Spectral analysis for nonstationary and nonlinear systems: a discrete-time-model-based approach.

PubMed

He, Fei; Billings, Stephen A; Wei, Hua-Liang; Sarrigiannis, Ptolemaios G; Zhao, Yifan

2013-08-01

A new frequency-domain analysis framework for nonlinear time-varying systems is introduced based on parametric time-varying nonlinear autoregressive with exogenous input models. It is shown how the time-varying effects can be mapped to the generalized frequency response functions (FRFs) to track nonlinear features in frequency, such as intermodulation and energy transfer effects. A new mapping to the nonlinear output FRF is also introduced. A simulated example and the application to intracranial electroencephalogram data are used to illustrate the theoretical results.

Structure-based control of complex networks with nonlinear dynamics.

PubMed

Zañudo, Jorge Gomez Tejeda; Yang, Gang; Albert, Réka

2017-07-11

What can we learn about controlling a system solely from its underlying network structure? Here we adapt a recently developed framework for control of networks governed by a broad class of nonlinear dynamics that includes the major dynamic models of biological, technological, and social processes. This feedback-based framework provides realizable node overrides that steer a system toward any of its natural long-term dynamic behaviors, regardless of the specific functional forms and system parameters. We use this framework on several real networks, identify the topological characteristics that underlie the predicted node overrides, and compare its predictions to those of structural controllability in control theory. Finally, we demonstrate this framework's applicability in dynamic models of gene regulatory networks and identify nodes whose override is necessary for control in the general case but not in specific model instances.

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

PubMed

Wan, Fei; Mitra, Nandita

2018-03-01

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.

The quadriceps muscle of knee joint modelling Using Hybrid Particle Swarm Optimization-Neural Network (PSO-NN)

NASA Astrophysics Data System (ADS)

Kamaruddin, Saadi Bin Ahmad; Marponga Tolos, Siti; Hee, Pah Chin; Ghani, Nor Azura Md; Ramli, Norazan Mohamed; Nasir, Noorhamizah Binti Mohamed; Ksm Kader, Babul Salam Bin; Saiful Huq, Mohammad

2017-03-01

Neural framework has for quite a while been known for its ability to handle a complex nonlinear system without a logical model and can learn refined nonlinear associations gives. Theoretically, the most surely understood computation to set up the framework is the backpropagation (BP) count which relies on upon the minimization of the mean square error (MSE). However, this algorithm is not totally efficient in the presence of outliers which usually exist in dynamic data. This paper exhibits the modelling of quadriceps muscle model by utilizing counterfeit smart procedures named consolidated backpropagation neural network nonlinear autoregressive (BPNN-NAR) and backpropagation neural network nonlinear autoregressive moving average (BPNN-NARMA) models in view of utilitarian electrical incitement (FES). We adapted particle swarm optimization (PSO) approach to enhance the performance of backpropagation algorithm. In this research, a progression of tests utilizing FES was led. The information that is gotten is utilized to build up the quadriceps muscle model. 934 preparing information, 200 testing and 200 approval information set are utilized as a part of the improvement of muscle model. It was found that both BPNN-NAR and BPNN-NARMA performed well in modelling this type of data. As a conclusion, the neural network time series models performed reasonably efficient for non-linear modelling such as active properties of the quadriceps muscle with one input, namely output namely muscle force.

General Nonlinear Ferroelectric Model v. Beta

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

Dong, Wen; Robbins, Josh

2017-03-14

The purpose of this software is to function as a generalized ferroelectric material model. The material model is designed to work with existing finite element packages by providing updated information on material properties that are nonlinear and dependent on loading history. The two major nonlinear phenomena this model captures are domain-switching and phase transformation. The software itself does not contain potentially sensitive material information and instead provides a framework for different physical phenomena observed within ferroelectric materials. The model is calibrated to a specific ferroelectric material through input parameters provided by the user.

The estimation of branching curves in the presence of subject-specific random effects.

PubMed

Elmi, Angelo; Ratcliffe, Sarah J; Guo, Wensheng

2014-12-20

Branching curves are a technique for modeling curves that change trajectory at a change (branching) point. Currently, the estimation framework is limited to independent data, and smoothing splines are used for estimation. This article aims to extend the branching curve framework to the longitudinal data setting where the branching point varies by subject. If the branching point is modeled as a random effect, then the longitudinal branching curve framework is a semiparametric nonlinear mixed effects model. Given existing issues with using random effects within a smoothing spline, we express the model as a B-spline based semiparametric nonlinear mixed effects model. Simple, clever smoothness constraints are enforced on the B-splines at the change point. The method is applied to Women's Health data where we model the shape of the labor curve (cervical dilation measured longitudinally) before and after treatment with oxytocin (a labor stimulant). Copyright © 2014 John Wiley & Sons, Ltd.

A Second-Order Conditionally Linear Mixed Effects Model with Observed and Latent Variable Covariates

ERIC Educational Resources Information Center

Harring, Jeffrey R.; Kohli, Nidhi; Silverman, Rebecca D.; Speece, Deborah L.

2012-01-01

A conditionally linear mixed effects model is an appropriate framework for investigating nonlinear change in a continuous latent variable that is repeatedly measured over time. The efficacy of the model is that it allows parameters that enter the specified nonlinear time-response function to be stochastic, whereas those parameters that enter in a…

Nonlinear degradation of a visible-light communication link: A Volterra-series approach

NASA Astrophysics Data System (ADS)

Kamalakis, Thomas; Dede, Georgia

2018-06-01

Visible light communications can be used to provide illumination and data communication at the same time. In this paper, a reverse-engineering approach is presented for assessing the impact of nonlinear signal distortion in visible light communication links. The approach is based on the Volterra series expansion and has the advantage of accurately accounting for memory effects in contrast to the static nonlinear models that are popular in the literature. Volterra kernels describe the end-to-end system response and can be inferred from measurements. Consequently, this approach does not rely on any particular physical models and assumptions regarding the individual link components. We provide the necessary framework for estimating the nonlinear distortion on the symbol estimates of a discrete multitone modulated link. Various design aspects such as waveform clipping and predistortion are also incorporated in the analysis. Using this framework, the nonlinear signal-to-interference is calculated for the system at hand. It is shown that at high signal amplitudes, the nonlinear signal-to-interference can be less than 25 dB.

Persistent model order reduction for complex dynamical systems using smooth orthogonal decomposition

NASA Astrophysics Data System (ADS)

Ilbeigi, Shahab; Chelidze, David

2017-11-01

Full-scale complex dynamic models are not effective for parametric studies due to the inherent constraints on available computational power and storage resources. A persistent reduced order model (ROM) that is robust, stable, and provides high-fidelity simulations for a relatively wide range of parameters and operating conditions can provide a solution to this problem. The fidelity of a new framework for persistent model order reduction of large and complex dynamical systems is investigated. The framework is validated using several numerical examples including a large linear system and two complex nonlinear systems with material and geometrical nonlinearities. While the framework is used for identifying the robust subspaces obtained from both proper and smooth orthogonal decompositions (POD and SOD, respectively), the results show that SOD outperforms POD in terms of stability, accuracy, and robustness.

Sequential state estimation of nonlinear/non-Gaussian systems with stochastic input for turbine degradation estimation

NASA Astrophysics Data System (ADS)

Hanachi, Houman; Liu, Jie; Banerjee, Avisekh; Chen, Ying

2016-05-01

Health state estimation of inaccessible components in complex systems necessitates effective state estimation techniques using the observable variables of the system. The task becomes much complicated when the system is nonlinear/non-Gaussian and it receives stochastic input. In this work, a novel sequential state estimation framework is developed based on particle filtering (PF) scheme for state estimation of general class of nonlinear dynamical systems with stochastic input. Performance of the developed framework is then validated with simulation on a Bivariate Non-stationary Growth Model (BNGM) as a benchmark. In the next step, three-year operating data of an industrial gas turbine engine (GTE) are utilized to verify the effectiveness of the developed framework. A comprehensive thermodynamic model for the GTE is therefore developed to formulate the relation of the observable parameters and the dominant degradation symptoms of the turbine, namely, loss of isentropic efficiency and increase of the mass flow. The results confirm the effectiveness of the developed framework for simultaneous estimation of multiple degradation symptoms in complex systems with noisy measured inputs.

Coupled Particle Transport and Pattern Formation in a Nonlinear Leaky-Box Model

NASA Technical Reports Server (NTRS)

Barghouty, A. F.; El-Nemr, K. W.; Baird, J. K.

2009-01-01

Effects of particle-particle coupling on particle characteristics in nonlinear leaky-box type descriptions of the acceleration and transport of energetic particles in space plasmas are examined in the framework of a simple two-particle model based on the Fokker-Planck equation in momentum space. In this model, the two particles are assumed coupled via a common nonlinear source term. In analogy with a prototypical mathematical system of diffusion-driven instability, this work demonstrates that steady-state patterns with strong dependence on the magnetic turbulence but a rather weak one on the coupled particles attributes can emerge in solutions of a nonlinearly coupled leaky-box model. The insight gained from this simple model may be of wider use and significance to nonlinearly coupled leaky-box type descriptions in general.

Nonlinearity analysis of measurement model for vision-based optical navigation system

NASA Astrophysics Data System (ADS)

Li, Jianguo; Cui, Hutao; Tian, Yang

2015-02-01

In the autonomous optical navigation system based on line-of-sight vector observation, nonlinearity of measurement model is highly correlated with the navigation performance. By quantitatively calculating the degree of nonlinearity of the focal plane model and the unit vector model, this paper focuses on determining which optical measurement model performs better. Firstly, measurement equations and measurement noise statistics of these two line-of-sight measurement models are established based on perspective projection co-linearity equation. Then the nonlinear effects of measurement model on the filter performance are analyzed within the framework of the Extended Kalman filter, also the degrees of nonlinearity of two measurement models are compared using the curvature measure theory from differential geometry. Finally, a simulation of star-tracker-based attitude determination is presented to confirm the superiority of the unit vector measurement model. Simulation results show that the magnitude of curvature nonlinearity measurement is consistent with the filter performance, and the unit vector measurement model yields higher estimation precision and faster convergence properties.

Nonlinear functional approximation with networks using adaptive neurons

NASA Technical Reports Server (NTRS)

Tawel, Raoul

1992-01-01

A novel mathematical framework for the rapid learning of nonlinear mappings and topological transformations is presented. It is based on allowing the neuron's parameters to adapt as a function of learning. This fully recurrent adaptive neuron model (ANM) has been successfully applied to complex nonlinear function approximation problems such as the highly degenerate inverse kinematics problem in robotics.

Economic growth and CO2 emissions: an investigation with smooth transition autoregressive distributed lag models for the 1800-2014 period in the USA.

PubMed

Bildirici, Melike; Ersin, Özgür Ömer

2018-01-01

The study aims to combine the autoregressive distributed lag (ARDL) cointegration framework with smooth transition autoregressive (STAR)-type nonlinear econometric models for causal inference. Further, the proposed STAR distributed lag (STARDL) models offer new insights in terms of modeling nonlinearity in the long- and short-run relations between analyzed variables. The STARDL method allows modeling and testing nonlinearity in the short-run and long-run parameters or both in the short- and long-run relations. To this aim, the relation between CO 2 emissions and economic growth rates in the USA is investigated for the 1800-2014 period, which is one of the largest data sets available. The proposed hybrid models are the logistic, exponential, and second-order logistic smooth transition autoregressive distributed lag (LSTARDL, ESTARDL, and LSTAR2DL) models combine the STAR framework with nonlinear ARDL-type cointegration to augment the linear ARDL approach with smooth transitional nonlinearity. The proposed models provide a new approach to the relevant econometrics and environmental economics literature. Our results indicated the presence of asymmetric long-run and short-run relations between the analyzed variables that are from the GDP towards CO 2 emissions. By the use of newly proposed STARDL models, the results are in favor of important differences in terms of the response of CO 2 emissions in regimes 1 and 2 for the estimated LSTAR2DL and LSTARDL models.

A comparison of linear and nonlinear statistical techniques in performance attribution.

PubMed

Chan, N H; Genovese, C R

2001-01-01

Performance attribution is usually conducted under the linear framework of multifactor models. Although commonly used by practitioners in finance, linear multifactor models are known to be less than satisfactory in many situations. After a brief survey of nonlinear methods, nonlinear statistical techniques are applied to performance attribution of a portfolio constructed from a fixed universe of stocks using factors derived from some commonly used cross sectional linear multifactor models. By rebalancing this portfolio monthly, the cumulative returns for procedures based on standard linear multifactor model and three nonlinear techniques-model selection, additive models, and neural networks-are calculated and compared. It is found that the first two nonlinear techniques, especially in combination, outperform the standard linear model. The results in the neural-network case are inconclusive because of the great variety of possible models. Although these methods are more complicated and may require some tuning, toolboxes are developed and suggestions on calibration are proposed. This paper demonstrates the usefulness of modern nonlinear statistical techniques in performance attribution.

Discriminative Nonlinear Analysis Operator Learning: When Cosparse Model Meets Image Classification.

PubMed

Wen, Zaidao; Hou, Biao; Jiao, Licheng

2017-05-03

Linear synthesis model based dictionary learning framework has achieved remarkable performances in image classification in the last decade. Behaved as a generative feature model, it however suffers from some intrinsic deficiencies. In this paper, we propose a novel parametric nonlinear analysis cosparse model (NACM) with which a unique feature vector will be much more efficiently extracted. Additionally, we derive a deep insight to demonstrate that NACM is capable of simultaneously learning the task adapted feature transformation and regularization to encode our preferences, domain prior knowledge and task oriented supervised information into the features. The proposed NACM is devoted to the classification task as a discriminative feature model and yield a novel discriminative nonlinear analysis operator learning framework (DNAOL). The theoretical analysis and experimental performances clearly demonstrate that DNAOL will not only achieve the better or at least competitive classification accuracies than the state-of-the-art algorithms but it can also dramatically reduce the time complexities in both training and testing phases.

A nonlinear bi-level programming approach for product portfolio management.

PubMed

Ma, Shuang

2016-01-01

Product portfolio management (PPM) is a critical decision-making for companies across various industries in today's competitive environment. Traditional studies on PPM problem have been motivated toward engineering feasibilities and marketing which relatively pay less attention to other competitors' actions and the competitive relations, especially in mathematical optimization domain. The key challenge lies in that how to construct a mathematical optimization model to describe this Stackelberg game-based leader-follower PPM problem and the competitive relations between them. The primary work of this paper is the representation of a decision framework and the optimization model to leverage the PPM problem of leader and follower. A nonlinear, integer bi-level programming model is developed based on the decision framework. Furthermore, a bi-level nested genetic algorithm is put forward to solve this nonlinear bi-level programming model for leader-follower PPM problem. A case study of notebook computer product portfolio optimization is reported. Results and analyses reveal that the leader-follower bi-level optimization model is robust and can empower product portfolio optimization.

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

DOE PAGES

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

2017-11-09

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

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

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

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

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

Parameter and Structure Inference for Nonlinear Dynamical Systems

NASA Technical Reports Server (NTRS)

Morris, Robin D.; Smelyanskiy, Vadim N.; Millonas, Mark

2006-01-01

A great many systems can be modeled in the non-linear dynamical systems framework, as x = f(x) + xi(t), where f() is the potential function for the system, and xi is the excitation noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications.

A general U-block model-based design procedure for nonlinear polynomial control systems

NASA Astrophysics Data System (ADS)

Zhu, Q. M.; Zhao, D. Y.; Zhang, Jianhua

2016-10-01

The proposition of U-model concept (in terms of 'providing concise and applicable solutions for complex problems') and a corresponding basic U-control design algorithm was originated in the first author's PhD thesis. The term of U-model appeared (not rigorously defined) for the first time in the first author's other journal paper, which established a framework for using linear polynomial control system design approaches to design nonlinear polynomial control systems (in brief, linear polynomial approaches → nonlinear polynomial plants). This paper represents the next milestone work - using linear state-space approaches to design nonlinear polynomial control systems (in brief, linear state-space approaches → nonlinear polynomial plants). The overall aim of the study is to establish a framework, defined as the U-block model, which provides a generic prototype for using linear state-space-based approaches to design the control systems with smooth nonlinear plants/processes described by polynomial models. For analysing the feasibility and effectiveness, sliding mode control design approach is selected as an exemplary case study. Numerical simulation studies provide a user-friendly step-by-step procedure for the readers/users with interest in their ad hoc applications. In formality, this is the first paper to present the U-model-oriented control system design in a formal way and to study the associated properties and theorems. The previous publications, in the main, have been algorithm-based studies and simulation demonstrations. In some sense, this paper can be treated as a landmark for the U-model-based research from intuitive/heuristic stage to rigour/formal/comprehensive studies.

Features of the Paired Soliton Interactions Within the Framework of the Gardner Equation

NASA Astrophysics Data System (ADS)

Shurgalina, E. G.

2018-02-01

We study the dynamics of the two-soliton interaction within the framework of a completely integrable model, namely, the Gardner equation with negative cubic nonlinearity, which admits the existence of a limiting soliton. The features of the soliton interaction with participation of a thick soliton are demonstrated. Special attention is paid to the nonlinear-interaction influence on the wave-field moments, which determine the skewness and the kurtosis in the theory of turbulence.

A micro-macro constitutive model for finite-deformation viscoelasticity of elastomers with nonlinear viscosity

NASA Astrophysics Data System (ADS)

Zhou, Jianyou; Jiang, Liying; Khayat, Roger E.

2018-01-01

Elastomers are known to exhibit viscoelastic behavior under deformation, which is linked to the diffusion processes of the highly mobile and flexible polymer chains. Inspired by the theories of polymer dynamics, a micro-macro constitutive model is developed to study the viscoelastic behaviors and the relaxation process of elastomeric materials under large deformation, in which the material parameters all have a microscopic foundation or a microstructural justification. The proposed model incorporates the nonlinear material viscosity into the continuum finite-deformation viscoelasticity theories which represent the polymer networks of elastomers with an elastic ground network and a few viscous subnetworks. The developed modeling framework is capable of adopting most of strain energy density functions for hyperelastic materials and thermodynamics evolution laws of viscoelastic solids. The modeling capacity of the framework is outlined by comparing the simulation results with the experimental data of three commonly used elastomeric materials, namely, VHB4910, HNBR50 and carbon black (CB) filled elastomers. The comparison shows that the stress responses and some typical behaviors of filled and unfilled elastomers can be quantitatively predicted by the model with suitable strain energy density functions. Particularly, the strain-softening effect of elastomers could be explained by the deformation-dependent (nonlinear) viscosity of the polymer chains. The presented modeling framework is expected to be useful as a modeling platform for further study on the performance of different type of elastomeric materials.

Nonlinear finite element model updating for damage identification of civil structures using batch Bayesian estimation

NASA Astrophysics Data System (ADS)

Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joel P.; de Callafon, Raymond A.

2017-02-01

This paper presents a framework for structural health monitoring (SHM) and damage identification of civil structures. This framework integrates advanced mechanics-based nonlinear finite element (FE) modeling and analysis techniques with a batch Bayesian estimation approach to estimate time-invariant model parameters used in the FE model of the structure of interest. The framework uses input excitation and dynamic response of the structure and updates a nonlinear FE model of the structure to minimize the discrepancies between predicted and measured response time histories. The updated FE model can then be interrogated to detect, localize, classify, and quantify the state of damage and predict the remaining useful life of the structure. As opposed to recursive estimation methods, in the batch Bayesian estimation approach, the entire time history of the input excitation and output response of the structure are used as a batch of data to estimate the FE model parameters through a number of iterations. In the case of non-informative prior, the batch Bayesian method leads to an extended maximum likelihood (ML) estimation method to estimate jointly time-invariant model parameters and the measurement noise amplitude. The extended ML estimation problem is solved efficiently using a gradient-based interior-point optimization algorithm. Gradient-based optimization algorithms require the FE response sensitivities with respect to the model parameters to be identified. The FE response sensitivities are computed accurately and efficiently using the direct differentiation method (DDM). The estimation uncertainties are evaluated based on the Cramer-Rao lower bound (CRLB) theorem by computing the exact Fisher Information matrix using the FE response sensitivities with respect to the model parameters. The accuracy of the proposed uncertainty quantification approach is verified using a sampling approach based on the unscented transformation. Two validation studies, based on realistic structural FE models of a bridge pier and a moment resisting steel frame, are performed to validate the performance and accuracy of the presented nonlinear FE model updating approach and demonstrate its application to SHM. These validation studies show the excellent performance of the proposed framework for SHM and damage identification even in the presence of high measurement noise and/or way-out initial estimates of the model parameters. Furthermore, the detrimental effects of the input measurement noise on the performance of the proposed framework are illustrated and quantified through one of the validation studies.

Structure-based control of complex networks with nonlinear dynamics

NASA Astrophysics Data System (ADS)

Zanudo, Jorge G. T.; Yang, Gang; Albert, Reka

What can we learn about controlling a system solely from its underlying network structure? Here we use a framework for control of networks governed by a broad class of nonlinear dynamics that includes the major dynamic models of biological, technological, and social processes. This feedback-based framework provides realizable node overrides that steer a system towards any of its natural long term dynamic behaviors, regardless of the dynamic details and system parameters. We use this framework on several real networks, identify the topological characteristics that underlie the predicted node overrides, and compare its predictions to those of classical structural control theory. Finally, we demonstrate this framework's applicability in dynamic models of gene regulatory networks and identify nodes whose override is necessary for control in the general case, but not in specific model instances. This work was supported by NSF Grants PHY 1205840 and IIS 1160995. JGTZ is a recipient of a Stand Up To Cancer - The V Foundation Convergence Scholar Award.

Estimation of Contextual Effects through Nonlinear Multilevel Latent Variable Modeling with a Metropolis-Hastings Robbins-Monro Algorithm

ERIC Educational Resources Information Center

Yang, Ji Seung; Cai, Li

2014-01-01

The main purpose of this study is to improve estimation efficiency in obtaining maximum marginal likelihood estimates of contextual effects in the framework of nonlinear multilevel latent variable model by adopting the Metropolis-Hastings Robbins-Monro algorithm (MH-RM). Results indicate that the MH-RM algorithm can produce estimates and standard…

Understanding climate impacts on vegetation using a spatiotemporal non-linear Granger causality framework

NASA Astrophysics Data System (ADS)

Papagiannopoulou, Christina; Decubber, Stijn; Miralles, Diego; Demuzere, Matthias; Dorigo, Wouter; Verhoest, Niko; Waegeman, Willem

2017-04-01

Satellite data provide an abundance of information about crucial climatic and environmental variables. These data - consisting of global records, spanning up to 35 years and having the form of multivariate time series with different spatial and temporal resolutions - enable the study of key climate-vegetation interactions. Although methods which are based on correlations and linear models are typically used for this purpose, their assumptions for linearity about the climate-vegetation relationships are too simplistic. Therefore, we adopt a recently proposed non-linear Granger causality analysis [1], in which we incorporate spatial information, concatenating data from neighboring pixels and training a joint model on the combined data. Experimental results based on global data sets show that considering non-linear relationships leads to a higher explained variance of past vegetation dynamics, compared to simple linear models. Our approach consists of several steps. First, we compile an extensive database [1], which includes multiple data sets for land surface temperature, near-surface air temperature, surface radiation, precipitation, snow water equivalents and surface soil moisture. Based on this database, high-level features are constructed and considered as predictors in our machine-learning framework. These high-level features include (de-trended) seasonal anomalies, lagged variables, past cumulative variables, and extreme indices, all calculated based on the raw climatic data. Second, we apply a spatiotemporal non-linear Granger causality framework - in which the linear predictive model is substituted for a non-linear machine learning algorithm - in order to assess which of these predictor variables Granger-cause vegetation dynamics at each 1° pixel. We use the de-trended anomalies of Normalized Difference Vegetation Index (NDVI) to characterize vegetation, being the target variable of our framework. Experimental results indicate that climate strongly (Granger-)causes vegetation dynamics in most regions globally. More specifically, water availability is the most dominant vegetation driver, being the dominant vegetation driver in 54% of the vegetated surface. Furthermore, our results show that precipitation and soil moisture have prolonged impacts on vegetation in semiarid regions, with up to 10% of additional explained variance on the vegetation dynamics occurring three months later. Finally, hydro-climatic extremes seem to have a remarkable impact on vegetation, since they also explain up to 10% of additional variance of vegetation in certain regions despite their infrequent occurrence. References [1] Papagiannopoulou, C., Miralles, D. G., Verhoest, N. E. C., Dorigo, W. A., and Waegeman, W.: A non-linear Granger causality framework to investigate climate-vegetation dynamics, Geosci. Model Dev. Discuss., doi:10.5194/gmd-2016-266, in review, 2016.

A framework for the automated data-driven constitutive characterization of composites

Treesearch

J.G. Michopoulos; John Hermanson; T. Furukawa; A. Iliopoulos

2010-01-01

We present advances on the development of a mechatronically and algorithmically automated framework for the data-driven identification of constitutive material models based on energy density considerations. These models can capture both the linear and nonlinear constitutive response of multiaxially loaded composite materials in a manner that accounts for progressive...

Restricted Complexity Framework for Nonlinear Adaptive Control in Complex Systems

NASA Astrophysics Data System (ADS)

Williams, Rube B.

2004-02-01

Control law adaptation that includes implicit or explicit adaptive state estimation, can be a fundamental underpinning for the success of intelligent control in complex systems, particularly during subsystem failures, where vital system states and parameters can be impractical or impossible to measure directly. A practical algorithm is proposed for adaptive state filtering and control in nonlinear dynamic systems when the state equations are unknown or are too complex to model analytically. The state equations and inverse plant model are approximated by using neural networks. A framework for a neural network based nonlinear dynamic inversion control law is proposed, as an extrapolation of prior developed restricted complexity methodology used to formulate the adaptive state filter. Examples of adaptive filter performance are presented for an SSME simulation with high pressure turbine failure to support extrapolations to adaptive control problems.

STATISTICAL GROWTH MODELING OF LONGITUDINAL DT-MRI FOR REGIONAL CHARACTERIZATION OF EARLY BRAIN DEVELOPMENT.

PubMed

Sadeghi, Neda; Prastawa, Marcel; Fletcher, P Thomas; Gilmore, John H; Lin, Weili; Gerig, Guido

2012-01-01

A population growth model that represents the growth trajectories of individual subjects is critical to study and understand neurodevelopment. This paper presents a framework for jointly estimating and modeling individual and population growth trajectories, and determining significant regional differences in growth pattern characteristics applied to longitudinal neuroimaging data. We use non-linear mixed effect modeling where temporal change is modeled by the Gompertz function. The Gompertz function uses intuitive parameters related to delay, rate of change, and expected asymptotic value; all descriptive measures which can answer clinical questions related to growth. Our proposed framework combines nonlinear modeling of individual trajectories, population analysis, and testing for regional differences. We apply this framework to the study of early maturation in white matter regions as measured with diffusion tensor imaging (DTI). Regional differences between anatomical regions of interest that are known to mature differently are analyzed and quantified. Experiments with image data from a large ongoing clinical study show that our framework provides descriptive, quantitative information on growth trajectories that can be directly interpreted by clinicians. To our knowledge, this is the first longitudinal analysis of growth functions to explain the trajectory of early brain maturation as it is represented in DTI.

Non-linear analytic and coanalytic problems ( L_p-theory, Clifford analysis, examples)

NASA Astrophysics Data System (ADS)

Dubinskii, Yu A.; Osipenko, A. S.

2000-02-01

Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the "orthogonal" sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented.

High angle of attack control law development for a free-flight wind tunnel model using direct eigenstructure assignment

NASA Technical Reports Server (NTRS)

Wendel, Thomas R.; Boland, Joseph R.; Hahne, David E.

1991-01-01

Flight-control laws are developed for a wind-tunnel aircraft model flying at a high angle of attack by using a synthesis technique called direct eigenstructure assignment. The method employs flight guidelines and control-power constraints to develop the control laws, and gain schedules and nonlinear feedback compensation provide a framework for considering the nonlinear nature of the attack angle. Linear and nonlinear evaluations show that the control laws are effective, a conclusion that is further confirmed by a scale model used for free-flight testing.

One-dimensional nonlinear elastodynamic models and their local conservation laws with applications to biological membranes.

PubMed

Cheviakov, A F; Ganghoffer, J-F

2016-05-01

The framework of incompressible nonlinear hyperelasticity and viscoelasticity is applied to the derivation of one-dimensional models of nonlinear wave propagation in fiber-reinforced elastic solids. Equivalence transformations are used to simplify the resulting wave equations and to reduce the number of parameters. Local conservation laws and global conserved quantities of the models are systematically computed and discussed, along with other related mathematical properties. Sample numerical solutions are presented. The models considered in the paper are appropriate for the mathematical description of certain aspects of the behavior of biological membranes and similar structures. Copyright © 2015 Elsevier Ltd. All rights reserved.

Bayesian parameter estimation for nonlinear modelling of biological pathways.

PubMed

Ghasemi, Omid; Lindsey, Merry L; Yang, Tianyi; Nguyen, Nguyen; Huang, Yufei; Jin, Yu-Fang

2011-01-01

The availability of temporal measurements on biological experiments has significantly promoted research areas in systems biology. To gain insight into the interaction and regulation of biological systems, mathematical frameworks such as ordinary differential equations have been widely applied to model biological pathways and interpret the temporal data. Hill equations are the preferred formats to represent the reaction rate in differential equation frameworks, due to their simple structures and their capabilities for easy fitting to saturated experimental measurements. However, Hill equations are highly nonlinearly parameterized functions, and parameters in these functions cannot be measured easily. Additionally, because of its high nonlinearity, adaptive parameter estimation algorithms developed for linear parameterized differential equations cannot be applied. Therefore, parameter estimation in nonlinearly parameterized differential equation models for biological pathways is both challenging and rewarding. In this study, we propose a Bayesian parameter estimation algorithm to estimate parameters in nonlinear mathematical models for biological pathways using time series data. We used the Runge-Kutta method to transform differential equations to difference equations assuming a known structure of the differential equations. This transformation allowed us to generate predictions dependent on previous states and to apply a Bayesian approach, namely, the Markov chain Monte Carlo (MCMC) method. We applied this approach to the biological pathways involved in the left ventricle (LV) response to myocardial infarction (MI) and verified our algorithm by estimating two parameters in a Hill equation embedded in the nonlinear model. We further evaluated our estimation performance with different parameter settings and signal to noise ratios. Our results demonstrated the effectiveness of the algorithm for both linearly and nonlinearly parameterized dynamic systems. Our proposed Bayesian algorithm successfully estimated parameters in nonlinear mathematical models for biological pathways. This method can be further extended to high order systems and thus provides a useful tool to analyze biological dynamics and extract information using temporal data.

A nonlinear autoregressive Volterra model of the Hodgkin-Huxley equations.

PubMed

Eikenberry, Steffen E; Marmarelis, Vasilis Z

2013-02-01

We propose a new variant of Volterra-type model with a nonlinear auto-regressive (NAR) component that is a suitable framework for describing the process of AP generation by the neuron membrane potential, and we apply it to input-output data generated by the Hodgkin-Huxley (H-H) equations. Volterra models use a functional series expansion to describe the input-output relation for most nonlinear dynamic systems, and are applicable to a wide range of physiologic systems. It is difficult, however, to apply the Volterra methodology to the H-H model because is characterized by distinct subthreshold and suprathreshold dynamics. When threshold is crossed, an autonomous action potential (AP) is generated, the output becomes temporarily decoupled from the input, and the standard Volterra model fails. Therefore, in our framework, whenever membrane potential exceeds some threshold, it is taken as a second input to a dual-input Volterra model. This model correctly predicts membrane voltage deflection both within the subthreshold region and during APs. Moreover, the model naturally generates a post-AP afterpotential and refractory period. It is known that the H-H model converges to a limit cycle in response to a constant current injection. This behavior is correctly predicted by the proposed model, while the standard Volterra model is incapable of generating such limit cycle behavior. The inclusion of cross-kernels, which describe the nonlinear interactions between the exogenous and autoregressive inputs, is found to be absolutely necessary. The proposed model is general, non-parametric, and data-derived.

LMI-Based Generation of Feedback Laws for a Robust Model Predictive Control Algorithm

NASA Technical Reports Server (NTRS)

Acikmese, Behcet; Carson, John M., III

2007-01-01

This technical note provides a mathematical proof of Corollary 1 from the paper 'A Nonlinear Model Predictive Control Algorithm with Proven Robustness and Resolvability' that appeared in the 2006 Proceedings of the American Control Conference. The proof was omitted for brevity in the publication. The paper was based on algorithms developed for the FY2005 R&TD (Research and Technology Development) project for Small-body Guidance, Navigation, and Control [2].The framework established by the Corollary is for a robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems that guarantees the resolvability of the associated nite-horizon optimal control problem in a receding-horizon implementation. Additional details of the framework are available in the publication.

Modeling exposure–lag–response associations with distributed lag non-linear models

PubMed Central

Gasparrini, Antonio

2014-01-01

In biomedical research, a health effect is frequently associated with protracted exposures of varying intensity sustained in the past. The main complexity of modeling and interpreting such phenomena lies in the additional temporal dimension needed to express the association, as the risk depends on both intensity and timing of past exposures. This type of dependency is defined here as exposure–lag–response association. In this contribution, I illustrate a general statistical framework for such associations, established through the extension of distributed lag non-linear models, originally developed in time series analysis. This modeling class is based on the definition of a cross-basis, obtained by the combination of two functions to flexibly model linear or nonlinear exposure-responses and the lag structure of the relationship, respectively. The methodology is illustrated with an example application to cohort data and validated through a simulation study. This modeling framework generalizes to various study designs and regression models, and can be applied to study the health effects of protracted exposures to environmental factors, drugs or carcinogenic agents, among others. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd. PMID:24027094

A general science-based framework for dynamical spatio-temporal models

USGS Publications Warehouse

Wikle, C.K.; Hooten, M.B.

2010-01-01

Spatio-temporal statistical models are increasingly being used across a wide variety of scientific disciplines to describe and predict spatially-explicit processes that evolve over time. Correspondingly, in recent years there has been a significant amount of research on new statistical methodology for such models. Although descriptive models that approach the problem from the second-order (covariance) perspective are important, and innovative work is being done in this regard, many real-world processes are dynamic, and it can be more efficient in some cases to characterize the associated spatio-temporal dependence by the use of dynamical models. The chief challenge with the specification of such dynamical models has been related to the curse of dimensionality. Even in fairly simple linear, first-order Markovian, Gaussian error settings, statistical models are often over parameterized. Hierarchical models have proven invaluable in their ability to deal to some extent with this issue by allowing dependency among groups of parameters. In addition, this framework has allowed for the specification of science based parameterizations (and associated prior distributions) in which classes of deterministic dynamical models (e. g., partial differential equations (PDEs), integro-difference equations (IDEs), matrix models, and agent-based models) are used to guide specific parameterizations. Most of the focus for the application of such models in statistics has been in the linear case. The problems mentioned above with linear dynamic models are compounded in the case of nonlinear models. In this sense, the need for coherent and sensible model parameterizations is not only helpful, it is essential. Here, we present an overview of a framework for incorporating scientific information to motivate dynamical spatio-temporal models. First, we illustrate the methodology with the linear case. We then develop a general nonlinear spatio-temporal framework that we call general quadratic nonlinearity and demonstrate that it accommodates many different classes of scientific-based parameterizations as special cases. The model is presented in a hierarchical Bayesian framework and is illustrated with examples from ecology and oceanography. ?? 2010 Sociedad de Estad??stica e Investigaci??n Operativa.

Coupled nonlinear aeroelasticity and flight dynamics of fully flexible aircraft

NASA Astrophysics Data System (ADS)

Su, Weihua

This dissertation introduces an approach to effectively model and analyze the coupled nonlinear aeroelasticity and flight dynamics of highly flexible aircraft. A reduced-order, nonlinear, strain-based finite element framework is used, which is capable of assessing the fundamental impact of structural nonlinear effects in preliminary vehicle design and control synthesis. The cross-sectional stiffness and inertia properties of the wings are calculated along the wing span, and then incorporated into the one-dimensional nonlinear beam formulation. Finite-state unsteady subsonic aerodynamics is used to compute airloads along lifting surfaces. Flight dynamic equations are then introduced to complete the aeroelastic/flight dynamic system equations of motion. Instead of merely considering the flexibility of the wings, the current work allows all members of the vehicle to be flexible. Due to their characteristics of being slender structures, the wings, tail, and fuselage of highly flexible aircraft can be modeled as beams undergoing three dimensional displacements and rotations. New kinematic relationships are developed to handle the split beam systems, such that fully flexible vehicles can be effectively modeled within the existing framework. Different aircraft configurations are modeled and studied, including Single-Wing, Joined-Wing, Blended-Wing-Body, and Flying-Wing configurations. The Lagrange Multiplier Method is applied to model the nodal displacement constraints at the joint locations. Based on the proposed models, roll response and stability studies are conducted on fully flexible and rigidized models. The impacts of the flexibility of different vehicle members on flutter with rigid body motion constraints, flutter in free flight condition, and roll maneuver performance are presented. Also, the static stability of the compressive member of the Joined-Wing configuration is studied. A spatially-distributed discrete gust model is incorporated into the time simulation of the framework. Gust responses of the Flying-Wing configuration subject to stall effects are investigated. A bilinear torsional stiffness model is introduced to study the skin wrinkling due to large bending curvature of the Flying-Wing. The numerical studies illustrate the improvements of the existing reduced-order formulation with new capabilities of both structural modeling and coupled aeroelastic and flight dynamic analysis of fully flexible aircraft.

Robustness Analysis of Integrated LPV-FDI Filters and LTI-FTC System for a Transport Aircraft

NASA Technical Reports Server (NTRS)

Khong, Thuan H.; Shin, Jong-Yeob

2007-01-01

This paper proposes an analysis framework for robustness analysis of a nonlinear dynamics system that can be represented by a polynomial linear parameter varying (PLPV) system with constant bounded uncertainty. The proposed analysis framework contains three key tools: 1) a function substitution method which can convert a nonlinear system in polynomial form into a PLPV system, 2) a matrix-based linear fractional transformation (LFT) modeling approach, which can convert a PLPV system into an LFT system with the delta block that includes key uncertainty and scheduling parameters, 3) micro-analysis, which is a well known robust analysis tool for linear systems. The proposed analysis framework is applied to evaluating the performance of the LPV-fault detection and isolation (FDI) filters of the closed-loop system of a transport aircraft in the presence of unmodeled actuator dynamics and sensor gain uncertainty. The robustness analysis results are compared with nonlinear time simulations.

Brain signal variability as a window into the bidirectionality between music and language processing: moving from a linear to a nonlinear model

PubMed Central

Hutka, Stefanie; Bidelman, Gavin M.; Moreno, Sylvain

2013-01-01

There is convincing empirical evidence for bidirectional transfer between music and language, such that experience in either domain can improve mental processes required by the other. This music-language relationship has been studied using linear models (e.g., comparing mean neural activity) that conceptualize brain activity as a static entity. The linear approach limits how we can understand the brain’s processing of music and language because the brain is a nonlinear system. Furthermore, there is evidence that the networks supporting music and language processing interact in a nonlinear manner. We therefore posit that the neural processing and transfer between the domains of language and music are best viewed through the lens of a nonlinear framework. Nonlinear analysis of neurophysiological activity may yield new insight into the commonalities, differences, and bidirectionality between these two cognitive domains not measurable in the local output of a cortical patch. We thus propose a novel application of brain signal variability (BSV) analysis, based on mutual information and signal entropy, to better understand the bidirectionality of music-to-language transfer in the context of a nonlinear framework. This approach will extend current methods by offering a nuanced, network-level understanding of the brain complexity involved in music-language transfer. PMID:24454295

Brain signal variability as a window into the bidirectionality between music and language processing: moving from a linear to a nonlinear model.

PubMed

Hutka, Stefanie; Bidelman, Gavin M; Moreno, Sylvain

2013-12-30

There is convincing empirical evidence for bidirectional transfer between music and language, such that experience in either domain can improve mental processes required by the other. This music-language relationship has been studied using linear models (e.g., comparing mean neural activity) that conceptualize brain activity as a static entity. The linear approach limits how we can understand the brain's processing of music and language because the brain is a nonlinear system. Furthermore, there is evidence that the networks supporting music and language processing interact in a nonlinear manner. We therefore posit that the neural processing and transfer between the domains of language and music are best viewed through the lens of a nonlinear framework. Nonlinear analysis of neurophysiological activity may yield new insight into the commonalities, differences, and bidirectionality between these two cognitive domains not measurable in the local output of a cortical patch. We thus propose a novel application of brain signal variability (BSV) analysis, based on mutual information and signal entropy, to better understand the bidirectionality of music-to-language transfer in the context of a nonlinear framework. This approach will extend current methods by offering a nuanced, network-level understanding of the brain complexity involved in music-language transfer.

PharmML in Action: an Interoperable Language for Modeling and Simulation

PubMed Central

Bizzotto, R; Smith, G; Yvon, F; Kristensen, NR; Swat, MJ

2017-01-01

PharmML1 is an XML‐based exchange format2, 3, 4 created with a focus on nonlinear mixed‐effect (NLME) models used in pharmacometrics,5, 6 but providing a very general framework that also allows describing mathematical and statistical models such as single‐subject or nonlinear and multivariate regression models. This tutorial provides an overview of the structure of this language, brief suggestions on how to work with it, and use cases demonstrating its power and flexibility. PMID:28575551

Shape Distributions of Nonlinear Dynamical Systems for Video-Based Inference.

PubMed

Venkataraman, Vinay; Turaga, Pavan

2016-12-01

This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and nonlinear methods with their respective drawbacks. A novel approach we propose is the use of descriptors of the shape of the dynamical attractor as a feature representation of nature of dynamics. The proposed framework has two main advantages over traditional approaches: a) representation of the dynamical system is derived directly from the observational data, without any inherent assumptions, and b) the proposed features show stability under different time-series lengths where traditional dynamical invariants fail. We illustrate our idea using nonlinear dynamical models such as Lorenz and Rossler systems, where our feature representations (shape distribution) support our hypothesis that the local shape of the reconstructed phase space can be used as a discriminative feature. Our experimental analyses on these models also indicate that the proposed framework show stability for different time-series lengths, which is useful when the available number of samples are small/variable. The specific applications of interest in this paper are: 1) activity recognition using motion capture and RGBD sensors, 2) activity quality assessment for applications in stroke rehabilitation, and 3) dynamical scene classification. We provide experimental validation through action and gesture recognition experiments on motion capture and Kinect datasets. In all these scenarios, we show experimental evidence of the favorable properties of the proposed representation.

From point process observations to collective neural dynamics: Nonlinear Hawkes process GLMs, low-dimensional dynamics and coarse graining

PubMed Central

Truccolo, Wilson

2017-01-01

This review presents a perspective on capturing collective dynamics in recorded neuronal ensembles based on multivariate point process models, inference of low-dimensional dynamics and coarse graining of spatiotemporal measurements. A general probabilistic framework for continuous time point processes reviewed, with an emphasis on multivariate nonlinear Hawkes processes with exogenous inputs. A point process generalized linear model (PP-GLM) framework for the estimation of discrete time multivariate nonlinear Hawkes processes is described. The approach is illustrated with the modeling of collective dynamics in neocortical neuronal ensembles recorded in human and non-human primates, and prediction of single-neuron spiking. A complementary approach to capture collective dynamics based on low-dimensional dynamics (“order parameters”) inferred via latent state-space models with point process observations is presented. The approach is illustrated by inferring and decoding low-dimensional dynamics in primate motor cortex during naturalistic reach and grasp movements. Finally, we briefly review hypothesis tests based on conditional inference and spatiotemporal coarse graining for assessing collective dynamics in recorded neuronal ensembles. PMID:28336305

From point process observations to collective neural dynamics: Nonlinear Hawkes process GLMs, low-dimensional dynamics and coarse graining.

PubMed

Truccolo, Wilson

2016-11-01

This review presents a perspective on capturing collective dynamics in recorded neuronal ensembles based on multivariate point process models, inference of low-dimensional dynamics and coarse graining of spatiotemporal measurements. A general probabilistic framework for continuous time point processes reviewed, with an emphasis on multivariate nonlinear Hawkes processes with exogenous inputs. A point process generalized linear model (PP-GLM) framework for the estimation of discrete time multivariate nonlinear Hawkes processes is described. The approach is illustrated with the modeling of collective dynamics in neocortical neuronal ensembles recorded in human and non-human primates, and prediction of single-neuron spiking. A complementary approach to capture collective dynamics based on low-dimensional dynamics ("order parameters") inferred via latent state-space models with point process observations is presented. The approach is illustrated by inferring and decoding low-dimensional dynamics in primate motor cortex during naturalistic reach and grasp movements. Finally, we briefly review hypothesis tests based on conditional inference and spatiotemporal coarse graining for assessing collective dynamics in recorded neuronal ensembles. Published by Elsevier Ltd.

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

A Multiscale Nested Modeling Framework to Simulate the Interaction of Surface Gravity Waves with Nonlinear Internal Gravity Waves

DTIC Science & Technology

2015-09-30

We aim at understanding the impact of tidal , seasonal, and mesoscale variability of the internal wave field and how it influences the surface waves ...Interaction of Surface Gravity Waves with Nonlinear Internal Gravity Waves Lian Shen St. Anthony Falls Laboratory and Department of Mechanical...on studying surface gravity wave evolution and spectrum in the presence of surface currents caused by strongly nonlinear internal solitary waves

General description and understanding of the nonlinear dynamics of mode-locked fiber lasers.

PubMed

Wei, Huai; Li, Bin; Shi, Wei; Zhu, Xiushan; Norwood, Robert A; Peyghambarian, Nasser; Jian, Shuisheng

2017-05-02

As a type of nonlinear system with complexity, mode-locked fiber lasers are known for their complex behaviour. It is a challenging task to understand the fundamental physics behind such complex behaviour, and a unified description for the nonlinear behaviour and the systematic and quantitative analysis of the underlying mechanisms of these lasers have not been developed. Here, we present a complexity science-based theoretical framework for understanding the behaviour of mode-locked fiber lasers by going beyond reductionism. This hierarchically structured framework provides a model with variable dimensionality, resulting in a simple view that can be used to systematically describe complex states. Moreover, research into the attractors' basins reveals the origin of stochasticity, hysteresis and multistability in these systems and presents a new method for quantitative analysis of these nonlinear phenomena. These findings pave the way for dynamics analysis and system designs of mode-locked fiber lasers. We expect that this paradigm will also enable potential applications in diverse research fields related to complex nonlinear phenomena.

Nonlinearities in Behavioral Macroeconomics.

PubMed

Gomes, Orlando

2017-07-01

This article undertakes a journey across the literature on behavioral macroeconomics, with attention concentrated on the nonlinearities that the behavioral approach typically suggests or implies. The emphasis is placed on thinking the macro economy as a living organism, composed of many interacting parts, each one having a will of its own, which is in sharp contrast with the mechanism of the orthodox view (well represented by the neoclassical or new Keynesian dynamic stochastic general equilibrium - DSGE - model). The paper advocates that a thorough understanding of individual behavior in collective contexts is the only possible avenue to further explore macroeconomic phenomena and the often observed 'anomalies' that the benchmark DSGE macro framework is unable to explain or justify. After a reflection on the role of behavioral traits as a fundamental component of a new way of thinking the economy, the article proceeds with a debate on some of the most relevant frameworks in the literature that somehow link macro behavior and nonlinearities; covered subjects include macro models with disequilibrium rules, agent-based models that highlight interaction and complexity, evolutionary switching frameworks, and inattention based decision problems. These subjects have, as a fundamental point in common, the use of behavioral elements to transform existing interpretations of the economic reality, making it more evident how irregular fluctuations emerge and unfold on the aggregate.

NL(q) Theory: A Neural Control Framework with Global Asymptotic Stability Criteria.

PubMed

Vandewalle, Joos; De Moor, Bart L.R.; Suykens, Johan A.K.

1997-06-01

In this paper a framework for model-based neural control design is presented, consisting of nonlinear state space models and controllers, parametrized by multilayer feedforward neural networks. The models and closed-loop systems are transformed into so-called NL(q) system form. NL(q) systems represent a large class of nonlinear dynamical systems consisting of q layers with alternating linear and static nonlinear operators that satisfy a sector condition. For such NL(q)s sufficient conditions for global asymptotic stability, input/output stability (dissipativity with finite L(2)-gain) and robust stability and performance are presented. The stability criteria are expressed as linear matrix inequalities. In the analysis problem it is shown how stability of a given controller can be checked. In the synthesis problem two methods for neural control design are discussed. In the first method Narendra's dynamic backpropagation for tracking on a set of specific reference inputs is modified with an NL(q) stability constraint in order to ensure, e.g., closed-loop stability. In a second method control design is done without tracking on specific reference inputs, but based on the input/output stability criteria itself, within a standard plant framework as this is done, for example, in H( infinity ) control theory and &mgr; theory. Copyright 1997 Elsevier Science Ltd.

Robust nonlinear control of vectored thrust aircraft

NASA Technical Reports Server (NTRS)

Doyle, John C.; Murray, Richard; Morris, John

1993-01-01

An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations.

A data-driven dynamics simulation framework for railway vehicles

NASA Astrophysics Data System (ADS)

Nie, Yinyu; Tang, Zhao; Liu, Fengjia; Chang, Jian; Zhang, Jianjun

2018-03-01

The finite element (FE) method is essential for simulating vehicle dynamics with fine details, especially for train crash simulations. However, factors such as the complexity of meshes and the distortion involved in a large deformation would undermine its calculation efficiency. An alternative method, the multi-body (MB) dynamics simulation provides satisfying time efficiency but limited accuracy when highly nonlinear dynamic process is involved. To maintain the advantages of both methods, this paper proposes a data-driven simulation framework for dynamics simulation of railway vehicles. This framework uses machine learning techniques to extract nonlinear features from training data generated by FE simulations so that specific mesh structures can be formulated by a surrogate element (or surrogate elements) to replace the original mechanical elements, and the dynamics simulation can be implemented by co-simulation with the surrogate element(s) embedded into a MB model. This framework consists of a series of techniques including data collection, feature extraction, training data sampling, surrogate element building, and model evaluation and selection. To verify the feasibility of this framework, we present two case studies, a vertical dynamics simulation and a longitudinal dynamics simulation, based on co-simulation with MATLAB/Simulink and Simpack, and a further comparison with a popular data-driven model (the Kriging model) is provided. The simulation result shows that using the legendre polynomial regression model in building surrogate elements can largely cut down the simulation time without sacrifice in accuracy.

A python framework for environmental model uncertainty analysis

USGS Publications Warehouse

White, Jeremy; Fienen, Michael N.; Doherty, John E.

2016-01-01

We have developed pyEMU, a python framework for Environmental Modeling Uncertainty analyses, open-source tool that is non-intrusive, easy-to-use, computationally efficient, and scalable to highly-parameterized inverse problems. The framework implements several types of linear (first-order, second-moment (FOSM)) and non-linear uncertainty analyses. The FOSM-based analyses can also be completed prior to parameter estimation to help inform important modeling decisions, such as parameterization and objective function formulation. Complete workflows for several types of FOSM-based and non-linear analyses are documented in example notebooks implemented using Jupyter that are available in the online pyEMU repository. Example workflows include basic parameter and forecast analyses, data worth analyses, and error-variance analyses, as well as usage of parameter ensemble generation and management capabilities. These workflows document the necessary steps and provides insights into the results, with the goal of educating users not only in how to apply pyEMU, but also in the underlying theory of applied uncertainty quantification.

Functional Nonlinear Mixed Effects Models For Longitudinal Image Data

PubMed Central

Luo, Xinchao; Zhu, Lixing; Kong, Linglong; Zhu, Hongtu

2015-01-01

Motivated by studying large-scale longitudinal image data, we propose a novel functional nonlinear mixed effects modeling (FN-MEM) framework to model the nonlinear spatial-temporal growth patterns of brain structure and function and their association with covariates of interest (e.g., time or diagnostic status). Our FNMEM explicitly quantifies a random nonlinear association map of individual trajectories. We develop an efficient estimation method to estimate the nonlinear growth function and the covariance operator of the spatial-temporal process. We propose a global test and a simultaneous confidence band for some specific growth patterns. We conduct Monte Carlo simulation to examine the finite-sample performance of the proposed procedures. We apply FNMEM to investigate the spatial-temporal dynamics of white-matter fiber skeletons in a national database for autism research. Our FNMEM may provide a valuable tool for charting the developmental trajectories of various neuropsychiatric and neurodegenerative disorders. PMID:26213453

Identification of nonlinear modes using phase-locked-loop experimental continuation and normal form

NASA Astrophysics Data System (ADS)

Denis, V.; Jossic, M.; Giraud-Audine, C.; Chomette, B.; Renault, A.; Thomas, O.

2018-06-01

In this article, we address the model identification of nonlinear vibratory systems, with a specific focus on systems modeled with distributed nonlinearities, such as geometrically nonlinear mechanical structures. The proposed strategy theoretically relies on the concept of nonlinear modes of the underlying conservative unforced system and the use of normal forms. Within this framework, it is shown that without internal resonance, a valid reduced order model for a nonlinear mode is a single Duffing oscillator. We then propose an efficient experimental strategy to measure the backbone curve of a particular nonlinear mode and we use it to identify the free parameters of the reduced order model. The experimental part relies on a Phase-Locked Loop (PLL) and enables a robust and automatic measurement of backbone curves as well as forced responses. It is theoretically and experimentally shown that the PLL is able to stabilize the unstable part of Duffing-like frequency responses, thus enabling its robust experimental measurement. Finally, the whole procedure is tested on three experimental systems: a circular plate, a chinese gong and a piezoelectric cantilever beam. It enable to validate the procedure by comparison to available theoretical models as well as to other experimental identification methods.

Transport through a network of capillaries from ultrametric diffusion equation with quadratic nonlinearity

NASA Astrophysics Data System (ADS)

Oleschko, K.; Khrennikov, A.

2017-10-01

This paper is about a novel mathematical framework to model transport (of, e.g., fluid or gas) through networks of capillaries. This framework takes into account the tree structure of the networks of capillaries. (Roughly speaking, we use the tree-like system of coordinates.) As is well known, tree-geometry can be topologically described as the geometry of an ultrametric space, i.e., a metric space in which the metric satisfies the strong triangle inequality: in each triangle, the third side is less than or equal to the maximum of two other sides. Thus transport (e.g., of oil or emulsion of oil and water in porous media, or blood and air in biological organisms) through networks of capillaries can be mathematically modelled as ultrametric diffusion. Such modelling was performed in a series of recently published papers of the authors. However, the process of transport through capillaries can be only approximately described by the linear diffusion, because the concentration of, e.g., oil droplets, in a capillary can essentially modify the dynamics. Therefore nonlinear dynamical equations provide a more adequate model of transport in a network of capillaries. We consider a nonlinear ultrametric diffusion equation with quadratic nonlinearity - to model transport in such a network. Here, as in the linear case, we apply the theory of ultrametric wavelets. The paper also contains a simple introduction to theory of ultrametric spaces and analysis on them.

Geomorphically based predictive mapping of soil thickness in upland watersheds

NASA Astrophysics Data System (ADS)

Pelletier, Jon D.; Rasmussen, Craig

2009-09-01

The hydrologic response of upland watersheds is strongly controlled by soil (regolith) thickness. Despite the need to quantify soil thickness for input into hydrologic models, there is currently no widely used, geomorphically based method for doing so. In this paper we describe and illustrate a new method for predictive mapping of soil thicknesses using high-resolution topographic data, numerical modeling, and field-based calibration. The model framework works directly with input digital elevation model data to predict soil thicknesses assuming a long-term balance between soil production and erosion. Erosion rates in the model are quantified using one of three geomorphically based sediment transport models: nonlinear slope-dependent transport, nonlinear area- and slope-dependent transport, and nonlinear depth- and slope-dependent transport. The model balances soil production and erosion locally to predict a family of solutions corresponding to a range of values of two unconstrained model parameters. A small number of field-based soil thickness measurements can then be used to calibrate the local value of those unconstrained parameters, thereby constraining which solution is applicable at a particular study site. As an illustration, the model is used to predictively map soil thicknesses in two small, ˜0.1 km2, drainage basins in the Marshall Gulch watershed, a semiarid drainage basin in the Santa Catalina Mountains of Pima County, Arizona. Field observations and calibration data indicate that the nonlinear depth- and slope-dependent sediment transport model is the most appropriate transport model for this site. The resulting framework provides a generally applicable, geomorphically based tool for predictive mapping of soil thickness using high-resolution topographic data sets.

Nonlinear Dynamical Modes as a Basis for Short-Term Forecast of Climate Variability

NASA Astrophysics Data System (ADS)

Feigin, A. M.; Mukhin, D.; Gavrilov, A.; Seleznev, A.; Loskutov, E.

2017-12-01

We study abilities of data-driven stochastic models constructed by nonlinear dynamical decomposition of spatially distributed data to quantitative (short-term) forecast of climate characteristics. We compare two data processing techniques: (i) widely used empirical orthogonal function approach, and (ii) nonlinear dynamical modes (NDMs) framework [1,2]. We also make comparison of two kinds of the prognostic models: (i) traditional autoregression (linear) model and (ii) model in the form of random ("stochastic") nonlinear dynamical system [3]. We apply all combinations of the above-mentioned data mining techniques and kinds of models to short-term forecasts of climate indices based on sea surface temperature (SST) data. We use NOAA_ERSST_V4 dataset (monthly SST with space resolution 20 × 20) covering the tropical belt and starting from the year 1960. We demonstrate that NDM-based nonlinear model shows better prediction skill versus EOF-based linear and nonlinear models. Finally we discuss capability of NDM-based nonlinear model for long-term (decadal) prediction of climate variability. [1] D. Mukhin, A. Gavrilov, E. Loskutov , A.Feigin, J.Kurths, 2015: Principal nonlinear dynamical modes of climate variability, Scientific Reports, rep. 5, 15510; doi: 10.1038/srep15510. [2] Gavrilov, A., Mukhin, D., Loskutov, E., Volodin, E., Feigin, A., & Kurths, J., 2016: Method for reconstructing nonlinear modes with adaptive structure from multidimensional data. Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(12), 123101. [3] Ya. Molkov, D. Mukhin, E. Loskutov, A. Feigin, 2012: Random dynamical models from time series. Phys. Rev. E, Vol. 85, n.3.

Stochastic foundations of undulatory transport phenomena: generalized Poisson-Kac processes—part III extensions and applications to kinetic theory and transport

NASA Astrophysics Data System (ADS)

Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

2017-08-01

This third part extends the theory of Generalized Poisson-Kac (GPK) processes to nonlinear stochastic models and to a continuum of states. Nonlinearity is treated in two ways: (i) as a dependence of the parameters (intensity of the stochastic velocity, transition rates) of the stochastic perturbation on the state variable, similarly to the case of nonlinear Langevin equations, and (ii) as the dependence of the stochastic microdynamic equations of motion on the statistical description of the process itself (nonlinear Fokker-Planck-Kac models). Several numerical and physical examples illustrate the theory. Gathering nonlinearity and a continuum of states, GPK theory provides a stochastic derivation of the nonlinear Boltzmann equation, furnishing a positive answer to the Kac’s program in kinetic theory. The transition from stochastic microdynamics to transport theory within the framework of the GPK paradigm is also addressed.

Reconstruction of Complex Directional Networks with Group Lasso Nonlinear Conditional Granger Causality.

PubMed

Yang, Guanxue; Wang, Lin; Wang, Xiaofan

2017-06-07

Reconstruction of networks underlying complex systems is one of the most crucial problems in many areas of engineering and science. In this paper, rather than identifying parameters of complex systems governed by pre-defined models or taking some polynomial and rational functions as a prior information for subsequent model selection, we put forward a general framework for nonlinear causal network reconstruction from time-series with limited observations. With obtaining multi-source datasets based on the data-fusion strategy, we propose a novel method to handle nonlinearity and directionality of complex networked systems, namely group lasso nonlinear conditional granger causality. Specially, our method can exploit different sets of radial basis functions to approximate the nonlinear interactions between each pair of nodes and integrate sparsity into grouped variables selection. The performance characteristic of our approach is firstly assessed with two types of simulated datasets from nonlinear vector autoregressive model and nonlinear dynamic models, and then verified based on the benchmark datasets from DREAM3 Challenge4. Effects of data size and noise intensity are also discussed. All of the results demonstrate that the proposed method performs better in terms of higher area under precision-recall curve.

Nonlinear transport theory in the metal with tunnel barrier

NASA Astrophysics Data System (ADS)

Zubov, E. E.

2018-02-01

Within the framework of the scattering matrix formalism, the nonlinear Kubo theory for electron transport in the metal with a tunnel barrier has been considered. A general expression for the mean electrical current was obtained. It significantly simplifies the calculation of nonlinear contributions to the conductivity of various hybrid structures. In the model of the tunnel Hamiltonian, all linear and nonlinear contributions to a mean electrical current are evaluated. The linear approximation agrees with results of other theories. For effective barrier transmission ?, the ballistic transport is realised with a value of the Landauer conductivity equal to ?.

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.

Nonlinear problems in flight dynamics

NASA Technical Reports Server (NTRS)

Chapman, G. T.; Tobak, M.

1984-01-01

A comprehensive framework is proposed for the description and analysis of nonlinear problems in flight dynamics. Emphasis is placed on the aerodynamic component as the major source of nonlinearities in the flight dynamic system. Four aerodynamic flows are examined to illustrate the richness and regularity of the flow structures and the nature of the flow structures and the nature of the resulting nonlinear aerodynamic forces and moments. A framework to facilitate the study of the aerodynamic system is proposed having parallel observational and mathematical components. The observational component, structure is described in the language of topology. Changes in flow structure are described via bifurcation theory. Chaos or turbulence is related to the analogous chaotic behavior of nonlinear dynamical systems characterized by the existence of strange attractors having fractal dimensionality. Scales of the flow are considered in the light of ideas from group theory. Several one and two degree of freedom dynamical systems with various mathematical models of the nonlinear aerodynamic forces and moments are examined to illustrate the resulting types of dynamical behavior. The mathematical ideas that proved useful in the description of fluid flows are shown to be similarly useful in the description of flight dynamic behavior.

Development of a Neural Network-Based Renewable Energy Forecasting Framework for Process Industries

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

Lee, Soobin; Ryu, Jun-Hyung; Hodge, Bri-Mathias

2016-06-25

This paper presents a neural network-based forecasting framework for photovoltaic power (PV) generation as a decision-supporting tool to employ renewable energies in the process industry. The applicability of the proposed framework is illustrated by comparing its performance against other methodologies such as linear and nonlinear time series modelling approaches. A case study of an actual PV power plant in South Korea is presented.

Formulation and Application of the Generalized Multilevel Facets Model

ERIC Educational Resources Information Center

Wang, Wen-Chung; Liu, Chih-Yu

2007-01-01

In this study, the authors develop a generalized multilevel facets model, which is not only a multilevel and two-parameter generalization of the facets model, but also a multilevel and facet generalization of the generalized partial credit model. Because the new model is formulated within a framework of nonlinear mixed models, no efforts are…

Remarks on Heisenberg-Euler-type electrodynamics

NASA Astrophysics Data System (ADS)

Kruglov, S. I.

2017-05-01

We consider Heisenberg-Euler-type model of nonlinear electrodynamics with two parameters. Heisenberg-Euler electrodynamics is a particular case of this model. Corrections to Coulomb’s law at r →∞ are obtained and energy conditions are studied. The total electrostatic energy of charged particles is finite. The charged black hole solution in the framework of nonlinear electrodynamics is investigated. We find the asymptotic of the metric and mass functions at r →∞. Corrections to the Reissner-Nordström solution are obtained.

PharmML in Action: an Interoperable Language for Modeling and Simulation.

PubMed

Bizzotto, R; Comets, E; Smith, G; Yvon, F; Kristensen, N R; Swat, M J

2017-10-01

PharmML is an XML-based exchange format created with a focus on nonlinear mixed-effect (NLME) models used in pharmacometrics, but providing a very general framework that also allows describing mathematical and statistical models such as single-subject or nonlinear and multivariate regression models. This tutorial provides an overview of the structure of this language, brief suggestions on how to work with it, and use cases demonstrating its power and flexibility. © 2017 The Authors CPT: Pharmacometrics & Systems Pharmacology published by Wiley Periodicals, Inc. on behalf of American Society for Clinical Pharmacology and Therapeutics.

Pions as gluons in higher dimensions

NASA Astrophysics Data System (ADS)

Cheung, Clifford; Remmen, Grant N.; Shen, Chia-Hsien; Wen, Congkao

2018-04-01

We derive the nonlinear sigma model as a peculiar dimensional reduction of Yang-Mills theory. In this framework, pions are reformulated as higher-dimensional gluons arranged in a kinematic configuration that only probes cubic interactions. This procedure yields a purely cubic action for the nonlinear sigma model that exhibits a symmetry enforcing color-kinematics duality. Remarkably, the associated kinematic algebra originates directly from the Poincaré algebra in higher dimensions. Applying the same construction to gravity yields a new quartic action for Born-Infeld theory and, applied once more, a cubic action for the special Galileon theory. Since the nonlinear sigma model and special Galileon are subtly encoded in the cubic sectors of Yang-Mills theory and gravity, respectively, their double copy relationship is automatic.

From linear to nonlinear control means: a practical progression.

PubMed

Gao, Zhiqiang

2002-04-01

With the rapid advance of digital control hardware, it is time to take the simple but effective proportional-integral-derivative (PID) control technology to the next level of performance and robustness. For this purpose, a nonlinear PID and active disturbance rejection framework are introduced in this paper. It complements the existing theory in that (1) it actively and systematically explores the use of nonlinear control mechanisms for better performance, even for linear plants; (2) it represents a control strategy that is rather independent of mathematical models of the plants, thus achieving inherent robustness and reducing design complexity. Stability analysis, as well as software/hardware test results, are presented. It is evident that the proposed framework lends itself well in seeking innovative solutions to practical problems while maintaining the simplicity and the intuitiveness of the existing technology.

On the coupling of nonlinear macro-fiber composite piezoelectric cantilever dynamics with hydrodynamic loads

NASA Astrophysics Data System (ADS)

Tan, D.; Erturk, A.

2018-03-01

For bio-inspired, fish-like robotic propulsion, the Macro-Fiber Composite (MFC) piezoelectric technology offers noiseless actuation with a balance between actuation force and velocity response. However, internal nonlinear- ities within the MFCs, such as piezoelectric softening, geometric hardening, inertial softening, and nonlinear dissipation, couple with the hydrodynamic loading on the structure from the surrounding fluid. In the present work, we explore nonlinear actuation of MFC cantilevers underwater and develop a mathematical framework for modeling and analysis. In vacuo resonant actuation experiments are conducted for a set of MFC cantilevers of varying length to width aspect ratios to validate the structural model in the absence of fluid loading. These MFC cantilevers are then subjected to underwater resonant actuation experiments, and model simulations are compared with nonlinear experimental frequency response functions. It is observed that semi-empirical hydro- dynamic loads obtained from quasilinear experiments have to be modified to account for amplitude dependent added mass, and additional nonlinear hydrodynamic effects might be present, yielding qualitative differences in the resulting underwater frequency respones curves with increased excitation amplitude.

Agent-based modeling of endotoxin-induced acute inflammatory response in human blood leukocytes.

PubMed

Dong, Xu; Foteinou, Panagiota T; Calvano, Steven E; Lowry, Stephen F; Androulakis, Ioannis P

2010-02-18

Inflammation is a highly complex biological response evoked by many stimuli. A persistent challenge in modeling this dynamic process has been the (nonlinear) nature of the response that precludes the single-variable assumption. Systems-based approaches offer a promising possibility for understanding inflammation in its homeostatic context. In order to study the underlying complexity of the acute inflammatory response, an agent-based framework is developed that models the emerging host response as the outcome of orchestrated interactions associated with intricate signaling cascades and intercellular immune system interactions. An agent-based modeling (ABM) framework is proposed to study the nonlinear dynamics of acute human inflammation. The model is implemented using NetLogo software. Interacting agents involve either inflammation-specific molecules or cells essential for the propagation of the inflammatory reaction across the system. Spatial orientation of molecule interactions involved in signaling cascades coupled with the cellular heterogeneity are further taken into account. The proposed in silico model is evaluated through its ability to successfully reproduce a self-limited inflammatory response as well as a series of scenarios indicative of the nonlinear dynamics of the response. Such scenarios involve either a persistent (non)infectious response or innate immune tolerance and potentiation effects followed by perturbations in intracellular signaling molecules and cascades. The ABM framework developed in this study provides insight on the stochastic interactions of the mediators involved in the propagation of endotoxin signaling at the cellular response level. The simulation results are in accordance with our prior research effort associated with the development of deterministic human inflammation models that include transcriptional dynamics, signaling, and physiological components. The hypothetical scenarios explored in this study would potentially improve our understanding of how manipulating the behavior of the molecular species could manifest into emergent behavior of the overall system.

Intrinsic two-dimensional features as textons

NASA Technical Reports Server (NTRS)

Barth, E.; Zetzsche, C.; Rentschler, I.

1998-01-01

We suggest that intrinsic two-dimensional (i2D) features, computationally defined as the outputs of nonlinear operators that model the activity of end-stopped neurons, play a role in preattentive texture discrimination. We first show that for discriminable textures with identical power spectra the predictions of traditional models depend on the type of nonlinearity and fail for energy measures. We then argue that the concept of intrinsic dimensionality, and the existence of end-stopped neurons, can help us to understand the role of the nonlinearities. Furthermore, we show examples in which models without strong i2D selectivity fail to predict the correct ranking order of perceptual segregation. Our arguments regarding the importance of i2D features resemble the arguments of Julesz and co-workers regarding textons such as terminators and crossings. However, we provide a computational framework that identifies textons with the outputs of nonlinear operators that are selective to i2D features.

An experimentally validated model for geometrically nonlinear plucking-based frequency up-conversion in energy harvesting

NASA Astrophysics Data System (ADS)

Kathpalia, B.; Tan, D.; Stern, I.; Erturk, A.

2018-01-01

It is well known that plucking-based frequency up-conversion can enhance the power output in piezoelectric energy harvesting by enabling cyclic free vibration at the fundamental bending mode of the harvester even for very low excitation frequencies. In this work, we present a geometrically nonlinear plucking-based framework for frequency up-conversion in piezoelectric energy harvesting under quasistatic excitations associated with low-frequency stimuli such as walking and similar rigid body motions. Axial shortening of the plectrum is essential to enable plucking excitation, which requires a nonlinear framework relating the plectrum parameters (e.g. overlap length between the plectrum and harvester) to the overall electrical power output. Von Kármán-type geometrically nonlinear deformation of the flexible plectrum cantilever is employed to relate the overlap length between the flexible (nonlinear) plectrum and the stiff (linear) harvester to the transverse quasistatic tip displacement of the plectrum, and thereby the tip load on the linear harvester in each plucking cycle. By combining the nonlinear plectrum mechanics and linear harvester dynamics with two-way electromechanical coupling, the electrical power output is obtained directly in terms of the overlap length. Experimental case studies and validations are presented for various overlap lengths and a set of electrical load resistance values. Further analysis results are reported regarding the combined effects of plectrum thickness and overlap length on the plucking force and harvested power output. The experimentally validated nonlinear plectrum-linear harvester framework proposed herein can be employed to design and optimize frequency up-conversion by properly choosing the plectrum parameters (geometry, material, overlap length, etc) as well as the harvester parameters.

Breather Rogue Waves in Random Seas

NASA Astrophysics Data System (ADS)

Wang, J.; Ma, Q. W.; Yan, S.; Chabchoub, A.

2018-01-01

Rogue or freak waves are extreme wave events that have heights exceeding 8 times the standard deviation of surrounding waves and emerge, for instance, in the ocean as well as in other physical dispersive wave guides, such as in optical fibers. One effective and convenient way to model such an extreme dynamics in laboratory environments within a controlled framework as well as for short process time and length scales is provided through the breather formalism. Breathers are pulsating localized structures known to model extreme waves in several nonlinear dispersive media in which the initial underlying process is assumed to be narrow banded. On the other hand, several recent studies suggest that breathers can also persist in more complex environments, such as in random seas, beyond the attributed physical limitations. In this work, we study the robustness of the Peregrine breather (PB) embedded in Joint North Sea Wave Project (JONSWAP) configurations using fully nonlinear hydrodynamic numerical simulations in order to validate its practicalness for ocean engineering applications. We provide a specific range for both the spectral bandwidth of the dynamical process as well as the background wave steepness and, thus, quantify the applicability of the PB in modeling rogue waves in realistic oceanic conditions. Our results may motivate analogous studies in fields of physics such as optics and plasma to quantify the limitations of exact weakly nonlinear models, such as solitons and breathers, within the framework of the fully nonlinear governing equations of the corresponding medium.

An approximation theory for the identification of nonlinear distributed parameter systems

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

Estimating linear-nonlinear models using Rényi divergences

PubMed Central

Kouh, Minjoon; Sharpee, Tatyana O.

2009-01-01

This paper compares a family of methods for characterizing neural feature selectivity using natural stimuli in the framework of the linear-nonlinear model. In this model, the spike probability depends in a nonlinear way on a small number of stimulus dimensions. The relevant stimulus dimensions can be found by optimizing a Rényi divergence that quantifies a change in the stimulus distribution associated with the arrival of single spikes. Generally, good reconstructions can be obtained based on optimization of Rényi divergence of any order, even in the limit of small numbers of spikes. However, the smallest error is obtained when the Rényi divergence of order 1 is optimized. This type of optimization is equivalent to information maximization, and is shown to saturate the Cramér-Rao bound describing the smallest error allowed for any unbiased method. We also discuss conditions under which information maximization provides a convenient way to perform maximum likelihood estimation of linear-nonlinear models from neural data. PMID:19568981

Estimating linear-nonlinear models using Renyi divergences.

PubMed

Kouh, Minjoon; Sharpee, Tatyana O

2009-01-01

This article compares a family of methods for characterizing neural feature selectivity using natural stimuli in the framework of the linear-nonlinear model. In this model, the spike probability depends in a nonlinear way on a small number of stimulus dimensions. The relevant stimulus dimensions can be found by optimizing a Rényi divergence that quantifies a change in the stimulus distribution associated with the arrival of single spikes. Generally, good reconstructions can be obtained based on optimization of Rényi divergence of any order, even in the limit of small numbers of spikes. However, the smallest error is obtained when the Rényi divergence of order 1 is optimized. This type of optimization is equivalent to information maximization, and is shown to saturate the Cramer-Rao bound describing the smallest error allowed for any unbiased method. We also discuss conditions under which information maximization provides a convenient way to perform maximum likelihood estimation of linear-nonlinear models from neural data.

Finite dimensional approximation of a class of constrained nonlinear optimal control problems

NASA Technical Reports Server (NTRS)

Gunzburger, Max D.; Hou, L. S.

1994-01-01

An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.

Melting of genomic DNA: Predictive modeling by nonlinear lattice dynamics

NASA Astrophysics Data System (ADS)

Theodorakopoulos, Nikos

2010-08-01

The melting behavior of long, heterogeneous DNA chains is examined within the framework of the nonlinear lattice dynamics based Peyrard-Bishop-Dauxois (PBD) model. Data for the pBR322 plasmid and the complete T7 phage have been used to obtain model fits and determine parameter dependence on salt content. Melting curves predicted for the complete fd phage and the Y1 and Y2 fragments of the ϕX174 phage without any adjustable parameters are in good agreement with experiment. The calculated probabilities for single base-pair opening are consistent with values obtained from imino proton exchange experiments.

Mixed linear-non-linear inversion of crustal deformation data: Bayesian inference of model, weighting and regularization parameters

NASA Astrophysics Data System (ADS)

Fukuda, Jun'ichi; Johnson, Kaj M.

2010-06-01

We present a unified theoretical framework and solution method for probabilistic, Bayesian inversions of crustal deformation data. The inversions involve multiple data sets with unknown relative weights, model parameters that are related linearly or non-linearly through theoretic models to observations, prior information on model parameters and regularization priors to stabilize underdetermined problems. To efficiently handle non-linear inversions in which some of the model parameters are linearly related to the observations, this method combines both analytical least-squares solutions and a Monte Carlo sampling technique. In this method, model parameters that are linearly and non-linearly related to observations, relative weights of multiple data sets and relative weights of prior information and regularization priors are determined in a unified Bayesian framework. In this paper, we define the mixed linear-non-linear inverse problem, outline the theoretical basis for the method, provide a step-by-step algorithm for the inversion, validate the inversion method using synthetic data and apply the method to two real data sets. We apply the method to inversions of multiple geodetic data sets with unknown relative data weights for interseismic fault slip and locking depth. We also apply the method to the problem of estimating the spatial distribution of coseismic slip on faults with unknown fault geometry, relative data weights and smoothing regularization weight.

Joint model-based clustering of nonlinear longitudinal trajectories and associated time-to-event data analysis, linked by latent class membership: with application to AIDS clinical studies.

PubMed

Huang, Yangxin; Lu, Xiaosun; Chen, Jiaqing; Liang, Juan; Zangmeister, Miriam

2017-10-27

Longitudinal and time-to-event data are often observed together. Finite mixture models are currently used to analyze nonlinear heterogeneous longitudinal data, which, by releasing the homogeneity restriction of nonlinear mixed-effects (NLME) models, can cluster individuals into one of the pre-specified classes with class membership probabilities. This clustering may have clinical significance, and be associated with clinically important time-to-event data. This article develops a joint modeling approach to a finite mixture of NLME models for longitudinal data and proportional hazard Cox model for time-to-event data, linked by individual latent class indicators, under a Bayesian framework. The proposed joint models and method are applied to a real AIDS clinical trial data set, followed by simulation studies to assess the performance of the proposed joint model and a naive two-step model, in which finite mixture model and Cox model are fitted separately.

DEPENDENCE OF STELLAR MAGNETIC ACTIVITY CYCLES ON ROTATIONAL PERIOD IN A NONLINEAR SOLAR-TYPE DYNAMO

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

Pipin, V. V.; Kosovichev, A. G.

2016-06-01

We study the turbulent generation of large-scale magnetic fields using nonlinear dynamo models for solar-type stars in the range of rotational periods from 14 to 30 days. Our models take into account nonlinear effects of dynamical quenching of magnetic helicity, and escape of magnetic field from the dynamo region due to magnetic buoyancy. The results show that the observed correlation between the period of rotation and the duration of activity cycles can be explained in the framework of a distributed dynamo model with a dynamical magnetic feedback acting on the turbulent generation from either magnetic buoyancy or magnetic helicity. Wemore » discuss implications of our findings for the understanding of dynamo processes operating in solar-like stars.« less

Multiphysics modeling of non-linear laser-matter interactions for optically active semiconductors

NASA Astrophysics Data System (ADS)

Kraczek, Brent; Kanp, Jaroslaw

Development of photonic devices for sensors and communications devices has been significantly enhanced by computational modeling. We present a new computational method for modelling laser propagation in optically-active semiconductors within the paraxial wave approximation (PWA). Light propagation is modeled using the Streamline-upwind/Petrov-Galerkin finite element method (FEM). Material response enters through the non-linear polarization, which serves as the right-hand side of the FEM calculation. Maxwell's equations for classical light propagation within the PWA can be written solely in terms of the electric field, producing a wave equation that is a form of the advection-diffusion-reaction equations (ADREs). This allows adaptation of the computational machinery developed for solving ADREs in fluid dynamics to light-propagation modeling. The non-linear polarization is incorporated using a flexible framework to enable the use of multiple methods for carrier-carrier interactions (e.g. relaxation-time-based or Monte Carlo) to enter through the non-linear polarization, as appropriate to the material type. We demonstrate using a simple carrier-carrier model approximating the response of GaN. Supported by ARL Materials Enterprise.

Nonlinear system identification of smart structures under high impact loads

NASA Astrophysics Data System (ADS)

Sarp Arsava, Kemal; Kim, Yeesock; El-Korchi, Tahar; Park, Hyo Seon

2013-05-01

The main purpose of this paper is to develop numerical models for the prediction and analysis of the highly nonlinear behavior of integrated structure control systems subjected to high impact loading. A time-delayed adaptive neuro-fuzzy inference system (TANFIS) is proposed for modeling of the complex nonlinear behavior of smart structures equipped with magnetorheological (MR) dampers under high impact forces. Experimental studies are performed to generate sets of input and output data for training and validation of the TANFIS models. The high impact load and current signals are used as the input disturbance and control signals while the displacement and acceleration responses from the structure-MR damper system are used as the output signals. The benchmark adaptive neuro-fuzzy inference system (ANFIS) is used as a baseline. Comparisons of the trained TANFIS models with experimental results demonstrate that the TANFIS modeling framework is an effective way to capture nonlinear behavior of integrated structure-MR damper systems under high impact loading. In addition, the performance of the TANFIS model is much better than that of ANFIS in both the training and the validation processes.

Nonlinear Fluid Model Of 3-D Field Effects In Tokamak Plasmas

NASA Astrophysics Data System (ADS)

Callen, J. D.; Hegna, C. C.; Beidler, M. T.

2017-10-01

Extended MHD codes (e.g., NIMROD, M3D-C1) are beginning to explore nonlinear effects of small 3-D magnetic fields on tokamak plasmas. To facilitate development of analogous physically understandable reduced models, a fluid-based dynamic nonlinear model of these added 3-D field effects in the base axisymmetric tokamak magnetic field geometry is being developed. The model incorporates kinetic-based closures within an extended MHD framework. Key 3-D field effects models that have been developed include: 1) a comprehensive modified Rutherford equation for the growth of a magnetic island that includes the classical tearing and NTM perturbed bootstrap current drives, externally applied magnetic field and current drives, and classical and neoclassical polarization current effects, and 2) dynamic nonlinear evolution of the plasma toroidal flow (radial electric field) in response to the 3-D fields. An application of this model to RMP ELM suppression precipitated by an ELM crash will be discussed. Supported by Office of Fusion Energy Sciences, Office of Science, Dept. of Energy Grants DE-FG02-86ER53218 and DE-FG02-92ER54139.

A wind turbine hybrid simulation framework considering aeroelastic effects

NASA Astrophysics Data System (ADS)

Song, Wei; Su, Weihua

2015-04-01

In performing an effective structural analysis for wind turbine, the simulation of turbine aerodynamic loads is of great importance. The interaction between the wake flow and the blades may impact turbine blades loading condition, energy yield and operational behavior. Direct experimental measurement of wind flow field and wind profiles around wind turbines is very helpful to support the wind turbine design. However, with the growth of the size of wind turbines for higher energy output, it is not convenient to obtain all the desired data in wind-tunnel and field tests. In this paper, firstly the modeling of dynamic responses of large-span wind turbine blades will consider nonlinear aeroelastic effects. A strain-based geometrically nonlinear beam formulation will be used for the basic structural dynamic modeling, which will be coupled with unsteady aerodynamic equations and rigid-body rotations of the rotor. Full wind turbines can be modeled by using the multi-connected beams. Then, a hybrid simulation experimental framework is proposed to potentially address this issue. The aerodynamic-dominant components, such as the turbine blades and rotor, are simulated as numerical components using the nonlinear aeroelastic model; while the turbine tower, where the collapse of failure may occur under high level of wind load, is simulated separately as the physical component. With the proposed framework, dynamic behavior of NREL's 5MW wind turbine blades will be studied and correlated with available numerical data. The current work will be the basis of the authors' further studies on flow control and hazard mitigation on wind turbine blades and towers.

Standard representation and unified stability analysis for dynamic artificial neural network models.

PubMed

Kim, Kwang-Ki K; Patrón, Ernesto Ríos; Braatz, Richard D

2018-02-01

An overview is provided of dynamic artificial neural network models (DANNs) for nonlinear dynamical system identification and control problems, and convex stability conditions are proposed that are less conservative than past results. The three most popular classes of dynamic artificial neural network models are described, with their mathematical representations and architectures followed by transformations based on their block diagrams that are convenient for stability and performance analyses. Classes of nonlinear dynamical systems that are universally approximated by such models are characterized, which include rigorous upper bounds on the approximation errors. A unified framework and linear matrix inequality-based stability conditions are described for different classes of dynamic artificial neural network models that take additional information into account such as local slope restrictions and whether the nonlinearities within the DANNs are odd. A theoretical example shows reduced conservatism obtained by the conditions. Copyright © 2017. Published by Elsevier Ltd.

Stochastic nonlinear mixed effects: a metformin case study.

PubMed

Matzuka, Brett; Chittenden, Jason; Monteleone, Jonathan; Tran, Hien

2016-02-01

In nonlinear mixed effect (NLME) modeling, the intra-individual variability is a collection of errors due to assay sensitivity, dosing, sampling, as well as model misspecification. Utilizing stochastic differential equations (SDE) within the NLME framework allows the decoupling of the measurement errors from the model misspecification. This leads the SDE approach to be a novel tool for model refinement. Using Metformin clinical pharmacokinetic (PK) data, the process of model development through the use of SDEs in population PK modeling was done to study the dynamics of absorption rate. A base model was constructed and then refined by using the system noise terms of the SDEs to track model parameters and model misspecification. This provides the unique advantage of making no underlying assumptions about the structural model for the absorption process while quantifying insufficiencies in the current model. This article focuses on implementing the extended Kalman filter and unscented Kalman filter in an NLME framework for parameter estimation and model development, comparing the methodologies, and illustrating their challenges and utility. The Kalman filter algorithms were successfully implemented in NLME models using MATLAB with run time differences between the ODE and SDE methods comparable to the differences found by Kakhi for their stochastic deconvolution.

A trajectory generation framework for modeling spacecraft entry in MDAO

NASA Astrophysics Data System (ADS)

D`Souza, Sarah N.; Sarigul-Klijn, Nesrin

2016-04-01

In this paper a novel trajectory generation framework was developed that optimizes trajectory event conditions for use in a Generalized Entry Guidance algorithm. The framework was developed to be adaptable via the use of high fidelity equations of motion and drag based analytical bank profiles. Within this framework, a novel technique was implemented that resolved the sensitivity of the bank profile to atmospheric non-linearities. The framework's adaptability was established by running two different entry bank conditions. Each case yielded a reference trajectory and set of transition event conditions that are flight feasible and implementable in a Generalized Entry Guidance algorithm.

A novel methodology for non-linear system identification of battery cells used in non-road hybrid electric vehicles

NASA Astrophysics Data System (ADS)

Unger, Johannes; Hametner, Christoph; Jakubek, Stefan; Quasthoff, Marcus

2014-12-01

An accurate state of charge (SoC) estimation of a traction battery in hybrid electric non-road vehicles, which possess higher dynamics and power densities than on-road vehicles, requires a precise battery cell terminal voltage model. This paper presents a novel methodology for non-linear system identification of battery cells to obtain precise battery models. The methodology comprises the architecture of local model networks (LMN) and optimal model based design of experiments (DoE). Three main novelties are proposed: 1) Optimal model based DoE, which aims to high dynamically excite the battery cells at load ranges frequently used in operation. 2) The integration of corresponding inputs in the LMN to regard the non-linearities SoC, relaxation, hysteresis as well as temperature effects. 3) Enhancements to the local linear model tree (LOLIMOT) construction algorithm, to achieve a physical appropriate interpretation of the LMN. The framework is applicable for different battery cell chemistries and different temperatures, and is real time capable, which is shown on an industrial PC. The accuracy of the obtained non-linear battery model is demonstrated on cells with different chemistries and temperatures. The results show significant improvement due to optimal experiment design and integration of the battery non-linearities within the LMN structure.

Modeling the Afferent Dynamics of the Baroreflex Control System

PubMed Central

Mahdi, Adam; Sturdy, Jacob; Ottesen, Johnny T.; Olufsen, Mette S.

2013-01-01

In this study we develop a modeling framework for predicting baroreceptor firing rate as a function of blood pressure. We test models within this framework both quantitatively and qualitatively using data from rats. The models describe three components: arterial wall deformation, stimulation of mechanoreceptors located in the BR nerve-endings, and modulation of the action potential frequency. The three sub-systems are modeled individually following well-established biological principles. The first submodel, predicting arterial wall deformation, uses blood pressure as an input and outputs circumferential strain. The mechanoreceptor stimulation model, uses circumferential strain as an input, predicting receptor deformation as an output. Finally, the neural model takes receptor deformation as an input predicting the BR firing rate as an output. Our results show that nonlinear dependence of firing rate on pressure can be accounted for by taking into account the nonlinear elastic properties of the artery wall. This was observed when testing the models using multiple experiments with a single set of parameters. We find that to model the response to a square pressure stimulus, giving rise to post-excitatory depression, it is necessary to include an integrate-and-fire model, which allows the firing rate to cease when the stimulus falls below a given threshold. We show that our modeling framework in combination with sensitivity analysis and parameter estimation can be used to test and compare models. Finally, we demonstrate that our preferred model can exhibit all known dynamics and that it is advantageous to combine qualitative and quantitative analysis methods. PMID:24348231

A nonlinear dynamical analogue model of geomagnetic activity

NASA Technical Reports Server (NTRS)

Klimas, A. J.; Baker, D. N.; Roberts, D. A.; Fairfield, D. H.; Buechner, J.

1992-01-01

Consideration is given to the solar wind-magnetosphere interaction within the framework of deterministic nonlinear dynamics. An earlier dripping faucet analog model of the low-dimensional solar wind-magnetosphere system is reviewed, and a plasma physical counterpart to that model is constructed. A Faraday loop in the magnetotail is considered, and the relationship of electric potentials on the loop to changes in the magnetic flux threading the loop is developed. This approach leads to a model of geomagnetic activity which is similar to the earlier mechanical model but described in terms of the geometry and plasma contents of the magnetotail. The model is characterized as an elementary time-dependent global convection model. The convection evolves within a magnetotail shape that varies in a prescribed manner in response to the dynamical evolution of the convection. The result is a nonlinear model capable of exhibiting a transition from regular to chaotic loading and unloading. The model's behavior under steady loading and also some elementary forms of time-dependent loading is discussed.

Models, Databases, and Simulation Tools Needed for the Realization of Integrated Computational Materials Engineering. Proceedings of the Symposium Held at Materials Science and Technology 2010

NASA Technical Reports Server (NTRS)

Arnold, Steven M. (Editor); Wong, Terry T. (Editor)

2011-01-01

Topics covered include: An Annotative Review of Multiscale Modeling and its Application to Scales Inherent in the Field of ICME; and A Multiscale, Nonlinear, Modeling Framework Enabling the Design and Analysis of Composite Materials and Structures.

Measurement and fitting techniques for the assessment of material nonlinearity using nonlinear Rayleigh waves

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

Torello, David; Kim, Jin-Yeon; Qu, Jianmin

2015-03-31

This research considers the effects of diffraction, attenuation, and the nonlinearity of generating sources on measurements of nonlinear ultrasonic Rayleigh wave propagation. A new theoretical framework for correcting measurements made with air-coupled and contact piezoelectric receivers for the aforementioned effects is provided based on analytical models and experimental considerations. A method for extracting the nonlinearity parameter β{sub 11} is proposed based on a nonlinear least squares curve-fitting algorithm that is tailored for Rayleigh wave measurements. Quantitative experiments are conducted to confirm the predictions for the nonlinearity of the piezoelectric source and to demonstrate the effectiveness of the curve-fitting procedure. Thesemore » experiments are conducted on aluminum 2024 and 7075 specimens and a β{sub 11}{sup 7075}/β{sub 11}{sup 2024} measure of 1.363 agrees well with previous literature and earlier work.« less

Local interaction simulation approach to modelling nonclassical, nonlinear elastic behavior in solids.

PubMed

Scalerandi, Marco; Agostini, Valentina; Delsanto, Pier Paolo; Van Den Abeele, Koen; Johnson, Paul A

2003-06-01

Recent studies show that a broad category of materials share "nonclassical" nonlinear elastic behavior much different from "classical" (Landau-type) nonlinearity. Manifestations of "nonclassical" nonlinearity include stress-strain hysteresis and discrete memory in quasistatic experiments, and specific dependencies of the harmonic amplitudes with respect to the drive amplitude in dynamic wave experiments, which are remarkably different from those predicted by the classical theory. These materials have in common soft "bond" elements, where the elastic nonlinearity originates, contained in hard matter (e.g., a rock sample). The bond system normally comprises a small fraction of the total material volume, and can be localized (e.g., a crack in a solid) or distributed, as in a rock. In this paper a model is presented in which the soft elements are treated as hysteretic or reversible elastic units connected in a one-dimensional lattice to elastic elements (grains), which make up the hard matrix. Calculations are performed in the framework of the local interaction simulation approach (LISA). Experimental observations are well predicted by the model, which is now ready both for basic investigations about the physical origins of nonlinear elasticity and for applications to material damage diagnostics.

Onboard Nonlinear Engine Sensor and Component Fault Diagnosis and Isolation Scheme

NASA Technical Reports Server (NTRS)

Tang, Liang; DeCastro, Jonathan A.; Zhang, Xiaodong

2011-01-01

A method detects and isolates in-flight sensor, actuator, and component faults for advanced propulsion systems. In sharp contrast to many conventional methods, which deal with either sensor fault or component fault, but not both, this method considers sensor fault, actuator fault, and component fault under one systemic and unified framework. The proposed solution consists of two main components: a bank of real-time, nonlinear adaptive fault diagnostic estimators for residual generation, and a residual evaluation module that includes adaptive thresholds and a Transferable Belief Model (TBM)-based residual evaluation scheme. By employing a nonlinear adaptive learning architecture, the developed approach is capable of directly dealing with nonlinear engine models and nonlinear faults without the need of linearization. Software modules have been developed and evaluated with the NASA C-MAPSS engine model. Several typical engine-fault modes, including a subset of sensor/actuator/components faults, were tested with a mild transient operation scenario. The simulation results demonstrated that the algorithm was able to successfully detect and isolate all simulated faults as long as the fault magnitudes were larger than the minimum detectable/isolable sizes, and no misdiagnosis occurred

A Novel Information-Theoretic Approach for Variable Clustering and Predictive Modeling Using Dirichlet Process Mixtures

PubMed Central

Chen, Yun; Yang, Hui

2016-01-01

In the era of big data, there are increasing interests on clustering variables for the minimization of data redundancy and the maximization of variable relevancy. Existing clustering methods, however, depend on nontrivial assumptions about the data structure. Note that nonlinear interdependence among variables poses significant challenges on the traditional framework of predictive modeling. In the present work, we reformulate the problem of variable clustering from an information theoretic perspective that does not require the assumption of data structure for the identification of nonlinear interdependence among variables. Specifically, we propose the use of mutual information to characterize and measure nonlinear correlation structures among variables. Further, we develop Dirichlet process (DP) models to cluster variables based on the mutual-information measures among variables. Finally, orthonormalized variables in each cluster are integrated with group elastic-net model to improve the performance of predictive modeling. Both simulation and real-world case studies showed that the proposed methodology not only effectively reveals the nonlinear interdependence structures among variables but also outperforms traditional variable clustering algorithms such as hierarchical clustering. PMID:27966581

A Novel Information-Theoretic Approach for Variable Clustering and Predictive Modeling Using Dirichlet Process Mixtures.

PubMed

Chen, Yun; Yang, Hui

2016-12-14

In the era of big data, there are increasing interests on clustering variables for the minimization of data redundancy and the maximization of variable relevancy. Existing clustering methods, however, depend on nontrivial assumptions about the data structure. Note that nonlinear interdependence among variables poses significant challenges on the traditional framework of predictive modeling. In the present work, we reformulate the problem of variable clustering from an information theoretic perspective that does not require the assumption of data structure for the identification of nonlinear interdependence among variables. Specifically, we propose the use of mutual information to characterize and measure nonlinear correlation structures among variables. Further, we develop Dirichlet process (DP) models to cluster variables based on the mutual-information measures among variables. Finally, orthonormalized variables in each cluster are integrated with group elastic-net model to improve the performance of predictive modeling. Both simulation and real-world case studies showed that the proposed methodology not only effectively reveals the nonlinear interdependence structures among variables but also outperforms traditional variable clustering algorithms such as hierarchical clustering.

From microscopic taxation and redistribution models to macroscopic income distributions

NASA Astrophysics Data System (ADS)

Bertotti, Maria Letizia; Modanese, Giovanni

2011-10-01

We present here a general framework, expressed by a system of nonlinear differential equations, suitable for the modeling of taxation and redistribution in a closed society. This framework allows one to describe the evolution of income distribution over the population and to explain the emergence of collective features based on knowledge of the individual interactions. By making different choices of the framework parameters, we construct different models, whose long-time behavior is then investigated. Asymptotic stationary distributions are found, which enjoy similar properties as those observed in empirical distributions. In particular, they exhibit power law tails of Pareto type and their Lorenz curves and Gini indices are consistent with some real world ones.

Using missing ordinal patterns to detect nonlinearity in time series data.

PubMed

Kulp, Christopher W; Zunino, Luciano; Osborne, Thomas; Zawadzki, Brianna

2017-08-01

The number of missing ordinal patterns (NMP) is the number of ordinal patterns that do not appear in a series after it has been symbolized using the Bandt and Pompe methodology. In this paper, the NMP is demonstrated as a test for nonlinearity using a surrogate framework in order to see if the NMP for a series is statistically different from the NMP of iterative amplitude adjusted Fourier transform (IAAFT) surrogates. It is found that the NMP works well as a test statistic for nonlinearity, even in the cases of very short time series. Both model and experimental time series are used to demonstrate the efficacy of the NMP as a test for nonlinearity.

Multi Length Scale Finite Element Design Framework for Advanced Woven Fabrics

NASA Astrophysics Data System (ADS)

Erol, Galip Ozan

Woven fabrics are integral parts of many engineering applications spanning from personal protective garments to surgical scaffolds. They provide a wide range of opportunities in designing advanced structures because of their high tenacity, flexibility, high strength-to-weight ratios and versatility. These advantages result from their inherent multi scale nature where the filaments are bundled together to create yarns while the yarns are arranged into different weave architectures. Their highly versatile nature opens up potential for a wide range of mechanical properties which can be adjusted based on the application. While woven fabrics are viable options for design of various engineering systems, being able to understand the underlying mechanisms of the deformation and associated highly nonlinear mechanical response is important and necessary. However, the multiscale nature and relationships between these scales make the design process involving woven fabrics a challenging task. The objective of this work is to develop a multiscale numerical design framework using experimentally validated mesoscopic and macroscopic length scale approaches by identifying important deformation mechanisms and recognizing the nonlinear mechanical response of woven fabrics. This framework is exercised by developing mesoscopic length scale constitutive models to investigate plain weave fabric response under a wide range of loading conditions. A hyperelastic transversely isotropic yarn material model with transverse material nonlinearity is developed for woven yarns (commonly used in personal protection garments). The material properties/parameters are determined through an inverse method where unit cell finite element simulations are coupled with experiments. The developed yarn material model is validated by simulating full scale uniaxial tensile, bias extension and indentation experiments, and comparing to experimentally observed mechanical response and deformation mechanisms. Moreover, mesoscopic unit cell finite elements are coupled with a design-of-experiments method to systematically identify the important yarn material properties for the macroscale response of various weave architectures. To demonstrate the macroscopic length scale approach, two new material models for woven fabrics were developed. The Planar Material Model (PMM) utilizes two important deformation mechanisms in woven fabrics: (1) yarn elongation, and (2) relative yarn rotation due to shear loads. The yarns' uniaxial tensile response is modeled with a nonlinear spring using constitutive relations while a nonlinear rotational spring is implemented to define fabric's shear stiffness. The second material model, Sawtooth Material Model (SMM) adopts the sawtooth geometry while recognizing the biaxial nature of woven fabrics by implementing the interactions between the yarns. Material properties/parameters required by both PMM and SMM can be directly determined from standard experiments. Both macroscopic material models are implemented within an explicit finite element code and validated by comparing to the experiments. Then, the developed macroscopic material models are compared under various loading conditions to determine their accuracy. Finally, the numerical models developed in the mesoscopic and macroscopic length scales are linked thus demonstrating the new systematic design framework involving linked mesoscopic and macroscopic length scale modeling approaches. The approach is demonstrated with both Planar and Sawtooth Material Models and the simulation results are verified by comparing the results obtained from meso and macro models.

Investigation on the effect of nonlinear processes on similarity law in high-pressure argon discharges

NASA Astrophysics Data System (ADS)

Fu, Yangyang; Parsey, Guy M.; Verboncoeur, John P.; Christlieb, Andrew J.

2017-11-01

In this paper, the effect of nonlinear processes (such as three-body collisions and stepwise ionizations) on the similarity law in high-pressure argon discharges has been studied by the use of the Kinetic Global Model framework. In the discharge model, the ground state argon atoms (Ar), electrons (e), atom ions (Ar+), molecular ions (Ar2+), and fourteen argon excited levels Ar*(4s and 4p) are considered. The steady-state electron and ion densities are obtained with nonlinear processes included and excluded in the designed models, respectively. It is found that in similar gas gaps, keeping the product of gas pressure and linear dimension unchanged, with the nonlinear processes included, the normalized density relations deviate from the similarity relations gradually as the scale-up factor decreases. Without the nonlinear processes, the parameter relations are in good agreement with the similarity law predictions. Furthermore, the pressure and the dimension effects are also investigated separately with and without the nonlinear processes. It is shown that the gas pressure effect on the results is less obvious than the dimension effect. Without the nonlinear processes, the pressure and the dimension effects could be estimated from one to the other based on the similarity relations.

Introduction to Communication Systems

DTIC Science & Technology

2013-08-18

nonlinear differential equations involved, and to compare the results with the linearized analysis. Nonlinear model for the first order PLL: Let us try to...approaches to scaling up data rates: increasing spatial reuse (i.e., using the same time -bandwidth resources at locations that are far enough apart), and... Even when this music is recorded onto a digital storage medium such as a CD ( using the digital communication framework outlined in Section 1.1.2), when

Nonlinear discrete-time multirate adaptive control of non-linear vibrations of smart beams

NASA Astrophysics Data System (ADS)

Georgiou, Georgios; Foutsitzi, Georgia A.; Stavroulakis, Georgios E.

2018-06-01

The nonlinear adaptive digital control of a smart piezoelectric beam is considered. It is shown that in the case of a sampled-data context, a multirate control strategy provides an appropriate framework in order to achieve vibration regulation, ensuring the stability of the whole control system. Under parametric uncertainties in the model parameters (damping ratios, frequencies, levels of non linearities and cross coupling, control input parameters), the scheme is completed with an adaptation law deduced from hyperstability concepts. This results in the asymptotic satisfaction of the control objectives at the sampling instants. Simulation results are presented.

A FSI computational framework for vascular physiopathology: A novel flow-tissue multiscale strategy.

PubMed

Bianchi, Daniele; Monaldo, Elisabetta; Gizzi, Alessio; Marino, Michele; Filippi, Simonetta; Vairo, Giuseppe

2017-09-01

A novel fluid-structure computational framework for vascular applications is herein presented. It is developed by combining the double multi-scale nature of vascular physiopathology in terms of both tissue properties and blood flow. Addressing arterial tissues, they are modelled via a nonlinear multiscale constitutive rationale, based only on parameters having a clear histological and biochemical meaning. Moreover, blood flow is described by coupling a three-dimensional fluid domain (undergoing physiological inflow conditions) with a zero-dimensional model, which allows to reproduce the influence of the downstream vasculature, furnishing a realistic description of the outflow proximal pressure. The fluid-structure interaction is managed through an explicit time-marching approach, able to accurately describe tissue nonlinearities within each computational step for the fluid problem. A case study associated to a patient-specific aortic abdominal aneurysmatic geometry is numerically investigated, highlighting advantages gained from the proposed multiscale strategy, as well as showing soundness and effectiveness of the established framework for assessing useful clinical quantities and risk indexes. Copyright © 2017 IPEM. Published by Elsevier Ltd. All rights reserved.

A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials

NASA Astrophysics Data System (ADS)

Matouš, Karel; Geers, Marc G. D.; Kouznetsova, Varvara G.; Gillman, Andrew

2017-02-01

Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today's electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platform in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world's largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.

A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials

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

Matouš, Karel, E-mail: kmatous@nd.edu; Geers, Marc G.D.; Kouznetsova, Varvara G.

2017-02-01

Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today's electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platformmore » in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world's largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.« less

Computational homogenisation for thermoviscoplasticity: application to thermally sprayed coatings

NASA Astrophysics Data System (ADS)

Berthelsen, Rolf; Denzer, Ralf; Oppermann, Philip; Menzel, Andreas

2017-11-01

Metal forming processes require wear-resistant tool surfaces in order to ensure a long life cycle of the expensive tools together with a constant high quality of the produced components. Thermal spraying is a relatively widely applied coating technique for the deposit of wear protection coatings. During these coating processes, heterogeneous coatings are deployed at high temperatures followed by quenching where residual stresses occur which strongly influence the performance of the coated tools. The objective of this article is to discuss and apply a thermo-mechanically coupled simulation framework which captures the heterogeneity of the deposited coating material. Therefore, a two-scale finite element framework for the solution of nonlinear thermo-mechanically coupled problems is elaborated and applied to the simulation of thermoviscoplastic material behaviour including nonlinear thermal softening in a geometrically linearised setting. The finite element framework and material model is demonstrated by means of numerical examples.

PetIGA: A framework for high-performance isogeometric analysis

DOE PAGES

Dalcin, Lisandro; Collier, Nathaniel; Vignal, Philippe; ...

2016-05-25

We present PetIGA, a code framework to approximate the solution of partial differential equations using isogeometric analysis. PetIGA can be used to assemble matrices and vectors which come from a Galerkin weak form, discretized with Non-Uniform Rational B-spline basis functions. We base our framework on PETSc, a high-performance library for the scalable solution of partial differential equations, which simplifies the development of large-scale scientific codes, provides a rich environment for prototyping, and separates parallelism from algorithm choice. We describe the implementation of PetIGA, and exemplify its use by solving a model nonlinear problem. To illustrate the robustness and flexibility ofmore » PetIGA, we solve some challenging nonlinear partial differential equations that include problems in both solid and fluid mechanics. Lastly, we show strong scaling results on up to 4096 cores, which confirm the suitability of PetIGA for large scale simulations.« less

Visual aftereffects and sensory nonlinearities from a single statistical framework

PubMed Central

Laparra, Valero; Malo, Jesús

2015-01-01

When adapted to a particular scenery our senses may fool us: colors are misinterpreted, certain spatial patterns seem to fade out, and static objects appear to move in reverse. A mere empirical description of the mechanisms tuned to color, texture, and motion may tell us where these visual illusions come from. However, such empirical models of gain control do not explain why these mechanisms work in this apparently dysfunctional manner. Current normative explanations of aftereffects based on scene statistics derive gain changes by (1) invoking decorrelation and linear manifold matching/equalization, or (2) using nonlinear divisive normalization obtained from parametric scene models. These principled approaches have different drawbacks: the first is not compatible with the known saturation nonlinearities in the sensors and it cannot fully accomplish information maximization due to its linear nature. In the second, gain change is almost determined a priori by the assumed parametric image model linked to divisive normalization. In this study we show that both the response changes that lead to aftereffects and the nonlinear behavior can be simultaneously derived from a single statistical framework: the Sequential Principal Curves Analysis (SPCA). As opposed to mechanistic models, SPCA is not intended to describe how physiological sensors work, but it is focused on explaining why they behave as they do. Nonparametric SPCA has two key advantages as a normative model of adaptation: (i) it is better than linear techniques as it is a flexible equalization that can be tuned for more sensible criteria other than plain decorrelation (either full information maximization or error minimization); and (ii) it makes no a priori functional assumption regarding the nonlinearity, so the saturations emerge directly from the scene data and the goal (and not from the assumed function). It turns out that the optimal responses derived from these more sensible criteria and SPCA are consistent with dysfunctional behaviors such as aftereffects. PMID:26528165

Modern meta-heuristics based on nonlinear physics processes: A review of models and design procedures

NASA Astrophysics Data System (ADS)

Salcedo-Sanz, S.

2016-10-01

Meta-heuristic algorithms are problem-solving methods which try to find good-enough solutions to very hard optimization problems, at a reasonable computation time, where classical approaches fail, or cannot even been applied. Many existing meta-heuristics approaches are nature-inspired techniques, which work by simulating or modeling different natural processes in a computer. Historically, many of the most successful meta-heuristic approaches have had a biological inspiration, such as evolutionary computation or swarm intelligence paradigms, but in the last few years new approaches based on nonlinear physics processes modeling have been proposed and applied with success. Non-linear physics processes, modeled as optimization algorithms, are able to produce completely new search procedures, with extremely effective exploration capabilities in many cases, which are able to outperform existing optimization approaches. In this paper we review the most important optimization algorithms based on nonlinear physics, how they have been constructed from specific modeling of a real phenomena, and also their novelty in terms of comparison with alternative existing algorithms for optimization. We first review important concepts on optimization problems, search spaces and problems' difficulty. Then, the usefulness of heuristics and meta-heuristics approaches to face hard optimization problems is introduced, and some of the main existing classical versions of these algorithms are reviewed. The mathematical framework of different nonlinear physics processes is then introduced as a preparatory step to review in detail the most important meta-heuristics based on them. A discussion on the novelty of these approaches, their main computational implementation and design issues, and the evaluation of a novel meta-heuristic based on Strange Attractors mutation will be carried out to complete the review of these techniques. We also describe some of the most important application areas, in broad sense, of meta-heuristics, and describe free-accessible software frameworks which can be used to make easier the implementation of these algorithms.

Multi-disease analysis of maternal antibody decay using non-linear mixed models accounting for censoring.

PubMed

Goeyvaerts, Nele; Leuridan, Elke; Faes, Christel; Van Damme, Pierre; Hens, Niel

2015-09-10

Biomedical studies often generate repeated measures of multiple outcomes on a set of subjects. It may be of interest to develop a biologically intuitive model for the joint evolution of these outcomes while assessing inter-subject heterogeneity. Even though it is common for biological processes to entail non-linear relationships, examples of multivariate non-linear mixed models (MNMMs) are still fairly rare. We contribute to this area by jointly analyzing the maternal antibody decay for measles, mumps, rubella, and varicella, allowing for a different non-linear decay model for each infectious disease. We present a general modeling framework to analyze multivariate non-linear longitudinal profiles subject to censoring, by combining multivariate random effects, non-linear growth and Tobit regression. We explore the hypothesis of a common infant-specific mechanism underlying maternal immunity using a pairwise correlated random-effects approach and evaluating different correlation matrix structures. The implied marginal correlation between maternal antibody levels is estimated using simulations. The mean duration of passive immunity was less than 4 months for all diseases with substantial heterogeneity between infants. The maternal antibody levels against rubella and varicella were found to be positively correlated, while little to no correlation could be inferred for the other disease pairs. For some pairs, computational issues occurred with increasing correlation matrix complexity, which underlines the importance of further developing estimation methods for MNMMs. Copyright © 2015 John Wiley & Sons, Ltd.

Tackling non-linearities with the effective field theory of dark energy and modified gravity

NASA Astrophysics Data System (ADS)

Frusciante, Noemi; Papadomanolakis, Georgios

2017-12-01

We present the extension of the effective field theory framework to the mildly non-linear scales. The effective field theory approach has been successfully applied to the late time cosmic acceleration phenomenon and it has been shown to be a powerful method to obtain predictions about cosmological observables on linear scales. However, mildly non-linear scales need to be consistently considered when testing gravity theories because a large part of the data comes from those scales. Thus, non-linear corrections to predictions on observables coming from the linear analysis can help in discriminating among different gravity theories. We proceed firstly by identifying the necessary operators which need to be included in the effective field theory Lagrangian in order to go beyond the linear order in perturbations and then we construct the corresponding non-linear action. Moreover, we present the complete recipe to map any single field dark energy and modified gravity models into the non-linear effective field theory framework by considering a general action in the Arnowitt-Deser-Misner formalism. In order to illustrate this recipe we proceed to map the beyond-Horndeski theory and low-energy Hořava gravity into the effective field theory formalism. As a final step we derived the 4th order action in term of the curvature perturbation. This allowed us to identify the non-linear contributions coming from the linear order perturbations which at the next order act like source terms. Moreover, we confirm that the stability requirements, ensuring the positivity of the kinetic term and the speed of propagation for scalar mode, are automatically satisfied once the viability of the theory is demanded at linear level. The approach we present here will allow to construct, in a model independent way, all the relevant predictions on observables at mildly non-linear scales.

VBA: A Probabilistic Treatment of Nonlinear Models for Neurobiological and Behavioural Data

PubMed Central

Daunizeau, Jean; Adam, Vincent; Rigoux, Lionel

2014-01-01

This work is in line with an on-going effort tending toward a computational (quantitative and refutable) understanding of human neuro-cognitive processes. Many sophisticated models for behavioural and neurobiological data have flourished during the past decade. Most of these models are partly unspecified (i.e. they have unknown parameters) and nonlinear. This makes them difficult to peer with a formal statistical data analysis framework. In turn, this compromises the reproducibility of model-based empirical studies. This work exposes a software toolbox that provides generic, efficient and robust probabilistic solutions to the three problems of model-based analysis of empirical data: (i) data simulation, (ii) parameter estimation/model selection, and (iii) experimental design optimization. PMID:24465198

Inferring Nonlinear Neuronal Computation Based on Physiologically Plausible Inputs

PubMed Central

McFarland, James M.; Cui, Yuwei; Butts, Daniel A.

2013-01-01

The computation represented by a sensory neuron's response to stimuli is constructed from an array of physiological processes both belonging to that neuron and inherited from its inputs. Although many of these physiological processes are known to be nonlinear, linear approximations are commonly used to describe the stimulus selectivity of sensory neurons (i.e., linear receptive fields). Here we present an approach for modeling sensory processing, termed the Nonlinear Input Model (NIM), which is based on the hypothesis that the dominant nonlinearities imposed by physiological mechanisms arise from rectification of a neuron's inputs. Incorporating such ‘upstream nonlinearities’ within the standard linear-nonlinear (LN) cascade modeling structure implicitly allows for the identification of multiple stimulus features driving a neuron's response, which become directly interpretable as either excitatory or inhibitory. Because its form is analogous to an integrate-and-fire neuron receiving excitatory and inhibitory inputs, model fitting can be guided by prior knowledge about the inputs to a given neuron, and elements of the resulting model can often result in specific physiological predictions. Furthermore, by providing an explicit probabilistic model with a relatively simple nonlinear structure, its parameters can be efficiently optimized and appropriately regularized. Parameter estimation is robust and efficient even with large numbers of model components and in the context of high-dimensional stimuli with complex statistical structure (e.g. natural stimuli). We describe detailed methods for estimating the model parameters, and illustrate the advantages of the NIM using a range of example sensory neurons in the visual and auditory systems. We thus present a modeling framework that can capture a broad range of nonlinear response functions while providing physiologically interpretable descriptions of neural computation. PMID:23874185

A modular approach for item response theory modeling with the R package flirt.

PubMed

Jeon, Minjeong; Rijmen, Frank

2016-06-01

The new R package flirt is introduced for flexible item response theory (IRT) modeling of psychological, educational, and behavior assessment data. flirt integrates a generalized linear and nonlinear mixed modeling framework with graphical model theory. The graphical model framework allows for efficient maximum likelihood estimation. The key feature of flirt is its modular approach to facilitate convenient and flexible model specifications. Researchers can construct customized IRT models by simply selecting various modeling modules, such as parametric forms, number of dimensions, item and person covariates, person groups, link functions, etc. In this paper, we describe major features of flirt and provide examples to illustrate how flirt works in practice.

A comparison of linear and non-linear data assimilation methods using the NEMO ocean model

NASA Astrophysics Data System (ADS)

Kirchgessner, Paul; Tödter, Julian; Nerger, Lars

2015-04-01

The assimilation behavior of the widely used LETKF is compared with the Equivalent Weight Particle Filter (EWPF) in a data assimilation application with an idealized configuration of the NEMO ocean model. The experiments show how the different filter methods behave when they are applied to a realistic ocean test case. The LETKF is an ensemble-based Kalman filter, which assumes Gaussian error distributions and hence implicitly requires model linearity. In contrast, the EWPF is a fully nonlinear data assimilation method that does not rely on a particular error distribution. The EWPF has been demonstrated to work well in highly nonlinear situations, like in a model solving a barotropic vorticity equation, but it is still unknown how the assimilation performance compares to ensemble Kalman filters in realistic situations. For the experiments, twin assimilation experiments with a square basin configuration of the NEMO model are performed. The configuration simulates a double gyre, which exhibits significant nonlinearity. The LETKF and EWPF are both implemented in PDAF (Parallel Data Assimilation Framework, http://pdaf.awi.de), which ensures identical experimental conditions for both filters. To account for the nonlinearity, the assimilation skill of the two methods is assessed by using different statistical metrics, like CRPS and Histograms.

Nonlinear finite-element analysis of nanoindentation of viral capsids

NASA Astrophysics Data System (ADS)

Gibbons, Melissa M.; Klug, William S.

2007-03-01

Recent atomic force microscope (AFM) nanoindentation experiments measuring mechanical response of the protein shells of viruses have provided a quantitative description of their strength and elasticity. To better understand and interpret these measurements, and to elucidate the underlying mechanisms, this paper adopts a course-grained modeling approach within the framework of three-dimensional nonlinear continuum elasticity. Homogeneous, isotropic, elastic, thick-shell models are proposed for two capsids: the spherical cowpea chlorotic mottle virus (CCMV), and the ellipsocylindrical bacteriophage ϕ29 . As analyzed by the finite-element method, these models enable parametric characterization of the effects of AFM tip geometry, capsid dimensions, and capsid constitutive descriptions. The generally nonlinear force response of capsids to indentation is shown to be insensitive to constitutive particulars, and greatly influenced by geometric and kinematic details. Nonlinear stiffening and softening of the force response is dependent on the AFM tip dimensions and shell thickness. Fits of the models capture the roughly linear behavior observed in experimental measurements and result in estimates of Young’s moduli of ≈280-360MPa for CCMV and ≈4.5GPa for ϕ29 .

Describing complex cells in primary visual cortex: a comparison of context and multi-filter LN models.

PubMed

Westö, Johan; May, Patrick J C

2018-05-02

Receptive field (RF) models are an important tool for deciphering neural responses to sensory stimuli. The two currently popular RF models are multi-filter linear-nonlinear (LN) models and context models. Models are, however, never correct and they rely on assumptions to keep them simple enough to be interpretable. As a consequence, different models describe different stimulus-response mappings, which may or may not be good approximations of real neural behavior. In the current study, we take up two tasks: First, we introduce new ways to estimate context models with realistic nonlinearities, that is, with logistic and exponential functions. Second, we evaluate context models and multi-filter LN models in terms of how well they describe recorded data from complex cells in cat primary visual cortex. Our results, based on single-spike information and correlation coefficients, indicate that context models outperform corresponding multi-filter LN models of equal complexity (measured in terms of number of parameters), with the best increase in performance being achieved by the novel context models. Consequently, our results suggest that the multi-filter LN-model framework is suboptimal for describing the behavior of complex cells: the context-model framework is clearly superior while still providing interpretable quantizations of neural behavior.

Results of including geometric nonlinearities in an aeroelastic model of an F/A-18

NASA Technical Reports Server (NTRS)

Buttrill, Carey S.

1989-01-01

An integrated, nonlinear simulation model suitable for aeroelastic modeling of fixed-wing aircraft has been developed. While the author realizes that the subject of modeling rotating, elastic structures is not closed, it is believed that the equations of motion developed and applied herein are correct to second order and are suitable for use with typical aircraft structures. The equations are not suitable for large elastic deformation. In addition, the modeling framework generalizes both the methods and terminology of non-linear rigid-body airplane simulation and traditional linear aeroelastic modeling. Concerning the importance of angular/elastic inertial coupling in the dynamic analysis of fixed-wing aircraft, the following may be said. The rigorous inclusion of said coupling is not without peril and must be approached with care. In keeping with the same engineering judgment that guided the development of the traditional aeroelastic equations, the effect of non-linear inertial effects for most airplane applications is expected to be small. A parameter does not tell the whole story, however, and modes flagged by the parameter as significant also need to be checked to see if the coupling is not a one-way path, i.e., the inertially affected modes can influence other modes.

Adaptive and neuroadaptive control for nonnegative and compartmental dynamical systems

NASA Astrophysics Data System (ADS)

Volyanskyy, Kostyantyn Y.

Neural networks have been extensively used for adaptive system identification as well as adaptive and neuroadaptive control of highly uncertain systems. The goal of adaptive and neuroadaptive control is to achieve system performance without excessive reliance on system models. To improve robustness and the speed of adaptation of adaptive and neuroadaptive controllers several controller architectures have been proposed in the literature. In this dissertation, we develop a new neuroadaptive control architecture for nonlinear uncertain dynamical systems. The proposed framework involves a novel controller architecture with additional terms in the update laws that are constructed using a moving window of the integrated system uncertainty. These terms can be used to identify the ideal system weights of the neural network as well as effectively suppress system uncertainty. Linear and nonlinear parameterizations of the system uncertainty are considered and state and output feedback neuroadaptive controllers are developed. Furthermore, we extend the developed framework to discrete-time dynamical systems. To illustrate the efficacy of the proposed approach we apply our results to an aircraft model with wing rock dynamics, a spacecraft model with unknown moment of inertia, and an unmanned combat aerial vehicle undergoing actuator failures, and compare our results with standard neuroadaptive control methods. Nonnegative systems are essential in capturing the behavior of a wide range of dynamical systems involving dynamic states whose values are nonnegative. A sub-class of nonnegative dynamical systems are compartmental systems. These systems are derived from mass and energy balance considerations and are comprised of homogeneous interconnected microscopic subsystems or compartments which exchange variable quantities of material via intercompartmental flow laws. In this dissertation, we develop direct adaptive and neuroadaptive control framework for stabilization, disturbance rejection and noise suppression for nonnegative and compartmental dynamical systems with noise and exogenous system disturbances. We then use the developed framework to control the infusion of the anesthetic drug propofol for maintaining a desired constant level of depth of anesthesia for surgery in the face of continuing hemorrhage and hemodilution. Critical care patients, whether undergoing surgery or recovering in intensive care units, require drug administration to regulate physiological variables such as blood pressure, cardiac output, heart rate, and degree of consciousness. The rate of infusion of each administered drug is critical, requiring constant monitoring and frequent adjustments. In this dissertation, we develop a neuroadaptive output feedback control framework for nonlinear uncertain nonnegative and compartmental systems with nonnegative control inputs and noisy measurements. The proposed framework is Lyapunov-based and guarantees ultimate boundedness of the error signals. In addition, the neuroadaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state space. Finally, the developed approach is used to control the infusion of the anesthetic drug propofol for maintaining a desired constant level of depth of anesthesia for surgery in the face of noisy electroencephalographic (EEG) measurements. Clinical trials demonstrate excellent regulation of unconsciousness allowing for a safe and effective administration of the anesthetic agent propofol. Furthermore, a neuroadaptive output feedback control architecture for nonlinear nonnegative dynamical systems with input amplitude and integral constraints is developed. Specifically, the neuroadaptive controller guarantees that the imposed amplitude and integral input constraints are satisfied and the physical system states remain in the nonnegative orthant of the state space. The proposed approach is used to control the infusion of the anesthetic drug propofol for maintaining a desired constant level of depth of anesthesia for noncardiac surgery in the face of infusion rate constraints and a drug dosing constraint over a specified period. In addition, the aforementioned control architecture is used to control lung volume and minute ventilation with input pressure constraints that also accounts for spontaneous breathing by the patient. Specifically, we develop a pressure- and work-limited neuroadaptive controller for mechanical ventilation based on a nonlinear multi-compartmental lung model. The control framework does not rely on any averaged data and is designed to automatically adjust the input pressure to the patient's physiological characteristics capturing lung resistance and compliance modeling uncertainty. Moreover, the controller accounts for input pressure constraints as well as work of breathing constraints. The effect of spontaneous breathing is incorporated within the lung model and the control framework. Finally, a neural network hybrid adaptive control framework for nonlinear uncertain hybrid dynamical systems is developed. The proposed hybrid adaptive control framework is Lyapunov-based and guarantees partial asymptotic stability of the closed-loop hybrid system; that is, asymptotic stability with respect to part of the closed-loop system states associated with the hybrid plant states. A numerical example is provided to demonstrate the efficacy of the proposed hybrid adaptive stabilization approach.

20th Annual Systems Engineering Conference, Thursday, Volume 4

DTIC Science & Technology

2017-10-26

Daniel Dault, Air Force Research Lab 19809 Physics Based Modeling & Simulation For Shock and Vulnerability Assessments - Navy Enhanced Sierra...19811 Version 1.0 of the New INCOSE Competency Framework u Mr. Don Gelosh 19515 A Proposed Engineering Training Framework and Competency Methodology...nonlinearity ▪ QEV, Transient, Frequency Domain ▪ Inverse Methods Capability ▪ Coupled Physics ▪ Fluids: nemo, aero and sigma ▪ Thermal (unidirection): fuego

Modeling spin magnetization transport in a spatially varying magnetic field

NASA Astrophysics Data System (ADS)

Picone, Rico A. R.; Garbini, Joseph L.; Sidles, John A.

2015-01-01

We present a framework for modeling the transport of any number of globally conserved quantities in any spatial configuration and apply it to obtain a model of magnetization transport for spin-systems that is valid in new regimes (including high-polarization). The framework allows an entropy function to define a model that explicitly respects the laws of thermodynamics. Three facets of the model are explored. First, it is expressed as nonlinear partial differential equations that are valid for the new regime of high dipole-energy and polarization. Second, the nonlinear model is explored in the limit of low dipole-energy (semi-linear), from which is derived a physical parameter characterizing separative magnetization transport (SMT). It is shown that the necessary and sufficient condition for SMT to occur is that the parameter is spatially inhomogeneous. Third, the high spin-temperature (linear) limit is shown to be equivalent to the model of nuclear spin transport of Genack and Redfield (1975) [1]. Differences among the three forms of the model are illustrated by numerical solution with parameters corresponding to a magnetic resonance force microscopy (MRFM) experiment (Degen et al., 2009 [2]; Kuehn et al., 2008 [3]; Sidles et al., 2003 [4]; Dougherty et al., 2000 [5]). A family of analytic, steady-state solutions to the nonlinear equation is derived and shown to be the spin-temperature analog of the Langevin paramagnetic equation and Curie's law. Finally, we analyze the separative quality of magnetization transport, and a steady-state solution for the magnetization is shown to be compatible with Fenske's separative mass transport equation (Fenske, 1932 [6]).

Coupling fluid-structure interaction with phase-field fracture

NASA Astrophysics Data System (ADS)

Wick, Thomas

2016-12-01

In this work, a concept for coupling fluid-structure interaction with brittle fracture in elasticity is proposed. The fluid-structure interaction problem is modeled in terms of the arbitrary Lagrangian-Eulerian technique and couples the isothermal, incompressible Navier-Stokes equations with nonlinear elastodynamics using the Saint-Venant Kirchhoff solid model. The brittle fracture model is based on a phase-field approach for cracks in elasticity and pressurized elastic solids. In order to derive a common framework, the phase-field approach is re-formulated in Lagrangian coordinates to combine it with fluid-structure interaction. A crack irreversibility condition, that is mathematically characterized as an inequality constraint in time, is enforced with the help of an augmented Lagrangian iteration. The resulting problem is highly nonlinear and solved with a modified Newton method (e.g., error-oriented) that specifically allows for a temporary increase of the residuals. The proposed framework is substantiated with several numerical tests. In these examples, computational stability in space and time is shown for several goal functionals, which demonstrates reliability of numerical modeling and algorithmic techniques. But also current limitations such as the necessity of using solid damping are addressed.

A unified perspective on robot control - The energy Lyapunov function approach

NASA Technical Reports Server (NTRS)

Wen, John T.

1990-01-01

A unified framework for the stability analysis of robot tracking control is presented. By using an energy-motivated Lyapunov function candidate, the closed-loop stability is shown for a large family of control laws sharing a common structure of proportional and derivative feedback and a model-based feedforward. The feedforward can be zero, partial or complete linearized dynamics, partial or complete nonlinear dynamics, or linearized or nonlinear dynamics with parameter adaptation. As result, the dichotomous approaches to the robot control problem based on the open-loop linearization and nonlinear Lyapunov analysis are both included in this treatment. Furthermore, quantitative estimates of the trade-offs between different schemes in terms of the tracking performance, steady state error, domain of convergence, realtime computation load and required a prior model information are derived.

Time-Reversal Generation of Rogue Waves

NASA Astrophysics Data System (ADS)

Chabchoub, Amin; Fink, Mathias

2014-03-01

The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schrödinger equation (NLS). Within the class of exact NLS breather solutions on a finite background, which describe the modulational instability of monochromatic wave trains, the hierarchy of rational solutions localized in both time and space is considered to provide appropriate prototypes to model rogue wave dynamics. Here, we use the time-reversal invariance of the NLS to propose and experimentally demonstrate a new approach to constructing strongly nonlinear localized waves focused in both time and space. The potential applications of this time-reversal approach include remote sensing and motivated analogous experimental analysis in other nonlinear dispersive media, such as optics, Bose-Einstein condensates, and plasma, where the wave motion dynamics is governed by the NLS.

Lotka-Volterra representation of general nonlinear systems.

PubMed

Hernández-Bermejo, B; Fairén, V

1997-02-01

In this article we elaborate on the structure of the generalized Lotka-Volterra (GLV) form for nonlinear differential equations. We discuss here the algebraic properties of the GLV family, such as the invariance under quasimonomial transformations and the underlying structure of classes of equivalence. Each class possesses a unique representative under the classical quadratic Lotka-Volterra form. We show how other standard modeling forms of biological interest, such as S-systems or mass-action systems, are naturally embedded into the GLV form, which thus provides a formal framework for their comparison and for the establishment of transformation rules. We also focus on the issue of recasting of general nonlinear systems into the GLV format. We present a procedure for doing so and point at possible sources of ambiguity that could make the resulting Lotka-Volterra system dependent on the path followed. We then provide some general theorems that define the operational and algorithmic framework in which this is not the case.

Non-linear modelling and control of semi-active suspensions with variable damping

NASA Astrophysics Data System (ADS)

Chen, Huang; Long, Chen; Yuan, Chao-Chun; Jiang, Hao-Bin

2013-10-01

Electro-hydraulic dampers can provide variable damping force that is modulated by varying the command current; furthermore, they offer advantages such as lower power, rapid response, lower cost, and simple hardware. However, accurate characterisation of non-linear f-v properties in pre-yield and force saturation in post-yield is still required. Meanwhile, traditional linear or quarter vehicle models contain various non-linearities. The development of a multi-body dynamics model is very complex, and therefore, SIMPACK was used with suitable improvements for model development and numerical simulations. A semi-active suspension was built based on a belief-desire-intention (BDI)-agent model framework. Vehicle handling dynamics were analysed, and a co-simulation analysis was conducted in SIMPACK and MATLAB to evaluate the BDI-agent controller. The design effectively improved ride comfort, handling stability, and driving safety. A rapid control prototype was built based on dSPACE to conduct a real vehicle test. The test and simulation results were consistent, which verified the simulation.

A robust model predictive control algorithm for uncertain nonlinear systems that guarantees resolvability

NASA Technical Reports Server (NTRS)

Acikmese, Ahmet Behcet; Carson, John M., III

2006-01-01

A robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems is developed that guarantees resolvability. With resolvability, initial feasibility of the finite-horizon optimal control problem implies future feasibility in a receding-horizon framework. The control consists of two components; (i) feed-forward, and (ii) feedback part. Feed-forward control is obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line based on a bound on the uncertainty in the system model. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives and derivatives in polytopes. An illustrative numerical example is also provided.

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

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

Dynamical processes and epidemic threshold on nonlinear coupled multiplex networks

NASA Astrophysics Data System (ADS)

Gao, Chao; Tang, Shaoting; Li, Weihua; Yang, Yaqian; Zheng, Zhiming

2018-04-01

Recently, the interplay between epidemic spreading and awareness diffusion has aroused the interest of many researchers, who have studied models mainly based on linear coupling relations between information and epidemic layers. However, in real-world networks the relation between two layers may be closely correlated with the property of individual nodes and exhibits nonlinear dynamical features. Here we propose a nonlinear coupled information-epidemic model (I-E model) and present a comprehensive analysis in a more generalized scenario where the upload rate differs from node to node, deletion rate varies between susceptible and infected states, and infection rate changes between unaware and aware states. In particular, we develop a theoretical framework of the intra- and inter-layer dynamical processes with a microscopic Markov chain approach (MMCA), and derive an analytic epidemic threshold. Our results suggest that the change of upload and deletion rate has little effect on the diffusion dynamics in the epidemic layer.

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

Bose, Benjamin; Koyama, Kazuya, E-mail: benjamin.bose@port.ac.uk, E-mail: kazuya.koyama@port.ac.uk

We develop a code to produce the power spectrum in redshift space based on standard perturbation theory (SPT) at 1-loop order. The code can be applied to a wide range of modified gravity and dark energy models using a recently proposed numerical method by A.Taruya to find the SPT kernels. This includes Horndeski's theory with a general potential, which accommodates both chameleon and Vainshtein screening mechanisms and provides a non-linear extension of the effective theory of dark energy up to the third order. Focus is on a recent non-linear model of the redshift space power spectrum which has been shownmore » to model the anisotropy very well at relevant scales for the SPT framework, as well as capturing relevant non-linear effects typical of modified gravity theories. We provide consistency checks of the code against established results and elucidate its application within the light of upcoming high precision RSD data.« less

On the modeling of epidemics under the influence of risk perception

NASA Astrophysics Data System (ADS)

de Lillo, S.; Fioriti, G.; Prioriello, M. L.

An epidemic spreading model is presented in the framework of the kinetic theory of active particles. The model is characterized by the influence of risk perception which can reduce the diffusion of infection. The evolution of the system is modeled through nonlinear interactions, whose output is described by stochastic games. The results of numerical simulations are discussed for different initial conditions.

Computational principles underlying recognition of acoustic signals in grasshoppers and crickets.

PubMed

Ronacher, Bernhard; Hennig, R Matthias; Clemens, Jan

2015-01-01

Grasshoppers and crickets independently evolved hearing organs and acoustic communication. They differ considerably in the organization of their auditory pathways, and the complexity of their songs, which are essential for mate attraction. Recent approaches aimed at describing the behavioral preference functions of females in both taxa by a simple modeling framework. The basic structure of the model consists of three processing steps: (1) feature extraction with a bank of 'LN models'-each containing a linear filter followed by a nonlinearity, (2) temporal integration, and (3) linear combination. The specific properties of the filters and nonlinearities were determined using a genetic learning algorithm trained on a large set of different song features and the corresponding behavioral response scores. The model showed an excellent prediction of the behavioral responses to the tested songs. Most remarkably, in both taxa the genetic algorithm found Gabor-like functions as the optimal filter shapes. By slight modifications of Gabor filters several types of preference functions could be modeled, which are observed in different cricket species. Furthermore, this model was able to explain several so far enigmatic results in grasshoppers. The computational approach offered a remarkably simple framework that can account for phenotypically rather different preference functions across several taxa.

A flexible cure rate model for spatially correlated survival data based on generalized extreme value distribution and Gaussian process priors.

PubMed

Li, Dan; Wang, Xia; Dey, Dipak K

2016-09-01

Our present work proposes a new survival model in a Bayesian context to analyze right-censored survival data for populations with a surviving fraction, assuming that the log failure time follows a generalized extreme value distribution. Many applications require a more flexible modeling of covariate information than a simple linear or parametric form for all covariate effects. It is also necessary to include the spatial variation in the model, since it is sometimes unexplained by the covariates considered in the analysis. Therefore, the nonlinear covariate effects and the spatial effects are incorporated into the systematic component of our model. Gaussian processes (GPs) provide a natural framework for modeling potentially nonlinear relationship and have recently become extremely powerful in nonlinear regression. Our proposed model adopts a semiparametric Bayesian approach by imposing a GP prior on the nonlinear structure of continuous covariate. With the consideration of data availability and computational complexity, the conditionally autoregressive distribution is placed on the region-specific frailties to handle spatial correlation. The flexibility and gains of our proposed model are illustrated through analyses of simulated data examples as well as a dataset involving a colon cancer clinical trial from the state of Iowa. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

On discrete control of nonlinear systems with applications to robotics

NASA Technical Reports Server (NTRS)

Eslami, Mansour

1989-01-01

Much progress has been reported in the areas of modeling and control of nonlinear dynamic systems in a continuous-time framework. From implementation point of view, however, it is essential to study these nonlinear systems directly in a discrete setting that is amenable for interfacing with digital computers. But to develop discrete models and discrete controllers for a nonlinear system such as robot is a nontrivial task. Robot is also inherently a variable-inertia dynamic system involving additional complications. Not only the computer-oriented models of these systems must satisfy the usual requirements for such models, but these must also be compatible with the inherent capabilities of computers and must preserve the fundamental physical characteristics of continuous-time systems such as the conservation of energy and/or momentum. Preliminary issues regarding discrete systems in general and discrete models of a typical industrial robot that is developed with full consideration of the principle of conservation of energy are presented. Some research on the pertinent tactile information processing is reviewed. Finally, system control methods and how to integrate these issues in order to complete the task of discrete control of a robot manipulator are also reviewed.

A unifying view of synchronization for data assimilation in complex nonlinear networks

NASA Astrophysics Data System (ADS)

Abarbanel, Henry D. I.; Shirman, Sasha; Breen, Daniel; Kadakia, Nirag; Rey, Daniel; Armstrong, Eve; Margoliash, Daniel

2017-12-01

Networks of nonlinear systems contain unknown parameters and dynamical degrees of freedom that may not be observable with existing instruments. From observable state variables, we want to estimate the connectivity of a model of such a network and determine the full state of the model at the termination of a temporal observation window during which measurements transfer information to a model of the network. The model state at the termination of a measurement window acts as an initial condition for predicting the future behavior of the network. This allows the validation (or invalidation) of the model as a representation of the dynamical processes producing the observations. Once the model has been tested against new data, it may be utilized as a predictor of responses to innovative stimuli or forcing. We describe a general framework for the tasks involved in the "inverse" problem of determining properties of a model built to represent measured output from physical, biological, or other processes when the measurements are noisy, the model has errors, and the state of the model is unknown when measurements begin. This framework is called statistical data assimilation and is the best one can do in estimating model properties through the use of the conditional probability distributions of the model state variables, conditioned on observations. There is a very broad arena of applications of the methods described. These include numerical weather prediction, properties of nonlinear electrical circuitry, and determining the biophysical properties of functional networks of neurons. Illustrative examples will be given of (1) estimating the connectivity among neurons with known dynamics in a network of unknown connectivity, and (2) estimating the biophysical properties of individual neurons in vitro taken from a functional network underlying vocalization in songbirds.

Suppression of Instabilities Generated by an Anti-Damper with a Nonlinear Magnetic Element in IOTA

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

Stern, E.

The Integrable Optics Test Accelerator (IOTA) storage ring is being constructed at Fermilab as a testbed for new accelerator concepts. One important series of experiments tests the use of a novel nonlinear magnetic insert to damp coherent instabilities. To test the damping power of the element, an instability of desired strength may be intentionally excited with an anti-damper. We report on simulations of beam stabilization using the Synergia modeling framework over ranges of driving and damping strengths.

Multiscale Support Vector Learning With Projection Operator Wavelet Kernel for Nonlinear Dynamical System Identification.

PubMed

Lu, Zhao; Sun, Jing; Butts, Kenneth

2016-02-03

A giant leap has been made in the past couple of decades with the introduction of kernel-based learning as a mainstay for designing effective nonlinear computational learning algorithms. In view of the geometric interpretation of conditional expectation and the ubiquity of multiscale characteristics in highly complex nonlinear dynamic systems [1]-[3], this paper presents a new orthogonal projection operator wavelet kernel, aiming at developing an efficient computational learning approach for nonlinear dynamical system identification. In the framework of multiresolution analysis, the proposed projection operator wavelet kernel can fulfill the multiscale, multidimensional learning to estimate complex dependencies. The special advantage of the projection operator wavelet kernel developed in this paper lies in the fact that it has a closed-form expression, which greatly facilitates its application in kernel learning. To the best of our knowledge, it is the first closed-form orthogonal projection wavelet kernel reported in the literature. It provides a link between grid-based wavelets and mesh-free kernel-based methods. Simulation studies for identifying the parallel models of two benchmark nonlinear dynamical systems confirm its superiority in model accuracy and sparsity.

Dynamical Systems Approach to Endothelial Heterogeneity

PubMed Central

Regan, Erzsébet Ravasz; Aird, William C.

2012-01-01

Rationale Objective Here we reexamine our current understanding of the molecular basis of endothelial heterogeneity. We introduce multistability as a new explanatory framework in vascular biology. Methods We draw on the field of non-linear dynamics to propose a dynamical systems framework for modeling multistability and its derivative properties, including robustness, memory, and plasticity. Conclusions Our perspective allows for both a conceptual and quantitative description of system-level features of endothelial regulation. PMID:22723222

Modeling the Effect of Fluid-Structure Interaction on the Impact Dynamics of Pressurized Tank Cars

DOT National Transportation Integrated Search

2009-11-13

This paper presents a computational framework that : analyzes the effect of fluid-structure interaction (FSI) on the : impact dynamics of pressurized commodity tank cars using the : nonlinear dynamic finite element code ABAQUS/Explicit. : There exist...

A Bayesian approach for estimating under-reported dengue incidence with a focus on non-linear associations between climate and dengue in Dhaka, Bangladesh.

PubMed

Sharmin, Sifat; Glass, Kathryn; Viennet, Elvina; Harley, David

2018-04-01

Determining the relation between climate and dengue incidence is challenging due to under-reporting of disease and consequent biased incidence estimates. Non-linear associations between climate and incidence compound this. Here, we introduce a modelling framework to estimate dengue incidence from passive surveillance data while incorporating non-linear climate effects. We estimated the true number of cases per month using a Bayesian generalised linear model, developed in stages to adjust for under-reporting. A semi-parametric thin-plate spline approach was used to quantify non-linear climate effects. The approach was applied to data collected from the national dengue surveillance system of Bangladesh. The model estimated that only 2.8% (95% credible interval 2.7-2.8) of all cases in the capital Dhaka were reported through passive case reporting. The optimal mean monthly temperature for dengue transmission is 29℃ and average monthly rainfall above 15 mm decreases transmission. Our approach provides an estimate of true incidence and an understanding of the effects of temperature and rainfall on dengue transmission in Dhaka, Bangladesh.

Analysis of nonlinear relationships in dual epidemics, and its application to the management of grapevine downy and powdery mildews.

PubMed

Savary, Serge; Delbac, Lionel; Rochas, Amélie; Taisant, Guillaume; Willocquet, Laetitia

2009-08-01

Dual epidemics are defined as epidemics developing on two or several plant organs in the course of a cropping season. Agricultural pathosystems where such epidemics develop are often very important, because the harvestable part is one of the organs affected. These epidemics also are often difficult to manage, because the linkage between epidemiological components occurring on different organs is poorly understood, and because prediction of the risk toward the harvestable organs is difficult. In the case of downy mildew (DM) and powdery mildew (PM) of grapevine, nonlinear modeling and logistic regression indicated nonlinearity in the foliage-cluster relationships. Nonlinear modeling enabled the parameterization of a transmission coefficient that numerically links the two components, leaves and clusters, in DM and PM epidemics. Logistic regression analysis yielded a series of probabilistic models that enabled predicting preset levels of cluster infection risks based on DM and PM severities on the foliage at successive crop stages. The usefulness of this framework for tactical decision-making for disease control is discussed.

Feedforward hysteresis compensation in trajectory control of piezoelectrically-driven nanostagers

NASA Astrophysics Data System (ADS)

Bashash, Saeid; Jalili, Nader

2006-03-01

Complex structural nonlinearities of piezoelectric materials drastically degrade their performance in variety of micro- and nano-positioning applications. From the precision positioning and control perspective, the multi-path time-history dependent hysteresis phenomenon is the most concerned nonlinearity in piezoelectric actuators to be analyzed. To realize the underlying physics of this phenomenon and to develop an efficient compensation strategy, the intelligent properties of hysteresis with the effects of non-local memories are discussed. Through performing a set of experiments on a piezoelectrically-driven nanostager with high resolution capacitive position sensor, it is shown that for the precise prediction of hysteresis path, certain memory units are required to store the previous hysteresis trajectory data. Based on the experimental observations, a constitutive memory-based mathematical modeling framework is developed and trained for the precise prediction of hysteresis path for arbitrarily assigned input profiles. Using the inverse hysteresis model, a feedforward control strategy is then developed and implemented on the nanostager to compensate for the system everpresent nonlinearity. Experimental results demonstrate that the controller remarkably eliminates the nonlinear effect if memory units are sufficiently chosen for the inverse model.

Comment on "Social Contagion, Adolescent Sexual Behavior, and Pregnancy: A Nonlinear Dynamic EMOSA Model."

ERIC Educational Resources Information Center

Stoolmiller, Mike

1998-01-01

Examines the Rodgers, Rowe, and Buster (1998) epidemic model of the onset of social activities for adolescent sexuality. Maintains that its strengths include its theoretical potential to generate new hypotheses for further testing at the individual level. Asserts that its limitations include the lack of a well-developed statistical framework and…

Empirical intrinsic geometry for nonlinear modeling and time series filtering.

PubMed

Talmon, Ronen; Coifman, Ronald R

2013-07-30

In this paper, we present a method for time series analysis based on empirical intrinsic geometry (EIG). EIG enables one to reveal the low-dimensional parametric manifold as well as to infer the underlying dynamics of high-dimensional time series. By incorporating concepts of information geometry, this method extends existing geometric analysis tools to support stochastic settings and parametrizes the geometry of empirical distributions. However, the statistical models are not required as priors; hence, EIG may be applied to a wide range of real signals without existing definitive models. We show that the inferred model is noise-resilient and invariant under different observation and instrumental modalities. In addition, we show that it can be extended efficiently to newly acquired measurements in a sequential manner. These two advantages enable us to revisit the Bayesian approach and incorporate empirical dynamics and intrinsic geometry into a nonlinear filtering framework. We show applications to nonlinear and non-Gaussian tracking problems as well as to acoustic signal localization.

Numerical studies of identification in nonlinear distributed parameter systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Lo, C. K.; Reich, Simeon; Rosen, I. G.

1989-01-01

An abstract approximation framework and convergence theory for the identification of first and second order nonlinear distributed parameter systems developed previously by the authors and reported on in detail elsewhere are summarized and discussed. The theory is based upon results for systems whose dynamics can be described by monotone operators in Hilbert space and an abstract approximation theorem for the resulting nonlinear evolution system. The application of the theory together with numerical evidence demonstrating the feasibility of the general approach are discussed in the context of the identification of a first order quasi-linear parabolic model for one dimensional heat conduction/mass transport and the identification of a nonlinear dissipation mechanism (i.e., damping) in a second order one dimensional wave equation. Computational and implementational considerations, in particular, with regard to supercomputing, are addressed.

Kernel-imbedded Gaussian processes for disease classification using microarray gene expression data

PubMed Central

Zhao, Xin; Cheung, Leo Wang-Kit

2007-01-01

Background Designing appropriate machine learning methods for identifying genes that have a significant discriminating power for disease outcomes has become more and more important for our understanding of diseases at genomic level. Although many machine learning methods have been developed and applied to the area of microarray gene expression data analysis, the majority of them are based on linear models, which however are not necessarily appropriate for the underlying connection between the target disease and its associated explanatory genes. Linear model based methods usually also bring in false positive significant features more easily. Furthermore, linear model based algorithms often involve calculating the inverse of a matrix that is possibly singular when the number of potentially important genes is relatively large. This leads to problems of numerical instability. To overcome these limitations, a few non-linear methods have recently been introduced to the area. Many of the existing non-linear methods have a couple of critical problems, the model selection problem and the model parameter tuning problem, that remain unsolved or even untouched. In general, a unified framework that allows model parameters of both linear and non-linear models to be easily tuned is always preferred in real-world applications. Kernel-induced learning methods form a class of approaches that show promising potentials to achieve this goal. Results A hierarchical statistical model named kernel-imbedded Gaussian process (KIGP) is developed under a unified Bayesian framework for binary disease classification problems using microarray gene expression data. In particular, based on a probit regression setting, an adaptive algorithm with a cascading structure is designed to find the appropriate kernel, to discover the potentially significant genes, and to make the optimal class prediction accordingly. A Gibbs sampler is built as the core of the algorithm to make Bayesian inferences. Simulation studies showed that, even without any knowledge of the underlying generative model, the KIGP performed very close to the theoretical Bayesian bound not only in the case with a linear Bayesian classifier but also in the case with a very non-linear Bayesian classifier. This sheds light on its broader usability to microarray data analysis problems, especially to those that linear methods work awkwardly. The KIGP was also applied to four published microarray datasets, and the results showed that the KIGP performed better than or at least as well as any of the referred state-of-the-art methods did in all of these cases. Conclusion Mathematically built on the kernel-induced feature space concept under a Bayesian framework, the KIGP method presented in this paper provides a unified machine learning approach to explore both the linear and the possibly non-linear underlying relationship between the target features of a given binary disease classification problem and the related explanatory gene expression data. More importantly, it incorporates the model parameter tuning into the framework. The model selection problem is addressed in the form of selecting a proper kernel type. The KIGP method also gives Bayesian probabilistic predictions for disease classification. These properties and features are beneficial to most real-world applications. The algorithm is naturally robust in numerical computation. The simulation studies and the published data studies demonstrated that the proposed KIGP performs satisfactorily and consistently. PMID:17328811

The influence of filtering and downsampling on the estimation of transfer entropy

PubMed Central

Florin, Esther; von Papen, Michael; Timmermann, Lars

2017-01-01

Transfer entropy (TE) provides a generalized and model-free framework to study Wiener-Granger causality between brain regions. Because of its nonparametric character, TE can infer directed information flow also from nonlinear systems. Despite its increasing number of applications in neuroscience, not much is known regarding the influence of common electrophysiological preprocessing on its estimation. We test the influence of filtering and downsampling on a recently proposed nearest neighborhood based TE estimator. Different filter settings and downsampling factors were tested in a simulation framework using a model with a linear coupling function and two nonlinear models with sigmoid and logistic coupling functions. For nonlinear coupling and progressively lower low-pass filter cut-off frequencies up to 72% false negative direct connections and up to 26% false positive connections were identified. In contrast, for the linear model, a monotonic increase was only observed for missed indirect connections (up to 86%). High-pass filtering (1 Hz, 2 Hz) had no impact on TE estimation. After low-pass filtering interaction delays were significantly underestimated. Downsampling the data by a factor greater than the assumed interaction delay erased most of the transmitted information and thus led to a very high percentage (67–100%) of false negative direct connections. Low-pass filtering increases the number of missed connections depending on the filters cut-off frequency. Downsampling should only be done if the sampling factor is smaller than the smallest assumed interaction delay of the analyzed network. PMID:29149201

Fully nonlinear theory of transcritical shallow-water flow past topography

NASA Astrophysics Data System (ADS)

El, Gennady; Grimshaw, Roger; Smyth, Noel

2010-05-01

In this talk recent results on the generation of undular bores in one-dimensional fully nonlinear shallow-water flows past localised topographies will be presented. The description is made in the framework of the forced Su-Gardner (a.k.a. 1D Green-Naghdi) system of equations, with a primary focus on the transcritical regime when the Froude number of the oncoming flow is close to unity. A combination of the local transcritical hydraulic solution over the localized topography, which produces upstream and downstream hydraulic jumps, and unsteady undular bore solutions describing the resolution of these hydraulic jumps, is used to describe various flow regimes depending on the combination of the topography height and the Froude number. We take advantage of the recently developed modulation theory of Su-Gardner undular bores to derive the main parameters of transcritical fully nonlinear shallow-water flow, such as the leading solitary wave amplitudes for the upstream and downstream undular bores, the speeds of the undular bores edges and the drag force. Our results confirm that most of the features of the previously developed description in the framework of the uni-directional forced KdV model hold up qualitatively for finite amplitude waves, while the quantitative description can be obtained in the framework of the bi-directional forced Su-Gardner system.

Modal testing for model validation of structures with discrete nonlinearities.

PubMed

Ewins, D J; Weekes, B; delli Carri, A

2015-09-28

Model validation using data from modal tests is now widely practiced in many industries for advanced structural dynamic design analysis, especially where structural integrity is a primary requirement. These industries tend to demand highly efficient designs for their critical structures which, as a result, are increasingly operating in regimes where traditional linearity assumptions are no longer adequate. In particular, many modern structures are found to contain localized areas, often around joints or boundaries, where the actual mechanical behaviour is far from linear. Such structures need to have appropriate representation of these nonlinear features incorporated into the otherwise largely linear models that are used for design and operation. This paper proposes an approach to this task which is an extension of existing linear techniques, especially in the testing phase, involving only just as much nonlinear analysis as is necessary to construct a model which is good enough, or 'valid': i.e. capable of predicting the nonlinear response behaviour of the structure under all in-service operating and test conditions with a prescribed accuracy. A short-list of methods described in the recent literature categorized using our framework is given, which identifies those areas in which further development is most urgently required. © 2015 The Authors.

Modal testing for model validation of structures with discrete nonlinearities

PubMed Central

Ewins, D. J.; Weekes, B.; delli Carri, A.

2015-01-01

Model validation using data from modal tests is now widely practiced in many industries for advanced structural dynamic design analysis, especially where structural integrity is a primary requirement. These industries tend to demand highly efficient designs for their critical structures which, as a result, are increasingly operating in regimes where traditional linearity assumptions are no longer adequate. In particular, many modern structures are found to contain localized areas, often around joints or boundaries, where the actual mechanical behaviour is far from linear. Such structures need to have appropriate representation of these nonlinear features incorporated into the otherwise largely linear models that are used for design and operation. This paper proposes an approach to this task which is an extension of existing linear techniques, especially in the testing phase, involving only just as much nonlinear analysis as is necessary to construct a model which is good enough, or ‘valid’: i.e. capable of predicting the nonlinear response behaviour of the structure under all in-service operating and test conditions with a prescribed accuracy. A short-list of methods described in the recent literature categorized using our framework is given, which identifies those areas in which further development is most urgently required. PMID:26303924

Data-based virtual unmodeled dynamics driven multivariable nonlinear adaptive switching control.

PubMed

Chai, Tianyou; Zhang, Yajun; Wang, Hong; Su, Chun-Yi; Sun, Jing

2011-12-01

For a complex industrial system, its multivariable and nonlinear nature generally make it very difficult, if not impossible, to obtain an accurate model, especially when the model structure is unknown. The control of this class of complex systems is difficult to handle by the traditional controller designs around their operating points. This paper, however, explores the concepts of controller-driven model and virtual unmodeled dynamics to propose a new design framework. The design consists of two controllers with distinct functions. First, using input and output data, a self-tuning controller is constructed based on a linear controller-driven model. Then the output signals of the controller-driven model are compared with the true outputs of the system to produce so-called virtual unmodeled dynamics. Based on the compensator of the virtual unmodeled dynamics, the second controller based on a nonlinear controller-driven model is proposed. Those two controllers are integrated by an adaptive switching control algorithm to take advantage of their complementary features: one offers stabilization function and another provides improved performance. The conditions on the stability and convergence of the closed-loop system are analyzed. Both simulation and experimental tests on a heavily coupled nonlinear twin-tank system are carried out to confirm the effectiveness of the proposed method.

Bayesian framework for modeling diffusion processes with nonlinear drift based on nonlinear and incomplete observations.

PubMed

Wu, Hao; Noé, Frank

2011-03-01

Diffusion processes are relevant for a variety of phenomena in the natural sciences, including diffusion of cells or biomolecules within cells, diffusion of molecules on a membrane or surface, and diffusion of a molecular conformation within a complex energy landscape. Many experimental tools exist now to track such diffusive motions in single cells or molecules, including high-resolution light microscopy, optical tweezers, fluorescence quenching, and Förster resonance energy transfer (FRET). Experimental observations are most often indirect and incomplete: (1) They do not directly reveal the potential or diffusion constants that govern the diffusion process, (2) they have limited time and space resolution, and (3) the highest-resolution experiments do not track the motion directly but rather probe it stochastically by recording single events, such as photons, whose properties depend on the state of the system under investigation. Here, we propose a general Bayesian framework to model diffusion processes with nonlinear drift based on incomplete observations as generated by various types of experiments. A maximum penalized likelihood estimator is given as well as a Gibbs sampling method that allows to estimate the trajectories that have caused the measurement, the nonlinear drift or potential function and the noise or diffusion matrices, as well as uncertainty estimates of these properties. The approach is illustrated on numerical simulations of FRET experiments where it is shown that trajectories, potentials, and diffusion constants can be efficiently and reliably estimated even in cases with little statistics or nonequilibrium measurement conditions.

Sensitivity of Dynamical Systems to Banach Space Parameters

DTIC Science & Technology

2005-02-13

We consider general nonlinear dynamical systems in a Banach space with dependence on parameters in a second Banach space. An abstract theoretical ... framework for sensitivity equations is developed. An application to measure dependent delay differential systems arising in a class of HIV models is presented.

A symbiotic approach to fluid equations and non-linear flux-driven simulations of plasma dynamics

NASA Astrophysics Data System (ADS)

Halpern, Federico

2017-10-01

The fluid framework is ubiquitous in studies of plasma transport and stability. Typical forms of the fluid equations are motivated by analytical work dating several decades ago, before computer simulations were indispensable, and can be, therefore, not optimal for numerical computation. We demonstrate a new first-principles approach to obtaining manifestly consistent, skew-symmetric fluid models, ensuring internal consistency and conservation properties even in discrete form. Mass, kinetic, and internal energy become quadratic (and always positive) invariants of the system. The model lends itself to a robust, straightforward discretization scheme with inherent non-linear stability. A simpler, drift-ordered form of the equations is obtained, and first results of their numerical implementation as a binary framework for bulk-fluid global plasma simulations are demonstrated. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, Theory Program, under Award No. DE-FG02-95ER54309.

Mathematical models of bipolar disorder

NASA Astrophysics Data System (ADS)

Daugherty, Darryl; Roque-Urrea, Tairi; Urrea-Roque, John; Troyer, Jessica; Wirkus, Stephen; Porter, Mason A.

2009-07-01

We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here.

A novel framework to simulating non-stationary, non-linear, non-Normal hydrological time series using Markov Switching Autoregressive Models

NASA Astrophysics Data System (ADS)

Birkel, C.; Paroli, R.; Spezia, L.; Tetzlaff, D.; Soulsby, C.

2012-12-01

In this paper we present a novel model framework using the class of Markov Switching Autoregressive Models (MSARMs) to examine catchments as complex stochastic systems that exhibit non-stationary, non-linear and non-Normal rainfall-runoff and solute dynamics. Hereby, MSARMs are pairs of stochastic processes, one observed and one unobserved, or hidden. We model the unobserved process as a finite state Markov chain and assume that the observed process, given the hidden Markov chain, is conditionally autoregressive, which means that the current observation depends on its recent past (system memory). The model is fully embedded in a Bayesian analysis based on Markov Chain Monte Carlo (MCMC) algorithms for model selection and uncertainty assessment. Hereby, the autoregressive order and the dimension of the hidden Markov chain state-space are essentially self-selected. The hidden states of the Markov chain represent unobserved levels of variability in the observed process that may result from complex interactions of hydroclimatic variability on the one hand and catchment characteristics affecting water and solute storage on the other. To deal with non-stationarity, additional meteorological and hydrological time series along with a periodic component can be included in the MSARMs as covariates. This extension allows identification of potential underlying drivers of temporal rainfall-runoff and solute dynamics. We applied the MSAR model framework to streamflow and conservative tracer (deuterium and oxygen-18) time series from an intensively monitored 2.3 km2 experimental catchment in eastern Scotland. Statistical time series analysis, in the form of MSARMs, suggested that the streamflow and isotope tracer time series are not controlled by simple linear rules. MSARMs showed that the dependence of current observations on past inputs observed by transport models often in form of the long-tailing of travel time and residence time distributions can be efficiently explained by non-stationarity either of the system input (climatic variability) and/or the complexity of catchment storage characteristics. The statistical model is also capable of reproducing short (event) and longer-term (inter-event) and wet and dry dynamical "hydrological states". These reflect the non-linear transport mechanisms of flow pathways induced by transient climatic and hydrological variables and modified by catchment characteristics. We conclude that MSARMs are a powerful tool to analyze the temporal dynamics of hydrological data, allowing for explicit integration of non-stationary, non-linear and non-Normal characteristics.

A first approach to the distortion analysis of nonlinear analog circuits utilizing X-parameters

NASA Astrophysics Data System (ADS)

Weber, H.; Widemann, C.; Mathis, W.

2013-07-01

In this contribution a first approach to the distortion analysis of nonlinear 2-port-networks with X-parameters1 is presented. The X-parameters introduced by Verspecht and Root (2006) offer the possibility to describe nonlinear microwave 2-port-networks under large signal conditions. On the basis of X-parameter measurements with a nonlinear network analyzer (NVNA) behavioral models can be extracted for the networks. These models can be used to consider the nonlinear behavior during the design process of microwave circuits. The idea of the present work is to extract the behavioral models in order to describe the influence of interfering signals on the output behavior of the nonlinear circuits. Hereby, a simulator is used instead of a NVNA to extract the X-parameters. Assuming that the interfering signals are relatively small compared to the nominal input signal, the output signal can be described as a superposition of the effects of each input signal. In order to determine the functional correlation between the scattering variables, a polynomial dependency is assumed. The required datasets for the approximation of the describing functions are simulated by a directional coupler model in Cadence Design Framework. The polynomial coefficients are obtained by a least-square method. The resulting describing functions can be used to predict the system's behavior under certain conditions as well as the effects of the interfering signal on the output signal. 1 X-parameter is a registered trademark of Agilent Technologies, Inc.

Stationary solutions for the nonlinear Schrödinger equation modeling three-dimensional spherical Bose-Einstein condensates in general potentials.

PubMed

Mallory, Kristina; Van Gorder, Robert A

2015-07-01

Stationary solutions for the cubic nonlinear Schrödinger equation modeling Bose-Einstein condensates (BECs) confined in three spatial dimensions by general forms of a potential are studied through a perturbation method and also numerically. Note that we study both repulsive and attractive BECs under similar frameworks in order to deduce the effects of the potentials in each case. After outlining the general framework, solutions for a collection of specific confining potentials of physical relevance to experiments on BECs are provided in order to demonstrate the approach. We make several observations regarding the influence of the particular potentials on the behavior of the BECs in these cases, comparing and contrasting the qualitative behavior of the attractive and repulsive BECs for potentials of various strengths and forms. Finally, we consider the nonperturbative where the potential or the amplitude of the solutions is large, obtaining various qualitative results. When the kinetic energy term is small (relative to the nonlinearity and the confining potential), we recover the expected Thomas-Fermi approximation for the stationary solutions. Naturally, this also occurs in the large mass limit. Through all of these results, we are able to understand the qualitative behavior of spherical three-dimensional BECs in weak, intermediate, or strong confining potentials.

Generation and propagation of nonlinear internal waves in Massachusetts Bay

USGS Publications Warehouse

Scotti, A.; Beardsley, R.C.; Butman, B.

2007-01-01

During the summer, nonlinear internal waves (NLIWs) are commonly observed propagating in Massachusetts Bay. The topography of the area is unique in the sense that the generation area (over Stellwagen Bank) is only 25 km away from the shoaling area, and thus it represents an excellent natural laboratory to study the life cycle of NLIWs. To assist in the interpretation of the data collected during the 1998 Massachusetts Bay Internal Wave Experiment (MBIWE98), a fully nonlinear and nonhydrostatic model covering the generation/shoaling region was developed, to investigate the response of the system to the range of background and driving conditions observed. Simplified models were also used to elucidate the role of nonlinearity and dispersion in shaping the NLIW field. This paper concentrates on the generation process and the subsequent evolution in the basin. The model was found to reproduce well the range of propagation characteristics observed (arrival time, propagation speed, amplitude), and provided a coherent framework to interpret the observations. Comparison with a fully nonlinear hydrostatic model shows that during the generation and initial evolution of the waves as they move away from Stellwagen Bank, dispersive effects play a negligible role. Thus the problem can be well understood considering the geometry of the characteristics along which the Riemann invariants of the hydrostatic problem propagate. Dispersion plays a role only during the evolution of the undular bore in the middle of Stellwagen Basin. The consequences for modeling NLIWs within hydrostatic models are briefly discussed at the end.

Reservoir Computing Beyond Memory-Nonlinearity Trade-off.

PubMed

Inubushi, Masanobu; Yoshimura, Kazuyuki

2017-08-31

Reservoir computing is a brain-inspired machine learning framework that employs a signal-driven dynamical system, in particular harnessing common-signal-induced synchronization which is a widely observed nonlinear phenomenon. Basic understanding of a working principle in reservoir computing can be expected to shed light on how information is stored and processed in nonlinear dynamical systems, potentially leading to progress in a broad range of nonlinear sciences. As a first step toward this goal, from the viewpoint of nonlinear physics and information theory, we study the memory-nonlinearity trade-off uncovered by Dambre et al. (2012). Focusing on a variational equation, we clarify a dynamical mechanism behind the trade-off, which illustrates why nonlinear dynamics degrades memory stored in dynamical system in general. Moreover, based on the trade-off, we propose a mixture reservoir endowed with both linear and nonlinear dynamics and show that it improves the performance of information processing. Interestingly, for some tasks, significant improvements are observed by adding a few linear dynamics to the nonlinear dynamical system. By employing the echo state network model, the effect of the mixture reservoir is numerically verified for a simple function approximation task and for more complex tasks.

Model reduction and frequency residuals for a robust estimation of nonlinearities in subspace identification

NASA Astrophysics Data System (ADS)

De Filippis, G.; Noël, J. P.; Kerschen, G.; Soria, L.; Stephan, C.

2017-09-01

The introduction of the frequency-domain nonlinear subspace identification (FNSI) method in 2013 constitutes one in a series of recent attempts toward developing a realistic, first-generation framework applicable to complex structures. If this method showed promising capabilities when applied to academic structures, it is still confronted with a number of limitations which needs to be addressed. In particular, the removal of nonphysical poles in the identified nonlinear models is a distinct challenge. In the present paper, it is proposed as a first contribution to operate directly on the identified state-space matrices to carry out spurious pole removal. A modal-space decomposition of the state and output matrices is examined to discriminate genuine from numerical poles, prior to estimating the extended input and feedthrough matrices. The final state-space model thus contains physical information only and naturally leads to nonlinear coefficients free of spurious variations. Besides spurious variations due to nonphysical poles, vibration modes lying outside the frequency band of interest may also produce drifts of the nonlinear coefficients. The second contribution of the paper is to include residual terms, accounting for the existence of these modes. The proposed improved FNSI methodology is validated numerically and experimentally using a full-scale structure, the Morane-Saulnier Paris aircraft.

Application of an Ensemble Smoother to Precipitation Assimilation

NASA Technical Reports Server (NTRS)

Zhang, Sara; Zupanski, Dusanka; Hou, Arthur; Zupanski, Milija

2008-01-01

Assimilation of precipitation in a global modeling system poses a special challenge in that the observation operators for precipitation processes are highly nonlinear. In the variational approach, substantial development work and model simplifications are required to include precipitation-related physical processes in the tangent linear model and its adjoint. An ensemble based data assimilation algorithm "Maximum Likelihood Ensemble Smoother (MLES)" has been developed to explore the ensemble representation of the precipitation observation operator with nonlinear convection and large-scale moist physics. An ensemble assimilation system based on the NASA GEOS-5 GCM has been constructed to assimilate satellite precipitation data within the MLES framework. The configuration of the smoother takes the time dimension into account for the relationship between state variables and observable rainfall. The full nonlinear forward model ensembles are used to represent components involving the observation operator and its transpose. Several assimilation experiments using satellite precipitation observations have been carried out to investigate the effectiveness of the ensemble representation of the nonlinear observation operator and the data impact of assimilating rain retrievals from the TMI and SSM/I sensors. Preliminary results show that this ensemble assimilation approach is capable of extracting information from nonlinear observations to improve the analysis and forecast if ensemble size is adequate, and a suitable localization scheme is applied. In addition to a dynamically consistent precipitation analysis, the assimilation system produces a statistical estimate of the analysis uncertainty.

An LMI approach to design H(infinity) controllers for discrete-time nonlinear systems based on unified models.

PubMed

Liu, Meiqin; Zhang, Senlin

2008-10-01

A unified neural network model termed standard neural network model (SNNM) is advanced. Based on the robust L(2) gain (i.e. robust H(infinity) performance) analysis of the SNNM with external disturbances, a state-feedback control law is designed for the SNNM to stabilize the closed-loop system and eliminate the effect of external disturbances. The control design constraints are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms (e.g. interior-point algorithms) to determine the control law. Most discrete-time recurrent neural network (RNNs) and discrete-time nonlinear systems modelled by neural networks or Takagi and Sugeno (T-S) fuzzy models can be transformed into the SNNMs to be robust H(infinity) performance analyzed or robust H(infinity) controller synthesized in a unified SNNM's framework. Finally, some examples are presented to illustrate the wide application of the SNNMs to the nonlinear systems, and the proposed approach is compared with related methods reported in the literature.

Laser-induced generation of surface periodic structures in media with nonlinear diffusion

NASA Astrophysics Data System (ADS)

Zhuravlev, V. M.; Zolotovskii, I. O.; Korobko, D. A.; Morozov, V. M.; Svetukhin, V. V.; Yavtushenko, I. O.; Yavtushenko, M. S.

2017-12-01

A model of fast formation of high-contrast periodic structure appearing on a semiconductor surface under action of laser radiation is proposed. The process of growing a surface structure due to the interaction surface plasmon- polaritons excited on nonequilibrium electrons with incident laser radiation are considered in the framework of a medium with nonlinear diffusion of nonequilibrium carriers (defects). A resonance effect of superfast pico- and subpicosecond amplification of the plasmon-polariton structure generated on the surface, the realization of which can result in a high-contrast defect lattice.

Implementation of a digital evaluation platform to analyze bifurcation based nonlinear amplifiers

NASA Astrophysics Data System (ADS)

Feldkord, Sven; Reit, Marco; Mathis, Wolfgang

2016-09-01

Recently, nonlinear amplifiers based on the supercritical Andronov-Hopf bifurcation have become a focus of attention, especially in the modeling of the mammalian hearing organ. In general, to gain deeper insights in the input-output behavior, the analysis of bifurcation based amplifiers requires a flexible framework to exchange equations and adjust certain parameters. A DSP implementation is presented which is capable to analyze various amplifier systems. Amplifiers based on the Andronov-Hopf and Neimark-Sacker bifurcations are implemented and compared exemplarily. It is shown that the Neimark-Sacker system remarkably outperforms the Andronov-Hopf amplifier regarding the CPU usage. Nevertheless, both show a similar input-output behavior over a wide parameter range. Combined with an USB-based control interface connected to a PC, the digital framework provides a powerful instrument to analyze bifurcation based amplifiers.

On the stability and dynamics of stochastic spiking neuron models: Nonlinear Hawkes process and point process GLMs

PubMed Central

Truccolo, Wilson

2017-01-01

Point process generalized linear models (PP-GLMs) provide an important statistical framework for modeling spiking activity in single-neurons and neuronal networks. Stochastic stability is essential when sampling from these models, as done in computational neuroscience to analyze statistical properties of neuronal dynamics and in neuro-engineering to implement closed-loop applications. Here we show, however, that despite passing common goodness-of-fit tests, PP-GLMs estimated from data are often unstable, leading to divergent firing rates. The inclusion of absolute refractory periods is not a satisfactory solution since the activity then typically settles into unphysiological rates. To address these issues, we derive a framework for determining the existence and stability of fixed points of the expected conditional intensity function (CIF) for general PP-GLMs. Specifically, in nonlinear Hawkes PP-GLMs, the CIF is expressed as a function of the previous spike history and exogenous inputs. We use a mean-field quasi-renewal (QR) approximation that decomposes spike history effects into the contribution of the last spike and an average of the CIF over all spike histories prior to the last spike. Fixed points for stationary rates are derived as self-consistent solutions of integral equations. Bifurcation analysis and the number of fixed points predict that the original models can show stable, divergent, and metastable (fragile) dynamics. For fragile models, fluctuations of the single-neuron dynamics predict expected divergence times after which rates approach unphysiologically high values. This metric can be used to estimate the probability of rates to remain physiological for given time periods, e.g., for simulation purposes. We demonstrate the use of the stability framework using simulated single-neuron examples and neurophysiological recordings. Finally, we show how to adapt PP-GLM estimation procedures to guarantee model stability. Overall, our results provide a stability framework for data-driven PP-GLMs and shed new light on the stochastic dynamics of state-of-the-art statistical models of neuronal spiking activity. PMID:28234899

On the stability and dynamics of stochastic spiking neuron models: Nonlinear Hawkes process and point process GLMs.

PubMed

Gerhard, Felipe; Deger, Moritz; Truccolo, Wilson

2017-02-01

Point process generalized linear models (PP-GLMs) provide an important statistical framework for modeling spiking activity in single-neurons and neuronal networks. Stochastic stability is essential when sampling from these models, as done in computational neuroscience to analyze statistical properties of neuronal dynamics and in neuro-engineering to implement closed-loop applications. Here we show, however, that despite passing common goodness-of-fit tests, PP-GLMs estimated from data are often unstable, leading to divergent firing rates. The inclusion of absolute refractory periods is not a satisfactory solution since the activity then typically settles into unphysiological rates. To address these issues, we derive a framework for determining the existence and stability of fixed points of the expected conditional intensity function (CIF) for general PP-GLMs. Specifically, in nonlinear Hawkes PP-GLMs, the CIF is expressed as a function of the previous spike history and exogenous inputs. We use a mean-field quasi-renewal (QR) approximation that decomposes spike history effects into the contribution of the last spike and an average of the CIF over all spike histories prior to the last spike. Fixed points for stationary rates are derived as self-consistent solutions of integral equations. Bifurcation analysis and the number of fixed points predict that the original models can show stable, divergent, and metastable (fragile) dynamics. For fragile models, fluctuations of the single-neuron dynamics predict expected divergence times after which rates approach unphysiologically high values. This metric can be used to estimate the probability of rates to remain physiological for given time periods, e.g., for simulation purposes. We demonstrate the use of the stability framework using simulated single-neuron examples and neurophysiological recordings. Finally, we show how to adapt PP-GLM estimation procedures to guarantee model stability. Overall, our results provide a stability framework for data-driven PP-GLMs and shed new light on the stochastic dynamics of state-of-the-art statistical models of neuronal spiking activity.

Computational system identification of continuous-time nonlinear systems using approximate Bayesian computation

NASA Astrophysics Data System (ADS)

Krishnanathan, Kirubhakaran; Anderson, Sean R.; Billings, Stephen A.; Kadirkamanathan, Visakan

2016-11-01

In this paper, we derive a system identification framework for continuous-time nonlinear systems, for the first time using a simulation-focused computational Bayesian approach. Simulation approaches to nonlinear system identification have been shown to outperform regression methods under certain conditions, such as non-persistently exciting inputs and fast-sampling. We use the approximate Bayesian computation (ABC) algorithm to perform simulation-based inference of model parameters. The framework has the following main advantages: (1) parameter distributions are intrinsically generated, giving the user a clear description of uncertainty, (2) the simulation approach avoids the difficult problem of estimating signal derivatives as is common with other continuous-time methods, and (3) as noted above, the simulation approach improves identification under conditions of non-persistently exciting inputs and fast-sampling. Term selection is performed by judging parameter significance using parameter distributions that are intrinsically generated as part of the ABC procedure. The results from a numerical example demonstrate that the method performs well in noisy scenarios, especially in comparison to competing techniques that rely on signal derivative estimation.

Inhomogeneous Point-Processes to Instantaneously Assess Affective Haptic Perception through Heartbeat Dynamics Information

NASA Astrophysics Data System (ADS)

Valenza, G.; Greco, A.; Citi, L.; Bianchi, M.; Barbieri, R.; Scilingo, E. P.

2016-06-01

This study proposes the application of a comprehensive signal processing framework, based on inhomogeneous point-process models of heartbeat dynamics, to instantaneously assess affective haptic perception using electrocardiogram-derived information exclusively. The framework relies on inverse-Gaussian point-processes with Laguerre expansion of the nonlinear Wiener-Volterra kernels, accounting for the long-term information given by the past heartbeat events. Up to cubic-order nonlinearities allow for an instantaneous estimation of the dynamic spectrum and bispectrum of the considered cardiovascular dynamics, as well as for instantaneous measures of complexity, through Lyapunov exponents and entropy. Short-term caress-like stimuli were administered for 4.3-25 seconds on the forearms of 32 healthy volunteers (16 females) through a wearable haptic device, by selectively superimposing two levels of force, 2 N and 6 N, and two levels of velocity, 9.4 mm/s and 65 mm/s. Results demonstrated that our instantaneous linear and nonlinear features were able to finely characterize the affective haptic perception, with a recognition accuracy of 69.79% along the force dimension, and 81.25% along the velocity dimension.

Quantification of Interactions between Dynamic Cellular Network Functionalities by Cascaded Layering

PubMed Central

Prescott, Thomas P.; Lang, Moritz; Papachristodoulou, Antonis

2015-01-01

Large, naturally evolved biomolecular networks typically fulfil multiple functions. When modelling or redesigning such systems, functional subsystems are often analysed independently first, before subsequent integration into larger-scale computational models. In the design and analysis process, it is therefore important to quantitatively analyse and predict the dynamics of the interactions between integrated subsystems; in particular, how the incremental effect of integrating a subsystem into a network depends on the existing dynamics of that network. In this paper we present a framework for simulating the contribution of any given functional subsystem when integrated together with one or more other subsystems. This is achieved through a cascaded layering of a network into functional subsystems, where each layer is defined by an appropriate subset of the reactions. We exploit symmetries in our formulation to exhaustively quantify each subsystem’s incremental effects with minimal computational effort. When combining subsystems, their isolated behaviour may be amplified, attenuated, or be subject to more complicated effects. We propose the concept of mutual dynamics to quantify such nonlinear phenomena, thereby defining the incompatibility and cooperativity between all pairs of subsystems when integrated into any larger network. We exemplify our theoretical framework by analysing diverse behaviours in three dynamic models of signalling and metabolic pathways: the effect of crosstalk mechanisms on the dynamics of parallel signal transduction pathways; reciprocal side-effects between several integral feedback mechanisms and the subsystems they stabilise; and consequences of nonlinear interactions between elementary flux modes in glycolysis for metabolic engineering strategies. Our analysis shows that it is not sufficient to just specify subsystems and analyse their pairwise interactions; the environment in which the interaction takes place must also be explicitly defined. Our framework provides a natural representation of nonlinear interaction phenomena, and will therefore be an important tool for modelling large-scale evolved or synthetic biomolecular networks. PMID:25933116

Network evolution by nonlinear preferential rewiring of edges

NASA Astrophysics Data System (ADS)

Xu, Xin-Jian; Hu, Xiao-Ming; Zhang, Li-Jie

2011-06-01

The mathematical framework for small-world networks proposed in a seminal paper by Watts and Strogatz sparked a widespread interest in modeling complex networks in the past decade. However, most of research contributing to static models is in contrast to real-world dynamic networks, such as social and biological networks, which are characterized by rearrangements of connections among agents. In this paper, we study dynamic networks evolved by nonlinear preferential rewiring of edges. The total numbers of vertices and edges of the network are conserved, but edges are continuously rewired according to the nonlinear preference. Assuming power-law kernels with exponents α and β, the network structures in stationary states display a distinct behavior, depending only on β. For β>1, the network is highly heterogeneous with the emergence of starlike structures. For β<1, the network is widely homogeneous with a typical connectivity. At β=1, the network is scale free with an exponential cutoff.

Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling.

PubMed

Perdikaris, P; Raissi, M; Damianou, A; Lawrence, N D; Karniadakis, G E

2017-02-01

Multi-fidelity modelling enables accurate inference of quantities of interest by synergistically combining realizations of low-cost/low-fidelity models with a small set of high-fidelity observations. This is particularly effective when the low- and high-fidelity models exhibit strong correlations, and can lead to significant computational gains over approaches that solely rely on high-fidelity models. However, in many cases of practical interest, low-fidelity models can only be well correlated to their high-fidelity counterparts for a specific range of input parameters, and potentially return wrong trends and erroneous predictions if probed outside of their validity regime. Here we put forth a probabilistic framework based on Gaussian process regression and nonlinear autoregressive schemes that is capable of learning complex nonlinear and space-dependent cross-correlations between models of variable fidelity, and can effectively safeguard against low-fidelity models that provide wrong trends. This introduces a new class of multi-fidelity information fusion algorithms that provide a fundamental extension to the existing linear autoregressive methodologies, while still maintaining the same algorithmic complexity and overall computational cost. The performance of the proposed methods is tested in several benchmark problems involving both synthetic and real multi-fidelity datasets from computational fluid dynamics simulations.

Fluid theory and simulations of instabilities, turbulent transport and coherent structures in partially-magnetized plasmas of \\mathbf{E}\\times \\mathbf{B} discharges

NASA Astrophysics Data System (ADS)

Smolyakov, A. I.; Chapurin, O.; Frias, W.; Koshkarov, O.; Romadanov, I.; Tang, T.; Umansky, M.; Raitses, Y.; Kaganovich, I. D.; Lakhin, V. P.

2017-01-01

Partially-magnetized plasmas with magnetized electrons and non-magnetized ions are common in Hall thrusters for electric propulsion and magnetron material processing devices. These plasmas are usually in strongly non-equilibrium state due to presence of crossed electric and magnetic fields, inhomogeneities of plasma density, temperature, magnetic field and beams of accelerated ions. Free energy from these sources make such plasmas prone to various instabilities resulting in turbulence, anomalous transport, and appearance of coherent structures as found in experiments. This paper provides an overview of instabilities that exist in such plasmas. A nonlinear fluid model has been developed for description of the Simon-Hoh, lower-hybrid and ion-sound instabilities. The model also incorporates electron gyroviscosity describing the effects of finite electron temperature. The nonlinear fluid model has been implemented in the BOUT++ framework. The results of nonlinear simulations are presented demonstrating turbulence, anomalous current and tendency toward the formation of coherent structures.

A Unified Nonlinear Adaptive Approach for Detection and Isolation of Engine Faults

NASA Technical Reports Server (NTRS)

Tang, Liang; DeCastro, Jonathan A.; Zhang, Xiaodong; Farfan-Ramos, Luis; Simon, Donald L.

2010-01-01

A challenging problem in aircraft engine health management (EHM) system development is to detect and isolate faults in system components (i.e., compressor, turbine), actuators, and sensors. Existing nonlinear EHM methods often deal with component faults, actuator faults, and sensor faults separately, which may potentially lead to incorrect diagnostic decisions and unnecessary maintenance. Therefore, it would be ideal to address sensor faults, actuator faults, and component faults under one unified framework. This paper presents a systematic and unified nonlinear adaptive framework for detecting and isolating sensor faults, actuator faults, and component faults for aircraft engines. The fault detection and isolation (FDI) architecture consists of a parallel bank of nonlinear adaptive estimators. Adaptive thresholds are appropriately designed such that, in the presence of a particular fault, all components of the residual generated by the adaptive estimator corresponding to the actual fault type remain below their thresholds. If the faults are sufficiently different, then at least one component of the residual generated by each remaining adaptive estimator should exceed its threshold. Therefore, based on the specific response of the residuals, sensor faults, actuator faults, and component faults can be isolated. The effectiveness of the approach was evaluated using the NASA C-MAPSS turbofan engine model, and simulation results are presented.

The knowledge-value chain: A conceptual framework for knowledge translation in health.

PubMed

Landry, Réjean; Amara, Nabil; Pablos-Mendes, Ariel; Shademani, Ramesh; Gold, Irving

2006-08-01

This article briefly discusses knowledge translation and lists the problems associated with it. Then it uses knowledge-management literature to develop and propose a knowledge-value chain framework in order to provide an integrated conceptual model of knowledge management and application in public health organizations. The knowledge-value chain is a non-linear concept and is based on the management of five dyadic capabilities: mapping and acquisition, creation and destruction, integration and sharing/transfer, replication and protection, and performance and innovation.

The knowledge-value chain: A conceptual framework for knowledge translation in health.

PubMed Central

Landry, Réjean; Amara, Nabil; Pablos-Mendes, Ariel; Shademani, Ramesh; Gold, Irving

2006-01-01

This article briefly discusses knowledge translation and lists the problems associated with it. Then it uses knowledge-management literature to develop and propose a knowledge-value chain framework in order to provide an integrated conceptual model of knowledge management and application in public health organizations. The knowledge-value chain is a non-linear concept and is based on the management of five dyadic capabilities: mapping and acquisition, creation and destruction, integration and sharing/transfer, replication and protection, and performance and innovation. PMID:16917645

A quasi-likelihood approach to non-negative matrix factorization

PubMed Central

Devarajan, Karthik; Cheung, Vincent C.K.

2017-01-01

A unified approach to non-negative matrix factorization based on the theory of generalized linear models is proposed. This approach embeds a variety of statistical models, including the exponential family, within a single theoretical framework and provides a unified view of such factorizations from the perspective of quasi-likelihood. Using this framework, a family of algorithms for handling signal-dependent noise is developed and its convergence proven using the Expectation-Maximization algorithm. In addition, a measure to evaluate the goodness-of-fit of the resulting factorization is described. The proposed methods allow modeling of non-linear effects via appropriate link functions and are illustrated using an application in biomedical signal processing. PMID:27348511

Multistate modelling extended by behavioural rules: An application to migration.

PubMed

Klabunde, Anna; Zinn, Sabine; Willekens, Frans; Leuchter, Matthias

2017-10-01

We propose to extend demographic multistate models by adding a behavioural element: behavioural rules explain intentions and thus transitions. Our framework is inspired by the Theory of Planned Behaviour. We exemplify our approach with a model of migration from Senegal to France. Model parameters are determined using empirical data where available. Parameters for which no empirical correspondence exists are determined by calibration. Age- and period-specific migration rates are used for model validation. Our approach adds to the toolkit of demographic projection by allowing for shocks and social influence, which alter behaviour in non-linear ways, while sticking to the general framework of multistate modelling. Our simulations yield that higher income growth in Senegal leads to higher emigration rates in the medium term, while a decrease in fertility yields lower emigration rates.

Macroscopic models for shape memory alloy characterization and design

NASA Astrophysics Data System (ADS)

Massad, Jordan Elias

Shape memory alloys (SMAs) are being considered for a number of high performance applications, such as deformable aircraft wings, earthquake-resistant structures, and microdevices, due to their capability to achieve very high work densities, produce large deformations, and generate high stresses. In general, the material behavior of SMAs is nonlinear and hysteresic. To achieve the full potential of SMA actuators, it is necessary to develop models that characterize the nonlinearities and hysteresis inherent in the constituent materials. Additionally, the design of SMA actuators necessitates the development of control algorithms based on those models. We develop two models that quantify the nonlinearities and hysteresis inherent to SMAs, each in formulations suitable for subsequent control design. In the first model, we employ domain theory to quantify SMA behavior under isothermal conditions. The model involves a single first-order, nonlinear ordinary differential equation and requires as few as seven parameters that are identifiable from measurements. We develop the second model using the Muller-Achenbach-Seelecke framework where a transition state theory of nonequilibrium processes is used to derive rate laws for the evolution of material phase fractions. The fully thermomechanical model predicts rate-dependent, polycrystalline SMA behavior, and it accommodates heat transfer issues pertinent to thin-film SMAs. Furthermore, the model admits a low-order formulation and has a small number of parameters which can be readily identified using attributes of measured data. We illustrate aspects of both models through comparison with experimental bulk and thin-film SMA data.

Dynamics of large-scale brain activity in normal arousal states and epileptic seizures

NASA Astrophysics Data System (ADS)

Robinson, P. A.; Rennie, C. J.; Rowe, D. L.

2002-04-01

Links between electroencephalograms (EEGs) and underlying aspects of neurophysiology and anatomy are poorly understood. Here a nonlinear continuum model of large-scale brain electrical activity is used to analyze arousal states and their stability and nonlinear dynamics for physiologically realistic parameters. A simple ordered arousal sequence in a reduced parameter space is inferred and found to be consistent with experimentally determined parameters of waking states. Instabilities arise at spectral peaks of the major clinically observed EEG rhythms-mainly slow wave, delta, theta, alpha, and sleep spindle-with each instability zone lying near its most common experimental precursor arousal states in the reduced space. Theta, alpha, and spindle instabilities evolve toward low-dimensional nonlinear limit cycles that correspond closely to EEGs of petit mal seizures for theta instability, and grand mal seizures for the other types. Nonlinear stimulus-induced entrainment and seizures are also seen, EEG spectra and potentials evoked by stimuli are reproduced, and numerous other points of experimental agreement are found. Inverse modeling enables physiological parameters underlying observed EEGs to be determined by a new, noninvasive route. This model thus provides a single, powerful framework for quantitative understanding of a wide variety of brain phenomena.

Nonlinear analysis of structures. [within framework of finite element method

NASA Technical Reports Server (NTRS)

Armen, H., Jr.; Levine, H.; Pifko, A.; Levy, A.

1974-01-01

The development of nonlinear analysis techniques within the framework of the finite-element method is reported. Although the emphasis is concerned with those nonlinearities associated with material behavior, a general treatment of geometric nonlinearity, alone or in combination with plasticity is included, and applications presented for a class of problems categorized as axisymmetric shells of revolution. The scope of the nonlinear analysis capabilities includes: (1) a membrane stress analysis, (2) bending and membrane stress analysis, (3) analysis of thick and thin axisymmetric bodies of revolution, (4) a general three dimensional analysis, and (5) analysis of laminated composites. Applications of the methods are made to a number of sample structures. Correlation with available analytic or experimental data range from good to excellent.

Prediction of Complex Aerodynamic Flows with Explicit Algebraic Stress Models

NASA Technical Reports Server (NTRS)

Abid, Ridha; Morrison, Joseph H.; Gatski, Thomas B.; Speziale, Charles G.

1996-01-01

An explicit algebraic stress equation, developed by Gatski and Speziale, is used in the framework of K-epsilon formulation to predict complex aerodynamic turbulent flows. The nonequilibrium effects are modeled through coefficients that depend nonlinearly on both rotational and irrotational strains. The proposed model was implemented in the ISAAC Navier-Stokes code. Comparisons with the experimental data are presented which clearly demonstrate that explicit algebraic stress models can predict the correct response to nonequilibrium flow.

On the pth moment estimates of solutions to stochastic functional differential equations in the G-framework.

PubMed

Faizullah, Faiz

2016-01-01

The aim of the current paper is to present the path-wise and moment estimates for solutions to stochastic functional differential equations with non-linear growth condition in the framework of G-expectation and G-Brownian motion. Under the nonlinear growth condition, the pth moment estimates for solutions to SFDEs driven by G-Brownian motion are proved. The properties of G-expectations, Hölder's inequality, Bihari's inequality, Gronwall's inequality and Burkholder-Davis-Gundy inequalities are used to develop the above mentioned theory. In addition, the path-wise asymptotic estimates and continuity of pth moment for the solutions to SFDEs in the G-framework, with non-linear growth condition are shown.

ECG Denoising Using Marginalized Particle Extended Kalman Filter With an Automatic Particle Weighting Strategy.

PubMed

Hesar, Hamed Danandeh; Mohebbi, Maryam

2017-05-01

In this paper, a model-based Bayesian filtering framework called the "marginalized particle-extended Kalman filter (MP-EKF) algorithm" is proposed for electrocardiogram (ECG) denoising. This algorithm does not have the extended Kalman filter (EKF) shortcoming in handling non-Gaussian nonstationary situations because of its nonlinear framework. In addition, it has less computational complexity compared with particle filter. This filter improves ECG denoising performance by implementing marginalized particle filter framework while reducing its computational complexity using EKF framework. An automatic particle weighting strategy is also proposed here that controls the reliance of our framework to the acquired measurements. We evaluated the proposed filter on several normal ECGs selected from MIT-BIH normal sinus rhythm database. To do so, artificial white Gaussian and colored noises as well as nonstationary real muscle artifact (MA) noise over a range of low SNRs from 10 to -5 dB were added to these normal ECG segments. The benchmark methods were the EKF and extended Kalman smoother (EKS) algorithms which are the first model-based Bayesian algorithms introduced in the field of ECG denoising. From SNR viewpoint, the experiments showed that in the presence of Gaussian white noise, the proposed framework outperforms the EKF and EKS algorithms in lower input SNRs where the measurements and state model are not reliable. Owing to its nonlinear framework and particle weighting strategy, the proposed algorithm attained better results at all input SNRs in non-Gaussian nonstationary situations (such as presence of pink noise, brown noise, and real MA). In addition, the impact of the proposed filtering method on the distortion of diagnostic features of the ECG was investigated and compared with EKF/EKS methods using an ECG diagnostic distortion measure called the "Multi-Scale Entropy Based Weighted Distortion Measure" or MSEWPRD. The results revealed that our proposed algorithm had the lowest MSEPWRD for all noise types at low input SNRs. Therefore, the morphology and diagnostic information of ECG signals were much better conserved compared with EKF/EKS frameworks, especially in non-Gaussian nonstationary situations.

A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

DOE PAGES

Hagos, Samson; Feng, Zhe; Plant, Robert S.; ...

2018-02-20

A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The framework follows the nonequilibrium statistical mechanical approach to constructing a master equation for representing the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics of convective cells: (i) the probability of growth, (ii) the probability of decay, and (iii)more » the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and the cloud-base mass flux is a nonlinear function of convective cell area, the mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated cloud-base mass flux variability under diurnally varying forcing. Finally, in addition to its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to serve as a nonequilibrium closure formulations for spectral mass flux parameterizations.« less

A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

NASA Astrophysics Data System (ADS)

Hagos, Samson; Feng, Zhe; Plant, Robert S.; Houze, Robert A.; Xiao, Heng

2018-02-01

A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The framework follows the nonequilibrium statistical mechanical approach to constructing a master equation for representing the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics of convective cells: (i) the probability of growth, (ii) the probability of decay, and (iii) the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and the cloud-base mass flux is a nonlinear function of convective cell area, the mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated cloud-base mass flux variability under diurnally varying forcing. In addition to its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to serve as a nonequilibrium closure formulations for spectral mass flux parameterizations.

A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

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

Hagos, Samson; Feng, Zhe; Plant, Robert S.

A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The framework follows the nonequilibrium statistical mechanical approach to constructing a master equation for representing the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics of convective cells: (i) the probability of growth, (ii) the probability of decay, and (iii)more » the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and the cloud-base mass flux is a nonlinear function of convective cell area, the mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated cloud-base mass flux variability under diurnally varying forcing. Finally, in addition to its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to serve as a nonequilibrium closure formulations for spectral mass flux parameterizations.« less

Overarching framework for data-based modelling

NASA Astrophysics Data System (ADS)

Schelter, Björn; Mader, Malenka; Mader, Wolfgang; Sommerlade, Linda; Platt, Bettina; Lai, Ying-Cheng; Grebogi, Celso; Thiel, Marco

2014-02-01

One of the main modelling paradigms for complex physical systems are networks. When estimating the network structure from measured signals, typically several assumptions such as stationarity are made in the estimation process. Violating these assumptions renders standard analysis techniques fruitless. We here propose a framework to estimate the network structure from measurements of arbitrary non-linear, non-stationary, stochastic processes. To this end, we propose a rigorous mathematical theory that underlies this framework. Based on this theory, we present a highly efficient algorithm and the corresponding statistics that are immediately sensibly applicable to measured signals. We demonstrate its performance in a simulation study. In experiments of transitions between vigilance stages in rodents, we infer small network structures with complex, time-dependent interactions; this suggests biomarkers for such transitions, the key to understand and diagnose numerous diseases such as dementia. We argue that the suggested framework combines features that other approaches followed so far lack.

Solving an emergency rescue materials problem under the joint reserves mode of government and framework agreement suppliers

PubMed Central

Sun, Xiao-Qing; Zhu, Rui; Li, Ming; Miao, Wang

2017-01-01

Emergency rescue material reserves are vital for the success of emergency rescue activities. In this study, we consider a situation where a government owned distribution center and framework agreement suppliers jointly store emergency rescue materials. Using a scenario-based approach to represent demand uncertainty, we propose a comprehensive transportation pattern for the following supply chain: “suppliers—government distribution center—disaster area.” Using a joint reserves model that includes the government and framework agreement suppliers, we develop a non-linear mathematic model that determines the choices of the framework suppliers, the corresponding optimal commitment quantities, and the quantity of materials that are stored at a government distribution center. Finally, we use IBM ILOG CPLEX to solve the numerical examples to verify the effectiveness of the mode and perform sensitivity analyses on the relevant parameters. PMID:29077722

Nonlinear and Dissipation Characteristics of Ocean Surface Waves in Estuarine Environments

DTIC Science & Technology

2013-09-30

developed models while using the general framework of operational wave models. We will conduct robustness tests of the system to determine the...and Guza (1984) model is weakly dispersive, in line with the assumptions behind the Boussinesq equations from which it was derived. The Kaihatu and...interactions across both frequency and directions. This system of equations is solved over a 2D frequency (f) and shore parallel wave number (κ) space. The

Dynamic simulation and numerical analysis of hurricane storm surge under sea level rise with geomorphologic changes along the northern Gulf of Mexico

USGS Publications Warehouse

Bilskie, Matthew V.; Hagen, S.C.; Alizad, K.A.; Medeiros, S.C.; Passeri, Davina L.; Needham, H.F.; Cox, A.

2016-01-01

This work outlines a dynamic modeling framework to examine the effects of global climate change, and sea level rise (SLR) in particular, on tropical cyclone-driven storm surge inundation. The methodology, applied across the northern Gulf of Mexico, adapts a present day large-domain, high resolution, tide, wind-wave, and hurricane storm surge model to characterize the potential outlook of the coastal landscape under four SLR scenarios for the year 2100. The modifications include shoreline and barrier island morphology, marsh migration, and land use land cover change. Hydrodynamics of 10 historic hurricanes were simulated through each of the five model configurations (present day and four SLR scenarios). Under SLR, the total inundated land area increased by 87% and developed and agricultural lands by 138% and 189%, respectively. Peak surge increased by as much as 1 m above the applied SLR in some areas, and other regions were subject to a reduction in peak surge, with respect to the applied SLR, indicating a nonlinear response. Analysis of time-series water surface elevation suggests the interaction between SLR and storm surge is nonlinear in time; SLR increased the time of inundation and caused an earlier arrival of the peak surge, which cannot be addressed using a static (“bathtub”) modeling framework. This work supports the paradigm shift to using a dynamic modeling framework to examine the effects of global climate change on coastal inundation. The outcomes have broad implications and ultimately support a better holistic understanding of the coastal system and aid restoration and long-term coastal sustainability.

Real-Time Fault Detection Approach for Nonlinear Systems and its Asynchronous T-S Fuzzy Observer-Based Implementation.

PubMed

Li, Linlin; Ding, Steven X; Qiu, Jianbin; Yang, Ying

2017-02-01

This paper is concerned with a real-time observer-based fault detection (FD) approach for a general type of nonlinear systems in the presence of external disturbances. To this end, in the first part of this paper, we deal with the definition and the design condition for an L ∞ / L 2 type of nonlinear observer-based FD systems. This analytical framework is fundamental for the development of real-time nonlinear FD systems with the aid of some well-established techniques. In the second part, we address the integrated design of the L ∞ / L 2 observer-based FD systems by applying Takagi-Sugeno (T-S) fuzzy dynamic modeling technique as the solution tool. This fuzzy observer-based FD approach is developed via piecewise Lyapunov functions, and can be applied to the case that the premise variables of the FD system is nonsynchronous with the premise variables of the fuzzy model of the plant. In the end, a case study on the laboratory setup of three-tank system is given to show the efficiency of the proposed results.

Breathing pulses in the damped-soliton model for nerves

NASA Astrophysics Data System (ADS)

Fongang Achu, G.; Moukam Kakmeni, F. M.; Dikande, A. M.

2018-01-01

Unlike the Hodgkin-Huxley picture in which the nerve impulse results from ion exchanges across the cell membrane through ion-gate channels, in the so-called soliton model the impulse is seen as an electromechanical process related to thermodynamical phenomena accompanying the generation of the action potential. In this work, account is taken of the effects of damping on the nerve impulse propagation, within the framework of the soliton model. Applying the reductive perturbation expansion on the resulting KdV-Burgers equation, a damped nonlinear Schrödinger equation is derived and shown to admit breathing-type solitary wave solutions. Under specific constraints, these breathing pulse solitons become self-trapped structures in which the damping is balanced by nonlinearity such that the pulse amplitude remains unchanged even in the presence of damping.

Stability analysis of host dynamics for hiv

NASA Astrophysics Data System (ADS)

Geetha, V.; Balamuralitharan, S.

2018-04-01

The phenomenon of disease modeling can be easily accomplished through mathematical framework. In this paper the transmission of disease in human is represented mathematically as a nonlinear system. We think about the components of the Human Immunodeficiency Virus (HIV) among the beginning periods of illness. Throughout this paper we have determined those logical representation of a three-compartmental HIV demonstrate for their stability evaluation. We tend to likewise explore the stimulating behavior of the model and acquire those Steady states for the disease-free and the endemic agreement. The framework can be evaluated by reproduction number R0. We additionally clarify the numerical recreation and their outcomes.

Machine Learning-based discovery of closures for reduced models of dynamical systems

NASA Astrophysics Data System (ADS)

Pan, Shaowu; Duraisamy, Karthik

2017-11-01

Despite the successful application of machine learning (ML) in fields such as image processing and speech recognition, only a few attempts has been made toward employing ML to represent the dynamics of complex physical systems. Previous attempts mostly focus on parameter calibration or data-driven augmentation of existing models. In this work we present a ML framework to discover closure terms in reduced models of dynamical systems and provide insights into potential problems associated with data-driven modeling. Based on exact closure models for linear system, we propose a general linear closure framework from viewpoint of optimization. The framework is based on trapezoidal approximation of convolution term. Hyperparameters that need to be determined include temporal length of memory effect, number of sampling points, and dimensions of hidden states. To circumvent the explicit specification of memory effect, a general framework inspired from neural networks is also proposed. We conduct both a priori and posteriori evaluations of the resulting model on a number of non-linear dynamical systems. This work was supported in part by AFOSR under the project ``LES Modeling of Non-local effects using Statistical Coarse-graining'' with Dr. Jean-Luc Cambier as the technical monitor.

A competitive binding model predicts the response of mammalian olfactory receptors to mixtures

NASA Astrophysics Data System (ADS)

Singh, Vijay; Murphy, Nicolle; Mainland, Joel; Balasubramanian, Vijay

Most natural odors are complex mixtures of many odorants, but due to the large number of possible mixtures only a small fraction can be studied experimentally. To get a realistic understanding of the olfactory system we need methods to predict responses to complex mixtures from single odorant responses. Focusing on mammalian olfactory receptors (ORs in mouse and human), we propose a simple biophysical model for odor-receptor interactions where only one odor molecule can bind to a receptor at a time. The resulting competition for occupancy of the receptor accounts for the experimentally observed nonlinear mixture responses. We first fit a dose-response relationship to individual odor responses and then use those parameters in a competitive binding model to predict mixture responses. With no additional parameters, the model predicts responses of 15 (of 18 tested) receptors to within 10 - 30 % of the observed values, for mixtures with 2, 3 and 12 odorants chosen from a panel of 30. Extensions of our basic model with odorant interactions lead to additional nonlinearities observed in mixture response like suppression, cooperativity, and overshadowing. Our model provides a systematic framework for characterizing and parameterizing such mixing nonlinearities from mixture response data.

"Globalized public health." A transdisciplinary comprehensive framework for analyzing contemporary globalization's influences on the field of public health.

PubMed

Lapaige, Véronique

2009-01-01

The current phase of globalization represents a "double-edged sword" challenge facing public health practitioners and health policy makers. The first "edge" throws light on two constructs in the field of public health: global health (formerly international health) and globalized public health. The second "edge" is that of global governance, and raises the question, "how can we construct public health regulations that adequately respond to both global and local complexities related to the two constructs mentioned earlier (global health and globalized public health)?" The two constructs call for the development of norms that will assure sustained population-wide health improvement and these two constructs have their own conceptual tools and theoretical models that permit a better understanding of them. In this paper, we introduce the "globalized public health" construct and we present an interactive comprehensive framework for critically analyzing contemporary globalization's influences on the field of public health. "Globalized public health", simultaneously a theoretical model and a conceptual framework, concerns the transformation of the field of public health in the sociohistorical context of globalization. The model is the fruit of an original theoretical research study conducted from 2005 to 2008 ("contextualized research," Gibbons' Mode II of knowledge production), founded on a QUAL-quant sequential mixed-method design. This research also reflects our political and ideological position, fuelled with aspirations of social democracy and cosmopolitical values. It is profoundly anchored in the pragmatic approach to globalization, looking to "reconcile" the market and equity. The model offers several features to users: (1) it is transdisciplinary; (2) it is interactive (CD-ROM); (3) it is nonlinear (nonlinear interrelations between the contextual globalization and the field of public health); (4) it is synchronic/diachronic (a double-crossed perspective permits analysis of global social change, the emergence of global agency and the transmutation of the field of public health, in the full complexity of their nonlinear interaction); (5) it offers five characteristics as an auto-eco-organized system of social interactions, or dynamic, nonlinear sociohistorical system. The model features a visual interface (five interrelated figures), a structure of 30 "integrator concepts" that integrates 114 other element-parts via 1,300 hypertext links. The model is both a knowledge translation tool and an interactive heuristic guide designed for practitioners and researchers in public health/community health/population health, as well as for decision-makers at all levels.

“Globalized public health.” A transdisciplinary comprehensive framework for analyzing contemporary globalization’s influences on the field of public health

PubMed Central

Lapaige, Véronique

2009-01-01

The current phase of globalization represents a “double-edged sword” challenge facing public health practitioners and health policy makers. The first “edge” throws light on two constructs in the field of public health: global health (formerly international health) and globalized public health. The second “edge” is that of global governance, and raises the question, “how can we construct public health regulations that adequately respond to both global and local complexities related to the two constructs mentioned earlier (global health and globalized public health)?” The two constructs call for the development of norms that will assure sustained population-wide health improvement and these two constructs have their own conceptual tools and theoretical models that permit a better understanding of them. In this paper, we introduce the “globalized public health” construct and we present an interactive comprehensive framework for critically analyzing contemporary globalization’s influences on the field of public health. “Globalized public health”, simultaneously a theoretical model and a conceptual framework, concerns the transformation of the field of public health in the sociohistorical context of globalization. The model is the fruit of an original theoretical research study conducted from 2005 to 2008 (“contextualized research,” Gibbons’ Mode II of knowledge production), founded on a QUAL-quant sequential mixed-method design. This research also reflects our political and ideological position, fuelled with aspirations of social democracy and cosmopolitical values. It is profoundly anchored in the pragmatic approach to globalization, looking to “reconcile” the market and equity. The model offers several features to users: (1) it is transdisciplinary; (2) it is interactive (CD-ROM); (3) it is nonlinear (nonlinear interrelations between the contextual globalization and the field of public health); (4) it is synchronic/diachronic (a double-crossed perspective permits analysis of global social change, the emergence of global agency and the transmutation of the field of public health, in the full complexity of their nonlinear interaction); (5) it offers five characteristics as an auto-eco-organized system of social interactions, or dynamic, nonlinear sociohistorical system. The model features a visual interface (five interrelated figures), a structure of 30 “integrator concepts” that integrates 114 other element-parts via 1,300 hypertext links. The model is both a knowledge translation tool and an interactive heuristic guide designed for practitioners and researchers in public health/community health/population health, as well as for decision-makers at all levels. PMID:22312210

High-order finite-volume solutions of the steady-state advection-diffusion equation with nonlinear Robin boundary conditions

NASA Astrophysics Data System (ADS)

Lin, Zhi; Zhang, Qinghai

2017-09-01

We propose high-order finite-volume schemes for numerically solving the steady-state advection-diffusion equation with nonlinear Robin boundary conditions. Although the original motivation comes from a mathematical model of blood clotting, the nonlinear boundary conditions may also apply to other scientific problems. The main contribution of this work is a generic algorithm for generating third-order, fourth-order, and even higher-order explicit ghost-filling formulas to enforce nonlinear Robin boundary conditions in multiple dimensions. Under the framework of finite volume methods, this appears to be the first algorithm of its kind. Numerical experiments on boundary value problems show that the proposed fourth-order formula can be much more accurate and efficient than a simple second-order formula. Furthermore, the proposed ghost-filling formulas may also be useful for solving other partial differential equations.

SEACAS Theory Manuals: Part 1. Problem Formulation in Nonlinear Solid Mechancis

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

Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

1998-08-01

This report gives an introduction to the basic concepts and principles involved in the formulation of nonlinear problems in solid mechanics. By way of motivation, the discussion begins with a survey of some of the important sources of nonlinearity in solid mechanics applications, using wherever possible simple one dimensional idealizations to demonstrate the physical concepts. This discussion is then generalized by presenting generic statements of initial/boundary value problems in solid mechanics, using linear elasticity as a template and encompassing such ideas as strong and weak forms of boundary value problems, boundary and initial conditions, and dynamic and quasistatic idealizations. Themore » notational framework used for the linearized problem is then extended to account for finite deformation of possibly inelastic solids, providing the context for the descriptions of nonlinear continuum mechanics, constitutive modeling, and finite element technology given in three companion reports.« less

Data Reduction Algorithm Using Nonnegative Matrix Factorization with Nonlinear Constraints

NASA Astrophysics Data System (ADS)

Sembiring, Pasukat

2017-12-01

Processing ofdata with very large dimensions has been a hot topic in recent decades. Various techniques have been proposed in order to execute the desired information or structure. Non- Negative Matrix Factorization (NMF) based on non-negatives data has become one of the popular methods for shrinking dimensions. The main strength of this method is non-negative object, the object model by a combination of some basic non-negative parts, so as to provide a physical interpretation of the object construction. The NMF is a dimension reduction method thathasbeen used widely for numerous applications including computer vision,text mining, pattern recognitions,and bioinformatics. Mathematical formulation for NMF did not appear as a convex optimization problem and various types of algorithms have been proposed to solve the problem. The Framework of Alternative Nonnegative Least Square(ANLS) are the coordinates of the block formulation approaches that have been proven reliable theoretically and empirically efficient. This paper proposes a new algorithm to solve NMF problem based on the framework of ANLS.This algorithm inherits the convergenceproperty of the ANLS framework to nonlinear constraints NMF formulations.

Numerical investigation of interactions between marine atmospheric boundary layer and offshore wind farm

NASA Astrophysics Data System (ADS)

Lyu, Pin; Chen, Wenli; Li, Hui; Shen, Lian

2017-11-01

In recent studies, Yang, Meneveau & Shen (Physics of Fluids, 2014; Renewable Energy, 2014) developed a hybrid numerical framework for simulation of offshore wind farm. The framework consists of simulation of nonlinear surface waves using a high-order spectral method, large-eddy simulation of wind turbulence on a wave-surface-fitted curvilinear grid, and an actuator disk model for wind turbines. In the present study, several more precise wind turbine models, including the actuator line model, actuator disk model with rotation, and nacelle model, are introduced into the computation. Besides offshore wind turbines on fixed piles, the new computational framework has the capability to investigate the interaction among wind, waves, and floating wind turbines. In this study, onshore, offshore fixed pile, and offshore floating wind farms are compared in terms of flow field statistics and wind turbine power extraction rate. The authors gratefully acknowledge financial support from China Scholarship Council (No. 201606120186) and the Institute on the Environment of University of Minnesota.

Nonlinear model predictive control applied to the separation of praziquantel in simulated moving bed chromatography.

PubMed

Andrade Neto, A S; Secchi, A R; Souza, M B; Barreto, A G

2016-10-28

An adaptive nonlinear model predictive control of a simulated moving bed unit for the enantioseparation of praziquantel is presented. A first principle model was applied at the proposed purity control scheme. The main concern about this kind of model in a control framework is in regard to the computational effort to solve it; however, a fast enough solution was achieved. In order to evaluate the controller's performance, several cases were simulated, including external pumps and switching valve malfunctions. The problem of plant-model mismatch was also investigated, and for that reason a parameter estimation step was introduced in the control strategy. In every studied scenario, the controller was able to maintain the purity levels at their set points, which were set to 99% and 98.6% for extract and raffinate, respectively. Additionally, fast responses and smooth actuation were achieved. Copyright © 2016 Elsevier B.V. All rights reserved.

Validation of High-Fidelity CFD/CAA Framework for Launch Vehicle Acoustic Environment Simulation against Scale Model Test Data

NASA Technical Reports Server (NTRS)

Liever, Peter A.; West, Jeffrey S.

2016-01-01

A hybrid Computational Fluid Dynamics and Computational Aero-Acoustics (CFD/CAA) modeling framework has been developed for launch vehicle liftoff acoustic environment predictions. The framework couples the existing highly-scalable NASA production CFD code, Loci/CHEM, with a high-order accurate discontinuous Galerkin solver developed in the same production framework, Loci/THRUST, to accurately resolve and propagate acoustic physics across the entire launch environment. Time-accurate, Hybrid RANS/LES CFD modeling is applied for predicting the acoustic generation physics at the plume source, and a high-order accurate unstructured discontinuous Galerkin (DG) method is employed to propagate acoustic waves away from the source across large distances using high-order accurate schemes. The DG solver is capable of solving 2nd, 3rd, and 4th order Euler solutions for non-linear, conservative acoustic field propagation. Initial application testing and validation has been carried out against high resolution acoustic data from the Ares Scale Model Acoustic Test (ASMAT) series to evaluate the capabilities and production readiness of the CFD/CAA system to resolve the observed spectrum of acoustic frequency content. This paper presents results from this validation and outlines efforts to mature and improve the computational simulation framework.

Algorithmic framework for group analysis of differential equations and its application to generalized Zakharov-Kuznetsov equations

NASA Astrophysics Data System (ADS)

Huang, Ding-jiang; Ivanova, Nataliya M.

2016-02-01

In this paper, we explain in more details the modern treatment of the problem of group classification of (systems of) partial differential equations (PDEs) from the algorithmic point of view. More precisely, we revise the classical Lie algorithm of construction of symmetries of differential equations, describe the group classification algorithm and discuss the process of reduction of (systems of) PDEs to (systems of) equations with smaller number of independent variables in order to construct invariant solutions. The group classification algorithm and reduction process are illustrated by the example of the generalized Zakharov-Kuznetsov (GZK) equations of form ut +(F (u)) xxx +(G (u)) xyy +(H (u)) x = 0. As a result, a complete group classification of the GZK equations is performed and a number of new interesting nonlinear invariant models which have non-trivial invariance algebras are obtained. Lie symmetry reductions and exact solutions for two important invariant models, i.e., the classical and modified Zakharov-Kuznetsov equations, are constructed. The algorithmic framework for group analysis of differential equations presented in this paper can also be applied to other nonlinear PDEs.

System health monitoring using multiple-model adaptive estimation techniques

NASA Astrophysics Data System (ADS)

Sifford, Stanley Ryan

Monitoring system health for fault detection and diagnosis by tracking system parameters concurrently with state estimates is approached using a new multiple-model adaptive estimation (MMAE) method. This novel method is called GRid-based Adaptive Parameter Estimation (GRAPE). GRAPE expands existing MMAE methods by using new techniques to sample the parameter space. GRAPE expands on MMAE with the hypothesis that sample models can be applied and resampled without relying on a predefined set of models. GRAPE is initially implemented in a linear framework using Kalman filter models. A more generalized GRAPE formulation is presented using extended Kalman filter (EKF) models to represent nonlinear systems. GRAPE can handle both time invariant and time varying systems as it is designed to track parameter changes. Two techniques are presented to generate parameter samples for the parallel filter models. The first approach is called selected grid-based stratification (SGBS). SGBS divides the parameter space into equally spaced strata. The second approach uses Latin Hypercube Sampling (LHS) to determine the parameter locations and minimize the total number of required models. LHS is particularly useful when the parameter dimensions grow. Adding more parameters does not require the model count to increase for LHS. Each resample is independent of the prior sample set other than the location of the parameter estimate. SGBS and LHS can be used for both the initial sample and subsequent resamples. Furthermore, resamples are not required to use the same technique. Both techniques are demonstrated for both linear and nonlinear frameworks. The GRAPE framework further formalizes the parameter tracking process through a general approach for nonlinear systems. These additional methods allow GRAPE to either narrow the focus to converged values within a parameter range or expand the range in the appropriate direction to track the parameters outside the current parameter range boundary. Customizable rules define the specific resample behavior when the GRAPE parameter estimates converge. Convergence itself is determined from the derivatives of the parameter estimates using a simple moving average window to filter out noise. The system can be tuned to match the desired performance goals by making adjustments to parameters such as the sample size, convergence criteria, resample criteria, initial sampling method, resampling method, confidence in prior sample covariances, sample delay, and others.

UNITY: Confronting Supernova Cosmology's Statistical and Systematic Uncertainties in a Unified Bayesian Framework

NASA Astrophysics Data System (ADS)

Rubin, D.; Aldering, G.; Barbary, K.; Boone, K.; Chappell, G.; Currie, M.; Deustua, S.; Fagrelius, P.; Fruchter, A.; Hayden, B.; Lidman, C.; Nordin, J.; Perlmutter, S.; Saunders, C.; Sofiatti, C.; Supernova Cosmology Project, The

2015-11-01

While recent supernova (SN) cosmology research has benefited from improved measurements, current analysis approaches are not statistically optimal and will prove insufficient for future surveys. This paper discusses the limitations of current SN cosmological analyses in treating outliers, selection effects, shape- and color-standardization relations, unexplained dispersion, and heterogeneous observations. We present a new Bayesian framework, called UNITY (Unified Nonlinear Inference for Type-Ia cosmologY), that incorporates significant improvements in our ability to confront these effects. We apply the framework to real SN observations and demonstrate smaller statistical and systematic uncertainties. We verify earlier results that SNe Ia require nonlinear shape and color standardizations, but we now include these nonlinear relations in a statistically well-justified way. This analysis was primarily performed blinded, in that the basic framework was first validated on simulated data before transitioning to real data. We also discuss possible extensions of the method.

Dark solitons in laser radiation build-up dynamics.

PubMed

Woodward, R I; Kelleher, E J R

2016-03-01

We reveal the existence of slowly decaying dark solitons in the radiation build-up dynamics of bright pulses in all-normal dispersion mode-locked fiber lasers, numerically modeled in the framework of a generalized nonlinear Schrödinger equation. The evolution of noise perturbations to quasistationary dark solitons is examined, and the significance of background shape and soliton-soliton collisions on the eventual soliton decay is established. We demonstrate the role of a restoring force in extending soliton interactions in conservative systems to include the effects of dissipation, as encountered in laser cavities, and generalize our observations to other nonlinear systems.

Goodwin accelerator model revisited with fixed time delays

NASA Astrophysics Data System (ADS)

Matsumoto, Akio; Merlone, Ugo; Szidarovszky, Ferenc

2018-05-01

Dynamics of Goodwin's accelerator business cycle model is reconsidered. The model is characterized by a nonlinear accelerator and an investment time delay. The role of the nonlinearity for the birth of persistent oscillations is fully discussed in the existing literature. On the other hand, not much of the role of the delay has yet been revealed. The purpose of this paper is to show that the delay really matters. In the original framework of Goodwin [6], it is first demonstrated that there is a threshold value of the delay: limit cycles arise for smaller values than the threshold and so do sawtooth oscillations for larger values. In the extended framework in which a consumption or saving delay, in addition to the investment delay, is introduced, three main results are demonstrated under assumption of the identical length of investment and consumption delays. The dynamics with consumption delay is basically the same as that of the single delay model. Second, in the case of saving delay, the steady state can coexist with the stable and unstable limit cycles in the stable case. Third, in the unstable case, there is an interval of delay in which the limit cycle or the sawtooth oscillation emerges depending on the choice of the constant initial function.

Understanding dynamics of Martian winter polar vortex with “improved” moist-convective shallow water model

NASA Astrophysics Data System (ADS)

Rostami, M.; Zeitlin, V.

2017-12-01

We show how the properties of the Mars polar vortex can be understood in the framework of a simple shallow-water type model obtained by vertical averaging of the adiabatic “primitive” equations, and “improved” by inclusion of thermal relaxation and convective fluxes due to the phase transitions of CO 2, the major constituent of the Martian atmosphere. We perform stability analysis of the vortex, show that corresponding mean zonal flow is unstable, and simulate numerically non-linear saturation of the instability. We show in this way that, while non-linear adiabatic saturation of the instability tends to reorganize the vortex, the diabatic effects prevent this, and thus provide an explanation of the vortex form and longevity.

Nonlinear integrable model of Frenkel-like excitations on a ribbon of triangular lattice

NASA Astrophysics Data System (ADS)

Vakhnenko, Oleksiy O.

2015-03-01

Following the considerable progress in nanoribbon technology, we propose to model the nonlinear Frenkel-like excitations on a triangular-lattice ribbon by the integrable nonlinear ladder system with the background-controlled intersite resonant coupling. The system of interest arises as a proper reduction of first general semidiscrete integrable system from an infinite hierarchy. The most significant local conservation laws related to the first general integrable system are found explicitly in the framework of generalized recursive approach. The obtained general local densities are equally applicable to any general semidiscrete integrable system from the respective infinite hierarchy. Using the recovered second densities, the Hamiltonian formulation of integrable nonlinear ladder system with background-controlled intersite resonant coupling is presented. In doing so, the relevant Poisson structure turns out to be essentially nontrivial. The Darboux transformation scheme as applied to the first general semidiscrete system is developed and the key role of Bäcklund transformation in justification of its self-consistency is pointed out. The spectral properties of Darboux matrix allow to restore the whole Darboux matrix thus ensuring generation one more soliton as compared with a priori known seed solution of integrable nonlinear system. The power of Darboux-dressing method is explicitly demonstrated in generating the multicomponent one-soliton solution to the integrable nonlinear ladder system with background-controlled intersite resonant coupling.

Multiscale modeling and characterization for performance and safety of lithium-ion batteries

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

Pannala, Sreekanth; Turner, John A.; Allu, Srikanth

Lithium-ion batteries are highly complex electrochemical systems whose performance and safety are governed by coupled nonlinear electrochemical-electrical-thermal-mechanical processes over a range of spatiotemporal scales. In this paper we describe a new, open source computational framework for Lithium-ion battery simulations that is designed to support a variety of model types and formulations. This framework has been used to create three-dimensional cell and battery pack models that explicitly simulate all the battery components (current collectors, electrodes, and separator). The models are used to predict battery performance under normal operations and to study thermal and mechanical safety aspects under adverse conditions. The modelmore » development and validation are supported by experimental methods such as IR-imaging, X-ray tomography and micro-Raman mapping.« less

Multiscale modeling and characterization for performance and safety of lithium-ion batteries

DOE PAGES

Pannala, Sreekanth; Turner, John A.; Allu, Srikanth; ...

2015-08-19

Lithium-ion batteries are highly complex electrochemical systems whose performance and safety are governed by coupled nonlinear electrochemical-electrical-thermal-mechanical processes over a range of spatiotemporal scales. In this paper we describe a new, open source computational framework for Lithium-ion battery simulations that is designed to support a variety of model types and formulations. This framework has been used to create three-dimensional cell and battery pack models that explicitly simulate all the battery components (current collectors, electrodes, and separator). The models are used to predict battery performance under normal operations and to study thermal and mechanical safety aspects under adverse conditions. The modelmore » development and validation are supported by experimental methods such as IR-imaging, X-ray tomography and micro-Raman mapping.« less

Mutual connectivity analysis (MCA) using generalized radial basis function neural networks for nonlinear functional connectivity network recovery in resting-state functional MRI

NASA Astrophysics Data System (ADS)

D'Souza, Adora M.; Abidin, Anas Zainul; Nagarajan, Mahesh B.; Wismüller, Axel

2016-03-01

We investigate the applicability of a computational framework, called mutual connectivity analysis (MCA), for directed functional connectivity analysis in both synthetic and resting-state functional MRI data. This framework comprises of first evaluating non-linear cross-predictability between every pair of time series prior to recovering the underlying network structure using community detection algorithms. We obtain the non-linear cross-prediction score between time series using Generalized Radial Basis Functions (GRBF) neural networks. These cross-prediction scores characterize the underlying functionally connected networks within the resting brain, which can be extracted using non-metric clustering approaches, such as the Louvain method. We first test our approach on synthetic models with known directional influence and network structure. Our method is able to capture the directional relationships between time series (with an area under the ROC curve = 0.92 +/- 0.037) as well as the underlying network structure (Rand index = 0.87 +/- 0.063) with high accuracy. Furthermore, we test this method for network recovery on resting-state fMRI data, where results are compared to the motor cortex network recovered from a motor stimulation sequence, resulting in a strong agreement between the two (Dice coefficient = 0.45). We conclude that our MCA approach is effective in analyzing non-linear directed functional connectivity and in revealing underlying functional network structure in complex systems.

Cross-entropy clustering framework for catchment classification

NASA Astrophysics Data System (ADS)

Tongal, Hakan; Sivakumar, Bellie

2017-09-01

There is an increasing interest in catchment classification and regionalization in hydrology, as they are useful for identification of appropriate model complexity and transfer of information from gauged catchments to ungauged ones, among others. This study introduces a nonlinear cross-entropy clustering (CEC) method for classification of catchments. The method specifically considers embedding dimension (m), sample entropy (SampEn), and coefficient of variation (CV) to represent dimensionality, complexity, and variability of the time series, respectively. The method is applied to daily streamflow time series from 217 gauging stations across Australia. The results suggest that a combination of linear and nonlinear parameters (i.e. m, SampEn, and CV), representing different aspects of the underlying dynamics of streamflows, could be useful for determining distinct patterns of flow generation mechanisms within a nonlinear clustering framework. For the 217 streamflow time series, nine hydrologically homogeneous clusters that have distinct patterns of flow regime characteristics and specific dominant hydrological attributes with different climatic features are obtained. Comparison of the results with those obtained using the widely employed k-means clustering method (which results in five clusters, with the loss of some information about the features of the clusters) suggests the superiority of the cross-entropy clustering method. The outcomes from this study provide a useful guideline for employing the nonlinear dynamic approaches based on hydrologic signatures and for gaining an improved understanding of streamflow variability at a large scale.

Mutual Connectivity Analysis (MCA) Using Generalized Radial Basis Function Neural Networks for Nonlinear Functional Connectivity Network Recovery in Resting-State Functional MRI.

PubMed

DSouza, Adora M; Abidin, Anas Zainul; Nagarajan, Mahesh B; Wismüller, Axel

2016-03-29

We investigate the applicability of a computational framework, called mutual connectivity analysis (MCA), for directed functional connectivity analysis in both synthetic and resting-state functional MRI data. This framework comprises of first evaluating non-linear cross-predictability between every pair of time series prior to recovering the underlying network structure using community detection algorithms. We obtain the non-linear cross-prediction score between time series using Generalized Radial Basis Functions (GRBF) neural networks. These cross-prediction scores characterize the underlying functionally connected networks within the resting brain, which can be extracted using non-metric clustering approaches, such as the Louvain method. We first test our approach on synthetic models with known directional influence and network structure. Our method is able to capture the directional relationships between time series (with an area under the ROC curve = 0.92 ± 0.037) as well as the underlying network structure (Rand index = 0.87 ± 0.063) with high accuracy. Furthermore, we test this method for network recovery on resting-state fMRI data, where results are compared to the motor cortex network recovered from a motor stimulation sequence, resulting in a strong agreement between the two (Dice coefficient = 0.45). We conclude that our MCA approach is effective in analyzing non-linear directed functional connectivity and in revealing underlying functional network structure in complex systems.

Directed dynamical influence is more detectable with noise

PubMed Central

Jiang, Jun-Jie; Huang, Zi-Gang; Huang, Liang; Liu, Huan; Lai, Ying-Cheng

2016-01-01

Successful identification of directed dynamical influence in complex systems is relevant to significant problems of current interest. Traditional methods based on Granger causality and transfer entropy have issues such as difficulty with nonlinearity and large data requirement. Recently a framework based on nonlinear dynamical analysis was proposed to overcome these difficulties. We find, surprisingly, that noise can counterintuitively enhance the detectability of directed dynamical influence. In fact, intentionally injecting a proper amount of asymmetric noise into the available time series has the unexpected benefit of dramatically increasing confidence in ascertaining the directed dynamical influence in the underlying system. This result is established based on both real data and model time series from nonlinear ecosystems. We develop a physical understanding of the beneficial role of noise in enhancing detection of directed dynamical influence. PMID:27066763

Directed dynamical influence is more detectable with noise.

PubMed

Jiang, Jun-Jie; Huang, Zi-Gang; Huang, Liang; Liu, Huan; Lai, Ying-Cheng

2016-04-12

Successful identification of directed dynamical influence in complex systems is relevant to significant problems of current interest. Traditional methods based on Granger causality and transfer entropy have issues such as difficulty with nonlinearity and large data requirement. Recently a framework based on nonlinear dynamical analysis was proposed to overcome these difficulties. We find, surprisingly, that noise can counterintuitively enhance the detectability of directed dynamical influence. In fact, intentionally injecting a proper amount of asymmetric noise into the available time series has the unexpected benefit of dramatically increasing confidence in ascertaining the directed dynamical influence in the underlying system. This result is established based on both real data and model time series from nonlinear ecosystems. We develop a physical understanding of the beneficial role of noise in enhancing detection of directed dynamical influence.

Isostable reduction with applications to time-dependent partial differential equations.

PubMed

Wilson, Dan; Moehlis, Jeff

2016-07-01

Isostables and isostable reduction, analogous to isochrons and phase reduction for oscillatory systems, are useful in the study of nonlinear equations which asymptotically approach a stationary solution. In this work, we present a general method for isostable reduction of partial differential equations, with the potential power to reduce the dimensionality of a nonlinear system from infinity to 1. We illustrate the utility of this reduction by applying it to two different models with biological relevance. In the first example, isostable reduction of the Fokker-Planck equation provides the necessary framework to design a simple control strategy to desynchronize a population of pathologically synchronized oscillatory neurons, as might be relevant to Parkinson's disease. Another example analyzes a nonlinear reaction-diffusion equation with relevance to action potential propagation in a cardiac system.

Efficient and Privacy-Preserving Online Medical Prediagnosis Framework Using Nonlinear SVM.

PubMed

Zhu, Hui; Liu, Xiaoxia; Lu, Rongxing; Li, Hui

2017-05-01

With the advances of machine learning algorithms and the pervasiveness of network terminals, the online medical prediagnosis system, which can provide the diagnosis of healthcare provider anywhere anytime, has attracted considerable interest recently. However, the flourish of online medical prediagnosis system still faces many challenges including information security and privacy preservation. In this paper, we propose an e fficient and privacy-preserving online medical prediagnosis framework, called eDiag, by using nonlinear kernel support vector machine (SVM). With eDiag, the sensitive personal health information can be processed without privacy disclosure during online prediagnosis service. Specifically, based on an improved expression for the nonlinear SVM, an efficient and privacy-preserving classification scheme is introduced with lightweight multiparty random masking and polynomial aggregation techniques. The encrypted user query is directly operated at the service provider without decryption, and the diagnosis result can only be decrypted by user. Through extensive analysis, we show that eDiag can ensure that users' health information and healthcare provider's prediction model are kept confidential, and has significantly less computation and communication overhead than existing schemes. In addition, performance evaluations via implementing eDiag on smartphone and computer demonstrate eDiag's effectiveness in term of real online environment.

Quadratic Solid⁻Shell Finite Elements for Geometrically Nonlinear Analysis of Functionally Graded Material Plates.

PubMed

Chalal, Hocine; Abed-Meraim, Farid

2018-06-20

In the current contribution, prismatic and hexahedral quadratic solid⁻shell (SHB) finite elements are proposed for the geometrically nonlinear analysis of thin structures made of functionally graded material (FGM). The proposed SHB finite elements are developed within a purely 3D framework, with displacements as the only degrees of freedom. Also, the in-plane reduced-integration technique is combined with the assumed-strain method to alleviate various locking phenomena. Furthermore, an arbitrary number of integration points are placed along a special direction, which represents the thickness. The developed elements are coupled with functionally graded behavior for the modeling of thin FGM plates. To this end, the Young modulus of the FGM plate is assumed to vary gradually in the thickness direction, according to a volume fraction distribution. The resulting formulations are implemented into the quasi-static ABAQUS/Standard finite element software in the framework of large displacements and rotations. Popular nonlinear benchmark problems are considered to assess the performance and accuracy of the proposed SHB elements. Comparisons with reference solutions from the literature demonstrate the good capabilities of the developed SHB elements for the 3D simulation of thin FGM plates.

Inhomogeneous Point-Processes to Instantaneously Assess Affective Haptic Perception through Heartbeat Dynamics Information

PubMed Central

Valenza, G.; Greco, A.; Citi, L.; Bianchi, M.; Barbieri, R.; Scilingo, E. P.

2016-01-01

This study proposes the application of a comprehensive signal processing framework, based on inhomogeneous point-process models of heartbeat dynamics, to instantaneously assess affective haptic perception using electrocardiogram-derived information exclusively. The framework relies on inverse-Gaussian point-processes with Laguerre expansion of the nonlinear Wiener-Volterra kernels, accounting for the long-term information given by the past heartbeat events. Up to cubic-order nonlinearities allow for an instantaneous estimation of the dynamic spectrum and bispectrum of the considered cardiovascular dynamics, as well as for instantaneous measures of complexity, through Lyapunov exponents and entropy. Short-term caress-like stimuli were administered for 4.3–25 seconds on the forearms of 32 healthy volunteers (16 females) through a wearable haptic device, by selectively superimposing two levels of force, 2 N and 6 N, and two levels of velocity, 9.4 mm/s and 65 mm/s. Results demonstrated that our instantaneous linear and nonlinear features were able to finely characterize the affective haptic perception, with a recognition accuracy of 69.79% along the force dimension, and 81.25% along the velocity dimension. PMID:27357966

A study of the effect of space-dependent neutronics on stochastically-induced bifurcations in BWR dynamics

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

Analytis, G.T.

1995-09-01

A non-linear one-group space-dependent neutronic model for a finite one-dimensional core is coupled with a simple BWR feed-back model. In agreement with results obtained by the authors who originally developed the point-kinetics version of this model, we shall show numerically that stochastic reactivity excitations may result in limit-cycles and eventually in a chaotic behaviour, depending on the magnitude of the feed-back coefficient K. In the framework of this simple space-dependent model, the effect of the non-linearities on the different spatial harmonics is studied and the importance of the space-dependent effects is exemplified and assessed in terms of the importance ofmore » the higher harmonics. It is shown that under certain conditions, when the limit-cycle-type develop, the neutron spectra may exhibit strong space-dependent effects.« less

Functional Additive Mixed Models

PubMed Central

Scheipl, Fabian; Staicu, Ana-Maria; Greven, Sonja

2014-01-01

We propose an extensive framework for additive regression models for correlated functional responses, allowing for multiple partially nested or crossed functional random effects with flexible correlation structures for, e.g., spatial, temporal, or longitudinal functional data. Additionally, our framework includes linear and nonlinear effects of functional and scalar covariates that may vary smoothly over the index of the functional response. It accommodates densely or sparsely observed functional responses and predictors which may be observed with additional error and includes both spline-based and functional principal component-based terms. Estimation and inference in this framework is based on standard additive mixed models, allowing us to take advantage of established methods and robust, flexible algorithms. We provide easy-to-use open source software in the pffr() function for the R-package refund. Simulations show that the proposed method recovers relevant effects reliably, handles small sample sizes well and also scales to larger data sets. Applications with spatially and longitudinally observed functional data demonstrate the flexibility in modeling and interpretability of results of our approach. PMID:26347592

Functional Additive Mixed Models.

PubMed

Scheipl, Fabian; Staicu, Ana-Maria; Greven, Sonja

2015-04-01

We propose an extensive framework for additive regression models for correlated functional responses, allowing for multiple partially nested or crossed functional random effects with flexible correlation structures for, e.g., spatial, temporal, or longitudinal functional data. Additionally, our framework includes linear and nonlinear effects of functional and scalar covariates that may vary smoothly over the index of the functional response. It accommodates densely or sparsely observed functional responses and predictors which may be observed with additional error and includes both spline-based and functional principal component-based terms. Estimation and inference in this framework is based on standard additive mixed models, allowing us to take advantage of established methods and robust, flexible algorithms. We provide easy-to-use open source software in the pffr() function for the R-package refund. Simulations show that the proposed method recovers relevant effects reliably, handles small sample sizes well and also scales to larger data sets. Applications with spatially and longitudinally observed functional data demonstrate the flexibility in modeling and interpretability of results of our approach.

High precision tracking of a piezoelectric nano-manipulator with parameterized hysteresis compensation

NASA Astrophysics Data System (ADS)

Yan, Peng; Zhang, Yangming

2018-06-01

High performance scanning of nano-manipulators is widely deployed in various precision engineering applications such as SPM (scanning probe microscope), where trajectory tracking of sophisticated reference signals is an challenging control problem. The situation is further complicated when rate dependent hysteresis of the piezoelectric actuators and the stress-stiffening induced nonlinear stiffness of the flexure mechanism are considered. In this paper, a novel control framework is proposed to achieve high precision tracking of a piezoelectric nano-manipulator subjected to hysteresis and stiffness nonlinearities. An adaptive parameterized rate-dependent Prandtl-Ishlinskii model is constructed and the corresponding adaptive inverse model based online compensation is derived. Meanwhile a robust adaptive control architecture is further introduced to improve the tracking accuracy and robustness of the compensated system, where the parametric uncertainties of the nonlinear dynamics can be well eliminated by on-line estimations. Comparative experimental studies of the proposed control algorithm are conducted on a PZT actuated nano-manipulating stage, where hysteresis modeling accuracy and excellent tracking performance are demonstrated in real-time implementations, with significant improvement over existing results.

Intelligence rules of hysteresis in the feedforward trajectory control of piezoelectrically-driven nanostagers

NASA Astrophysics Data System (ADS)

Bashash, Saeid; Jalili, Nader

2007-02-01

Piezoelectrically-driven nanostagers have limited performance in a variety of feedforward and feedback positioning applications because of their nonlinear hysteretic response to input voltage. The hysteresis phenomenon is well known for its complex and multi-path behavior. To realize the underlying physics of this phenomenon and to develop an efficient compensation strategy, the intelligence properties of hysteresis with the effects of non-local memories are discussed here. Through performing a set of experiments on a piezoelectrically-driven nanostager with a high resolution capacitive position sensor, it is shown that for the precise prediction of the hysteresis path, certain memory units are required to store the previous hysteresis trajectory data. Based on the experimental observations, a constitutive memory-based mathematical modeling framework is developed and trained for the precise prediction of the hysteresis path for arbitrarily assigned input profiles. Using the inverse hysteresis model, a feedforward control strategy is then developed and implemented on the nanostager to compensate for the ever-present nonlinearity. Experimental results demonstrate that the controller remarkably eliminates the nonlinear effect, if memory units are sufficiently chosen for the inverse model.

Small perturbations in a finger-tapping task reveal inherent nonlinearities of the underlying error correction mechanism.

PubMed

Bavassi, M Luz; Tagliazucchi, Enzo; Laje, Rodrigo

2013-02-01

Time processing in the few hundred milliseconds range is involved in the human skill of sensorimotor synchronization, like playing music in an ensemble or finger tapping to an external beat. In finger tapping, a mechanistic explanation in biologically plausible terms of how the brain achieves synchronization is still missing despite considerable research. In this work we show that nonlinear effects are important for the recovery of synchronization following a perturbation (a step change in stimulus period), even for perturbation magnitudes smaller than 10% of the period, which is well below the amount of perturbation needed to evoke other nonlinear effects like saturation. We build a nonlinear mathematical model for the error correction mechanism and test its predictions, and further propose a framework that allows us to unify the description of the three common types of perturbations. While previous authors have used two different model mechanisms for fitting different perturbation types, or have fitted different parameter value sets for different perturbation magnitudes, we propose the first unified description of the behavior following all perturbation types and magnitudes as the dynamical response of a compound model with fixed terms and a single set of parameter values. Copyright © 2012 Elsevier B.V. All rights reserved.

Multiscale asymmetric orthogonal wavelet kernel for linear programming support vector learning and nonlinear dynamic systems identification.

PubMed

Lu, Zhao; Sun, Jing; Butts, Kenneth

2014-05-01

Support vector regression for approximating nonlinear dynamic systems is more delicate than the approximation of indicator functions in support vector classification, particularly for systems that involve multitudes of time scales in their sampled data. The kernel used for support vector learning determines the class of functions from which a support vector machine can draw its solution, and the choice of kernel significantly influences the performance of a support vector machine. In this paper, to bridge the gap between wavelet multiresolution analysis and kernel learning, the closed-form orthogonal wavelet is exploited to construct new multiscale asymmetric orthogonal wavelet kernels for linear programming support vector learning. The closed-form multiscale orthogonal wavelet kernel provides a systematic framework to implement multiscale kernel learning via dyadic dilations and also enables us to represent complex nonlinear dynamics effectively. To demonstrate the superiority of the proposed multiscale wavelet kernel in identifying complex nonlinear dynamic systems, two case studies are presented that aim at building parallel models on benchmark datasets. The development of parallel models that address the long-term/mid-term prediction issue is more intricate and challenging than the identification of series-parallel models where only one-step ahead prediction is required. Simulation results illustrate the effectiveness of the proposed multiscale kernel learning.

Optimization-Based Inverse Identification of the Parameters of a Concrete Cap Material Model

NASA Astrophysics Data System (ADS)

Král, Petr; Hokeš, Filip; Hušek, Martin; Kala, Jiří; Hradil, Petr

2017-10-01

Issues concerning the advanced numerical analysis of concrete building structures in sophisticated computing systems currently require the involvement of nonlinear mechanics tools. The efforts to design safer, more durable and mainly more economically efficient concrete structures are supported via the use of advanced nonlinear concrete material models and the geometrically nonlinear approach. The application of nonlinear mechanics tools undoubtedly presents another step towards the approximation of the real behaviour of concrete building structures within the framework of computer numerical simulations. However, the success rate of this application depends on having a perfect understanding of the behaviour of the concrete material models used and having a perfect understanding of the used material model parameters meaning. The effective application of nonlinear concrete material models within computer simulations often becomes very problematic because these material models very often contain parameters (material constants) whose values are difficult to obtain. However, getting of the correct values of material parameters is very important to ensure proper function of a concrete material model used. Today, one possibility, which permits successful solution of the mentioned problem, is the use of optimization algorithms for the purpose of the optimization-based inverse material parameter identification. Parameter identification goes hand in hand with experimental investigation while it trying to find parameter values of the used material model so that the resulting data obtained from the computer simulation will best approximate the experimental data. This paper is focused on the optimization-based inverse identification of the parameters of a concrete cap material model which is known under the name the Continuous Surface Cap Model. Within this paper, material parameters of the model are identified on the basis of interaction between nonlinear computer simulations, gradient based and nature inspired optimization algorithms and experimental data, the latter of which take the form of a load-extension curve obtained from the evaluation of uniaxial tensile test results. The aim of this research was to obtain material model parameters corresponding to the quasi-static tensile loading which may be further used for the research involving dynamic and high-speed tensile loading. Based on the obtained results it can be concluded that the set goal has been reached.

A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

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

Hagos, Samson; Feng, Zhe; Plant, Robert S.

A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The approach used follows the non-equilibrium statistical mechanical approach through a master equation. The aim is to represent the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics: (i) the probability of growth, (ii) the probability of decay, and (iii)more » the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and mass flux is a non-linear function of convective cell area, mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated mass flux variability under diurnally varying forcing. Besides its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to be capable of providing alternative, non-equilibrium, closure formulations for spectral mass flux parameterizations.« less

Molecular Modeling and Experimental Investigations of Nonlinear Optical Compounds Monosubstituted Derivatives of Dicyanovinylbenzene

NASA Technical Reports Server (NTRS)

Timofeeva, Tatiana V.; Nesterov, Vladimir N.; Antipin, Mikhail Yu.; Clark, Ronald D.; Sanghadasa, Mohan; Cardelino, Beatriz H.; Moore, Craig E.; Frazier, Donald O.

1999-01-01

A search for potential nonlinear optical compounds was performed using the Cambridge Structure Database and molecular modeling. We investigated a series of monosubstituted derivatives of dicyanovinylbenzene, since the nonlinear optical (NLO) properties of such derivatives (o-methoxy-dicyanovinylbenzene, DIVA) were studied earlier. The molecular geometry of these compounds was investigated with x-ray analysis and discussed along with the results of molecular mechanics and ab initio quantum chemical calculations. The influence of crystal packing on the planarity of the molecules of this series has been revealed. Two new compounds from the series studied, ortho-F and para-Cl-dicyanovinylbenzene, according to powder measurements, were found to be NLO compounds in the crystal state about 10 times more active than urea. The peculiarities of crystal structure formation in the framework of balance between van der Waals and electrostatic interactions have been discussed. The crystal shape of DIVA and two new NLO compounds have been calculated on the basis of the known crystal structure.

Stochastic stability of sigma-point Unscented Predictive Filter.

PubMed

Cao, Lu; Tang, Yu; Chen, Xiaoqian; Zhao, Yong

2015-07-01

In this paper, the Unscented Predictive Filter (UPF) is derived based on unscented transformation for nonlinear estimation, which breaks the confine of conventional sigma-point filters by employing Kalman filter as subject investigated merely. In order to facilitate the new method, the algorithm flow of UPF is given firstly. Then, the theoretical analyses demonstrate that the estimate accuracy of the model error and system for the UPF is higher than that of the conventional PF. Moreover, the authors analyze the stochastic boundedness and the error behavior of Unscented Predictive Filter (UPF) for general nonlinear systems in a stochastic framework. In particular, the theoretical results present that the estimation error remains bounded and the covariance keeps stable if the system׳s initial estimation error, disturbing noise terms as well as the model error are small enough, which is the core part of the UPF theory. All of the results have been demonstrated by numerical simulations for a nonlinear example system. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Sequential bearings-only-tracking initiation with particle filtering method.

PubMed

Liu, Bin; Hao, Chengpeng

2013-01-01

The tracking initiation problem is examined in the context of autonomous bearings-only-tracking (BOT) of a single appearing/disappearing target in the presence of clutter measurements. In general, this problem suffers from a combinatorial explosion in the number of potential tracks resulted from the uncertainty in the linkage between the target and the measurement (a.k.a the data association problem). In addition, the nonlinear measurements lead to a non-Gaussian posterior probability density function (pdf) in the optimal Bayesian sequential estimation framework. The consequence of this nonlinear/non-Gaussian context is the absence of a closed-form solution. This paper models the linkage uncertainty and the nonlinear/non-Gaussian estimation problem jointly with solid Bayesian formalism. A particle filtering (PF) algorithm is derived for estimating the model's parameters in a sequential manner. Numerical results show that the proposed solution provides a significant benefit over the most commonly used methods, IPDA and IMMPDA. The posterior Cramér-Rao bounds are also involved for performance evaluation.

Multivariate meta-analysis for non-linear and other multi-parameter associations

PubMed Central

Gasparrini, A; Armstrong, B; Kenward, M G

2012-01-01

In this paper, we formalize the application of multivariate meta-analysis and meta-regression to synthesize estimates of multi-parameter associations obtained from different studies. This modelling approach extends the standard two-stage analysis used to combine results across different sub-groups or populations. The most straightforward application is for the meta-analysis of non-linear relationships, described for example by regression coefficients of splines or other functions, but the methodology easily generalizes to any setting where complex associations are described by multiple correlated parameters. The modelling framework of multivariate meta-analysis is implemented in the package mvmeta within the statistical environment R. As an illustrative example, we propose a two-stage analysis for investigating the non-linear exposure–response relationship between temperature and non-accidental mortality using time-series data from multiple cities. Multivariate meta-analysis represents a useful analytical tool for studying complex associations through a two-stage procedure. Copyright © 2012 John Wiley & Sons, Ltd. PMID:22807043

Nonlinear filtering techniques for noisy geophysical data: Using big data to predict the future

NASA Astrophysics Data System (ADS)

Moore, J. M.

2014-12-01

Chaos is ubiquitous in physical systems. Within the Earth sciences it is readily evident in seismology, groundwater flows and drilling data. Models and workflows have been applied successfully to understand and even to predict chaotic systems in other scientific fields, including electrical engineering, neurology and oceanography. Unfortunately, the high levels of noise characteristic of our planet's chaotic processes often render these frameworks ineffective. This contribution presents techniques for the reduction of noise associated with measurements of nonlinear systems. Our ultimate aim is to develop data assimilation techniques for forward models that describe chaotic observations, such as episodic tremor and slip (ETS) events in fault zones. A series of nonlinear filters are presented and evaluated using classical chaotic systems. To investigate whether the filters can successfully mitigate the effect of noise typical of Earth science, they are applied to sunspot data. The filtered data can be used successfully to forecast sunspot evolution for up to eight years (see figure).

Experimental and Computational Investigation of Viscoelasticity of Native and Engineered Ligament and Tendon

NASA Astrophysics Data System (ADS)

Ma, J.; Narayanan, H.; Garikipati, K.; Grosh, K.; Arruda, E. M.

The important mechanisms by which soft collagenous tissues such as ligament and tendon respond to mechanical deformation include non-linear elasticity, viscoelasticity and poroelasticity. These contributions to the mechanical response are modulated by the content and morphology of structural proteins such as type I collagen and elastin, other molecules such as glycosaminoglycans, and fluid. Our ligament and tendon constructs, engineered from either primary cells or bone marrow stromal cells and their autogenous matricies, exhibit histological and mechanical characteristics of native tissues of different levels of maturity. In order to establish whether the constructs have optimal mechanical function for implantation and utility for regenerative medicine, constitutive relationships for the constructs and native tissues at different developmental levels must be established. A micromechanical model incorporating viscoelastic collagen and non-linear elastic elastin is used to describe the non-linear viscoelastic response of our homogeneous engineered constructs in vitro. This model is incorporated within a finite element framework to examine the heterogeneity of the mechanical responses of native ligament and tendon.

Properties of internal solitary waves in a symmetric three-layer fluid

NASA Astrophysics Data System (ADS)

Vladykina, E. A.; Polukhina, O. E.; Kurkin, A. A.

2009-04-01

Though all the natural media have smooth density stratifications (with the exception of special cases such as sea surface, inversion layer in the atmosphere), the scales of density variations can be different, and some of them can be considered as very sharp. Therefore for the description of internal wave propagation and interaction in the ocean and atmosphere the n-layer models are often used. In these models density profile is usually approximated by a piecewise-constant function. The advantage of the layered models is the finite number of parameters and relatively simple solutions of linear and weakly nonlinear problems. Layered models are also very popular in the laboratory experiments with stratified fluid. In this study we consider symmetric, continuously stratified, smoothed three-layer fluid bounded by rigid horizontal surface and bottom. Three-layer stratification is proved to be a proper approximation of sea water density profile in some basins in the World Ocean with specific hydrological conditions. Such a medium is interesting from the point of view of internal gravity wave dynamics, because in the symmetric case it leads to disappearing of quadratic nonlinearity when described in the framework of weakly nonlinear evolutionary models, that are derived through the asymptotic expansion in small parameters of nonlinearity and dispersion. The goal of our study is to determine the properties of localized stationary internal gravity waveforms (solitary waves) in this symmetric three-layer fluid. The investigation is carried out in the framework of improved mathematical model describing the transformation of internal wave fields generated by an initial disturbance. The model is based on the program complex for the numerical simulation of the two-dimensional (vertical plane) fully nonlinear Euler equations for incompressible stratified fluid under the Boussinesq approximation. Initial disturbances of both polarities evolve into stationary, solitary-like waves of corresponding polarity, for which we found the amplitude-width, amplitude-velocity, mass-amplitude, and energy-amplitude relations. Small-amplitude impulses to a good approximation can be described by the modified Korteweg-de Vries equation, but larger waves tend to become wide, and absolute value of their amplitude is bounded by the upper limit. Authors thank prof. K.G. Lamb for the opportunity to use the program code for numerical simulations of Euler equations. The research was supported by RFBR (09-05-00447, 09-05-00204) and by President of RF (MD-3024.2008.5 for young doctors of science).

Laminar and orientation-dependent characteristics of spatial nonlinearities: implications for the computational architecture of visual cortex.

PubMed

Victor, Jonathan D; Mechler, Ferenc; Ohiorhenuan, Ifije; Schmid, Anita M; Purpura, Keith P

2009-12-01

A full understanding of the computations performed in primary visual cortex is an important yet elusive goal. Receptive field models consisting of cascades of linear filters and static nonlinearities may be adequate to account for responses to simple stimuli such as gratings and random checkerboards, but their predictions of responses to complex stimuli such as natural scenes are only approximately correct. It is unclear whether these discrepancies are limited to quantitative inaccuracies that reflect well-recognized mechanisms such as response normalization, gain controls, and cross-orientation suppression or, alternatively, imply additional qualitative features of the underlying computations. To address this question, we examined responses of V1 and V2 neurons in the monkey and area 17 neurons in the cat to two-dimensional Hermite functions (TDHs). TDHs are intermediate in complexity between traditional analytic stimuli and natural scenes and have mathematical properties that facilitate their use to test candidate models. By exploiting these properties, along with the laminar organization of V1, we identify qualitative aspects of neural computations beyond those anticipated from the above-cited model framework. Specifically, we find that V1 neurons receive signals from orientation-selective mechanisms that are highly nonlinear: they are sensitive to phase correlations, not just spatial frequency content. That is, the behavior of V1 neurons departs from that of linear-nonlinear cascades with standard modulatory mechanisms in a qualitative manner: even relatively simple stimuli evoke responses that imply complex spatial nonlinearities. The presence of these findings in the input layers suggests that these nonlinearities act in a feedback fashion.

Uncertainty quantification for PZT bimorph actuators

NASA Astrophysics Data System (ADS)

Bravo, Nikolas; Smith, Ralph C.; Crews, John

2018-03-01

In this paper, we discuss the development of a high fidelity model for a PZT bimorph actuator used for micro-air vehicles, which includes the Robobee. We developed a high-fidelity model for the actuator using the homogenized energy model (HEM) framework, which quantifies the nonlinear, hysteretic, and rate-dependent behavior inherent to PZT in dynamic operating regimes. We then discussed an inverse problem on the model. We included local and global sensitivity analysis of the parameters in the high-fidelity model. Finally, we will discuss the results of Bayesian inference and uncertainty quantification on the HEM.

Dynamic updating atlas for heart segmentation with a nonlinear field-based model.

PubMed

Cai, Ken; Yang, Rongqian; Yue, Hongwei; Li, Lihua; Ou, Shanxing; Liu, Feng

2017-09-01

Segmentation of cardiac computed tomography (CT) images is an effective method for assessing the dynamic function of the heart and lungs. In the atlas-based heart segmentation approach, the quality of segmentation usually relies upon atlas images, and the selection of those reference images is a key step. The optimal goal in this selection process is to have the reference images as close to the target image as possible. This study proposes an atlas dynamic update algorithm using a scheme of nonlinear deformation field. The proposed method is based on the features among double-source CT (DSCT) slices. The extraction of these features will form a base to construct an average model and the created reference atlas image is updated during the registration process. A nonlinear field-based model was used to effectively implement a 4D cardiac segmentation. The proposed segmentation framework was validated with 14 4D cardiac CT sequences. The algorithm achieved an acceptable accuracy (1.0-2.8 mm). Our proposed method that combines a nonlinear field-based model and dynamic updating atlas strategies can provide an effective and accurate way for whole heart segmentation. The success of the proposed method largely relies on the effective use of the prior knowledge of the atlas and the similarity explored among the to-be-segmented DSCT sequences. Copyright © 2016 John Wiley & Sons, Ltd.

Development of an Integrated Modeling Framework for Simulations of Coastal Processes in Deltaic Environments Using High-Performance Computing

DTIC Science & Technology

2009-01-01

attenuation and mass transport of a water -mud system due to a solitary wave on the free surface has been modeled by using the Chebyshev-Chebyshev...in Lagrangian coordinates and perturbation equations for shallow water waves were 3 derived. An iteration-by-subdomain technique was introduced to...found. Although the model is focused on solitary waves and Newtonian fluid-mud, the methodology can be extended to oscillatory, nonlinear water waves

Models of inertial range spectra of interplanetary magnetohydrodynamic turbulence

NASA Technical Reports Server (NTRS)

Zhou, YE; Matthaeus, William H.

1990-01-01

A framework based on turbulence theory is presented to develop approximations for the local turbulence effects that are required in transport models. An approach based on Kolmogoroff-style dimensional analysis is presented as well as one based on a wave-number diffusion picture. Particular attention is given to the case of MHD turbulence with arbitrary cross helicity and with arbitrary ratios of the Alfven time scale and the nonlinear time scale.

Development of a Framework for Model-Based Analysis, Uncertainty Quantification, and Robust Control Design of Nonlinear Smart Composite Systems

DTIC Science & Technology

2015-06-04

control, vibration and noise control, health monitoring, and energy harvesting . However, these advantages come at the cost of rate-dependent hysteresis...configuration used for energy harvesting . Uncertainty Quantification Uncertainty quantification is pursued in two steps: (i) determination of densities...Crews and R.C. Smith, “Quantification of parameter and model uncertainty for shape mem- ory alloy bending actuators,” Journal of Intelligent material

The Role of Nonlinear Gradients in Parallel Imaging: A k-Space Based Analysis.

PubMed

Galiana, Gigi; Stockmann, Jason P; Tam, Leo; Peters, Dana; Tagare, Hemant; Constable, R Todd

2012-09-01

Sequences that encode the spatial information of an object using nonlinear gradient fields are a new frontier in MRI, with potential to provide lower peripheral nerve stimulation, windowed fields of view, tailored spatially-varying resolution, curved slices that mirror physiological geometry, and, most importantly, very fast parallel imaging with multichannel coils. The acceleration for multichannel images is generally explained by the fact that curvilinear gradient isocontours better complement the azimuthal spatial encoding provided by typical receiver arrays. However, the details of this complementarity have been more difficult to specify. We present a simple and intuitive framework for describing the mechanics of image formation with nonlinear gradients, and we use this framework to review some the main classes of nonlinear encoding schemes.

Penalized gaussian process regression and classification for high-dimensional nonlinear data.

PubMed

Yi, G; Shi, J Q; Choi, T

2011-12-01

The model based on Gaussian process (GP) prior and a kernel covariance function can be used to fit nonlinear data with multidimensional covariates. It has been used as a flexible nonparametric approach for curve fitting, classification, clustering, and other statistical problems, and has been widely applied to deal with complex nonlinear systems in many different areas particularly in machine learning. However, it is a challenging problem when the model is used for the large-scale data sets and high-dimensional data, for example, for the meat data discussed in this article that have 100 highly correlated covariates. For such data, it suffers from large variance of parameter estimation and high predictive errors, and numerically, it suffers from unstable computation. In this article, penalized likelihood framework will be applied to the model based on GPs. Different penalties will be investigated, and their ability in application given to suit the characteristics of GP models will be discussed. The asymptotic properties will also be discussed with the relevant proofs. Several applications to real biomechanical and bioinformatics data sets will be reported. © 2011, The International Biometric Society No claim to original US government works.

Predictor-corrector framework for the sequential assembly of optical systems based on wavefront sensing.

PubMed

Schindlbeck, Christopher; Pape, Christian; Reithmeier, Eduard

2018-04-16

Alignment of optical components is crucial for the assembly of optical systems to ensure their full functionality. In this paper we present a novel predictor-corrector framework for the sequential assembly of serial optical systems. Therein, we use a hybrid optical simulation model that comprises virtual and identified component positions. The hybrid model is constantly adapted throughout the assembly process with the help of nonlinear identification techniques and wavefront measurements. This enables prediction of the future wavefront at the detector plane and therefore allows for taking corrective measures accordingly during the assembly process if a user-defined tolerance on the wavefront error is violated. We present a novel notation for the so-called hybrid model and outline the work flow of the presented predictor-corrector framework. A beam expander is assembled as demonstrator for experimental verification of the framework. The optical setup consists of a laser, two bi-convex spherical lenses each mounted to a five degree-of-freedom stage to misalign and correct components, and a Shack-Hartmann sensor for wavefront measurements.

An overview of modelling approaches and potential solution towards an endgame of tobacco

NASA Astrophysics Data System (ADS)

Halim, Tisya Farida Abdul; Sapiri, Hasimah; Abidin, Norhaslinda Zainal

2015-12-01

A high number of premature mortality due to tobacco use has increased worldwide. Despite control policies being implemented to reduce premature mortality, the rate of smoking prevalence is still high. Moreover, tobacco issues become increasingly difficult since many aspects need to be considered simultaneously. Thus, the purpose of this paper is to present an overview of existing modelling studies on tobacco control system. The background section describes the tobacco issues and its current trends. These models have been categorised according to their modelling approaches either individual or integrated approaches. Next, a framework of modelling approaches based on the integration of multi-criteria decision making, system dynamics and nonlinear programming is proposed, expected to reduce the smoking prevalence. This framework provides guideline for modelling the interaction between smoking behaviour and its impacts, tobacco control policies and the effectiveness of each strategy in healthcare.

Chaos synchronization and Nelder-Mead search for parameter estimation in nonlinear pharmacological systems: Estimating tumor antigenicity in a model of immunotherapy.

PubMed

Pillai, Nikhil; Craig, Morgan; Dokoumetzidis, Aristeidis; Schwartz, Sorell L; Bies, Robert; Freedman, Immanuel

2018-06-19

In mathematical pharmacology, models are constructed to confer a robust method for optimizing treatment. The predictive capability of pharmacological models depends heavily on the ability to track the system and to accurately determine parameters with reference to the sensitivity in projected outcomes. To closely track chaotic systems, one may choose to apply chaos synchronization. An advantageous byproduct of this methodology is the ability to quantify model parameters. In this paper, we illustrate the use of chaos synchronization combined with Nelder-Mead search to estimate parameters of the well-known Kirschner-Panetta model of IL-2 immunotherapy from noisy data. Chaos synchronization with Nelder-Mead search is shown to provide more accurate and reliable estimates than Nelder-Mead search based on an extended least squares (ELS) objective function. Our results underline the strength of this approach to parameter estimation and provide a broader framework of parameter identification for nonlinear models in pharmacology. Copyright © 2018 Elsevier Ltd. All rights reserved.

Systematic Computation of Nonlinear Cellular and Molecular Dynamics with Low-Power CytoMimetic Circuits: A Simulation Study

PubMed Central

Papadimitriou, Konstantinos I.; Stan, Guy-Bart V.; Drakakis, Emmanuel M.

2013-01-01

This paper presents a novel method for the systematic implementation of low-power microelectronic circuits aimed at computing nonlinear cellular and molecular dynamics. The method proposed is based on the Nonlinear Bernoulli Cell Formalism (NBCF), an advanced mathematical framework stemming from the Bernoulli Cell Formalism (BCF) originally exploited for the modular synthesis and analysis of linear, time-invariant, high dynamic range, logarithmic filters. Our approach identifies and exploits the striking similarities existing between the NBCF and coupled nonlinear ordinary differential equations (ODEs) typically appearing in models of naturally encountered biochemical systems. The resulting continuous-time, continuous-value, low-power CytoMimetic electronic circuits succeed in simulating fast and with good accuracy cellular and molecular dynamics. The application of the method is illustrated by synthesising for the first time microelectronic CytoMimetic topologies which simulate successfully: 1) a nonlinear intracellular calcium oscillations model for several Hill coefficient values and 2) a gene-protein regulatory system model. The dynamic behaviours generated by the proposed CytoMimetic circuits are compared and found to be in very good agreement with their biological counterparts. The circuits exploit the exponential law codifying the low-power subthreshold operation regime and have been simulated with realistic parameters from a commercially available CMOS process. They occupy an area of a fraction of a square-millimetre, while consuming between 1 and 12 microwatts of power. Simulations of fabrication-related variability results are also presented. PMID:23393550

Study on the influence of supplying compressed air channels and evicting channels on pneumatical oscillation systems for vibromooshing

NASA Astrophysics Data System (ADS)

Glăvan, D. O.; Radu, I.; Babanatsas, T.; Babanatis Merce, R. M.; Kiss, I.; Gaspar, M. C.

2018-01-01

The paper presents a pneumatic system with two oscillating masses. The system is composed of a cylinder (framework) with mass m1, which has a piston with mass m2 inside. The cylinder (framework system) has one supplying channel for compressed air and one evicting channel for each work chamber (left and right of the piston). Functionality of the piston position comparatively with the cylinder (framework) is possible through the supplying or evicting of compressed air. The variable force that keeps the movement depends on variation of the pressure that is changing depending on the piston position according to the cylinder (framework) and to the section form that is supplying and evicting channels with compressed air. The paper presents the physical model/pattern, the mathematical model/pattern (differential equations) and numerical solution of the differential equations in hypothesis with the section form of supplying and evicting channels with compressed air is rectangular (variation linear) or circular (variation nonlinear).

Validation of High-Fidelity CFD/CAA Framework for Launch Vehicle Acoustic Environment Simulation against Scale Model Test Data

NASA Technical Reports Server (NTRS)

Liever, Peter A.; West, Jeffrey S.; Harris, Robert E.

2016-01-01

A hybrid Computational Fluid Dynamics and Computational Aero-Acoustics (CFD/CAA) modeling framework has been developed for launch vehicle liftoff acoustic environment predictions. The framework couples the existing highly-scalable NASA production CFD code, Loci/CHEM, with a high-order accurate Discontinuous Galerkin solver developed in the same production framework, Loci/THRUST, to accurately resolve and propagate acoustic physics across the entire launch environment. Time-accurate, Hybrid RANS/LES CFD modeling is applied for predicting the acoustic generation physics at the plume source, and a high-order accurate unstructured mesh Discontinuous Galerkin (DG) method is employed to propagate acoustic waves away from the source across large distances using high-order accurate schemes. The DG solver is capable of solving 2nd, 3rd, and 4th order Euler solutions for non-linear, conservative acoustic field propagation. Initial application testing and validation has been carried out against high resolution acoustic data from the Ares Scale Model Acoustic Test (ASMAT) series to evaluate the capabilities and production readiness of the CFD/CAA system to resolve the observed spectrum of acoustic frequency content. This paper presents results from this validation and outlines efforts to mature and improve the computational simulation framework.

Integrating cognitive and peripheral factors in predicting hearing-aid processing effectiveness

PubMed Central

Kates, James M.; Arehart, Kathryn H.; Souza, Pamela E.

2013-01-01

Individual factors beyond the audiogram, such as age and cognitive abilities, can influence speech intelligibility and speech quality judgments. This paper develops a neural network framework for combining multiple subject factors into a single model that predicts speech intelligibility and quality for a nonlinear hearing-aid processing strategy. The nonlinear processing approach used in the paper is frequency compression, which is intended to improve the audibility of high-frequency speech sounds by shifting them to lower frequency regions where listeners with high-frequency loss have better hearing thresholds. An ensemble averaging approach is used for the neural network to avoid the problems associated with overfitting. Models are developed for two subject groups, one having nearly normal hearing and the other mild-to-moderate sloping losses. PMID:25669257

Aperiodic Robust Model Predictive Control for Constrained Continuous-Time Nonlinear Systems: An Event-Triggered Approach.

PubMed

Liu, Changxin; Gao, Jian; Li, Huiping; Xu, Demin

2018-05-01

The event-triggered control is a promising solution to cyber-physical systems, such as networked control systems, multiagent systems, and large-scale intelligent systems. In this paper, we propose an event-triggered model predictive control (MPC) scheme for constrained continuous-time nonlinear systems with bounded disturbances. First, a time-varying tightened state constraint is computed to achieve robust constraint satisfaction, and an event-triggered scheduling strategy is designed in the framework of dual-mode MPC. Second, the sufficient conditions for ensuring feasibility and closed-loop robust stability are developed, respectively. We show that robust stability can be ensured and communication load can be reduced with the proposed MPC algorithm. Finally, numerical simulations and comparison studies are performed to verify the theoretical results.

Unveiling Galaxy Bias via the Halo Model, KiDS and GAMA

NASA Astrophysics Data System (ADS)

Dvornik, Andrej; Hoekstra, Henk; Kuijken, Konrad; Schneider, Peter; Amon, Alexandra; Nakajima, Reiko; Viola, Massimo; Choi, Ami; Erben, Thomas; Farrow, Daniel J.; Heymans, Catherine; Hildebrandt, Hendrik; Sifón, Cristóbal; Wang, Lingyu

2018-06-01

We measure the projected galaxy clustering and galaxy-galaxy lensing signals using the Galaxy And Mass Assembly (GAMA) survey and Kilo-Degree Survey (KiDS) to study galaxy bias. We use the concept of non-linear and stochastic galaxy biasing in the framework of halo occupation statistics to constrain the parameters of the halo occupation statistics and to unveil the origin of galaxy biasing. The bias function Γgm(rp), where rp is the projected comoving separation, is evaluated using the analytical halo model from which the scale dependence of Γgm(rp), and the origin of the non-linearity and stochasticity in halo occupation models can be inferred. Our observations unveil the physical reason for the non-linearity and stochasticity, further explored using hydrodynamical simulations, with the stochasticity mostly originating from the non-Poissonian behaviour of satellite galaxies in the dark matter haloes and their spatial distribution, which does not follow the spatial distribution of dark matter in the halo. The observed non-linearity is mostly due to the presence of the central galaxies, as was noted from previous theoretical work on the same topic. We also see that overall, more massive galaxies reveal a stronger scale dependence, and out to a larger radius. Our results show that a wealth of information about galaxy bias is hidden in halo occupation models. These models should therefore be used to determine the influence of galaxy bias in cosmological studies.

Optimization-Based Robust Nonlinear Control

DTIC Science & Technology

2006-08-01

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

Beating Heart Motion Accurate Prediction Method Based on Interactive Multiple Model: An Information Fusion Approach

PubMed Central

Xie, Weihong; Yu, Yang

2017-01-01

Robot-assisted motion compensated beating heart surgery has the advantage over the conventional Coronary Artery Bypass Graft (CABG) in terms of reduced trauma to the surrounding structures that leads to shortened recovery time. The severe nonlinear and diverse nature of irregular heart rhythm causes enormous difficulty for the robot to realize the clinic requirements, especially under arrhythmias. In this paper, we propose a fusion prediction framework based on Interactive Multiple Model (IMM) estimator, allowing each model to cover a distinguishing feature of the heart motion in underlying dynamics. We find that, at normal state, the nonlinearity of the heart motion with slow time-variant changing dominates the beating process. When an arrhythmia occurs, the irregularity mode, the fast uncertainties with random patterns become the leading factor of the heart motion. We deal with prediction problem in the case of arrhythmias by estimating the state with two behavior modes which can adaptively “switch” from one to the other. Also, we employed the signal quality index to adaptively determine the switch transition probability in the framework of IMM. We conduct comparative experiments to evaluate the proposed approach with four distinguished datasets. The test results indicate that the new proposed approach reduces prediction errors significantly. PMID:29124062

Beating Heart Motion Accurate Prediction Method Based on Interactive Multiple Model: An Information Fusion Approach.

PubMed

Liang, Fan; Xie, Weihong; Yu, Yang

2017-01-01

Robot-assisted motion compensated beating heart surgery has the advantage over the conventional Coronary Artery Bypass Graft (CABG) in terms of reduced trauma to the surrounding structures that leads to shortened recovery time. The severe nonlinear and diverse nature of irregular heart rhythm causes enormous difficulty for the robot to realize the clinic requirements, especially under arrhythmias. In this paper, we propose a fusion prediction framework based on Interactive Multiple Model (IMM) estimator, allowing each model to cover a distinguishing feature of the heart motion in underlying dynamics. We find that, at normal state, the nonlinearity of the heart motion with slow time-variant changing dominates the beating process. When an arrhythmia occurs, the irregularity mode, the fast uncertainties with random patterns become the leading factor of the heart motion. We deal with prediction problem in the case of arrhythmias by estimating the state with two behavior modes which can adaptively "switch" from one to the other. Also, we employed the signal quality index to adaptively determine the switch transition probability in the framework of IMM. We conduct comparative experiments to evaluate the proposed approach with four distinguished datasets. The test results indicate that the new proposed approach reduces prediction errors significantly.

A 1.26 μW Cytomimetic IC Emulating Complex Nonlinear Mammalian Cell Cycle Dynamics: Synthesis, Simulation and Proof-of-Concept Measured Results.

PubMed

Houssein, Alexandros; Papadimitriou, Konstantinos I; Drakakis, Emmanuel M

2015-08-01

Cytomimetic circuits represent a novel, ultra low-power, continuous-time, continuous-value class of circuits, capable of mapping on silicon cellular and molecular dynamics modelled by means of nonlinear ordinary differential equations (ODEs). Such monolithic circuits are in principle able to emulate on chip, single or multiple cell operations in a highly parallel fashion. Cytomimetic topologies can be synthesized by adopting the Nonlinear Bernoulli Cell Formalism (NBCF), a mathematical framework that exploits the striking similarities between the equations describing weakly-inverted Metal-Oxide Semiconductor (MOS) devices and coupled nonlinear ODEs, typically appearing in models of naturally encountered biochemical systems. The NBCF maps biological state variables onto strictly positive subthreshold MOS circuit currents. This paper presents the synthesis, the simulation and proof-of-concept chip results corresponding to the emulation of a complex cellular network mechanism, the skeleton model for the network of Cyclin-dependent Kinases (CdKs) driving the mammalian cell cycle. This five variable nonlinear biological model, when appropriate model parameter values are assigned, can exhibit multiple oscillatory behaviors, varying from simple periodic oscillations, to complex oscillations such as quasi-periodicity and chaos. The validity of our approach is verified by simulated results with realistic process parameters from the commercially available AMS 0.35 μm technology and by chip measurements. The fabricated chip occupies an area of 2.27 mm2 and consumes a power of 1.26 μW from a power supply of 3 V. The presented cytomimetic topology follows closely the behavior of its biological counterpart, exhibiting similar time-dependent solutions of the Cdk complexes, the transcription factors and the proteins.

A 2D nonlinear multiring model for blood flow in large elastic arteries

NASA Astrophysics Data System (ADS)

Ghigo, Arthur R.; Fullana, Jose-Maria; Lagrée, Pierre-Yves

2017-12-01

In this paper, we propose a two-dimensional nonlinear ;multiring; model to compute blood flow in axisymmetric elastic arteries. This model is designed to overcome the numerical difficulties of three-dimensional fluid-structure interaction simulations of blood flow without using the over-simplifications necessary to obtain one-dimensional blood flow models. This multiring model is derived by integrating over concentric rings of fluid the simplified long-wave Navier-Stokes equations coupled to an elastic model of the arterial wall. The resulting system of balance laws provides a unified framework in which both the motion of the fluid and the displacement of the wall are dealt with simultaneously. The mathematical structure of the multiring model allows us to use a finite volume method that guarantees the conservation of mass and the positivity of the numerical solution and can deal with nonlinear flows and large deformations of the arterial wall. We show that the finite volume numerical solution of the multiring model provides at a reasonable computational cost an asymptotically valid description of blood flow velocity profiles and other averaged quantities (wall shear stress, flow rate, ...) in large elastic and quasi-rigid arteries. In particular, we validate the multiring model against well-known solutions such as the Womersley or the Poiseuille solutions as well as against steady boundary layer solutions in quasi-rigid constricted and expanded tubes.

Emergent geometries and nonlinear-wave dynamics in photon fluids.

PubMed

Marino, F; Maitland, C; Vocke, D; Ortolan, A; Faccio, D

2016-03-22

Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation of a shock. This phenomenon can be associated to a curvature singularity of the emergent metric. Our analysis offers an alternative insight into the problem of shock formation and provides a demonstration of an analogue gravity model that goes beyond the kinematic level.

Emergent geometries and nonlinear-wave dynamics in photon fluids

NASA Astrophysics Data System (ADS)

Marino, F.; Maitland, C.; Vocke, D.; Ortolan, A.; Faccio, D.

2016-03-01

Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation of a shock. This phenomenon can be associated to a curvature singularity of the emergent metric. Our analysis offers an alternative insight into the problem of shock formation and provides a demonstration of an analogue gravity model that goes beyond the kinematic level.

Undular bore theory for the Gardner equation

NASA Astrophysics Data System (ADS)

Kamchatnov, A. M.; Kuo, Y.-H.; Lin, T.-C.; Horng, T.-L.; Gou, S.-C.; Clift, R.; El, G. A.; Grimshaw, R. H. J.

2012-09-01

We develop modulation theory for undular bores (dispersive shock waves) in the framework of the Gardner, or extended Korteweg-de Vries (KdV), equation, which is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation, when effects of higher order nonlinearity become important. Using a reduced version of the finite-gap integration method we derive the Gardner-Whitham modulation system in a Riemann invariant form and show that it can be mapped onto the well-known modulation system for the Korteweg-de Vries equation. The transformation between the two counterpart modulation systems is, however, not invertible. As a result, the study of the resolution of an initial discontinuity for the Gardner equation reveals a rich phenomenology of solutions which, along with the KdV-type simple undular bores, include nonlinear trigonometric bores, solibores, rarefaction waves, and composite solutions representing various combinations of the above structures. We construct full parametric maps of such solutions for both signs of the cubic nonlinear term in the Gardner equation. Our classification is supported by numerical simulations.

Distributed adaptive neural network control for a class of heterogeneous nonlinear multi-agent systems subject to actuation failures

NASA Astrophysics Data System (ADS)

Cui, Bing; Zhao, Chunhui; Ma, Tiedong; Feng, Chi

2017-02-01

In this paper, the cooperative adaptive consensus tracking problem for heterogeneous nonlinear multi-agent systems on directed graph is addressed. Each follower is modelled as a general nonlinear system with the unknown and nonidentical nonlinear dynamics, disturbances and actuator failures. Cooperative fault tolerant neural network tracking controllers with online adaptive learning features are proposed to guarantee that all agents synchronise to the trajectory of one leader with bounded adjustable synchronisation errors. With the help of linear quadratic regulator-based optimal design, a graph-dependent Lyapunov proof provides error bounds that depend on the graph topology, one virtual matrix and some design parameters. Of particular interest is that if the control gain is selected appropriately, the proposed control scheme can be implemented in a unified framework no matter whether there are faults or not. Furthermore, the fault detection and isolation are not needed to implement. Finally, a simulation is given to verify the effectiveness of the proposed method.

Unifying different interpretations of the nonlinear response in glass-forming liquids

NASA Astrophysics Data System (ADS)

Gadige, P.; Albert, S.; Michl, M.; Bauer, Th.; Lunkenheimer, P.; Loidl, A.; Tourbot, R.; Wiertel-Gasquet, C.; Biroli, G.; Bouchaud, J.-P.; Ladieu, F.

2017-09-01

This work aims at reconsidering several interpretations coexisting in the recent literature concerning nonlinear susceptibilities in supercooled liquids. We present experimental results on glycerol and propylene carbonate, showing that the three independent cubic susceptibilities have very similar frequency and temperature dependences, for both their amplitudes and phases. This strongly suggests a unique physical mechanism responsible for the growth of these nonlinear susceptibilities. We show that the framework proposed by two of us [J.-P. Bouchaud and G. Biroli, Phys. Rev. B 72, 064204 (2005), 10.1103/PhysRevB.72.064204], where the growth of nonlinear susceptibilities is intimately related to the growth of glassy domains, accounts for all the salient experimental features. We then review several complementary and/or alternative models and show that the notion of cooperatively rearranging glassy domains is a key (implicit or explicit) ingredient to all of them. This paves the way for future experiments, which should deepen our understanding of glasses.

FEAST fundamental framework for electronic structure calculations: Reformulation and solution of the muffin-tin problem

NASA Astrophysics Data System (ADS)

Levin, Alan R.; Zhang, Deyin; Polizzi, Eric

2012-11-01

In a recent article Polizzi (2009) [15], the FEAST algorithm has been presented as a general purpose eigenvalue solver which is ideally suited for addressing the numerical challenges in electronic structure calculations. Here, FEAST is presented beyond the “black-box” solver as a fundamental modeling framework which can naturally address the original numerical complexity of the electronic structure problem as formulated by Slater in 1937 [3]. The non-linear eigenvalue problem arising from the muffin-tin decomposition of the real-space domain is first derived and then reformulated to be solved exactly within the FEAST framework. This new framework is presented as a fundamental and practical solution for performing both accurate and scalable electronic structure calculations, bypassing the various issues of using traditional approaches such as linearization and pseudopotential techniques. A finite element implementation of this FEAST framework along with simulation results for various molecular systems is also presented and discussed.

Constructing an Efficient Self-Tuning Aircraft Engine Model for Control and Health Management Applications

NASA Technical Reports Server (NTRS)

Armstrong, Jeffrey B.; Simon, Donald L.

2012-01-01

Self-tuning aircraft engine models can be applied for control and health management applications. The self-tuning feature of these models minimizes the mismatch between any given engine and the underlying engineering model describing an engine family. This paper provides details of the construction of a self-tuning engine model centered on a piecewise linear Kalman filter design. Starting from a nonlinear transient aerothermal model, a piecewise linear representation is first extracted. The linearization procedure creates a database of trim vectors and state-space matrices that are subsequently scheduled for interpolation based on engine operating point. A series of steady-state Kalman gains can next be constructed from a reduced-order form of the piecewise linear model. Reduction of the piecewise linear model to an observable dimension with respect to available sensed engine measurements can be achieved using either a subset or an optimal linear combination of "health" parameters, which describe engine performance. The resulting piecewise linear Kalman filter is then implemented for faster-than-real-time processing of sensed engine measurements, generating outputs appropriate for trending engine performance, estimating both measured and unmeasured parameters for control purposes, and performing on-board gas-path fault diagnostics. Computational efficiency is achieved by designing multidimensional interpolation algorithms that exploit the shared scheduling of multiple trim vectors and system matrices. An example application illustrates the accuracy of a self-tuning piecewise linear Kalman filter model when applied to a nonlinear turbofan engine simulation. Additional discussions focus on the issue of transient response accuracy and the advantages of a piecewise linear Kalman filter in the context of validation and verification. The techniques described provide a framework for constructing efficient self-tuning aircraft engine models from complex nonlinear simulations.Self-tuning aircraft engine models can be applied for control and health management applications. The self-tuning feature of these models minimizes the mismatch between any given engine and the underlying engineering model describing an engine family. This paper provides details of the construction of a self-tuning engine model centered on a piecewise linear Kalman filter design. Starting from a nonlinear transient aerothermal model, a piecewise linear representation is first extracted. The linearization procedure creates a database of trim vectors and state-space matrices that are subsequently scheduled for interpolation based on engine operating point. A series of steady-state Kalman gains can next be constructed from a reduced-order form of the piecewise linear model. Reduction of the piecewise linear model to an observable dimension with respect to available sensed engine measurements can be achieved using either a subset or an optimal linear combination of "health" parameters, which describe engine performance. The resulting piecewise linear Kalman filter is then implemented for faster-than-real-time processing of sensed engine measurements, generating outputs appropriate for trending engine performance, estimating both measured and unmeasured parameters for control purposes, and performing on-board gas-path fault diagnostics. Computational efficiency is achieved by designing multidimensional interpolation algorithms that exploit the shared scheduling of multiple trim vectors and system matrices. An example application illustrates the accuracy of a self-tuning piecewise linear Kalman filter model when applied to a nonlinear turbofan engine simulation. Additional discussions focus on the issue of transient response accuracy and the advantages of a piecewise linear Kalman filter in the context of validation and verification. The techniques described provide a framework for constructing efficient self-tuning aircraft engine models from complex nonlinear simulatns.

Design and architecture of the Mars relay network planning and analysis framework

NASA Technical Reports Server (NTRS)

Cheung, K. M.; Lee, C. H.

2002-01-01

In this paper we describe the design and architecture of the Mars Network planning and analysis framework that supports generation and validation of efficient planning and scheduling strategy. The goals are to minimize the transmitting time, minimize the delaying time, and/or maximize the network throughputs. The proposed framework would require (1) a client-server architecture to support interactive, batch, WEB, and distributed analysis and planning applications for the relay network analysis scheme, (2) a high-fidelity modeling and simulation environment that expresses link capabilities between spacecraft to spacecraft and spacecraft to Earth stations as time-varying resources, and spacecraft activities, link priority, Solar System dynamic events, the laws of orbital mechanics, and other limiting factors as spacecraft power and thermal constraints, (3) an optimization methodology that casts the resource and constraint models into a standard linear and nonlinear constrained optimization problem that lends itself to commercial off-the-shelf (COTS)planning and scheduling algorithms.

Computational Modeling of Neurotransmitter Release Evoked by Electrical Stimulation: Nonlinear Approaches to Predicting Stimulation-Evoked Dopamine Release.

PubMed

Trevathan, James K; Yousefi, Ali; Park, Hyung Ook; Bartoletta, John J; Ludwig, Kip A; Lee, Kendall H; Lujan, J Luis

2017-02-15

Neurochemical changes evoked by electrical stimulation of the nervous system have been linked to both therapeutic and undesired effects of neuromodulation therapies used to treat obsessive-compulsive disorder, depression, epilepsy, Parkinson's disease, stroke, hypertension, tinnitus, and many other indications. In fact, interest in better understanding the role of neurochemical signaling in neuromodulation therapies has been a focus of recent government- and industry-sponsored programs whose ultimate goal is to usher in an era of personalized medicine by creating neuromodulation therapies that respond to real-time changes in patient status. A key element to achieving these precision therapeutic interventions is the development of mathematical modeling approaches capable of describing the nonlinear transfer function between neuromodulation parameters and evoked neurochemical changes. Here, we propose two computational modeling frameworks, based on artificial neural networks (ANNs) and Volterra kernels, that can characterize the input/output transfer functions of stimulation-evoked neurochemical release. We evaluate the ability of these modeling frameworks to characterize subject-specific neurochemical kinetics by accurately describing stimulation-evoked dopamine release across rodent (R 2 = 0.83 Volterra kernel, R 2 = 0.86 ANN), swine (R 2 = 0.90 Volterra kernel, R 2 = 0.93 ANN), and non-human primate (R 2 = 0.98 Volterra kernel, R 2 = 0.96 ANN) models of brain stimulation. Ultimately, these models will not only improve understanding of neurochemical signaling in healthy and diseased brains but also facilitate the development of neuromodulation strategies capable of controlling neurochemical release via closed-loop strategies.

An efficient fully-implicit multislope MUSCL method for multiphase flow with gravity in discrete fractured media

NASA Astrophysics Data System (ADS)

Jiang, Jiamin; Younis, Rami M.

2017-06-01

The first-order methods commonly employed in reservoir simulation for computing the convective fluxes introduce excessive numerical diffusion leading to severe smoothing of displacement fronts. We present a fully-implicit cell-centered finite-volume (CCFV) framework that can achieve second-order spatial accuracy on smooth solutions, while at the same time maintain robustness and nonlinear convergence performance. A novel multislope MUSCL method is proposed to construct the required values at edge centroids in a straightforward and effective way by taking advantage of the triangular mesh geometry. In contrast to the monoslope methods in which a unique limited gradient is used, the multislope concept constructs specific scalar slopes for the interpolations on each edge of a given element. Through the edge centroids, the numerical diffusion caused by mesh skewness is reduced, and optimal second order accuracy can be achieved. Moreover, an improved smooth flux-limiter is introduced to ensure monotonicity on non-uniform meshes. The flux-limiter provides high accuracy without degrading nonlinear convergence performance. The CCFV framework is adapted to accommodate a lower-dimensional discrete fracture-matrix (DFM) model. Several numerical tests with discrete fractured system are carried out to demonstrate the efficiency and robustness of the numerical model.

Enhancing Data Assimilation by Evolutionary Particle Filter and Markov Chain Monte Carlo

NASA Astrophysics Data System (ADS)

Moradkhani, H.; Abbaszadeh, P.; Yan, H.

2016-12-01

Particle Filters (PFs) have received increasing attention by the researchers from different disciplines in hydro-geosciences as an effective method to improve model predictions in nonlinear and non-Gaussian dynamical systems. The implication of dual state and parameter estimation by means of data assimilation in hydrology and geoscience has evolved since 2005 from SIR-PF to PF-MCMC and now to the most effective and robust framework through evolutionary PF approach based on Genetic Algorithm (GA) and Markov Chain Monte Carlo (MCMC), the so-called EPF-MCMC. In this framework, the posterior distribution undergoes an evolutionary process to update an ensemble of prior states that more closely resemble realistic posterior probability distribution. The premise of this approach is that the particles move to optimal position using the GA optimization coupled with MCMC increasing the number of effective particles, hence the particle degeneracy is avoided while the particle diversity is improved. The proposed algorithm is applied on a conceptual and highly nonlinear hydrologic model and the effectiveness, robustness and reliability of the method in jointly estimating the states and parameters and also reducing the uncertainty is demonstrated for few river basins across the United States.

A Unified Point Process Probabilistic Framework to Assess Heartbeat Dynamics and Autonomic Cardiovascular Control

PubMed Central

Chen, Zhe; Purdon, Patrick L.; Brown, Emery N.; Barbieri, Riccardo

2012-01-01

In recent years, time-varying inhomogeneous point process models have been introduced for assessment of instantaneous heartbeat dynamics as well as specific cardiovascular control mechanisms and hemodynamics. Assessment of the model’s statistics is established through the Wiener-Volterra theory and a multivariate autoregressive (AR) structure. A variety of instantaneous cardiovascular metrics, such as heart rate (HR), heart rate variability (HRV), respiratory sinus arrhythmia (RSA), and baroreceptor-cardiac reflex (baroreflex) sensitivity (BRS), are derived within a parametric framework and instantaneously updated with adaptive and local maximum likelihood estimation algorithms. Inclusion of second-order non-linearities, with subsequent bispectral quantification in the frequency domain, further allows for definition of instantaneous metrics of non-linearity. We here present a comprehensive review of the devised methods as applied to experimental recordings from healthy subjects during propofol anesthesia. Collective results reveal interesting dynamic trends across the different pharmacological interventions operated within each anesthesia session, confirming the ability of the algorithm to track important changes in cardiorespiratory elicited interactions, and pointing at our mathematical approach as a promising monitoring tool for an accurate, non-invasive assessment in clinical practice. We also discuss the limitations and other alternative modeling strategies of our point process approach. PMID:22375120

A Framework for Performing Multiscale Stochastic Progressive Failure Analysis of Composite Structures

NASA Technical Reports Server (NTRS)

Bednarcyk, Brett A.; Arnold, Steven M.

2006-01-01

A framework is presented that enables coupled multiscale analysis of composite structures. The recently developed, free, Finite Element Analysis - Micromechanics Analysis Code (FEAMAC) software couples the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) with ABAQUS to perform micromechanics based FEA such that the nonlinear composite material response at each integration point is modeled at each increment by MAC/GMC. As a result, the stochastic nature of fiber breakage in composites can be simulated through incorporation of an appropriate damage and failure model that operates within MAC/GMC on the level of the fiber. Results are presented for the progressive failure analysis of a titanium matrix composite tensile specimen that illustrate the power and utility of the framework and address the techniques needed to model the statistical nature of the problem properly. In particular, it is shown that incorporating fiber strength randomness on multiple scales improves the quality of the simulation by enabling failure at locations other than those associated with structural level stress risers.

A Framework for Performing Multiscale Stochastic Progressive Failure Analysis of Composite Structures

NASA Technical Reports Server (NTRS)

Bednarcyk, Brett A.; Arnold, Steven M.

2007-01-01

A framework is presented that enables coupled multiscale analysis of composite structures. The recently developed, free, Finite Element Analysis-Micromechanics Analysis Code (FEAMAC) software couples the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) with ABAQUS to perform micromechanics based FEA such that the nonlinear composite material response at each integration point is modeled at each increment by MAC/GMC. As a result, the stochastic nature of fiber breakage in composites can be simulated through incorporation of an appropriate damage and failure model that operates within MAC/GMC on the level of the fiber. Results are presented for the progressive failure analysis of a titanium matrix composite tensile specimen that illustrate the power and utility of the framework and address the techniques needed to model the statistical nature of the problem properly. In particular, it is shown that incorporating fiber strength randomness on multiple scales improves the quality of the simulation by enabling failure at locations other than those associated with structural level stress risers.

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

NASA Astrophysics Data System (ADS)

Khawaja, Taimoor Saleem

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

A Workflow for Global Sensitivity Analysis of PBPK Models

PubMed Central

McNally, Kevin; Cotton, Richard; Loizou, George D.

2011-01-01

Physiologically based pharmacokinetic (PBPK) models have a potentially significant role in the development of a reliable predictive toxicity testing strategy. The structure of PBPK models are ideal frameworks into which disparate in vitro and in vivo data can be integrated and utilized to translate information generated, using alternative to animal measures of toxicity and human biological monitoring data, into plausible corresponding exposures. However, these models invariably include the description of well known non-linear biological processes such as, enzyme saturation and interactions between parameters such as, organ mass and body mass. Therefore, an appropriate sensitivity analysis (SA) technique is required which can quantify the influences associated with individual parameters, interactions between parameters and any non-linear processes. In this report we have defined the elements of a workflow for SA of PBPK models that is computationally feasible, accounts for interactions between parameters, and can be displayed in the form of a bar chart and cumulative sum line (Lowry plot), which we believe is intuitive and appropriate for toxicologists, risk assessors, and regulators. PMID:21772819

Self-sustaining turbulence in a restricted nonlinear model of plane Couette flow

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

Thomas, Vaughan L.; Gayme, Dennice F.; Lieu, Binh K.

2014-10-15

This paper demonstrates the maintenance of self-sustaining turbulence in a restricted nonlinear (RNL) model of plane Couette flow. The RNL system is derived directly from the Navier-Stokes equations and permits higher resolution studies of the dynamical system associated with the stochastic structural stability theory (S3T) model, which is a second order approximation of the statistical state dynamics of the flow. The RNL model shares the dynamical restrictions of the S3T model but can be easily implemented by reducing a DNS code so that it retains only the RNL dynamics. Comparisons of turbulence arising from DNS and RNL simulations demonstrate thatmore » the RNL system supports self-sustaining turbulence with a mean flow as well as structural and dynamical features that are consistent with DNS. These results demonstrate that the simplified RNL system captures fundamental aspects of fully developed turbulence in wall-bounded shear flows and motivate use of the RNL/S3T framework for further study of wall-turbulence.« less

Design of optimal nonlinear network controllers for Alzheimer's disease.

PubMed

Sanchez-Rodriguez, Lazaro M; Iturria-Medina, Yasser; Baines, Erica A; Mallo, Sabela C; Dousty, Mehdy; Sotero, Roberto C

2018-05-01

Brain stimulation can modulate the activity of neural circuits impaired by Alzheimer's disease (AD), having promising clinical benefit. However, all individuals with the same condition currently receive identical brain stimulation, with limited theoretical basis for this generic approach. In this study, we introduce a control theory framework for obtaining exogenous signals that revert pathological electroencephalographic activity in AD at a minimal energetic cost, while reflecting patients' biological variability. We used anatomical networks obtained from diffusion magnetic resonance images acquired by the Alzheimer's Disease Neuroimaging Initiative (ADNI) as mediators for the interaction between Duffing oscillators. The nonlinear nature of the brain dynamics is preserved, given that we extend the so-called state-dependent Riccati equation control to reflect the stimulation objective in the high-dimensional neural system. By considering nonlinearities in our model, we identified regions for which control inputs fail to correct abnormal activity. There are changes to the way stimulated regions are ranked in terms of the energetic cost of controlling the entire network, from a linear to a nonlinear approach. We also found that limbic system and basal ganglia structures constitute the top target locations for stimulation in AD. Patients with highly integrated anatomical networks-namely, networks having low average shortest path length, high global efficiency-are the most suitable candidates for the propagation of stimuli and consequent success on the control task. Other diseases associated with alterations in brain dynamics and the self-control mechanisms of the brain can be addressed through our framework.

Evaluation of automated decisionmaking methodologies and development of an integrated robotic system simulation. Volume 1: Study results

NASA Technical Reports Server (NTRS)

Lowrie, J. W.; Fermelia, A. J.; Haley, D. C.; Gremban, K. D.; Vanbaalen, J.; Walsh, R. W.

1982-01-01

A variety of artificial intelligence techniques which could be used with regard to NASA space applications and robotics were evaluated. The techniques studied were decision tree manipulators, problem solvers, rule based systems, logic programming languages, representation language languages, and expert systems. The overall structure of a robotic simulation tool was defined and a framework for that tool developed. Nonlinear and linearized dynamics equations were formulated for n link manipulator configurations. A framework for the robotic simulation was established which uses validated manipulator component models connected according to a user defined configuration.

Construction of pore network models for Berea and Fontainebleau sandstones using non-linear programing and optimization techniques

NASA Astrophysics Data System (ADS)

Sharqawy, Mostafa H.

2016-12-01

Pore network models (PNM) of Berea and Fontainebleau sandstones were constructed using nonlinear programming (NLP) and optimization methods. The constructed PNMs are considered as a digital representation of the rock samples which were based on matching the macroscopic properties of the porous media and used to conduct fluid transport simulations including single and two-phase flow. The PNMs consisted of cubic networks of randomly distributed pores and throats sizes and with various connectivity levels. The networks were optimized such that the upper and lower bounds of the pore sizes are determined using the capillary tube bundle model and the Nelder-Mead method instead of guessing them, which reduces the optimization computational time significantly. An open-source PNM framework was employed to conduct transport and percolation simulations such as invasion percolation and Darcian flow. The PNM model was subsequently used to compute the macroscopic properties; porosity, absolute permeability, specific surface area, breakthrough capillary pressure, and primary drainage curve. The pore networks were optimized to allow for the simulation results of the macroscopic properties to be in excellent agreement with the experimental measurements. This study demonstrates that non-linear programming and optimization methods provide a promising method for pore network modeling when computed tomography imaging may not be readily available.

Nonlinear modeling, strength-based design, and testing of flexible piezoelectric energy harvesters under large dynamic loads for rotorcraft applications

NASA Astrophysics Data System (ADS)

Leadenham, Stephen; Erturk, Alper

2014-04-01

There has been growing interest in enabling wireless health and usage monitoring for rotorcraft applications, such as helicopter rotor systems. Large dynamic loads and acceleration fluctuations available in these environments make the implementation of vibration-based piezoelectric energy harvesters a very promising choice. However, such extreme loads transmitted to the harvester can also be detrimental to piezoelectric laminates and overall system reliability. Particularly flexible resonant cantilever configurations tuned to match the dominant excitation frequency can be subject to very large deformations and failure of brittle piezoelectric laminates due to excessive bending stresses at the root of the harvester. Design of resonant piezoelectric energy harvesters for use in these environments require nonlinear electroelastic dynamic modeling and strength-based analysis to maximize the power output while ensuring that the harvester is still functional. This paper presents a mathematical framework to design and analyze the dynamics of nonlinear flexible piezoelectric energy harvesters under large base acceleration levels. A strength-based limit is imposed to design the piezoelectric energy harvester with a proof mass while accounting for material, geometric, and dissipative nonlinearities, with a focus on two demonstrative case studies having the same linear fundamental resonance frequency but different overhang length and proof mass values. Experiments are conducted at different excitation levels for validation of the nonlinear design approach proposed in this work. The case studies in this work reveal that harvesters exhibiting similar behavior and power generation performance at low excitation levels (e.g. less than 0.1g) can have totally different strength-imposed performance limitations under high excitations (e.g. above 1g). Nonlinear modeling and strength-based design is necessary for such excitation levels especially when using resonant cantilevers with no geometric constraint.

Modelling vortex-induced fluid-structure interaction.

PubMed

Benaroya, Haym; Gabbai, Rene D

2008-04-13

The principal goal of this research is developing physics-based, reduced-order, analytical models of nonlinear fluid-structure interactions associated with offshore structures. Our primary focus is to generalize the Hamilton's variational framework so that systems of flow-oscillator equations can be derived from first principles. This is an extension of earlier work that led to a single energy equation describing the fluid-structure interaction. It is demonstrated here that flow-oscillator models are a subclass of the general, physical-based framework. A flow-oscillator model is a reduced-order mechanical model, generally comprising two mechanical oscillators, one modelling the structural oscillation and the other a nonlinear oscillator representing the fluid behaviour coupled to the structural motion.Reduced-order analytical model development continues to be carried out using a Hamilton's principle-based variational approach. This provides flexibility in the long run for generalizing the modelling paradigm to complex, three-dimensional problems with multiple degrees of freedom, although such extension is very difficult. As both experimental and analytical capabilities advance, the critical research path to developing and implementing fluid-structure interaction models entails-formulating generalized equations of motion, as a superset of the flow-oscillator models; and-developing experimentally derived, semi-analytical functions to describe key terms in the governing equations of motion. The developed variational approach yields a system of governing equations. This will allow modelling of multiple d.f. systems. The extensions derived generalize the Hamilton's variational formulation for such problems. The Navier-Stokes equations are derived and coupled to the structural oscillator. This general model has been shown to be a superset of the flow-oscillator model. Based on different assumptions, one can derive a variety of flow-oscillator models.

Multiobjective optimization of temporal processes.

PubMed

Song, Zhe; Kusiak, Andrew

2010-06-01

This paper presents a dynamic predictive-optimization framework of a nonlinear temporal process. Data-mining (DM) and evolutionary strategy algorithms are integrated in the framework for solving the optimization model. DM algorithms learn dynamic equations from the process data. An evolutionary strategy algorithm is then applied to solve the optimization problem guided by the knowledge extracted by the DM algorithm. The concept presented in this paper is illustrated with the data from a power plant, where the goal is to maximize the boiler efficiency and minimize the limestone consumption. This multiobjective optimization problem can be either transformed into a single-objective optimization problem through preference aggregation approaches or into a Pareto-optimal optimization problem. The computational results have shown the effectiveness of the proposed optimization framework.

Fully Associative, Nonisothermal, Potential-Based Unified Viscoplastic Model for Titanium-Based Matrices

NASA Technical Reports Server (NTRS)

2005-01-01

A number of titanium matrix composite (TMC) systems are currently being investigated for high-temperature air frame and propulsion system applications. As a result, numerous computational methodologies for predicting both deformation and life for this class of materials are under development. An integral part of these methodologies is an accurate and computationally efficient constitutive model for the metallic matrix constituent. Furthermore, because these systems are designed to operate at elevated temperatures, the required constitutive models must account for both time-dependent and time-independent deformations. To accomplish this, the NASA Lewis Research Center is employing a recently developed, complete, potential-based framework. This framework, which utilizes internal state variables, was put forth for the derivation of reversible and irreversible constitutive equations. The framework, and consequently the resulting constitutive model, is termed complete because the existence of the total (integrated) form of the Gibbs complementary free energy and complementary dissipation potentials are assumed a priori. The specific forms selected here for both the Gibbs and complementary dissipation potentials result in a fully associative, multiaxial, nonisothermal, unified viscoplastic model with nonlinear kinematic hardening. This model constitutes one of many models in the Generalized Viscoplasticity with Potential Structure (GVIPS) class of inelastic constitutive equations.

A high-fidelity airbus benchmark for system fault detection and isolation and flight control law clearance

NASA Astrophysics Data System (ADS)

Goupil, Ph.; Puyou, G.

2013-12-01

This paper presents a high-fidelity generic twin engine civil aircraft model developed by Airbus for advanced flight control system research. The main features of this benchmark are described to make the reader aware of the model complexity and representativeness. It is a complete representation including the nonlinear rigid-body aircraft model with a full set of control surfaces, actuator models, sensor models, flight control laws (FCL), and pilot inputs. Two applications of this benchmark in the framework of European projects are presented: FCL clearance using optimization and advanced fault detection and diagnosis (FDD).

Auditory models for speech analysis

NASA Astrophysics Data System (ADS)

Maybury, Mark T.

This paper reviews the psychophysical basis for auditory models and discusses their application to automatic speech recognition. First an overview of the human auditory system is presented, followed by a review of current knowledge gleaned from neurological and psychoacoustic experimentation. Next, a general framework describes established peripheral auditory models which are based on well-understood properties of the peripheral auditory system. This is followed by a discussion of current enhancements to that models to include nonlinearities and synchrony information as well as other higher auditory functions. Finally, the initial performance of auditory models in the task of speech recognition is examined and additional applications are mentioned.

Sparsity enabled cluster reduced-order models for control

NASA Astrophysics Data System (ADS)

Kaiser, Eurika; Morzyński, Marek; Daviller, Guillaume; Kutz, J. Nathan; Brunton, Bingni W.; Brunton, Steven L.

2018-01-01

Characterizing and controlling nonlinear, multi-scale phenomena are central goals in science and engineering. Cluster-based reduced-order modeling (CROM) was introduced to exploit the underlying low-dimensional dynamics of complex systems. CROM builds a data-driven discretization of the Perron-Frobenius operator, resulting in a probabilistic model for ensembles of trajectories. A key advantage of CROM is that it embeds nonlinear dynamics in a linear framework, which enables the application of standard linear techniques to the nonlinear system. CROM is typically computed on high-dimensional data; however, access to and computations on this full-state data limit the online implementation of CROM for prediction and control. Here, we address this key challenge by identifying a small subset of critical measurements to learn an efficient CROM, referred to as sparsity-enabled CROM. In particular, we leverage compressive measurements to faithfully embed the cluster geometry and preserve the probabilistic dynamics. Further, we show how to identify fewer optimized sensor locations tailored to a specific problem that outperform random measurements. Both of these sparsity-enabled sensing strategies significantly reduce the burden of data acquisition and processing for low-latency in-time estimation and control. We illustrate this unsupervised learning approach on three different high-dimensional nonlinear dynamical systems from fluids with increasing complexity, with one application in flow control. Sparsity-enabled CROM is a critical facilitator for real-time implementation on high-dimensional systems where full-state information may be inaccessible.

Nonlinearity Domination in Hassellmann Equation as a Reason for Alternative Framework of its Numerical Simulation

DTIC Science & Technology

2014-09-30

nonlinear Schrodinger equation. It is well known that dark solitons are exact solutions of such equation. In the present paper it has been shown that gray...Reason for Alternative Framework of its Numerical Simulation Vladimir Zakharov, Andrei Pushkarev Waves and Solitons LLC 1719 W. Marlette Ave...situation; study of the implications of modulational instability on solitons , rogue waves and air-surface interaction. APPROACH Numerical methods

High-order accurate finite-volume formulations for the pressure gradient force in layered ocean models

NASA Astrophysics Data System (ADS)

Engwirda, Darren; Kelley, Maxwell; Marshall, John

2017-08-01

Discretisation of the horizontal pressure gradient force in layered ocean models is a challenging task, with non-trivial interactions between the thermodynamics of the fluid and the geometry of the layers often leading to numerical difficulties. We present two new finite-volume schemes for the pressure gradient operator designed to address these issues. In each case, the horizontal acceleration is computed as an integration of the contact pressure force that acts along the perimeter of an associated momentum control-volume. A pair of new schemes are developed by exploring different control-volume geometries. Non-linearities in the underlying equation-of-state definitions and thermodynamic profiles are treated using a high-order accurate numerical integration framework, designed to preserve hydrostatic balance in a non-linear manner. Numerical experiments show that the new methods achieve high levels of consistency, maintaining hydrostatic and thermobaric equilibrium in the presence of strongly-sloping layer geometries, non-linear equations-of-state and non-uniform vertical stratification profiles. These results suggest that the new pressure gradient formulations may be appropriate for general circulation models that employ hybrid vertical coordinates and/or terrain-following representations.

Governing Laws of Complex System Predictability under Co-evolving Uncertainty Sources: Theory and Nonlinear Geophysical Applications

NASA Astrophysics Data System (ADS)

Perdigão, R. A. P.

2017-12-01

Predictability assessments are traditionally made on a case-by-case basis, often by running the particular model of interest with randomly perturbed initial/boundary conditions and parameters, producing computationally expensive ensembles. These approaches provide a lumped statistical view of uncertainty evolution, without eliciting the fundamental processes and interactions at play in the uncertainty dynamics. In order to address these limitations, we introduce a systematic dynamical framework for predictability assessment and forecast, by analytically deriving governing equations of predictability in terms of the fundamental architecture of dynamical systems, independent of any particular problem under consideration. The framework further relates multiple uncertainty sources along with their coevolutionary interplay, enabling a comprehensive and explicit treatment of uncertainty dynamics along time, without requiring the actual model to be run. In doing so, computational resources are freed and a quick and effective a-priori systematic dynamic evaluation is made of predictability evolution and its challenges, including aspects in the model architecture and intervening variables that may require optimization ahead of initiating any model runs. It further brings out universal dynamic features in the error dynamics elusive to any case specific treatment, ultimately shedding fundamental light on the challenging issue of predictability. The formulated approach, framed with broad mathematical physics generality in mind, is then implemented in dynamic models of nonlinear geophysical systems with various degrees of complexity, in order to evaluate their limitations and provide informed assistance on how to optimize their design and improve their predictability in fundamental dynamical terms.

ADM Analysis of gravity models within the framework of bimetric variational formalism

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

Golovnev, Alexey; Karčiauskas, Mindaugas; Nyrhinen, Hannu J., E-mail: agolovnev@yandex.ru, E-mail: mindaugas.karciauskas@helsinki.fi, E-mail: hannu.nyrhinen@helsinki.fi

2015-05-01

Bimetric variational formalism was recently employed to construct novel bimetric gravity models. In these models an affine connection is generated by an additional tensor field which is independent of the physical metric. In this work we demonstrate how the ADM decomposition can be applied to study such models and provide some technical intermediate details. Using ADM decomposition we are able to prove that a linear model is unstable as has previously been indicated by perturbative analysis. Moreover, we show that it is also very difficult if not impossible to construct a non-linear model which is ghost-free within the framework ofmore » bimetric variational formalism. However, we demonstrate that viable models are possible along similar lines of thought. To this end, we consider a set up in which the affine connection is a variation of the Levi-Civita one. As a proof of principle we construct a gravity model with a massless scalar field obtained this way.« less

Selection vector filter framework

NASA Astrophysics Data System (ADS)

Lukac, Rastislav; Plataniotis, Konstantinos N.; Smolka, Bogdan; Venetsanopoulos, Anastasios N.

2003-10-01

We provide a unified framework of nonlinear vector techniques outputting the lowest ranked vector. The proposed framework constitutes a generalized filter class for multichannel signal processing. A new class of nonlinear selection filters are based on the robust order-statistic theory and the minimization of the weighted distance function to other input samples. The proposed method can be designed to perform a variety of filtering operations including previously developed filtering techniques such as vector median, basic vector directional filter, directional distance filter, weighted vector median filters and weighted directional filters. A wide range of filtering operations is guaranteed by the filter structure with two independent weight vectors for angular and distance domains of the vector space. In order to adapt the filter parameters to varying signal and noise statistics, we provide also the generalized optimization algorithms taking the advantage of the weighted median filters and the relationship between standard median filter and vector median filter. Thus, we can deal with both statistical and deterministic aspects of the filter design process. It will be shown that the proposed method holds the required properties such as the capability of modelling the underlying system in the application at hand, the robustness with respect to errors in the model of underlying system, the availability of the training procedure and finally, the simplicity of filter representation, analysis, design and implementation. Simulation studies also indicate that the new filters are computationally attractive and have excellent performance in environments corrupted by bit errors and impulsive noise.

Data-driven Analysis and Prediction of Arctic Sea Ice

NASA Astrophysics Data System (ADS)

Kondrashov, D. A.; Chekroun, M.; Ghil, M.; Yuan, X.; Ting, M.

2015-12-01

We present results of data-driven predictive analyses of sea ice over the main Arctic regions. Our approach relies on the Multilayer Stochastic Modeling (MSM) framework of Kondrashov, Chekroun and Ghil [Physica D, 2015] and it leads to prognostic models of sea ice concentration (SIC) anomalies on seasonal time scales.This approach is applied to monthly time series of leading principal components from the multivariate Empirical Orthogonal Function decomposition of SIC and selected climate variables over the Arctic. We evaluate the predictive skill of MSM models by performing retrospective forecasts with "no-look ahead" forup to 6-months ahead. It will be shown in particular that the memory effects included in our non-Markovian linear MSM models improve predictions of large-amplitude SIC anomalies in certain Arctic regions. Furtherimprovements allowed by the MSM framework will adopt a nonlinear formulation, as well as alternative data-adaptive decompositions.

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

PubMed Central

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

2014-01-01

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

Evolving RBF neural networks for adaptive soft-sensor design.

PubMed

Alexandridis, Alex

2013-12-01

This work presents an adaptive framework for building soft-sensors based on radial basis function (RBF) neural network models. The adaptive fuzzy means algorithm is utilized in order to evolve an RBF network, which approximates the unknown system based on input-output data from it. The methodology gradually builds the RBF network model, based on two separate levels of adaptation: On the first level, the structure of the hidden layer is modified by adding or deleting RBF centers, while on the second level, the synaptic weights are adjusted with the recursive least squares with exponential forgetting algorithm. The proposed approach is tested on two different systems, namely a simulated nonlinear DC Motor and a real industrial reactor. The results show that the produced soft-sensors can be successfully applied to model the two nonlinear systems. A comparison with two different adaptive modeling techniques, namely a dynamic evolving neural-fuzzy inference system (DENFIS) and neural networks trained with online backpropagation, highlights the advantages of the proposed methodology.

A linear framework for time-scale separation in nonlinear biochemical systems.

PubMed

Gunawardena, Jeremy

2012-01-01

Cellular physiology is implemented by formidably complex biochemical systems with highly nonlinear dynamics, presenting a challenge for both experiment and theory. Time-scale separation has been one of the few theoretical methods for distilling general principles from such complexity. It has provided essential insights in areas such as enzyme kinetics, allosteric enzymes, G-protein coupled receptors, ion channels, gene regulation and post-translational modification. In each case, internal molecular complexity has been eliminated, leading to rational algebraic expressions among the remaining components. This has yielded familiar formulas such as those of Michaelis-Menten in enzyme kinetics, Monod-Wyman-Changeux in allostery and Ackers-Johnson-Shea in gene regulation. Here we show that these calculations are all instances of a single graph-theoretic framework. Despite the biochemical nonlinearity to which it is applied, this framework is entirely linear, yet requires no approximation. We show that elimination of internal complexity is feasible when the relevant graph is strongly connected. The framework provides a new methodology with the potential to subdue combinatorial explosion at the molecular level.

Augmented Lagrange Programming Neural Network for Localization Using Time-Difference-of-Arrival Measurements.

PubMed

Han, Zifa; Leung, Chi Sing; So, Hing Cheung; Constantinides, Anthony George

2017-08-15

A commonly used measurement model for locating a mobile source is time-difference-of-arrival (TDOA). As each TDOA measurement defines a hyperbola, it is not straightforward to compute the mobile source position due to the nonlinear relationship in the measurements. This brief exploits the Lagrange programming neural network (LPNN), which provides a general framework to solve nonlinear constrained optimization problems, for the TDOA-based localization. The local stability of the proposed LPNN solution is also analyzed. Simulation results are included to evaluate the localization accuracy of the LPNN scheme by comparing with the state-of-the-art methods and the optimality benchmark of Cramér-Rao lower bound.

Nonlinear Dynamic Theory of Acute Cell Injuries and Brain Ischemia

NASA Astrophysics Data System (ADS)

Taha, Doaa; Anggraini, Fika; Degracia, Donald; Huang, Zhi-Feng

2015-03-01

Cerebral ischemia in the form of stroke and cardiac arrest brain damage affect over 1 million people per year in the USA alone. In spite of close to 200 clinical trials and decades of research, there are no treatments to stop post-ischemic neuron death. We have argued that a major weakness of current brain ischemia research is lack of a deductive theoretical framework of acute cell injury to guide empirical studies. A previously published autonomous model based on the concept of nonlinear dynamic network was shown to capture important facets of cell injury, linking the concept of therapeutic to bistable dynamics. Here we present an improved, non-autonomous formulation of the nonlinear dynamic model of cell injury that allows multiple acute injuries over time, thereby allowing simulations of both therapeutic treatment and preconditioning. Our results are connected to the experimental data of gene expression and proteomics of neuron cells. Importantly, this new model may be construed as a novel approach to pharmacodynamics of acute cell injury. The model makes explicit that any pro-survival therapy is always a form of sub-lethal injury. This insight is expected to widely influence treatment of acute injury conditions that have defied successful treatment to date. This work is supported by NIH NINDS (NS081347) and Wayne State University President's Research Enhancement Award.

Analyzing systemic risk using non-linear marginal expected shortfall and its minimum spanning tree

NASA Astrophysics Data System (ADS)

Song, Jae Wook; Ko, Bonggyun; Chang, Woojin

2018-02-01

The aim of this paper is to propose a new theoretical framework for analyzing the systemic risk using the marginal expected shortfall (MES) and its correlation-based minimum spanning tree (MST). At first, we develop two parametric models of MES with their closed-form solutions based on the Capital Asset Pricing Model. Our models are derived from the non-symmetric quadratic form, which allows them to consolidate the non-linear relationship between the stock and market returns. Secondly, we discover the evidences related to the utility of our models and the possible association in between the non-linear relationship and the emergence of severe systemic risk by considering the US financial system as a benchmark. In this context, the evolution of MES also can be regarded as a reasonable proxy of systemic risk. Lastly, we analyze the structural properties of the systemic risk using the MST based on the computed series of MES. The topology of MST conveys the presence of sectoral clustering and strong co-movements of systemic risk leaded by few hubs during the crisis. Specifically, we discover that the Depositories are the majority sector leading the connections during the Non-Crisis period, whereas the Broker-Dealers are majority during the Crisis period.

A parametrisation of modified gravity on nonlinear cosmological scales

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

Lombriser, Lucas, E-mail: llo@roe.ac.uk

2016-11-01

Viable modifications of gravity on cosmological scales predominantly rely on screening mechanisms to recover Einstein's Theory of General Relativity in the Solar System, where it has been well tested. A parametrisation of the effects of such modifications in the spherical collapse model is presented here for the use of modelling the modified nonlinear cosmological structure. The formalism allows an embedding of the different screening mechanisms operating in scalar-tensor theories through large values of the gravitational potential or its first or second derivatives as well as of linear suppression effects or more general transitions between modified and Einstein gravity limits. Eachmore » screening or suppression mechanism is parametrised by a time, mass, and environment dependent screening scale, an effective modified gravitational coupling in the fully unscreened limit that can be matched to linear theory, the exponent of a power-law radial profile of the screened coupling, determined by derivatives, symmetries, and potentials in the scalar field equation, and an interpolation rate between the screened and unscreened limits. Along with generalised perturbative methods, the parametrisation may be used to formulate a nonlinear extension to the linear parametrised post-Friedmannian framework to enable generalised tests of gravity with the wealth of observations from the nonlinear cosmological regime.« less

Feature selection and classifier parameters estimation for EEG signals peak detection using particle swarm optimization.

PubMed

Adam, Asrul; Shapiai, Mohd Ibrahim; Tumari, Mohd Zaidi Mohd; Mohamad, Mohd Saberi; Mubin, Marizan

2014-01-01

Electroencephalogram (EEG) signal peak detection is widely used in clinical applications. The peak point can be detected using several approaches, including time, frequency, time-frequency, and nonlinear domains depending on various peak features from several models. However, there is no study that provides the importance of every peak feature in contributing to a good and generalized model. In this study, feature selection and classifier parameters estimation based on particle swarm optimization (PSO) are proposed as a framework for peak detection on EEG signals in time domain analysis. Two versions of PSO are used in the study: (1) standard PSO and (2) random asynchronous particle swarm optimization (RA-PSO). The proposed framework tries to find the best combination of all the available features that offers good peak detection and a high classification rate from the results in the conducted experiments. The evaluation results indicate that the accuracy of the peak detection can be improved up to 99.90% and 98.59% for training and testing, respectively, as compared to the framework without feature selection adaptation. Additionally, the proposed framework based on RA-PSO offers a better and reliable classification rate as compared to standard PSO as it produces low variance model.

Mapping the Energy Cascade in the North Atlantic Ocean: The Coarse-graining Approach

DOE PAGES

Aluie, Hussein; Hecht, Matthew; Vallis, Geoffrey K.

2017-11-14

A coarse-graining framework is implemented to analyze nonlinear processes, measure energy transfer rates and map out the energy pathways from simulated global ocean data. Traditional tools to measure the energy cascade from turbulence theory, such as spectral flux or spectral transfer rely on the assumption of statistical homogeneity, or at least a large separation between the scales of motion and the scales of statistical inhomogeneity. The coarse-graining framework allows for probing the fully nonlinear dynamics simultaneously in scale and in space, and is not restricted by those assumptions. This study describes how the framework can be applied to ocean flows.

Mapping the Energy Cascade in the North Atlantic Ocean: The Coarse-graining Approach

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

Aluie, Hussein; Hecht, Matthew; Vallis, Geoffrey K.

A coarse-graining framework is implemented to analyze nonlinear processes, measure energy transfer rates and map out the energy pathways from simulated global ocean data. Traditional tools to measure the energy cascade from turbulence theory, such as spectral flux or spectral transfer rely on the assumption of statistical homogeneity, or at least a large separation between the scales of motion and the scales of statistical inhomogeneity. The coarse-graining framework allows for probing the fully nonlinear dynamics simultaneously in scale and in space, and is not restricted by those assumptions. This study describes how the framework can be applied to ocean flows.

Statistical Modeling of Fire Occurrence Using Data from the Tōhoku, Japan Earthquake and Tsunami.

PubMed

Anderson, Dana; Davidson, Rachel A; Himoto, Keisuke; Scawthorn, Charles

2016-02-01

In this article, we develop statistical models to predict the number and geographic distribution of fires caused by earthquake ground motion and tsunami inundation in Japan. Using new, uniquely large, and consistent data sets from the 2011 Tōhoku earthquake and tsunami, we fitted three types of models-generalized linear models (GLMs), generalized additive models (GAMs), and boosted regression trees (BRTs). This is the first time the latter two have been used in this application. A simple conceptual framework guided identification of candidate covariates. Models were then compared based on their out-of-sample predictive power, goodness of fit to the data, ease of implementation, and relative importance of the framework concepts. For the ground motion data set, we recommend a Poisson GAM; for the tsunami data set, a negative binomial (NB) GLM or NB GAM. The best models generate out-of-sample predictions of the total number of ignitions in the region within one or two. Prefecture-level prediction errors average approximately three. All models demonstrate predictive power far superior to four from the literature that were also tested. A nonlinear relationship is apparent between ignitions and ground motion, so for GLMs, which assume a linear response-covariate relationship, instrumental intensity was the preferred ground motion covariate because it captures part of that nonlinearity. Measures of commercial exposure were preferred over measures of residential exposure for both ground motion and tsunami ignition models. This may vary in other regions, but nevertheless highlights the value of testing alternative measures for each concept. Models with the best predictive power included two or three covariates. © 2015 Society for Risk Analysis.

Inverse scattering transform analysis of rogue waves using local periodization procedure

NASA Astrophysics Data System (ADS)

Randoux, Stéphane; Suret, Pierre; El, Gennady

2016-07-01

The nonlinear Schrödinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear physics. The question of random input problems in the one-dimensional and integrable NLSE enters within the framework of integrable turbulence, and the specific question of the formation of rogue waves (RWs) has been recently extensively studied in this context. The determination of exact analytic solutions of the focusing 1D-NLSE prototyping RW events of statistical relevance is now considered as the problem of central importance. Here we address this question from the perspective of the inverse scattering transform (IST) method that relies on the integrable nature of the wave equation. We develop a conceptually new approach to the RW classification in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical IST procedure relying on a spatial periodization of the object under consideration. Using this approach we extend the existing classifications of the prototypes of RWs from standard breathers and their collisions to more general nonlinear modes characterized by their nonlinear spectra.

Inverse scattering transform analysis of rogue waves using local periodization procedure

PubMed Central

Randoux, Stéphane; Suret, Pierre; El, Gennady

2016-01-01

The nonlinear Schrödinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear physics. The question of random input problems in the one-dimensional and integrable NLSE enters within the framework of integrable turbulence, and the specific question of the formation of rogue waves (RWs) has been recently extensively studied in this context. The determination of exact analytic solutions of the focusing 1D-NLSE prototyping RW events of statistical relevance is now considered as the problem of central importance. Here we address this question from the perspective of the inverse scattering transform (IST) method that relies on the integrable nature of the wave equation. We develop a conceptually new approach to the RW classification in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical IST procedure relying on a spatial periodization of the object under consideration. Using this approach we extend the existing classifications of the prototypes of RWs from standard breathers and their collisions to more general nonlinear modes characterized by their nonlinear spectra. PMID:27385164

Spline approximations for nonlinear hereditary control systems

NASA Technical Reports Server (NTRS)

Daniel, P. L.

1982-01-01

A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.

Development of a railway wagon-track interaction model: Case studies on excited tracks

NASA Astrophysics Data System (ADS)

Xu, Lei; Chen, Xianmai; Li, Xuwei; He, Xianglin

2018-02-01

In this paper, a theoretical framework for modeling the railway wagon-ballast track interactions is presented, in which the dynamic equations of motion of wagon-track systems are constructed by effectively coupling the linear and nonlinear dynamic characteristics of system components. For the linear components, the energy-variational principle is directly used to derive their dynamic matrices, while for the nonlinear components, the dynamic equilibrium method is implemented to deduce the load vectors, based on which a novel railway wagon-ballast track interaction model is developed, and being validated by comparing with the experimental data measured from a heavy haul railway and another advanced model. With this study, extensive contributions in figuring out the critical speed of instability, limits and localizations of track irregularities over derailment accidents are presented by effectively integrating the dynamic simulation model, the track irregularity probabilistic model and time-frequency analysis method. The proposed approaches can provide crucial information to guarantee the running safety and stability of the wagon-track system when considering track geometries and various running speeds.

A Generic Guidance and Control Structure for Six-Degree-of-Freedom Conceptual Aircraft Design

NASA Technical Reports Server (NTRS)

Cotting, M. Christopher; Cox, Timothy H.

2005-01-01

A control system framework is presented for both real-time and batch six-degree-of-freedom simulation. This framework allows stabilization and control with multiple command options, from body rate control to waypoint guidance. Also, pilot commands can be used to operate the simulation in a pilot-in-the-loop environment. This control system framework is created by using direct vehicle state feedback with nonlinear dynamic inversion. A direct control allocation scheme is used to command aircraft effectors. Online B-matrix estimation is used in the control allocation algorithm for maximum algorithm flexibility. Primary uses for this framework include conceptual design and early preliminary design of aircraft, where vehicle models change rapidly and a knowledge of vehicle six-degree-of-freedom performance is required. A simulated airbreathing hypersonic vehicle and a simulated high performance fighter are controlled to demonstrate the flexibility and utility of the control system.

A Symbiotic Framework for coupling Machine Learning and Geosciences in Prediction and Predictability

NASA Astrophysics Data System (ADS)

Ravela, S.

2017-12-01

In this presentation we review the two directions of a symbiotic relationship between machine learning and the geosciences in relation to prediction and predictability. In the first direction, we develop ensemble, information theoretic and manifold learning framework to adaptively improve state and parameter estimates in nonlinear high-dimensional non-Gaussian problems, showing in particular that tractable variational approaches can be produced. We demonstrate these applications in the context of autonomous mapping of environmental coherent structures and other idealized problems. In the reverse direction, we show that data assimilation, particularly probabilistic approaches for filtering and smoothing offer a novel and useful way to train neural networks, and serve as a better basis than gradient based approaches when we must quantify uncertainty in association with nonlinear, chaotic processes. In many inference problems in geosciences we seek to build reduced models to characterize local sensitivies, adjoints or other mechanisms that propagate innovations and errors. Here, the particular use of neural approaches for such propagation trained using ensemble data assimilation provides a novel framework. Through these two examples of inference problems in the earth sciences, we show that not only is learning useful to broaden existing methodology, but in reverse, geophysical methodology can be used to influence paradigms in learning.

Design optimization for active twist rotor blades

NASA Astrophysics Data System (ADS)

Mok, Ji Won

This dissertation introduces the process of optimizing active twist rotor blades in the presence of embedded anisotropic piezo-composite actuators. Optimum design of active twist blades is a complex task, since it involves a rich design space with tightly coupled design variables. The study presents the development of an optimization framework for active helicopter rotor blade cross-sectional design. This optimization framework allows for exploring a rich and highly nonlinear design space in order to optimize the active twist rotor blades. Different analytical components are combined in the framework: cross-sectional analysis (UM/VABS), an automated mesh generator, a beam solver (DYMORE), a three-dimensional local strain recovery module, and a gradient based optimizer within MATLAB. Through the mathematical optimization problem, the static twist actuation performance of a blade is maximized while satisfying a series of blade constraints. These constraints are associated with locations of the center of gravity and elastic axis, blade mass per unit span, fundamental rotating blade frequencies, and the blade strength based on local three-dimensional strain fields under worst loading conditions. Through pre-processing, limitations of the proposed process have been studied. When limitations were detected, resolution strategies were proposed. These include mesh overlapping, element distortion, trailing edge tab modeling, electrode modeling and foam implementation of the mesh generator, and the initial point sensibility of the current optimization scheme. Examples demonstrate the effectiveness of this process. Optimization studies were performed on the NASA/Army/MIT ATR blade case. Even though that design was built and shown significant impact in vibration reduction, the proposed optimization process showed that the design could be improved significantly. The second example, based on a model scale of the AH-64D Apache blade, emphasized the capability of this framework to explore the nonlinear design space of complex planform. Especially for this case, detailed design is carried out to make the actual blade manufacturable. The proposed optimization framework is shown to be an effective tool to design high authority active twist blades to reduce vibration in future helicopter rotor blades.

A conceptual framework for road safety and mobility applied to cycling safety.

PubMed

Schepers, Paul; Hagenzieker, Marjan; Methorst, Rob; van Wee, Bert; Wegman, Fred

2014-01-01

Scientific literature lacks a model which combines exposure to risk, risk, and the relationship between them. This paper presents a conceptual road safety framework comprising mutually interacting factors for exposure to risk resulting from travel behaviour (volumes, modal split, and distribution of traffic over time and space) and for risk (crash and injury risk). The framework's three determinants for travel behaviour are locations of activities; resistances (generalized transport costs); needs, opportunities, and abilities. Crash and injury risks are modelled by the three 'safety pillars': infrastructure, road users and the vehicles they use. Creating a link in the framework between risk and exposure is important because of the 'non-linear relationship' between them, i.e. risk tends to decrease as exposure increases. Furthermore, 'perceived' risk (a type of travel resistance) plays a role in mode choice, i.e. the perception that a certain type of vehicle is unsafe can be a deterrent to its use. This paper uses theories to explain how the elements in the model interact. Cycling is an area where governments typically have goals for both mobility and safety. To exemplify application of the model, the paper uses the framework to link research on cycling (safety) to land use and infrastructure. The model's value lies in its ability to identify potential consequences of measures and policies for both exposure and risk. This is important from a scientific perspective and for policy makers who often have objectives for both mobility and safety. Copyright © 2013 Elsevier Ltd. All rights reserved.

Fluid-structure interaction for nonlinear response of shells conveying pulsatile flow

NASA Astrophysics Data System (ADS)

Tubaldi, Eleonora; Amabili, Marco; Païdoussis, Michael P.

2016-06-01

Circular cylindrical shells with flexible boundary conditions conveying pulsatile flow and subjected to pulsatile pressure are investigated. The equations of motion are obtained based on the nonlinear Novozhilov shell theory via Lagrangian approach. The flow is set in motion by a pulsatile pressure gradient. The fluid is modeled as a Newtonian pulsatile flow and it is formulated using a hybrid model that contains the unsteady effects obtained from the linear potential flow theory and the pulsatile viscous effects obtained from the unsteady time-averaged Navier-Stokes equations. A numerical bifurcation analysis employs a refined reduced order model to investigate the dynamic behavior. The case of shells containing quiescent fluid subjected to the action of a pulsatile transmural pressure is also addressed. Geometrically nonlinear vibration response to pulsatile flow and transmural pressure are here presented via frequency-response curves and time histories. The vibrations involving both a driven mode and a companion mode, which appear due to the axial symmetry, are also investigated. This theoretical framework represents a pioneering study that could be of great interest for biomedical applications. In particular, in the future, a more refined model of the one here presented will possibly be applied to reproduce the dynamic behavior of vascular prostheses used for repairing and replacing damaged and diseased thoracic aorta in cases of aneurysm, dissection or coarctation. For this purpose, a pulsatile time-dependent blood flow model is here considered by applying physiological waveforms of velocity and pressure during the heart beating period. This study provides, for the first time in literature, a fully coupled fluid-structure interaction model with deep insights in the nonlinear vibrations of circular cylindrical shells subjected to pulsatile pressure and pulsatile flow.

Structured functional additive regression in reproducing kernel Hilbert spaces.

PubMed

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

2014-06-01

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

Mixed linear-nonlinear fault slip inversion: Bayesian inference of model, weighting, and smoothing parameters

NASA Astrophysics Data System (ADS)

Fukuda, J.; Johnson, K. M.

2009-12-01

Studies utilizing inversions of geodetic data for the spatial distribution of coseismic slip on faults typically present the result as a single fault plane and slip distribution. Commonly the geometry of the fault plane is assumed to be known a priori and the data are inverted for slip. However, sometimes there is not strong a priori information on the geometry of the fault that produced the earthquake and the data is not always strong enough to completely resolve the fault geometry. We develop a method to solve for the full posterior probability distribution of fault slip and fault geometry parameters in a Bayesian framework using Monte Carlo methods. The slip inversion problem is particularly challenging because it often involves multiple data sets with unknown relative weights (e.g. InSAR, GPS), model parameters that are related linearly (slip) and nonlinearly (fault geometry) through the theoretical model to surface observations, prior information on model parameters, and a regularization prior to stabilize the inversion. We present the theoretical framework and solution method for a Bayesian inversion that can handle all of these aspects of the problem. The method handles the mixed linear/nonlinear nature of the problem through combination of both analytical least-squares solutions and Monte Carlo methods. We first illustrate and validate the inversion scheme using synthetic data sets. We then apply the method to inversion of geodetic data from the 2003 M6.6 San Simeon, California earthquake. We show that the uncertainty in strike and dip of the fault plane is over 20 degrees. We characterize the uncertainty in the slip estimate with a volume around the mean fault solution in which the slip most likely occurred. Slip likely occurred somewhere in a volume that extends 5-10 km in either direction normal to the fault plane. We implement slip inversions with both traditional, kinematic smoothing constraints on slip and a simple physical condition of uniform stress drop.

Protein-ion binding process on finite macromolecular concentration. A Poisson-Boltzmann and Monte Carlo study.

PubMed

de Carvalho, Sidney Jurado; Fenley, Márcia O; da Silva, Fernando Luís Barroso

2008-12-25

Electrostatic interactions are one of the key driving forces for protein-ligands complexation. Different levels for the theoretical modeling of such processes are available on the literature. Most of the studies on the Molecular Biology field are performed within numerical solutions of the Poisson-Boltzmann Equation and the dielectric continuum models framework. In such dielectric continuum models, there are two pivotal questions: (a) how the protein dielectric medium should be modeled, and (b) what protocol should be used when solving this effective Hamiltonian. By means of Monte Carlo (MC) and Poisson-Boltzmann (PB) calculations, we define the applicability of the PB approach with linear and nonlinear responses for macromolecular electrostatic interactions in electrolyte solution, revealing some physical mechanisms and limitations behind it especially due the raise of both macromolecular charge and concentration out of the strong coupling regime. A discrepancy between PB and MC for binding constant shifts is shown and explained in terms of the manner PB approximates the excess chemical potentials of the ligand, and not as a consequence of the nonlinear thermal treatment and/or explicit ion-ion interactions as it could be argued. Our findings also show that the nonlinear PB predictions with a low dielectric response well reproduce the pK shifts calculations carried out with an uniform dielectric model. This confirms and completes previous results obtained by both MC and linear PB calculations.

Arbitrary order 2D virtual elements for polygonal meshes: part II, inelastic problem

NASA Astrophysics Data System (ADS)

Artioli, E.; Beirão da Veiga, L.; Lovadina, C.; Sacco, E.

2017-10-01

The present paper is the second part of a twofold work, whose first part is reported in Artioli et al. (Comput Mech, 2017. doi: 10.1007/s00466-017-1404-5), concerning a newly developed Virtual element method (VEM) for 2D continuum problems. The first part of the work proposed a study for linear elastic problem. The aim of this part is to explore the features of the VEM formulation when material nonlinearity is considered, showing that the accuracy and easiness of implementation discovered in the analysis inherent to the first part of the work are still retained. Three different nonlinear constitutive laws are considered in the VEM formulation. In particular, the generalized viscoelastic model, the classical Mises plasticity with isotropic/kinematic hardening and a shape memory alloy constitutive law are implemented. The versatility with respect to all the considered nonlinear material constitutive laws is demonstrated through several numerical examples, also remarking that the proposed 2D VEM formulation can be straightforwardly implemented as in a standard nonlinear structural finite element method framework.

Intelligent Systems Approaches to Product Sound Quality Analysis

NASA Astrophysics Data System (ADS)

Pietila, Glenn M.

As a product market becomes more competitive, consumers become more discriminating in the way in which they differentiate between engineered products. The consumer often makes a purchasing decision based on the sound emitted from the product during operation by using the sound to judge quality or annoyance. Therefore, in recent years, many sound quality analysis tools have been developed to evaluate the consumer preference as it relates to a product sound and to quantify this preference based on objective measurements. This understanding can be used to direct a product design process in order to help differentiate the product from competitive products or to establish an impression on consumers regarding a product's quality or robustness. The sound quality process is typically a statistical tool that is used to model subjective preference, or merit score, based on objective measurements, or metrics. In this way, new product developments can be evaluated in an objective manner without the laborious process of gathering a sample population of consumers for subjective studies each time. The most common model used today is the Multiple Linear Regression (MLR), although recently non-linear Artificial Neural Network (ANN) approaches are gaining popularity. This dissertation will review publicly available published literature and present additional intelligent systems approaches that can be used to improve on the current sound quality process. The focus of this work is to address shortcomings in the current paired comparison approach to sound quality analysis. This research will propose a framework for an adaptive jury analysis approach as an alternative to the current Bradley-Terry model. The adaptive jury framework uses statistical hypothesis testing to focus on sound pairings that are most interesting and is expected to address some of the restrictions required by the Bradley-Terry model. It will also provide a more amicable framework for an intelligent systems approach. Next, an unsupervised jury clustering algorithm is used to identify and classify subgroups within a jury who have conflicting preferences. In addition, a nested Artificial Neural Network (ANN) architecture is developed to predict subjective preference based on objective sound quality metrics, in the presence of non-linear preferences. Finally, statistical decomposition and correlation algorithms are reviewed that can help an analyst establish a clear understanding of the variability of the product sounds used as inputs into the jury study and to identify correlations between preference scores and sound quality metrics in the presence of non-linearities.

A nonlinear CDM based damage growth law for ductile materials

NASA Astrophysics Data System (ADS)

Gautam, Abhinav; Priya Ajit, K.; Sarkar, Prabir Kumar

2018-02-01

A nonlinear ductile damage growth criterion is proposed based on continuum damage mechanics (CDM) approach. The model is derived in the framework of thermodynamically consistent CDM assuming damage to be isotropic. In this study, the damage dissipation potential is also derived to be a function of varying strain hardening exponent in addition to damage strain energy release rate density. Uniaxial tensile tests and load-unload-cyclic tensile tests for AISI 1020 steel, AISI 1030 steel and Al 2024 aluminum alloy are considered for the determination of their respective damage variable D and other parameters required for the model(s). The experimental results are very closely predicted, with a deviation of 0%-3%, by the proposed model for each of the materials. The model is also tested with predictabilities of damage growth by other models in the literature. Present model detects the state of damage quantitatively at any level of plastic strain and uses simpler material tests to find the parameters of the model. So, it should be useful in metal forming industries to assess the damage growth for the desired deformation level a priori. The superiority of the new model is clarified by the deviations in the predictability of test results by other models.

Non-Gaussian and Multivariate Noise Models for Signal Detection.

DTIC Science & Technology

1982-09-01

follow, some of the basic results of asymptotic "theory are presented. both to make the notation clear. and to give some i ~ background for the...densities are considered within a detection framework. The discussions include specific examples and also some general methods of density generation ...densities generated by a memoryless, nonlinear transformation of a correlated, Gaussian source is discussed in some detail. A member of this class has the

Enhancing hydrologic data assimilation by evolutionary Particle Filter and Markov Chain Monte Carlo

NASA Astrophysics Data System (ADS)

Abbaszadeh, Peyman; Moradkhani, Hamid; Yan, Hongxiang

2018-01-01

Particle Filters (PFs) have received increasing attention by researchers from different disciplines including the hydro-geosciences, as an effective tool to improve model predictions in nonlinear and non-Gaussian dynamical systems. The implication of dual state and parameter estimation using the PFs in hydrology has evolved since 2005 from the PF-SIR (sampling importance resampling) to PF-MCMC (Markov Chain Monte Carlo), and now to the most effective and robust framework through evolutionary PF approach based on Genetic Algorithm (GA) and MCMC, the so-called EPFM. In this framework, the prior distribution undergoes an evolutionary process based on the designed mutation and crossover operators of GA. The merit of this approach is that the particles move to an appropriate position by using the GA optimization and then the number of effective particles is increased by means of MCMC, whereby the particle degeneracy is avoided and the particle diversity is improved. In this study, the usefulness and effectiveness of the proposed EPFM is investigated by applying the technique on a conceptual and highly nonlinear hydrologic model over four river basins located in different climate and geographical regions of the United States. Both synthetic and real case studies demonstrate that the EPFM improves both the state and parameter estimation more effectively and reliably as compared with the PF-MCMC.

Deformation-Aware Log-Linear Models

NASA Astrophysics Data System (ADS)

Gass, Tobias; Deselaers, Thomas; Ney, Hermann

In this paper, we present a novel deformation-aware discriminative model for handwritten digit recognition. Unlike previous approaches our model directly considers image deformations and allows discriminative training of all parameters, including those accounting for non-linear transformations of the image. This is achieved by extending a log-linear framework to incorporate a latent deformation variable. The resulting model has an order of magnitude less parameters than competing approaches to handling image deformations. We tune and evaluate our approach on the USPS task and show its generalization capabilities by applying the tuned model to the MNIST task. We gain interesting insights and achieve highly competitive results on both tasks.

A review of nonlinear constitutive models for metals

NASA Technical Reports Server (NTRS)

Allen, David H.; Harris, Charles E.

1990-01-01

Over the past two decades a number of thermomechanical constitutive theories have been proposed for viscoplastic metals. These models are in most cases similar in that they utilize a set of internal state variables which provide locally averaged representations of microphysical phenomena such as dislocation rearrangement and grain boundary sliding. The state of development of several of these models is now at the point where accurate theoretical solutions can be obtained for a wide variety of structural problems at elevated temperatures. The fundamentals of viscoplasticity are briefly reviewed and a general framework is outlined. Several of the more prominent models are reviewed, and predictions from models are compared to experimental results.

Online optimal obstacle avoidance for rotary-wing autonomous unmanned aerial vehicles

NASA Astrophysics Data System (ADS)

Kang, Keeryun

This thesis presents an integrated framework for online obstacle avoidance of rotary-wing unmanned aerial vehicles (UAVs), which can provide UAVs an obstacle field navigation capability in a partially or completely unknown obstacle-rich environment. The framework is composed of a LIDAR interface, a local obstacle grid generation, a receding horizon (RH) trajectory optimizer, a global shortest path search algorithm, and a climb rate limit detection logic. The key feature of the framework is the use of an optimization-based trajectory generation in which the obstacle avoidance problem is formulated as a nonlinear trajectory optimization problem with state and input constraints over the finite range of the sensor. This local trajectory optimization is combined with a global path search algorithm which provides a useful initial guess to the nonlinear optimization solver. Optimization is the natural process of finding the best trajectory that is dynamically feasible, safe within the vehicle's flight envelope, and collision-free at the same time. The optimal trajectory is continuously updated in real time by the numerical optimization solver, Nonlinear Trajectory Generation (NTG), which is a direct solver based on the spline approximation of trajectory for dynamically flat systems. In fact, the overall approach of this thesis to finding the optimal trajectory is similar to the model predictive control (MPC) or the receding horizon control (RHC), except that this thesis followed a two-layer design; thus, the optimal solution works as a guidance command to be followed by the controller of the vehicle. The framework is implemented in a real-time simulation environment, the Georgia Tech UAV Simulation Tool (GUST), and integrated in the onboard software of the rotary-wing UAV test-bed at Georgia Tech. Initially, the 2D vertical avoidance capability of real obstacles was tested in flight. The flight test evaluations were extended to the benchmark tests for 3D avoidance capability over the virtual obstacles, and finally it was demonstrated on real obstacles located at the McKenna MOUT site in Fort Benning, Georgia. Simulations and flight test evaluations demonstrate the feasibility of the developed framework for UAV applications involving low-altitude flight in an urban area.

A network-base analysis of CMIP5 "historical" experiments

NASA Astrophysics Data System (ADS)

Bracco, A.; Foudalis, I.; Dovrolis, C.

2012-12-01

In computer science, "complex network analysis" refers to a set of metrics, modeling tools and algorithms commonly used in the study of complex nonlinear dynamical systems. Its main premise is that the underlying topology or network structure of a system has a strong impact on its dynamics and evolution. By allowing to investigate local and non-local statistical interaction, network analysis provides a powerful, but only marginally explored, framework to validate climate models and investigate teleconnections, assessing their strength, range, and impacts on the climate system. In this work we propose a new, fast, robust and scalable methodology to examine, quantify, and visualize climate sensitivity, while constraining general circulation models (GCMs) outputs with observations. The goal of our novel approach is to uncover relations in the climate system that are not (or not fully) captured by more traditional methodologies used in climate science and often adopted from nonlinear dynamical systems analysis, and to explain known climate phenomena in terms of the network structure or its metrics. Our methodology is based on a solid theoretical framework and employs mathematical and statistical tools, exploited only tentatively in climate research so far. Suitably adapted to the climate problem, these tools can assist in visualizing the trade-offs in representing global links and teleconnections among different data sets. Here we present the methodology, and compare network properties for different reanalysis data sets and a suite of CMIP5 coupled GCM outputs. With an extensive model intercomparison in terms of the climate network that each model leads to, we quantify how each model reproduces major teleconnections, rank model performances, and identify common or specific errors in comparing model outputs and observations.

Probabilistic inversion of AVO seismic data for reservoir properties and related uncertainty estimation

NASA Astrophysics Data System (ADS)

Zunino, Andrea; Mosegaard, Klaus

2017-04-01

Sought-after reservoir properties of interest are linked only indirectly to the observable geophysical data which are recorded at the earth's surface. In this framework, seismic data represent one of the most reliable tool to study the structure and properties of the subsurface for natural resources. Nonetheless, seismic analysis is not an end in itself, as physical properties such as porosity are often of more interest for reservoir characterization. As such, inference of those properties implies taking into account also rock physics models linking porosity and other physical properties to elastic parameters. In the framework of seismic reflection data, we address this challenge for a reservoir target zone employing a probabilistic method characterized by a multi-step complex nonlinear forward modeling that combines: 1) a rock physics model with 2) the solution of full Zoeppritz equations and 3) a convolutional seismic forward modeling. The target property of this work is porosity, which is inferred using a Monte Carlo approach where porosity models, i.e., solutions to the inverse problem, are directly sampled from the posterior distribution. From a theoretical point of view, the Monte Carlo strategy can be particularly useful in the presence of nonlinear forward models, which is often the case when employing sophisticated rock physics models and full Zoeppritz equations and to estimate related uncertainty. However, the resulting computational challenge is huge. We propose to alleviate this computational burden by assuming some smoothness of the subsurface parameters and consequently parameterizing the model in terms of spline bases. This allows us a certain flexibility in that the number of spline bases and hence the resolution in each spatial direction can be controlled. The method is tested on a 3-D synthetic case and on a 2-D real data set.

TerraFERMA: Harnessing Advanced Computational Libraries in Earth Science

NASA Astrophysics Data System (ADS)

Wilson, C. R.; Spiegelman, M.; van Keken, P.

2012-12-01

Many important problems in Earth sciences can be described by non-linear coupled systems of partial differential equations. These "multi-physics" problems include thermo-chemical convection in Earth and planetary interiors, interactions of fluids and magmas with the Earth's mantle and crust and coupled flow of water and ice. These problems are of interest to a large community of researchers but are complicated to model and understand. Much of this complexity stems from the nature of multi-physics where small changes in the coupling between variables or constitutive relations can lead to radical changes in behavior, which in turn affect critical computational choices such as discretizations, solvers and preconditioners. To make progress in understanding such coupled systems requires a computational framework where multi-physics problems can be described at a high-level while maintaining the flexibility to easily modify the solution algorithm. Fortunately, recent advances in computational science provide a basis for implementing such a framework. Here we present the Transparent Finite Element Rapid Model Assembler (TerraFERMA), which leverages several advanced open-source libraries for core functionality. FEniCS (fenicsproject.org) provides a high level language for describing the weak forms of coupled systems of equations, and an automatic code generator that produces finite element assembly code. PETSc (www.mcs.anl.gov/petsc) provides a wide range of scalable linear and non-linear solvers that can be composed into effective multi-physics preconditioners. SPuD (amcg.ese.ic.ac.uk/Spud) is an application neutral options system that provides both human and machine-readable interfaces based on a single xml schema. Our software integrates these libraries and provides the user with a framework for exploring multi-physics problems. A single options file fully describes the problem, including all equations, coefficients and solver options. Custom compiled applications are generated from this file but share an infrastructure for services common to all models, e.g. diagnostics, checkpointing and global non-linear convergence monitoring. This maximizes code reusability, reliability and longevity ensuring that scientific results and the methods used to acquire them are transparent and reproducible. TerraFERMA has been tested against many published geodynamic benchmarks including 2D/3D thermal convection problems, the subduction zone benchmarks and benchmarks for magmatic solitary waves. It is currently being used in the investigation of reactive cracking phenomena with applications to carbon sequestration, but we will principally discuss its use in modeling the migration of fluids in subduction zones. Subduction zones require an understanding of the highly nonlinear interactions of fluids with solids and thus provide an excellent scientific driver for the development of multi-physics software.

Lichnerowicz-type equations with sign-changing nonlinearities on complete manifolds with boundary

NASA Astrophysics Data System (ADS)

Albanese, Guglielmo; Rigoli, Marco

2017-12-01

We prove an existence theorem for positive solutions to Lichnerowicz-type equations on complete manifolds with boundary (M , ∂ M , 〈 , 〉) and nonlinear Neumann conditions. This kind of nonlinear problems arise quite naturally in the study of solutions for the Einstein-scalar field equations of General Relativity in the framework of the so called Conformal Method.

Causality Analysis of fMRI Data Based on the Directed Information Theory Framework.

PubMed

Wang, Zhe; Alahmadi, Ahmed; Zhu, David C; Li, Tongtong

2016-05-01

This paper aims to conduct fMRI-based causality analysis in brain connectivity by exploiting the directed information (DI) theory framework. Unlike the well-known Granger causality (GC) analysis, which relies on the linear prediction technique, the DI theory framework does not have any modeling constraints on the sequences to be evaluated and ensures estimation convergence. Moreover, it can be used to generate the GC graphs. In this paper, first, we introduce the core concepts in the DI framework. Second, we present how to conduct causality analysis using DI measures between two time series. We provide the detailed procedure on how to calculate the DI for two finite-time series. The two major steps involved here are optimal bin size selection for data digitization and probability estimation. Finally, we demonstrate the applicability of DI-based causality analysis using both the simulated data and experimental fMRI data, and compare the results with that of the GC analysis. Our analysis indicates that GC analysis is effective in detecting linear or nearly linear causal relationship, but may have difficulty in capturing nonlinear causal relationships. On the other hand, DI-based causality analysis is more effective in capturing both linear and nonlinear causal relationships. Moreover, it is observed that brain connectivity among different regions generally involves dynamic two-way information transmissions between them. Our results show that when bidirectional information flow is present, DI is more effective than GC to quantify the overall causal relationship.

A model-free characterization of recurrences in stationary time series

NASA Astrophysics Data System (ADS)

Chicheportiche, Rémy; Chakraborti, Anirban

2017-05-01

Study of recurrences in earthquakes, climate, financial time-series, etc. is crucial to better forecast disasters and limit their consequences. Most of the previous phenomenological studies of recurrences have involved only a long-ranged autocorrelation function, and ignored the multi-scaling properties induced by potential higher order dependencies. We argue that copulas is a natural model-free framework to study non-linear dependencies in time series and related concepts like recurrences. Consequently, we arrive at the facts that (i) non-linear dependences do impact both the statistics and dynamics of recurrence times, and (ii) the scaling arguments for the unconditional distribution may not be applicable. Hence, fitting and/or simulating the intertemporal distribution of recurrence intervals is very much system specific, and cannot actually benefit from universal features, in contrast to the previous claims. This has important implications in epilepsy prognosis and financial risk management applications.

Nonlinear gearshifts control of dual-clutch transmissions during inertia phase.

PubMed

Hu, Yunfeng; Tian, Lu; Gao, Bingzhao; Chen, Hong

2014-07-01

In this paper, a model-based nonlinear gearshift controller is designed by the backstepping method to improve the shift quality of vehicles with a dual-clutch transmission (DCT). Considering easy-implementation, the controller is rearranged into a concise structure which contains a feedforward control and a feedback control. Then, robustness of the closed-loop error system is discussed in the framework of the input to state stability (ISS) theory, where model uncertainties are considered as the additive disturbance inputs. Furthermore, due to the application of the backstepping method, the closed-loop error system is ordered as a linear system. Using the linear system theory, a guideline for selecting the controller parameters is deduced which could reduce the workload of parameters tuning. Finally, simulation results and Hardware in the Loop (HiL) simulation are presented to validate the effectiveness of the designed controller. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Coupling Osmolarity Dynamics within Human Tear Film on an Eye-Shaped Domain

NASA Astrophysics Data System (ADS)

Li, Longfei; Braun, R. J.; Driscoll, T. A.; Henshaw, W. D.; Banks, J. W.; King-Smith, P. E.

2013-11-01

The concentration of ions in the tear film (osmolarity) is a key variable in understanding dry eye symptoms and disease. We derived a mathematical model that couples osmolarity (treated as a single solute) and fluid dynamics within the tear film on a 2D eye-shaped domain. The model concerns the physical effects of evaporation, surface tension, viscosity, ocular surface wettability, osmolarity, osmosis and tear fluid supply and drainage. We solved the governing system of coupled nonlinear PDEs using the Overture computational framework developed at LLNL, together with a new hybrid time stepping scheme (using variable step BDF and RKC) that was added to the framework. Results of our numerical simulations show good agreement with existing 1D models (for both tear film and osmolarity dynamics) and provide new insight about the osmolarity distribution over the ocular surface during the interblink.

A modeling framework for deriving the structural and functional architecture of a short-term memory microcircuit.

PubMed

Fisher, Dimitry; Olasagasti, Itsaso; Tank, David W; Aksay, Emre R F; Goldman, Mark S

2013-09-04

Although many studies have identified neural correlates of memory, relatively little is known about the circuit properties connecting single-neuron physiology to behavior. Here we developed a modeling framework to bridge this gap and identify circuit interactions capable of maintaining short-term memory. Unlike typical studies that construct a phenomenological model and test whether it reproduces select aspects of neuronal data, we directly fit the synaptic connectivity of an oculomotor memory circuit to a broad range of anatomical, electrophysiological, and behavioral data. Simultaneous fits to all data, combined with sensitivity analyses, revealed complementary roles of synaptic and neuronal recruitment thresholds in providing the nonlinear interactions required to generate the observed circuit behavior. This work provides a methodology for identifying the cellular and synaptic mechanisms underlying short-term memory and demonstrates how the anatomical structure of a circuit may belie its functional organization. Copyright © 2013 Elsevier Inc. All rights reserved.

Principal Dynamic Mode Analysis of the Hodgkin–Huxley Equations

PubMed Central

Eikenberry, Steffen E.; Marmarelis, Vasilis Z.

2015-01-01

We develop an autoregressive model framework based on the concept of Principal Dynamic Modes (PDMs) for the process of action potential (AP) generation in the excitable neuronal membrane described by the Hodgkin–Huxley (H–H) equations. The model's exogenous input is injected current, and whenever the membrane potential output exceeds a specified threshold, it is fed back as a second input. The PDMs are estimated from the previously developed Nonlinear Autoregressive Volterra (NARV) model, and represent an efficient functional basis for Volterra kernel expansion. The PDM-based model admits a modular representation, consisting of the forward and feedback PDM bases as linear filterbanks for the exogenous and autoregressive inputs, respectively, whose outputs are then fed to a static nonlinearity composed of polynomials operating on the PDM outputs and cross-terms of pair-products of PDM outputs. A two-step procedure for model reduction is performed: first, influential subsets of the forward and feedback PDM bases are identified and selected as the reduced PDM bases. Second, the terms of the static nonlinearity are pruned. The first step reduces model complexity from a total of 65 coefficients to 27, while the second further reduces the model coefficients to only eight. It is demonstrated that the performance cost of model reduction in terms of out-of-sample prediction accuracy is minimal. Unlike the full model, the eight coefficient pruned model can be easily visualized to reveal the essential system components, and thus the data-derived PDM model can yield insight into the underlying system structure and function. PMID:25630480

Strongly nonlinear dynamics of electrolytes in large ac voltages.

PubMed

Højgaard Olesen, Laurits; Bazant, Martin Z; Bruus, Henrik

2010-07-01

We study the response of a model microelectrochemical cell to a large ac voltage of frequency comparable to the inverse cell relaxation time. To bring out the basic physics, we consider the simplest possible model of a symmetric binary electrolyte confined between parallel-plate blocking electrodes, ignoring any transverse instability or fluid flow. We analyze the resulting one-dimensional problem by matched asymptotic expansions in the limit of thin double layers and extend previous work into the strongly nonlinear regime, which is characterized by two features--significant salt depletion in the electrolyte near the electrodes and, at very large voltage, the breakdown of the quasiequilibrium structure of the double layers. The former leads to the prediction of "ac capacitive desalination" since there is a time-averaged transfer of salt from the bulk to the double layers, via oscillating diffusion layers. The latter is associated with transient diffusion limitation, which drives the formation and collapse of space-charge layers, even in the absence of any net Faradaic current through the cell. We also predict that steric effects of finite ion sizes (going beyond dilute-solution theory) act to suppress the strongly nonlinear regime in the limit of concentrated electrolytes, ionic liquids, and molten salts. Beyond the model problem, our reduced equations for thin double layers, based on uniformly valid matched asymptotic expansions, provide a useful mathematical framework to describe additional nonlinear responses to large ac voltages, such as Faradaic reactions, electro-osmotic instabilities, and induced-charge electrokinetic phenomena.

Nonlinear data assimilation: towards a prediction of the solar cycle

NASA Astrophysics Data System (ADS)

Svedin, Andreas

The solar cycle is the cyclic variation of solar activity, with a span of 9-14 years. The prediction of the solar cycle is an important and unsolved problem with implications for communications, aviation and other aspects of our high-tech society. Our interest is model-based prediction, and we present a self-consistent procedure for parameter estimation and model state estimation, even when only one of several model variables can be observed. Data assimilation is the art of comparing, combining and transferring observed data into a mathematical model or computer simulation. We use the 3DVAR methodology, based on the notion of least squares, to present an implementation of a traditional data assimilation. Using the Shadowing Filter — a recently developed method for nonlinear data assimilation — we outline a path towards model based prediction of the solar cycle. To achieve this end we solve a number of methodological challenges related to unobserved variables. We also provide a new framework for interpretation that can guide future predictions of the Sun and other astrophysical objects.

A new line-of-sight approach to the non-linear Cosmic Microwave Background

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

Fidler, Christian; Koyama, Kazuya; Pettinari, Guido W., E-mail: christian.fidler@port.ac.uk, E-mail: kazuya.koyama@port.ac.uk, E-mail: guido.pettinari@gmail.com

2015-04-01

We develop the transport operator formalism, a new line-of-sight integration framework to calculate the anisotropies of the Cosmic Microwave Background (CMB) at the linear and non-linear level. This formalism utilises a transformation operator that removes all inhomogeneous propagation effects acting on the photon distribution function, thus achieving a split between perturbative collisional effects at recombination and non-perturbative line-of-sight effects at later times. The former can be computed in the framework of standard cosmological perturbation theory with a second-order Boltzmann code such as SONG, while the latter can be treated within a separate perturbative scheme allowing the use of non-linear Newtonianmore » potentials. We thus provide a consistent framework to compute all physical effects contained in the Boltzmann equation and to combine the standard remapping approach with Boltzmann codes at any order in perturbation theory, without assuming that all sources are localised at recombination.« less

Robustness Analysis and Optimally Robust Control Design via Sum-of-Squares

NASA Technical Reports Server (NTRS)

Dorobantu, Andrei; Crespo, Luis G.; Seiler, Peter J.

2012-01-01

A control analysis and design framework is proposed for systems subject to parametric uncertainty. The underlying strategies are based on sum-of-squares (SOS) polynomial analysis and nonlinear optimization to design an optimally robust controller. The approach determines a maximum uncertainty range for which the closed-loop system satisfies a set of stability and performance requirements. These requirements, de ned as inequality constraints on several metrics, are restricted to polynomial functions of the uncertainty. To quantify robustness, SOS analysis is used to prove that the closed-loop system complies with the requirements for a given uncertainty range. The maximum uncertainty range, calculated by assessing a sequence of increasingly larger ranges, serves as a robustness metric for the closed-loop system. To optimize the control design, nonlinear optimization is used to enlarge the maximum uncertainty range by tuning the controller gains. Hence, the resulting controller is optimally robust to parametric uncertainty. This approach balances the robustness margins corresponding to each requirement in order to maximize the aggregate system robustness. The proposed framework is applied to a simple linear short-period aircraft model with uncertain aerodynamic coefficients.

Have artificial neural networks met expectations in drug discovery as implemented in QSAR framework?

PubMed

Dobchev, Dimitar; Karelson, Mati

2016-07-01

Artificial neural networks (ANNs) are highly adaptive nonlinear optimization algorithms that have been applied in many diverse scientific endeavors, ranging from economics, engineering, physics, and chemistry to medical science. Notably, in the past two decades, ANNs have been used widely in the process of drug discovery. In this review, the authors discuss advantages and disadvantages of ANNs in drug discovery as incorporated into the quantitative structure-activity relationships (QSAR) framework. Furthermore, the authors examine the recent studies, which span over a broad area with various diseases in drug discovery. In addition, the authors attempt to answer the question about the expectations of the ANNs in drug discovery and discuss the trends in this field. The old pitfalls of overtraining and interpretability are still present with ANNs. However, despite these pitfalls, the authors believe that ANNs have likely met many of the expectations of researchers and are still considered as excellent tools for nonlinear data modeling in QSAR. It is likely that ANNs will continue to be used in drug development in the future.

Numerical solution of a non-linear conservation law applicable to the interior dynamics of partially molten planets

NASA Astrophysics Data System (ADS)

Bower, Dan J.; Sanan, Patrick; Wolf, Aaron S.

2018-01-01

The energy balance of a partially molten rocky planet can be expressed as a non-linear diffusion equation using mixing length theory to quantify heat transport by both convection and mixing of the melt and solid phases. Crucially, in this formulation the effective or eddy diffusivity depends on the entropy gradient, ∂S / ∂r , as well as entropy itself. First we present a simplified model with semi-analytical solutions that highlights the large dynamic range of ∂S / ∂r -around 12 orders of magnitude-for physically-relevant parameters. It also elucidates the thermal structure of a magma ocean during the earliest stage of crystal formation. This motivates the development of a simple yet stable numerical scheme able to capture the large dynamic range of ∂S / ∂r and hence provide a flexible and robust method for time-integrating the energy equation. Using insight gained from the simplified model, we consider a full model, which includes energy fluxes associated with convection, mixing, gravitational separation, and conduction that all depend on the thermophysical properties of the melt and solid phases. This model is discretised and evolved by applying the finite volume method (FVM), allowing for extended precision calculations and using ∂S / ∂r as the solution variable. The FVM is well-suited to this problem since it is naturally energy conserving, flexible, and intuitive to incorporate arbitrary non-linear fluxes that rely on lookup data. Special attention is given to the numerically challenging scenario in which crystals first form in the centre of a magma ocean. The computational framework we devise is immediately applicable to modelling high melt fraction phenomena in Earth and planetary science research. Furthermore, it provides a template for solving similar non-linear diffusion equations that arise in other science and engineering disciplines, particularly for non-linear functional forms of the diffusion coefficient.

A Physics-driven Neural Networks-based Simulation System (PhyNNeSS) for multimodal interactive virtual environments involving nonlinear deformable objects

PubMed Central

De, Suvranu; Deo, Dhannanjay; Sankaranarayanan, Ganesh; Arikatla, Venkata S.

2012-01-01

Background While an update rate of 30 Hz is considered adequate for real time graphics, a much higher update rate of about 1 kHz is necessary for haptics. Physics-based modeling of deformable objects, especially when large nonlinear deformations and complex nonlinear material properties are involved, at these very high rates is one of the most challenging tasks in the development of real time simulation systems. While some specialized solutions exist, there is no general solution for arbitrary nonlinearities. Methods In this work we present PhyNNeSS - a Physics-driven Neural Networks-based Simulation System - to address this long-standing technical challenge. The first step is an off-line pre-computation step in which a database is generated by applying carefully prescribed displacements to each node of the finite element models of the deformable objects. In the next step, the data is condensed into a set of coefficients describing neurons of a Radial Basis Function network (RBFN). During real-time computation, these neural networks are used to reconstruct the deformation fields as well as the interaction forces. Results We present realistic simulation examples from interactive surgical simulation with real time force feedback. As an example, we have developed a deformable human stomach model and a Penrose-drain model used in the Fundamentals of Laparoscopic Surgery (FLS) training tool box. Conclusions A unique computational modeling system has been developed that is capable of simulating the response of nonlinear deformable objects in real time. The method distinguishes itself from previous efforts in that a systematic physics-based pre-computational step allows training of neural networks which may be used in real time simulations. We show, through careful error analysis, that the scheme is scalable, with the accuracy being controlled by the number of neurons used in the simulation. PhyNNeSS has been integrated into SoFMIS (Software Framework for Multimodal Interactive Simulation) for general use. PMID:22629108

A unifying framework for ghost-free Lorentz-invariant Lagrangian field theories

NASA Astrophysics Data System (ADS)

Li, Wenliang

2018-04-01

We propose a framework for Lorentz-invariant Lagrangian field theories where Ostrogradsky's scalar ghosts could be absent. A key ingredient is the generalized Kronecker delta. The general Lagrangians are reformulated in the language of differential forms. The absence of higher order equations of motion for the scalar modes stems from the basic fact that every exact form is closed. The well-established Lagrangian theories for spin-0, spin-1, p-form, spin-2 fields have natural formulations in this framework. We also propose novel building blocks for Lagrangian field theories. Some of them are novel nonlinear derivative terms for spin-2 fields. It is nontrivial that Ostrogradsky's scalar ghosts are absent in these fully nonlinear theories.

Essentially Entropic Lattice Boltzmann Model

NASA Astrophysics Data System (ADS)

Atif, Mohammad; Kolluru, Praveen Kumar; Thantanapally, Chakradhar; Ansumali, Santosh

2017-12-01

The entropic lattice Boltzmann model (ELBM), a discrete space-time kinetic theory for hydrodynamics, ensures nonlinear stability via the discrete time version of the second law of thermodynamics (the H theorem). Compliance with the H theorem is numerically enforced in this methodology and involves a search for the maximal discrete path length corresponding to the zero dissipation state by iteratively solving a nonlinear equation. We demonstrate that an exact solution for the path length can be obtained by assuming a natural criterion of negative entropy change, thereby reducing the problem to solving an inequality. This inequality is solved by creating a new framework for construction of Padé approximants via quadrature on appropriate convex function. This exact solution also resolves the issue of indeterminacy in case of nonexistence of the entropic involution step. Since our formulation is devoid of complex mathematical library functions, the computational cost is drastically reduced. To illustrate this, we have simulated a model setup of flow over the NACA-0012 airfoil at a Reynolds number of 2.88 ×106.

Multiscale Modeling of Dewetting Damage in Highly Filled Particulate Composites

NASA Astrophysics Data System (ADS)

Geubelle, P. H.; Inglis, H. M.; Kramer, J. D.; Patel, J. J.; Kumar, N. C.; Tan, H.

2008-02-01

Particle debonding or dewetting constitutes one of the key damage processes in highly filled particulate composites such as solid propellant and other energetic materials. To analyze this failure process, we have developed a multiscale finite element framework that combines, at the microscale, a nonlinear description of the binder response with a cohesive model of the damage process taking place in a representative periodic unit cell (PUC). To relate micro-scale damage to the macroscopic constitutive response of the material, we employ the mathematical theory of homogenization (MTH). After a description of the numerical scheme, we present the results of the damage response of a highly filled particulate composite subjected to a uniaxial macroscopic strain, and show the direct correlation between the complex damage processes taking place in the PUC and the nonlinear macroscopic constitutive response. We also present a detailed study of the PUC size and a comparison between the finite element MTH-based study and a micromechanics model of the dewetting process.

Statistical model based iterative reconstruction in clinical CT systems. Part III. Task-based kV/mAs optimization for radiation dose reduction

PubMed Central

Li, Ke; Gomez-Cardona, Daniel; Hsieh, Jiang; Lubner, Meghan G.; Pickhardt, Perry J.; Chen, Guang-Hong

2015-01-01

Purpose: For a given imaging task and patient size, the optimal selection of x-ray tube potential (kV) and tube current-rotation time product (mAs) is pivotal in achieving the maximal radiation dose reduction while maintaining the needed diagnostic performance. Although contrast-to-noise (CNR)-based strategies can be used to optimize kV/mAs for computed tomography (CT) imaging systems employing the linear filtered backprojection (FBP) reconstruction method, a more general framework needs to be developed for systems using the nonlinear statistical model-based iterative reconstruction (MBIR) method. The purpose of this paper is to present such a unified framework for the optimization of kV/mAs selection for both FBP- and MBIR-based CT systems. Methods: The optimal selection of kV and mAs was formulated as a constrained optimization problem to minimize the objective function, Dose(kV,mAs), under the constraint that the achievable detectability index d′(kV,mAs) is not lower than the prescribed value of d℞′ for a given imaging task. Since it is difficult to analytically model the dependence of d′ on kV and mAs for the highly nonlinear MBIR method, this constrained optimization problem is solved with comprehensive measurements of Dose(kV,mAs) and d′(kV,mAs) at a variety of kV–mAs combinations, after which the overlay of the dose contours and d′ contours is used to graphically determine the optimal kV–mAs combination to achieve the lowest dose while maintaining the needed detectability for the given imaging task. As an example, d′ for a 17 mm hypoattenuating liver lesion detection task was experimentally measured with an anthropomorphic abdominal phantom at four tube potentials (80, 100, 120, and 140 kV) and fifteen mA levels (25 and 50–700) with a sampling interval of 50 mA at a fixed rotation time of 0.5 s, which corresponded to a dose (CTDIvol) range of [0.6, 70] mGy. Using the proposed method, the optimal kV and mA that minimized dose for the prescribed detectability level of d℞′=16 were determined. As another example, the optimal kV and mA for an 8 mm hyperattenuating liver lesion detection task were also measured using the developed framework. Both an in vivo animal and human subject study were used as demonstrations of how the developed framework can be applied to the clinical work flow. Results: For the first task, the optimal kV and mAs were measured to be 100 and 500, respectively, for FBP, which corresponded to a dose level of 24 mGy. In comparison, the optimal kV and mAs for MBIR were 80 and 150, respectively, which corresponded to a dose level of 4 mGy. The topographies of the iso-d′ map and the iso-CNR map were the same for FBP; thus, the use of d′- and CNR-based optimization methods generated the same results for FBP. However, the topographies of the iso-d′ and iso-CNR map were significantly different in MBIR; the CNR-based method overestimated the performance of MBIR, predicting an overly aggressive dose reduction factor. For the second task, the developed framework generated the following optimization results: for FBP, kV = 140, mA = 350, dose = 37.5 mGy; for MBIR, kV = 120, mA = 250, dose = 18.8 mGy. Again, the CNR-based method overestimated the performance of MBIR. Results of the preliminary in vivo studies were consistent with those of the phantom experiments. Conclusions: A unified and task-driven kV/mAs optimization framework has been developed in this work. The framework is applicable to both linear and nonlinear CT systems such as those using the MBIR method. As expected, the developed framework can be reduced to the conventional CNR-based kV/mAs optimization frameworks if the system is linear. For MBIR-based nonlinear CT systems, however, the developed task-based kV/mAs optimization framework is needed to achieve the maximal dose reduction while maintaining the desired diagnostic performance. PMID:26328971

A novel Lagrangian approach for the stable numerical simulation of fault and fracture mechanics

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

Franceschini, Andrea; Ferronato, Massimiliano, E-mail: massimiliano.ferronato@unipd.it; Janna, Carlo

The simulation of the mechanics of geological faults and fractures is of paramount importance in several applications, such as ensuring the safety of the underground storage of wastes and hydrocarbons or predicting the possible seismicity triggered by the production and injection of subsurface fluids. However, the stable numerical modeling of ground ruptures is still an open issue. The present work introduces a novel formulation based on the use of the Lagrange multipliers to prescribe the constraints on the contact surfaces. The variational formulation is modified in order to take into account the frictional work along the activated fault portion accordingmore » to the principle of maximum plastic dissipation. The numerical model, developed in the framework of the Finite Element method, provides stable solutions with a fast convergence of the non-linear problem. The stabilizing properties of the proposed model are emphasized with the aid of a realistic numerical example dealing with the generation of ground fractures due to groundwater withdrawal in arid regions. - Highlights: • A numerical model is developed for the simulation of fault and fracture mechanics. • The model is implemented in the framework of the Finite Element method and with the aid of Lagrange multipliers. • The proposed formulation introduces a new contribution due to the frictional work on the portion of activated fault. • The resulting algorithm is highly non-linear as the portion of activated fault is itself unknown. • The numerical solution is validated against analytical results and proves to be stable also in realistic applications.« less

Observability and Controllability of Networks: Symmetry in Representations of Brains and Controllers for Epidemics

NASA Astrophysics Data System (ADS)

Schiff, Steven

Observability and controllability are essential concepts to the design of predictive observer models and feedback controllers of networked systems. We present a numerical and group representational framework, to quantify the observability and controllability of nonlinear networks with explicit symmetries that shows the connection between symmetries and nonlinear measures of observability and controllability. In addition to the topology of brain networks, we have advanced our ability to represent network nodes within the brain using conservation principles and more accurate biophysics that unifies the dynamics of spikes, seizures, and spreading depression. Lastly, we show how symmetries in controller design can be applied to infectious disease epidemics. NIH Grants 1R01EB014641, 1DP1HD086071.

Exact solutions for oscillatory shear sweep behaviors of complex fluids from the Oldroyd 8-constant framework

NASA Astrophysics Data System (ADS)

Saengow, Chaimongkol; Giacomin, A. Jeffrey

2018-03-01

In this paper, we provide a new exact framework for analyzing the most commonly measured behaviors in large-amplitude oscillatory shear flow (LAOS), a popular flow for studying the nonlinear physics of complex fluids. Specifically, the strain rate sweep (also called the strain sweep) is used routinely to identify the onset of nonlinearity. By the strain rate sweep, we mean a sequence of LAOS experiments conducted at the same frequency, performed one after another, with increasing shear rate amplitude. In this paper, we give exact expressions for the nonlinear complex viscosity and the corresponding nonlinear complex normal stress coefficients, for the Oldroyd 8-constant framework for oscillatory shear sweeps. We choose the Oldroyd 8-constant framework for its rich diversity of popular special cases (we list 18 of these). We evaluate the Fourier integrals of our previous exact solution to get exact expressions for the real and imaginary parts of the complex viscosity, and for the complex normal stress coefficients, as functions of both test frequency and shear rate amplitude. We explore the role of infinite shear rate viscosity on strain rate sweep responses for the special case of the corotational Jeffreys fluid. We find that raising η∞ raises the real part of the complex viscosity and lowers the imaginary. In our worked examples, we thus first use the corotational Jeffreys fluid, and then, for greater accuracy, we use the Johnson-Segalman fluid, to describe the strain rate sweep response of molten atactic polystyrene. For our comparisons with data, we use the Spriggs relations to generalize the Oldroyd 8-constant framework to multimode. Our generalization yields unequivocally, a longest fluid relaxation time, used to assign Weissenberg and Deborah numbers to each oscillatory shear flow experiment. We then locate each experiment in the Pipkin space.

Semiparametric bivariate zero-inflated Poisson models with application to studies of abundance for multiple species

USGS Publications Warehouse

Arab, Ali; Holan, Scott H.; Wikle, Christopher K.; Wildhaber, Mark L.

2012-01-01

Ecological studies involving counts of abundance, presence–absence or occupancy rates often produce data having a substantial proportion of zeros. Furthermore, these types of processes are typically multivariate and only adequately described by complex nonlinear relationships involving externally measured covariates. Ignoring these aspects of the data and implementing standard approaches can lead to models that fail to provide adequate scientific understanding of the underlying ecological processes, possibly resulting in a loss of inferential power. One method of dealing with data having excess zeros is to consider the class of univariate zero-inflated generalized linear models. However, this class of models fails to address the multivariate and nonlinear aspects associated with the data usually encountered in practice. Therefore, we propose a semiparametric bivariate zero-inflated Poisson model that takes into account both of these data attributes. The general modeling framework is hierarchical Bayes and is suitable for a broad range of applications. We demonstrate the effectiveness of our model through a motivating example on modeling catch per unit area for multiple species using data from the Missouri River Benthic Fishes Study, implemented by the United States Geological Survey.

Methodical fitting for mathematical models of rubber-like materials

NASA Astrophysics Data System (ADS)

Destrade, Michel; Saccomandi, Giuseppe; Sgura, Ivonne

2017-02-01

A great variety of models can describe the nonlinear response of rubber to uniaxial tension. Yet an in-depth understanding of the successive stages of large extension is still lacking. We show that the response can be broken down in three steps, which we delineate by relying on a simple formatting of the data, the so-called Mooney plot transform. First, the small-to-moderate regime, where the polymeric chains unfold easily and the Mooney plot is almost linear. Second, the strain-hardening regime, where blobs of bundled chains unfold to stiffen the response in correspondence to the `upturn' of the Mooney plot. Third, the limiting-chain regime, with a sharp stiffening occurring as the chains extend towards their limit. We provide strain-energy functions with terms accounting for each stage that (i) give an accurate local and then global fitting of the data; (ii) are consistent with weak nonlinear elasticity theory and (iii) can be interpreted in the framework of statistical mechanics. We apply our method to Treloar's classical experimental data and also to some more recent data. Our method not only provides models that describe the experimental data with a very low quantitative relative error, but also shows that the theory of nonlinear elasticity is much more robust that seemed at first sight.

MOOSE: A PARALLEL COMPUTATIONAL FRAMEWORK FOR COUPLED SYSTEMS OF NONLINEAR EQUATIONS.

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

G. Hansen; C. Newman; D. Gaston

Systems of coupled, nonlinear partial di?erential equations often arise in sim- ulation of nuclear processes. MOOSE: Multiphysics Ob ject Oriented Simulation Environment, a parallel computational framework targeted at solving these systems is presented. As opposed to traditional data / ?ow oriented com- putational frameworks, MOOSE is instead founded on mathematics based on Jacobian-free Newton Krylov (JFNK). Utilizing the mathematical structure present in JFNK, physics are modularized into “Kernels” allowing for rapid production of new simulation tools. In addition, systems are solved fully cou- pled and fully implicit employing physics based preconditioning allowing for a large amount of ?exibility even withmore » large variance in time scales. Background on the mathematics, an inspection of the structure of MOOSE and several rep- resentative solutions from applications built on the framework are presented.« less

MOOSE: A parallel computational framework for coupled systems of nonlinear equations.

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

Derek Gaston; Chris Newman; Glen Hansen

Systems of coupled, nonlinear partial differential equations (PDEs) often arise in simulation of nuclear processes. MOOSE: Multiphysics Object Oriented Simulation Environment, a parallel computational framework targeted at the solution of such systems, is presented. As opposed to traditional data-flow oriented computational frameworks, MOOSE is instead founded on the mathematical principle of Jacobian-free Newton-Krylov (JFNK) solution methods. Utilizing the mathematical structure present in JFNK, physics expressions are modularized into `Kernels,'' allowing for rapid production of new simulation tools. In addition, systems are solved implicitly and fully coupled, employing physics based preconditioning, which provides great flexibility even with large variance in timemore » scales. A summary of the mathematics, an overview of the structure of MOOSE, and several representative solutions from applications built on the framework are presented.« less

The Influence of the Enhanced Vector Meson Sector on the Properties of the Matter of Neutron Stars

PubMed Central

Bednarek, Ilona; Manka, Ryszard; Pienkos, Monika

2014-01-01

This paper gives an overview of the model of a neutron star with non-zero strangeness constructed within the framework of the nonlinear realization of the chiral symmetry. The emphasis is put on the physical properties of the matter of a neutron star as well as on its internal structure. The obtained solution is particularly aimed at the problem of the construction of a theoretical model of a neutron star matter with hyperons that will give high value of the maximum mass. PMID:25188304

Long-Lived Plasma Formations in the Atmosphere as an Alternative Energy Source

NASA Astrophysics Data System (ADS)

Dvornikov, M. S.; Mekhdieva, G. Sh.; Agamalieva, L. A.

2018-01-01

A model of a stable plasma formation, based on radial quantum oscillations of charged particles, is discussed. The given plasmoid is described with the help of the nonlinear Schrödinger equation. A new phenomenon of effective attraction between oscillating charged particles is considered within the framework of the proposed model. The possible existence of a composite plasma structure is also discussed. Hypotheses about using the obtained results to describe natural long-lived plasma formations which can serve as alternative energy sources are advanced.

Final technical report for DE-SC00012633 AToM (Advanced Tokamak Modeling)

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

Holland, Christopher; Orlov, Dmitri; Izzo, Valerie

This final report for the AToM project documents contributions from University of California, San Diego researchers over the period of 9/1/2014 – 8/31/2017. The primary focus of these efforts was on performing validation studies of core tokamak transport models using the OMFIT framework, including development of OMFIT workflow scripts. Additional work was performed to develop tools for use of the nonlinear magnetohydrodynamics code NIMROD in OMFIT, and its use in the study of runaway electron dynamics in tokamak disruptions.

Predicting Statistical Response and Extreme Events in Uncertainty Quantification through Reduced-Order Models

NASA Astrophysics Data System (ADS)

Qi, D.; Majda, A.

2017-12-01

A low-dimensional reduced-order statistical closure model is developed for quantifying the uncertainty in statistical sensitivity and intermittency in principal model directions with largest variability in high-dimensional turbulent system and turbulent transport models. Imperfect model sensitivity is improved through a recent mathematical strategy for calibrating model errors in a training phase, where information theory and linear statistical response theory are combined in a systematic fashion to achieve the optimal model performance. The idea in the reduced-order method is from a self-consistent mathematical framework for general systems with quadratic nonlinearity, where crucial high-order statistics are approximated by a systematic model calibration procedure. Model efficiency is improved through additional damping and noise corrections to replace the expensive energy-conserving nonlinear interactions. Model errors due to the imperfect nonlinear approximation are corrected by tuning the model parameters using linear response theory with an information metric in a training phase before prediction. A statistical energy principle is adopted to introduce a global scaling factor in characterizing the higher-order moments in a consistent way to improve model sensitivity. Stringent models of barotropic and baroclinic turbulence are used to display the feasibility of the reduced-order methods. Principal statistical responses in mean and variance can be captured by the reduced-order models with accuracy and efficiency. Besides, the reduced-order models are also used to capture crucial passive tracer field that is advected by the baroclinic turbulent flow. It is demonstrated that crucial principal statistical quantities like the tracer spectrum and fat-tails in the tracer probability density functions in the most important large scales can be captured efficiently with accuracy using the reduced-order tracer model in various dynamical regimes of the flow field with distinct statistical structures.

Inexact nonlinear improved fuzzy chance-constrained programming model for irrigation water management under uncertainty

NASA Astrophysics Data System (ADS)

Zhang, Chenglong; Zhang, Fan; Guo, Shanshan; Liu, Xiao; Guo, Ping

2018-01-01

An inexact nonlinear mλ-measure fuzzy chance-constrained programming (INMFCCP) model is developed for irrigation water allocation under uncertainty. Techniques of inexact quadratic programming (IQP), mλ-measure, and fuzzy chance-constrained programming (FCCP) are integrated into a general optimization framework. The INMFCCP model can deal with not only nonlinearities in the objective function, but also uncertainties presented as discrete intervals in the objective function, variables and left-hand side constraints and fuzziness in the right-hand side constraints. Moreover, this model improves upon the conventional fuzzy chance-constrained programming by introducing a linear combination of possibility measure and necessity measure with varying preference parameters. To demonstrate its applicability, the model is then applied to a case study in the middle reaches of Heihe River Basin, northwest China. An interval regression analysis method is used to obtain interval crop water production functions in the whole growth period under uncertainty. Therefore, more flexible solutions can be generated for optimal irrigation water allocation. The variation of results can be examined by giving different confidence levels and preference parameters. Besides, it can reflect interrelationships among system benefits, preference parameters, confidence levels and the corresponding risk levels. Comparison between interval crop water production functions and deterministic ones based on the developed INMFCCP model indicates that the former is capable of reflecting more complexities and uncertainties in practical application. These results can provide more reliable scientific basis for supporting irrigation water management in arid areas.

Omnibus Risk Assessment via Accelerated Failure Time Kernel Machine Modeling

PubMed Central

Sinnott, Jennifer A.; Cai, Tianxi

2013-01-01

Summary Integrating genomic information with traditional clinical risk factors to improve the prediction of disease outcomes could profoundly change the practice of medicine. However, the large number of potential markers and possible complexity of the relationship between markers and disease make it difficult to construct accurate risk prediction models. Standard approaches for identifying important markers often rely on marginal associations or linearity assumptions and may not capture non-linear or interactive effects. In recent years, much work has been done to group genes into pathways and networks. Integrating such biological knowledge into statistical learning could potentially improve model interpretability and reliability. One effective approach is to employ a kernel machine (KM) framework, which can capture nonlinear effects if nonlinear kernels are used (Scholkopf and Smola, 2002; Liu et al., 2007, 2008). For survival outcomes, KM regression modeling and testing procedures have been derived under a proportional hazards (PH) assumption (Li and Luan, 2003; Cai et al., 2011). In this paper, we derive testing and prediction methods for KM regression under the accelerated failure time model, a useful alternative to the PH model. We approximate the null distribution of our test statistic using resampling procedures. When multiple kernels are of potential interest, it may be unclear in advance which kernel to use for testing and estimation. We propose a robust Omnibus Test that combines information across kernels, and an approach for selecting the best kernel for estimation. The methods are illustrated with an application in breast cancer. PMID:24328713

Linear and Nonlinear Viscoelastic Modeling of Aorta and Carotid Pressure-Area Dynamics under in vivo and ex vivo Conditions

PubMed Central

Valdez-Jasso, Daniela; Bia, Daniel; Zócalo, Yanina; Armentano, Ricardo L.; Haider, Mansoor A.; Olufsen, Mette S.

2013-01-01

A better understanding of the biomechanical properties of the arterial wall provides important insight into arterial vascular biology under normal (healthy) and pathological conditions. This insight has potential to improve tracking of disease progression and to aid in vascular graft design and implementation. In this study, we use linear and nonlinear viscoelastic models to predict biomechanical properties of the thoracic descending aorta and the carotid artery under ex vivo and in vivo conditions in ovine and human arteries. Models analyzed include a four-parameter (linear) Kelvin viscoelastic model and two five-parameter nonlinear viscoelastic models (an arctangent and a sigmoid model) that relate changes in arterial blood pressure to the vessel cross-sectional area (via estimation of vessel strain). These models were developed using the framework of Quasilinear Viscoelasticity (QLV) theory and were validated using measurements from the thoracic descending aorta and the carotid artery obtained from human and ovine arteries. In vivo measurements were obtained from ten ovine aortas and ten human carotid arteries. Ex vivo measurements (from both locations) were made in eleven male Merino sheep. Biomechanical properties were obtained through constrained estimation of model parameters. To further investigate the parameter estimates we computed standard errors and confidence intervals and we used analysis of variance to compare results within and between groups. Overall, our results indicate that optimal model selection depends on the arterial type. Results showed that for the thoracic descending aorta (under both experimental conditions) the best predictions were obtained with the nonlinear sigmoid model, while under healthy physiological pressure loading the carotid arteries nonlinear stiffening with increasing pressure is negligible, and consequently, the linear (Kelvin) viscoelastic model better describes the pressure-area dynamics in this vessel. Results comparing biomechanical properties show that the Kelvin and sigmoid models were able to predict the zero-pressure vessel radius; that under ex vivo conditions vessels are more rigid, and comparatively, that the carotid artery is stiffer than the thoracic descending aorta; and that the viscoelastic gain and relaxation parameters do not differ significantly between vessels or experimental conditions. In conclusion, our study demonstrates that the proposed models can predict pressure-area dynamics and that model parameters can be extracted for further interpretation of biomechanical properties. PMID:21203846

Nonlinear Model Predictive Control for Cooperative Control and Estimation

NASA Astrophysics Data System (ADS)

Ru, Pengkai

Recent advances in computational power have made it possible to do expensive online computations for control systems. It is becoming more realistic to perform computationally intensive optimization schemes online on systems that are not intrinsically stable and/or have very small time constants. Being one of the most important optimization based control approaches, model predictive control (MPC) has attracted a lot of interest from the research community due to its natural ability to incorporate constraints into its control formulation. Linear MPC has been well researched and its stability can be guaranteed in the majority of its application scenarios. However, one issue that still remains with linear MPC is that it completely ignores the system's inherent nonlinearities thus giving a sub-optimal solution. On the other hand, if achievable, nonlinear MPC, would naturally yield a globally optimal solution and take into account all the innate nonlinear characteristics. While an exact solution to a nonlinear MPC problem remains extremely computationally intensive, if not impossible, one might wonder if there is a middle ground between the two. We tried to strike a balance in this dissertation by employing a state representation technique, namely, the state dependent coefficient (SDC) representation. This new technique would render an improved performance in terms of optimality compared to linear MPC while still keeping the problem tractable. In fact, the computational power required is bounded only by a constant factor of the completely linearized MPC. The purpose of this research is to provide a theoretical framework for the design of a specific kind of nonlinear MPC controller and its extension into a general cooperative scheme. The controller is designed and implemented on quadcopter systems.

Two Studies of Complex Nonlinear Systems: Engineered Granular Crystals and Coarse-Graining Optimization Problems

NASA Astrophysics Data System (ADS)

Pozharskiy, Dmitry

In recent years a nonlinear, acoustic metamaterial, named granular crystals, has gained prominence due to its high accessibility, both experimentally and computationally. The observation of a wide range of dynamical phenomena in the system, due to its inherent nonlinearities, has suggested its importance in many engineering applications related to wave propagation. In the first part of this dissertation, we explore the nonlinear dynamics of damped-driven granular crystals. In one case, we consider a highly nonlinear setting, also known as a sonic vacuum, and derive a nonlinear analogue of a linear spectrum, corresponding to resonant periodic propagation and antiresonances. Experimental studies confirm the computational findings and the assimilation of experimental data into a numerical model is demonstrated. In the second case, global bifurcations in a precompressed granular crystal are examined, and their involvement in the appearance of chaotic dynamics is demonstrated. Both results highlight the importance of exploring the nonlinear dynamics, to gain insight into how a granular crystal responds to different external excitations. In the second part, we borrow established ideas from coarse-graining of dynamical systems, and extend them to optimization problems. We combine manifold learning algorithms, such as Diffusion Maps, with stochastic optimization methods, such as Simulated Annealing, and show that we can retrieve an ensemble, of few, important parameters that should be explored in detail. This framework can lead to acceleration of convergence when dealing with complex, high-dimensional optimization, and could potentially be applied to design engineered granular crystals.

Vegetation anomalies caused by antecedent precipitation in most of the world

NASA Astrophysics Data System (ADS)

Papagiannopoulou, C.; Miralles, D. G.; Dorigo, W. A.; Verhoest, N. E. C.; Depoorter, M.; Waegeman, W.

2017-07-01

Quantifying environmental controls on vegetation is critical to predict the net effect of climate change on global ecosystems and the subsequent feedback on climate. Following a non-linear Granger causality framework based on a random forest predictive model, we exploit the current wealth of multi-decadal satellite data records to uncover the main drivers of monthly vegetation variability at the global scale. Results indicate that water availability is the most dominant factor driving vegetation globally: about 61% of the vegetated surface was primarily water-limited during 1981-2010. This included semiarid climates but also transitional ecoregions. Intra-annually, temperature controls Northern Hemisphere deciduous forests during the growing season, while antecedent precipitation largely dominates vegetation dynamics during the senescence period. The uncovered dependency of global vegetation on water availability is substantially larger than previously reported. This is owed to the ability of the framework to (1) disentangle the co-linearities between radiation/temperature and precipitation, and (2) quantify non-linear impacts of climate on vegetation. Our results reveal a prolonged effect of precipitation anomalies in dry regions: due to the long memory of soil moisture and the cumulative, non-linear, response of vegetation, water-limited regions show sensitivity to the values of precipitation occurring three months earlier. Meanwhile, the impacts of temperature and radiation anomalies are more immediate and dissipate shortly, pointing to a higher resilience of vegetation to these anomalies. Despite being infrequent by definition, hydro-climatic extremes are responsible for up to 10% of the vegetation variability during the 1981-2010 period in certain areas, particularly in water-limited ecosystems. Our approach is a first step towards a quantitative comparison of the resistance and resilience signature of different ecosystems, and can be used to benchmark Earth system models in their representations of past vegetation sensitivity to changes in climate.

Novel nonlinear knowledge-based mean force potentials based on machine learning.

PubMed

Dong, Qiwen; Zhou, Shuigeng

2011-01-01

The prediction of 3D structures of proteins from amino acid sequences is one of the most challenging problems in molecular biology. An essential task for solving this problem with coarse-grained models is to deduce effective interaction potentials. The development and evaluation of new energy functions is critical to accurately modeling the properties of biological macromolecules. Knowledge-based mean force potentials are derived from statistical analysis of proteins of known structures. Current knowledge-based potentials are almost in the form of weighted linear sum of interaction pairs. In this study, a class of novel nonlinear knowledge-based mean force potentials is presented. The potential parameters are obtained by nonlinear classifiers, instead of relative frequencies of interaction pairs against a reference state or linear classifiers. The support vector machine is used to derive the potential parameters on data sets that contain both native structures and decoy structures. Five knowledge-based mean force Boltzmann-based or linear potentials are introduced and their corresponding nonlinear potentials are implemented. They are the DIH potential (single-body residue-level Boltzmann-based potential), the DFIRE-SCM potential (two-body residue-level Boltzmann-based potential), the FS potential (two-body atom-level Boltzmann-based potential), the HR potential (two-body residue-level linear potential), and the T32S3 potential (two-body atom-level linear potential). Experiments are performed on well-established decoy sets, including the LKF data set, the CASP7 data set, and the Decoys “R”Us data set. The evaluation metrics include the energy Z score and the ability of each potential to discriminate native structures from a set of decoy structures. Experimental results show that all nonlinear potentials significantly outperform the corresponding Boltzmann-based or linear potentials, and the proposed discriminative framework is effective in developing knowledge-based mean force potentials. The nonlinear potentials can be widely used for ab initio protein structure prediction, model quality assessment, protein docking, and other challenging problems in computational biology.

The nurse scheduling problem: a goal programming and nonlinear optimization approaches

NASA Astrophysics Data System (ADS)

Hakim, L.; Bakhtiar, T.; Jaharuddin

2017-01-01

Nurses scheduling is an activity of allocating nurses to conduct a set of tasks at certain room at a hospital or health centre within a certain period. One of obstacles in the nurse scheduling is the lack of resources in order to fulfil the needs of the hospital. Nurse scheduling which is undertaken manually will be at risk of not fulfilling some nursing rules set by the hospital. Therefore, this study aimed to perform scheduling models that satisfy all the specific rules set by the management of Bogor State Hospital. We have developed three models to overcome the scheduling needs. Model 1 is designed to schedule nurses who are solely assigned to a certain inpatient unit and Model 2 is constructed to manage nurses who are assigned to an inpatient room as well as at Polyclinic room as conjunct nurses. As the assignment of nurses on each shift is uneven, then we propose Model 3 to minimize the variance of the workload in order to achieve equitable assignment on every shift. The first two models are formulated in goal programming framework, while the last model is in nonlinear optimization form.

Numerical simulation of solitary waves on deep water with constant vorticity

NASA Astrophysics Data System (ADS)

Dosaev, A. S.; Shishina, M. I.; Troitskaya, Yu I.

2018-01-01

Characteristics of solitary deep water waves on a flow with constant vorticity are investigated by numerical simulation within the framework of fully nonlinear equations of motion (Euler equations) using the method of surface-tracking conformal coordinates. To ensure that solutions observed are stable, soliton formation as a result of disintegration of an initial pulse-like disturbance is modeled. Evidence is obtained that solitary waves with height above a certain threshold are unstable.

Nonlinear viscoelastic characterization of structural adhesives

NASA Technical Reports Server (NTRS)

Rochefort, M. A.; Brinson, H. F.

1983-01-01

Measurements of the nonliner viscoelastic behavior of two adhesives, FM-73 and FM-300, are presented and discussed. Analytical methods to quantify the measurements are given and fitted into a framework of an accelerated testing and analysis procedure. The single integral model used is shown to function well and is analogous to a time-temperature stress-superposition procedure (TTSSP). Advantages and disadvantages of the creep power law method used in this study are given.

Breaking Computational Barriers: Real-time Analysis and Optimization with Large-scale Nonlinear Models via Model Reduction

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

Carlberg, Kevin Thomas; Drohmann, Martin; Tuminaro, Raymond S.

2014-10-01

Model reduction for dynamical systems is a promising approach for reducing the computational cost of large-scale physics-based simulations to enable high-fidelity models to be used in many- query (e.g., Bayesian inference) and near-real-time (e.g., fast-turnaround simulation) contexts. While model reduction works well for specialized problems such as linear time-invariant systems, it is much more difficult to obtain accurate, stable, and efficient reduced-order models (ROMs) for systems with general nonlinearities. This report describes several advances that enable nonlinear reduced-order models (ROMs) to be deployed in a variety of time-critical settings. First, we present an error bound for the Gauss-Newton with Approximatedmore » Tensors (GNAT) nonlinear model reduction technique. This bound allows the state-space error for the GNAT method to be quantified when applied with the backward Euler time-integration scheme. Second, we present a methodology for preserving classical Lagrangian structure in nonlinear model reduction. This technique guarantees that important properties--such as energy conservation and symplectic time-evolution maps--are preserved when performing model reduction for models described by a Lagrangian formalism (e.g., molecular dynamics, structural dynamics). Third, we present a novel technique for decreasing the temporal complexity --defined as the number of Newton-like iterations performed over the course of the simulation--by exploiting time-domain data. Fourth, we describe a novel method for refining projection-based reduced-order models a posteriori using a goal-oriented framework similar to mesh-adaptive h -refinement in finite elements. The technique allows the ROM to generate arbitrarily accurate solutions, thereby providing the ROM with a 'failsafe' mechanism in the event of insufficient training data. Finally, we present the reduced-order model error surrogate (ROMES) method for statistically quantifying reduced- order-model errors. This enables ROMs to be rigorously incorporated in uncertainty-quantification settings, as the error model can be treated as a source of epistemic uncertainty. This work was completed as part of a Truman Fellowship appointment. We note that much additional work was performed as part of the Fellowship. One salient project is the development of the Trilinos-based model-reduction software module Razor , which is currently bundled with the Albany PDE code and currently allows nonlinear reduced-order models to be constructed for any application supported in Albany. Other important projects include the following: 1. ROMES-equipped ROMs for Bayesian inference: K. Carlberg, M. Drohmann, F. Lu (Lawrence Berkeley National Laboratory), M. Morzfeld (Lawrence Berkeley National Laboratory). 2. ROM-enabled Krylov-subspace recycling: K. Carlberg, V. Forstall (University of Maryland), P. Tsuji, R. Tuminaro. 3. A pseudo balanced POD method using only dual snapshots: K. Carlberg, M. Sarovar. 4. An analysis of discrete v. continuous optimality in nonlinear model reduction: K. Carlberg, M. Barone, H. Antil (George Mason University). Journal articles for these projects are in progress at the time of this writing.« less

Human Cognition and a Pile of Sand: A Discussion on Serial Correlations and Self-Organized Criticality

PubMed Central

Wagenmakers, Eric-Jan; Farrell, Simon; Ratcliff, Roger

2005-01-01

Recently, G. C. Van Orden, J. G. Holden, and M. T. Turvey (2003) proposed to abandon the conventional framework of cognitive psychology in favor of the framework of nonlinear dynamical systems theory. Van Orden et al. presented evidence that “purposive behavior originates in self-organized criticality” (p. 333). Here, the authors show that Van Orden et al.’s analyses do not test their hypotheses. Further, the authors argue that a confirmation of Van Orden et al.’s hypotheses would not have constituted firm evidence in support of their framework. Finally, the absence of a specific model for how self-organized criticality produces the observed behavior makes it very difficult to derive testable predictions. The authors conclude that the proposed paradigm shift is presently unwarranted. PMID:15702966

Clustered Multi-Task Learning for Automatic Radar Target Recognition

PubMed Central

Li, Cong; Bao, Weimin; Xu, Luping; Zhang, Hua

2017-01-01

Model training is a key technique for radar target recognition. Traditional model training algorithms in the framework of single task leaning ignore the relationships among multiple tasks, which degrades the recognition performance. In this paper, we propose a clustered multi-task learning, which can reveal and share the multi-task relationships for radar target recognition. To further make full use of these relationships, the latent multi-task relationships in the projection space are taken into consideration. Specifically, a constraint term in the projection space is proposed, the main idea of which is that multiple tasks within a close cluster should be close to each other in the projection space. In the proposed method, the cluster structures and multi-task relationships can be autonomously learned and utilized in both of the original and projected space. In view of the nonlinear characteristics of radar targets, the proposed method is extended to a non-linear kernel version and the corresponding non-linear multi-task solving method is proposed. Comprehensive experimental studies on simulated high-resolution range profile dataset and MSTAR SAR public database verify the superiority of the proposed method to some related algorithms. PMID:28953267

Structured functional additive regression in reproducing kernel Hilbert spaces

PubMed Central

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

2013-01-01

Summary Functional additive models (FAMs) provide a flexible yet simple framework for regressions involving functional predictors. The utilization of data-driven basis in an additive rather than linear structure naturally extends the classical functional linear model. However, the critical issue of selecting nonlinear additive components has been less studied. In this work, we propose a new regularization framework for the structure estimation in the context of Reproducing Kernel Hilbert Spaces. The proposed approach takes advantage of the functional principal components which greatly facilitates the implementation and the theoretical analysis. The selection and estimation are achieved by penalized least squares using a penalty which encourages the sparse structure of the additive components. Theoretical properties such as the rate of convergence are investigated. The empirical performance is demonstrated through simulation studies and a real data application. PMID:25013362

Computed tear film and osmolarity dynamics on an eye-shaped domain

PubMed Central

Li, Longfei; Braun, Richard J.; Driscoll, Tobin A.; Henshaw, William D.; Banks, Jeffrey W.; King-Smith, P. Ewen

2016-01-01

The concentration of ions, or osmolarity, in the tear film is a key variable in understanding dry eye symptoms and disease. In this manuscript, we derive a mathematical model that couples osmolarity (treated as a single solute) and fluid dynamics within the tear film on a 2D eye-shaped domain. The model includes the physical effects of evaporation, surface tension, viscosity, ocular surface wettability, osmolarity, osmosis and tear fluid supply and drainage. The governing system of coupled non-linear partial differential equations is solved using the Overture computational framework, together with a hybrid time-stepping scheme, using a variable step backward differentiation formula and a Runge–Kutta–Chebyshev method that were added to the framework. The results of our numerical simulations provide new insight into the osmolarity distribution over the ocular surface during the interblink. PMID:25883248

Multi-flexible-body analysis for application to wind turbine control design

NASA Astrophysics Data System (ADS)

Lee, Donghoon

The objective of the present research is to build a theoretical and computational framework for the aeroelastic analysis of flexible rotating systems, more specifically with special application to a wind turbine control design. The methodology is based on the integration of Kane's approach for the analysis of the multi-rigid-body subsystem and a mixed finite element method for the analysis of the flexible-body subsystem. The combined analysis is then strongly coupled with an aerodynamic model based on Blade Element Momentum theory for inflow model. The unified framework from the analysis of subsystems is represented as, in a symbolic manner, a set of nonlinear ordinary differential equations with time-variant, periodic coefficients, which describe the aeroelastic behavior of whole system. The framework can be directly applied to control design due to its symbolic characteristics. The solution procedures for the equations are presented for the study of nonlinear simulation, periodic steady-state solution, and Floquet stability of the linearized system about the steady-state solution. Finally the linear periodic system equation can be obtained with both system and control matrices as explicit functions of time, which can be directly applicable to control design. The structural model is validated by comparison of its results with those from software, some of which is commercial. The stability of the linearized system about periodic steady-state solution is different from that obtained about a constant steady-state solution, which have been conventional in the field of wind turbine dynamics. Parametric studies are performed on a wind turbine model with various pitch angles, precone angles, and rotor speeds. Combined with composite material, their effects on wind turbine aeroelastic stability are investigated. Finally it is suggested that the aeroelastic stability analysis and control design for the whole system is crucial for the design of wind turbines, and the present research breaks new ground in the ability to treat the issue.

Feature Selection and Classifier Parameters Estimation for EEG Signals Peak Detection Using Particle Swarm Optimization

PubMed Central

Adam, Asrul; Mohd Tumari, Mohd Zaidi; Mohamad, Mohd Saberi

2014-01-01

Electroencephalogram (EEG) signal peak detection is widely used in clinical applications. The peak point can be detected using several approaches, including time, frequency, time-frequency, and nonlinear domains depending on various peak features from several models. However, there is no study that provides the importance of every peak feature in contributing to a good and generalized model. In this study, feature selection and classifier parameters estimation based on particle swarm optimization (PSO) are proposed as a framework for peak detection on EEG signals in time domain analysis. Two versions of PSO are used in the study: (1) standard PSO and (2) random asynchronous particle swarm optimization (RA-PSO). The proposed framework tries to find the best combination of all the available features that offers good peak detection and a high classification rate from the results in the conducted experiments. The evaluation results indicate that the accuracy of the peak detection can be improved up to 99.90% and 98.59% for training and testing, respectively, as compared to the framework without feature selection adaptation. Additionally, the proposed framework based on RA-PSO offers a better and reliable classification rate as compared to standard PSO as it produces low variance model. PMID:25243236

How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity

PubMed Central

2017-01-01

The mechanical response of a homogeneous isotropic linearly elastic material can be fully characterized by two physical constants, the Young’s modulus and the Poisson’s ratio, which can be derived by simple tensile experiments. Any other linear elastic parameter can be obtained from these two constants. By contrast, the physical responses of nonlinear elastic materials are generally described by parameters which are scalar functions of the deformation, and their particular choice is not always clear. Here, we review in a unified theoretical framework several nonlinear constitutive parameters, including the stretch modulus, the shear modulus and the Poisson function, that are defined for homogeneous isotropic hyperelastic materials and are measurable under axial or shear experimental tests. These parameters represent changes in the material properties as the deformation progresses, and can be identified with their linear equivalent when the deformations are small. Universal relations between certain of these parameters are further established, and then used to quantify nonlinear elastic responses in several hyperelastic models for rubber, soft tissue and foams. The general parameters identified here can also be viewed as a flexible basis for coupling elastic responses in multi-scale processes, where an open challenge is the transfer of meaningful information between scales. PMID:29225507

Calculation of a double reactive azeotrope using stochastic optimization approaches

NASA Astrophysics Data System (ADS)

Mendes Platt, Gustavo; Pinheiro Domingos, Roberto; Oliveira de Andrade, Matheus

2013-02-01

An homogeneous reactive azeotrope is a thermodynamic coexistence condition of two phases under chemical and phase equilibrium, where compositions of both phases (in the Ung-Doherty sense) are equal. This kind of nonlinear phenomenon arises from real world situations and has applications in chemical and petrochemical industries. The modeling of reactive azeotrope calculation is represented by a nonlinear algebraic system with phase equilibrium, chemical equilibrium and azeotropy equations. This nonlinear system can exhibit more than one solution, corresponding to a double reactive azeotrope. The robust calculation of reactive azeotropes can be conducted by several approaches, such as interval-Newton/generalized bisection algorithms and hybrid stochastic-deterministic frameworks. In this paper, we investigate the numerical aspects of the calculation of reactive azeotropes using two metaheuristics: the Luus-Jaakola adaptive random search and the Firefly algorithm. Moreover, we present results for a system (with industrial interest) with more than one azeotrope, the system isobutene/methanol/methyl-tert-butyl-ether (MTBE). We present convergence patterns for both algorithms, illustrating - in a bidimensional subdomain - the identification of reactive azeotropes. A strategy for calculation of multiple roots in nonlinear systems is also applied. The results indicate that both algorithms are suitable and robust when applied to reactive azeotrope calculations for this "challenging" nonlinear system.

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves.

PubMed

Tsitoura, F; Gietz, U; Chabchoub, A; Hoffmann, N

2018-06-01

We report a theoretical derivation, an experimental observation and a numerical validation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schrödinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wave vector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. Our present results demonstrate that nonlinear domain walls do exist in the weakly nonlinear regime of general systems exhibiting dispersive waves.

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves

NASA Astrophysics Data System (ADS)

Tsitoura, F.; Gietz, U.; Chabchoub, A.; Hoffmann, N.

2018-06-01

We report a theoretical derivation, an experimental observation and a numerical validation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schrödinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wave vector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. Our present results demonstrate that nonlinear domain walls do exist in the weakly nonlinear regime of general systems exhibiting dispersive waves.

A Collection of Nonlinear Aircraft Simulations in MATLAB

NASA Technical Reports Server (NTRS)

Garza, Frederico R.; Morelli, Eugene A.

2003-01-01

Nonlinear six degree-of-freedom simulations for a variety of aircraft were created using MATLAB. Data for aircraft geometry, aerodynamic characteristics, mass / inertia properties, and engine characteristics were obtained from open literature publications documenting wind tunnel experiments and flight tests. Each nonlinear simulation was implemented within a common framework in MATLAB, and includes an interface with another commercially-available program to read pilot inputs and produce a three-dimensional (3-D) display of the simulated airplane motion. Aircraft simulations include the General Dynamics F-16 Fighting Falcon, Convair F-106B Delta Dart, Grumman F-14 Tomcat, McDonnell Douglas F-4 Phantom, NASA Langley Free-Flying Aircraft for Sub-scale Experimental Research (FASER), NASA HL-20 Lifting Body, NASA / DARPA X-31 Enhanced Fighter Maneuverability Demonstrator, and the Vought A-7 Corsair II. All nonlinear simulations and 3-D displays run in real time in response to pilot inputs, using contemporary desktop personal computer hardware. The simulations can also be run in batch mode. Each nonlinear simulation includes the full nonlinear dynamics of the bare airframe, with a scaled direct connection from pilot inputs to control surface deflections to provide adequate pilot control. Since all the nonlinear simulations are implemented entirely in MATLAB, user-defined control laws can be added in a straightforward fashion, and the simulations are portable across various computing platforms. Routines for trim, linearization, and numerical integration are included. The general nonlinear simulation framework and the specifics for each particular aircraft are documented.

Registering Cortical Surfaces Based on Whole-Brain Structural Connectivity and Continuous Connectivity Analysis

PubMed Central

Gutman, Boris; Leonardo, Cassandra; Jahanshad, Neda; Hibar, Derrek; Eschen-burg, Kristian; Nir, Talia; Villalon, Julio; Thompson, Paul

2014-01-01

We present a framework for registering cortical surfaces based on tractography-informed structural connectivity. We define connectivity as a continuous kernel on the product space of the cortex, and develop a method for estimating this kernel from tractography fiber models. Next, we formulate the kernel registration problem, and present a means to non-linearly register two brains’ continuous connectivity profiles. We apply theoretical results from operator theory to develop an algorithm for decomposing the connectome into its shared and individual components. Lastly, we extend two discrete connectivity measures to the continuous case, and apply our framework to 98 Alzheimer’s patients and controls. Our measures show significant differences between the two groups. PMID:25320795

Synchronism of nonlinear internal waves in a three-layer fluid

NASA Astrophysics Data System (ADS)

Talipova, Tatiana; Kurkina, Oxana; Terletska, Katerina; Rouvinskaya, Ekaterina

2017-04-01

In a three layer fluid with arbitrary layer widths and densities the existence of long internal solitons and breathers is proven theoretically and numerically, see for example (Pelinovsky et al., 2007; Lamb et al., 2007). The existence of breather-like waves of the intermediate length is also shown in numerical simulations (Terletska et al., 2016). For such waves conditions of synchronism are valid when a breather of the first mode and a soliton of the second mode move together with the same speed and form an asymmetric solitary wave of the second mode. The process of strong interaction of long nonlinear internal waves in the framework of three-layer Camassa-Choi model demonstrates the same effect (Jo&Choi, 2014; Barros, 2016). We analyze possible synchronism conditions for steady-state internal waves in a three-layer fluid analytically the framework of the Gardner equation, which is valid for long weakly nonlinear internal waves. The equations for synchronism conditions are derived and considered in terms of wave amplitudes, layer widths and density jumps. The configurations of three-layer fluid are found for which such a synchronism is possible. References: Barros R. Large amplitude internal waves in three-layer flows. The forth international conference "Nonlinear Waves - Theory and Applications", MS7, Beijing, China, June 25 - 28, 2016 Pelinovsky E., Polukhina O., Slunyaev A., Talipova T. Internal solitary waves // Chapter 4 in the book "Solitary Waves in Fluids". WIT Press. Southampton, Boston. 2007. P. 85 - 110. K. Terletska., K. T. Jung, T. Talipova, V. Maderich, I. Brovchenko and R. Grimshaw Internal breather-like wave generation by the second mode solitary wave interaction with a step// Physics of Fluids, 2016, accepted

Electric train energy consumption modeling

DOE PAGES

Wang, Jinghui; Rakha, Hesham A.

2017-05-01

For this paper we develop an electric train energy consumption modeling framework considering instantaneous regenerative braking efficiency in support of a rail simulation system. The model is calibrated with data from Portland, Oregon using an unconstrained non-linear optimization procedure, and validated using data from Chicago, Illinois by comparing model predictions against the National Transit Database (NTD) estimates. The results demonstrate that regenerative braking efficiency varies as an exponential function of the deceleration level, rather than an average constant as assumed in previous studies. The model predictions are demonstrated to be consistent with the NTD estimates, producing a predicted error ofmore » 1.87% and -2.31%. The paper demonstrates that energy recovery reduces the overall power consumption by 20% for the tested Chicago route. Furthermore, the paper demonstrates that the proposed modeling approach is able to capture energy consumption differences associated with train, route and operational parameters, and thus is applicable for project-level analysis. The model can be easily implemented in traffic simulation software, used in smartphone applications and eco-transit programs given its fast execution time and easy integration in complex frameworks.« less

Electric train energy consumption modeling

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

Wang, Jinghui; Rakha, Hesham A.

For this paper we develop an electric train energy consumption modeling framework considering instantaneous regenerative braking efficiency in support of a rail simulation system. The model is calibrated with data from Portland, Oregon using an unconstrained non-linear optimization procedure, and validated using data from Chicago, Illinois by comparing model predictions against the National Transit Database (NTD) estimates. The results demonstrate that regenerative braking efficiency varies as an exponential function of the deceleration level, rather than an average constant as assumed in previous studies. The model predictions are demonstrated to be consistent with the NTD estimates, producing a predicted error ofmore » 1.87% and -2.31%. The paper demonstrates that energy recovery reduces the overall power consumption by 20% for the tested Chicago route. Furthermore, the paper demonstrates that the proposed modeling approach is able to capture energy consumption differences associated with train, route and operational parameters, and thus is applicable for project-level analysis. The model can be easily implemented in traffic simulation software, used in smartphone applications and eco-transit programs given its fast execution time and easy integration in complex frameworks.« less

QED multi-dimensional vacuum polarization finite-difference solver

NASA Astrophysics Data System (ADS)

Carneiro, Pedro; Grismayer, Thomas; Silva, Luís; Fonseca, Ricardo

2015-11-01

The Extreme Light Infrastructure (ELI) is expected to deliver peak intensities of 1023 - 1024 W/cm2 allowing to probe nonlinear Quantum Electrodynamics (QED) phenomena in an unprecedented regime. Within the framework of QED, the second order process of photon-photon scattering leads to a set of extended Maxwell's equations [W. Heisenberg and H. Euler, Z. Physik 98, 714] effectively creating nonlinear polarization and magnetization terms that account for the nonlinear response of the vacuum. To model this in a self-consistent way, we present a multi dimensional generalized Maxwell equation finite difference solver with significantly enhanced dispersive properties, which was implemented in the OSIRIS particle-in-cell code [R.A. Fonseca et al. LNCS 2331, pp. 342-351, 2002]. We present a detailed numerical analysis of this electromagnetic solver. As an illustration of the properties of the solver, we explore several examples in extreme conditions. We confirm the theoretical prediction of vacuum birefringence of a pulse propagating in the presence of an intense static background field [arXiv:1301.4918 [quant-ph

Nonlinear image registration with bidirectional metric and reciprocal regularization

PubMed Central

Ying, Shihui; Li, Dan; Xiao, Bin; Peng, Yaxin; Du, Shaoyi; Xu, Meifeng

2017-01-01

Nonlinear registration is an important technique to align two different images and widely applied in medical image analysis. In this paper, we develop a novel nonlinear registration framework based on the diffeomorphic demons, where a reciprocal regularizer is introduced to assume that the deformation between two images is an exact diffeomorphism. In detail, first, we adopt a bidirectional metric to improve the symmetry of the energy functional, whose variables are two reciprocal deformations. Secondly, we slack these two deformations into two independent variables and introduce a reciprocal regularizer to assure the deformations being the exact diffeomorphism. Then, we utilize an alternating iterative strategy to decouple the model into two minimizing subproblems, where a new closed form for the approximate velocity of deformation is calculated. Finally, we compare our proposed algorithm on two data sets of real brain MR images with two relative and conventional methods. The results validate that our proposed method improves accuracy and robustness of registration, as well as the gained bidirectional deformations are actually reciprocal. PMID:28231342

Stochastic Stability of Nonlinear Sampled Data Systems with a Jump Linear Controller

NASA Technical Reports Server (NTRS)

Gonzalez, Oscar R.; Herencia-Zapana, Heber; Gray, W. Steven

2004-01-01

This paper analyzes the stability of a sampled- data system consisting of a deterministic, nonlinear, time- invariant, continuous-time plant and a stochastic, discrete- time, jump linear controller. The jump linear controller mod- els, for example, computer systems and communication net- works that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. To analyze stability, appropriate topologies are introduced for the signal spaces of the sampled- data system. With these topologies, the ideal sampling and zero-order-hold operators are shown to be measurable maps. This paper shows that the known equivalence between the stability of a deterministic, linear sampled-data system and its associated discrete-time representation as well as between a nonlinear sampled-data system and a linearized representation holds even in a stochastic framework.

Dissipative quantum trajectories in complex space: Damped harmonic oscillator

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

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation formore » the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.« less

Analysis and design of gain scheduled control systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Shamma, Jeff S.

1988-01-01

Gain scheduling, as an idea, is to construct a global feedback control system for a time varying and/or nonlinear plant from a collection of local time invariant designs. However in the absence of a sound analysis, these designs come with no guarantees on the robustness, performance, or even nominal stability of the overall gain schedule design. Such an analysis is presented for three types of gain scheduling situations: (1) a linear parameter varying plant scheduling on its exogenous parameters, (2) a nonlinear plant scheduling on a prescribed reference trajectory, and (3) a nonlinear plant scheduling on the current plant output. Conditions are given which guarantee that the stability, robustness, and performance properties of the fixed operating point designs carry over to the global gain scheduled designs, such as the scheduling variable should vary slowly and capture the plants nonlinearities. Finally, an alternate design framework is proposed which removes the slowing varying restriction or gain scheduled systems. This framework addresses some fundamental feedback issues previously ignored in standard gain.

A framework with nonlinear system model and nonparametric noise for gas turbine degradation state estimation

NASA Astrophysics Data System (ADS)

Hanachi, Houman; Liu, Jie; Banerjee, Avisekh; Chen, Ying

2015-06-01

Modern health management approaches for gas turbine engines (GTEs) aim to precisely estimate the health state of the GTE components to optimize maintenance decisions with respect to both economy and safety. In this research, we propose an advanced framework to identify the most likely degradation state of the turbine section in a GTE for prognostics and health management (PHM) applications. A novel nonlinear thermodynamic model is used to predict the performance parameters of the GTE given the measurements. The ratio between real efficiency of the GTE and simulated efficiency in the newly installed condition is defined as the health indicator and provided at each sequence. The symptom of nonrecoverable degradations in the turbine section, i.e. loss of turbine efficiency, is assumed to be the internal degradation state. A regularized auxiliary particle filter (RAPF) is developed to sequentially estimate the internal degradation state in nonuniform time sequences upon receiving sets of new measurements. The effectiveness of the technique is examined using the operating data over an entire time-between-overhaul cycle of a simple-cycle industrial GTE. The results clearly show the trend of degradation in the turbine section and the occasional fluctuations, which are well supported by the service history of the GTE. The research also suggests the efficacy of the proposed technique to monitor the health state of the turbine section of a GTE by implementing model-based PHM without the need for additional instrumentation.

Refined Models for an Analysis of Internal and External Buckling Modes of a Monolayer in a Layered Composite

NASA Astrophysics Data System (ADS)

Paimushin, V. N.

2017-11-01

For an analysis of internal and external buckling modes of a monolayer inside or at the periphery of a layered composite, refined geometrically nonlinear equations are constructed. They are based on modeling the monolayer as a thin plate interacting with binder layers at the points of boundary surfaces. The binder layer is modeled as a transversely soft foundation. It is assumed the foundations, previously compressed in the transverse direction (the first loading stage), have zero displacements of its external boundary surfaces at the second loading stage, but the contact interaction of the plate with foundations occurs without slippage or delamination. The deformation of the plate at a medium flexure is described by geometrically nonlinear relations of the classical plate theory based on the Kirchhoff-Love hypothesis (the first variant) or the refined Timoshenko model with account of the transverse shear and compression (the second variant). The foundation is described by linearized 3D equations of elasticity theory, which are simplified within the framework of the model of a transversely soft layer. Integrating the linearized equations along the transverse coordinate and satisfying the kinematic joining conditions of the plate with foundations, with account of their initial compression in the thickness direction, a system of 2D geometrically nonlinear equations and appropriate boundary conditions are derived. These equations describe the contact interaction between elements of the deformable system. The relations obtained are simplified for the case of a symmetric stacking sequence.

Cluster-based control of a separating flow over a smoothly contoured ramp

NASA Astrophysics Data System (ADS)

Kaiser, Eurika; Noack, Bernd R.; Spohn, Andreas; Cattafesta, Louis N.; Morzyński, Marek

2017-12-01

The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications. The proposed closed-loop control framework addresses a key issue of model-based control: The actuation effect often results from slow dynamics of strongly nonlinear interactions which the flow reveals at timescales much longer than the prediction horizon of any model. Hence, we employ a probabilistic approach based on a cluster-based discretization of the Liouville equation for the evolution of the probability distribution. The proposed methodology frames high-dimensional, nonlinear dynamics into low-dimensional, probabilistic, linear dynamics which considerably simplifies the optimal control problem while preserving nonlinear actuation mechanisms. The data-driven approach builds upon a state space discretization using a clustering algorithm which groups kinematically similar flow states into a low number of clusters. The temporal evolution of the probability distribution on this set of clusters is then described by a control-dependent Markov model. This Markov model can be used as predictor for the ergodic probability distribution for a particular control law. This probability distribution approximates the long-term behavior of the original system on which basis the optimal control law is determined. We examine how the approach can be used to improve the open-loop actuation in a separating flow dominated by Kelvin-Helmholtz shedding. For this purpose, the feature space, in which the model is learned, and the admissible control inputs are tailored to strongly oscillatory flows.

Data-driven model reference control of MIMO vertical tank systems with model-free VRFT and Q-Learning.

PubMed

Radac, Mircea-Bogdan; Precup, Radu-Emil; Roman, Raul-Cristian

2018-02-01

This paper proposes a combined Virtual Reference Feedback Tuning-Q-learning model-free control approach, which tunes nonlinear static state feedback controllers to achieve output model reference tracking in an optimal control framework. The novel iterative Batch Fitted Q-learning strategy uses two neural networks to represent the value function (critic) and the controller (actor), and it is referred to as a mixed Virtual Reference Feedback Tuning-Batch Fitted Q-learning approach. Learning convergence of the Q-learning schemes generally depends, among other settings, on the efficient exploration of the state-action space. Handcrafting test signals for efficient exploration is difficult even for input-output stable unknown processes. Virtual Reference Feedback Tuning can ensure an initial stabilizing controller to be learned from few input-output data and it can be next used to collect substantially more input-state data in a controlled mode, in a constrained environment, by compensating the process dynamics. This data is used to learn significantly superior nonlinear state feedback neural networks controllers for model reference tracking, using the proposed Batch Fitted Q-learning iterative tuning strategy, motivating the original combination of the two techniques. The mixed Virtual Reference Feedback Tuning-Batch Fitted Q-learning approach is experimentally validated for water level control of a multi input-multi output nonlinear constrained coupled two-tank system. Discussions on the observed control behavior are offered. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Principal dynamic mode analysis of neural mass model for the identification of epileptic states

NASA Astrophysics Data System (ADS)

Cao, Yuzhen; Jin, Liu; Su, Fei; Wang, Jiang; Deng, Bin

2016-11-01

The detection of epileptic seizures in Electroencephalography (EEG) signals is significant for the diagnosis and treatment of epilepsy. In this paper, in order to obtain characteristics of various epileptiform EEGs that may differentiate different states of epilepsy, the concept of Principal Dynamic Modes (PDMs) was incorporated to an autoregressive model framework. First, the neural mass model was used to simulate the required intracerebral EEG signals of various epileptiform activities. Then, the PDMs estimated from the nonlinear autoregressive Volterra models, as well as the corresponding Associated Nonlinear Functions (ANFs), were used for the modeling of epileptic EEGs. The efficient PDM modeling approach provided physiological interpretation of the system. Results revealed that the ANFs of the 1st and 2nd PDMs for the auto-regressive input exhibited evident differences among different states of epilepsy, where the ANFs of the sustained spikes' activity encountered at seizure onset or during a seizure were the most differentiable from that of the normal state. Therefore, the ANFs may be characteristics for the classification of normal and seizure states in the clinical detection of seizures and thus provide assistance for the diagnosis of epilepsy.

The effects of structure anisotropy on lensing observables in an exact general relativistic setting for precision cosmology

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

Troxel, M. A.; Ishak, Mustapha; Peel, Austin, E-mail: troxel@utdallas.edu, E-mail: mishak@utdallas.edu, E-mail: austin.peel@utdallas.edu

2014-03-01

The study of relativistic, higher order, and nonlinear effects has become necessary in recent years in the pursuit of precision cosmology. We develop and apply here a framework to study gravitational lensing in exact models in general relativity that are not restricted to homogeneity and isotropy, and where full nonlinearity and relativistic effects are thus naturally included. We apply the framework to a specific, anisotropic galaxy cluster model which is based on a modified NFW halo density profile and described by the Szekeres metric. We examine the effects of increasing levels of anisotropy in the galaxy cluster on lensing observablesmore » like the convergence and shear for various lensing geometries, finding a strong nonlinear response in both the convergence and shear for rays passing through anisotropic regions of the cluster. Deviation from the expected values in a spherically symmetric structure are asymmetric with respect to path direction and thus will persist as a statistical effect when averaged over some ensemble of such clusters. The resulting relative difference in various geometries can be as large as approximately 2%, 8%, and 24% in the measure of convergence (1−κ) for levels of anisotropy of 5%, 10%, and 15%, respectively, as a fraction of total cluster mass. For the total magnitude of shear, the relative difference can grow near the center of the structure to be as large as 15%, 32%, and 44% for the same levels of anisotropy, averaged over the two extreme geometries. The convergence is impacted most strongly for rays which pass in directions along the axis of maximum dipole anisotropy in the structure, while the shear is most strongly impacted for rays which pass in directions orthogonal to this axis, as expected. The rich features found in the lensing signal due to anisotropic substructure are nearly entirely lost when one treats the cluster in the traditional FLRW lensing framework. These effects due to anisotropic structures are thus likely to impact lensing measurements and must be fully examined in an era of precision cosmology.« less

Unified Framework for Deriving Simultaneous Equation Algorithms for Water Distribution Networks

EPA Science Inventory

The known formulations for steady state hydraulics within looped water distribution networks are re-derived in terms of linear and non-linear transformations of the original set of partly linear and partly non-linear equations that express conservation of mass and energy. All of ...

Frequency Preference Response to Oscillatory Inputs in Two-dimensional Neural Models: A Geometric Approach to Subthreshold Amplitude and Phase Resonance.

PubMed

Rotstein, Horacio G

2014-01-01

We investigate the dynamic mechanisms of generation of subthreshold and phase resonance in two-dimensional linear and linearized biophysical (conductance-based) models, and we extend our analysis to account for the effect of simple, but not necessarily weak, types of nonlinearities. Subthreshold resonance refers to the ability of neurons to exhibit a peak in their voltage amplitude response to oscillatory input currents at a preferred non-zero (resonant) frequency. Phase-resonance refers to the ability of neurons to exhibit a zero-phase (or zero-phase-shift) response to oscillatory input currents at a non-zero (phase-resonant) frequency. We adapt the classical phase-plane analysis approach to account for the dynamic effects of oscillatory inputs and develop a tool, the envelope-plane diagrams, that captures the role that conductances and time scales play in amplifying the voltage response at the resonant frequency band as compared to smaller and larger frequencies. We use envelope-plane diagrams in our analysis. We explain why the resonance phenomena do not necessarily arise from the presence of imaginary eigenvalues at rest, but rather they emerge from the interplay of the intrinsic and input time scales. We further explain why an increase in the time-scale separation causes an amplification of the voltage response in addition to shifting the resonant and phase-resonant frequencies. This is of fundamental importance for neural models since neurons typically exhibit a strong separation of time scales. We extend this approach to explain the effects of nonlinearities on both resonance and phase-resonance. We demonstrate that nonlinearities in the voltage equation cause amplifications of the voltage response and shifts in the resonant and phase-resonant frequencies that are not predicted by the corresponding linearized model. The differences between the nonlinear response and the linear prediction increase with increasing levels of the time scale separation between the voltage and the gating variable, and they almost disappear when both equations evolve at comparable rates. In contrast, voltage responses are almost insensitive to nonlinearities located in the gating variable equation. The method we develop provides a framework for the investigation of the preferred frequency responses in three-dimensional and nonlinear neuronal models as well as simple models of coupled neurons.

Quantitative diagnosis and prognosis framework for concrete degradation due to alkali-silica reaction

NASA Astrophysics Data System (ADS)

Mahadevan, Sankaran; Neal, Kyle; Nath, Paromita; Bao, Yanqing; Cai, Guowei; Orme, Peter; Adams, Douglas; Agarwal, Vivek

2017-02-01

This research is seeking to develop a probabilistic framework for health diagnosis and prognosis of aging concrete structures in nuclear power plants that are subjected to physical, chemical, environment, and mechanical degradation. The proposed framework consists of four elements: monitoring, data analytics, uncertainty quantification, and prognosis. The current work focuses on degradation caused by ASR (alkali-silica reaction). Controlled concrete specimens with reactive aggregate are prepared to develop accelerated ASR degradation. Different monitoring techniques — infrared thermography, digital image correlation (DIC), mechanical deformation measurements, nonlinear impact resonance acoustic spectroscopy (NIRAS), and vibro-acoustic modulation (VAM) — are studied for ASR diagnosis of the specimens. Both DIC and mechanical measurements record the specimen deformation caused by ASR gel expansion. Thermography is used to compare the thermal response of pristine and damaged concrete specimens and generate a 2-D map of the damage (i.e., ASR gel and cracked area), thus facilitating localization and quantification of damage. NIRAS and VAM are two separate vibration-based techniques that detect nonlinear changes in dynamic properties caused by the damage. The diagnosis results from multiple techniques are then fused using a Bayesian network, which also helps to quantify the uncertainty in the diagnosis. Prognosis of ASR degradation is then performed based on the current state of degradation obtained from diagnosis, by using a coupled thermo-hydro-mechanical-chemical (THMC) model for ASR degradation. This comprehensive approach of monitoring, data analytics, and uncertainty-quantified diagnosis and prognosis will facilitate the development of a quantitative, risk informed framework that will support continuous assessment and risk management of structural health and performance.

Reservoir Modeling by Data Integration via Intermediate Spaces and Artificial Intelligence Tools in MPS Simulation Frameworks

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

Ahmadi, Rouhollah, E-mail: rouhollahahmadi@yahoo.com; Khamehchi, Ehsan

Conditioning stochastic simulations are very important in many geostatistical applications that call for the introduction of nonlinear and multiple-point data in reservoir modeling. Here, a new methodology is proposed for the incorporation of different data types into multiple-point statistics (MPS) simulation frameworks. Unlike the previous techniques that call for an approximate forward model (filter) for integration of secondary data into geologically constructed models, the proposed approach develops an intermediate space where all the primary and secondary data are easily mapped onto. Definition of the intermediate space, as may be achieved via application of artificial intelligence tools like neural networks andmore » fuzzy inference systems, eliminates the need for using filters as in previous techniques. The applicability of the proposed approach in conditioning MPS simulations to static and geologic data is verified by modeling a real example of discrete fracture networks using conventional well-log data. The training patterns are well reproduced in the realizations, while the model is also consistent with the map of secondary data.« less

A new polytopic approach for the unknown input functional observer design

NASA Astrophysics Data System (ADS)

Bezzaoucha, Souad; Voos, Holger; Darouach, Mohamed

2018-03-01

In this paper, a constructive procedure to design Functional Unknown Input Observers for nonlinear continuous time systems is proposed under the Polytopic Takagi-Sugeno framework. An equivalent representation for the nonlinear model is achieved using the sector nonlinearity transformation. Applying the Lyapunov theory and the ? attenuation, linear matrix inequalities conditions are deduced which are solved for feasibility to obtain the observer design matrices. To cope with the effect of unknown inputs, classical approach of decoupling the unknown input for the linear case is used. Both algebraic and solver-based solutions are proposed (relaxed conditions). Necessary and sufficient conditions for the existence of the functional polytopic observer are given. For both approaches, the general and particular cases (measurable premise variables, full state estimation with full and reduced order cases) are considered and it is shown that the proposed conditions correspond to the one presented for standard linear case. To illustrate the proposed theoretical results, detailed numerical simulations are presented for a Quadrotor Aerial Robots Landing and a Waste Water Treatment Plant. Both systems are highly nonlinear and represented in a T-S polytopic form with unmeasurable premise variables and unknown inputs.

Hilbert complexes of nonlinear elasticity

NASA Astrophysics Data System (ADS)

Angoshtari, Arzhang; Yavari, Arash

2016-12-01

We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.

Self-consistent modelling of electrochemical strain microscopy in mixed ionic-electronic conductors: Nonlinear and dynamic regimes

DOE PAGES

Varenyk, O. V.; Silibin, M. V.; Kiselev, Dmitri A.; ...

2015-08-19

The frequency dependent Electrochemical Strain Microscopy (ESM) response of mixed ionic-electronic conductors is analyzed within the framework of Fermi-Dirac statistics and the Vegard law, accounting for steric effects from mobile donors. The emergence of dynamic charge waves and nonlinear deformation of the surface in response to bias applied to the tip-surface junction is numerically explored. The 2D maps of the strain and concentration distributions across the mixed ionic-electronic conductor and bias-induced surface displacements are calculated. Furthermore, the obtained numerical results can be applied to quantify the ESM response of Li-based solid electrolytes, materials with resistive switching, and electroactive ferroelectric polymers,more » which are of potential interest for flexible and high-density non-volatile memory devices.« less

Self-consistent modelling of electrochemical strain microscopy in mixed ionic-electronic conductors: Nonlinear and dynamic regimes

NASA Astrophysics Data System (ADS)

Varenyk, O. V.; Silibin, M. V.; Kiselev, D. A.; Eliseev, E. A.; Kalinin, S. V.; Morozovska, A. N.

2015-08-01

The frequency dependent Electrochemical Strain Microscopy (ESM) response of mixed ionic-electronic conductors is analyzed within the framework of Fermi-Dirac statistics and the Vegard law, accounting for steric effects from mobile donors. The emergence of dynamic charge waves and nonlinear deformation of the surface in response to bias applied to the tip-surface junction is numerically explored. The 2D maps of the strain and concentration distributions across the mixed ionic-electronic conductor and bias-induced surface displacements are calculated. The obtained numerical results can be applied to quantify the ESM response of Li-based solid electrolytes, materials with resistive switching, and electroactive ferroelectric polymers, which are of potential interest for flexible and high-density non-volatile memory devices.

Interaction between two point-like charges in nonlinear electrostatics

NASA Astrophysics Data System (ADS)

Breev, A. I.; Shabad, A. E.

2018-01-01

We consider two point-like charges in electrostatic interaction within the framework of a nonlinear model, associated with QED, that provides finiteness of their field energy. We find the common field of the two charges in a dipole-like approximation, where the separation between them R is much smaller than the observation distance r : with the linear accuracy with respect to the ratio R / r, and in the opposite approximation, where R≫ r, up to the term quadratic in the ratio r / R. The consideration proposes the law a+b R^{1/3} for the energy, when the charges are close to one another, R→ 0. This leads to the singularity of the force between them to be R^{-2/3}, which is weaker than the Coulomb law, R^{-2}.

A Novel Approach of Understanding and Incorporating Error of Chemical Transport Models into a Geostatistical Framework

NASA Astrophysics Data System (ADS)

Reyes, J.; Vizuete, W.; Serre, M. L.; Xu, Y.

2015-12-01

The EPA employs a vast monitoring network to measure ambient PM2.5 concentrations across the United States with one of its goals being to quantify exposure within the population. However, there are several areas of the country with sparse monitoring spatially and temporally. One means to fill in these monitoring gaps is to use PM2.5 modeled estimates from Chemical Transport Models (CTMs) specifically the Community Multi-scale Air Quality (CMAQ) model. CMAQ is able to provide complete spatial coverage but is subject to systematic and random error due to model uncertainty. Due to the deterministic nature of CMAQ, often these uncertainties are not quantified. Much effort is employed to quantify the efficacy of these models through different metrics of model performance. Currently evaluation is specific to only locations with observed data. Multiyear studies across the United States are challenging because the error and model performance of CMAQ are not uniform over such large space/time domains. Error changes regionally and temporally. Because of the complex mix of species that constitute PM2.5, CMAQ error is also a function of increasing PM2.5 concentration. To address this issue we introduce a model performance evaluation for PM2.5 CMAQ that is regionalized and non-linear. This model performance evaluation leads to error quantification for each CMAQ grid. Areas and time periods of error being better qualified. The regionalized error correction approach is non-linear and is therefore more flexible at characterizing model performance than approaches that rely on linearity assumptions and assume homoscedasticity of CMAQ predictions errors. Corrected CMAQ data are then incorporated into the modern geostatistical framework of Bayesian Maximum Entropy (BME). Through cross validation it is shown that incorporating error-corrected CMAQ data leads to more accurate estimates than just using observed data by themselves.

Dark solitons in mode-locked lasers.

PubMed

Ablowitz, Mark J; Horikis, Theodoros P; Nixon, Sean D; Frantzeskakis, Dimitri J

2011-03-15

Dark soliton formation in mode-locked lasers is investigated by means of a power-energy saturation model that incorporates gain and filtering saturated with energy, and loss saturated with power. It is found that general initial conditions evolve (mode-lock) into dark solitons under appropriate requirements also met in experimental observations. The resulting pulses are essentially dark solitons of the unperturbed nonlinear Schrödinger equation. Notably, the same framework also describes bright pulses in anomalous and normally dispersive lasers.

Finite‐fault Bayesian inversion of teleseismic body waves

USGS Publications Warehouse

Clayton, Brandon; Hartzell, Stephen; Moschetti, Morgan P.; Minson, Sarah E.

2017-01-01

Inverting geophysical data has provided fundamental information about the behavior of earthquake rupture. However, inferring kinematic source model parameters for finite‐fault ruptures is an intrinsically underdetermined problem (the problem of nonuniqueness), because we are restricted to finite noisy observations. Although many studies use least‐squares techniques to make the finite‐fault problem tractable, these methods generally lack the ability to apply non‐Gaussian error analysis and the imposition of nonlinear constraints. However, the Bayesian approach can be employed to find a Gaussian or non‐Gaussian distribution of all probable model parameters, while utilizing nonlinear constraints. We present case studies to quantify the resolving power and associated uncertainties using only teleseismic body waves in a Bayesian framework to infer the slip history for a synthetic case and two earthquakes: the 2011 Mw 7.1 Van, east Turkey, earthquake and the 2010 Mw 7.2 El Mayor–Cucapah, Baja California, earthquake. In implementing the Bayesian method, we further present two distinct solutions to investigate the uncertainties by performing the inversion with and without velocity structure perturbations. We find that the posterior ensemble becomes broader when including velocity structure variability and introduces a spatial smearing of slip. Using the Bayesian framework solely on teleseismic body waves, we find rake is poorly constrained by the observations and rise time is poorly resolved when slip amplitude is low.

A Bayesian estimation of a stochastic predator-prey model of economic fluctuations

NASA Astrophysics Data System (ADS)

Dibeh, Ghassan; Luchinsky, Dmitry G.; Luchinskaya, Daria D.; Smelyanskiy, Vadim N.

2007-06-01

In this paper, we develop a Bayesian framework for the empirical estimation of the parameters of one of the best known nonlinear models of the business cycle: The Marx-inspired model of a growth cycle introduced by R. M. Goodwin. The model predicts a series of closed cycles representing the dynamics of labor's share and the employment rate in the capitalist economy. The Bayesian framework is used to empirically estimate a modified Goodwin model. The original model is extended in two ways. First, we allow for exogenous periodic variations of the otherwise steady growth rates of the labor force and productivity per worker. Second, we allow for stochastic variations of those parameters. The resultant modified Goodwin model is a stochastic predator-prey model with periodic forcing. The model is then estimated using a newly developed Bayesian estimation method on data sets representing growth cycles in France and Italy during the years 1960-2005. Results show that inference of the parameters of the stochastic Goodwin model can be achieved. The comparison of the dynamics of the Goodwin model with the inferred values of parameters demonstrates quantitative agreement with the growth cycle empirical data.

Data-driven discovery of partial differential equations.

PubMed

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

2017-04-01

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

Advances in nowcasting influenza-like illness rates using search query logs

NASA Astrophysics Data System (ADS)

Lampos, Vasileios; Miller, Andrew C.; Crossan, Steve; Stefansen, Christian

2015-08-01

User-generated content can assist epidemiological surveillance in the early detection and prevalence estimation of infectious diseases, such as influenza. Google Flu Trends embodies the first public platform for transforming search queries to indications about the current state of flu in various places all over the world. However, the original model significantly mispredicted influenza-like illness rates in the US during the 2012-13 flu season. In this work, we build on the previous modeling attempt, proposing substantial improvements. Firstly, we investigate the performance of a widely used linear regularized regression solver, known as the Elastic Net. Then, we expand on this model by incorporating the queries selected by the Elastic Net into a nonlinear regression framework, based on a composite Gaussian Process. Finally, we augment the query-only predictions with an autoregressive model, injecting prior knowledge about the disease. We assess predictive performance using five consecutive flu seasons spanning from 2008 to 2013 and qualitatively explain certain shortcomings of the previous approach. Our results indicate that a nonlinear query modeling approach delivers the lowest cumulative nowcasting error, and also suggest that query information significantly improves autoregressive inferences, obtaining state-of-the-art performance.

Advances in nowcasting influenza-like illness rates using search query logs.

PubMed

Lampos, Vasileios; Miller, Andrew C; Crossan, Steve; Stefansen, Christian

2015-08-03

User-generated content can assist epidemiological surveillance in the early detection and prevalence estimation of infectious diseases, such as influenza. Google Flu Trends embodies the first public platform for transforming search queries to indications about the current state of flu in various places all over the world. However, the original model significantly mispredicted influenza-like illness rates in the US during the 2012-13 flu season. In this work, we build on the previous modeling attempt, proposing substantial improvements. Firstly, we investigate the performance of a widely used linear regularized regression solver, known as the Elastic Net. Then, we expand on this model by incorporating the queries selected by the Elastic Net into a nonlinear regression framework, based on a composite Gaussian Process. Finally, we augment the query-only predictions with an autoregressive model, injecting prior knowledge about the disease. We assess predictive performance using five consecutive flu seasons spanning from 2008 to 2013 and qualitatively explain certain shortcomings of the previous approach. Our results indicate that a nonlinear query modeling approach delivers the lowest cumulative nowcasting error, and also suggest that query information significantly improves autoregressive inferences, obtaining state-of-the-art performance.

An Optimization Framework for Dynamic Hybrid Energy Systems

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

Wenbo Du; Humberto E Garcia; Christiaan J.J. Paredis

A computational framework for the efficient analysis and optimization of dynamic hybrid energy systems (HES) is developed. A microgrid system with multiple inputs and multiple outputs (MIMO) is modeled using the Modelica language in the Dymola environment. The optimization loop is implemented in MATLAB, with the FMI Toolbox serving as the interface between the computational platforms. Two characteristic optimization problems are selected to demonstrate the methodology and gain insight into the system performance. The first is an unconstrained optimization problem that optimizes the dynamic properties of the battery, reactor and generator to minimize variability in the HES. The second problemmore » takes operating and capital costs into consideration by imposing linear and nonlinear constraints on the design variables. The preliminary optimization results obtained in this study provide an essential step towards the development of a comprehensive framework for designing HES.« less

Numerical analysis of behaviour of cross laminated timber (CLT) in blast loading

NASA Astrophysics Data System (ADS)

Šliseris, J.; Gaile, L.; Pakrastiņš, L.

2017-10-01

A non-linear computation model for CLT wall element that includes explicit dynamics and composite damage constitutive model was developed. The numerical model was compared with classical beam theory and it turned out that shear wood layer has significant shear deformations that must be taken into account when designing CLT. It turned out that impulse duration time has a major effect on the strength of CLT. Special attention must be payed when designing CLT wall, window and door architectural system in order to guarantee the robustness of structure. The proposed numerical modelling framework can be used when designing CLT buildings that can be affected by blast loading, whilst structural robustness must be guaranteed.

Omnibus risk assessment via accelerated failure time kernel machine modeling.

PubMed

Sinnott, Jennifer A; Cai, Tianxi

2013-12-01

Integrating genomic information with traditional clinical risk factors to improve the prediction of disease outcomes could profoundly change the practice of medicine. However, the large number of potential markers and possible complexity of the relationship between markers and disease make it difficult to construct accurate risk prediction models. Standard approaches for identifying important markers often rely on marginal associations or linearity assumptions and may not capture non-linear or interactive effects. In recent years, much work has been done to group genes into pathways and networks. Integrating such biological knowledge into statistical learning could potentially improve model interpretability and reliability. One effective approach is to employ a kernel machine (KM) framework, which can capture nonlinear effects if nonlinear kernels are used (Scholkopf and Smola, 2002; Liu et al., 2007, 2008). For survival outcomes, KM regression modeling and testing procedures have been derived under a proportional hazards (PH) assumption (Li and Luan, 2003; Cai, Tonini, and Lin, 2011). In this article, we derive testing and prediction methods for KM regression under the accelerated failure time (AFT) model, a useful alternative to the PH model. We approximate the null distribution of our test statistic using resampling procedures. When multiple kernels are of potential interest, it may be unclear in advance which kernel to use for testing and estimation. We propose a robust Omnibus Test that combines information across kernels, and an approach for selecting the best kernel for estimation. The methods are illustrated with an application in breast cancer. © 2013, The International Biometric Society.

Statistically accurate low-order models for uncertainty quantification in turbulent dynamical systems.

PubMed

Sapsis, Themistoklis P; Majda, Andrew J

2013-08-20

A framework for low-order predictive statistical modeling and uncertainty quantification in turbulent dynamical systems is developed here. These reduced-order, modified quasilinear Gaussian (ROMQG) algorithms apply to turbulent dynamical systems in which there is significant linear instability or linear nonnormal dynamics in the unperturbed system and energy-conserving nonlinear interactions that transfer energy from the unstable modes to the stable modes where dissipation occurs, resulting in a statistical steady state; such turbulent dynamical systems are ubiquitous in geophysical and engineering turbulence. The ROMQG method involves constructing a low-order, nonlinear, dynamical system for the mean and covariance statistics in the reduced subspace that has the unperturbed statistics as a stable fixed point and optimally incorporates the indirect effect of non-Gaussian third-order statistics for the unperturbed system in a systematic calibration stage. This calibration procedure is achieved through information involving only the mean and covariance statistics for the unperturbed equilibrium. The performance of the ROMQG algorithm is assessed on two stringent test cases: the 40-mode Lorenz 96 model mimicking midlatitude atmospheric turbulence and two-layer baroclinic models for high-latitude ocean turbulence with over 125,000 degrees of freedom. In the Lorenz 96 model, the ROMQG algorithm with just a single mode captures the transient response to random or deterministic forcing. For the baroclinic ocean turbulence models, the inexpensive ROMQG algorithm with 252 modes, less than 0.2% of the total, captures the nonlinear response of the energy, the heat flux, and even the one-dimensional energy and heat flux spectra.

Chaotic inflation from nonlinear sigma models in supergravity

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

Hellerman, Simeon; Kehayias, John; Yanagida, Tsutomu T.

2015-02-11

We present a common solution to the puzzles of the light Higgs or quark masses and the need for a shift symmetry and large field values in high scale chaotic inflation. One way to protect, for example, the Higgs from a large supersymmetric mass term is if it is the Nambu–Goldstone boson (NGB) of a nonlinear sigma model. However, it is well known that nonlinear sigma models (NLSMs) with nontrivial Kähler transformations are problematic to couple to supergravity. An additional field is necessary to make theKähler potential of the NLSM invariant in supergravity. This field must have a shift symmetrymore » — making it a candidate for the inflaton (or axion). We give an explicit example of such a model for the coset space SU(3)/SU(2) × U(1), with the Higgs as the NGB, including breaking the inflaton’s shift symmetry and producing a chaotic inflation potential. This construction can also be applied to other models, such as one based on E₇/SO(10) × U(1) × U(1) which incorporates the first two generations of (light) quarks as the Nambu–Goldstone multiplets, and has an axion in addition to the inflaton. Along the way we clarify and connect previous work on understanding NLSMs in supergravity and the origin of the extra field (which is the inflaton here), including a connection to Witten–Bagger quantization. This framework has wide applications to model building; a light particle from a NLSM requires, in supergravity, exactly the structure for chaotic inflaton or an axion« less

A joint modeling and estimation method for multivariate longitudinal data with mixed types of responses to analyze physical activity data generated by accelerometers.

PubMed

Li, Haocheng; Zhang, Yukun; Carroll, Raymond J; Keadle, Sarah Kozey; Sampson, Joshua N; Matthews, Charles E

2017-11-10

A mixed effect model is proposed to jointly analyze multivariate longitudinal data with continuous, proportion, count, and binary responses. The association of the variables is modeled through the correlation of random effects. We use a quasi-likelihood type approximation for nonlinear variables and transform the proposed model into a multivariate linear mixed model framework for estimation and inference. Via an extension to the EM approach, an efficient algorithm is developed to fit the model. The method is applied to physical activity data, which uses a wearable accelerometer device to measure daily movement and energy expenditure information. Our approach is also evaluated by a simulation study. Copyright © 2017 John Wiley & Sons, Ltd.

Qualitative dynamical analysis of chaotic plasma perturbations model

NASA Astrophysics Data System (ADS)

Elsadany, A. A.; Elsonbaty, Amr; Agiza, H. N.

2018-06-01

In this work, an analytical framework to understand nonlinear dynamics of plasma perturbations model is introduced. In particular, we analyze the model presented by Constantinescu et al. [20] which consists of three coupled ODEs and contains three parameters. The basic dynamical properties of the system are first investigated by the ways of bifurcation diagrams, phase portraits and Lyapunov exponents. Then, the normal form technique and perturbation methods are applied so as to the different types of bifurcations that exist in the model are investigated. It is proved that pitcfork, Bogdanov-Takens, Andronov-Hopf bifurcations, degenerate Hopf and homoclinic bifurcation can occur in phase space of the model. Also, the model can exhibit quasiperiodicity and chaotic behavior. Numerical simulations confirm our theoretical analytical results.

Thermodynamic Model of Spatial Memory

NASA Astrophysics Data System (ADS)

Kaufman, Miron; Allen, P.

1998-03-01

We develop and test a thermodynamic model of spatial memory. Our model is an application of statistical thermodynamics to cognitive science. It is related to applications of the statistical mechanics framework in parallel distributed processes research. Our macroscopic model allows us to evaluate an entropy associated with spatial memory tasks. We find that older adults exhibit higher levels of entropy than younger adults. Thurstone's Law of Categorical Judgment, according to which the discriminal processes along the psychological continuum produced by presentations of a single stimulus are normally distributed, is explained by using a Hooke spring model of spatial memory. We have also analyzed a nonlinear modification of the ideal spring model of spatial memory. This work is supported by NIH/NIA grant AG09282-06.

The influence of the enhanced vector meson sector on the properties of the matter of neutron stars.

PubMed

Bednarek, Ilona; Manka, Ryszard; Pienkos, Monika

2014-01-01

This paper gives an overview of the model of a neutron star with non-zero strangeness constructed within the framework of the nonlinear realization of the chiral SU(3)L x SU(3)R symmetry. The emphasis is put on the physical properties of the matter of a neutron star as well as on its internal structure. The obtained solution is particularly aimed at the problem of the construction of a theoretical model of a neutron star matter with hyperons that will give high value of the maximum mass.

Polyelectrolyte hydrogel instabilities in ionic solutions

NASA Astrophysics Data System (ADS)

English, Anthony E.; Tanaka, Toyoichi; Edelman, Elazer R.

1996-12-01

The phase behavior of polyelectrolyte hydrogels has been examined as a function of relative charge composition, bath salt concentration, and solvent quality. Nonlinear swelling instabilities of 2-hydroxyethyl methacrylate (HEMA) and methacrylic acid (MAAc) copolymer hydrogels manifested themselves as discontinuous first order swelling transitions as a function of bath salt concentration. A modified Flory-Huggins model was used to describe the regions of instability when bath salt concentration and solvent quality are considered as control variables. The role of ion dissociation equilibrium in the change from local or smooth transitions to nonlocal or discontinuous swelling transitions is illustrated within the framework of our model.

Intrinsic Bayesian Active Contours for Extraction of Object Boundaries in Images

PubMed Central

Srivastava, Anuj

2010-01-01

We present a framework for incorporating prior information about high-probability shapes in the process of contour extraction and object recognition in images. Here one studies shapes as elements of an infinite-dimensional, non-linear quotient space, and statistics of shapes are defined and computed intrinsically using differential geometry of this shape space. Prior models on shapes are constructed using probability distributions on tangent bundles of shape spaces. Similar to the past work on active contours, where curves are driven by vector fields based on image gradients and roughness penalties, we incorporate the prior shape knowledge in the form of vector fields on curves. Through experimental results, we demonstrate the use of prior shape models in the estimation of object boundaries, and their success in handling partial obscuration and missing data. Furthermore, we describe the use of this framework in shape-based object recognition or classification. PMID:21076692

Emergent universe with wormholes in massive gravity

NASA Astrophysics Data System (ADS)

Paul, B. C.; Majumdar, A. S.

2018-03-01

An emergent universe (EU) scenario is proposed to obtain a universe free from big-bang singularity. In this framework the present universe emerged from a static Einstein universe phase in the infinite past. A flat EU scenario is found to exist in Einstein’s gravity with a non-linear equation of state (EoS). It has been shown subsequently that a physically realistic EU model can be obtained considering cosmic fluid composed of interacting fluids with a non-linear equation of state. It results a viable cosmological model accommodating both early inflation and present accelerating phases. In the present paper, the origin of an initial static Einstein universe needed in the EU model is explored in a massive gravity theory which subsequently emerged to be a dynamically evolving universe. A new gravitational instanton solution in a flat universe is obtained in the massive gravity theory which is a dynamical wormhole that might play an important role in realizing the origin of the initial state of the emergent universe. The emergence of a Lorentzian universe from a Euclidean gravity is understood by a Wick rotation τ = i t . A universe with radiation at the beginning finally transits into the present observed universe with a non-linear EoS as the interactions among the fluids set in. Thus a viable flat EU scenario where the universe stretches back into time infinitely, with no big bang is permitted in a massive gravity.

A discrete mesoscopic particle model of the mechanics of a multi-constituent arterial wall.

PubMed

Witthoft, Alexandra; Yazdani, Alireza; Peng, Zhangli; Bellini, Chiara; Humphrey, Jay D; Karniadakis, George Em

2016-01-01

Blood vessels have unique properties that allow them to function together within a complex, self-regulating network. The contractile capacity of the wall combined with complex mechanical properties of the extracellular matrix enables vessels to adapt to changes in haemodynamic loading. Homogenized phenomenological and multi-constituent, structurally motivated continuum models have successfully captured these mechanical properties, but truly describing intricate microstructural details of the arterial wall may require a discrete framework. Such an approach would facilitate modelling interactions between or the separation of layers of the wall and would offer the advantage of seamless integration with discrete models of complex blood flow. We present a discrete particle model of a multi-constituent, nonlinearly elastic, anisotropic arterial wall, which we develop using the dissipative particle dynamics method. Mimicking basic features of the microstructure of the arterial wall, the model comprises an elastin matrix having isotropic nonlinear elastic properties plus anisotropic fibre reinforcement that represents the stiffer collagen fibres of the wall. These collagen fibres are distributed evenly and are oriented in four directions, symmetric to the vessel axis. Experimental results from biaxial mechanical tests of an artery are used for model validation, and a delamination test is simulated to demonstrate the new capabilities of the model. © 2016 The Author(s).

Low-rank regularization for learning gene expression programs.

PubMed

Ye, Guibo; Tang, Mengfan; Cai, Jian-Feng; Nie, Qing; Xie, Xiaohui

2013-01-01

Learning gene expression programs directly from a set of observations is challenging due to the complexity of gene regulation, high noise of experimental measurements, and insufficient number of experimental measurements. Imposing additional constraints with strong and biologically motivated regularizations is critical in developing reliable and effective algorithms for inferring gene expression programs. Here we propose a new form of regulation that constrains the number of independent connectivity patterns between regulators and targets, motivated by the modular design of gene regulatory programs and the belief that the total number of independent regulatory modules should be small. We formulate a multi-target linear regression framework to incorporate this type of regulation, in which the number of independent connectivity patterns is expressed as the rank of the connectivity matrix between regulators and targets. We then generalize the linear framework to nonlinear cases, and prove that the generalized low-rank regularization model is still convex. Efficient algorithms are derived to solve both the linear and nonlinear low-rank regularized problems. Finally, we test the algorithms on three gene expression datasets, and show that the low-rank regularization improves the accuracy of gene expression prediction in these three datasets.

Data-Driven Modeling and Prediction of Arctic Sea Ice

NASA Astrophysics Data System (ADS)

Kondrashov, Dmitri; Chekroun, Mickael; Ghil, Michael

2016-04-01

We present results of data-driven predictive analyses of sea ice over the main Arctic regions. Our approach relies on the Multilayer Stochastic Modeling (MSM) framework of Kondrashov, Chekroun and Ghil [Physica D, 2015] and it leads to probabilistic prognostic models of sea ice concentration (SIC) anomalies on seasonal time scales. This approach is applied to monthly time series of state-of-the-art data-adaptive decompositions of SIC and selected climate variables over the Arctic. We evaluate the predictive skill of MSM models by performing retrospective forecasts with "no-look ahead" for up to 6-months ahead. It will be shown in particular that the memory effects included intrinsically in the formulation of our non-Markovian MSM models allow for improvements of the prediction skill of large-amplitude SIC anomalies in certain Arctic regions on the one hand, and of September Sea Ice Extent, on the other. Further improvements allowed by the MSM framework will adopt a nonlinear formulation and explore next-generation data-adaptive decompositions, namely modification of Principal Oscillation Patterns (POPs) and rotated Multichannel Singular Spectrum Analysis (M-SSA).

A model for finite-deformation nonlinear thermomechanical response of single crystal copper under shock conditions

NASA Astrophysics Data System (ADS)

Luscher, Darby J.; Bronkhorst, Curt A.; Alleman, Coleman N.; Addessio, Francis L.

2013-09-01

A physically consistent framework for combining pressure-volume-temperature equations of state with crystal plasticity models is developed for the application of modeling the response of single and polycrystals under shock conditions. The particular model is developed for copper, thus the approach focuses on crystals of cubic symmetry although many of the concepts in the approach are applicable to crystals of lower symmetry. We employ a multiplicative decomposition of the deformation gradient into isochoric elastic, thermoelastic dilation, and plastic parts leading to a definition of isochoric elastic Green-Lagrange strain. This finite deformation kinematic decomposition enables a decomposition of Helmholtz free-energy into terms reflecting dilatational thermoelasticity, strain energy due to long-range isochoric elastic deformation of the lattice and a term reflecting energy stored in short range elastic lattice deformation due to evolving defect structures. A model for the single crystal response of copper is implemented consistent with the framework into a three-dimensional Lagrangian finite element code. Simulations exhibit favorable agreement with single and bicrystal experimental data for shock pressures ranging from 3 to 110 GPa.

The water-energy nexus at water supply and its implications on the integrated water and energy management.

PubMed

Khalkhali, Masoumeh; Westphal, Kirk; Mo, Weiwei

2018-09-15

Water and energy are highly interdependent in the modern world, and hence, it is important to understand their constantly changing and nonlinear interconnections to inform the integrated management of water and energy. In this study, a hydrologic model, a water systems model, and an energy model were developed and integrated into a system dynamics modeling framework. This framework was then applied to a water supply system in the northeast US to capture its water-energy interactions under a set of future population, climate, and system operation scenarios. A hydrologic model was first used to simulate the system's hydrologic inflows and outflows under temperature and precipitation changes on a weekly-basis. A water systems model that combines the hydrologic model and management rules (e.g., water release and transfer) was then developed to dynamically simulate the system's water storage and water head. Outputs from the water systems model were used in the energy model to estimate hydropower generation. It was found that critical water-energy synergies and tradeoffs exist, and there is a possibility for integrated water and energy management to achieve better outcomes. This analysis also shows the importance of a holistic understanding of the systems as a whole, which would allow utility managers to make proactive long-term management decisions. The modeling framework is generalizable to other water supply systems with hydropower generation capacities to inform the integrated management of water and energy resources. Copyright © 2018 Elsevier B.V. All rights reserved.

Nonlinear extension of a hemodynamic linear model for coherent hemodynamics spectroscopy.

PubMed

Sassaroli, Angelo; Kainerstorfer, Jana M; Fantini, Sergio

2016-01-21

In this work, we are proposing an extension of a recent hemodynamic model (Fantini, 2014a), which was developed within the framework of a novel approach to the study of tissue hemodynamics, named coherent hemodynamics spectroscopy (CHS). The previous hemodynamic model, from a signal processing viewpoint, treats the tissue microvasculature as a linear time-invariant system, and considers changes of blood volume, capillary blood flow velocity and the rate of oxygen diffusion as inputs, and the changes of oxy-, deoxy-, and total hemoglobin concentrations (measured in near infrared spectroscopy) as outputs. The model has been used also as a forward solver in an inversion procedure to retrieve quantitative parameters that assess physiological and biological processes such as microcirculation, cerebral autoregulation, tissue metabolic rate of oxygen, and oxygen extraction fraction. Within the assumption of "small" capillary blood flow velocity oscillations the model showed that the capillary and venous compartments "respond" to this input as low pass filters, characterized by two distinct impulse response functions. In this work, we do not make the assumption of "small" perturbations of capillary blood flow velocity by solving without approximations the partial differential equation that governs the spatio-temporal behavior of hemoglobin saturation in capillary and venous blood. Preliminary comparison between the linear time-invariant model and the extended model (here identified as nonlinear model) are shown for the relevant parameters measured in CHS as a function of the oscillation frequency (CHS spectra). We have found that for capillary blood flow velocity oscillations with amplitudes up to 10% of the baseline value (which reflect typical scenarios in CHS), the discrepancies between CHS spectra obtained with the linear and nonlinear models are negligible. For larger oscillations (~50%) the linear and nonlinear models yield CHS spectra with differences within typical experimental errors, but further investigation is needed to assess the effect of these differences. Flow oscillations larger than 10-20% are not typically induced in CHS; therefore, the results presented in this work indicate that a linear hemodynamic model, combined with a method to elicit controlled hemodynamic oscillations (as done for CHS), is appropriate for the quantitative assessment of cerebral microcirculation. Copyright © 2015 Elsevier Ltd. All rights reserved.

Expectation propagation for large scale Bayesian inference of non-linear molecular networks from perturbation data.

PubMed

Narimani, Zahra; Beigy, Hamid; Ahmad, Ashar; Masoudi-Nejad, Ali; Fröhlich, Holger

2017-01-01

Inferring the structure of molecular networks from time series protein or gene expression data provides valuable information about the complex biological processes of the cell. Causal network structure inference has been approached using different methods in the past. Most causal network inference techniques, such as Dynamic Bayesian Networks and ordinary differential equations, are limited by their computational complexity and thus make large scale inference infeasible. This is specifically true if a Bayesian framework is applied in order to deal with the unavoidable uncertainty about the correct model. We devise a novel Bayesian network reverse engineering approach using ordinary differential equations with the ability to include non-linearity. Besides modeling arbitrary, possibly combinatorial and time dependent perturbations with unknown targets, one of our main contributions is the use of Expectation Propagation, an algorithm for approximate Bayesian inference over large scale network structures in short computation time. We further explore the possibility of integrating prior knowledge into network inference. We evaluate the proposed model on DREAM4 and DREAM8 data and find it competitive against several state-of-the-art existing network inference methods.

Dielectric elastomer peristaltic pump module with finite deformation

NASA Astrophysics Data System (ADS)

Mao, Guoyong; Huang, Xiaoqiang; Liu, Junjie; Li, Tiefeng; Qu, Shaoxing; Yang, Wei

2015-07-01

Inspired by various peristaltic structures existing in nature, several bionic peristaltic actuators have been developed. In this study, we propose a novel dielectric elastomer peristaltic pump consisting of short tubular modules, with the saline solution as the electrodes. We investigate the performance of this soft pump module under hydraulic pressure and voltage via experiments and an analytical model based on nonlinear field theory. It is observed that the individual pump module undergoes finite deformation and may experience electromechanical instability during operations. The driving pressure and displaced volume of the peristaltic pump module can be modulated by applied voltage. The efficiency of the pump module is enhanced by alternating current voltage, which can suppress the electromechanical pull-in instability. An analytical model is developed within the framework of the nonlinear field theory, and its predictive capacity is checked by experimental observations. The effects of the prestretch, aspect ratio, and voltage on the performance of the pump modules are characterized by the analytical model. This work can guide the designs of soft active peristaltic pumps in the field of artificial organs and industrial conveying systems.

A Lagrangian effective field theory

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

Vlah, Zvonimir; White, Martin; Aviles, Alejandro

We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.« less

A Lagrangian effective field theory

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

Vlah, Zvonimir; White, Martin; Aviles, Alejandro, E-mail: zvlah@stanford.edu, E-mail: mwhite@berkeley.edu, E-mail: aviles@berkeley.edu

We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The 'new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. All the perturbative models fare better than linear theory.« less

A Lagrangian effective field theory

DOE PAGES

Vlah, Zvonimir; White, Martin; Aviles, Alejandro

2015-09-02

We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.« less

Nonlinear Fano interferences in open quantum systems: An exactly solvable model

NASA Astrophysics Data System (ADS)

Finkelstein-Shapiro, Daniel; Calatayud, Monica; Atabek, Osman; Mujica, Vladimiro; Keller, Arne

2016-06-01

We obtain an explicit solution for the stationary-state populations of a dissipative Fano model, where a discrete excited state is coupled to a continuum set of states; both excited sets of states are reachable by photoexcitation from the ground state. The dissipative dynamic is described by a Liouville equation in Lindblad form and the field intensity can take arbitrary values within the model. We show that the population of the continuum states as a function of laser frequency can always be expressed as a Fano profile plus a Lorentzian function with effective parameters whose explicit expressions are given in the case of a closed system coupled to a bath as well as for the original Fano scattering framework. Although the solution is intricate, it can be elegantly expressed as a linear transformation of the kernel of a 4 ×4 matrix which has the meaning of an effective Liouvillian. We unveil key notable processes related to the optical nonlinearity and which had not been reported to date: electromagnetic-induced transparency, population inversions, power narrowing and broadening, as well as an effective reduction of the Fano asymmetry parameter.

Market-implied spread for earthquake CAT bonds: financial implications of engineering decisions.

PubMed

Damnjanovic, Ivan; Aslan, Zafer; Mander, John

2010-12-01

In the event of natural and man-made disasters, owners of large-scale infrastructure facilities (assets) need contingency plans to effectively restore the operations within the acceptable timescales. Traditionally, the insurance sector provides the coverage against potential losses. However, there are many problems associated with this traditional approach to risk transfer including counterparty risk and litigation. Recently, a number of innovative risk mitigation methods, termed alternative risk transfer (ART) methods, have been introduced to address these problems. One of the most important ART methods is catastrophe (CAT) bonds. The objective of this article is to develop an integrative model that links engineering design parameters with financial indicators including spread and bond rating. The developed framework is based on a four-step structural loss model and transformed survival model to determine expected excess returns. We illustrate the framework for a seismically designed bridge using two unique CAT bond contracts. The results show a nonlinear relationship between engineering design parameters and market-implied spread. © 2010 Society for Risk Analysis.

FPGA-Based Efficient Hardware/Software Co-Design for Industrial Systems with Consideration of Output Selection

NASA Astrophysics Data System (ADS)

Deliparaschos, Kyriakos M.; Michail, Konstantinos; Zolotas, Argyrios C.; Tzafestas, Spyros G.

2016-05-01

This work presents a field programmable gate array (FPGA)-based embedded software platform coupled with a software-based plant, forming a hardware-in-the-loop (HIL) that is used to validate a systematic sensor selection framework. The systematic sensor selection framework combines multi-objective optimization, linear-quadratic-Gaussian (LQG)-type control, and the nonlinear model of a maglev suspension. A robustness analysis of the closed-loop is followed (prior to implementation) supporting the appropriateness of the solution under parametric variation. The analysis also shows that quantization is robust under different controller gains. While the LQG controller is implemented on an FPGA, the physical process is realized in a high-level system modeling environment. FPGA technology enables rapid evaluation of the algorithms and test designs under realistic scenarios avoiding heavy time penalty associated with hardware description language (HDL) simulators. The HIL technique facilitates significant speed-up in the required execution time when compared to its software-based counterpart model.

Soft sensor development for Mooney viscosity prediction in rubber mixing process based on GMMDJITGPR algorithm

NASA Astrophysics Data System (ADS)

Yang, Kai; Chen, Xiangguang; Wang, Li; Jin, Huaiping

2017-01-01

In rubber mixing process, the key parameter (Mooney viscosity), which is used to evaluate the property of the product, can only be obtained with 4-6h delay offline. It is quite helpful for the industry, if the parameter can be estimate on line. Various data driven soft sensors have been used to prediction in the rubber mixing. However, it always not functions well due to the phase and nonlinear property in the process. The purpose of this paper is to develop an efficient soft sensing algorithm to solve the problem. Based on the proposed GMMD local sample selecting criterion, the phase information is extracted in the local modeling. Using the Gaussian local modeling method within Just-in-time (JIT) learning framework, nonlinearity of the process is well handled. Efficiency of the new method is verified by comparing the performance with various mainstream soft sensors, using the samples from real industrial rubber mixing process.

Experimental Chaos - Proceedings of the 3rd Conference

NASA Astrophysics Data System (ADS)

Harrison, Robert G.; Lu, Weiping; Ditto, William; Pecora, Lou; Spano, Mark; Vohra, Sandeep

1996-10-01

The Table of Contents for the full book PDF is as follows: * Preface * Spatiotemporal Chaos and Patterns * Scale Segregation via Formation of Domains in a Nonlinear Optical System * Laser Dynamics as Hydrodynamics * Spatiotemporal Dynamics of Human Epileptic Seizures * Experimental Transition to Chaos in a Quasi 1D Chain of Oscillators * Measuring Coupling in Spatiotemporal Dynamical Systems * Chaos in Vortex Breakdown * Dynamical Analysis * Radial Basis Function Modelling and Prediction of Time Series * Nonlinear Phenomena in Polyrhythmic Hand Movements * Using Models to Diagnose, Test and Control Chaotic Systems * New Real-Time Analysis of Time Series Data with Physical Wavelets * Control and Synchronization * Measuring and Controlling Chaotic Dynamics in a Slugging Fluidized Bed * Control of Chaos in a Laser with Feedback * Synchronization and Chaotic Diode Resonators * Control of Chaos by Continuous-time Feedback with Delay * A Framework for Communication using Chaos Sychronization * Control of Chaos in Switching Circuits * Astrophysics, Meteorology and Oceanography * Solar-Wind-Magnetospheric Dynamics via Satellite Data * Nonlinear Dynamics of the Solar Atmosphere * Fractal Dimension of Scalar and Vector Variables from Turbulence Measurements in the Atmospheric Surface Layer * Mechanics * Escape and Overturning: Subtle Transient Behavior in Nonlinear Mechanical Models * Organising Centres in the Dynamics of Parametrically Excited Double Pendulums * Intermittent Behaviour in a Heating System Driven by Phase Transitions * Hydrodynamics * Size Segregation in Couette Flow of Granular Material * Routes to Chaos in Rotational Taylor-Couette Flow * Experimental Study of the Laminar-Turbulent Transition in an Open Flow System * Chemistry * Order and Chaos in Excitable Media under External Forcing * A Chemical Wave Propagation with Accelerating Speed Accompanied by Hydrodynamic Flow * Optics * Instabilities in Semiconductor Lasers with Optical Injection * Spatio-Temporal Dynamics of a Bimode CO2 Laser with Saturable Absorber * Chaotic Homoclinic Phenomena in Opto-Thermal Devices * Observation and Characterisation of Low-Frequency Chaos in Semiconductor Lasers with External Feedback * Condensed Matter * The Application of Nonlinear Dynamics in the Study of Ferroelectric Materials * Cellular Convection in a Small Aspect Ratio Liquid Crystal Device * Driven Spin-Wave Dynamics in YIG Films * Quantum Chaology in Quartz * Small Signal Amplification Caused by Nonlinear Properties of Ferroelectrics * Composite Materials Evolved from Chaos * Electronics and Circuits * Controlling a Chaotic Array of Pulse-Coupled Fitzhugh-Nagumo Circuits * Experimental Observation of On-Off Intermittency * Phase Lock-In of Chaotic Relaxation Oscillators * Biology and Medicine * Singular Value Decomposition and Circuit Structure in Invertebrate Ganglia * Nonlinear Forecasting of Spike Trains from Neurons of a Mollusc * Ultradian Rhythm in the Sensitive Plants: Chaos or Coloured Noise? * Chaos and the Crayfish Sixth Ganglion * Hardware Coupled Nonlinear Oscillators as a Model of Retina

Multi-state succession in wetlands: a novel use of state and transition models

USGS Publications Warehouse

Zweig, Christa L.; Kitchens, Wiley M.

2009-01-01

The complexity of ecosystems and mechanisms of succession are often simplified by linear and mathematical models used to understand and predict system behavior. Such models often do not incorporate multivariate, nonlinear feedbacks in pattern and process that include multiple scales of organization inherent within real-world systems. Wetlands are ecosystems with unique, nonlinear patterns of succession due to the regular, but often inconstant, presence of water on the landscape. We develop a general, nonspatial state and transition (S and T) succession conceptual model for wetlands and apply the general framework by creating annotated succession/management models and hypotheses for use in impact analysis on a portion of an imperiled wetland. The S and T models for our study area, Water Conservation Area 3A South (WCA3), Florida, USA, included hydrologic and peat depth values from multivariate analyses and classification and regression trees. We used the freeware Vegetation Dynamics Development Tool as an exploratory application to evaluate our S and T models with different management actions (equal chance [a control condition], deeper conditions, dry conditions, and increased hydrologic range) for three communities: slough, sawgrass (Cladium jamaicense), and wet prairie. Deeper conditions and increased hydrologic range behaved similarly, with the transition of community states to deeper states, particularly for sawgrass and slough. Hydrology is the primary mechanism for multi-state transitions within our study period, and we show both an immediate and lagged effect on vegetation, depending on community state. We consider these S and T succession models as a fraction of the framework for the Everglades. They are hypotheses for use in adaptive management, represent the community response to hydrology, and illustrate which aspects of hydrologic variability are important to community structure. We intend for these models to act as a foundation for further restoration management and experimentation which will refine transition and threshold concepts. 

Geometry of behavioral spaces: A computational approach to analysis and understanding of agent based models and agent behaviors

NASA Astrophysics Data System (ADS)

Cenek, Martin; Dahl, Spencer K.

2016-11-01

Systems with non-linear dynamics frequently exhibit emergent system behavior, which is important to find and specify rigorously to understand the nature of the modeled phenomena. Through this analysis, it is possible to characterize phenomena such as how systems assemble or dissipate and what behaviors lead to specific final system configurations. Agent Based Modeling (ABM) is one of the modeling techniques used to study the interaction dynamics between a system's agents and its environment. Although the methodology of ABM construction is well understood and practiced, there are no computational, statistically rigorous, comprehensive tools to evaluate an ABM's execution. Often, a human has to observe an ABM's execution in order to analyze how the ABM functions, identify the emergent processes in the agent's behavior, or study a parameter's effect on the system-wide behavior. This paper introduces a new statistically based framework to automatically analyze agents' behavior, identify common system-wide patterns, and record the probability of agents changing their behavior from one pattern of behavior to another. We use network based techniques to analyze the landscape of common behaviors in an ABM's execution. Finally, we test the proposed framework with a series of experiments featuring increasingly emergent behavior. The proposed framework will allow computational comparison of ABM executions, exploration of a model's parameter configuration space, and identification of the behavioral building blocks in a model's dynamics.

Geometry of behavioral spaces: A computational approach to analysis and understanding of agent based models and agent behaviors.

PubMed

Cenek, Martin; Dahl, Spencer K

2016-11-01

Systems with non-linear dynamics frequently exhibit emergent system behavior, which is important to find and specify rigorously to understand the nature of the modeled phenomena. Through this analysis, it is possible to characterize phenomena such as how systems assemble or dissipate and what behaviors lead to specific final system configurations. Agent Based Modeling (ABM) is one of the modeling techniques used to study the interaction dynamics between a system's agents and its environment. Although the methodology of ABM construction is well understood and practiced, there are no computational, statistically rigorous, comprehensive tools to evaluate an ABM's execution. Often, a human has to observe an ABM's execution in order to analyze how the ABM functions, identify the emergent processes in the agent's behavior, or study a parameter's effect on the system-wide behavior. This paper introduces a new statistically based framework to automatically analyze agents' behavior, identify common system-wide patterns, and record the probability of agents changing their behavior from one pattern of behavior to another. We use network based techniques to analyze the landscape of common behaviors in an ABM's execution. Finally, we test the proposed framework with a series of experiments featuring increasingly emergent behavior. The proposed framework will allow computational comparison of ABM executions, exploration of a model's parameter configuration space, and identification of the behavioral building blocks in a model's dynamics.

Narrowing the range of water availability projections in China using the Budyko framework

NASA Astrophysics Data System (ADS)

Osborne, Joe; Lambert, Hugo

2017-04-01

There is a growing demand for reliable 21st-century projections of water availability at the regional scale. Used alone, global climate models (GCMs) are unsuitable for generating such projections at catchment scales in the presence of simulated aridity biases. This is because the Budyko framework dictates that the partitioning of precipitation into runoff and evapotranspiration scales as a non-linear function of aridity. Therefore, GCMs are typically used in tandem with global hydrological models (GHMs), but this process is computationally expensive. Here, considering a Chinese case study, we utilise the Budyko framework to make use of plentiful GCM output, without the need for GHMs. We first apply the framework to 20th-century observations to show that the significant declines in Yellow river discharge between 1951 and 2000 cannot be accounted for by modelled climate change alone, with human activities playing a larger but poorly quantified role. We further show that the Budyko framework can be used to narrow the range of water availability projections in the Yangtze and Yellow river catchments by 33% an 72%, respectively, in the 21st-century RCP8.5 business-as-usual emission scenario. In the Yellow catchment the best-guess end-of-21st-century change in runoff decreases from an increase of 0.09 mm/d in raw multi-model mean output to an increase of 0.04 mm/d in Budyko corrected multi-model mean output. While this is a valuable finding, we stress that these changes could be dwarfed by changes due to human activity in the 21st century, unless strict water management policies are implemented.

Application of Two Cobalt-Based Metal-Organic Frameworks as Oxidative Desulfurization Catalysts.

PubMed

Masoomi, Mohammad Yaser; Bagheri, Minoo; Morsali, Ali

2015-12-07

Two new porous cobalt-based metal-organic frameworks, [Co6(oba)5(OH)2(H2O)2(DMF)4]n · 5DMF (TMU-10) and [Co3(oba)3(O) (Py)0.5] n · 4DMF · Py (TMU-12) have been synthesized by solvothermal method using a nonlinear dicarboxylate ligand. Under mild reaction conditions, these compounds exhibited good catalytic activity and reusability in oxidative desulfurization (ODS) reaction of model oil which was prepared by dissolving dibenzothiophene (DBT) in n-hexane. FT-IR and Mass analysis showed that the main product of DBT oxidation is its corresponding sulfone, which was adsorbed on the surfaces of catalysts. The activation energy was obtained as 13.4 kJ/mol.

Do oil shocks predict economic policy uncertainty?

NASA Astrophysics Data System (ADS)

Rehman, Mobeen Ur

2018-05-01

Oil price fluctuations have influential role in global economic policies for developed as well as emerging countries. I investigate the role of international oil prices disintegrated into structural (i) oil supply shock, (ii) aggregate demand shock and (iii) oil market specific demand shocks, based on the work of Kilian (2009) using structural VAR framework on economic policies uncertainty of sampled markets. Economic policy uncertainty, due to its non-linear behavior is modeled in a regime switching framework with disintegrated structural oil shocks. Our results highlight that Indian, Spain and Japanese economic policy uncertainty responds to the global oil price shocks, however aggregate demand shocks fail to induce any change. Oil specific demand shocks are significant only for China and India in high volatility state.

Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms

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

Feng, Wenqiang, E-mail: wfeng1@vols.utk.edu; Salgado, Abner J., E-mail: asalgad1@utk.edu; Wang, Cheng, E-mail: cwang1@umassd.edu

We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of the equations are constant-coefficient, positive linear operators, which suggests a natural preconditioning strategy. Such nonlinear elliptic equations often arise from time discretization of parabolic equations that model various biological and physical phenomena, in particular, liquid crystals, thin film epitaxial growth and phase transformations. The analyses of the schemes involve the characterization of the strictly convex energies associated with the equations. We first give a generalmore » framework for PSD in Hilbert spaces. Based on certain reasonable assumptions of the linear pre-conditioner, a geometric convergence rate is shown for the nonlinear PSD iteration. We then apply the general theory to the fourth and sixth-order problems of interest, making use of Sobolev embedding and regularity results to confirm the appropriateness of our pre-conditioners for the regularized p-Lapacian problems. Our results include a sharper theoretical convergence result for p-Laplacian systems compared to what may be found in existing works. We demonstrate rigorously how to apply the theory in the finite dimensional setting using finite difference discretization methods. Numerical simulations for some important physical application problems – including thin film epitaxy with slope selection and the square phase field crystal model – are carried out to verify the efficiency of the scheme.« less

Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms

NASA Astrophysics Data System (ADS)

Feng, Wenqiang; Salgado, Abner J.; Wang, Cheng; Wise, Steven M.

2017-04-01

We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of the equations are constant-coefficient, positive linear operators, which suggests a natural preconditioning strategy. Such nonlinear elliptic equations often arise from time discretization of parabolic equations that model various biological and physical phenomena, in particular, liquid crystals, thin film epitaxial growth and phase transformations. The analyses of the schemes involve the characterization of the strictly convex energies associated with the equations. We first give a general framework for PSD in Hilbert spaces. Based on certain reasonable assumptions of the linear pre-conditioner, a geometric convergence rate is shown for the nonlinear PSD iteration. We then apply the general theory to the fourth and sixth-order problems of interest, making use of Sobolev embedding and regularity results to confirm the appropriateness of our pre-conditioners for the regularized p-Lapacian problems. Our results include a sharper theoretical convergence result for p-Laplacian systems compared to what may be found in existing works. We demonstrate rigorously how to apply the theory in the finite dimensional setting using finite difference discretization methods. Numerical simulations for some important physical application problems - including thin film epitaxy with slope selection and the square phase field crystal model - are carried out to verify the efficiency of the scheme.

On multilevel RBF collocation to solve nonlinear PDEs arising from endogenous stochastic volatility models

NASA Astrophysics Data System (ADS)

Bastani, Ali Foroush; Dastgerdi, Maryam Vahid; Mighani, Abolfazl

2018-06-01

The main aim of this paper is the analytical and numerical study of a time-dependent second-order nonlinear partial differential equation (PDE) arising from the endogenous stochastic volatility model, introduced in [Bensoussan, A., Crouhy, M. and Galai, D., Stochastic equity volatility related to the leverage effect (I): equity volatility behavior. Applied Mathematical Finance, 1, 63-85, 1994]. As the first step, we derive a consistent set of initial and boundary conditions to complement the PDE, when the firm is financed by equity and debt. In the sequel, we propose a Newton-based iteration scheme for nonlinear parabolic PDEs which is an extension of a method for solving elliptic partial differential equations introduced in [Fasshauer, G. E., Newton iteration with multiquadrics for the solution of nonlinear PDEs. Computers and Mathematics with Applications, 43, 423-438, 2002]. The scheme is based on multilevel collocation using radial basis functions (RBFs) to solve the resulting locally linearized elliptic PDEs obtained at each level of the Newton iteration. We show the effectiveness of the resulting framework by solving a prototypical example from the field and compare the results with those obtained from three different techniques: (1) a finite difference discretization; (2) a naive RBF collocation and (3) a benchmark approximation, introduced for the first time in this paper. The numerical results confirm the robustness, higher convergence rate and good stability properties of the proposed scheme compared to other alternatives. We also comment on some possible research directions in this field.

Plasticity - Theory and finite element applications.

NASA Technical Reports Server (NTRS)

Armen, H., Jr.; Levine, H. S.

1972-01-01

A unified presentation is given of the development and distinctions associated with various incremental solution procedures used to solve the equations governing the nonlinear behavior of structures, and this is discussed within the framework of the finite-element method. Although the primary emphasis here is on material nonlinearities, consideration is also given to geometric nonlinearities acting separately or in combination with nonlinear material behavior. The methods discussed here are applicable to a broad spectrum of structures, ranging from simple beams to general three-dimensional bodies. The finite-element analysis methods for material nonlinearity are general in the sense that any of the available plasticity theories can be incorporated to treat strain hardening or ideally plastic behavior.

Bayesian population receptive field modelling.

PubMed

Zeidman, Peter; Silson, Edward Harry; Schwarzkopf, Dietrich Samuel; Baker, Chris Ian; Penny, Will

2017-09-08

We introduce a probabilistic (Bayesian) framework and associated software toolbox for mapping population receptive fields (pRFs) based on fMRI data. This generic approach is intended to work with stimuli of any dimension and is demonstrated and validated in the context of 2D retinotopic mapping. The framework enables the experimenter to specify generative (encoding) models of fMRI timeseries, in which experimental stimuli enter a pRF model of neural activity, which in turns drives a nonlinear model of neurovascular coupling and Blood Oxygenation Level Dependent (BOLD) response. The neuronal and haemodynamic parameters are estimated together on a voxel-by-voxel or region-of-interest basis using a Bayesian estimation algorithm (variational Laplace). This offers several novel contributions to receptive field modelling. The variance/covariance of parameters are estimated, enabling receptive fields to be plotted while properly representing uncertainty about pRF size and location. Variability in the haemodynamic response across the brain is accounted for. Furthermore, the framework introduces formal hypothesis testing to pRF analysis, enabling competing models to be evaluated based on their log model evidence (approximated by the variational free energy), which represents the optimal tradeoff between accuracy and complexity. Using simulations and empirical data, we found that parameters typically used to represent pRF size and neuronal scaling are strongly correlated, which is taken into account by the Bayesian methods we describe when making inferences. We used the framework to compare the evidence for six variants of pRF model using 7 T functional MRI data and we found a circular Difference of Gaussians (DoG) model to be the best explanation for our data overall. We hope this framework will prove useful for mapping stimulus spaces with any number of dimensions onto the anatomy of the brain. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

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

NASA Astrophysics Data System (ADS)

Spiegelman, M.; Wilson, C. R.

2011-12-01

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

An entropic framework for modeling economies

NASA Astrophysics Data System (ADS)

Caticha, Ariel; Golan, Amos

2014-08-01

We develop an information-theoretic framework for economic modeling. This framework is based on principles of entropic inference that are designed for reasoning on the basis of incomplete information. We take the point of view of an external observer who has access to limited information about broad macroscopic economic features. We view this framework as complementary to more traditional methods. The economy is modeled as a collection of agents about whom we make no assumptions of rationality (in the sense of maximizing utility or profit). States of statistical equilibrium are introduced as those macrostates that maximize entropy subject to the relevant information codified into constraints. The basic assumption is that this information refers to supply and demand and is expressed in the form of the expected values of certain quantities (such as inputs, resources, goods, production functions, utility functions and budgets). The notion of economic entropy is introduced. It provides a measure of the uniformity of the distribution of goods and resources. It captures both the welfare state of the economy as well as the characteristics of the market (say, monopolistic, concentrated or competitive). Prices, which turn out to be the Lagrange multipliers, are endogenously generated by the economy. Further studies include the equilibrium between two economies and the conditions for stability. As an example, the case of the nonlinear economy that arises from linear production and utility functions is treated in some detail.

Agent-based models in translational systems biology

PubMed Central

An, Gary; Mi, Qi; Dutta-Moscato, Joyeeta; Vodovotz, Yoram

2013-01-01

Effective translational methodologies for knowledge representation are needed in order to make strides against the constellation of diseases that affect the world today. These diseases are defined by their mechanistic complexity, redundancy, and nonlinearity. Translational systems biology aims to harness the power of computational simulation to streamline drug/device design, simulate clinical trials, and eventually to predict the effects of drugs on individuals. The ability of agent-based modeling to encompass multiple scales of biological process as well as spatial considerations, coupled with an intuitive modeling paradigm, suggests that this modeling framework is well suited for translational systems biology. This review describes agent-based modeling and gives examples of its translational applications in the context of acute inflammation and wound healing. PMID:20835989

A Multiscale Nested Modeling Framework to Simulate the Interaction of Surface Gravity Waves with Nonlinear Internal Gravity Waves

DTIC Science & Technology

2015-09-30

Meneveau, C., and L. Shen (2014), Large-eddy simulation of offshore wind farm , Physics of Fluids, 26, 025101. Zhang, Z., Fringer, O.B., and S.R...being centimeter scale, surface mixed layer processes arising from the combined actions of tides, winds and mesoscale currents. Issues related to...the internal wave field and how it impacts the surface waves. APPROACH We are focusing on the problem of modification of the wind -wave field

Rise time of voltage pulses in NbN superconducting single photon detectors

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

Smirnov, K. V.; CJSC “Superconducting Nanotechnology”; National Research University Higher School of Economics, Moscow Institute of Electronics and Mathematics, 34 Tallinskaya St., 109028 Moscow

2016-08-01

We have found experimentally that the rise time of voltage pulse in NbN superconducting single photon detectors increases nonlinearly with increasing the length of the detector L. The effect is connected with dependence of resistance of the detector R{sub n}, which appears after photon absorption, on its kinetic inductance L{sub k} and, hence, on the length of the detector. This conclusion is confirmed by our calculations in the framework of two temperature model.

Fully Explicit Nonlinear Optics Model in a Particle-in-Cell Framework

DTIC Science & Technology

2013-04-19

brirjrj ] = q m Ei (4) where the subscripts vary over Cartesian coordinates, and q/m is the charge to mass ratio . The anisotropy of the medium is...linear refractive index and η0 is the impedance of free space (see appendix). Note that the charge to mass ratio qs/ms amounts to an extraneous free...parameter that could have been absorbed into qsNs, as, and bs. In this work, the electronic charge to mass ratio is always assumed. As an example

Re-Mediating Classroom Activity with a Non-Linear, Multi-Display Presentation Tool

ERIC Educational Resources Information Center

Bligh, Brett; Coyle, Do

2013-01-01

This paper uses an Activity Theory framework to evaluate the use of a novel, multi-screen, non-linear presentation tool. The Thunder tool allows presenters to manipulate and annotate multiple digital slides and to concurrently display a selection of juxtaposed resources across a wall-sized projection area. Conventional, single screen presentation…

Computational Studies on Optoelectronic and Nonlinear Properties of Octaphyrin Derivatives

PubMed Central

Islam, Nasarul; Lone, Irfan H.

2017-01-01

The electronic and nonlinear optical (NLO) properties of octaphyrin derivatives were studied by employing the DFT/TDFT at CAM-B3LYP/6-311++G (2d, 2p) level of the theory. Thiophene, phenyl, methyl and cyano moieties were substituted on the molecular framework of octaphyrin core, in order to observe the change in optoelectronic and nonlinear response of these systems. The frontier molecular orbital studies and values of electron affinity reveals that the studied compounds are stable against the oxygen and moisture present in air. The calculated ionization energies, adiabatic electron affinity and reorganization energy values indicate that octaphyrin derivatives can be employed as effective n-type material for Organic Light Emitting Diodes (OLEDs). This character shows an enhancement with the introduction of an electron withdrawing group in the octaphyrin framework. The polarizability and hyperpolarizability values of octaphyrin derivatives demonstrate that they are good candidates for NLO devices. The nonlinear response of these systems shows enhancement on the introduction of electron donating groups on octaphyrin moiety. However, these claims needs further experimental verification. PMID:28321394

Reconstructing Mammalian Sleep Dynamics with Data Assimilation

PubMed Central

Sedigh-Sarvestani, Madineh; Schiff, Steven J.; Gluckman, Bruce J.

2012-01-01

Data assimilation is a valuable tool in the study of any complex system, where measurements are incomplete, uncertain, or both. It enables the user to take advantage of all available information including experimental measurements and short-term model forecasts of a system. Although data assimilation has been used to study other biological systems, the study of the sleep-wake regulatory network has yet to benefit from this toolset. We present a data assimilation framework based on the unscented Kalman filter (UKF) for combining sparse measurements together with a relatively high-dimensional nonlinear computational model to estimate the state of a model of the sleep-wake regulatory system. We demonstrate with simulation studies that a few noisy variables can be used to accurately reconstruct the remaining hidden variables. We introduce a metric for ranking relative partial observability of computational models, within the UKF framework, that allows us to choose the optimal variables for measurement and also provides a methodology for optimizing framework parameters such as UKF covariance inflation. In addition, we demonstrate a parameter estimation method that allows us to track non-stationary model parameters and accommodate slow dynamics not included in the UKF filter model. Finally, we show that we can even use observed discretized sleep-state, which is not one of the model variables, to reconstruct model state and estimate unknown parameters. Sleep is implicated in many neurological disorders from epilepsy to schizophrenia, but simultaneous observation of the many brain components that regulate this behavior is difficult. We anticipate that this data assimilation framework will enable better understanding of the detailed interactions governing sleep and wake behavior and provide for better, more targeted, therapies. PMID:23209396

Coupled Thermo-Hydro-Mechanical Numerical Framework for Simulating Unconventional Formations

NASA Astrophysics Data System (ADS)

Garipov, T. T.; White, J. A.; Lapene, A.; Tchelepi, H.

2016-12-01

Unconventional deposits are found in all world oil provinces. Modeling these systems is challenging, however, due to complex thermo-hydro-mechanical processes that govern their behavior. As a motivating example, we consider in situ thermal processing of oil shale deposits. When oil shale is heated to sufficient temperatures, kerogen can be converted to oil and gas products over a relatively short timespan. This phase change dramatically impact both the mechanical and hydrologic properties of the rock, leading to strongly coupled THMC interactions. Here, we present a numerical framework for simulating tightly-coupled chemistry, geomechanics, and multiphase flow within a reservoir simulator (the AD-GPRS General Purpose Research Simulator). We model changes in constitutive behavior of the rock using a thermoplasticity model that accounts for microstructural evolution. The multi-component, multiphase flow and transport processes of both mass and heat are modeled at the macroscopic (e.g., Darcy) scale. The phase compositions and properties are described by a cubic equation of state; Arrhenius-type chemical reactions are used to represent kerogen conversion. The system of partial differential equations is discretized using a combination of finite-volumes and finite-elements, respectively, for the flow and mechanics problems. Fully implicit and sequentially implicit method are used to solve resulting nonlinear problem. The proposed framework is verified against available analytical and numerical benchmark cases. We demonstrate the efficiency, performance, and capabilities of the proposed simulation framework by analyzing near well deformation in an oil shale formation.

Computational dynamics of soft machines

NASA Astrophysics Data System (ADS)

Hu, Haiyan; Tian, Qiang; Liu, Cheng

2017-06-01

Soft machine refers to a kind of mechanical system made of soft materials to complete sophisticated missions, such as handling a fragile object and crawling along a narrow tunnel corner, under low cost control and actuation. Hence, soft machines have raised great challenges to computational dynamics. In this review article, recent studies of the authors on the dynamic modeling, numerical simulation, and experimental validation of soft machines are summarized in the framework of multibody system dynamics. The dynamic modeling approaches are presented first for the geometric nonlinearities of coupled overall motions and large deformations of a soft component, the physical nonlinearities of a soft component made of hyperelastic or elastoplastic materials, and the frictional contacts/impacts of soft components, respectively. Then the computation approach is outlined for the dynamic simulation of soft machines governed by a set of differential-algebraic equations of very high dimensions, with an emphasis on the efficient computations of the nonlinear elastic force vector of finite elements. The validations of the proposed approaches are given via three case studies, including the locomotion of a soft quadrupedal robot, the spinning deployment of a solar sail of a spacecraft, and the deployment of a mesh reflector of a satellite antenna, as well as the corresponding experimental studies. Finally, some remarks are made for future studies.

Multi-Target Regression via Robust Low-Rank Learning.

PubMed

Zhen, Xiantong; Yu, Mengyang; He, Xiaofei; Li, Shuo

2018-02-01

Multi-target regression has recently regained great popularity due to its capability of simultaneously learning multiple relevant regression tasks and its wide applications in data mining, computer vision and medical image analysis, while great challenges arise from jointly handling inter-target correlations and input-output relationships. In this paper, we propose Multi-layer Multi-target Regression (MMR) which enables simultaneously modeling intrinsic inter-target correlations and nonlinear input-output relationships in a general framework via robust low-rank learning. Specifically, the MMR can explicitly encode inter-target correlations in a structure matrix by matrix elastic nets (MEN); the MMR can work in conjunction with the kernel trick to effectively disentangle highly complex nonlinear input-output relationships; the MMR can be efficiently solved by a new alternating optimization algorithm with guaranteed convergence. The MMR leverages the strength of kernel methods for nonlinear feature learning and the structural advantage of multi-layer learning architectures for inter-target correlation modeling. More importantly, it offers a new multi-layer learning paradigm for multi-target regression which is endowed with high generality, flexibility and expressive ability. Extensive experimental evaluation on 18 diverse real-world datasets demonstrates that our MMR can achieve consistently high performance and outperforms representative state-of-the-art algorithms, which shows its great effectiveness and generality for multivariate prediction.

Fast estimation of diffusion tensors under Rician noise by the EM algorithm.

PubMed

Liu, Jia; Gasbarra, Dario; Railavo, Juha

2016-01-15

Diffusion tensor imaging (DTI) is widely used to characterize, in vivo, the white matter of the central nerve system (CNS). This biological tissue contains much anatomic, structural and orientational information of fibers in human brain. Spectral data from the displacement distribution of water molecules located in the brain tissue are collected by a magnetic resonance scanner and acquired in the Fourier domain. After the Fourier inversion, the noise distribution is Gaussian in both real and imaginary parts and, as a consequence, the recorded magnitude data are corrupted by Rician noise. Statistical estimation of diffusion leads a non-linear regression problem. In this paper, we present a fast computational method for maximum likelihood estimation (MLE) of diffusivities under the Rician noise model based on the expectation maximization (EM) algorithm. By using data augmentation, we are able to transform a non-linear regression problem into the generalized linear modeling framework, reducing dramatically the computational cost. The Fisher-scoring method is used for achieving fast convergence of the tensor parameter. The new method is implemented and applied using both synthetic and real data in a wide range of b-amplitudes up to 14,000s/mm(2). Higher accuracy and precision of the Rician estimates are achieved compared with other log-normal based methods. In addition, we extend the maximum likelihood (ML) framework to the maximum a posteriori (MAP) estimation in DTI under the aforementioned scheme by specifying the priors. We will describe how close numerically are the estimators of model parameters obtained through MLE and MAP estimation. Copyright © 2015 Elsevier B.V. All rights reserved.

A physics based approach to the pulse wave velocity prediction in compliant arterial segments.

PubMed

Liberson, Alexander S; Lillie, Jeffrey S; Day, Steven W; Borkholder, David A

2016-10-03

Pulse wave velocity (PWV) quantification commonly serves as a highly robust prognostic parameter being used in a preventative cardiovascular therapy. Being dependent on arterial elastance, it can serve as a marker of cardiovascular risk. Since it is influenced by a blood pressure (BP), the pertaining theory can lay the foundation in developing a technique for noninvasive blood pressure measurement. Previous studies have reported application of PWV, measured noninvasively, for both the estimation of arterial compliance and blood pressure, based on simplified physical or statistical models. A new theoretical model for pulse wave propagation in a compliant arterial segment is presented within the framework of pseudo-elastic deformation of biological tissue undergoing finite deformation. An essential ingredient is the dependence of results on nonlinear aspects of the model: convective fluid phenomena, hyperelastic constitutive relation, large deformation and a longitudinal pre-stress load. An exact analytical solution for PWV is presented as a function of pressure, flow and pseudo-elastic orthotropic parameters. Results from our model are compared with published in-vivo PWV measurements under diverse physiological conditions. Contributions of each of the nonlinearities are analyzed. It was found that the totally nonlinear model achieves the best match with the experimental data. To retrieve individual vascular information of a patient, the inverse problem of hemodynamics is presented, calculating local orthotropic hyperelastic properties of the arterial wall. The proposed technique can be used for non-invasive assessment of arterial elastance, and blood pressure using direct measurement of PWV, with account of hyperelastic orthotropic properties. Copyright © 2016 Elsevier Ltd. All rights reserved.

Nonlinear Interactions between Climate and Atmospheric Carbon Dioxide Drivers of Terrestrial and Marine Carbon Cycle Changes

NASA Astrophysics Data System (ADS)

Hoffman, F. M.; Randerson, J. T.; Moore, J. K.; Goulden, M.; Fu, W.; Koven, C.; Swann, A. L. S.; Mahowald, N. M.; Lindsay, K. T.; Munoz, E.

2017-12-01

Quantifying interactions between global biogeochemical cycles and the Earth system is important for predicting future atmospheric composition and informing energy policy. We applied a feedback analysis framework to three sets of Historical (1850-2005), Representative Concentration Pathway 8.5 (2006-2100), and its extension (2101-2300) simulations from the Community Earth System Model version 1.0 (CESM1(BGC)) to quantify drivers of terrestrial and ocean responses of carbon uptake. In the biogeochemically coupled simulation (BGC), the effects of CO2 fertilization and nitrogen deposition influenced marine and terrestrial carbon cycling. In the radiatively coupled simulation (RAD), the effects of rising temperature and circulation changes due to radiative forcing from CO2, other greenhouse gases, and aerosols were the sole drivers of carbon cycle changes. In the third, fully coupled simulation (FC), both the biogeochemical and radiative coupling effects acted simultaneously. We found that climate-carbon sensitivities derived from RAD simulations produced a net ocean carbon storage climate sensitivity that was weaker and a net land carbon storage climate sensitivity that was stronger than those diagnosed from the FC and BGC simulations. For the ocean, this nonlinearity was associated with warming-induced weakening of ocean circulation and mixing that limited exchange of dissolved inorganic carbon between surface and deeper water masses. For the land, this nonlinearity was associated with strong gains in gross primary production in the FC simulation, driven by enhancements in the hydrological cycle and increased nutrient availability. We developed and applied a nonlinearity metric to rank model responses and driver variables. The climate-carbon cycle feedback gain at 2300 was 42% higher when estimated from climate-carbon sensitivities derived from the difference between FC and BGC than when derived from RAD. We re-analyzed other CMIP5 model results to quantify the effects of such nonlinearities on their projected climate-carbon cycle feedback gains.

Nonlinear Theory of The Geostrophic Adjustment

NASA Astrophysics Data System (ADS)

Zeitlin, V.

Nonlinear geostrophic adjustment and splitting of the fast and slow dynamical vari- ables are analysed in the framework of multi-layer and continuously stratified prim- itive equations by means of the multi-scale perturbation theory in the Rossby num- ber applied to localized initial disturbances. Two basic dynamical regimes: the quasi- geostrophic (QG) and the frontal geostrophic (FG) with small and large deviations of the isopycnal surfaces, respectively, are considered and differences in corresponding adjustment scenarios are displayed. Decoupling of the fast component of the flow is proven up to the third order in Rossby number and long-time corrections to the stan- dard balanced QG and FG models are found. Peculiarities of splitting in the FG regime due to the quasi-inertial oscillations are displayed and a Schrodinger-like modulation equations for the envelope of these latter are derived.

Wave theory of turbulence in compressible media (acoustic theory of turbulence)

NASA Technical Reports Server (NTRS)

Kentzer, C. P.

1975-01-01

The generation and the transmission of sound in turbulent flows are treated as one of the several aspects of wave propagation in turbulence. Fluid fluctuations are decomposed into orthogonal Fourier components, with five interacting modes of wave propagation: two vorticity modes, one entropy mode, and two acoustic modes. Wave interactions, governed by the inhomogeneous and nonlinear terms of the perturbed Navier-Stokes equations, are modeled by random functions which give the rates of change of wave amplitudes equal to the averaged interaction terms. The statistical framework adopted is a quantum-like formulation in terms of complex distribution functions. The spatial probability distributions are given by the squares of the absolute values of the complex characteristic functions. This formulation results in nonlinear diffusion-type transport equations for the probability densities of the five modes of wave propagation.

Tracer-aided modelling to explore non-linearities in flow paths, hydrological connectivity and faecal contamination risk

NASA Astrophysics Data System (ADS)

Neill, A. J.; Tetzlaff, D.; Strachan, N.; Soulsby, C.

2016-12-01

The non-linearities of runoff generation processes are strongly influenced by the connectivity of hillslopes and channel networks, particularly where overland flow is an important runoff mechanism. Despite major advances in understanding hydrological connectivity and runoff generation, the role of connectivity in the contamination of potable water supplies by faecal pathogens from grazing animals remains unclear. This is a water quality issue with serious implications for public health. Here, we sought to understand the dynamics of hydrological connectivity, flow paths and linked faecal pathogen transport in a montane catchment in Scotland with high deer populations. We firstly calibrated, within an uncertainty framework, a parsimonious tracer-aided hydrological model to daily discharge and stream isotope data. The model, developed on the basis of past empirical and tracer studies, conceptualises the catchment as three interacting hydrological source areas (dynamic saturation zone, dynamic hillslope, and groundwater) for which water fluxes, water ages and storage-based connectivity can be simulated. We next coupled several faecal indicator organism (FIO; a common indicator of faecal pathogen contamination) behaviour and transport schemes to the robust hydrological models. A further calibration was then undertaken based on the ability of each coupled model to simulate daily FIO concentrations. This gave us a final set of coupled behavioural models from which we explored how in-stream FIO dynamics could be related to the changing connectivity between the three hydrological source areas, flow paths, water ages and consequent dominant runoff generation processes. We found that high levels of FIOs were transient and episodic, and strongly correlated with periods of high connectivity through overland flow. This non-linearity in connectivity and FIO flux was successfully captured within our dynamic, tracer-aided hydrological model.

Time-Dependent Testing Evaluation and Modeling for Rubber Stopper Seal Performance.

PubMed

Zeng, Qingyu; Zhao, Xia

2018-01-01

Sufficient rubber stopper sealing performance throughout the entire sealed product life cycle is essential for maintaining container closure integrity in the parenteral packaging industry. However, prior publications have lacked systematic considerations for the time-dependent influence on sealing performance that results from the viscoelastic characteristics of the rubber stoppers. In this paper, we report results of an effort to study these effects by applying both compression stress relaxation testing and residual seal force testing for time-dependent experimental data collection. These experiments were followed by modeling fit calculations based on the Maxwell-Wiechert theory modified with the Kohlrausch-Williams-Watts stretched exponential function, resulting in a nonlinear, time-dependent sealing force model. By employing both testing evaluations and modeling calculations, an in-depth understanding of the time-dependent effects on rubber stopper sealing force was developed. Both testing and modeling data show good consistency, demonstrating that the sealing force decays exponentially over time and eventually levels off because of the viscoelastic nature of the rubber stoppers. The nonlinearity of stress relaxation derives from the viscoelastic characteristics of the rubber stoppers coupled with the large stopper compression deformation into restrained geometry conditions. The modeling fit with capability to handle actual testing data can be employed as a tool to calculate the compression stress relaxation and residual seal force throughout the entire sealed product life cycle. In addition to being time-dependent, stress relaxation is also experimentally shown to be temperature-dependent. The present work provides a new, integrated methodology framework and some fresh insights to the parenteral packaging industry for practically and proactively considering, designing, setting up, controlling, and managing stopper sealing performance throughout the entire sealed product life cycle. LAY ABSTRACT: Historical publications in the parenteral packaging industry have lacked systematic considerations for the time-dependent influence on the sealing performance that results from effects of viscoelastic characteristic of the rubber stoppers. This study applied compression stress relaxation testing and residual seal force testing for time-dependent experimental data collection. These experiments were followed by modeling fit calculations based on the Maxwell-Wiechert theory modified with the Kohlrausch-Williams-Watts stretched exponential function, resulting in a nonlinear, time-dependent sealing force model. Experimental and modeling data show good consistency, demonstrating that sealing force decays exponentially over time and eventually levels off. The nonlinearity of stress relaxation derives from the viscoelastic characteristics of the rubber stoppers coupled with the large stopper compression deformation into restrained geometry conditions. In addition to being time-dependent stress relaxation, it is also experimentally shown to be temperature-dependent. The present work provides a new, integrated methodology framework and some fresh insights to the industry for practically and proactively considering, designing, setting up, controlling, and managing of the stopper sealing performance throughout the entire sealed product life cycle. © PDA, Inc. 2018.

Registration of 4D time-series of cardiac images with multichannel Diffeomorphic Demons.

PubMed

Peyrat, Jean-Marc; Delingette, Hervé; Sermesant, Maxime; Pennec, Xavier; Xu, Chenyang; Ayache, Nicholas

2008-01-01

In this paper, we propose a generic framework for intersubject non-linear registration of 4D time-series images. In this framework, spatio-temporal registration is defined by mapping trajectories of physical points as opposed to spatial registration that solely aims at mapping homologous points. First, we determine the trajectories we want to register in each sequence using a motion tracking algorithm based on the Diffeomorphic Demons algorithm. Then, we perform simultaneously pairwise registrations of corresponding time-points with the constraint to map the same physical points over time. We show this trajectory registration can be formulated as a multichannel registration of 3D images. We solve it using the Diffeomorphic Demons algorithm extended to vector-valued 3D images. This framework is applied to the inter-subject non-linear registration of 4D cardiac CT sequences.

Hybrid Optimization Parallel Search PACKage

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

2009-11-10

HOPSPACK is open source software for solving optimization problems without derivatives. Application problems may have a fully nonlinear objective function, bound constraints, and linear and nonlinear constraints. Problem variables may be continuous, integer-valued, or a mixture of both. The software provides a framework that supports any derivative-free type of solver algorithm. Through the framework, solvers request parallel function evaluation, which may use MPI (multiple machines) or multithreading (multiple processors/cores on one machine). The framework provides a Cache and Pending Cache of saved evaluations that reduces execution time and facilitates restarts. Solvers can dynamically create other algorithms to solve subproblems, amore » useful technique for handling multiple start points and integer-valued variables. HOPSPACK ships with the Generating Set Search (GSS) algorithm, developed at Sandia as part of the APPSPACK open source software project.« less

A non-linear data mining parameter selection algorithm for continuous variables

PubMed Central

Razavi, Marianne; Brady, Sean

2017-01-01

In this article, we propose a new data mining algorithm, by which one can both capture the non-linearity in data and also find the best subset model. To produce an enhanced subset of the original variables, a preferred selection method should have the potential of adding a supplementary level of regression analysis that would capture complex relationships in the data via mathematical transformation of the predictors and exploration of synergistic effects of combined variables. The method that we present here has the potential to produce an optimal subset of variables, rendering the overall process of model selection more efficient. This algorithm introduces interpretable parameters by transforming the original inputs and also a faithful fit to the data. The core objective of this paper is to introduce a new estimation technique for the classical least square regression framework. This new automatic variable transformation and model selection method could offer an optimal and stable model that minimizes the mean square error and variability, while combining all possible subset selection methodology with the inclusion variable transformations and interactions. Moreover, this method controls multicollinearity, leading to an optimal set of explanatory variables. PMID:29131829

A tree-parenchyma coupled model for lung ventilation simulation.

PubMed

Pozin, Nicolas; Montesantos, Spyridon; Katz, Ira; Pichelin, Marine; Vignon-Clementel, Irene; Grandmont, Céline

2017-11-01

In this article, we develop a lung ventilation model. The parenchyma is described as an elastic homogenized media. It is irrigated by a space-filling dyadic resistive pipe network, which represents the tracheobronchial tree. In this model, the tree and the parenchyma are strongly coupled. The tree induces an extra viscous term in the system constitutive relation, which leads, in the finite element framework, to a full matrix. We consider an efficient algorithm that takes advantage of the tree structure to enable a fast matrix-vector product computation. This framework can be used to model both free and mechanically induced respiration, in health and disease. Patient-specific lung geometries acquired from computed tomography scans are considered. Realistic Dirichlet boundary conditions can be deduced from surface registration on computed tomography images. The model is compared to a more classical exit compartment approach. Results illustrate the coupling between the tree and the parenchyma, at global and regional levels, and how conditions for the purely 0D model can be inferred. Different types of boundary conditions are tested, including a nonlinear Robin model of the surrounding lung structures. Copyright © 2017 John Wiley & Sons, Ltd.

Potential for wind extraction from 4D-Var assimilation of aerosols and moisture

NASA Astrophysics Data System (ADS)

Zaplotnik, Žiga; Žagar, Nedjeljka

2017-04-01

We discuss the potential of the four-dimensional variational data assimilation (4D-Var) to retrieve the unobserved wind field from observations of atmospheric tracers and the mass field through internal model dynamics and the multivariate relationships in the background-error term for 4D-Var. The presence of non-linear moist dynamics makes the wind retrieval from tracers very difficult. On the other hand, it has been shown that moisture observations strongly influence both tropical and mid-latitude wind field in 4D-Var. We present an intermediate complexity model that describes nonlinear interactions between the wind, temperature, aerosols and moisture including their sinks and sources in the framework of the so-called first baroclinic mode atmosphere envisaged by A. Gill. Aerosol physical processes, which are included in the model, are the non-linear advection, diffusion and sources and sinks that exist as dry and wet deposition and diffusion. Precipitation is parametrized according to the Betts-Miller scheme. The control vector for 4D-Var includes aerosols, moisture and the three dynamical variables. The former is analysed univariately whereas wind field and mass field are analysed in a multivariate fashion taking into account quasi-geostrophic and unbalanced dynamics. The OSSE type of studies are performed for the tropical region to assess the ability of 4D-Var to extract wind-field information from the time series of observations of tracers as a function of the flow nonlinearity, the observations density and the length of the assimilation window (12 hours and 24 hours), in dry and moist environment. Results show that the 4D-Var assimilation of aerosols and temperature data is beneficial for the wind analysis with analysis errors strongly dependent on the moist processes and reliable background-error covariances.

Emulation of the MBM-MEDUSA model: exploring the sea level and the basin-to-shelf transfer influence on the system dynamics

NASA Astrophysics Data System (ADS)

Ermakov, Ilya; Crucifix, Michel; Munhoven, Guy

2013-04-01

Complex climate models require high computational burden. However, computational limitations may be avoided by using emulators. In this work we present several approaches for dynamical emulation (also called metamodelling) of the Multi-Box Model (MBM) coupled to the Model of Early Diagenesis in the Upper Sediment A (MEDUSA) that simulates the carbon cycle of the ocean and atmosphere [1]. We consider two experiments performed on the MBM-MEDUSA that explore the Basin-to-Shelf Transfer (BST) dynamics. In both experiments the sea level is varied according to a paleo sea level reconstruction. Such experiments are interesting because the BST is an important cause of the CO2 variation and the dynamics is potentially nonlinear. The output that we are interested in is the variation of the carbon dioxide partial pressure in the atmosphere over the Pleistocene. The first experiment considers that the BST is fixed constant during the simulation. In the second experiment the BST is interactively adjusted according to the sea level, since the sea level is the primary control of the growth and decay of coral reefs and other shelf carbon reservoirs. The main aim of the present contribution is to create a metamodel of the MBM-MEDUSA using the Dynamic Emulation Modelling methodology [2] and compare the results obtained using linear and non-linear methods. The first step in the emulation methodology used in this work is to identify the structure of the metamodel. In order to select an optimal approach for emulation we compare the results of identification obtained by the simple linear and more complex nonlinear models. In order to identify the metamodel in the first experiment the simple linear regression and the least-squares method is sufficient to obtain a 99,9% fit between the temporal outputs of the model and the metamodel. For the second experiment the MBM's output is highly nonlinear. In this case we apply nonlinear models, such as, NARX, Hammerstein model, and an 'ad-hoc' switching model. After the identification we perform the parameter mapping using spline interpolation and validate the emulator on a new set of parameters. References: [1] G. Munhoven, "Glacial-interglacial rain ratio changes: Implications for atmospheric CO2 and ocean-sediment interaction," Deep-Sea Res Pt II, vol. 54, pp. 722-746, 2007. [2] A. Castelletti et al., "A general framework for Dynamic Emulation Modelling in environmental problems," Environ Modell Softw, vol. 34, pp. 5-18, 2012.

Nonlinear Polarimetric Microscopy for Biomedical Imaging

NASA Astrophysics Data System (ADS)

Samim, Masood

A framework for the nonlinear optical polarimetry and polarimetric microscopy is developed. Mathematical equations are derived in terms of linear and nonlinear Stokes Mueller formalism, which comprehensively characterize the polarization properties of the incoming and outgoing radiations, and provide structural information about the organization of the investigated materials. The algebraic formalism developed in this thesis simplifies many predictions for a nonlinear polarimetry study and provides an intuitive understanding of various polarization properties for radiations and the intervening medium. For polarimetric microscopy experiments, a custom fast-scanning differential polarization microscope is developed, which is also capable of real-time three-dimensional imaging. The setup is equipped with a pair of high-speed resonant and galvanometric scanning mirrors, and supplemented by advanced adaptive optics and data acquisition modules. The scanning mirrors when combined with the adaptive optics deformable mirror enable fast 3D imaging. Deformable membrane mirrors and genetic algorithm optimization routines are employed to improve the imaging conditions including correcting the optical aberrations, maximizing signal intensities, and minimizing point-spread-functions of the focal volume. A field-programmable-gate array (FPGA) chip is exploited to rapidly acquire and process the multidimensional data. Using the nonlinear optical polarimetry framework and the home-built polarization microscope, a few biologically important tissues are measured and analyzed to gain insight as to their structure and dynamics. The structure and distribution of muscle sarcomere myosins, connective tissue collagen, carbohydrate-rich starch, and fruit fly eye retinal molecules are characterized with revealing polarization studies. In each case, using the theoretical framework, polarization sensitive data are analyzed to decipher the molecular orientations and nonlinear optical susceptibilities. The developed nonlinear optical polarimetric microscopy is applicable to a wide variety of structural studies on ordered materials, and provides a non-invasive possibility to study the structural organization and dynamics within biological samples. For example, the technique is well suited for studies of a muscle contraction, histopathology of collagen structure for cancer tissue diagnostics, investigations of the polysacharide structural organization within a starch granule of a plant, or developmental study of the retina in an eye, among other applications.

IMPLICATIONS OF NON-LOCALITY OF TRANSPORT IN GEOMORPHIC TRANSPORT LAWS: HILLSLOPES AND LANDSCAPE EVOLUTION MODELING

NASA Astrophysics Data System (ADS)

Foufoula-Georgiou, E.; Ganti, V. K.; Dietrich, W. E.

2009-12-01

Sediment transport on hillslopes can be thought of as a hopping process, where the sediment moves in a series of jumps. A wide range of processes shape the hillslopes which can move sediment to a large distance in the downslope direction, thus, resulting in a broad-tail in the probability density function (PDF) of hopping lengths. Here, we argue that such a broad-tailed distribution calls for a non-local computation of sediment flux, where the sediment flux is not only a function of local topographic quantities but is an integral flux which takes into account the upslope topographic “memory” of the point of interest. We encapsulate this non-local behavior into a simple fractional diffusive model that involves fractional (non-integer) derivatives. We present theoretical predictions from this nonlocal model and demonstrate a nonlinear dependence of sediment flux on local gradient, consistent with observations. Further, we demonstrate that the non-local model naturally eliminates the scale-dependence exhibited by any local (linear or nonlinear) sediment transport model. An extension to a 2-D framework, where the fractional derivative can be cast into a mixture of directional derivatives, is discussed together with the implications of introducing non-locality into existing landscape evolution models.

High-order nonlinear susceptibilities of He

NASA Astrophysics Data System (ADS)

Liu, W.-C.; Clark, Charles W.

1996-05-01

High-order nonlinear optical response of noble gases to intense laser radiation is of considerable experimental interest, but is difficult to measure or calculate accurately. We have begun a set of calculations of frequency-dependent nonlinear susceptibilities of He 1s^2, within the framework of Rayleigh-Schrödinger perturbation theory at lowest applicable order, with the goal of providing critically evaluated atomic data for modelling high harmonic generation processes. The atomic Hamiltonian is decomposed in term of Hylleraas coordinates and spherical harmonics using the formalism of Pont and Shakeshaft (M. Pont and R. Shakeshaft, Phy. Rev. A 51), 257 (1995), and the hierarchy of inhomogeneous equations of perturbation theory is solved iteratively. A combination of Hylleraas and Frankowski basis functions is used(J. D. Baker, Master thesis, U. Delaware (1988); J. D. Baker, R. N. Hill, and J. D. Morgan, AIP Conference Proceedings 189) 123(1989); the compact Hylleraas basis provides a highly accurate representation of the ground state wavefunction, whereas the diffuse Frankowski basis functions efficiently reproduce the correct asymptotic structure of the perturbed orbitals.

A Tensor-Product-Kernel Framework for Multiscale Neural Activity Decoding and Control

PubMed Central

Li, Lin; Brockmeier, Austin J.; Choi, John S.; Francis, Joseph T.; Sanchez, Justin C.; Príncipe, José C.

2014-01-01

Brain machine interfaces (BMIs) have attracted intense attention as a promising technology for directly interfacing computers or prostheses with the brain's motor and sensory areas, thereby bypassing the body. The availability of multiscale neural recordings including spike trains and local field potentials (LFPs) brings potential opportunities to enhance computational modeling by enriching the characterization of the neural system state. However, heterogeneity on data type (spike timing versus continuous amplitude signals) and spatiotemporal scale complicates the model integration of multiscale neural activity. In this paper, we propose a tensor-product-kernel-based framework to integrate the multiscale activity and exploit the complementary information available in multiscale neural activity. This provides a common mathematical framework for incorporating signals from different domains. The approach is applied to the problem of neural decoding and control. For neural decoding, the framework is able to identify the nonlinear functional relationship between the multiscale neural responses and the stimuli using general purpose kernel adaptive filtering. In a sensory stimulation experiment, the tensor-product-kernel decoder outperforms decoders that use only a single neural data type. In addition, an adaptive inverse controller for delivering electrical microstimulation patterns that utilizes the tensor-product kernel achieves promising results in emulating the responses to natural stimulation. PMID:24829569