Influence of muscle metabolic heterogeneity in determining the V̇o2p kinetic response to ramp-incremental exercise

The pulmonary O2 uptake (V̇o2p) response to ramp-incremental (RI) exercise increases linearly with work rate (WR) after an early exponential phase, implying that a single time constant (τ) and gain (G) describe the response. However, variability in τ and G of V̇o2p kinetics to different step increments in WR is documented. We hypothesized that the “linear” V̇o2p-WR relationship during RI exercise results from the conflation between WR-dependent changes in τ and G. Nine men performed three or four repeats of RI exercise (30 W/min) and two step-incremental protocols consisting of four 60-W increments beginning from 20 W or 50 W. During testing, breath-by-breath V̇o2p was measured by mass spectrometry and volume turbine. For each individual, the V̇o2p RI response was characterized with exponential functions containing either constant or variable τ and G values. A relationship between τ and G vs. WR was determined from the step-incremental protocols to derive the variable model parameters. τ and G increased from 21 ± 5 to 98 ± 20 s and from 8.7 ± 0.6 to 12.0 ± 1.9 ml·min−1·W−1 for WRs of 20-230 W, respectively, and were best described by a second-order (τ) and a first-order (G) polynomial function of WR (lowest Akaike information criterion score). The sum of squared residuals was not different ( P > 0.05) when the V̇o2p RI response was characterized with either the constant or variable models, indicating that they described the response equally well. Results suggest that τ and G increase progressively with WR during RI exercise. Importantly, these relationships may conflate to produce a linear V̇o2p-WR response, emphasizing the influence of metabolic heterogeneity in determining the apparent V̇o2p-WR relationship during RI exercise.

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First-Order Learning Models With the GDINA: Estimation With the EM Algorithm and Applications

Applied Psychological Measurement ◽

10.1177/0146621621990746 ◽

2021 ◽

Vol 45 (3) ◽

pp. 143-158

Author(s):

Hulya D. Yigit ◽

Jeffrey A. Douglas

Keyword(s):

Em Algorithm ◽

Spatial Reasoning ◽

Computation Time ◽

Information Criterion ◽

Measurement Model ◽

Error Rates ◽

Estimation Accuracy ◽

Model Parameters ◽

Parameter Recovery ◽

First Order

In learning environments, understanding the longitudinal path of learning is one of the main goals. Cognitive diagnostic models (CDMs) for measurement combined with a transition model for mastery may be beneficial for providing fine-grained information about students’ knowledge profiles over time. An efficient algorithm to estimate model parameters would augment the practicality of this combination. In this study, the Expectation–Maximization (EM) algorithm is presented for the estimation of student learning trajectories with the GDINA (generalized deterministic inputs, noisy, “and” gate) and some of its submodels for the measurement component, and a first-order Markov model for learning transitions is implemented. A simulation study is conducted to investigate the efficiency of the algorithm in estimation accuracy of student and model parameters under several factors—sample size, number of attributes, number of time points in a test, and complexity of the measurement model. Attribute- and vector-level agreement rates as well as the root mean square error rates of the model parameters are investigated. In addition, the computer run times for converging are recorded. The result shows that for a majority of the conditions, the accuracy rates of the parameters are quite promising in conjunction with relatively short computation times. Only for the conditions with relatively low sample sizes and high numbers of attributes, the computation time increases with a reduction parameter recovery rate. An application using spatial reasoning data is given. Based on the Bayesian information criterion (BIC), the model fit analysis shows that the DINA (deterministic inputs, noisy, “and” gate) model is preferable to the GDINA with these data.

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Fate of false vacua in holographic first-order phase transitions

Journal of High Energy Physics ◽

10.1007/jhep12(2020)200 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Francesco Bigazzi ◽

Alessio Caddeo ◽

Aldo L. Cotrone ◽

Angel Paredes

Keyword(s):

Phase Transitions ◽

Chiral Symmetry ◽

Metastable Phase ◽

Chiral Symmetry Breaking ◽

Model Parameters ◽

Temperature Phase ◽

Thin Wall ◽

Critical Temperatures ◽

First Order ◽

First Order Phase

Abstract Using the holographic correspondence as a tool, we study the dynamics of first-order phase transitions in strongly coupled gauge theories at finite temperature. Considering an evolution from the large to the small temperature phase, we compute the nucleation rate of bubbles of true vacuum in the metastable phase. For this purpose, we find the relevant configurations (bounces) interpolating between the vacua and we compute the related effective actions. We start by revisiting the compact Randall-Sundrum model at high temperature. Using holographic renormalization, we compute the derivative term in the effective bounce action, that was missing in the literature. Then, we address the full problem within the top-down Witten-Sakai-Sugimoto model. It displays both a confinement/deconfinement and a chiral symmetry breaking/restoration phase transition which, depending on the model parameters, can happen at different critical temperatures. For the confinement/deconfinement case we perform the numerical analysis of an effective description of the transition and also provide analytic expressions using thick and thin wall approximations. For the chiral symmetry transition, we implement a variational approach that allows us to address the challenging non-linear problem stemming from the Dirac-Born-Infeld action.

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Gaussian Processes Proxy Model with Latent Variable Models and Variogram-Based Sensitivity Analysis for Assisted History Matching

Energies ◽

10.3390/en13174290 ◽

2020 ◽

Vol 13 (17) ◽

pp. 4290

Author(s):

Dongmei Zhang ◽

Yuyang Zhang ◽

Bohou Jiang ◽

Xinwei Jiang ◽

Zhijiang Kang

Keyword(s):

Sensitivity Analysis ◽

Gaussian Processes ◽

Latent Variable ◽

History Matching ◽

Latent Variable Models ◽

High Dimensional ◽

Model Parameters ◽

Variable Model ◽

Assisted History Matching ◽

Proxy Models

Reservoir history matching is a well-known inverse problem for production prediction where enormous uncertain reservoir parameters of a reservoir numerical model are optimized by minimizing the misfit between the simulated and history production data. Gaussian Process (GP) has shown promising performance for assisted history matching due to the efficient nonparametric and nonlinear model with few model parameters to be tuned automatically. Recently introduced Gaussian Processes proxy models and Variogram Analysis of Response Surface-based sensitivity analysis (GP-VARS) uses forward and inverse Gaussian Processes (GP) based proxy models with the VARS-based sensitivity analysis to optimize the high-dimensional reservoir parameters. However, the inverse GP solution (GPIS) in GP-VARS are unsatisfactory especially for enormous reservoir parameters where the mapping from low-dimensional misfits to high-dimensional uncertain reservoir parameters could be poorly modeled by GP. To improve the performance of GP-VARS, in this paper we propose the Gaussian Processes proxy models with Latent Variable Models and VARS-based sensitivity analysis (GPLVM-VARS) where Gaussian Processes Latent Variable Model (GPLVM)-based inverse solution (GPLVMIS) instead of GP-based GPIS is provided with the inputs and outputs of GPIS reversed. The experimental results demonstrate the effectiveness of the proposed GPLVM-VARS in terms of accuracy and complexity. The source code of the proposed GPLVM-VARS is available at https://github.com/XinweiJiang/GPLVM-VARS.

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Determination of exothermic batch reactor specific model parameters

MATEC Web of Conferences ◽

10.1051/matecconf/201929201063 ◽

2019 ◽

Vol 292 ◽

pp. 01063

Author(s):

Lubomír Macků

Keyword(s):

Rate Constant ◽

Reaction Rate ◽

Batch Reactor ◽

Specific Model ◽

Reaction Rate Constant ◽

Order Reaction ◽

First Order Reaction ◽

Model Parameters ◽

Reactor Model ◽

First Order

An alternative method of determining exothermic reactor model parameters which include first order reaction rate constant is described in this paper. The method is based on known in reactor temperature development and is suitable for processes with changing quality of input substances. This method allows us to evaluate the reaction substances composition change and is also capable of the reaction rate constant (parameters of the Arrhenius equation) determination. Method can be used in exothermic batch or semi- batch reactors running processes based on the first order reaction. An example of such process is given here and the problem is shown on its mathematical model with the help of simulations.

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New Mathematical Modeling Approach for Predicting Microbial Inactivation by High Hydrostatic Pressure

Applied and Environmental Microbiology ◽

10.1128/aem.02211-06 ◽

2007 ◽

Vol 73 (8) ◽

pp. 2468-2478 ◽

Cited By ~ 35

Author(s):

Bernadette Klotz ◽

D. Leo Pyle ◽

Bernard M. Mackey

Keyword(s):

Microbial Inactivation ◽

Inactivation Kinetics ◽

Published Data ◽

Model Parameters ◽

Order Kinetic ◽

Square Root ◽

Additional Time ◽

Decimal Reduction Time ◽

First Order ◽

Primary Model

ABSTRACT A new primary model based on a thermodynamically consistent first-order kinetic approach was constructed to describe non-log-linear inactivation kinetics of pressure-treated bacteria. The model assumes a first-order process in which the specific inactivation rate changes inversely with the square root of time. The model gave reasonable fits to experimental data over six to seven orders of magnitude. It was also tested on 138 published data sets and provided good fits in about 70% of cases in which the shape of the curve followed the typical convex upward form. In the remainder of published examples, curves contained additional shoulder regions or extended tail regions. Curves with shoulders could be accommodated by including an additional time delay parameter and curves with tails shoulders could be accommodated by omitting points in the tail beyond the point at which survival levels remained more or less constant. The model parameters varied regularly with pressure, which may reflect a genuine mechanistic basis for the model. This property also allowed the calculation of (a) parameters analogous to the decimal reduction time D and z, the temperature increase needed to change the D value by a factor of 10, in thermal processing, and hence the processing conditions needed to attain a desired level of inactivation; and (b) the apparent thermodynamic volumes of activation associated with the lethal events. The hypothesis that inactivation rates changed as a function of the square root of time would be consistent with a diffusion-limited process.

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Complexity versus simplicity: an example of groundwater model ranking with the Akaike Information Criterion

Hydrology and Earth System Sciences Discussions ◽

10.5194/hessd-9-9687-2012 ◽

2012 ◽

Vol 9 (8) ◽

pp. 9687-9714 ◽

Cited By ~ 6

Author(s):

I. Engelhardt ◽

J. G. De Aguinaga ◽

H. Mikat ◽

C. Schüth ◽

O. Lenz ◽

...

Keyword(s):

Akaike Information Criterion ◽

Conceptual Models ◽

Information Criterion ◽

Model Parameters ◽

Groundwater Model ◽

Piezometric Head ◽

Simulated Groundwater ◽

Pumping Rates ◽

Uncalibrated Model ◽

Piezometric Heads

Abstract. A groundwater model characterized by a lack of field data to estimate hydraulic model parameters and boundary conditions combined with many piezometric head observations was investigated concerning model uncertainty. Different conceptual models with a stepwise increase from 0 to 30 adjustable parameters were calibrated using PEST. Residuals, sensitivities, the Akaike Information Criterion (AIC), and the likelihood of each model were computed. As expected, residuals and standard errors decreased with an increasing amount of adjustable model parameters. However, the model with only 15 adjusted parameters was evaluated by AIC as the best option with a likelihood of 98%, while the uncalibrated model obtained the worst AIC value. Computing of the AIC yielded the most important information to assess the model likelihood. Comparing only residuals of different conceptual models was less valuable and would result in an overparameterization of the conceptual model approach. Sensitivities of piezometric heads were highest for the model with five adjustable parameters reflecting also changes of extracted groundwater volumes. With increasing amount of adjustable parameters piezometric heads became less sensitive for the model calibration and changes of pumping rates were no longer displayed by the sensitivity coefficients. Therefore, when too many model parameters were adjusted, these parameters lost their impact on the model results. Additionally, using only sedimentological data to derive hydraulic parameters resulted in a large bias between measured and simulated groundwater level.

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Determination of the Order of a Markov Chain for Daily Rainfall Data of North East India: "Application AIC criterion"

Journal of Applied and Natural Science ◽

10.31018/jans.v10i1.1583 ◽

2018 ◽

Vol 10 (1) ◽

pp. 80-87

Author(s):

Surobhi Deka

Keyword(s):

Markov Chain ◽

Markov Chains ◽

Akaike Information Criterion ◽

Markov Chain Model ◽

Information Criterion ◽

Chain Model ◽

Adequate Model ◽

First Order ◽

North East India ◽

North East

The paper aims at demonstrating the application of the Akaike information criterion to determine the order of two state Markov chain for studying the pattern of occurrence of wet and dry days during the rainy season (April to September) in North-East India. For each station, each day is classified as dry day if the amount of rainfall is less than 3 mm and wet day if the amount of rainfall is greater than or equal to 3 mm. We apply Markov chain of order up to three to the sequences of wet and dry days observed at seven distantly located stations in North East region of India. The Markov chain model of appropriate order for analyzing wet and dry days is determined. This is done using the Akaike Information Criterion (AIC) by checking the minimum of AIC estimate. Markov chain of order one is found to be superior to the majority of the stations in comparison to the other order Markov chains. More precisely, first order Markov chain model is an adequate model for the stations North Bank, Tocklai, Silcoorie, Mohanbari and Guwahati. Further, it is observed that second order and third order Markov chains are competing with first order in the stations Cherrapunji and Imphal, respectively. A fore-knowledge of rainfall pattern is of immense help not only to farmers, but also to the authorities concerned with planning of irrigation schemes. The outcomes are useful for taking decisions well in advance for transplanting of rice as well as for other input management and farm activities during different stages of the crop growing season.

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Aircraft Health Diagnosis Method Based on ARMA Model and Probabilistic Neural Network

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.225-226.527 ◽

2011 ◽

Vol 225-226 ◽

pp. 527-530 ◽

Cited By ~ 1

Author(s):

Jian Guo Cui ◽

Bo Han Song ◽

Shi Liang Dong ◽

Hai Gang Liu ◽

Qing Zhao

Keyword(s):

Neural Network ◽

Probabilistic Neural Network ◽

Arma Model ◽

Information Criterion ◽

Model Parameters ◽

Health State ◽

Feature Vectors ◽

Emission Signal ◽

Diagnosis Method ◽

Health Diagnosis

In order to diagnose the health state of Aircraft effectively, a new method based on ARMA Model and probabilistic neural network(PNN) is proposed in this paper. First, an ARMA model is built using the original acoustic emission signal of aircraft crucial components, then use the autoregressive approximation theory to estimate model parameters, and order of the model is calculated according to Akaike Information Criterion(AIC). Use the autoregressive parameters to build feature vectors, then the probabilistic neural network is used to carry out the recognition of these feature vectors, and the health state of aircraft crucial components is effectively diagnosed. After the application on certain type of real aircraft, this method is proved to be capable of detecting the fatigue crack on crucial structural components. And we can conclude that the method is an effective way to carry out aircraft health diagnosis.

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Modelling of the Transport of Chlorinated Hydrocarbon Solvents in Groundwater: A Case Study

Water Science & Technology ◽

10.2166/wst.1985.0079 ◽

1985 ◽

Vol 17 (9) ◽

pp. 13-21 ◽

Cited By ~ 7

Author(s):

W K. H. Kinzelbach

Keyword(s):

Transport Model ◽

Model Parameters ◽

Dispersive Transport ◽

Transport Models ◽

Chlorinated Hydrocarbon ◽

First Order ◽

Hydrocarbon Solvents ◽

Simplifying Assumptions ◽

Environmental Engineer

At present chlorinated hydrocarbon solvents rank among the major pollutants found in groundwater. In the interpretation of field data and the planning of decontamination measures numerical transport models may be a valuable tool of the environmental engineer. The applicability of one such model is tested on a case of groundwater pollution by 1,1,1,-trichloroethane. The model is composed of a horizontally 2-D flow model and a 3-D ‘random-walk' transport model. It takes into account convective and dispersive transport as well as linear adsorption and a first order decay reaction. Under certain simplifying assumptions the model allows an adequate reproduction of observed concentrations. Due to uncertainty in data and limited comparabili ty of simulated and measured concentrations the model parameters can only be estimated within bounds. The decay rate of 1,1,1-trichloroethane is estimated to lie between 0 and 0.0005 l/d.

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Generalized second-order slip for unsteady convective flow of a nanofluid: a utilization of Buongiorno’s two-component nonhomogeneous equilibrium model

Nonlinear Engineering ◽

10.1515/nleng-2020-0005 ◽

2020 ◽

Vol 9 (1) ◽

pp. 156-168

Author(s):

Seyed Mahdi Mousavi ◽

Saeed Dinarvand ◽

Mohammad Eftekhari Yazdi

Keyword(s):

Boundary Layer ◽

Equilibrium Model ◽

Second Order ◽

Model Parameters ◽

Slip Parameter ◽

Two Phase ◽

Convective Boundary ◽

First Order ◽

Special Cases ◽

Two Component

AbstractThe unsteady convective boundary layer flow of a nanofluid along a permeable shrinking/stretching plate under suction and second-order slip effects has been developed. Buongiorno’s two-component nonhomogeneous equilibrium model is implemented to take the effects of Brownian motion and thermophoresis into consideration. It can be emphasized that, our two-phase nanofluid model along with slip concentration at the wall shows better physical aspects relative to taking the constant volume concentration at the wall. The similarity transformation method (STM), allows us to reducing nonlinear governing PDEs to nonlinear dimensionless ODEs, before being solved numerically by employing the Keller-box method (KBM). The graphical results portray the effects of model parameters on boundary layer behavior. Moreover, results validation has been demonstrated as the skin friction and the reduced Nusselt number. We understand shrinking plate case is a key factor affecting non-uniqueness of the solutions and the range of the shrinking parameter for which the solution exists, increases with the first order slip parameter, the absolute value of the second order slip parameter as well as the transpiration rate parameter. Besides, the second-order slip at the interface decreases the rate of heat transfer in a nanofluid. Finally, the analysis for no-slip and first-order slip boundary conditions can also be retrieved as special cases of the present model.

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