals, the regression-kriging model generally achieved higher prediction accuracy than the stepwise multiple linear regression model. Most strikingly, a 50% increase in prediction accuracy was shown in soil sodium concentration. Potential usages of regression-kriging in future precision agriculture applications include real-time soil sensor development and digital soil mapping.

  17. Poisson Mixture Regression Models for Heart Disease Prediction.

    PubMed

    Mufudza, Chipo; Erol, Hamza

    2016-01-01

    Early heart disease control can be achieved by high disease prediction and diagnosis efficiency. This paper focuses on the use of model based clustering techniques to predict and diagnose heart disease via Poisson mixture regression models. Analysis and application of Poisson mixture regression models is here addressed under two different classes: standard and concomitant variable mixture regression models. Results show that a two-component concomitant variable Poisson mixture regression model predicts heart disease better than both the standard Poisson mixture regression model and the ordinary general linear Poisson regression model due to its low Bayesian Information Criteria value. Furthermore, a Zero Inflated Poisson Mixture Regression model turned out to be the best model for heart prediction over all models as it both clusters individuals into high or low risk category and predicts rate to heart disease componentwise given clusters available. It is deduced that heart disease prediction can be effectively done by identifying the major risks componentwise using Poisson mixture regression model.

  18. Automation of Flight Software Regression Testing

    NASA Technical Reports Server (NTRS)

    Tashakkor, Scott B.

    2016-01-01

    NASA is developing the Space Launch System (SLS) to be a heavy lift launch vehicle supporting human and scientific exploration beyond earth orbit. SLS will have a common core stage, an upper stage, and different permutations of boosters and fairings to perform various crewed or cargo missions. Marshall Space Flight Center (MSFC) is writing the Flight Software (FSW) that will operate the SLS launch vehicle. The FSW is developed in an incremental manner based on "Agile" software techniques. As the FSW is incrementally developed, testing the functionality of the code needs to be performed continually to ensure that the integrity of the software is maintained. Manually testing the functionality on an ever-growing set of requirements and features is not an efficient solution and therefore needs to be done automatically to ensure testing is comprehensive. To support test automation, a framework for a regression test harness has been developed and used on SLS FSW. The test harness provides a modular design approach that can compile or read in the required information specified by the developer of the test. The modularity provides independence between groups of tests and the ability to add and remove tests without disturbing others. This provides the SLS FSW team a time saving feature that is essential to meeting SLS Program technical and programmatic requirements. During development of SLS FSW, this technique has proved to be a useful tool to ensure all requirements have been tested, and that desired functionality is maintained, as changes occur. It also provides a mechanism for developers to check functionality of the code that they have developed. With this system, automation of regression testing is accomplished through a scheduling tool and/or commit hooks. Key advantages of this test harness capability includes execution support for multiple independent test cases, the ability for developers to specify precisely what they are testing and how, the ability to add

  19. Testing the gonadal regression-cytoprotection hypothesis.

    PubMed

    Crawford, B A; Spaliviero, J A; Simpson, J M; Handelsman, D J

    1998-11-15

    Germinal damage is an almost universal accompaniment of cancer treatment as the result of bystander damage to the testis from cytotoxic drugs and/or irradiation. Cancer treatment for the most common cancers of the reproductive age group in men has improved such that most are now treated with curative intent, and many others are treated with likelihood of prolonged survival, so that the preservation of fertility is an important component of posttreatment quality of life. This has led to the consideration of developing adjuvant treatments that may reduce the gonadal toxicity of cancer therapy. One dominant hypothesis has been based on the supposition that the immature testis was resistant to cytotoxin damage. Hence, if hormonal treatment were able to cause spermatogenic regression to an immature state via an effective withdrawal of gonadotrophin secretion, the testis might be maintained temporarily in a protected state during cytotoxin exposure. However, clinical studies have been disappointing but have also been unable to test the hypothesis definitively thus far, due to the inability to completely suppress gonadotrophin secretion. Similarly, experimental models have also given conflicting results and, at best, a modest cytoprotection. To definitively test this hypothesis experimentally, we used the fact that the functionally hpg mouse has complete gonadotrophin deficiency but can undergo the induction of full spermatogenesis by testosterone. Thus, if complete gonadotrophin deficiency were an advantage during cytotoxin exposure, then the hpg mouse should exhibit some degree of germinal protection against cytotoxin-induced damage. We therefore administered three different cytotoxins (200 mg/kg procarbazine, 9 mg/kg doxorubicin, 8 Gy of X irradiation) to produce a range of severity in testicular damage and mechanism of action to either phenotypically normal or hpg mice. Testis weight and homogenization-resistant spermatid numbers were measured to evaluate the

  20. Survival Regression Modeling Strategies in CVD Prediction

    PubMed Central

    Barkhordari, Mahnaz; Padyab, Mojgan; Sardarinia, Mahsa; Hadaegh, Farzad; Azizi, Fereidoun; Bozorgmanesh, Mohammadreza

    2016-01-01

    Background A fundamental part of prevention is prediction. Potential predictors are the sine qua non of prediction models. However, whether incorporating novel predictors to prediction models could be directly translated to added predictive value remains an area of dispute. The difference between the predictive power of a predictive model with (enhanced model) and without (baseline model) a certain predictor is generally regarded as an indicator of the predictive value added by that predictor. Indices such as discrimination and calibration have long been used in this regard. Recently, the use of added predictive value has been suggested while comparing the predictive performances of the predictive models with and without novel biomarkers. Objectives User-friendly statistical software capable of implementing novel statistical procedures is conspicuously lacking. This shortcoming has restricted implementation of such novel model assessment methods. We aimed to construct Stata commands to help researchers obtain the aforementioned statistical indices. Materials and Methods We have written Stata commands that are intended to help researchers obtain the following. 1, Nam-D’Agostino X2 goodness of fit test; 2, Cut point-free and cut point-based net reclassification improvement index (NRI), relative absolute integrated discriminatory improvement index (IDI), and survival-based regression analyses. We applied the commands to real data on women participating in the Tehran lipid and glucose study (TLGS) to examine if information relating to a family history of premature cardiovascular disease (CVD), waist circumference, and fasting plasma glucose can improve predictive performance of Framingham’s general CVD risk algorithm. Results The command is adpredsurv for survival models. Conclusions Herein we have described the Stata package “adpredsurv” for calculation of the Nam-D’Agostino X2 goodness of fit test as well as cut point-free and cut point-based NRI, relative

  1. Laplacian embedded regression for scalable manifold regularization.

    PubMed

    Chen, Lin; Tsang, Ivor W; Xu, Dong

    2012-06-01

    Semi-supervised learning (SSL), as a powerful tool to learn from a limited number of labeled data and a large number of unlabeled data, has been attracting increasing attention in the machine learning community. In particular, the manifold regularization framework has laid solid theoretical foundations for a large family of SSL algorithms, such as Laplacian support vector machine (LapSVM) and Laplacian regularized least squares (LapRLS). However, most of these algorithms are limited to small scale problems due to the high computational cost of the matrix inversion operation involved in the optimization problem. In this paper, we propose a novel framework called Laplacian embedded regression by introducing an intermediate decision variable into the manifold regularization framework. By using ∈-insensitive loss, we obtain the Laplacian embedded support vector regression (LapESVR) algorithm, which inherits the sparse solution from SVR. Also, we derive Laplacian embedded RLS (LapERLS) corresponding to RLS under the proposed framework. Both LapESVR and LapERLS possess a simpler form of a transformed kernel, which is the summation of the original kernel and a graph kernel that captures the manifold structure. The benefits of the transformed kernel are two-fold: (1) we can deal with the original kernel matrix and the graph Laplacian matrix in the graph kernel separately and (2) if the graph Laplacian matrix is sparse, we only need to perform the inverse operation for a sparse matrix, which is much more efficient when compared with that for a dense one. Inspired by kernel principal component analysis, we further propose to project the introduced decision variable into a subspace spanned by a few eigenvectors of the graph Laplacian matrix in order to better reflect the data manifold, as well as accelerate the calculation of the graph kernel, allowing our methods to efficiently and effectively cope with large scale SSL problems. Extensive experiments on both toy and real

  2. Relationship between Multiple Regression and Selected Multivariable Methods.

    ERIC Educational Resources Information Center

    Schumacker, Randall E.

    The relationship of multiple linear regression to various multivariate statistical techniques is discussed. The importance of the standardized partial regression coefficient (beta weight) in multiple linear regression as it is applied in path, factor, LISREL, and discriminant analyses is emphasized. The multivariate methods discussed in this paper…

  3. Using Dominance Analysis to Determine Predictor Importance in Logistic Regression

    ERIC Educational Resources Information Center

    Azen, Razia; Traxel, Nicole

    2009-01-01

    This article proposes an extension of dominance analysis that allows researchers to determine the relative importance of predictors in logistic regression models. Criteria for choosing logistic regression R[superscript 2] analogues were determined and measures were selected that can be used to perform dominance analysis in logistic regression. A…

  4. Using Time-Series Regression to Predict Academic Library Circulations.

    ERIC Educational Resources Information Center

    Brooks, Terrence A.

    1984-01-01

    Four methods were used to forecast monthly circulation totals in 15 midwestern academic libraries: dummy time-series regression, lagged time-series regression, simple average (straight-line forecasting), monthly average (naive forecasting). In tests of forecasting accuracy, dummy regression method and monthly mean method exhibited smallest average…

  5. Orthogonal Projection in Teaching Regression and Financial Mathematics

    ERIC Educational Resources Information Center

    Kachapova, Farida; Kachapov, Ilias

    2010-01-01

    Two improvements in teaching linear regression are suggested. The first is to include the population regression model at the beginning of the topic. The second is to use a geometric approach: to interpret the regression estimate as an orthogonal projection and the estimation error as the distance (which is minimized by the projection). Linear…

  6. NUCLEI SEGMENTATION VIA SPARSITY CONSTRAINED CONVOLUTIONAL REGRESSION

    PubMed Central

    Zhou, Yin; Chang, Hang; Barner, Kenneth E.; Parvin, Bahram

    2017-01-01

    Automated profiling of nuclear architecture, in histology sections, can potentially help predict the clinical outcomes. However, the task is challenging as a result of nuclear pleomorphism and cellular states (e.g., cell fate, cell cycle), which are compounded by the batch effect (e.g., variations in fixation and staining). Present methods, for nuclear segmentation, are based on human-designed features that may not effectively capture intrinsic nuclear architecture. In this paper, we propose a novel approach, called sparsity constrained convolutional regression (SCCR), for nuclei segmentation. Specifically, given raw image patches and the corresponding annotated binary masks, our algorithm jointly learns a bank of convolutional filters and a sparse linear regressor, where the former is used for feature extraction, and the latter aims to produce a likelihood for each pixel being nuclear region or background. During classification, the pixel label is simply determined by a thresholding operation applied on the likelihood map. The method has been evaluated using the benchmark dataset collected from The Cancer Genome Atlas (TCGA). Experimental results demonstrate that our method outperforms traditional nuclei segmentation algorithms and is able to achieve competitive performance compared to the state-of-the-art algorithm built upon human-designed features with biological prior knowledge. PMID:28101301

  7. Semiparametric Bayesian Regression with Applications in Astronomy

    NASA Astrophysics Data System (ADS)

    Broadbent, Mary Elizabeth

    In this thesis we describe a class of Bayesian semiparametric models, known as Levy Adaptive Regression Kernels (LARK); a novel method for posterior computation for those models; and the applications of these models in astronomy, in particular to the analysis of the photon fluence time series of gamma-ray bursts. Gamma-ray bursts are bursts of photons which arrive in a varying number of overlapping pulses with a distinctive "fast-rise, exponential decay" shape in the time domain. LARK models allow us to do inference both on the number of pulses, but also on the parameters which describe the pulses, such as incident time, or decay rate. In Chapter 2, we describe a novel method to aid posterior computation in infinitely-divisible models, of which LARK models are a special case, when the posterior is evaluated through Markov chain Monte Carlo. This is applied in Chapter 3, where time series representing the photon fluence in a single energy channel is analyzed using LARK methods. Due to the effect of the discriminators on BATSE and other instruments, it is important to model the gamma-ray bursts in the incident space. Chapter 4 describes the first to model bursts in the incident photon space, instead of after they have been distorted by the discriminators; since to model photons as they enter the detector is to model both the energy and the arrival time of the incident photon, this model is also the first to jointly model the time and energy domains.

  8. A rotor optimization using regression analysis

    NASA Technical Reports Server (NTRS)

    Giansante, N.

    1984-01-01

    The design and development of helicopter rotors is subject to the many design variables and their interactions that effect rotor operation. Until recently, selection of rotor design variables to achieve specified rotor operational qualities has been a costly, time consuming, repetitive task. For the past several years, Kaman Aerospace Corporation has successfully applied multiple linear regression analysis, coupled with optimization and sensitivity procedures, in the analytical design of rotor systems. It is concluded that approximating equations can be developed rapidly for a multiplicity of objective and constraint functions and optimizations can be performed in a rapid and cost effective manner; the number and/or range of design variables can be increased by expanding the data base and developing approximating functions to reflect the expanded design space; the order of the approximating equations can be expanded easily to improve correlation between analyzer results and the approximating equations; gradients of the approximating equations can be calculated easily and these gradients are smooth functions reducing the risk of numerical problems in the optimization; the use of approximating functions allows the problem to be started easily and rapidly from various initial designs to enhance the probability of finding a global optimum; and the approximating equations are independent of the analysis or optimization codes used.

  9. Data selection using support vector regression

    NASA Astrophysics Data System (ADS)

    Richman, Michael B.; Leslie, Lance M.; Trafalis, Theodore B.; Mansouri, Hicham

    2015-03-01

    Geophysical data sets are growing at an ever-increasing rate, requiring computationally efficient data selection (thinning) methods to preserve essential information. Satellites, such as WindSat, provide large data sets for assessing the accuracy and computational efficiency of data selection techniques. A new data thinning technique, based on support vector regression (SVR), is developed and tested. To manage large on-line satellite data streams, observations from WindSat are formed into subsets by Voronoi tessellation and then each is thinned by SVR (TSVR). Three experiments are performed. The first confirms the viability of TSVR for a relatively small sample, comparing it to several commonly used data thinning methods (random selection, averaging and Barnes filtering), producing a 10% thinning rate (90% data reduction), low mean absolute errors (MAE) and large correlations with the original data. A second experiment, using a larger dataset, shows TSVR retrievals with MAE < 1 m s-1 and correlations ⩽ 0.98. TSVR was an order of magnitude faster than the commonly used thinning methods. A third experiment applies a two-stage pipeline to TSVR, to accommodate online data. The pipeline subsets reconstruct the wind field with the same accuracy as the second experiment, is an order of magnitude faster than the nonpipeline TSVR. Therefore, pipeline TSVR is two orders of magnitude faster than commonly used thinning methods that ingest the entire data set. This study demonstrates that TSVR pipeline thinning is an accurate and computationally efficient alternative to commonly used data selection techniques.

  10. Father regression. Clinical narratives and theoretical reflections.

    PubMed

    Stein, Ruth

    2006-08-01

    The author deals with love-hate enthrallment and submission to a primitive paternal object. This is a father-son relationship that extends through increasing degrees of 'primitiveness' or extremeness, and is illustrated through three different constellations that constitute a continuum. One pole of the continuum encompasses certain male patients who show a loving, de-individuated connection to a father experienced as trustworthy, soft, and in need of protection. Further along the continuum is the case of a transsexual patient whose analysis revealed an intense 'God-transference', a bondage to an idealized, feared, and ostensibly protective father-God introject. A great part of this patient's analysis consisted in a fierce struggle to liberate himself from this figure. The other end of the continuum is occupied by religious terrorists, who exemplify the most radical thralldom to a persecutory, godly object, a regressive submission that banishes woman and enthrones a cruel superego, and that ends in destruction and self-destruction. Psychoanalytic thinking has traditionally dealt with the oedipal father and recently with the nurturing father, but there is a gap in thinking about the phallic, archaic father, and his relations with his son(s). The author aims at filling this gap, at the same time as she also raises the very question of 'What is a father?' linking it with literary and religious themes.

  11. Gravitational Wave Emulation Using Gaussian Process Regression

    NASA Astrophysics Data System (ADS)

    Doctor, Zoheyr; Farr, Ben; Holz, Daniel

    2017-01-01

    Parameter estimation (PE) for gravitational wave signals from compact binary coalescences (CBCs) requires reliable template waveforms which span the parameter space. Waveforms from numerical relativity are accurate but computationally expensive, so approximate templates are typically used for PE. These `approximants', while quick to compute, can introduce systematic errors and bias PE results. We describe a machine learning method for generating CBC waveforms and uncertainties using existing accurate waveforms as a training set. Coefficients of a reduced order waveform model are computed and each treated as arising from a Gaussian process. These coefficients and their uncertainties are then interpolated using Gaussian process regression (GPR). As a proof of concept, we construct a training set of approximant waveforms (rather than NR waveforms) in the two-dimensional space of chirp mass and mass ratio and interpolate new waveforms with GPR. We demonstrate that the mismatch between interpolated waveforms and approximants is below the 1% level for an appropriate choice of training set and GPR kernel hyperparameters.

  12. Cyclodextrin promotes atherosclerosis regression via macrophage reprogramming

    PubMed Central

    Zimmer, Sebastian; Grebe, Alena; Bakke, Siril S.; Bode, Niklas; Halvorsen, Bente; Ulas, Thomas; Skjelland, Mona; De Nardo, Dominic; Labzin, Larisa I.; Kerksiek, Anja; Hempel, Chris; Heneka, Michael T.; Hawxhurst, Victoria; Fitzgerald, Michael L; Trebicka, Jonel; Gustafsson, Jan-Åke; Westerterp, Marit; Tall, Alan R.; Wright, Samuel D.; Espevik, Terje; Schultze, Joachim L.; Nickenig, Georg; Lütjohann, Dieter; Latz, Eicke

    2016-01-01

    Atherosclerosis is an inflammatory disease linked to elevated blood cholesterol levels. Despite ongoing advances in the prevention and treatment of atherosclerosis, cardiovascular disease remains the leading cause of death worldwide. Continuous retention of apolipoprotein B-containing lipoproteins in the subendothelial space causes a local overabundance of free cholesterol. Since cholesterol accumulation and deposition of cholesterol crystals (CCs) triggers a complex inflammatory response, we tested the efficacy of the cyclic oligosaccharide 2-hydroxypropyl-β-cyclodextrin (CD), a compound that increases cholesterol solubility, in preventing and reversing atherosclerosis. Here we show that CD treatment of murine atherosclerosis reduced atherosclerotic plaque size and CC load, and promoted plaque regression even with a continued cholesterol-rich diet. Mechanistically, CD increased oxysterol production in both macrophages and human atherosclerotic plaques, and promoted liver X receptor (LXR)-mediated transcriptional reprogramming to improve cholesterol efflux and exert anti-inflammatory effects. In vivo, this CD-mediated LXR agonism was required for the anti-atherosclerotic and anti-inflammatory effects of CD as well as for augmented reverse cholesterol transport. Since CD treatment in humans is safe and CD beneficially affects key mechanisms of atherogenesis, it may therefore be used clinically to prevent or treat human atherosclerosis. PMID:27053774

  13. Cyclodextrin promotes atherosclerosis regression via macrophage reprogramming.

    PubMed

    Zimmer, Sebastian; Grebe, Alena; Bakke, Siril S; Bode, Niklas; Halvorsen, Bente; Ulas, Thomas; Skjelland, Mona; De Nardo, Dominic; Labzin, Larisa I; Kerksiek, Anja; Hempel, Chris; Heneka, Michael T; Hawxhurst, Victoria; Fitzgerald, Michael L; Trebicka, Jonel; Björkhem, Ingemar; Gustafsson, Jan-Åke; Westerterp, Marit; Tall, Alan R; Wright, Samuel D; Espevik, Terje; Schultze, Joachim L; Nickenig, Georg; Lütjohann, Dieter; Latz, Eicke

    2016-04-06

    Atherosclerosis is an inflammatory disease linked to elevated blood cholesterol concentrations. Despite ongoing advances in the prevention and treatment of atherosclerosis, cardiovascular disease remains the leading cause of death worldwide. Continuous retention of apolipoprotein B-containing lipoproteins in the subendothelial space causes a local overabundance of free cholesterol. Because cholesterol accumulation and deposition of cholesterol crystals (CCs) trigger a complex inflammatory response, we tested the efficacy of the cyclic oligosaccharide 2-hydroxypropyl-β-cyclodextrin (CD), a compound that increases cholesterol solubility in preventing and reversing atherosclerosis. We showed that CD treatment of murine atherosclerosis reduced atherosclerotic plaque size and CC load and promoted plaque regression even with a continued cholesterol-rich diet. Mechanistically, CD increased oxysterol production in both macrophages and human atherosclerotic plaques and promoted liver X receptor (LXR)-mediated transcriptional reprogramming to improve cholesterol efflux and exert anti-inflammatory effects. In vivo, this CD-mediated LXR agonism was required for the antiatherosclerotic and anti-inflammatory effects of CD as well as for augmented reverse cholesterol transport. Because CD treatment in humans is safe and CD beneficially affects key mechanisms of atherogenesis, it may therefore be used clinically to prevent or treat human atherosclerosis.

  14. Regression calibration when foods (measured with error) are the variables of interest: markedly non-Gaussian data with many zeroes.

    PubMed

    Fraser, Gary E; Stram, Daniel O

    2012-02-15

    Regression calibration has been described as a means of correcting effects of measurement error for normally distributed dietary variables. When foods are the items of interest, true distributions of intake are often positively skewed, may contain many zeroes, and are usually not described by well-known statistical distributions. The authors considered the validity of regression calibration assumptions where data are non-Gaussian. Such data (including many zeroes) were simulated, and use of the regression calibration algorithm was evaluated. An example used data from Adventist Health Study 2 (2002-2008). In this special situation, a linear calibration model does (as usual) at least approximately correct the parameter that captures the exposure-disease association in the "disease" model. Poor fit in the calibration model does not produce biased calibrated estimates when the "disease" model is linear, and it produces little bias in a nonlinear "disease" model if the model is approximately linear. Poor fit will adversely affect statistical power, but more complex linear calibration models can help here. The authors conclude that non-Gaussian data with many zeroes do not invalidate regression calibration. Irrespective of fit, linear regression calibration in this situation at least approximately corrects bias. More complex linear calibration equations that improve fit may increase power over that of uncalibrated regressions.

  15. Nonlinear models for estimating GSFC travel requirements

    NASA Technical Reports Server (NTRS)

    Buffalano, C.; Hagan, F. J.

    1974-01-01

    A methodology is presented for estimating travel requirements for a particular period of time. Travel models were generated using nonlinear regression analysis techniques on a data base of FY-72 and FY-73 information from 79 GSFC projects. Although the subject matter relates to GSFX activities, the type of analysis used and the manner of selecting the relevant variables would be of interest to other NASA centers, government agencies, private corporations and, in general, any organization with a significant travel budget. Models were developed for each of six types of activity: flight projects (in-house and out-of-house), experiments on non-GSFC projects, international projects, ART/SRT, data analysis, advanced studies, tracking and data, and indirects.

  16. Rank-preserving regression: a more robust rank regression model against outliers.

    PubMed

    Chen, Tian; Kowalski, Jeanne; Chen, Rui; Wu, Pan; Zhang, Hui; Feng, Changyong; Tu, Xin M

    2016-08-30

    Mean-based semi-parametric regression models such as the popular generalized estimating equations are widely used to improve robustness of inference over parametric models. Unfortunately, such models are quite sensitive to outlying observations. The Wilcoxon-score-based rank regression (RR) provides more robust estimates over generalized estimating equations against outliers. However, the RR and its extensions do not sufficiently address missing data arising in longitudinal studies. In this paper, we propose a new approach to address outliers under a different framework based on the functional response models. This functional-response-model-based alternative not only addresses limitations of the RR and its extensions for longitudinal data, but, with its rank-preserving property, even provides more robust estimates than these alternatives. The proposed approach is illustrated with both real and simulated data. Copyright © 2016 John Wiley & Sons, Ltd.

  17. Nonlinear scattering in plasmonic nanostructures

    NASA Astrophysics Data System (ADS)

    Chu, Shi-Wei

    2016-09-01

    Nonlinear phenomena provide novel light manipulation capabilities and innovative applications. Recently, we discovered nonlinear saturation on single-particle scattering of gold nanospheres by continuous-wave laser excitation and innovatively applied to improve microscopic resolution down to λ/8. However, the nonlinearity was limited to the green-orange plasmonic band of gold nanosphere, and the underlying mechanism has not yet been fully understood. In this work, we demonstrated that nonlinear scattering exists for various material/geometry combinations, thus expanding the applicable wavelength range. For near-infrared, gold nanorod is used, while for blue-violet, silver nanospheres are adopted. In terms of mechanism, the nonlinearity may originate from interband/intraband absorption, hot electron, or hot lattice, which are spectrally mixed in the case of gold nanosphere. For gold nanorod and silver nanosphere, nonlinear scattering occurs at plasmonic resonances, which are spectrally far from interband/intraband absorptions, so they are excluded. We found that the nonlinear index is much larger than possible contributions from hot electrons in literature. Therefore, we conclude that hot lattice is the major mechanism. In addition, we propose that similar to z-scan, which is the standard method to characterize nonlinearity of a thin sample, laser scanning microscopy should be adopted as the standard method to characterize nonlinearity from a nanostructure. Our work not only provides the physical mechanism of the nonlinear scattering, but also paves the way toward multi-color superresolution imaging based on non-bleaching plasmonic scattering.

  18. Comparison of stopped Cox regression with direct methods such as pseudo-values and binomial regression.

    PubMed

    van Houwelingen, Hans C; Putter, Hein

    2015-04-01

    By far the most popular model to obtain survival predictions for individual patients is the Cox model. The Cox model does not make any assumptions on the underlying hazard, but it relies heavily on the proportional hazards assumption. The most common ways to circumvent this robustness problem are 1) to categorize patients based on their prognostic risk score and to base predictions on Kaplan-Meier curves for the risk categories, or 2) to include interactions with the covariates and suitable functions of time. Robust estimators of the t(0)-year survival probabilities can also be obtained from a "stopped Cox" regression model, in which all observations are administratively censored at t(0). Other recent approaches to solve this robustness problem, originally proposed in the context of competing risks, are pseudo-values and direct binomial regression, based on unbiased estimating equations. In this paper stopped Cox regression is compared with these direct approaches. This is done by means of a simulation study to assess the biases of the different approaches and an analysis of breast cancer data to get some feeling for the performance in practice. The tentative conclusion is that stopped Cox and direct models agree well if the follow-up is not too long. There are larger differences for long-term follow-up data. There stopped Cox might be more efficient, but less robust.

  19. [Spatial interpolation of soil organic matter using regression Kriging and geographically weighted regression Kriging].

    PubMed

    Yang, Shun-hua; Zhang, Hai-tao; Guo, Long; Ren, Yan

    2015-06-01

    Relative elevation and stream power index were selected as auxiliary variables based on correlation analysis for mapping soil organic matter. Geographically weighted regression Kriging (GWRK) and regression Kriging (RK) were used for spatial interpolation of soil organic matter and compared with ordinary Kriging (OK), which acts as a control. The results indicated that soil or- ganic matter was significantly positively correlated with relative elevation whilst it had a significantly negative correlation with stream power index. Semivariance analysis showed that both soil organic matter content and its residuals (including ordinary least square regression residual and GWR resi- dual) had strong spatial autocorrelation. Interpolation accuracies by different methods were esti- mated based on a data set of 98 validation samples. Results showed that the mean error (ME), mean absolute error (MAE) and root mean square error (RMSE) of RK were respectively 39.2%, 17.7% and 20.6% lower than the corresponding values of OK, with a relative-improvement (RI) of 20.63. GWRK showed a similar tendency, having its ME, MAE and RMSE to be respectively 60.6%, 23.7% and 27.6% lower than those of OK, with a RI of 59.79. Therefore, both RK and GWRK significantly improved the accuracy of OK interpolation of soil organic matter due to their in- corporation of auxiliary variables. In addition, GWRK performed obviously better than RK did in this study, and its improved performance should be attributed to the consideration of sample spatial locations.

  20. Regional flood frequency analysis using spatial proximity and basin characteristics: Quantile regression vs. parameter regression technique

    NASA Astrophysics Data System (ADS)

    Ahn, Kuk-Hyun; Palmer, Richard

    2016-09-01

    Despite wide use of regression-based regional flood frequency analysis (RFFA) methods, the majority are based on either ordinary least squares (OLS) or generalized least squares (GLS). This paper proposes 'spatial proximity' based RFFA methods using the spatial lagged model (SLM) and spatial error model (SEM). The proposed methods are represented by two frameworks: the quantile regression technique (QRT) and parameter regression technique (PRT). The QRT develops prediction equations for flooding quantiles in average recurrence intervals (ARIs) of 2, 5, 10, 20, and 100 years whereas the PRT provides prediction of three parameters for the selected distribution. The proposed methods are tested using data incorporating 30 basin characteristics from 237 basins in Northeastern United States. Results show that generalized extreme value (GEV) distribution properly represents flood frequencies in the study gages. Also, basin area, stream network, and precipitation seasonality are found to be the most effective explanatory variables in prediction modeling by the QRT and PRT. 'Spatial proximity' based RFFA methods provide reliable flood quantile estimates compared to simpler methods. Compared to the QRT, the PRT may be recommended due to its accuracy and computational simplicity. The results presented in this paper may serve as one possible guidepost for hydrologists interested in flood analysis at ungaged sites.

  1. Kepler AutoRegressive Planet Search

    NASA Astrophysics Data System (ADS)

    Feigelson, Eric

    NASA's Kepler mission is the source of more exoplanets than any other instrument, but the discovery depends on complex statistical analysis procedures embedded in the Kepler pipeline. A particular challenge is mitigating irregular stellar variability without loss of sensitivity to faint periodic planetary transits. This proposal presents a two-stage alternative analysis procedure. First, parametric autoregressive ARFIMA models, commonly used in econometrics, remove most of the stellar variations. Second, a novel matched filter is used to create a periodogram from which transit-like periodicities are identified. This analysis procedure, the Kepler AutoRegressive Planet Search (KARPS), is confirming most of the Kepler Objects of Interest and is expected to identify additional planetary candidates. The proposed research will complete application of the KARPS methodology to the prime Kepler mission light curves of 200,000: stars, and compare the results with Kepler Objects of Interest obtained with the Kepler pipeline. We will then conduct a variety of astronomical studies based on the KARPS results. Important subsamples will be extracted including Habitable Zone planets, hot super-Earths, grazing-transit hot Jupiters, and multi-planet systems. Groundbased spectroscopy of poorly studied candidates will be performed to better characterize the host stars. Studies of stellar variability will then be pursued based on KARPS analysis. The autocorrelation function and nonstationarity measures will be used to identify spotted stars at different stages of autoregressive modeling. Periodic variables with folded light curves inconsistent with planetary transits will be identified; they may be eclipsing or mutually-illuminating binary star systems. Classification of stellar variables with KARPS-derived statistical properties will be attempted. KARPS procedures will then be applied to archived K2 data to identify planetary transits and characterize stellar variability.

  2. Deep Human Parsing with Active Template Regression.

    PubMed

    Liang, Xiaodan; Liu, Si; Shen, Xiaohui; Yang, Jianchao; Liu, Luoqi; Dong, Jian; Lin, Liang; Yan, Shuicheng

    2015-12-01

    In this work, the human parsing task, namely decomposing a human image into semantic fashion/body regions, is formulated as an active template regression (ATR) problem, where the normalized mask of each fashion/body item is expressed as the linear combination of the learned mask templates, and then morphed to a more precise mask with the active shape parameters, including position, scale and visibility of each semantic region. The mask template coefficients and the active shape parameters together can generate the human parsing results, and are thus called the structure outputs for human parsing. The deep Convolutional Neural Network (CNN) is utilized to build the end-to-end relation between the input human image and the structure outputs for human parsing. More specifically, the structure outputs are predicted by two separate networks. The first CNN network is with max-pooling, and designed to predict the template coefficients for each label mask, while the second CNN network is without max-pooling to preserve sensitivity to label mask position and accurately predict the active shape parameters. For a new image, the structure outputs of the two networks are fused to generate the probability of each label for each pixel, and super-pixel smoothing is finally used to refine the human parsing result. Comprehensive evaluations on a large dataset well demonstrate the significant superiority of the ATR framework over other state-of-the-arts for human parsing. In particular, the F1-score reaches 64.38 percent by our ATR framework, significantly higher than 44.76 percent based on the state-of-the-art algorithm [28].

  3. Extensive regression in pigmented skin lesions: a dangerous confounding feature

    PubMed Central

    Lallas, Aimilios; Apalla, Zoe; Moscarella, Elvira; Zalaudek, Iris; Tzellos, Thrasivoulos; Lefaki, Ioanna; Cota, Carlo; Argenziano, Giuseppe

    2012-01-01

    Spontaneous regression in melanomas is not an uncommon phenomenon, as it has been described in 10–35% of primary cutaneous lesions [1]. Regression does not appear to predict a more favorable course, since even fully regressed melanomas may progress into metastatic disease [2]. Several dermoscopic features have been correlated with the regression process, including white scar-like depigmented areas and gray-blue, pepper-like granules, which correspond to dermal scarring, pigment incontinence and presence of melanophages [3,4]. Regression may occur not only in melanomas, but also in melanocytic nevi, which similarly may exhibit white areas and gray-blue granules or areas under dermoscopy [5]. Overall, white areas have been proposed to be associated with the fibrosis type of regression and gray-blue areas to the melanosis type of regression of melanocytic tumors [3]. Lichen planus like keratosis (LPLK) is considered to represent a regressed solar lentigo or seborrheic keratosis. Dermoscopy of LPLK at the late stage of the regression process reveals a diffuse gray-blue granular pattern, similar to that observed in regressed melanocytic lesions [6]. In this context, when evaluating skin lesions that exhibit high degree of regression, interpretation of dermoscopic findings may be problematic, especially when no other dermoscopic clues can be recognized. PMID:23785596

  4. Extensive regression in pigmented skin lesions: a dangerous confounding feature.

    PubMed

    Lallas, Aimilios; Apalla, Zoe; Moscarella, Elvira; Zalaudek, Iris; Tzellos, Thrasivoulos; Lefaki, Ioanna; Cota, Carlo; Argenziano, Giuseppe

    2012-04-01

    Spontaneous regression in melanomas is not an uncommon phenomenon, as it has been described in 10-35% of primary cutaneous lesions [1]. Regression does not appear to predict a more favorable course, since even fully regressed melanomas may progress into metastatic disease [2]. Several dermoscopic features have been correlated with the regression process, including white scar-like depigmented areas and gray-blue, pepper-like granules, which correspond to dermal scarring, pigment incontinence and presence of melanophages [3,4]. Regression may occur not only in melanomas, but also in melanocytic nevi, which similarly may exhibit white areas and gray-blue granules or areas under dermoscopy [5]. Overall, white areas have been proposed to be associated with the fibrosis type of regression and gray-blue areas to the melanosis type of regression of melanocytic tumors [3]. Lichen planus like keratosis (LPLK) is considered to represent a regressed solar lentigo or seborrheic keratosis. Dermoscopy of LPLK at the late stage of the regression process reveals a diffuse gray-blue granular pattern, similar to that observed in regressed melanocytic lesions [6]. In this context, when evaluating skin lesions that exhibit high degree of regression, interpretation of dermoscopic findings may be problematic, especially when no other dermoscopic clues can be recognized.

  5. Combined genetic algorithm and multiple linear regression (GA-MLR) optimizer: Application to multi-exponential fluorescence decay surface.

    PubMed

    Fisz, Jacek J

    2006-12-07

    The optimization approach based on the genetic algorithm (GA) combined with multiple linear regression (MLR) method, is discussed. The GA-MLR optimizer is designed for the nonlinear least-squares problems in which the model functions are linear combinations of nonlinear functions. GA optimizes the nonlinear parameters, and the linear parameters are calculated from MLR. GA-MLR is an intuitive optimization approach and it exploits all advantages of the genetic algorithm technique. This optimization method results from an appropriate combination of two well-known optimization methods. The MLR method is embedded in the GA optimizer and linear and nonlinear model parameters are optimized in parallel. The MLR method is the only one strictly mathematical "tool" involved in GA-MLR. The GA-MLR approach simplifies and accelerates considerably the optimization process because the linear parameters are not the fitted ones. Its properties are exemplified by the analysis of the kinetic biexponential fluorescence decay surface corresponding to a two-excited-state interconversion process. A short discussion of the variable projection (VP) algorithm, designed for the same class of the optimization problems, is presented. VP is a very advanced mathematical formalism that involves the methods of nonlinear functionals, algebra of linear projectors, and the formalism of Fréchet derivatives and pseudo-inverses. Additional explanatory comments are added on the application of recently introduced the GA-NR optimizer to simultaneous recovery of linear and weakly nonlinear parameters occurring in the same optimization problem together with nonlinear parameters. The GA-NR optimizer combines the GA method with the NR method, in which the minimum-value condition for the quadratic approximation to chi(2), obtained from the Taylor series expansion of chi(2), is recovered by means of the Newton-Raphson algorithm. The application of the GA-NR optimizer to model functions which are multi

  6. A robust background regression based score estimation algorithm for hyperspectral anomaly detection

    NASA Astrophysics Data System (ADS)

    Zhao, Rui; Du, Bo; Zhang, Liangpei; Zhang, Lefei

    2016-12-01

    Anomaly detection has become a hot topic in the hyperspectral image analysis and processing fields in recent years. The most important issue for hyperspectral anomaly detection is the background estimation and suppression. Unreasonable or non-robust background estimation usually leads to unsatisfactory anomaly detection results. Furthermore, the inherent nonlinearity of hyperspectral images may cover up the intrinsic data structure in the anomaly detection. In order to implement robust background estimation, as well as to explore the intrinsic data structure of the hyperspectral image, we propose a robust background regression based score estimation algorithm (RBRSE) for hyperspectral anomaly detection. The Robust Background Regression (RBR) is actually a label assignment procedure which segments the hyperspectral data into a robust background dataset and a potential anomaly dataset with an intersection boundary. In the RBR, a kernel expansion technique, which explores the nonlinear structure of the hyperspectral data in a reproducing kernel Hilbert space, is utilized to formulate the data as a density feature representation. A minimum squared loss relationship is constructed between the data density feature and the corresponding assigned labels of the hyperspectral data, to formulate the foundation of the regression. Furthermore, a manifold regularization term which explores the manifold smoothness of the hyperspectral data, and a maximization term of the robust background average density, which suppresses the bias caused by the potential anomalies, are jointly appended in the RBR procedure. After this, a paired-dataset based k-nn score estimation method is undertaken on the robust background and potential anomaly datasets, to implement the detection output. The experimental results show that RBRSE achieves superior ROC curves, AUC values, and background-anomaly separation than some of the other state-of-the-art anomaly detection methods, and is easy to implement

  7. Frequency domain nonlinear optics

    NASA Astrophysics Data System (ADS)

    Legare, Francois

    2016-05-01

    The universal dilemma of gain narrowing occurring in fs amplifiers prevents ultra-high power lasers from delivering few-cycle pulses. This problem is overcome by a new amplification concept: Frequency domain Optical Parametric Amplification - FOPA. It enables simultaneous up-scaling of peak power and amplified spectral bandwidth and can be performed at any wavelength range of conventional amplification schemes, however, with the capability to amplify single cycles of light. The key idea for amplification of octave-spanning spectra without loss of spectral bandwidth is to amplify the broad spectrum ``slice by slice'' in the frequency domain, i.e. in the Fourier plane of a 4f-setup. The striking advantages of this scheme, are its capability to amplify (more than) one octave of bandwidth without shorting the corresponding pulse duration. This is because ultrabroadband phase matching is not defined by the properties of the nonlinear crystal employed but the number of crystals employed. In the same manner, to increase the output energy one simply has to increase the spectral extension in the Fourier plane and to add one more crystal. Thus, increasing pulse energy and shortening its duration accompany each other. A proof of principle experiment was carried out at ALLS on the sub-two cycle IR beam line and yielded record breaking performance in the field of few-cycle IR lasers. 100 μJ two-cycle pulses from a hollow core fibre compression setup were amplified to 1.43mJ without distorting spatial or temporal properties. Pulse duration at the input of FOPA and after FOPA remains the same. Recently, we have started upgrading this system to be pumped by 250 mJ to reach 40 mJ two-cycle IR few-cycle pulses and latest results will be presented at the conference. Furthermore, the extension of the concept of FOPA to other nonlinear optical processes will be discussed. Frequency domain nonlinear optics.

  8. Linearization of Nonlinear Systems.

    DTIC Science & Technology

    1986-11-24

    series. IEEE Trans. Circuits Syst., CAS-32(11):1150-1171, November 1985. [BC85b] S. Boyd and L. 0. Chua. Uniqueness of circuits and systems containing...Control and Information Sciences vol. 58, p10 1- 1 19 , June 1983. [BC85c] S. Boyd and L. 0. Chua. Volterra series for nonlinear circuits . In Proc. IEEE...ISCAS, Tokyo, June 1985. [BCD84] S. Boyd, L. 0. Chua, and C. A. Desoer . Analytical foundations of Volterra series. IMA Journal of Mathematical

  9. Nonlinear backreaction in cosmology

    NASA Astrophysics Data System (ADS)

    Green, Stephen Roland

    This thesis, based on two papers by Green and Wald, investigates the problem of nonlinear backreaction in cosmology. We first analyze the problem in a general context by developing a new, mathematically precise framework for treating the effects of nonlinear phenomena occurring on small scales in general relativity. Our framework requires the metric to be close to a background metric (not necessarily a cosmological metric), but allows arbitrarily large stress-energy fluctuations on small scales. We prove that, within our framework, if the matter stress-energy tensor satisfies the weak energy condition (i.e., positivity of energy density in all frames), then the only effect that small-scale inhomogeneities can have on the background metric is to provide an effective stress-energy tensor that is traceless and satisfies the weak energy condition itself—corresponding to the presence of gravitational radiation. In particular, nonlinear effects produced by small-scale inhomogeneities cannot mimic the effects of dark energy. We also develop perturbation theory off of the background metric. We derive an equation for the long-wavelength part of the leading order deviation of the metric from the background metric, which contains the usual terms occurring in linearized perturbation theory plus additional contributions from the small-scale inhomogeneities. Next, we apply our framework to the cosmological context, specializing our background metric to be of the Friedmann-Lemaitre-Robertson-Walker form. We demonstrate that, in the case of dust matter, a cosmological constant, and vanishing spatial curvature (i.e., our universe today), Newtonian gravity alone provides a good global description of an inhomogeneous general relativistic cosmology, even when there is significant nonlinear dynamical behavior at small scales. Namely, we find a relatively straightforward dictionary—which is exact at the linearized level—that maps Newtonian dust cosmologies into

  10. The simplex method for nonlinear mass determinations

    NASA Astrophysics Data System (ADS)

    Branham, Richard L.

    1988-03-01

    The Gauss-Newton method, and calculating a mass that minimizes the variation of residuals are standard techniques for determining planetary masses, but both may fail under certain circums tances. The Gauss-Newton method, in particular, may diverge, and when it converges may converge to a local, rather than global, minimum of the nonlinear regression problem. The simplex method of nonlinear optimization needs no initial estimate for the solution and can be made to converge to a global minimum. It may also be used with non-least squares criteria, such as the L1 criterion, for greater robustness. But the simplex method achieves these advantages at a high computational price. To test the method as a tool for dynamical astronomy, over 12,000 observations of Neptune were used to calculate Pluto's mass. From an initial estimate of 1/1, 812,000 the Gauss-Newton method diverged. The simplex method converged to a more satisfactory 1/22,000,000 with a range of 1/47,000,000 to 1/14,000,000 as indicated by the mean error. Because the simplex method is considerably slower than competing methods, it should be reserved for refractory problems that do not yield facil solutions when tackled by other methods.

  11. Finite elements of nonlinear continua.

    NASA Technical Reports Server (NTRS)

    Oden, J. T.

    1972-01-01

    The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.

  12. Nonlinear Ultrasonic Phased Array Imaging

    NASA Astrophysics Data System (ADS)

    Potter, J. N.; Croxford, A. J.; Wilcox, P. D.

    2014-10-01

    This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging through depth.

  13. Nonlinear ultrasonic phased array imaging.

    PubMed

    Potter, J N; Croxford, A J; Wilcox, P D

    2014-10-03

    This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging through depth.

  14. Non-Stationary Hydrologic Frequency Analysis using B-Splines Quantile Regression

    NASA Astrophysics Data System (ADS)

    Nasri, B.; St-Hilaire, A.; Bouezmarni, T.; Ouarda, T.

    2015-12-01

    Hydrologic frequency analysis is commonly used by engineers and hydrologists to provide the basic information on planning, design and management of hydraulic structures and water resources system under the assumption of stationarity. However, with increasing evidence of changing climate, it is possible that the assumption of stationarity would no longer be valid and the results of conventional analysis would become questionable. In this study, we consider a framework for frequency analysis of extreme flows based on B-Splines quantile regression, which allows to model non-stationary data that have a dependence on covariates. Such covariates may have linear or nonlinear dependence. A Markov Chain Monte Carlo (MCMC) algorithm is used to estimate quantiles and their posterior distributions. A coefficient of determination for quantiles regression is proposed to evaluate the estimation of the proposed model for each quantile level. The method is applied on annual maximum and minimum streamflow records in Ontario, Canada. Climate indices are considered to describe the non-stationarity in these variables and to estimate the quantiles in this case. The results show large differences between the non-stationary quantiles and their stationary equivalents for annual maximum and minimum discharge with high annual non-exceedance probabilities. Keywords: Quantile regression, B-Splines functions, MCMC, Streamflow, Climate indices, non-stationarity.

  15. Comparative analysis of neural network and regression based condition monitoring approaches for wind turbine fault detection

    NASA Astrophysics Data System (ADS)

    Schlechtingen, Meik; Ferreira Santos, Ilmar

    2011-07-01

    This paper presents the research results of a comparison of three different model based approaches for wind turbine fault detection in online SCADA data, by applying developed models to five real measured faults and anomalies. The regression based model as the simplest approach to build a normal behavior model is compared to two artificial neural network based approaches, which are a full signal reconstruction and an autoregressive normal behavior model. Based on a real time series containing two generator bearing damages the capabilities of identifying the incipient fault prior to the actual failure are investigated. The period after the first bearing damage is used to develop the three normal behavior models. The developed or trained models are used to investigate how the second damage manifests in the prediction error. Furthermore the full signal reconstruction and the autoregressive approach are applied to further real time series containing gearbox bearing damages and stator temperature anomalies. The comparison revealed all three models being capable of detecting incipient faults. However, they differ in the effort required for model development and the remaining operational time after first indication of damage. The general nonlinear neural network approaches outperform the regression model. The remaining seasonality in the regression model prediction error makes it difficult to detect abnormality and leads to increased alarm levels and thus a shorter remaining operational period. For the bearing damages and the stator anomalies under investigation the full signal reconstruction neural network gave the best fault visibility and thus led to the highest confidence level.

  16. Multiple regression technique for Pth degree polynominals with and without linear cross products

    NASA Technical Reports Server (NTRS)

    Davis, J. W.

    1973-01-01

    A multiple regression technique was developed by which the nonlinear behavior of specified independent variables can be related to a given dependent variable. The polynomial expression can be of Pth degree and can incorporate N independent variables. Two cases are treated such that mathematical models can be studied both with and without linear cross products. The resulting surface fits can be used to summarize trends for a given phenomenon and provide a mathematical relationship for subsequent analysis. To implement this technique, separate computer programs were developed for the case without linear cross products and for the case incorporating such cross products which evaluate the various constants in the model regression equation. In addition, the significance of the estimated regression equation is considered and the standard deviation, the F statistic, the maximum absolute percent error, and the average of the absolute values of the percent of error evaluated. The computer programs and their manner of utilization are described. Sample problems are included to illustrate the use and capability of the technique which show the output formats and typical plots comparing computer results to each set of input data.

  17. Delineation of homogenous regions using hydrological variables predicted by projection pursuit regression

    NASA Astrophysics Data System (ADS)

    Durocher, Martin; Chebana, Fateh; Ouarda, Taha B. M. J.

    2016-11-01

    This study investigates the utilization of hydrological information in regional flood frequency analysis (RFFA) to enforce desired properties for a group of gauged stations. Neighbourhoods are particular types of regions that are centred on target locations. A challenge for using neighbourhoods in RFFA is that hydrological information is not available at target locations and cannot be completely replaced by the available physiographical information. Instead of using the available physiographic characteristics to define the centre of a target location, this study proposes to introduce estimates of reference hydrological variables to ensure a better homogeneity. These reference variables represent nonlinear relations with the site characteristics obtained by projection pursuit regression, a nonparametric regression method. The resulting neighbourhoods are investigated in combination with commonly used regional models: the index-flood model and regression-based models. The complete approach is illustrated in a real-world case study with gauged sites from the southern part of the province of Québec, Canada, and is compared with the traditional approaches such as region of influence and canonical correlation analysis. The evaluation focuses on the neighbourhood properties as well as prediction performances, with special attention devoted to problematic stations. Results show clear improvements in neighbourhood definitions and quantile estimates.

  18. Neural Network and Regression Approximations in High Speed Civil Transport Aircraft Design Optimization

    NASA Technical Reports Server (NTRS)

    Patniak, Surya N.; Guptill, James D.; Hopkins, Dale A.; Lavelle, Thomas M.

    1998-01-01

    Nonlinear mathematical-programming-based design optimization can be an elegant method. However, the calculations required to generate the merit function, constraints, and their gradients, which are frequently required, can make the process computational intensive. The computational burden can be greatly reduced by using approximating analyzers derived from an original analyzer utilizing neural networks and linear regression methods. The experience gained from using both of these approximation methods in the design optimization of a high speed civil transport aircraft is the subject of this paper. The Langley Research Center's Flight Optimization System was selected for the aircraft analysis. This software was exercised to generate a set of training data with which a neural network and a regression method were trained, thereby producing the two approximating analyzers. The derived analyzers were coupled to the Lewis Research Center's CometBoards test bed to provide the optimization capability. With the combined software, both approximation methods were examined for use in aircraft design optimization, and both performed satisfactorily. The CPU time for solution of the problem, which had been measured in hours, was reduced to minutes with the neural network approximation and to seconds with the regression method. Instability encountered in the aircraft analysis software at certain design points was also eliminated. On the other hand, there were costs and difficulties associated with training the approximating analyzers. The CPU time required to generate the input-output pairs and to train the approximating analyzers was seven times that required for solution of the problem.

  19. Bayesian nonparametric regression analysis of data with random effects covariates from longitudinal measurements.

    PubMed

    Ryu, Duchwan; Li, Erning; Mallick, Bani K

    2011-06-01

    We consider nonparametric regression analysis in a generalized linear model (GLM) framework for data with covariates that are the subject-specific random effects of longitudinal measurements. The usual assumption that the effects of the longitudinal covariate processes are linear in the GLM may be unrealistic and if this happens it can cast doubt on the inference of observed covariate effects. Allowing the regression functions to be unknown, we propose to apply Bayesian nonparametric methods including cubic smoothing splines or P-splines for the possible nonlinearity and use an additive model in this complex setting. To improve computational efficiency, we propose the use of data-augmentation schemes. The approach allows flexible covariance structures for the random effects and within-subject measurement errors of the longitudinal processes. The posterior model space is explored through a Markov chain Monte Carlo (MCMC) sampler. The proposed methods are illustrated and compared to other approaches, the "naive" approach and the regression calibration, via simulations and by an application that investigates the relationship between obesity in adulthood and childhood growth curves.

  20. Kepler AutoRegressive Planet Search

    NASA Astrophysics Data System (ADS)

    Caceres, Gabriel Antonio; Feigelson, Eric

    2016-01-01

    The Kepler AutoRegressive Planet Search (KARPS) project uses statistical methodology associated with autoregressive (AR) processes to model Kepler lightcurves in order to improve exoplanet transit detection in systems with high stellar variability. We also introduce a planet-search algorithm to detect transits in time-series residuals after application of the AR models. One of the main obstacles in detecting faint planetary transits is the intrinsic stellar variability of the host star. The variability displayed by many stars may have autoregressive properties, wherein later flux values are correlated with previous ones in some manner. Our analysis procedure consisting of three steps: pre-processing of the data to remove discontinuities, gaps and outliers; AR-type model selection and fitting; and transit signal search of the residuals using a new Transit Comb Filter (TCF) that replaces traditional box-finding algorithms. The analysis procedures of the project are applied to a portion of the publicly available Kepler light curve data for the full 4-year mission duration. Tests of the methods have been made on a subset of Kepler Objects of Interest (KOI) systems, classified both as planetary `candidates' and `false positives' by the Kepler Team, as well as a random sample of unclassified systems. We find that the ARMA-type modeling successfully reduces the stellar variability, by a factor of 10 or more in active stars and by smaller factors in more quiescent stars. A typical quiescent Kepler star has an interquartile range (IQR) of ~10 e-/sec, which may improve slightly after modeling, while those with IQR ranging from 20 to 50 e-/sec, have improvements from 20% up to 70%. High activity stars (IQR exceeding 100) markedly improve. A periodogram based on the TCF is constructed to concentrate the signal of these periodic spikes. When a periodic transit is found, the model is displayed on a standard period-folded averaged light curve. Our findings to date on real

  1. Problems in nonlinear resistive MHD

    SciTech Connect

    Turnbull, A.D.; Strait, E.J.; La Haye, R.J.; Chu, M.S.; Miller, R.L.

    1998-12-31

    Two experimentally relevant problems can relatively easily be tackled by nonlinear MHD codes. Both problems require plasma rotation in addition to the nonlinear mode coupling and full geometry already incorporated into the codes, but no additional physics seems to be crucial. These problems discussed here are: (1) nonlinear coupling and interaction of multiple MHD modes near the B limit and (2) nonlinear coupling of the m/n = 1/1 sawtooth mode with higher n gongs and development of seed islands outside q = 1.

  2. Nonlinear Peltier effect in semiconductors

    NASA Astrophysics Data System (ADS)

    Zebarjadi, Mona; Esfarjani, Keivan; Shakouri, Ali

    2007-09-01

    Nonlinear Peltier coefficient of a doped InGaAs semiconductor is calculated numerically using the Monte Carlo technique. The Peltier coefficient is also obtained analytically for single parabolic band semiconductors assuming a shifted Fermi-Dirac electronic distribution under an applied bias. Analytical results are in agreement with numerical simulations. Key material parameters affecting the nonlinear behavior are doping concentration, effective mass, and electron-phonon coupling. Current density thresholds at which nonlinear behavior is observable are extracted from numerical data. It is shown that the nonlinear Peltier effect can be used to enhance cooling of thin film microrefrigerator devices especially at low temperatures.

  3. Nonlinear Attitude Filtering Methods

    NASA Technical Reports Server (NTRS)

    Markley, F. Landis; Crassidis, John L.; Cheng, Yang

    2005-01-01

    This paper provides a survey of modern nonlinear filtering methods for attitude estimation. Early applications relied mostly on the extended Kalman filter for attitude estimation. Since these applications, several new approaches have been developed that have proven to be superior to the extended Kalman filter. Several of these approaches maintain the basic structure of the extended Kalman filter, but employ various modifications in order to provide better convergence or improve other performance characteristics. Examples of such approaches include: filter QUEST, extended QUEST, the super-iterated extended Kalman filter, the interlaced extended Kalman filter, and the second-order Kalman filter. Filters that propagate and update a discrete set of sigma points rather than using linearized equations for the mean and covariance are also reviewed. A two-step approach is discussed with a first-step state that linearizes the measurement model and an iterative second step to recover the desired attitude states. These approaches are all based on the Gaussian assumption that the probability density function is adequately specified by its mean and covariance. Other approaches that do not require this assumption are reviewed, including particle filters and a Bayesian filter based on a non-Gaussian, finite-parameter probability density function on SO(3). Finally, the predictive filter, nonlinear observers and adaptive approaches are shown. The strengths and weaknesses of the various approaches are discussed.

  4. NONLINEAR ATOM OPTICS

    SciTech Connect

    T. MILONNI; G. CSANAK; ET AL

    1999-07-01

    This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). The project objectives were to explore theoretically various aspects of nonlinear atom optics effects in cold-atom waves and traps. During the project a major development occurred the observation, by as many as a dozen experimental groups, of Bose-Einstein condensation (BEC) in cold-atom traps. This stimulated us to focus our attention on those aspects of nonlinear atom optics relating to BEC, in addition to continuing our work on a nonequilibrium formalism for dealing with the interaction of an electromagnetic field with multi-level atomic systems, allowing for macroscopic coherence effects such as BEC. Studies of several problems in BEC physics have been completed or are near completion, including the suggested use of external electric fields to modify the nature of the interatomic interaction in cold-atom traps; properties of two-phase condensates; and molecular loss processes associated with BEC experiments involving a so-called Feshbach resonance.

  5. Improved nonlinear prediction method

    NASA Astrophysics Data System (ADS)

    Adenan, Nur Hamiza; Md Noorani, Mohd Salmi

    2014-06-01

    The analysis and prediction of time series data have been addressed by researchers. Many techniques have been developed to be applied in various areas, such as weather forecasting, financial markets and hydrological phenomena involving data that are contaminated by noise. Therefore, various techniques to improve the method have been introduced to analyze and predict time series data. In respect of the importance of analysis and the accuracy of the prediction result, a study was undertaken to test the effectiveness of the improved nonlinear prediction method for data that contain noise. The improved nonlinear prediction method involves the formation of composite serial data based on the successive differences of the time series. Then, the phase space reconstruction was performed on the composite data (one-dimensional) to reconstruct a number of space dimensions. Finally the local linear approximation method was employed to make a prediction based on the phase space. This improved method was tested with data series Logistics that contain 0%, 5%, 10%, 20% and 30% of noise. The results show that by using the improved method, the predictions were found to be in close agreement with the observed ones. The correlation coefficient was close to one when the improved method was applied on data with up to 10% noise. Thus, an improvement to analyze data with noise without involving any noise reduction method was introduced to predict the time series data.

  6. Understanding Child Stunting in India: A Comprehensive Analysis of Socio-Economic, Nutritional and Environmental Determinants Using Additive Quantile Regression

    PubMed Central

    Fenske, Nora; Burns, Jacob; Hothorn, Torsten; Rehfuess, Eva A.

    2013-01-01

    Background Most attempts to address undernutrition, responsible for one third of global child deaths, have fallen behind expectations. This suggests that the assumptions underlying current modelling and intervention practices should be revisited. Objective We undertook a comprehensive analysis of the determinants of child stunting in India, and explored whether the established focus on linear effects of single risks is appropriate. Design Using cross-sectional data for children aged 0–24 months from the Indian National Family Health Survey for 2005/2006, we populated an evidence-based diagram of immediate, intermediate and underlying determinants of stunting. We modelled linear, non-linear, spatial and age-varying effects of these determinants using additive quantile regression for four quantiles of the Z-score of standardized height-for-age and logistic regression for stunting and severe stunting. Results At least one variable within each of eleven groups of determinants was significantly associated with height-for-age in the 35% Z-score quantile regression. The non-modifiable risk factors child age and sex, and the protective factors household wealth, maternal education and BMI showed the largest effects. Being a twin or multiple birth was associated with dramatically decreased height-for-age. Maternal age, maternal BMI, birth order and number of antenatal visits influenced child stunting in non-linear ways. Findings across the four quantile and two logistic regression models were largely comparable. Conclusions Our analysis confirms the multifactorial nature of child stunting. It emphasizes the need to pursue a systems-based approach and to consider non-linear effects, and suggests that differential effects across the height-for-age distribution do not play a major role. PMID:24223839

  7. [The net analyte preprocessing combined with radial basis partial least squares regression applied in noninvasive measurement of blood glucose].

    PubMed

    Li, Qing-Bo; Huang, Zheng-Wei

    2014-02-01

    In order to improve the prediction accuracy of quantitative analysis model in the near-infrared spectroscopy of blood glucose, this paper, by combining net analyte preprocessing (NAP) algorithm and radial basis functions partial least squares (RBFPLS) regression, builds a nonlinear model building method which is suitable for glucose measurement of human, named as NAP-RBFPLS. First, NAP is used to pre-process the near-infrared spectroscopy of blood glucose, in order to effectively extract the information which only relates to glucose signal from the original near-infrared spectra, so that it could effectively weaken the occasional correlation problems of the glucose changes and the interference factors which are caused by the absorption of water, albumin, hemoglobin, fat and other components of the blood in human body, the change of temperature of human body, the drift of measuring instruments, the changes of measuring environment, and the changes of measuring conditions; and then a nonlinear quantitative analysis model is built with the near-infrared spectroscopy data after NAP, in order to solve the nonlinear relationship between glucose concentrations and near-infrared spectroscopy which is caused by body strong scattering. In this paper, the new method is compared with other three quantitative analysis models building on partial least squares (PLS), net analyte preprocessing partial least squares (NAP-PLS) and RBFPLS respectively. At last, the experimental results show that the nonlinear calibration model, developed by combining NAP algorithm and RBFPLS regression, which was put forward in this paper, greatly improves the prediction accuracy of prediction sets, and what has been proved in this paper is that the nonlinear model building method will produce practical applications for the research of non-invasive detection techniques on human glucose concentrations.

  8. Can Flexible Non-Linear Modeling Tell Us Anything New about Educational Productivity?

    ERIC Educational Resources Information Center

    Baker, Bruce D.

    2001-01-01

    Explores whether flexible nonlinear models (including neural networks and genetic algorithms) can reveal otherwise unexpected patterns of relationship in typical school-productivity data. Applying three types of algorithms alongside regression modeling to school-level data in 183 elementary schools proves the hypothesis and reveals new directions…

  9. Visualizing Confidence Bands for Semiparametrically Estimated Nonlinear Relations among Latent Variables

    ERIC Educational Resources Information Center

    Pek, Jolynn; Chalmers, R. Philip; Kok, Bethany E.; Losardo, Diane

    2015-01-01

    Structural equation mixture models (SEMMs), when applied as a semiparametric model (SPM), can adequately recover potentially nonlinear latent relationships without their specification. This SPM is useful for exploratory analysis when the form of the latent regression is unknown. The purpose of this article is to help users familiar with structural…

  10. Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data

    ERIC Educational Resources Information Center

    Lee, Sik-Yum

    2006-01-01

    A Bayesian approach is developed for analyzing nonlinear structural equation models with nonignorable missing data. The nonignorable missingness mechanism is specified by a logistic regression model. A hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm is used to produce the joint Bayesian estimates of…

  11. On Insensitivity of the Chi-Square Model Test to Nonlinear Misspecification in Structural Equation Models

    ERIC Educational Resources Information Center

    Mooijaart, Ab; Satorra, Albert

    2009-01-01

    In this paper, we show that for some structural equation models (SEM), the classical chi-square goodness-of-fit test is unable to detect the presence of nonlinear terms in the model. As an example, we consider a regression model with latent variables and interactions terms. Not only the model test has zero power against that type of…

  12. Estimating peak flow characteristics at ungaged sites by ridge regression

    USGS Publications Warehouse

    Tasker, Gary D.

    1982-01-01

    A regression simulation model, is combined with a multisite streamflow generator to simulate a regional regression of 50-year peak discharge against a set of basin characteristics. Monte Carlo experiments are used to compare the unbiased ordinary lease squares parameter estimator with Hoerl and Kennard's (1970a) ridge estimator in which the biasing parameter is that proposed by Hoerl, Kennard, and Baldwin (1975). The simulation results indicate a substantial improvement in parameter estimation using ridge regression when the correlation between basin characteristics is more than about 0.90. In addition, results indicate a strong potential for improving the mean square error of prediction of a peak-flow characteristic versus basin characteristics regression model when the basin characteristics are approximately colinear. The simulation covers a range of regression parameters, streamflow statistics, and basin characteristics commonly found in regional regression studies.

  13. Inference in Adaptive Regression via the Kac-Rice Formula

    DTIC Science & Technology

    2014-05-15

    Inference in Adaptive Regression via the Kac- Rice Formula Jonathan Taylor∗, Joshua Loftus, Ryan J. Tibshirani Department of Statistics Stanford...general adaptive regression setting. Our approach uses the Kac- Rice formula (as described in Adler & Taylor 2007) applied to the problem of maximizing a...SUBTITLE Inference in Adaptive Regression via the Kac- Rice Formula 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d

  14. Algorithm For Solution Of Subset-Regression Problems

    NASA Technical Reports Server (NTRS)

    Verhaegen, Michel

    1991-01-01

    Reliable and flexible algorithm for solution of subset-regression problem performs QR decomposition with new column-pivoting strategy, enables selection of subset directly from originally defined regression parameters. This feature, in combination with number of extensions, makes algorithm very flexible for use in analysis of subset-regression problems in which parameters have physical meanings. Also extended to enable joint processing of columns contaminated by noise with those free of noise, without using scaling techniques.

  15. Union Support Recovery in High-Dimensional Multivariate Regression

    DTIC Science & Technology

    2008-08-01

    view the Lasso as a shrinkage estimator to be compared to traditional least squares or ridge regression ; in this case, it is natural to study the `2... instance , in a hierarchical regression model, groups of regression coefficients may be required to be zero or non-zero in a blockwise manner; for example...Neural Information Processing Systems, 18. MIT Press, Cambridge, MA. Bach, F. (2008). Consistency of the group Lasso and multiple kernel learning

  16. Nonlinearities in spacecraft structural dynamics

    NASA Technical Reports Server (NTRS)

    Taylor, Larry; Latimer, Kelly

    1988-01-01

    In considering nonlinearities in spacecraft structural dynamics, the following are examined: (1) SCOLE Configuration-Equations of Motion; (2) Modeling Error Sources; (3) Approximate Solutions; (4) Comparison of Model Accuracy; (5) Linear and Nonlinear Damping; (6) Experimental Results; and, (7) Future Work.

  17. Chaos synchronization by nonlinear coupling

    NASA Astrophysics Data System (ADS)

    Petereit, Johannes; Pikovsky, Arkady

    2017-03-01

    We study synchronization properties of three nonlinearly coupled chaotic maps. Coupling is introduced in such a way, that it cannot be reduced to pairwise terms, but includes combined action of all interacting units. For two models of nonlinear coupling we characterize the transition to complete synchrony, as well as partially synchronized states. Relation to hypernetworks of chaotic units is also discussed.

  18. Solving Nonlinear Coupled Differential Equations

    NASA Technical Reports Server (NTRS)

    Mitchell, L.; David, J.

    1986-01-01

    Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.

  19. Nonlinear diffusion and superconducting hysteresis

    SciTech Connect

    Mayergoyz, I.D.

    1996-12-31

    Nonlinear diffusion of electromagnetic fields in superconductors with ideal and gradual resistive transitions is studied. Analytical results obtained for linear and nonlinear polarizations of electromagnetic fields are reported. These results lead to various extensions of the critical state model for superconducting hysteresis.

  20. Linearization of Conservative Nonlinear Oscillators

    ERIC Educational Resources Information Center

    Belendez, A.; Alvarez, M. L.; Fernandez, E.; Pascual, I.

    2009-01-01

    A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for…