Importance Of Model Parameters Research Articles

Using Self-Organizing Map Algorithm to Reveal Stabilities of Parameter Sensitivity Rankings in Microbial Kinetic Models: A Case for Microalgae

Microalgae are multi-purpose microbial agents due to their capability to efficiently sequester carbon dioxide and produce valuable biomass such as protein and single-cell oils. Formulation and tuning of microalgae kinetics models can significantly contribute to the successful design and operation of microalgae reactors. This work aimed to demonstrate the capability of self-organizing map (SOM) algorithm to elucidate the patterns of parameter rankings in microalgae models subject to stochastic variations of input forcing functions–bioprocess influent component concentration levels. These stochastic variations were implemented on a modeled chemostat with a deterministic microalgae kinetic model consists of ten time-dependent variables and eighteen model parameters. The methodology consists of two major stages: (1) global sensitivity analysis (GSA) on the importance of model parameters with stochastic sampling of bioreactor influent component concentrations, and (2) training of self-organizing maps on the datasets of model parameter rankings derived from the GSA indices. Results reveal that functional principal components analysis can project at least 99% of the time-dependent dynamic patterns of the model variables on B-splines basis functions. The component planes for hexagonal lattice SOMs reveal that the sensitivity rankings some parameters in the algae model tested can be stable over a wide range of variations in the levels of influent component concentrations. Therefore, SOM can be used to reveal the trends in multi-dimensional data arrays arising from the implementation of GSA of kinetic models under stochastic perturbation of input forcing functions.

A simple two-strain HSV epidemic model with palliative treatment

A two-strain model of the transmission dynamics of herpes simplex virus (HSV) with treatment is formulated as a deterministic system of nonlinear ordinary differential equations. The model is then analyzed qualitatively, with numerical simulations provided to support the theoretical results. The basic reproduction number \(R_0\) is computed with \(R_0=\text{max}\lbrace R_1, R_2 \rbrace \) where \(R_1\) and \(R_2\) represent respectively the reproduction number for HSV1 and HSV2. We also compute the invasion reproductive numbers \(\tilde{R}_1\) for strain 1 when strain 2 is at endemic equilibrium and \(\tilde{R}_2\) for strain 2 when strain 1 is at endemic equilibrium. To determine the relative importance of model parameters to disease transmission, sensitivity analysis is carried out. The reproduction number is most sensitive respectively to the contact rates \(\beta_1\), \(\beta_2\) and the recruitment rate \(\pi\). Numerical simulations indicate the co-existence of the two strains, with HSV1, dominating but not driving out HSV2 whenever \(R_1 > R_2 > 1\) and vice versa.

Modeling the health impact of water and sanitation service deficits on waterborne disease transmission

Cholera is a waterborne disease that continues to pose serious public health problems in many developing countries. Increasing water and sanitation coverage is a goal for local authorities in these countries, as it can eliminate one of the root causes of cholera transmission. The SIWDR (susceptible–infected–water–dumpsite–recovered) model is proposed here to evaluate the effects of the improved coverage of water and sanitation services in a community at risk of a cholera outbreak. This paper provides a mathematical study of the dynamics of the water and sanitation (WatSan) deficits and their public health impact in a community. The theoretical analysis of the SIWDR model gave a certain threshold value (known as the basic reproductive number and denoted mathcal{R}_{0}) to stop the transmission of cholera. It was found that the disease-free equilibrium was globally asymptotically stable whenever mathcal{R}_{0} leq 1. The unique endemic equilibrium was globally asymptotically stable whenever mathcal{R}_{0} >1. Sensitivity analysis was performed to determine the relative importance of model parameters to disease transmission and prevention. The numerical simulation results, using realistic parameter values in describing cholera transmission in Haiti, showed that improving the drinking water supply, wastewater and sewage treatment, and solid waste disposal services would be effective strategies for controlling the transmission pathways of this waterborne disease.

A Human-Bovine Schistosomiasis Mathematical Model with Treatment and Mollusciciding.

To mitigate the spread of schistosomiasis, a deterministic human-bovine mathematical model of its transmission dynamics accounting for contaminated water reservoirs, including treatment of bovines and humans and mollusciciding is formulated and theoretically analyzed. The disease-free equilibrium is locally and globally asymptotically stable whenever the basic reproduction number [Formula: see text], while global stability of the endemic equilibrium is investigated by constructing a suitable Lyapunov function. To support the analytical results, parameter values from published literature are used for numerical simulations and where applicable, uncertainty analysis on the non-dimensional system parameters is performed using the Latin Hypercube Sampling and Partial Rank Correlation Coefficient techniques. Sensitivity analysis to determine the relative importance of model parameters to disease transmission shows that the environment-related parameters namely, [Formula: see text] (snails shedding rate of cercariae), [Formula: see text] (probability that cercariae shed by snails survive), c (fraction of the contaminated environment sprayed by molluscicides) and [Formula: see text] (mortality rate of cercariae) are the most significant to mitigate the spread of schistosomiasis. Mollusciciding, which directly impacts the contaminated environment as a single control strategy is more effective compared to treatment. However, concurrently applying mollusciciding and treatment will yield a better outcome.

A Research on Waste-Gated Turbine Performance Under Unsteady Flow Condition

Turbochargers are key components of engine air-paths that must be carefully considered during the development process. The combination of fluid, mechanical, and thermal phenomenon make the turbocharger a highly dynamic and nonlinear modeling challenge. The aim of this study is to quantify the dynamic response of the turbocharger system across a frequency spectrum from 0.003 Hz to 500 Hz, i.e., for exhaust gas pulsation in steady state, load steps, and cold start drive cycles, to validate the assumption of quasi-steady assumptions for particular modeling problems. A waste-gated turbine was modeled using the dual orifice approach, a lumped capacitance heat transfer model, and novel, physics-based pneumatic actuator mechanism model. Each submodel has been validated individually against the experimental measurements. The turbine inlet pressure and temperature and the waste-gate actuator pressure were perturbed across the full frequency range both individually and simultaneously in separate numerical investigations. The dynamic responses of turbine housing temperature, turbocharger rotor speed, waste-gate opening, mass flow, and gas temperatures/pressures were all investigated. The mass flow parameter exhibits significant dynamic behavior above 100 Hz, illustrating that the quasi-steady assumption is invalid in this frequency range. The waste-gate actuator system showed quasi-steady behavior below 10 Hz, while the mechanical inertia of the turbine attenuated fluctuations in shaft speed for frequencies between 0.1 and 10 Hz. The thermal inertia of the turbocharger housing meant that housing temperature variations were supressed at frequencies above 0.01 Hz. The results have been used to illustrate the importance of model parameters for three transient simulation scenarios (cold start, load step, and pulsating exhaust flow).

A Comparison of Input Data Used to Represent Phase Transformations during the Quenching of a Large Nuclear Forging

The present work explores the importance of model parameters and input variables when simulating the quenching of thick sectioned nuclear forgings. The modelling approach adopted uses values of specific heat capacity, containing latent heat release, to simulate cooling curves; rather than calculating transformation kinetics based upon a mathematical model. Termed the effective specific heat (Cpeff), two different methods were used to establish values: differential scanning calorimetry (DSC) and thermos dynamic predictive software. Values were then included in finite element (FE) models to simulate the characteristic cooling at the mid-wall position in a thick section forging and were validated against production thermocouple data. The investigation found that the formation of ferrite, bainite and martensite or lower bainite were all represented by the data established using DSC and critical formation temperatures were comparable with others in the literature. Conversely, values calculated using the thermodynamic software failed to represent ferrite formation and predicted different critical transformation temperatures for bainite. The simulated cooling curve that used the software predicted Cpeff data was comparable to the thermocouple data either side of the bainite transformation, however during the transformation the effects of latent heat on cooling rate were over predicting leading to disparities. The equivalent DSC cooling curves produced a near exact match.

Squares of different sizes: effect of geographical projection on model parameter estimates in species distribution modeling.

In species distribution analyses, environmental predictors and distribution data for large spatial extents are often available in long-lat format, such as degree raster grids. Long-lat projections suffer from unequal cell sizes, as a degree of longitude decreases in length from approximately 110 km at the equator to 0 km at the poles. Here we investigate whether long-lat and equal-area projections yield similar model parameter estimates, or result in a consistent bias. We analyzed the environmental effects on the distribution of 12 ungulate species with a northern distribution, as models for these species should display the strongest effect of projectional distortion. Additionally we choose four species with entirely continental distributions to investigate the effect of incomplete cell coverage at the coast. We expected that including model weights proportional to the actual cell area should compensate for the observed bias in model coefficients, and similarly that using land coverage of a cell should decrease bias in species with coastal distribution. As anticipated, model coefficients were different between long-lat and equal-area projections. Having progressively smaller and a higher number of cells with increasing latitude influenced the importance of parameters in models, increased the sample size for the northernmost parts of species ranges, and reduced the subcell variability of those areas. However, this bias could be largely removed by weighting long-lat cells by the area they cover, and marginally by correcting for land coverage. Overall we found little effect of using long-lat rather than equal-area projections in our analysis. The fitted relationship between environmental parameters and occurrence probability differed only very little between the two projection types. We still recommend using equal-area projections to avoid possible bias. More importantly, our results suggest that the cell area and the proportion of a cell covered by land should be used as a weight when analyzing distribution of terrestrial species.

Modeling the Dynamics of Arboviral Diseases with Vaccination Perspective

In this paper, we propose a model of transmission of arboviruses, which take into account a future vaccination strategy in human population. A qualitative analysis based on stability and bifurcation theory reveals that the phenomenon of backward bifurcation may occur; the stable disease-free equilibrium of the model coexists with a stable endemic equilibrium when the associated reproduction number is less than unity. We show that the backward bifurcation phenomenon is caused by the arbovirus induced mortality in humans. Using theВ direct Lyapunov method, we show the global stability of the trivial equilibrium. Through global sensitivity analysis, wedetermine the relative importance of model parameters for disease transmission. Simulation results using a qualitatively stable numerical scheme, are provide to illustrate the impact of vaccination strategy in human community.

Parameter estimation through ignorance

Dynamical modeling lies at the heart of our understanding of physical systems. Its role in science is deeper than mere operational forecasting, in that it allows us to evaluate the adequacy of the mathematical structure of our models. Despite the importance of model parameters, there is no general method of parameter estimation outside linear systems. A relatively simple method of parameter estimation for nonlinear systems is introduced, based on variations in the accuracy of probability forecasts. It is illustrated on the logistic map, the Henon map, and the 12-dimensional Lorenz96 flow, and its ability to outperform linear least squares in these systems is explored at various noise levels and sampling rates. As expected, it is more effective when the forecast error distributions are non-Gaussian. The method selects parameter values by minimizing a proper, local skill score for continuous probability forecasts as a function of the parameter values. This approach is easier to implement in practice than alternative nonlinear methods based on the geometry of attractors or the ability of the model to shadow the observations. Direct measures of inadequacy in the model, the "implied ignorance," and the information deficit are introduced.

Regulated transport as a mechanism for pattern generation: Capabilities for phyllotaxis and beyond

Large-scale pattern formation is a frequently occurring phenomenon in biological organisms, and several local interaction rules for generating such patterns have been suggested. A mechanism driven by feedback between the plant hormone auxin and its polarly localized transport mediator PINFORMED1 has been proposed as a model for phyllotactic patterns in plants. It has been shown to agree with current biological experiments at a molecular level as well as with respect to the resulting patterns. We present a thorough investigation of variants of models based on auxin-regulated polarized transport and use analytical and numerical tools to derive requirements for these models to drive spontaneous pattern formation. We find that auxin concentrations in neighboring cells can feed back either on exocytosis or endocytosis and still produce patterns. In agreement with mutant experiments, the active cellular efflux is shown to be more important for pattern capabilities as compared to active influx. We also find that the feedback must originate from neighboring cells rather than from neighboring walls and that intracellular competition for the transport mediator is required for patterning. The importance of model parameters is investigated, especially regarding robustness to perturbations of experimentally estimated parameter values. Finally, the regulated transport mechanism is shown to be able to generate Turing patterns of various types.

Thermodynamics and kinetics of metallic amorphous phases in the framework of the CALPHAD approach

Amorphous alloys are metastable phases which have generated considerable interest in recent years because of their promising properties. This review considers thermodynamic and kinetic aspects in the modelling of metallic amorphous phases. The relevant literature on the glass transition and the thermodynamics of amorphous phases is discussed in detail. The CALPHAD approach is used for thermodynamic modelling: it employs collected experimental data to obtain a reliable assessment of properties and metastable phase diagrams. Thermodynamic modelling of Short Range Order (SRO) in the liquid and glass transition is described and critically discussed with regard to rapid solidification experiments. Solid state amorphization and amorphization by means of deposition are also discussed. The extension to kinetics is then described, involving a number of modelling parameters. Predictions can thus be carried out of the Glass Forming Range (GFR), i.e. the composition range where glass formation is expected, according to different levels of approximation and for various processes. The importance of model parameters (thermodynamic driving force, interfacial energy, transport properties) is also assessed and some case studies (Cu–Zr, Fe–B and Cu–Mg–Y) are discussed. Recent results on the simulation of nanocrystals growth in amorphous materials are reported.

Sensitivity of the tibio-femoral response to finite element modeling parameters

A generic finite element (FE) model of the lower limb was used to study the knee response in-vivo during a one-legged hop. The approach uses an explicit FE code and a combination of estimated muscle forces and measured three-dimensional tibio-femoral kinematics and ground reaction force as input to the FE model. The sensitivity of the simulated tibio-femoral response to variations of key geometric and material parameters was investigated by performing a total of 38 different simulations. The amplitudes of both kinematic and kinetic responses were affected by the change of these parameters. For the current approach, the results suggest that while cartilage mechanical and geometric properties are very important for the estimation of tibio-femoral cartilage pressure, they have limited effects on the overall kinematic response. The study may help to better define the relative importance of modeling parameters for the development of subject-specific models.

Development of a framework of automated water quality parameter optimization and its application

This paper presents a methodology and framework for the development of an automated least-squares optimization tool for calibrating water quality parameters in QUAL2E. The method has been applied to estimate the optimal water quality parameters in simulation of stream water quality for the Anyang stream in Korea. The Monte Carlo analysis is used to assess the relative importance of model parameters for water quality constituents. It is found that μmax and ρ are the most influential parameters for Chlorophyll-a modeling and K1 and K3 are critical parameters for variation of DO and BOD in the Anyang stream. A computer program for automated parameter calibration has been developed using a nonlinear GRG optimization algorithm. The application framework provides an intuitive and easy-to-use interface and allows visual evaluation of results. According to the simulation results, the automated approach is computationally efficient for evaluation of model parameters and converges on a best fit more rapidly and reliably than a trial and error method. The methodology proposed herein can be extended to other models to obtain the best possible parameter values.

Importance of model parameters in the assessment of intra-oral remineralization.

Since the introduction of the Intra-oral Cariogenicity Test by Koulourides et al. (1974), many groups around the world have been developing and using intra-oral models to test new caries-preventive products, as well as to study physiological processes in the oral cavity. In spite of the large numbers of papers reporting these methods, very little research has been done to determine the importance of the many variable parameters which influence the performance of these models. Among these, the following can be identified: (a) panelist criteria, (b) the use of sound vs. pre-demineralized enamel of human or bovine origin, (c) the use of gauze or a recess to accumulate plaque, (d) the method to create incipient lesions, (e) the duration of the experiment, (f) the number of panelists required for statistical significance to be obtained, (g) the assessment techniques for mineral and/or fluoride uptake/loss, and (h) the choice of contralateral, 'cross-over', or 'monadic' experimental designs. Our results, supported by data from the literature, indicate that the choices made with respect to these parameters are of paramount importance in determination of the outcome of the respective study.