Framework Of Nonlinear Model Research Articles

Model Error, Information Barriers, State Estimation and Prediction in Complex Multiscale Systems.

Complex multiscale systems are ubiquitous in many areas. This research expository article discusses the development and applications of a recent information-theoretic framework as well as novel reduced-order nonlinear modeling strategies for understanding and predicting complex multiscale systems. The topics include the basic mathematical properties and qualitative features of complex multiscale systems, statistical prediction and uncertainty quantification, state estimation or data assimilation, and coping with the inevitable model errors in approximating such complex systems. Here, the information-theoretic framework is applied to rigorously quantify the model fidelity, model sensitivity and information barriers arising from different approximation strategies. It also succeeds in assessing the skill of filtering and predicting complex dynamical systems and overcomes the shortcomings in traditional path-wise measurements such as the failure in measuring extreme events. In addition, information theory is incorporated into a systematic data-driven nonlinear stochastic modeling framework that allows effective predictions of nonlinear intermittent time series. Finally, new efficient reduced-order nonlinear modeling strategies combined with information theory for model calibration provide skillful predictions of intermittent extreme events in spatially-extended complex dynamical systems. The contents here include the general mathematical theories, effective numerical procedures, instructive qualitative models, and concrete models from climate, atmosphere and ocean science.

Assimilation of semi‐qualitative observations with a stochastic ensemble Kalman filter

The ensemble Kalman filter assumes observations to be Gaussian random variables with a pre‐specified mean and variance. In practice, observations may also have detection limits, for instance when a gauge has a minimum or maximum value. In such cases, most data assimilation schemes discard out‐of‐range values, treating them as “not a number,” with the loss of possibly useful qualitative information.The current work focuses on the development of a data assimilation scheme that tackles observations with a detection limit. We present the Ensemble Kalman Filter Semi‐Qualitative (EnKF‐SQ) and test its performance against the Partial Deterministic Ensemble Kalman Filter (PDEnKF) of Borup et al. Both are designed to assimilate out‐of‐range observations explicitly: the out‐of‐range values are qualitative by nature (inequalities), but one can postulate a probability distribution for them and then update the ensemble members accordingly. The EnKF‐SQ is tested within the framework of twin experiments, using both linear and nonlinear toy models. Different sensitivity experiments are conducted to assess the influence of the ensemble size, observation detection limit and number of observations on the performance of the filter. Our numerical results show that assimilating qualitative observations using the proposed scheme improves the overall forecast mean, making it viable for testing on more realistic applications such as sea‐ice models.

Can trees at high elevations compensate for growth reductions at low elevations due to climate warming?

Radial tree stem growth of Norway spruce (Picea abies (L.) H. Karst.), European beech (Fagus sylvatica L.), Scots pine (Pinus sylvestris L.), and stone pine (Pinus cembra L.) was monitored from 2012 to 2015 across sites in Austria with high-resolution dendrometers. Seasonal cumulative diameter increment was modeled using a hierarchical nonlinear mixed-effects model framework based on a logistic growth curve. In the dry and warm year 2015, the average annual diameter increment of 0.30 cm decreased by 50% on lower elevation sites and by 10% on higher elevation sites. In the cool and moist year 2014, Norway spruce achieved a higher annual diameter increment than European beech, whereas the opposite occurred in the dry and warm years 2013 and 2015. In the mixed beech–spruce stand, beech’s consumptive water-use strategy has obviously caused intensified stress for spruce in these drought periods. On higher elevation sites, Norway spruce reacted more sensitively to climate fluctuation compared with stone pine, but overall reactions were only weak. Productivity varied strongly depending on the social status of the tree, with dominant and intermediate trees suffering more from drought. As warming and drought lowers increment rates on lower elevation sites and as trees on higher elevation sites react less flexibly, productivity losses are expected for Austrian forests due to climate warming.

Ask Your Doctor Whether This Product is Right for You: A Bayesian Joint Model for Patient Drug Requests and Physician Prescriptions

SummaryThe goal of this research is to study jointly physician prescription decisions and patient drug request behaviours. We have adopted a binary logit model and a multinomial logit model to study patient drug request data with excessive zero requests and a multinomial logit model to capture physician prescription decisions. These models are further joined by a flexible non-parametric multivariate distribution for their random effects. We also adopt an analytically consistent expression for interaction effects in our non-linear and joint modelling framework. We apply our model to a unique physician panel data set from the erectile dysfunction category. Our key empirical findings include that the triggering of drug requests by direct-to-consumer advertising (DTCA) is complex with category level DTCA reducing patients’ probabilities of making drug requests and drug-specific DTCA driving drug requests for the drug advertised, patients’ characteristics may play a role in both the influence of DTCA on drug requests and the influence of patients’ requests on physicians’ prescription decisions, patients’ drug requests have a positive effect on physicians’ prescription decisions and patients can be consistent with physicians in choosing a drug based on their diagnosis levels and some unobserved factors, and there are significant correlations between physician level random effects that drive both patients’ drug requests and physicians’ prescription decisions, which validate the joint modelling approach.

재정지출 수준이 실질환율에 미치는 임계효과 : 41개국 패널 자료 분석

The purpose of this paper is to investigate threshold effects of changes in government expenditure on real exchange rate for a panel of 41 countries during the period of 2000– 2015 in a nonlinear model framework. Panel threshold regression(PTR) model of Hansen(1999) is employed to estimate effects of possible threshold(s) of government expenditure on the real exchange rate. The results indicate that a threshold of government expenditure relative to GDP exists at about 17.65% level and a positive shock to government expenditure tends to induce real exchange rate appreciation at the government expenditure level below the threshold. However, no significant effect was detected when it was above the threshold level.

Magnetically charged black hole in framework of nonlinear electrodynamics model

A model of nonlinear electrodynamics is proposed and investigated in general relativity. We consider the magnetic black hole and find a regular solution which gives corrections into the Reissner–Nordström solution. At [Formula: see text] the asymptotic space–time becomes flat. The magnetic mass of the black hole is calculated and the metric function is obtained. At some values of the model parameter there can be one, two or no horizons. Thermodynamics of black holes is studied and we calculate the Hawking temperature and heat capacity of black holes. It is demonstrated that there is a phase transition of second order. At some parameters of the model black holes are thermodynamically stable.

TIPS and the VIX: Spillovers from Financial Panic to Breakeven Inflation in an Automated, Nonlinear Modeling Framework

AbstractThis paper examines the determinants of the breakeven inflation rate (BEI) on U.S. Treasury Inflation Protected Securities. After controlling for several measures of liquidity, inflation expectations and inflation uncertainty; financial fear itself (proxied with the Volatility Index or VIX) remains a primary influence on BEI. To delve into the mechanism underlying this association, the VIX is decomposed, using intraday data, into conditional variance and the variance premium capturing risk aversion. Aside from the 2008 crisis, most of the effect emanated from the variance premium. Following the crisis, indicators of bank insolvency risk gain prominence as well. Lastly, an automated nonlinear model finds convex effects of variance, and diminishing returns to insolvency risk and liquidity.

Statistical Characterization of the State-of-Health of Lithium-Ion Batteries with Weibull Distribution Function—A Consideration of Random Effect Model in Charge Capacity Decay Estimation

Effective prognosis of lithium-ion batteries involves the inclusion of the influences of uncertainties that can be incorporated through random effect parameters in a nonlinear mixed effect degradation model framework. This study is geared towards the estimation of the reliability of lithium-ion batteries, using parametric effects determination involving uncertainty, using a multiphase decay patterned sigmoidal model, experimental data and the Weibull distribution function. The random effect model, which uses Maximum Likelihood Estimation (MLE) and Stochastic Approximation Expectation Maximization (SAEM) algorithm to predict the parametric values, was found to estimate the remaining useful life (RUL) to an accuracy of more than 98%. The State-of-Health (SOH) of the batteries was estimated using the Weibull distribution function, which is found to be an appropriate formulation to use.

Waves in porous media saturated with bubbly liquid

Wave processes in a porous medium saturated with bubbly liquid, taking into account the nonlinearity of the oscillations of the bubbles, are numerically investigated. The nonlinearity is accounted in the equation of gas state and the equation of Rayleigh - Lamb. Numerical study in the framework of nonlinear model is performed for the first time. The dispersion relations for linear waves in a porous medium containing bubbly liquid, as well as for the main acoustic mode in a cylindrical cavity in such a medium, are obtained. Frequency dependences of velocity and attenuation of harmonic waves in a cylindrical waveguide are calculated. The influence properties of the bubbly liquid saturated porous medium on the wave velocity and attenuation and the penetration depth of perturbation into the surrounding porous medium are analyzed. The passage of the step wave from fluid into a porous medium saturated with bubbly liquid is investigated. The influence of porous medium parameters and intensity of the incident wave on the wave evolution in bubbly liquid saturated porous medium is studied. The calculation results show good qualitative agreement with the experimental data of other authors.

Integrated TK-TD modeling for drug-induced concurrent tachycardia and QT changes in beagle dogs.

Drug-induced cardiotoxicity, including tachycardia and QT prolongation, remains a major safety concern that needs to be identified and its risk mitigated in early stages of drug development. In the present study, an integrated toxicokinetic-toxicodynamic (TK-TD) modeling approach within a nonlinear mixed-effect modeling framework is applied to investigate concurrent abnormal heart rate and QT changes in three beagle dogs, using a Novartis internal compound (NVS001) as the case example. By accounting for saturable drug absorption, circadian rhythms, drug-effect tolerance, and nonlinear rate-dependency of QT interval, the dynamic TK-TD model captures the experimentally observed drug effects on heart rate and QT interval across a wide dosing range of NVS001 in beagle dogs. Further analyses reveal that the NVS001-induced QT prolongation observed in the low-dose groups is potentially caused by direct drug inhibition on the hERG channel, while the apparent QT shortening in the high-dose groups may be due to strong rate-dependency of QT at high heart rates. This study also suggests that the TK-TD model can be used to identify direct drug effects on the non-rate-dependent QT component by dissociating QT changes from tachycardia and deriving a new QT correction method. The integrated TK-TD model presented here may serve as a novel quantitative framework for evaluating drug-induced concurrent changes in heart rate and QT to potentially facilitate preclinical and clinical safety studies.

Modeling the spatiotemporal variations in brucellosis transmission

In this paper, we propose a nonlinear modeling framework to investigate the transmission dynamics of brucellosis, incorporating both the spatial and seasonal variations. The spatial modeling is based on a patch structure, and the seasonal impact is represented by utilizing time-periodic model parameters. We demonstrate this framework through a two-patch model and conduct detailed analysis, for the cases with and without seasonal oscillations, respectively. In particular, we establish the threshold dynamics results using the reproduction numbers defined under different scenarios. Our findings underscore the importance of including spatial and seasonal heterogeneities in the design of control strategies for brucellosis.

Efficient and robust nonlinear model for smart materials with application to composite magnetostrictive plates

This paper presents a computationally efficient and robust nonlinear modeling framework for smart materials. The framework describes a smart material system through a new 3D inversion scheme for coupled nonlinear constitutive equations which can be integrated with the variational form of governing equations. Building on the Newton technique, the inversion scheme can be applied to any nonlinear smart material with a differentiable direct constitutive model. To further improve computational efficiency, the inversion scheme is integrated with a reduced dimensional (2D) model for smart composite structures. The resulting coupled 2D framework is applied to an aluminum-Galfenol composite plate that operates in actuation mode, and is solved using multiphysics finite element software. Major and minor magnetostriction curves are obtained for the actuator displacements at the tip of the Galfenol element by applying unbiased and biased magnetic fields. A significant advantage in numerical convergence and computational time, an almost six-time speedup for a dynamic simulation case, is demonstrated via comparison with an existing approach for magnetostrictive material modeling. The framework is suitable for fast design and optimization of nonlinear smart material structures.

A non-linear mixed model approach for excess of loss benchmark rating

This paper proposes market conform individual benchmark rates for the excess of loss reinsurance of long tail insurance portfolios, that offer market references for the premium rates taking individual contractual conditions into account. The premium rates are expressed in terms of the percentage of the expected premium income of the covered insurance portfolio. We incorporate the specific reinsurance contractual conditions like stabilisation, interest sharing and deposit clauses as well as payment patterns and ’incurred but not (enough) reported’ information. The parameters of the benchmark model are estimated within the framework of non-linear mixed models. This approach allows to correct for different cedent specific conditions in the model, and so we refine the results from Verlaak et al. (Astin Bull 39, 2009) where only one benchmark was proposed for the whole market. The method is applied to the Belgian Motor Third Party Liability XL rates observed from 2001 till 2004.

Ask Your Doctor If this Product is Right for You: A Bayesian Zero-Inflated Multinomial Joint Model for Patient Drug Requests and Physician Prescriptions

The goal of this research is to study physicians' prescription decisions and patients' drug request behaviors jointly. We have developed a new zero-inflated multinomial (ZiMNL) choice model to study patient drug request data with excessive zero requests and a standard multinomial logit (MNL) model to capture physician prescriptions decisions. The two models are joined by a flexible nonparametric multivariate distribution for their random effects. We also adopt an analytically consistent expression for the interaction effect in our non-linear and joint modeling framework. We apply our model to a unique physician panel data set from the Erectile Dysfunction category. Our key empirical findings include the following: (1) the triggering of drug requests by DTCA is complicated with category level DTCA reducing patients' probability of making drug requests and drug specific DTCA driving drug requests for the advertised drug; (2) patient characteristics may play a role in the impact of DTCA on drug requests and the impact of patient requests on physicians' prescription decisions; (3) patient drug requests have a significant impact on physicians' prescription decisions and patients can be consistent with physicians in choosing a drug based on patient diagnosis level and some unobserved factors; (4) there are significant correlations among physician-level random effects that drive both patients' drug requests and physicians' prescription decisions, which validates the joint modeling approach.

Properties of strongly magnetized ultradense matter and its effects on magnetar pulsations

We investigate the effect of strong magnetic fields on the adiabatic radial oscillations of hadronic stars. We describe magnetized hadronic matter within the framework of the relativistic nonlinear Walecka model and integrate the equations of relativistic radial oscillations to determine the fundamental pulsation mode. We consider that the magnetic field increases, in a density dependent way, from the surface, where it has a typical magnetar value of ${10}^{15}\phantom{\rule{4pt}{0ex}}\mathrm{G}$, to the interior of the star, where it can be as large as $3\ifmmode\times\else\texttimes\fi{}{10}^{18}\phantom{\rule{4pt}{0ex}}\mathrm{G}$. We show that magnetic fields of the order of ${10}^{18}\phantom{\rule{4pt}{0ex}}\mathrm{G}$ at the stellar core produce a significant change in the frequency of neutron star pulsations with respect to unmagnetized objects. If radial pulsations are excited in magnetar flares, they can leave an imprint in the flare lightcurves and open a new window for the study of highly magnetized ultradense matter.

The Influence of Patient Characteristics on Anticholinergic Events in Older People

Aims: To examine patient characteristics that predict adverse anticholinergic-type events in older people. Methods: This retrospective population-level study included 2,248 hospitalised patients. Individual data on medicines that are commonly associated with anticholinergic events (delirium, constipation and urinary retention) were identified. Patient characteristics examined were medicines with anticholinergic effects (ACh burden), age, sex, non-anticholinergic medicines (non-ACM), Charlson comorbidity index scores and ethnicity. The Akaike information criterion was used for model selection. The data were analysed using logistic regression models for anticholinergic events using the software NONMEM. Results: ACh burden was found to be a significant independent predictor for developing an anticholinergic event [adjusted odds ratio (aOR): 3.21, 95% CI: 1.23-5.81] for those taking an average of 5 anticholinergic medicines compared to those taking 1. Both non-ACM and age were also independent risk factors (aOR: 1.41, 95% CI: 1.31-1.51 and aOR: 1.08, 95% CI: 1.05-1.10, respectively). Conclusion: To our knowledge, this is the first study that has examined population-level data in a nonlinear model framework to predict anticholinergic-type adverse events. This study evaluated the relationship between important patient characteristics and the occurrence of anticholinergic-type events. These findings reinforce the clinical significance of reviewing anticholinergic medicines in older people.

Dynamic Modeling and Analysis of a High Pressure Regulator

Pressure regulator is a common device used to regulate the working pressure for plants and machines. In aerospace propulsion systems, it is used to pressurize liquid propellant rocket tanks at specified pressure for obtaining the required propellant mass flow rate. In this paper, a generalized model is developed to perform dynamic analysis of a pressure regulator so that constant pressure at outlet can be attained. A nonlinear mathematical model of pressure regulator is developed that consists of dynamic equation of pressure, temperature, equation of mass flow rate, and moving shaft inside regulator. The system of nonlinear and coupled differential equations is numerically simulated and computation of pressure and temperature is carried out for required conditions and given design parameters. Valve opening and mass flow rate are also found as a function of given inlet pressure and time. In the end, an analytical solution based on constant mass flow rate assumption is compared with nonlinear formulation. The results demonstrate a high degree of confidence in the nonlinear modeling framework proposed in this paper. The proposed model solves a real problem of liquid rocket propulsion system. For the real system under consideration, inlet pressure of regulator is decreased linearly from 150 bar to 60 bar and outlet pressure of nearly 15 bar is required from pressure regulator for the complete operating time of 19 s.

An accurate circuit-based description of retinal ganglion cell computation

Visual processing depends on computations performed by complex neural circuits. Although the circuitry in the retina has been extensively characterized, common functional models of how ganglion cell spike trains represent visual stimuli typically rely on linear descriptions of their receptive field [1]. Different types of nonlinear models have offered improvements in spike train prediction, but such improvements are often incremental, and in most cases not linked to known elements of the retinal circuit. Here, we describe a new nonlinear model framework designed to represent key elements of the retinal circuit, which can predict recorded retinal ganglion cell spike trains with high temporal precision. We used recordings of both synaptic currents (via voltage-clamp recordings) and spike (via loose patch recordings) from the same ON Alpha ganglion cells in the mouse retina in order to build a two-stage nonlinear model. This model describes ganglion cell computation as sums and products of excitatory and inhibitory inputs [2]. Model parameters were estimated based on either intracellular or spike train data using a maximum-likelihood framework. We found that excitatory synaptic currents to the ganglion cell are well described by an excitatory input combined with divisive suppression, both elements described by LN models fit to intracellular data. Using stimuli with center-surround structure, we demonstrate that this divisive suppression arises from the surround, and is the likely result of presynaptic inhibition mediated by amacrine cells [3], rather than synaptic depression [4]. We then extended this nonlinear model of synaptic currents to explain spike response of the ganglion cell by incorporating a spiking nonlinearity with spike refractoriness. All model parameters could be fit using the spike trains alone, resulting in a prediction of the excitatory currents that closely matched the models fit directly to the currents. The resulting model had unprecedented ability to predict both synaptic current and spike trains (with >90% of the explainable variance) at one millisecond resolution on cross-validation datasets, capturing both fast transient responses in synaptic current, as well as the high precision of spike train responses. Furthermore, the model output automatically adapted to contrast, and could predict the responses across contrast levels with similar accuracy without any change in model parameters. Notably, the nonlinear structure of the model was particular to ON Alpha ganglion cells, and other retinal ganglion cell types had distinct computational structures, likely corresponding to different underlying connectivity within the retina governing their processing of vision. Thus, by targeting a nonlinear model based on the specific computations performed by retinal circuit elements, we uncovered an extremely accurate description of retinal processing, and identified two-stage computational properties that can be linked to elements of the retinal circuit. In addition to providing an accurate description of ON Alpha cells, such computational framework also sets a foundation for understanding the different roles of the ~20 ganglion cell types that comprise the input to the rest of the visual system.

On the observability of turbulent transport rates by Argo: supporting evidence from an inversion experiment

Abstract. Although estimation of turbulent transport parameters using inverse methods is not new, there is little evaluation of the method in the literature. Here, it is shown that extended observation of the broad-scale hydrography by Argo provides a path to improved estimates of regional turbulent transport rates. Results from a 20-year ocean state estimate produced with the ECCO v4 (Estimating the Circulation and Climate of the Ocean, version 4) non-linear inverse modeling framework provide supporting evidence. Turbulent transport parameter maps are estimated under the constraints of fitting the extensive collection of Argo profiles collected through 2011. The adjusted parameters dramatically reduce misfits to in situ profiles as compared with earlier ECCO solutions. They also yield a clear reduction in the model drift away from observations over multi-century-long simulations, both for assimilated variables (temperature and salinity) and independent variables (biogeochemical tracers). Despite the minimal constraints imposed specifically on the estimated parameters, their geography is physically plausible and exhibits close connections with the upper-ocean stratification as observed by Argo. The estimated parameter adjustments furthermore have first-order impacts on upper-ocean stratification and mixed layer depths over 20 years. These results identify the constraint of fitting Argo profiles as an effective observational basis for regional turbulent transport rate inversions. Uncertainties and further improvements of the method are discussed.

ECCO version 4: an integrated framework for non-linear inverse modeling and global ocean state estimation

Abstract. This paper presents the ECCO v4 non-linear inverse modeling framework and its baseline solution for the evolving ocean state over the period 1992–2011. Both components are publicly available and subjected to regular, automated regression tests. The modeling framework includes sets of global conformal grids, a global model setup, implementations of data constraints and control parameters, an interface to algorithmic differentiation, as well as a grid-independent, fully capable Matlab toolbox. The baseline ECCO v4 solution is a dynamically consistent ocean state estimate without unidentified sources of heat and buoyancy, which any interested user will be able to reproduce accurately. The solution is an acceptable fit to most data and has been found to be physically plausible in many respects, as documented here and in related publications. Users are being provided with capabilities to assess model–data misfits for themselves. The synergy between modeling and data synthesis is asserted through the joint presentation of the modeling framework and the state estimate. In particular, the inverse estimate of parameterized physics was instrumental in improving the fit to the observed hydrography, and becomes an integral part of the ocean model setup available for general use. More generally, a first assessment of the relative importance of external, parametric and structural model errors is presented. Parametric and external model uncertainties appear to be of comparable importance and dominate over structural model uncertainty. The results generally underline the importance of including turbulent transport parameters in the inverse problem.